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+{"instance_id":"countdown_8k_0","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [15, 3, 21, 26]\nTarget: 24","reference_output":"# Search Procedure\nInitial number set: [15, 3, 21, 26], target: 24. Options for choosing two numbers: [(15, 3), (15, 21), (15, 26), (3, 21), (3, 26), (21, 26)].\n |- Pick two numbers (15, 3) (numbers left: [21, 26]). Try possible operations.\n  |- Try 15 + 3 = 18. Add 18 to the number set. Current number set: [18, 21, 26], target: 24. Options for choosing two numbers: [(18, 21), (18, 26), (21, 26)].\n   |- Pick two numbers (18, 21) (numbers left: [26]). Try possible operations.\n    |- Try 21 + 18 = 39. Add 39 to the number set. Current number set: [39, 26], target: 24, just two numbers left.\n     |- Try 39 + 26 = 65. Evaluate 65 != 24, drop this branch.\n     |- Try 39 - 26 = 13. Evaluate 13 != 24, drop this branch.\n     |- Try 39 * 26 = 1014. Evaluate 1014 != 24, drop this branch.\n     |- Try 39 \/ 26 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 21 - 18 = 3. Add 3 to the number set. Current number set: [3, 26], target: 24, just two numbers left.\n     |- Try 26 + 3 = 29. Evaluate 29 != 24, drop this branch.\n     |- Try 26 - 3 = 23. Evaluate 23 != 24, drop this branch.\n     |- Try 26 * 3 = 78. Evaluate 78 != 24, drop this branch.\n     |- Try 26 \/ 3 = 8.7. 8.7 is a decimal, drop this branch.\n    |- Try 21 * 18 = 378. Add 378 to the number set. Current number set: [378, 26], target: 24, just two numbers left.\n     |- Try 378 + 26 = 404. Evaluate 404 != 24, drop this branch.\n     |- Try 378 - 26 = 352. Evaluate 352 != 24, drop this branch.\n     |- Try 378 * 26 = 9828. 9828 exceeds the maximum intermediate result, drop this branch.\n     |- Try 378 \/ 26 = 14.5. 14.5 is a decimal, drop this branch.\n    |- Try 21 \/ 18 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (18, 26) (numbers left: [21]). Try possible operations.\n    |- Try 26 + 18 = 44. Add 44 to the number set. Current number set: [44, 21], target: 24, just two numbers left.\n     |- Try 44 + 21 = 65. Evaluate 65 != 24, drop this branch.\n     |- Try 44 - 21 = 23. Evaluate 23 != 24, drop this branch.\n     |- Try 44 * 21 = 924. Evaluate 924 != 24, drop this branch.\n     |- Try 44 \/ 21 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 26 - 18 = 8. Add 8 to the number set. Current number set: [8, 21], target: 24, just two numbers left.\n     |- Try 21 + 8 = 29. Evaluate 29 != 24, drop this branch.\n     |- Try 21 - 8 = 13. Evaluate 13 != 24, drop this branch.\n     |- Try 21 * 8 = 168. Evaluate 168 != 24, drop this branch.\n     |- Try 21 \/ 8 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 26 * 18 = 468. Add 468 to the number set. Current number set: [468, 21], target: 24, just two numbers left.\n     |- Try 468 + 21 = 489. Evaluate 489 != 24, drop this branch.\n     |- Try 468 - 21 = 447. Evaluate 447 != 24, drop this branch.\n     |- Try 468 * 21 = 9828. 9828 exceeds the maximum intermediate result, drop this branch.\n     |- Try 468 \/ 21 = 22.3. 22.3 is a decimal, drop this branch.\n    |- Try 26 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (21, 26) (numbers left: [18]). Try possible operations.\n    |- Try 26 + 21 = 47. Add 47 to the number set. Current number set: [47, 18], target: 24, just two numbers left.\n     |- Try 47 + 18 = 65. Evaluate 65 != 24, drop this branch.\n     |- Try 47 - 18 = 29. Evaluate 29 != 24, drop this branch.\n     |- Try 47 * 18 = 846. Evaluate 846 != 24, drop this branch.\n     |- Try 47 \/ 18 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 26 - 21 = 5. Add 5 to the number set. Current number set: [5, 18], target: 24, just two numbers left.\n     |- Try 18 + 5 = 23. Evaluate 23 != 24, drop this branch.\n     |- Try 18 - 5 = 13. Evaluate 13 != 24, drop this branch.\n     |- Try 18 * 5 = 90. Evaluate 90 != 24, drop this branch.\n     |- Try 18 \/ 5 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 26 * 21 = 546. Add 546 to the number set. Current number set: [546, 18], target: 24, just two numbers left.\n     |- Try 546 + 18 = 564. Evaluate 564 != 24, drop this branch.\n     |- Try 546 - 18 = 528. Evaluate 528 != 24, drop this branch.\n     |- Try 546 * 18 = 9828. 9828 exceeds the maximum intermediate result, drop this branch.\n     |- Try 546 \/ 18 = 30.3. 30.3 is a decimal, drop this branch.\n    |- Try 26 \/ 21 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 15 - 3 = 12. Add 12 to the number set. Current number set: [12, 21, 26], target: 24. Options for choosing two numbers: [(12, 21), (12, 26), (21, 26)].\n   |- Pick two numbers (12, 21) (numbers left: [26]). Try possible operations.\n    |- Try 21 + 12 = 33. Add 33 to the number set. Current number set: [33, 26], target: 24, just two numbers left.\n     |- Try 33 + 26 = 59. Evaluate 59 != 24, drop this branch.\n     |- Try 33 - 26 = 7. Evaluate 7 != 24, drop this branch.\n     |- Try 33 * 26 = 858. Evaluate 858 != 24, drop this branch.\n     |- Try 33 \/ 26 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 21 - 12 = 9. Add 9 to the number set. Current number set: [9, 26], target: 24, just two numbers left.\n     |- Try 26 + 9 = 35. Evaluate 35 != 24, drop this branch.\n     |- Try 26 - 9 = 17. Evaluate 17 != 24, drop this branch.\n     |- Try 26 * 9 = 234. Evaluate 234 != 24, drop this branch.\n     |- Try 26 \/ 9 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 21 * 12 = 252. Add 252 to the number set. Current number set: [252, 26], target: 24, just two numbers left.\n     |- Try 252 + 26 = 278. Evaluate 278 != 24, drop this branch.\n     |- Try 252 - 26 = 226. Evaluate 226 != 24, drop this branch.\n     |- Try 252 * 26 = 6552. 6552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 252 \/ 26 = 9.7. 9.7 is a decimal, drop this branch.\n    |- Try 21 \/ 12 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (12, 26) (numbers left: [21]). Try possible operations.\n    |- Try 26 + 12 = 38. Add 38 to the number set. Current number set: [38, 21], target: 24, just two numbers left.\n     |- Try 38 + 21 = 59. Evaluate 59 != 24, drop this branch.\n     |- Try 38 - 21 = 17. Evaluate 17 != 24, drop this branch.\n     |- Try 38 * 21 = 798. Evaluate 798 != 24, drop this branch.\n     |- Try 38 \/ 21 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 26 - 12 = 14. Add 14 to the number set. Current number set: [14, 21], target: 24, just two numbers left.\n     |- Try 21 + 14 = 35. Evaluate 35 != 24, drop this branch.\n     |- Try 21 - 14 = 7. Evaluate 7 != 24, drop this branch.\n     |- Try 21 * 14 = 294. Evaluate 294 != 24, drop this branch.\n     |- Try 21 \/ 14 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 26 * 12 = 312. Add 312 to the number set. Current number set: [312, 21], target: 24, just two numbers left.\n     |- Try 312 + 21 = 333. Evaluate 333 != 24, drop this branch.\n     |- Try 312 - 21 = 291. Evaluate 291 != 24, drop this branch.\n     |- Try 312 * 21 = 6552. 6552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 312 \/ 21 = 14.9. 14.9 is a decimal, drop this branch.\n    |- Try 26 \/ 12 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (21, 26) (numbers left: [12]). Try possible operations.\n    |- Try 26 + 21 = 47. Add 47 to the number set. Current number set: [47, 12], target: 24, just two numbers left.\n     |- Try 47 + 12 = 59. Evaluate 59 != 24, drop this branch.\n     |- Try 47 - 12 = 35. Evaluate 35 != 24, drop this branch.\n     |- Try 47 * 12 = 564. Evaluate 564 != 24, drop this branch.\n     |- Try 47 \/ 12 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 26 - 21 = 5. Add 5 to the number set. Current number set: [5, 12], target: 24, just two numbers left.\n     |- Try 12 + 5 = 17. Evaluate 17 != 24, drop this branch.\n     |- Try 12 - 5 = 7. Evaluate 7 != 24, drop this branch.\n     |- Try 12 * 5 = 60. Evaluate 60 != 24, drop this branch.\n     |- Try 12 \/ 5 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 26 * 21 = 546. Add 546 to the number set. Current number set: [546, 12], target: 24, just two numbers left.\n     |- Try 546 + 12 = 558. Evaluate 558 != 24, drop this branch.\n     |- Try 546 - 12 = 534. Evaluate 534 != 24, drop this branch.\n     |- Try 546 * 12 = 6552. 6552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 546 \/ 12 = 45.5. 45.5 is a decimal, drop this branch.\n    |- Try 26 \/ 21 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 15 * 3 = 45. Add 45 to the number set. Current number set: [45, 21, 26], target: 24. Options for choosing two numbers: [(45, 21), (45, 26), (21, 26)].\n   |- Pick two numbers (45, 21) (numbers left: [26]). Try possible operations.\n    |- Try 45 + 21 = 66. Add 66 to the number set. Current number set: [66, 26], target: 24, just two numbers left.\n     |- Try 66 + 26 = 92. Evaluate 92 != 24, drop this branch.\n     |- Try 66 - 26 = 40. Evaluate 40 != 24, drop this branch.\n     |- Try 66 * 26 = 1716. Evaluate 1716 != 24, drop this branch.\n     |- Try 66 \/ 26 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 45 - 21 = 24. Add 24 to the number set. Current number set: [24, 26], target: 24, just two numbers left.\n     |- Try 26 + 24 = 50. Evaluate 50 != 24, drop this branch.\n     |- Try 26 - 24 = 2. Evaluate 2 != 24, drop this branch.\n     |- Try 26 * 24 = 624. Evaluate 624 != 24, drop this branch.\n     |- Try 26 \/ 24 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 45 * 21 = 945. Add 945 to the number set. Current number set: [945, 26], target: 24, just two numbers left.\n     |- Try 945 + 26 = 971. Evaluate 971 != 24, drop this branch.\n     |- Try 945 - 26 = 919. Evaluate 919 != 24, drop this branch.\n     |- Try 945 * 26 = 24570. 24570 exceeds the maximum intermediate result, drop this branch.\n     |- Try 945 \/ 26 = 36.3. 36.3 is a decimal, drop this branch.\n    |- Try 45 \/ 21 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (45, 26) (numbers left: [21]). Try possible operations.\n    |- Try 45 + 26 = 71. Add 71 to the number set. Current number set: [71, 21], target: 24, just two numbers left.\n     |- Try 71 + 21 = 92. Evaluate 92 != 24, drop this branch.\n     |- Try 71 - 21 = 50. Evaluate 50 != 24, drop this branch.\n     |- Try 71 * 21 = 1491. Evaluate 1491 != 24, drop this branch.\n     |- Try 71 \/ 21 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 45 - 26 = 19. Add 19 to the number set. Current number set: [19, 21], target: 24, just two numbers left.\n     |- Try 21 + 19 = 40. Evaluate 40 != 24, drop this branch.\n     |- Try 21 - 19 = 2. Evaluate 2 != 24, drop this branch.\n     |- Try 21 * 19 = 399. Evaluate 399 != 24, drop this branch.\n     |- Try 21 \/ 19 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 45 * 26 = 1170. Add 1170 to the number set. Current number set: [1170, 21], target: 24, just two numbers left.\n     |- Try 1170 + 21 = 1191. Evaluate 1191 != 24, drop this branch.\n     |- Try 1170 - 21 = 1149. Evaluate 1149 != 24, drop this branch.\n     |- Try 1170 * 21 = 24570. 24570 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1170 \/ 21 = 55.7. 55.7 is a decimal, drop this branch.\n    |- Try 45 \/ 26 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (21, 26) (numbers left: [45]). Try possible operations.\n    |- Try 26 + 21 = 47. Add 47 to the number set. Current number set: [47, 45], target: 24, just two numbers left.\n     |- Try 47 + 45 = 92. Evaluate 92 != 24, drop this branch.\n     |- Try 47 - 45 = 2. Evaluate 2 != 24, drop this branch.\n     |- Try 47 * 45 = 2115. 2115 exceeds the maximum intermediate result, drop this branch.\n     |- Try 47 \/ 45 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 26 - 21 = 5. Add 5 to the number set. Current number set: [5, 45], target: 24, just two numbers left.\n     |- Try 45 + 5 = 50. Evaluate 50 != 24, drop this branch.\n     |- Try 45 - 5 = 40. Evaluate 40 != 24, drop this branch.\n     |- Try 45 * 5 = 225. Evaluate 225 != 24, drop this branch.\n     |- Try 45 \/ 5 = 9. Evaluate 9 != 24, drop this branch.\n    |- Try 26 * 21 = 546. Add 546 to the number set. Current number set: [546, 45], target: 24, just two numbers left.\n     |- Try 546 + 45 = 591. Evaluate 591 != 24, drop this branch.\n     |- Try 546 - 45 = 501. Evaluate 501 != 24, drop this branch.\n     |- Try 546 * 45 = 24570. 24570 exceeds the maximum intermediate result, drop this branch.\n     |- Try 546 \/ 45 = 12.1. 12.1 is a decimal, drop this branch.\n    |- Try 26 \/ 21 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 15 \/ 3 = 5. Add 5 to the number set. Current number set: [5, 21, 26], target: 24. Options for choosing two numbers: [(5, 21), (5, 26), (21, 26)].\n   |- Pick two numbers (5, 21) (numbers left: [26]). Try possible operations.\n    |- Try 21 + 5 = 26. Add 26 to the number set. Current number set: [26, 26], target: 24, just two numbers left.\n     |- Try 26 + 26 = 52. Evaluate 52 != 24, drop this branch.\n     |- Try 26 - 26 = 0. Evaluate 0 != 24, drop this branch.\n     |- Try 26 * 26 = 676. Evaluate 676 != 24, drop this branch.\n     |- Try 26 \/ 26 = 1. Evaluate 1 != 24, drop this branch.\n    |- Try 21 - 5 = 16. Add 16 to the number set. Current number set: [16, 26], target: 24, just two numbers left.\n     |- Try 26 + 16 = 42. Evaluate 42 != 24, drop this branch.\n     |- Try 26 - 16 = 10. Evaluate 10 != 24, drop this branch.\n     |- Try 26 * 16 = 416. Evaluate 416 != 24, drop this branch.\n     |- Try 26 \/ 16 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 21 * 5 = 105. Add 105 to the number set. Current number set: [105, 26], target: 24, just two numbers left.\n     |- Try 105 + 26 = 131. Evaluate 131 != 24, drop this branch.\n     |- Try 105 - 26 = 79. Evaluate 79 != 24, drop this branch.\n     |- Try 105 * 26 = 2730. 2730 exceeds the maximum intermediate result, drop this branch.\n     |- Try 105 \/ 26 = 4.0. 4.0 is a decimal, drop this branch.\n    |- Try 21 \/ 5 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (5, 26) (numbers left: [21]). Try possible operations.\n    |- Try 26 + 5 = 31. Add 31 to the number set. Current number set: [31, 21], target: 24, just two numbers left.\n     |- Try 31 + 21 = 52. Evaluate 52 != 24, drop this branch.\n     |- Try 31 - 21 = 10. Evaluate 10 != 24, drop this branch.\n     |- Try 31 * 21 = 651. Evaluate 651 != 24, drop this branch.\n     |- Try 31 \/ 21 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 26 - 5 = 21. Add 21 to the number set. Current number set: [21, 21], target: 24, just two numbers left.\n     |- Try 21 + 21 = 42. Evaluate 42 != 24, drop this branch.\n     |- Try 21 - 21 = 0. Evaluate 0 != 24, drop this branch.\n     |- Try 21 * 21 = 441. Evaluate 441 != 24, drop this branch.\n     |- Try 21 \/ 21 = 1. Evaluate 1 != 24, drop this branch.\n    |- Try 26 * 5 = 130. Add 130 to the number set. Current number set: [130, 21], target: 24, just two numbers left.\n     |- Try 130 + 21 = 151. Evaluate 151 != 24, drop this branch.\n     |- Try 130 - 21 = 109. Evaluate 109 != 24, drop this branch.\n     |- Try 130 * 21 = 2730. 2730 exceeds the maximum intermediate result, drop this branch.\n     |- Try 130 \/ 21 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 26 \/ 5 = 5.2. 5.2 is a decimal, drop this branch.\n   |- Pick two numbers (21, 26) (numbers left: [5]). Try possible operations.\n    |- Try 26 + 21 = 47. Add 47 to the number set. Current number set: [47, 5], target: 24, just two numbers left.\n     |- Try 47 + 5 = 52. Evaluate 52 != 24, drop this branch.\n     |- Try 47 - 5 = 42. Evaluate 42 != 24, drop this branch.\n     |- Try 47 * 5 = 235. Evaluate 235 != 24, drop this branch.\n     |- Try 47 \/ 5 = 9.4. 9.4 is a decimal, drop this branch.\n    |- Try 26 - 21 = 5. Add 5 to the number set. Current number set: [5, 5], target: 24, just two numbers left.\n     |- Try 5 + 5 = 10. Evaluate 10 != 24, drop this branch.\n     |- Try 5 - 5 = 0. Evaluate 0 != 24, drop this branch.\n     |- Try 5 * 5 = 25. Evaluate 25 != 24, drop this branch.\n     |- Try 5 \/ 5 = 1. Evaluate 1 != 24, drop this branch.\n    |- Try 26 * 21 = 546. Add 546 to the number set. Current number set: [546, 5], target: 24, just two numbers left.\n     |- Try 546 + 5 = 551. Evaluate 551 != 24, drop this branch.\n     |- Try 546 - 5 = 541. Evaluate 541 != 24, drop this branch.\n     |- Try 546 * 5 = 2730. 2730 exceeds the maximum intermediate result, drop this branch.\n     |- Try 546 \/ 5 = 109.2. 109.2 is a decimal, drop this branch.\n    |- Try 26 \/ 21 = 1.2. 1.2 is a decimal, drop this branch.\n |- Pick two numbers (15, 21) (numbers left: [3, 26]). Try possible operations.\n  |- Try 21 + 15 = 36. Add 36 to the number set. Current number set: [36, 3, 26], target: 24. Options for choosing two numbers: [(36, 3), (36, 26), (3, 26)].\n   |- Pick two numbers (36, 3) (numbers left: [26]). Try possible operations.\n    |- Try 36 + 3 = 39. Add 39 to the number set. Current number set: [39, 26], target: 24, just two numbers left.\n     |- Try 39 + 26 = 65. Evaluate 65 != 24, drop this branch.\n     |- Try 39 - 26 = 13. Evaluate 13 != 24, drop this branch.\n     |- Try 39 * 26 = 1014. Evaluate 1014 != 24, drop this branch.\n     |- Try 39 \/ 26 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 36 - 3 = 33. Add 33 to the number set. Current number set: [33, 26], target: 24, just two numbers left.\n     |- Try 33 + 26 = 59. Evaluate 59 != 24, drop this branch.\n     |- Try 33 - 26 = 7. Evaluate 7 != 24, drop this branch.\n     |- Try 33 * 26 = 858. Evaluate 858 != 24, drop this branch.\n     |- Try 33 \/ 26 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 36 * 3 = 108. Add 108 to the number set. Current number set: [108, 26], target: 24, just two numbers left.\n     |- Try 108 + 26 = 134. Evaluate 134 != 24, drop this branch.\n     |- Try 108 - 26 = 82. Evaluate 82 != 24, drop this branch.\n     |- Try 108 * 26 = 2808. 2808 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 26 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 36 \/ 3 = 12. Add 12 to the number set. Current number set: [12, 26], target: 24, just two numbers left.\n     |- Try 26 + 12 = 38. Evaluate 38 != 24, drop this branch.\n     |- Try 26 - 12 = 14. Evaluate 14 != 24, drop this branch.\n     |- Try 26 * 12 = 312. Evaluate 312 != 24, drop this branch.\n     |- Try 26 \/ 12 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (36, 26) (numbers left: [3]). Try possible operations.\n    |- Try 36 + 26 = 62. Add 62 to the number set. Current number set: [62, 3], target: 24, just two numbers left.\n     |- Try 62 + 3 = 65. Evaluate 65 != 24, drop this branch.\n     |- Try 62 - 3 = 59. Evaluate 59 != 24, drop this branch.\n     |- Try 62 * 3 = 186. Evaluate 186 != 24, drop this branch.\n     |- Try 62 \/ 3 = 20.7. 20.7 is a decimal, drop this branch.\n    |- Try 36 - 26 = 10. Add 10 to the number set. Current number set: [10, 3], target: 24, just two numbers left.\n     |- Try 10 + 3 = 13. Evaluate 13 != 24, drop this branch.\n     |- Try 10 - 3 = 7. Evaluate 7 != 24, drop this branch.\n     |- Try 10 * 3 = 30. Evaluate 30 != 24, drop this branch.\n     |- Try 10 \/ 3 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 36 * 26 = 936. Add 936 to the number set. Current number set: [936, 3], target: 24, just two numbers left.\n     |- Try 936 + 3 = 939. Evaluate 939 != 24, drop this branch.\n     |- Try 936 - 3 = 933. Evaluate 933 != 24, drop this branch.\n     |- Try 936 * 3 = 2808. 2808 exceeds the maximum intermediate result, drop this branch.\n     |- Try 936 \/ 3 = 312. Evaluate 312 != 24, drop this branch.\n    |- Try 36 \/ 26 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (3, 26) (numbers left: [36]). Try possible operations.\n    |- Try 26 + 3 = 29. Add 29 to the number set. Current number set: [29, 36], target: 24, just two numbers left.\n     |- Try 36 + 29 = 65. Evaluate 65 != 24, drop this branch.\n     |- Try 36 - 29 = 7. Evaluate 7 != 24, drop this branch.\n     |- Try 36 * 29 = 1044. Evaluate 1044 != 24, drop this branch.\n     |- Try 36 \/ 29 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 26 - 3 = 23. Add 23 to the number set. Current number set: [23, 36], target: 24, just two numbers left.\n     |- Try 36 + 23 = 59. Evaluate 59 != 24, drop this branch.\n     |- Try 36 - 23 = 13. Evaluate 13 != 24, drop this branch.\n     |- Try 36 * 23 = 828. Evaluate 828 != 24, drop this branch.\n     |- Try 36 \/ 23 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 26 * 3 = 78. Add 78 to the number set. Current number set: [78, 36], target: 24, just two numbers left.\n     |- Try 78 + 36 = 114. Evaluate 114 != 24, drop this branch.\n     |- Try 78 - 36 = 42. Evaluate 42 != 24, drop this branch.\n     |- Try 78 * 36 = 2808. 2808 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 36 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 26 \/ 3 = 8.7. 8.7 is a decimal, drop this branch.\n  |- Try 21 - 15 = 6. Add 6 to the number set. Current number set: [6, 3, 26], target: 24. Options for choosing two numbers: [(6, 3), (6, 26), (3, 26)].\n   |- Pick two numbers (6, 3) (numbers left: [26]). Try possible operations.\n    |- Try 6 + 3 = 9. Add 9 to the number set. Current number set: [9, 26], target: 24, just two numbers left.\n     |- Try 26 + 9 = 35. Evaluate 35 != 24, drop this branch.\n     |- Try 26 - 9 = 17. Evaluate 17 != 24, drop this branch.\n     |- Try 26 * 9 = 234. Evaluate 234 != 24, drop this branch.\n     |- Try 26 \/ 9 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 6 - 3 = 3. Add 3 to the number set. Current number set: [3, 26], target: 24, just two numbers left.\n     |- Try 26 + 3 = 29. Evaluate 29 != 24, drop this branch.\n     |- Try 26 - 3 = 23. Evaluate 23 != 24, drop this branch.\n     |- Try 26 * 3 = 78. Evaluate 78 != 24, drop this branch.\n     |- Try 26 \/ 3 = 8.7. 8.7 is a decimal, drop this branch.\n    |- Try 6 * 3 = 18. Add 18 to the number set. Current number set: [18, 26], target: 24, just two numbers left.\n     |- Try 26 + 18 = 44. Evaluate 44 != 24, drop this branch.\n     |- Try 26 - 18 = 8. Evaluate 8 != 24, drop this branch.\n     |- Try 26 * 18 = 468. Evaluate 468 != 24, drop this branch.\n     |- Try 26 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 6 \/ 3 = 2. Add 2 to the number set. Current number set: [2, 26], target: 24, just two numbers left.\n     |- Try 26 + 2 = 28. Evaluate 28 != 24, drop this branch.\n     |- Try 26 - 2 = 24. Evaluate 24 == 24, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 26 - 2 = 24\nThe step before: 6 \/ 3 = 2\nThe first step: 21 - 15 = 6\n\nOutput the solution in the required format:\n<Solution>\n21 - 15 = 6\n6 \/ 3 = 2\n26 - 2 = 24\n<\/Solution>\n","item":{"nums":[15,3,21,26],"solution":["21 - 15 = 6","6 \/ 3 = 2","26 - 2 = 24"],"target":24}}
+{"instance_id":"countdown_8k_1","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [31, 16, 31, 27]\nTarget: 27","reference_output":"# Search Procedure\nInitial number set: [31, 16, 31, 27], target: 27. Options for choosing two numbers: [(31, 16), (31, 31), (31, 27), (16, 31), (16, 27), (31, 27)].\n |- Pick two numbers (31, 16) (numbers left: [31, 27]). Try possible operations.\n  |- Try 31 + 16 = 47. Add 47 to the number set. Current number set: [47, 31, 27], target: 27. Options for choosing two numbers: [(47, 31), (47, 27), (31, 27)].\n   |- Pick two numbers (47, 31) (numbers left: [27]). Try possible operations.\n    |- Try 47 + 31 = 78. Add 78 to the number set. Current number set: [78, 27], target: 27, just two numbers left.\n     |- Try 78 + 27 = 105. Evaluate 105 != 27, drop this branch.\n     |- Try 78 - 27 = 51. Evaluate 51 != 27, drop this branch.\n     |- Try 78 * 27 = 2106. 2106 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 27 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 47 - 31 = 16. Add 16 to the number set. Current number set: [16, 27], target: 27, just two numbers left.\n     |- Try 27 + 16 = 43. Evaluate 43 != 27, drop this branch.\n     |- Try 27 - 16 = 11. Evaluate 11 != 27, drop this branch.\n     |- Try 27 * 16 = 432. Evaluate 432 != 27, drop this branch.\n     |- Try 27 \/ 16 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 47 * 31 = 1457. Add 1457 to the number set. Current number set: [1457, 27], target: 27, just two numbers left.\n     |- Try 1457 + 27 = 1484. Evaluate 1484 != 27, drop this branch.\n     |- Try 1457 - 27 = 1430. Evaluate 1430 != 27, drop this branch.\n     |- Try 1457 * 27 = 39339. 39339 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1457 \/ 27 = 54.0. 54.0 is a decimal, drop this branch.\n    |- Try 47 \/ 31 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (47, 27) (numbers left: [31]). Try possible operations.\n    |- Try 47 + 27 = 74. Add 74 to the number set. Current number set: [74, 31], target: 27, just two numbers left.\n     |- Try 74 + 31 = 105. Evaluate 105 != 27, drop this branch.\n     |- Try 74 - 31 = 43. Evaluate 43 != 27, drop this branch.\n     |- Try 74 * 31 = 2294. 2294 exceeds the maximum intermediate result, drop this branch.\n     |- Try 74 \/ 31 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 47 - 27 = 20. Add 20 to the number set. Current number set: [20, 31], target: 27, just two numbers left.\n     |- Try 31 + 20 = 51. Evaluate 51 != 27, drop this branch.\n     |- Try 31 - 20 = 11. Evaluate 11 != 27, drop this branch.\n     |- Try 31 * 20 = 620. Evaluate 620 != 27, drop this branch.\n     |- Try 31 \/ 20 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 47 * 27 = 1269. Add 1269 to the number set. Current number set: [1269, 31], target: 27, just two numbers left.\n     |- Try 1269 + 31 = 1300. Evaluate 1300 != 27, drop this branch.\n     |- Try 1269 - 31 = 1238. Evaluate 1238 != 27, drop this branch.\n     |- Try 1269 * 31 = 39339. 39339 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1269 \/ 31 = 40.9. 40.9 is a decimal, drop this branch.\n    |- Try 47 \/ 27 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (31, 27) (numbers left: [47]). Try possible operations.\n    |- Try 31 + 27 = 58. Add 58 to the number set. Current number set: [58, 47], target: 27, just two numbers left.\n     |- Try 58 + 47 = 105. Evaluate 105 != 27, drop this branch.\n     |- Try 58 - 47 = 11. Evaluate 11 != 27, drop this branch.\n     |- Try 58 * 47 = 2726. 2726 exceeds the maximum intermediate result, drop this branch.\n     |- Try 58 \/ 47 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 31 - 27 = 4. Add 4 to the number set. Current number set: [4, 47], target: 27, just two numbers left.\n     |- Try 47 + 4 = 51. Evaluate 51 != 27, drop this branch.\n     |- Try 47 - 4 = 43. Evaluate 43 != 27, drop this branch.\n     |- Try 47 * 4 = 188. Evaluate 188 != 27, drop this branch.\n     |- Try 47 \/ 4 = 11.8. 11.8 is a decimal, drop this branch.\n    |- Try 31 * 27 = 837. Add 837 to the number set. Current number set: [837, 47], target: 27, just two numbers left.\n     |- Try 837 + 47 = 884. Evaluate 884 != 27, drop this branch.\n     |- Try 837 - 47 = 790. Evaluate 790 != 27, drop this branch.\n     |- Try 837 * 47 = 39339. 39339 exceeds the maximum intermediate result, drop this branch.\n     |- Try 837 \/ 47 = 17.8. 17.8 is a decimal, drop this branch.\n    |- Try 31 \/ 27 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 31 - 16 = 15. Add 15 to the number set. Current number set: [15, 31, 27], target: 27. Options for choosing two numbers: [(15, 31), (15, 27), (31, 27)].\n   |- Pick two numbers (15, 31) (numbers left: [27]). Try possible operations.\n    |- Try 31 + 15 = 46. Add 46 to the number set. Current number set: [46, 27], target: 27, just two numbers left.\n     |- Try 46 + 27 = 73. Evaluate 73 != 27, drop this branch.\n     |- Try 46 - 27 = 19. Evaluate 19 != 27, drop this branch.\n     |- Try 46 * 27 = 1242. Evaluate 1242 != 27, drop this branch.\n     |- Try 46 \/ 27 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 31 - 15 = 16. Add 16 to the number set. Current number set: [16, 27], target: 27, just two numbers left.\n     |- Try 27 + 16 = 43. Evaluate 43 != 27, drop this branch.\n     |- Try 27 - 16 = 11. Evaluate 11 != 27, drop this branch.\n     |- Try 27 * 16 = 432. Evaluate 432 != 27, drop this branch.\n     |- Try 27 \/ 16 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 31 * 15 = 465. Add 465 to the number set. Current number set: [465, 27], target: 27, just two numbers left.\n     |- Try 465 + 27 = 492. Evaluate 492 != 27, drop this branch.\n     |- Try 465 - 27 = 438. Evaluate 438 != 27, drop this branch.\n     |- Try 465 * 27 = 12555. 12555 exceeds the maximum intermediate result, drop this branch.\n     |- Try 465 \/ 27 = 17.2. 17.2 is a decimal, drop this branch.\n    |- Try 31 \/ 15 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (15, 27) (numbers left: [31]). Try possible operations.\n    |- Try 27 + 15 = 42. Add 42 to the number set. Current number set: [42, 31], target: 27, just two numbers left.\n     |- Try 42 + 31 = 73. Evaluate 73 != 27, drop this branch.\n     |- Try 42 - 31 = 11. Evaluate 11 != 27, drop this branch.\n     |- Try 42 * 31 = 1302. Evaluate 1302 != 27, drop this branch.\n     |- Try 42 \/ 31 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 27 - 15 = 12. Add 12 to the number set. Current number set: [12, 31], target: 27, just two numbers left.\n     |- Try 31 + 12 = 43. Evaluate 43 != 27, drop this branch.\n     |- Try 31 - 12 = 19. Evaluate 19 != 27, drop this branch.\n     |- Try 31 * 12 = 372. Evaluate 372 != 27, drop this branch.\n     |- Try 31 \/ 12 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 27 * 15 = 405. Add 405 to the number set. Current number set: [405, 31], target: 27, just two numbers left.\n     |- Try 405 + 31 = 436. Evaluate 436 != 27, drop this branch.\n     |- Try 405 - 31 = 374. Evaluate 374 != 27, drop this branch.\n     |- Try 405 * 31 = 12555. 12555 exceeds the maximum intermediate result, drop this branch.\n     |- Try 405 \/ 31 = 13.1. 13.1 is a decimal, drop this branch.\n    |- Try 27 \/ 15 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (31, 27) (numbers left: [15]). Try possible operations.\n    |- Try 31 + 27 = 58. Add 58 to the number set. Current number set: [58, 15], target: 27, just two numbers left.\n     |- Try 58 + 15 = 73. Evaluate 73 != 27, drop this branch.\n     |- Try 58 - 15 = 43. Evaluate 43 != 27, drop this branch.\n     |- Try 58 * 15 = 870. Evaluate 870 != 27, drop this branch.\n     |- Try 58 \/ 15 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 31 - 27 = 4. Add 4 to the number set. Current number set: [4, 15], target: 27, just two numbers left.\n     |- Try 15 + 4 = 19. Evaluate 19 != 27, drop this branch.\n     |- Try 15 - 4 = 11. Evaluate 11 != 27, drop this branch.\n     |- Try 15 * 4 = 60. Evaluate 60 != 27, drop this branch.\n     |- Try 15 \/ 4 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 31 * 27 = 837. Add 837 to the number set. Current number set: [837, 15], target: 27, just two numbers left.\n     |- Try 837 + 15 = 852. Evaluate 852 != 27, drop this branch.\n     |- Try 837 - 15 = 822. Evaluate 822 != 27, drop this branch.\n     |- Try 837 * 15 = 12555. 12555 exceeds the maximum intermediate result, drop this branch.\n     |- Try 837 \/ 15 = 55.8. 55.8 is a decimal, drop this branch.\n    |- Try 31 \/ 27 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 31 * 16 = 496. Add 496 to the number set. Current number set: [496, 31, 27], target: 27. Options for choosing two numbers: [(496, 31), (496, 27), (31, 27)].\n   |- Pick two numbers (496, 31) (numbers left: [27]). Try possible operations.\n    |- Try 496 + 31 = 527. Add 527 to the number set. Current number set: [527, 27], target: 27, just two numbers left.\n     |- Try 527 + 27 = 554. Evaluate 554 != 27, drop this branch.\n     |- Try 527 - 27 = 500. Evaluate 500 != 27, drop this branch.\n     |- Try 527 * 27 = 14229. 14229 exceeds the maximum intermediate result, drop this branch.\n     |- Try 527 \/ 27 = 19.5. 19.5 is a decimal, drop this branch.\n    |- Try 496 - 31 = 465. Add 465 to the number set. Current number set: [465, 27], target: 27, just two numbers left.\n     |- Try 465 + 27 = 492. Evaluate 492 != 27, drop this branch.\n     |- Try 465 - 27 = 438. Evaluate 438 != 27, drop this branch.\n     |- Try 465 * 27 = 12555. 12555 exceeds the maximum intermediate result, drop this branch.\n     |- Try 465 \/ 27 = 17.2. 17.2 is a decimal, drop this branch.\n    |- Try 496 * 31 = 15376. 15376 exceeds the maximum intermediate result, drop this branch.\n    |- Try 496 \/ 31 = 16. Add 16 to the number set. Current number set: [16, 27], target: 27, just two numbers left.\n     |- Try 27 + 16 = 43. Evaluate 43 != 27, drop this branch.\n     |- Try 27 - 16 = 11. Evaluate 11 != 27, drop this branch.\n     |- Try 27 * 16 = 432. Evaluate 432 != 27, drop this branch.\n     |- Try 27 \/ 16 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (496, 27) (numbers left: [31]). Try possible operations.\n    |- Try 496 + 27 = 523. Add 523 to the number set. Current number set: [523, 31], target: 27, just two numbers left.\n     |- Try 523 + 31 = 554. Evaluate 554 != 27, drop this branch.\n     |- Try 523 - 31 = 492. Evaluate 492 != 27, drop this branch.\n     |- Try 523 * 31 = 16213. 16213 exceeds the maximum intermediate result, drop this branch.\n     |- Try 523 \/ 31 = 16.9. 16.9 is a decimal, drop this branch.\n    |- Try 496 - 27 = 469. Add 469 to the number set. Current number set: [469, 31], target: 27, just two numbers left.\n     |- Try 469 + 31 = 500. Evaluate 500 != 27, drop this branch.\n     |- Try 469 - 31 = 438. Evaluate 438 != 27, drop this branch.\n     |- Try 469 * 31 = 14539. 14539 exceeds the maximum intermediate result, drop this branch.\n     |- Try 469 \/ 31 = 15.1. 15.1 is a decimal, drop this branch.\n    |- Try 496 * 27 = 13392. 13392 exceeds the maximum intermediate result, drop this branch.\n    |- Try 496 \/ 27 = 18.4. 18.4 is a decimal, drop this branch.\n   |- Pick two numbers (31, 27) (numbers left: [496]). Try possible operations.\n    |- Try 31 + 27 = 58. Add 58 to the number set. Current number set: [58, 496], target: 27, just two numbers left.\n     |- Try 496 + 58 = 554. Evaluate 554 != 27, drop this branch.\n     |- Try 496 - 58 = 438. Evaluate 438 != 27, drop this branch.\n     |- Try 496 * 58 = 28768. 28768 exceeds the maximum intermediate result, drop this branch.\n     |- Try 496 \/ 58 = 8.6. 8.6 is a decimal, drop this branch.\n    |- Try 31 - 27 = 4. Add 4 to the number set. Current number set: [4, 496], target: 27, just two numbers left.\n     |- Try 496 + 4 = 500. Evaluate 500 != 27, drop this branch.\n     |- Try 496 - 4 = 492. Evaluate 492 != 27, drop this branch.\n     |- Try 496 * 4 = 1984. Evaluate 1984 != 27, drop this branch.\n     |- Try 496 \/ 4 = 124. Evaluate 124 != 27, drop this branch.\n    |- Try 31 * 27 = 837. Add 837 to the number set. Current number set: [837, 496], target: 27, just two numbers left.\n     |- Try 837 + 496 = 1333. Evaluate 1333 != 27, drop this branch.\n     |- Try 837 - 496 = 341. Evaluate 341 != 27, drop this branch.\n     |- Try 837 * 496 = 415152. 415152 exceeds the maximum intermediate result, drop this branch.\n     |- Try 837 \/ 496 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 31 \/ 27 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 31 \/ 16 = 1.9. 1.9 is a decimal, drop this branch.\n |- Pick two numbers (31, 31) (numbers left: [16, 27]). Try possible operations.\n  |- Try 31 + 31 = 62. Add 62 to the number set. Current number set: [62, 16, 27], target: 27. Options for choosing two numbers: [(62, 16), (62, 27), (16, 27)].\n   |- Pick two numbers (62, 16) (numbers left: [27]). Try possible operations.\n    |- Try 62 + 16 = 78. Add 78 to the number set. Current number set: [78, 27], target: 27, just two numbers left.\n     |- Try 78 + 27 = 105. Evaluate 105 != 27, drop this branch.\n     |- Try 78 - 27 = 51. Evaluate 51 != 27, drop this branch.\n     |- Try 78 * 27 = 2106. 2106 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 27 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 62 - 16 = 46. Add 46 to the number set. Current number set: [46, 27], target: 27, just two numbers left.\n     |- Try 46 + 27 = 73. Evaluate 73 != 27, drop this branch.\n     |- Try 46 - 27 = 19. Evaluate 19 != 27, drop this branch.\n     |- Try 46 * 27 = 1242. Evaluate 1242 != 27, drop this branch.\n     |- Try 46 \/ 27 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 62 * 16 = 992. Add 992 to the number set. Current number set: [992, 27], target: 27, just two numbers left.\n     |- Try 992 + 27 = 1019. Evaluate 1019 != 27, drop this branch.\n     |- Try 992 - 27 = 965. Evaluate 965 != 27, drop this branch.\n     |- Try 992 * 27 = 26784. 26784 exceeds the maximum intermediate result, drop this branch.\n     |- Try 992 \/ 27 = 36.7. 36.7 is a decimal, drop this branch.\n    |- Try 62 \/ 16 = 3.9. 3.9 is a decimal, drop this branch.\n   |- Pick two numbers (62, 27) (numbers left: [16]). Try possible operations.\n    |- Try 62 + 27 = 89. Add 89 to the number set. Current number set: [89, 16], target: 27, just two numbers left.\n     |- Try 89 + 16 = 105. Evaluate 105 != 27, drop this branch.\n     |- Try 89 - 16 = 73. Evaluate 73 != 27, drop this branch.\n     |- Try 89 * 16 = 1424. Evaluate 1424 != 27, drop this branch.\n     |- Try 89 \/ 16 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 62 - 27 = 35. Add 35 to the number set. Current number set: [35, 16], target: 27, just two numbers left.\n     |- Try 35 + 16 = 51. Evaluate 51 != 27, drop this branch.\n     |- Try 35 - 16 = 19. Evaluate 19 != 27, drop this branch.\n     |- Try 35 * 16 = 560. Evaluate 560 != 27, drop this branch.\n     |- Try 35 \/ 16 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 62 * 27 = 1674. Add 1674 to the number set. Current number set: [1674, 16], target: 27, just two numbers left.\n     |- Try 1674 + 16 = 1690. Evaluate 1690 != 27, drop this branch.\n     |- Try 1674 - 16 = 1658. Evaluate 1658 != 27, drop this branch.\n     |- Try 1674 * 16 = 26784. 26784 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1674 \/ 16 = 104.6. 104.6 is a decimal, drop this branch.\n    |- Try 62 \/ 27 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (16, 27) (numbers left: [62]). Try possible operations.\n    |- Try 27 + 16 = 43. Add 43 to the number set. Current number set: [43, 62], target: 27, just two numbers left.\n     |- Try 62 + 43 = 105. Evaluate 105 != 27, drop this branch.\n     |- Try 62 - 43 = 19. Evaluate 19 != 27, drop this branch.\n     |- Try 62 * 43 = 2666. 2666 exceeds the maximum intermediate result, drop this branch.\n     |- Try 62 \/ 43 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 27 - 16 = 11. Add 11 to the number set. Current number set: [11, 62], target: 27, just two numbers left.\n     |- Try 62 + 11 = 73. Evaluate 73 != 27, drop this branch.\n     |- Try 62 - 11 = 51. Evaluate 51 != 27, drop this branch.\n     |- Try 62 * 11 = 682. Evaluate 682 != 27, drop this branch.\n     |- Try 62 \/ 11 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 27 * 16 = 432. Add 432 to the number set. Current number set: [432, 62], target: 27, just two numbers left.\n     |- Try 432 + 62 = 494. Evaluate 494 != 27, drop this branch.\n     |- Try 432 - 62 = 370. Evaluate 370 != 27, drop this branch.\n     |- Try 432 * 62 = 26784. 26784 exceeds the maximum intermediate result, drop this branch.\n     |- Try 432 \/ 62 = 7.0. 7.0 is a decimal, drop this branch.\n    |- Try 27 \/ 16 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 31 - 31 = 0. Add 0 to the number set. Current number set: [0, 16, 27], target: 27. Options for choosing two numbers: [(0, 16), (0, 27), (16, 27)].\n   |- Pick two numbers (0, 16) (numbers left: [27]). Try possible operations.\n    |- Try 16 + 0 = 16. Add 16 to the number set. Current number set: [16, 27], target: 27, just two numbers left.\n     |- Try 27 + 16 = 43. Evaluate 43 != 27, drop this branch.\n     |- Try 27 - 16 = 11. Evaluate 11 != 27, drop this branch.\n     |- Try 27 * 16 = 432. Evaluate 432 != 27, drop this branch.\n     |- Try 27 \/ 16 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 16 - 0 = 16. Add 16 to the number set. Current number set: [16, 27], target: 27, just two numbers left.\n     |- Try 27 + 16 = 43. Evaluate 43 != 27, drop this branch.\n     |- Try 27 - 16 = 11. Evaluate 11 != 27, drop this branch.\n     |- Try 27 * 16 = 432. Evaluate 432 != 27, drop this branch.\n     |- Try 27 \/ 16 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 16 * 0 = 0. Add 0 to the number set. Current number set: [0, 27], target: 27, just two numbers left.\n     |- Try 27 + 0 = 27. Evaluate 27 == 27, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 27 + 0 = 27\nThe step before: 16 * 0 = 0\nThe first step: 31 - 31 = 0\n\nOutput the solution in the required format:\n<Solution>\n31 - 31 = 0\n16 * 0 = 0\n27 + 0 = 27\n<\/Solution>\n","item":{"nums":[31,16,31,27],"solution":["31 - 31 = 0","16 * 0 = 0","27 + 0 = 27"],"target":27}}
+{"instance_id":"countdown_8k_2","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [36, 7, 4, 42]\nTarget: 38","reference_output":"# Search Procedure\nInitial number set: [36, 7, 4, 42], target: 38. Options for choosing two numbers: [(36, 7), (36, 4), (36, 42), (7, 4), (7, 42), (4, 42)].\n |- Pick two numbers (36, 7) (numbers left: [4, 42]). Try possible operations.\n  |- Try 36 + 7 = 43. Add 43 to the number set. Current number set: [43, 4, 42], target: 38. Options for choosing two numbers: [(43, 4), (43, 42), (4, 42)].\n   |- Pick two numbers (43, 4) (numbers left: [42]). Try possible operations.\n    |- Try 43 + 4 = 47. Add 47 to the number set. Current number set: [47, 42], target: 38, just two numbers left.\n     |- Try 47 + 42 = 89. Evaluate 89 != 38, drop this branch.\n     |- Try 47 - 42 = 5. Evaluate 5 != 38, drop this branch.\n     |- Try 47 * 42 = 1974. Evaluate 1974 != 38, drop this branch.\n     |- Try 47 \/ 42 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 43 - 4 = 39. Add 39 to the number set. Current number set: [39, 42], target: 38, just two numbers left.\n     |- Try 42 + 39 = 81. Evaluate 81 != 38, drop this branch.\n     |- Try 42 - 39 = 3. Evaluate 3 != 38, drop this branch.\n     |- Try 42 * 39 = 1638. Evaluate 1638 != 38, drop this branch.\n     |- Try 42 \/ 39 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 43 * 4 = 172. Add 172 to the number set. Current number set: [172, 42], target: 38, just two numbers left.\n     |- Try 172 + 42 = 214. Evaluate 214 != 38, drop this branch.\n     |- Try 172 - 42 = 130. Evaluate 130 != 38, drop this branch.\n     |- Try 172 * 42 = 7224. 7224 exceeds the maximum intermediate result, drop this branch.\n     |- Try 172 \/ 42 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 43 \/ 4 = 10.8. 10.8 is a decimal, drop this branch.\n   |- Pick two numbers (43, 42) (numbers left: [4]). Try possible operations.\n    |- Try 43 + 42 = 85. Add 85 to the number set. Current number set: [85, 4], target: 38, just two numbers left.\n     |- Try 85 + 4 = 89. Evaluate 89 != 38, drop this branch.\n     |- Try 85 - 4 = 81. Evaluate 81 != 38, drop this branch.\n     |- Try 85 * 4 = 340. Evaluate 340 != 38, drop this branch.\n     |- Try 85 \/ 4 = 21.2. 21.2 is a decimal, drop this branch.\n    |- Try 43 - 42 = 1. Add 1 to the number set. Current number set: [1, 4], target: 38, just two numbers left.\n     |- Try 4 + 1 = 5. Evaluate 5 != 38, drop this branch.\n     |- Try 4 - 1 = 3. Evaluate 3 != 38, drop this branch.\n     |- Try 4 * 1 = 4. Evaluate 4 != 38, drop this branch.\n     |- Try 4 \/ 1 = 4. Evaluate 4 != 38, drop this branch.\n    |- Try 43 * 42 = 1806. Add 1806 to the number set. Current number set: [1806, 4], target: 38, just two numbers left.\n     |- Try 1806 + 4 = 1810. Evaluate 1810 != 38, drop this branch.\n     |- Try 1806 - 4 = 1802. Evaluate 1802 != 38, drop this branch.\n     |- Try 1806 * 4 = 7224. 7224 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1806 \/ 4 = 451.5. 451.5 is a decimal, drop this branch.\n    |- Try 43 \/ 42 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (4, 42) (numbers left: [43]). Try possible operations.\n    |- Try 42 + 4 = 46. Add 46 to the number set. Current number set: [46, 43], target: 38, just two numbers left.\n     |- Try 46 + 43 = 89. Evaluate 89 != 38, drop this branch.\n     |- Try 46 - 43 = 3. Evaluate 3 != 38, drop this branch.\n     |- Try 46 * 43 = 1978. Evaluate 1978 != 38, drop this branch.\n     |- Try 46 \/ 43 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 42 - 4 = 38. Add 38 to the number set. Current number set: [38, 43], target: 38, just two numbers left.\n     |- Try 43 + 38 = 81. Evaluate 81 != 38, drop this branch.\n     |- Try 43 - 38 = 5. Evaluate 5 != 38, drop this branch.\n     |- Try 43 * 38 = 1634. Evaluate 1634 != 38, drop this branch.\n     |- Try 43 \/ 38 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 42 * 4 = 168. Add 168 to the number set. Current number set: [168, 43], target: 38, just two numbers left.\n     |- Try 168 + 43 = 211. Evaluate 211 != 38, drop this branch.\n     |- Try 168 - 43 = 125. Evaluate 125 != 38, drop this branch.\n     |- Try 168 * 43 = 7224. 7224 exceeds the maximum intermediate result, drop this branch.\n     |- Try 168 \/ 43 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 42 \/ 4 = 10.5. 10.5 is a decimal, drop this branch.\n  |- Try 36 - 7 = 29. Add 29 to the number set. Current number set: [29, 4, 42], target: 38. Options for choosing two numbers: [(29, 4), (29, 42), (4, 42)].\n   |- Pick two numbers (29, 4) (numbers left: [42]). Try possible operations.\n    |- Try 29 + 4 = 33. Add 33 to the number set. Current number set: [33, 42], target: 38, just two numbers left.\n     |- Try 42 + 33 = 75. Evaluate 75 != 38, drop this branch.\n     |- Try 42 - 33 = 9. Evaluate 9 != 38, drop this branch.\n     |- Try 42 * 33 = 1386. Evaluate 1386 != 38, drop this branch.\n     |- Try 42 \/ 33 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 29 - 4 = 25. Add 25 to the number set. Current number set: [25, 42], target: 38, just two numbers left.\n     |- Try 42 + 25 = 67. Evaluate 67 != 38, drop this branch.\n     |- Try 42 - 25 = 17. Evaluate 17 != 38, drop this branch.\n     |- Try 42 * 25 = 1050. Evaluate 1050 != 38, drop this branch.\n     |- Try 42 \/ 25 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 29 * 4 = 116. Add 116 to the number set. Current number set: [116, 42], target: 38, just two numbers left.\n     |- Try 116 + 42 = 158. Evaluate 158 != 38, drop this branch.\n     |- Try 116 - 42 = 74. Evaluate 74 != 38, drop this branch.\n     |- Try 116 * 42 = 4872. 4872 exceeds the maximum intermediate result, drop this branch.\n     |- Try 116 \/ 42 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 29 \/ 4 = 7.2. 7.2 is a decimal, drop this branch.\n   |- Pick two numbers (29, 42) (numbers left: [4]). Try possible operations.\n    |- Try 42 + 29 = 71. Add 71 to the number set. Current number set: [71, 4], target: 38, just two numbers left.\n     |- Try 71 + 4 = 75. Evaluate 75 != 38, drop this branch.\n     |- Try 71 - 4 = 67. Evaluate 67 != 38, drop this branch.\n     |- Try 71 * 4 = 284. Evaluate 284 != 38, drop this branch.\n     |- Try 71 \/ 4 = 17.8. 17.8 is a decimal, drop this branch.\n    |- Try 42 - 29 = 13. Add 13 to the number set. Current number set: [13, 4], target: 38, just two numbers left.\n     |- Try 13 + 4 = 17. Evaluate 17 != 38, drop this branch.\n     |- Try 13 - 4 = 9. Evaluate 9 != 38, drop this branch.\n     |- Try 13 * 4 = 52. Evaluate 52 != 38, drop this branch.\n     |- Try 13 \/ 4 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 42 * 29 = 1218. Add 1218 to the number set. Current number set: [1218, 4], target: 38, just two numbers left.\n     |- Try 1218 + 4 = 1222. Evaluate 1222 != 38, drop this branch.\n     |- Try 1218 - 4 = 1214. Evaluate 1214 != 38, drop this branch.\n     |- Try 1218 * 4 = 4872. 4872 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1218 \/ 4 = 304.5. 304.5 is a decimal, drop this branch.\n    |- Try 42 \/ 29 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (4, 42) (numbers left: [29]). Try possible operations.\n    |- Try 42 + 4 = 46. Add 46 to the number set. Current number set: [46, 29], target: 38, just two numbers left.\n     |- Try 46 + 29 = 75. Evaluate 75 != 38, drop this branch.\n     |- Try 46 - 29 = 17. Evaluate 17 != 38, drop this branch.\n     |- Try 46 * 29 = 1334. Evaluate 1334 != 38, drop this branch.\n     |- Try 46 \/ 29 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 42 - 4 = 38. Add 38 to the number set. Current number set: [38, 29], target: 38, just two numbers left.\n     |- Try 38 + 29 = 67. Evaluate 67 != 38, drop this branch.\n     |- Try 38 - 29 = 9. Evaluate 9 != 38, drop this branch.\n     |- Try 38 * 29 = 1102. Evaluate 1102 != 38, drop this branch.\n     |- Try 38 \/ 29 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 42 * 4 = 168. Add 168 to the number set. Current number set: [168, 29], target: 38, just two numbers left.\n     |- Try 168 + 29 = 197. Evaluate 197 != 38, drop this branch.\n     |- Try 168 - 29 = 139. Evaluate 139 != 38, drop this branch.\n     |- Try 168 * 29 = 4872. 4872 exceeds the maximum intermediate result, drop this branch.\n     |- Try 168 \/ 29 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 42 \/ 4 = 10.5. 10.5 is a decimal, drop this branch.\n  |- Try 36 * 7 = 252. Add 252 to the number set. Current number set: [252, 4, 42], target: 38. Options for choosing two numbers: [(252, 4), (252, 42), (4, 42)].\n   |- Pick two numbers (252, 4) (numbers left: [42]). Try possible operations.\n    |- Try 252 + 4 = 256. Add 256 to the number set. Current number set: [256, 42], target: 38, just two numbers left.\n     |- Try 256 + 42 = 298. Evaluate 298 != 38, drop this branch.\n     |- Try 256 - 42 = 214. Evaluate 214 != 38, drop this branch.\n     |- Try 256 * 42 = 10752. 10752 exceeds the maximum intermediate result, drop this branch.\n     |- Try 256 \/ 42 = 6.1. 6.1 is a decimal, drop this branch.\n    |- Try 252 - 4 = 248. Add 248 to the number set. Current number set: [248, 42], target: 38, just two numbers left.\n     |- Try 248 + 42 = 290. Evaluate 290 != 38, drop this branch.\n     |- Try 248 - 42 = 206. Evaluate 206 != 38, drop this branch.\n     |- Try 248 * 42 = 10416. 10416 exceeds the maximum intermediate result, drop this branch.\n     |- Try 248 \/ 42 = 5.9. 5.9 is a decimal, drop this branch.\n    |- Try 252 * 4 = 1008. Add 1008 to the number set. Current number set: [1008, 42], target: 38, just two numbers left.\n     |- Try 1008 + 42 = 1050. Evaluate 1050 != 38, drop this branch.\n     |- Try 1008 - 42 = 966. Evaluate 966 != 38, drop this branch.\n     |- Try 1008 * 42 = 42336. 42336 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1008 \/ 42 = 24. Evaluate 24 != 38, drop this branch.\n    |- Try 252 \/ 4 = 63. Add 63 to the number set. Current number set: [63, 42], target: 38, just two numbers left.\n     |- Try 63 + 42 = 105. Evaluate 105 != 38, drop this branch.\n     |- Try 63 - 42 = 21. Evaluate 21 != 38, drop this branch.\n     |- Try 63 * 42 = 2646. 2646 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 42 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (252, 42) (numbers left: [4]). Try possible operations.\n    |- Try 252 + 42 = 294. Add 294 to the number set. Current number set: [294, 4], target: 38, just two numbers left.\n     |- Try 294 + 4 = 298. Evaluate 298 != 38, drop this branch.\n     |- Try 294 - 4 = 290. Evaluate 290 != 38, drop this branch.\n     |- Try 294 * 4 = 1176. Evaluate 1176 != 38, drop this branch.\n     |- Try 294 \/ 4 = 73.5. 73.5 is a decimal, drop this branch.\n    |- Try 252 - 42 = 210. Add 210 to the number set. Current number set: [210, 4], target: 38, just two numbers left.\n     |- Try 210 + 4 = 214. Evaluate 214 != 38, drop this branch.\n     |- Try 210 - 4 = 206. Evaluate 206 != 38, drop this branch.\n     |- Try 210 * 4 = 840. Evaluate 840 != 38, drop this branch.\n     |- Try 210 \/ 4 = 52.5. 52.5 is a decimal, drop this branch.\n    |- Try 252 * 42 = 10584. 10584 exceeds the maximum intermediate result, drop this branch.\n    |- Try 252 \/ 42 = 6. Add 6 to the number set. Current number set: [6, 4], target: 38, just two numbers left.\n     |- Try 6 + 4 = 10. Evaluate 10 != 38, drop this branch.\n     |- Try 6 - 4 = 2. Evaluate 2 != 38, drop this branch.\n     |- Try 6 * 4 = 24. Evaluate 24 != 38, drop this branch.\n     |- Try 6 \/ 4 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (4, 42) (numbers left: [252]). Try possible operations.\n    |- Try 42 + 4 = 46. Add 46 to the number set. Current number set: [46, 252], target: 38, just two numbers left.\n     |- Try 252 + 46 = 298. Evaluate 298 != 38, drop this branch.\n     |- Try 252 - 46 = 206. Evaluate 206 != 38, drop this branch.\n     |- Try 252 * 46 = 11592. 11592 exceeds the maximum intermediate result, drop this branch.\n     |- Try 252 \/ 46 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 42 - 4 = 38. Add 38 to the number set. Current number set: [38, 252], target: 38, just two numbers left.\n     |- Try 252 + 38 = 290. Evaluate 290 != 38, drop this branch.\n     |- Try 252 - 38 = 214. Evaluate 214 != 38, drop this branch.\n     |- Try 252 * 38 = 9576. 9576 exceeds the maximum intermediate result, drop this branch.\n     |- Try 252 \/ 38 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 42 * 4 = 168. Add 168 to the number set. Current number set: [168, 252], target: 38, just two numbers left.\n     |- Try 252 + 168 = 420. Evaluate 420 != 38, drop this branch.\n     |- Try 252 - 168 = 84. Evaluate 84 != 38, drop this branch.\n     |- Try 252 * 168 = 42336. 42336 exceeds the maximum intermediate result, drop this branch.\n     |- Try 252 \/ 168 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 42 \/ 4 = 10.5. 10.5 is a decimal, drop this branch.\n  |- Try 36 \/ 7 = 5.1. 5.1 is a decimal, drop this branch.\n |- Pick two numbers (36, 4) (numbers left: [7, 42]). Try possible operations.\n  |- Try 36 + 4 = 40. Add 40 to the number set. Current number set: [40, 7, 42], target: 38. Options for choosing two numbers: [(40, 7), (40, 42), (7, 42)].\n   |- Pick two numbers (40, 7) (numbers left: [42]). Try possible operations.\n    |- Try 40 + 7 = 47. Add 47 to the number set. Current number set: [47, 42], target: 38, just two numbers left.\n     |- Try 47 + 42 = 89. Evaluate 89 != 38, drop this branch.\n     |- Try 47 - 42 = 5. Evaluate 5 != 38, drop this branch.\n     |- Try 47 * 42 = 1974. Evaluate 1974 != 38, drop this branch.\n     |- Try 47 \/ 42 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 40 - 7 = 33. Add 33 to the number set. Current number set: [33, 42], target: 38, just two numbers left.\n     |- Try 42 + 33 = 75. Evaluate 75 != 38, drop this branch.\n     |- Try 42 - 33 = 9. Evaluate 9 != 38, drop this branch.\n     |- Try 42 * 33 = 1386. Evaluate 1386 != 38, drop this branch.\n     |- Try 42 \/ 33 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 40 * 7 = 280. Add 280 to the number set. Current number set: [280, 42], target: 38, just two numbers left.\n     |- Try 280 + 42 = 322. Evaluate 322 != 38, drop this branch.\n     |- Try 280 - 42 = 238. Evaluate 238 != 38, drop this branch.\n     |- Try 280 * 42 = 11760. 11760 exceeds the maximum intermediate result, drop this branch.\n     |- Try 280 \/ 42 = 6.7. 6.7 is a decimal, drop this branch.\n    |- Try 40 \/ 7 = 5.7. 5.7 is a decimal, drop this branch.\n   |- Pick two numbers (40, 42) (numbers left: [7]). Try possible operations.\n    |- Try 42 + 40 = 82. Add 82 to the number set. Current number set: [82, 7], target: 38, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 38, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 38, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 38, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 42 - 40 = 2. Add 2 to the number set. Current number set: [2, 7], target: 38, just two numbers left.\n     |- Try 7 + 2 = 9. Evaluate 9 != 38, drop this branch.\n     |- Try 7 - 2 = 5. Evaluate 5 != 38, drop this branch.\n     |- Try 7 * 2 = 14. Evaluate 14 != 38, drop this branch.\n     |- Try 7 \/ 2 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 42 * 40 = 1680. Add 1680 to the number set. Current number set: [1680, 7], target: 38, just two numbers left.\n     |- Try 1680 + 7 = 1687. Evaluate 1687 != 38, drop this branch.\n     |- Try 1680 - 7 = 1673. Evaluate 1673 != 38, drop this branch.\n     |- Try 1680 * 7 = 11760. 11760 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1680 \/ 7 = 240. Evaluate 240 != 38, drop this branch.\n    |- Try 42 \/ 40 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (7, 42) (numbers left: [40]). Try possible operations.\n    |- Try 42 + 7 = 49. Add 49 to the number set. Current number set: [49, 40], target: 38, just two numbers left.\n     |- Try 49 + 40 = 89. Evaluate 89 != 38, drop this branch.\n     |- Try 49 - 40 = 9. Evaluate 9 != 38, drop this branch.\n     |- Try 49 * 40 = 1960. Evaluate 1960 != 38, drop this branch.\n     |- Try 49 \/ 40 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 42 - 7 = 35. Add 35 to the number set. Current number set: [35, 40], target: 38, just two numbers left.\n     |- Try 40 + 35 = 75. Evaluate 75 != 38, drop this branch.\n     |- Try 40 - 35 = 5. Evaluate 5 != 38, drop this branch.\n     |- Try 40 * 35 = 1400. Evaluate 1400 != 38, drop this branch.\n     |- Try 40 \/ 35 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 42 * 7 = 294. Add 294 to the number set. Current number set: [294, 40], target: 38, just two numbers left.\n     |- Try 294 + 40 = 334. Evaluate 334 != 38, drop this branch.\n     |- Try 294 - 40 = 254. Evaluate 254 != 38, drop this branch.\n     |- Try 294 * 40 = 11760. 11760 exceeds the maximum intermediate result, drop this branch.\n     |- Try 294 \/ 40 = 7.3. 7.3 is a decimal, drop this branch.\n    |- Try 42 \/ 7 = 6. Add 6 to the number set. Current number set: [6, 40], target: 38, just two numbers left.\n     |- Try 40 + 6 = 46. Evaluate 46 != 38, drop this branch.\n     |- Try 40 - 6 = 34. Evaluate 34 != 38, drop this branch.\n     |- Try 40 * 6 = 240. Evaluate 240 != 38, drop this branch.\n     |- Try 40 \/ 6 = 6.7. 6.7 is a decimal, drop this branch.\n  |- Try 36 - 4 = 32. Add 32 to the number set. Current number set: [32, 7, 42], target: 38. Options for choosing two numbers: [(32, 7), (32, 42), (7, 42)].\n   |- Pick two numbers (32, 7) (numbers left: [42]). Try possible operations.\n    |- Try 32 + 7 = 39. Add 39 to the number set. Current number set: [39, 42], target: 38, just two numbers left.\n     |- Try 42 + 39 = 81. Evaluate 81 != 38, drop this branch.\n     |- Try 42 - 39 = 3. Evaluate 3 != 38, drop this branch.\n     |- Try 42 * 39 = 1638. Evaluate 1638 != 38, drop this branch.\n     |- Try 42 \/ 39 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 32 - 7 = 25. Add 25 to the number set. Current number set: [25, 42], target: 38, just two numbers left.\n     |- Try 42 + 25 = 67. Evaluate 67 != 38, drop this branch.\n     |- Try 42 - 25 = 17. Evaluate 17 != 38, drop this branch.\n     |- Try 42 * 25 = 1050. Evaluate 1050 != 38, drop this branch.\n     |- Try 42 \/ 25 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 32 * 7 = 224. Add 224 to the number set. Current number set: [224, 42], target: 38, just two numbers left.\n     |- Try 224 + 42 = 266. Evaluate 266 != 38, drop this branch.\n     |- Try 224 - 42 = 182. Evaluate 182 != 38, drop this branch.\n     |- Try 224 * 42 = 9408. 9408 exceeds the maximum intermediate result, drop this branch.\n     |- Try 224 \/ 42 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 32 \/ 7 = 4.6. 4.6 is a decimal, drop this branch.\n   |- Pick two numbers (32, 42) (numbers left: [7]). Try possible operations.\n    |- Try 42 + 32 = 74. Add 74 to the number set. Current number set: [74, 7], target: 38, just two numbers left.\n     |- Try 74 + 7 = 81. Evaluate 81 != 38, drop this branch.\n     |- Try 74 - 7 = 67. Evaluate 67 != 38, drop this branch.\n     |- Try 74 * 7 = 518. Evaluate 518 != 38, drop this branch.\n     |- Try 74 \/ 7 = 10.6. 10.6 is a decimal, drop this branch.\n    |- Try 42 - 32 = 10. Add 10 to the number set. Current number set: [10, 7], target: 38, just two numbers left.\n     |- Try 10 + 7 = 17. Evaluate 17 != 38, drop this branch.\n     |- Try 10 - 7 = 3. Evaluate 3 != 38, drop this branch.\n     |- Try 10 * 7 = 70. Evaluate 70 != 38, drop this branch.\n     |- Try 10 \/ 7 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 42 * 32 = 1344. Add 1344 to the number set. Current number set: [1344, 7], target: 38, just two numbers left.\n     |- Try 1344 + 7 = 1351. Evaluate 1351 != 38, drop this branch.\n     |- Try 1344 - 7 = 1337. Evaluate 1337 != 38, drop this branch.\n     |- Try 1344 * 7 = 9408. 9408 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1344 \/ 7 = 192. Evaluate 192 != 38, drop this branch.\n    |- Try 42 \/ 32 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (7, 42) (numbers left: [32]). Try possible operations.\n    |- Try 42 + 7 = 49. Add 49 to the number set. Current number set: [49, 32], target: 38, just two numbers left.\n     |- Try 49 + 32 = 81. Evaluate 81 != 38, drop this branch.\n     |- Try 49 - 32 = 17. Evaluate 17 != 38, drop this branch.\n     |- Try 49 * 32 = 1568. Evaluate 1568 != 38, drop this branch.\n     |- Try 49 \/ 32 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 42 - 7 = 35. Add 35 to the number set. Current number set: [35, 32], target: 38, just two numbers left.\n     |- Try 35 + 32 = 67. Evaluate 67 != 38, drop this branch.\n     |- Try 35 - 32 = 3. Evaluate 3 != 38, drop this branch.\n     |- Try 35 * 32 = 1120. Evaluate 1120 != 38, drop this branch.\n     |- Try 35 \/ 32 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 42 * 7 = 294. Add 294 to the number set. Current number set: [294, 32], target: 38, just two numbers left.\n     |- Try 294 + 32 = 326. Evaluate 326 != 38, drop this branch.\n     |- Try 294 - 32 = 262. Evaluate 262 != 38, drop this branch.\n     |- Try 294 * 32 = 9408. 9408 exceeds the maximum intermediate result, drop this branch.\n     |- Try 294 \/ 32 = 9.2. 9.2 is a decimal, drop this branch.\n    |- Try 42 \/ 7 = 6. Add 6 to the number set. Current number set: [6, 32], target: 38, just two numbers left.\n     |- Try 32 + 6 = 38. Evaluate 38 == 38, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 32 + 6 = 38\nThe step before: 42 \/ 7 = 6\nThe first step: 36 - 4 = 32\n\nOutput the solution in the required format:\n<Solution>\n36 - 4 = 32\n42 \/ 7 = 6\n32 + 6 = 38\n<\/Solution>\n","item":{"nums":[36,7,4,42],"solution":["36 - 4 = 32","42 \/ 7 = 6","32 + 6 = 38"],"target":38}}
+{"instance_id":"countdown_8k_3","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [6, 12, 5, 39]\nTarget: 13","reference_output":"# Search Procedure\nInitial number set: [6, 12, 5, 39], target: 13. Options for choosing two numbers: [(6, 12), (6, 5), (6, 39), (12, 5), (12, 39), (5, 39)].\n |- Pick two numbers (6, 12) (numbers left: [5, 39]). Try possible operations.\n  |- Try 12 + 6 = 18. Add 18 to the number set. Current number set: [18, 5, 39], target: 13. Options for choosing two numbers: [(18, 5), (18, 39), (5, 39)].\n   |- Pick two numbers (18, 5) (numbers left: [39]). Try possible operations.\n    |- Try 18 + 5 = 23. Add 23 to the number set. Current number set: [23, 39], target: 13, just two numbers left.\n     |- Try 39 + 23 = 62. Evaluate 62 != 13, drop this branch.\n     |- Try 39 - 23 = 16. Evaluate 16 != 13, drop this branch.\n     |- Try 39 * 23 = 897. Evaluate 897 != 13, drop this branch.\n     |- Try 39 \/ 23 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 - 5 = 13. Add 13 to the number set. Current number set: [13, 39], target: 13, just two numbers left.\n     |- Try 39 + 13 = 52. Evaluate 52 != 13, drop this branch.\n     |- Try 39 - 13 = 26. Evaluate 26 != 13, drop this branch.\n     |- Try 39 * 13 = 507. Evaluate 507 != 13, drop this branch.\n     |- Try 39 \/ 13 = 3. Evaluate 3 != 13, drop this branch.\n    |- Try 18 * 5 = 90. Add 90 to the number set. Current number set: [90, 39], target: 13, just two numbers left.\n     |- Try 90 + 39 = 129. Evaluate 129 != 13, drop this branch.\n     |- Try 90 - 39 = 51. Evaluate 51 != 13, drop this branch.\n     |- Try 90 * 39 = 3510. 3510 exceeds the maximum intermediate result, drop this branch.\n     |- Try 90 \/ 39 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 18 \/ 5 = 3.6. 3.6 is a decimal, drop this branch.\n   |- Pick two numbers (18, 39) (numbers left: [5]). Try possible operations.\n    |- Try 39 + 18 = 57. Add 57 to the number set. Current number set: [57, 5], target: 13, just two numbers left.\n     |- Try 57 + 5 = 62. Evaluate 62 != 13, drop this branch.\n     |- Try 57 - 5 = 52. Evaluate 52 != 13, drop this branch.\n     |- Try 57 * 5 = 285. Evaluate 285 != 13, drop this branch.\n     |- Try 57 \/ 5 = 11.4. 11.4 is a decimal, drop this branch.\n    |- Try 39 - 18 = 21. Add 21 to the number set. Current number set: [21, 5], target: 13, just two numbers left.\n     |- Try 21 + 5 = 26. Evaluate 26 != 13, drop this branch.\n     |- Try 21 - 5 = 16. Evaluate 16 != 13, drop this branch.\n     |- Try 21 * 5 = 105. Evaluate 105 != 13, drop this branch.\n     |- Try 21 \/ 5 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 39 * 18 = 702. Add 702 to the number set. Current number set: [702, 5], target: 13, just two numbers left.\n     |- Try 702 + 5 = 707. Evaluate 707 != 13, drop this branch.\n     |- Try 702 - 5 = 697. Evaluate 697 != 13, drop this branch.\n     |- Try 702 * 5 = 3510. 3510 exceeds the maximum intermediate result, drop this branch.\n     |- Try 702 \/ 5 = 140.4. 140.4 is a decimal, drop this branch.\n    |- Try 39 \/ 18 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (5, 39) (numbers left: [18]). Try possible operations.\n    |- Try 39 + 5 = 44. Add 44 to the number set. Current number set: [44, 18], target: 13, just two numbers left.\n     |- Try 44 + 18 = 62. Evaluate 62 != 13, drop this branch.\n     |- Try 44 - 18 = 26. Evaluate 26 != 13, drop this branch.\n     |- Try 44 * 18 = 792. Evaluate 792 != 13, drop this branch.\n     |- Try 44 \/ 18 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 39 - 5 = 34. Add 34 to the number set. Current number set: [34, 18], target: 13, just two numbers left.\n     |- Try 34 + 18 = 52. Evaluate 52 != 13, drop this branch.\n     |- Try 34 - 18 = 16. Evaluate 16 != 13, drop this branch.\n     |- Try 34 * 18 = 612. Evaluate 612 != 13, drop this branch.\n     |- Try 34 \/ 18 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 39 * 5 = 195. Add 195 to the number set. Current number set: [195, 18], target: 13, just two numbers left.\n     |- Try 195 + 18 = 213. Evaluate 213 != 13, drop this branch.\n     |- Try 195 - 18 = 177. Evaluate 177 != 13, drop this branch.\n     |- Try 195 * 18 = 3510. 3510 exceeds the maximum intermediate result, drop this branch.\n     |- Try 195 \/ 18 = 10.8. 10.8 is a decimal, drop this branch.\n    |- Try 39 \/ 5 = 7.8. 7.8 is a decimal, drop this branch.\n  |- Try 12 - 6 = 6. Add 6 to the number set. Current number set: [6, 5, 39], target: 13. Options for choosing two numbers: [(6, 5), (6, 39), (5, 39)].\n   |- Pick two numbers (6, 5) (numbers left: [39]). Try possible operations.\n    |- Try 6 + 5 = 11. Add 11 to the number set. Current number set: [11, 39], target: 13, just two numbers left.\n     |- Try 39 + 11 = 50. Evaluate 50 != 13, drop this branch.\n     |- Try 39 - 11 = 28. Evaluate 28 != 13, drop this branch.\n     |- Try 39 * 11 = 429. Evaluate 429 != 13, drop this branch.\n     |- Try 39 \/ 11 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 6 - 5 = 1. Add 1 to the number set. Current number set: [1, 39], target: 13, just two numbers left.\n     |- Try 39 + 1 = 40. Evaluate 40 != 13, drop this branch.\n     |- Try 39 - 1 = 38. Evaluate 38 != 13, drop this branch.\n     |- Try 39 * 1 = 39. Evaluate 39 != 13, drop this branch.\n     |- Try 39 \/ 1 = 39. Evaluate 39 != 13, drop this branch.\n    |- Try 6 * 5 = 30. Add 30 to the number set. Current number set: [30, 39], target: 13, just two numbers left.\n     |- Try 39 + 30 = 69. Evaluate 69 != 13, drop this branch.\n     |- Try 39 - 30 = 9. Evaluate 9 != 13, drop this branch.\n     |- Try 39 * 30 = 1170. Evaluate 1170 != 13, drop this branch.\n     |- Try 39 \/ 30 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 6 \/ 5 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (6, 39) (numbers left: [5]). Try possible operations.\n    |- Try 39 + 6 = 45. Add 45 to the number set. Current number set: [45, 5], target: 13, just two numbers left.\n     |- Try 45 + 5 = 50. Evaluate 50 != 13, drop this branch.\n     |- Try 45 - 5 = 40. Evaluate 40 != 13, drop this branch.\n     |- Try 45 * 5 = 225. Evaluate 225 != 13, drop this branch.\n     |- Try 45 \/ 5 = 9. Evaluate 9 != 13, drop this branch.\n    |- Try 39 - 6 = 33. Add 33 to the number set. Current number set: [33, 5], target: 13, just two numbers left.\n     |- Try 33 + 5 = 38. Evaluate 38 != 13, drop this branch.\n     |- Try 33 - 5 = 28. Evaluate 28 != 13, drop this branch.\n     |- Try 33 * 5 = 165. Evaluate 165 != 13, drop this branch.\n     |- Try 33 \/ 5 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 39 * 6 = 234. Add 234 to the number set. Current number set: [234, 5], target: 13, just two numbers left.\n     |- Try 234 + 5 = 239. Evaluate 239 != 13, drop this branch.\n     |- Try 234 - 5 = 229. Evaluate 229 != 13, drop this branch.\n     |- Try 234 * 5 = 1170. Evaluate 1170 != 13, drop this branch.\n     |- Try 234 \/ 5 = 46.8. 46.8 is a decimal, drop this branch.\n    |- Try 39 \/ 6 = 6.5. 6.5 is a decimal, drop this branch.\n   |- Pick two numbers (5, 39) (numbers left: [6]). Try possible operations.\n    |- Try 39 + 5 = 44. Add 44 to the number set. Current number set: [44, 6], target: 13, just two numbers left.\n     |- Try 44 + 6 = 50. Evaluate 50 != 13, drop this branch.\n     |- Try 44 - 6 = 38. Evaluate 38 != 13, drop this branch.\n     |- Try 44 * 6 = 264. Evaluate 264 != 13, drop this branch.\n     |- Try 44 \/ 6 = 7.3. 7.3 is a decimal, drop this branch.\n    |- Try 39 - 5 = 34. Add 34 to the number set. Current number set: [34, 6], target: 13, just two numbers left.\n     |- Try 34 + 6 = 40. Evaluate 40 != 13, drop this branch.\n     |- Try 34 - 6 = 28. Evaluate 28 != 13, drop this branch.\n     |- Try 34 * 6 = 204. Evaluate 204 != 13, drop this branch.\n     |- Try 34 \/ 6 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 39 * 5 = 195. Add 195 to the number set. Current number set: [195, 6], target: 13, just two numbers left.\n     |- Try 195 + 6 = 201. Evaluate 201 != 13, drop this branch.\n     |- Try 195 - 6 = 189. Evaluate 189 != 13, drop this branch.\n     |- Try 195 * 6 = 1170. Evaluate 1170 != 13, drop this branch.\n     |- Try 195 \/ 6 = 32.5. 32.5 is a decimal, drop this branch.\n    |- Try 39 \/ 5 = 7.8. 7.8 is a decimal, drop this branch.\n  |- Try 12 * 6 = 72. Add 72 to the number set. Current number set: [72, 5, 39], target: 13. Options for choosing two numbers: [(72, 5), (72, 39), (5, 39)].\n   |- Pick two numbers (72, 5) (numbers left: [39]). Try possible operations.\n    |- Try 72 + 5 = 77. Add 77 to the number set. Current number set: [77, 39], target: 13, just two numbers left.\n     |- Try 77 + 39 = 116. Evaluate 116 != 13, drop this branch.\n     |- Try 77 - 39 = 38. Evaluate 38 != 13, drop this branch.\n     |- Try 77 * 39 = 3003. 3003 exceeds the maximum intermediate result, drop this branch.\n     |- Try 77 \/ 39 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 72 - 5 = 67. Add 67 to the number set. Current number set: [67, 39], target: 13, just two numbers left.\n     |- Try 67 + 39 = 106. Evaluate 106 != 13, drop this branch.\n     |- Try 67 - 39 = 28. Evaluate 28 != 13, drop this branch.\n     |- Try 67 * 39 = 2613. 2613 exceeds the maximum intermediate result, drop this branch.\n     |- Try 67 \/ 39 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 72 * 5 = 360. Add 360 to the number set. Current number set: [360, 39], target: 13, just two numbers left.\n     |- Try 360 + 39 = 399. Evaluate 399 != 13, drop this branch.\n     |- Try 360 - 39 = 321. Evaluate 321 != 13, drop this branch.\n     |- Try 360 * 39 = 14040. 14040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 360 \/ 39 = 9.2. 9.2 is a decimal, drop this branch.\n    |- Try 72 \/ 5 = 14.4. 14.4 is a decimal, drop this branch.\n   |- Pick two numbers (72, 39) (numbers left: [5]). Try possible operations.\n    |- Try 72 + 39 = 111. Add 111 to the number set. Current number set: [111, 5], target: 13, just two numbers left.\n     |- Try 111 + 5 = 116. Evaluate 116 != 13, drop this branch.\n     |- Try 111 - 5 = 106. Evaluate 106 != 13, drop this branch.\n     |- Try 111 * 5 = 555. Evaluate 555 != 13, drop this branch.\n     |- Try 111 \/ 5 = 22.2. 22.2 is a decimal, drop this branch.\n    |- Try 72 - 39 = 33. Add 33 to the number set. Current number set: [33, 5], target: 13, just two numbers left.\n     |- Try 33 + 5 = 38. Evaluate 38 != 13, drop this branch.\n     |- Try 33 - 5 = 28. Evaluate 28 != 13, drop this branch.\n     |- Try 33 * 5 = 165. Evaluate 165 != 13, drop this branch.\n     |- Try 33 \/ 5 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 72 * 39 = 2808. 2808 exceeds the maximum intermediate result, drop this branch.\n    |- Try 72 \/ 39 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (5, 39) (numbers left: [72]). Try possible operations.\n    |- Try 39 + 5 = 44. Add 44 to the number set. Current number set: [44, 72], target: 13, just two numbers left.\n     |- Try 72 + 44 = 116. Evaluate 116 != 13, drop this branch.\n     |- Try 72 - 44 = 28. Evaluate 28 != 13, drop this branch.\n     |- Try 72 * 44 = 3168. 3168 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 44 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 39 - 5 = 34. Add 34 to the number set. Current number set: [34, 72], target: 13, just two numbers left.\n     |- Try 72 + 34 = 106. Evaluate 106 != 13, drop this branch.\n     |- Try 72 - 34 = 38. Evaluate 38 != 13, drop this branch.\n     |- Try 72 * 34 = 2448. 2448 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 34 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 39 * 5 = 195. Add 195 to the number set. Current number set: [195, 72], target: 13, just two numbers left.\n     |- Try 195 + 72 = 267. Evaluate 267 != 13, drop this branch.\n     |- Try 195 - 72 = 123. Evaluate 123 != 13, drop this branch.\n     |- Try 195 * 72 = 14040. 14040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 195 \/ 72 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 39 \/ 5 = 7.8. 7.8 is a decimal, drop this branch.\n  |- Try 12 \/ 6 = 2. Add 2 to the number set. Current number set: [2, 5, 39], target: 13. Options for choosing two numbers: [(2, 5), (2, 39), (5, 39)].\n   |- Pick two numbers (2, 5) (numbers left: [39]). Try possible operations.\n    |- Try 5 + 2 = 7. Add 7 to the number set. Current number set: [7, 39], target: 13, just two numbers left.\n     |- Try 39 + 7 = 46. Evaluate 46 != 13, drop this branch.\n     |- Try 39 - 7 = 32. Evaluate 32 != 13, drop this branch.\n     |- Try 39 * 7 = 273. Evaluate 273 != 13, drop this branch.\n     |- Try 39 \/ 7 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 5 - 2 = 3. Add 3 to the number set. Current number set: [3, 39], target: 13, just two numbers left.\n     |- Try 39 + 3 = 42. Evaluate 42 != 13, drop this branch.\n     |- Try 39 - 3 = 36. Evaluate 36 != 13, drop this branch.\n     |- Try 39 * 3 = 117. Evaluate 117 != 13, drop this branch.\n     |- Try 39 \/ 3 = 13. Evaluate 13 == 13, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 39 \/ 3 = 13\nThe step before: 5 - 2 = 3\nThe first step: 12 \/ 6 = 2\n\nOutput the solution in the required format:\n<Solution>\n12 \/ 6 = 2\n5 - 2 = 3\n39 \/ 3 = 13\n<\/Solution>\n","item":{"nums":[6,12,5,39],"solution":["12 \/ 6 = 2","5 - 2 = 3","39 \/ 3 = 13"],"target":13}}
+{"instance_id":"countdown_8k_4","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [18, 19, 39, 14]\nTarget: 17","reference_output":"# Search Procedure\nInitial number set: [18, 19, 39, 14], target: 17. Options for choosing two numbers: [(18, 19), (18, 39), (18, 14), (19, 39), (19, 14), (39, 14)].\n |- Pick two numbers (18, 19) (numbers left: [39, 14]). Try possible operations.\n  |- Try 19 + 18 = 37. Add 37 to the number set. Current number set: [37, 39, 14], target: 17. Options for choosing two numbers: [(37, 39), (37, 14), (39, 14)].\n   |- Pick two numbers (37, 39) (numbers left: [14]). Try possible operations.\n    |- Try 39 + 37 = 76. Add 76 to the number set. Current number set: [76, 14], target: 17, just two numbers left.\n     |- Try 76 + 14 = 90. Evaluate 90 != 17, drop this branch.\n     |- Try 76 - 14 = 62. Evaluate 62 != 17, drop this branch.\n     |- Try 76 * 14 = 1064. Evaluate 1064 != 17, drop this branch.\n     |- Try 76 \/ 14 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 39 - 37 = 2. Add 2 to the number set. Current number set: [2, 14], target: 17, just two numbers left.\n     |- Try 14 + 2 = 16. Evaluate 16 != 17, drop this branch.\n     |- Try 14 - 2 = 12. Evaluate 12 != 17, drop this branch.\n     |- Try 14 * 2 = 28. Evaluate 28 != 17, drop this branch.\n     |- Try 14 \/ 2 = 7. Evaluate 7 != 17, drop this branch.\n    |- Try 39 * 37 = 1443. Add 1443 to the number set. Current number set: [1443, 14], target: 17, just two numbers left.\n     |- Try 1443 + 14 = 1457. Evaluate 1457 != 17, drop this branch.\n     |- Try 1443 - 14 = 1429. Evaluate 1429 != 17, drop this branch.\n     |- Try 1443 * 14 = 20202. 20202 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1443 \/ 14 = 103.1. 103.1 is a decimal, drop this branch.\n    |- Try 39 \/ 37 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (37, 14) (numbers left: [39]). Try possible operations.\n    |- Try 37 + 14 = 51. Add 51 to the number set. Current number set: [51, 39], target: 17, just two numbers left.\n     |- Try 51 + 39 = 90. Evaluate 90 != 17, drop this branch.\n     |- Try 51 - 39 = 12. Evaluate 12 != 17, drop this branch.\n     |- Try 51 * 39 = 1989. Evaluate 1989 != 17, drop this branch.\n     |- Try 51 \/ 39 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 37 - 14 = 23. Add 23 to the number set. Current number set: [23, 39], target: 17, just two numbers left.\n     |- Try 39 + 23 = 62. Evaluate 62 != 17, drop this branch.\n     |- Try 39 - 23 = 16. Evaluate 16 != 17, drop this branch.\n     |- Try 39 * 23 = 897. Evaluate 897 != 17, drop this branch.\n     |- Try 39 \/ 23 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 37 * 14 = 518. Add 518 to the number set. Current number set: [518, 39], target: 17, just two numbers left.\n     |- Try 518 + 39 = 557. Evaluate 557 != 17, drop this branch.\n     |- Try 518 - 39 = 479. Evaluate 479 != 17, drop this branch.\n     |- Try 518 * 39 = 20202. 20202 exceeds the maximum intermediate result, drop this branch.\n     |- Try 518 \/ 39 = 13.3. 13.3 is a decimal, drop this branch.\n    |- Try 37 \/ 14 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (39, 14) (numbers left: [37]). Try possible operations.\n    |- Try 39 + 14 = 53. Add 53 to the number set. Current number set: [53, 37], target: 17, just two numbers left.\n     |- Try 53 + 37 = 90. Evaluate 90 != 17, drop this branch.\n     |- Try 53 - 37 = 16. Evaluate 16 != 17, drop this branch.\n     |- Try 53 * 37 = 1961. Evaluate 1961 != 17, drop this branch.\n     |- Try 53 \/ 37 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 39 - 14 = 25. Add 25 to the number set. Current number set: [25, 37], target: 17, just two numbers left.\n     |- Try 37 + 25 = 62. Evaluate 62 != 17, drop this branch.\n     |- Try 37 - 25 = 12. Evaluate 12 != 17, drop this branch.\n     |- Try 37 * 25 = 925. Evaluate 925 != 17, drop this branch.\n     |- Try 37 \/ 25 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 39 * 14 = 546. Add 546 to the number set. Current number set: [546, 37], target: 17, just two numbers left.\n     |- Try 546 + 37 = 583. Evaluate 583 != 17, drop this branch.\n     |- Try 546 - 37 = 509. Evaluate 509 != 17, drop this branch.\n     |- Try 546 * 37 = 20202. 20202 exceeds the maximum intermediate result, drop this branch.\n     |- Try 546 \/ 37 = 14.8. 14.8 is a decimal, drop this branch.\n    |- Try 39 \/ 14 = 2.8. 2.8 is a decimal, drop this branch.\n  |- Try 19 - 18 = 1. Add 1 to the number set. Current number set: [1, 39, 14], target: 17. Options for choosing two numbers: [(1, 39), (1, 14), (39, 14)].\n   |- Pick two numbers (1, 39) (numbers left: [14]). Try possible operations.\n    |- Try 39 + 1 = 40. Add 40 to the number set. Current number set: [40, 14], target: 17, just two numbers left.\n     |- Try 40 + 14 = 54. Evaluate 54 != 17, drop this branch.\n     |- Try 40 - 14 = 26. Evaluate 26 != 17, drop this branch.\n     |- Try 40 * 14 = 560. Evaluate 560 != 17, drop this branch.\n     |- Try 40 \/ 14 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 39 - 1 = 38. Add 38 to the number set. Current number set: [38, 14], target: 17, just two numbers left.\n     |- Try 38 + 14 = 52. Evaluate 52 != 17, drop this branch.\n     |- Try 38 - 14 = 24. Evaluate 24 != 17, drop this branch.\n     |- Try 38 * 14 = 532. Evaluate 532 != 17, drop this branch.\n     |- Try 38 \/ 14 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 39 * 1 = 39. Add 39 to the number set. Current number set: [39, 14], target: 17, just two numbers left.\n     |- Try 39 + 14 = 53. Evaluate 53 != 17, drop this branch.\n     |- Try 39 - 14 = 25. Evaluate 25 != 17, drop this branch.\n     |- Try 39 * 14 = 546. Evaluate 546 != 17, drop this branch.\n     |- Try 39 \/ 14 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 39 \/ 1 = 39. Add 39 to the number set. Current number set: [39, 14], target: 17, just two numbers left.\n     |- Try 39 + 14 = 53. Evaluate 53 != 17, drop this branch.\n     |- Try 39 - 14 = 25. Evaluate 25 != 17, drop this branch.\n     |- Try 39 * 14 = 546. Evaluate 546 != 17, drop this branch.\n     |- Try 39 \/ 14 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (1, 14) (numbers left: [39]). Try possible operations.\n    |- Try 14 + 1 = 15. Add 15 to the number set. Current number set: [15, 39], target: 17, just two numbers left.\n     |- Try 39 + 15 = 54. Evaluate 54 != 17, drop this branch.\n     |- Try 39 - 15 = 24. Evaluate 24 != 17, drop this branch.\n     |- Try 39 * 15 = 585. Evaluate 585 != 17, drop this branch.\n     |- Try 39 \/ 15 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 14 - 1 = 13. Add 13 to the number set. Current number set: [13, 39], target: 17, just two numbers left.\n     |- Try 39 + 13 = 52. Evaluate 52 != 17, drop this branch.\n     |- Try 39 - 13 = 26. Evaluate 26 != 17, drop this branch.\n     |- Try 39 * 13 = 507. Evaluate 507 != 17, drop this branch.\n     |- Try 39 \/ 13 = 3. Evaluate 3 != 17, drop this branch.\n    |- Try 14 * 1 = 14. Add 14 to the number set. Current number set: [14, 39], target: 17, just two numbers left.\n     |- Try 39 + 14 = 53. Evaluate 53 != 17, drop this branch.\n     |- Try 39 - 14 = 25. Evaluate 25 != 17, drop this branch.\n     |- Try 39 * 14 = 546. Evaluate 546 != 17, drop this branch.\n     |- Try 39 \/ 14 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 14 \/ 1 = 14. Add 14 to the number set. Current number set: [14, 39], target: 17, just two numbers left.\n     |- Try 39 + 14 = 53. Evaluate 53 != 17, drop this branch.\n     |- Try 39 - 14 = 25. Evaluate 25 != 17, drop this branch.\n     |- Try 39 * 14 = 546. Evaluate 546 != 17, drop this branch.\n     |- Try 39 \/ 14 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (39, 14) (numbers left: [1]). Try possible operations.\n    |- Try 39 + 14 = 53. Add 53 to the number set. Current number set: [53, 1], target: 17, just two numbers left.\n     |- Try 53 + 1 = 54. Evaluate 54 != 17, drop this branch.\n     |- Try 53 - 1 = 52. Evaluate 52 != 17, drop this branch.\n     |- Try 53 * 1 = 53. Evaluate 53 != 17, drop this branch.\n     |- Try 53 \/ 1 = 53. Evaluate 53 != 17, drop this branch.\n    |- Try 39 - 14 = 25. Add 25 to the number set. Current number set: [25, 1], target: 17, just two numbers left.\n     |- Try 25 + 1 = 26. Evaluate 26 != 17, drop this branch.\n     |- Try 25 - 1 = 24. Evaluate 24 != 17, drop this branch.\n     |- Try 25 * 1 = 25. Evaluate 25 != 17, drop this branch.\n     |- Try 25 \/ 1 = 25. Evaluate 25 != 17, drop this branch.\n    |- Try 39 * 14 = 546. Add 546 to the number set. Current number set: [546, 1], target: 17, just two numbers left.\n     |- Try 546 + 1 = 547. Evaluate 547 != 17, drop this branch.\n     |- Try 546 - 1 = 545. Evaluate 545 != 17, drop this branch.\n     |- Try 546 * 1 = 546. Evaluate 546 != 17, drop this branch.\n     |- Try 546 \/ 1 = 546. Evaluate 546 != 17, drop this branch.\n    |- Try 39 \/ 14 = 2.8. 2.8 is a decimal, drop this branch.\n  |- Try 19 * 18 = 342. Add 342 to the number set. Current number set: [342, 39, 14], target: 17. Options for choosing two numbers: [(342, 39), (342, 14), (39, 14)].\n   |- Pick two numbers (342, 39) (numbers left: [14]). Try possible operations.\n    |- Try 342 + 39 = 381. Add 381 to the number set. Current number set: [381, 14], target: 17, just two numbers left.\n     |- Try 381 + 14 = 395. Evaluate 395 != 17, drop this branch.\n     |- Try 381 - 14 = 367. Evaluate 367 != 17, drop this branch.\n     |- Try 381 * 14 = 5334. 5334 exceeds the maximum intermediate result, drop this branch.\n     |- Try 381 \/ 14 = 27.2. 27.2 is a decimal, drop this branch.\n    |- Try 342 - 39 = 303. Add 303 to the number set. Current number set: [303, 14], target: 17, just two numbers left.\n     |- Try 303 + 14 = 317. Evaluate 317 != 17, drop this branch.\n     |- Try 303 - 14 = 289. Evaluate 289 != 17, drop this branch.\n     |- Try 303 * 14 = 4242. 4242 exceeds the maximum intermediate result, drop this branch.\n     |- Try 303 \/ 14 = 21.6. 21.6 is a decimal, drop this branch.\n    |- Try 342 * 39 = 13338. 13338 exceeds the maximum intermediate result, drop this branch.\n    |- Try 342 \/ 39 = 8.8. 8.8 is a decimal, drop this branch.\n   |- Pick two numbers (342, 14) (numbers left: [39]). Try possible operations.\n    |- Try 342 + 14 = 356. Add 356 to the number set. Current number set: [356, 39], target: 17, just two numbers left.\n     |- Try 356 + 39 = 395. Evaluate 395 != 17, drop this branch.\n     |- Try 356 - 39 = 317. Evaluate 317 != 17, drop this branch.\n     |- Try 356 * 39 = 13884. 13884 exceeds the maximum intermediate result, drop this branch.\n     |- Try 356 \/ 39 = 9.1. 9.1 is a decimal, drop this branch.\n    |- Try 342 - 14 = 328. Add 328 to the number set. Current number set: [328, 39], target: 17, just two numbers left.\n     |- Try 328 + 39 = 367. Evaluate 367 != 17, drop this branch.\n     |- Try 328 - 39 = 289. Evaluate 289 != 17, drop this branch.\n     |- Try 328 * 39 = 12792. 12792 exceeds the maximum intermediate result, drop this branch.\n     |- Try 328 \/ 39 = 8.4. 8.4 is a decimal, drop this branch.\n    |- Try 342 * 14 = 4788. 4788 exceeds the maximum intermediate result, drop this branch.\n    |- Try 342 \/ 14 = 24.4. 24.4 is a decimal, drop this branch.\n   |- Pick two numbers (39, 14) (numbers left: [342]). Try possible operations.\n    |- Try 39 + 14 = 53. Add 53 to the number set. Current number set: [53, 342], target: 17, just two numbers left.\n     |- Try 342 + 53 = 395. Evaluate 395 != 17, drop this branch.\n     |- Try 342 - 53 = 289. Evaluate 289 != 17, drop this branch.\n     |- Try 342 * 53 = 18126. 18126 exceeds the maximum intermediate result, drop this branch.\n     |- Try 342 \/ 53 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 39 - 14 = 25. Add 25 to the number set. Current number set: [25, 342], target: 17, just two numbers left.\n     |- Try 342 + 25 = 367. Evaluate 367 != 17, drop this branch.\n     |- Try 342 - 25 = 317. Evaluate 317 != 17, drop this branch.\n     |- Try 342 * 25 = 8550. 8550 exceeds the maximum intermediate result, drop this branch.\n     |- Try 342 \/ 25 = 13.7. 13.7 is a decimal, drop this branch.\n    |- Try 39 * 14 = 546. Add 546 to the number set. Current number set: [546, 342], target: 17, just two numbers left.\n     |- Try 546 + 342 = 888. Evaluate 888 != 17, drop this branch.\n     |- Try 546 - 342 = 204. Evaluate 204 != 17, drop this branch.\n     |- Try 546 * 342 = 186732. 186732 exceeds the maximum intermediate result, drop this branch.\n     |- Try 546 \/ 342 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 39 \/ 14 = 2.8. 2.8 is a decimal, drop this branch.\n  |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n |- Pick two numbers (18, 39) (numbers left: [19, 14]). Try possible operations.\n  |- Try 39 + 18 = 57. Add 57 to the number set. Current number set: [57, 19, 14], target: 17. Options for choosing two numbers: [(57, 19), (57, 14), (19, 14)].\n   |- Pick two numbers (57, 19) (numbers left: [14]). Try possible operations.\n    |- Try 57 + 19 = 76. Add 76 to the number set. Current number set: [76, 14], target: 17, just two numbers left.\n     |- Try 76 + 14 = 90. Evaluate 90 != 17, drop this branch.\n     |- Try 76 - 14 = 62. Evaluate 62 != 17, drop this branch.\n     |- Try 76 * 14 = 1064. Evaluate 1064 != 17, drop this branch.\n     |- Try 76 \/ 14 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 57 - 19 = 38. Add 38 to the number set. Current number set: [38, 14], target: 17, just two numbers left.\n     |- Try 38 + 14 = 52. Evaluate 52 != 17, drop this branch.\n     |- Try 38 - 14 = 24. Evaluate 24 != 17, drop this branch.\n     |- Try 38 * 14 = 532. Evaluate 532 != 17, drop this branch.\n     |- Try 38 \/ 14 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 57 * 19 = 1083. Add 1083 to the number set. Current number set: [1083, 14], target: 17, just two numbers left.\n     |- Try 1083 + 14 = 1097. Evaluate 1097 != 17, drop this branch.\n     |- Try 1083 - 14 = 1069. Evaluate 1069 != 17, drop this branch.\n     |- Try 1083 * 14 = 15162. 15162 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1083 \/ 14 = 77.4. 77.4 is a decimal, drop this branch.\n    |- Try 57 \/ 19 = 3. Add 3 to the number set. Current number set: [3, 14], target: 17, just two numbers left.\n     |- Try 14 + 3 = 17. Evaluate 17 == 17, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 14 + 3 = 17\nThe step before: 57 \/ 19 = 3\nThe first step: 39 + 18 = 57\n\nOutput the solution in the required format:\n<Solution>\n39 + 18 = 57\n57 \/ 19 = 3\n14 + 3 = 17\n<\/Solution>\n","item":{"nums":[18,19,39,14],"solution":["39 + 18 = 57","57 \/ 19 = 3","14 + 3 = 17"],"target":17}}
+{"instance_id":"countdown_8k_5","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [17, 3, 7, 39]\nTarget: 11","reference_output":"# Search Procedure\nInitial number set: [17, 3, 7, 39], target: 11. Options for choosing two numbers: [(17, 3), (17, 7), (17, 39), (3, 7), (3, 39), (7, 39)].\n |- Pick two numbers (17, 3) (numbers left: [7, 39]). Try possible operations.\n  |- Try 17 + 3 = 20. Add 20 to the number set. Current number set: [20, 7, 39], target: 11. Options for choosing two numbers: [(20, 7), (20, 39), (7, 39)].\n   |- Pick two numbers (20, 7) (numbers left: [39]). Try possible operations.\n    |- Try 20 + 7 = 27. Add 27 to the number set. Current number set: [27, 39], target: 11, just two numbers left.\n     |- Try 39 + 27 = 66. Evaluate 66 != 11, drop this branch.\n     |- Try 39 - 27 = 12. Evaluate 12 != 11, drop this branch.\n     |- Try 39 * 27 = 1053. Evaluate 1053 != 11, drop this branch.\n     |- Try 39 \/ 27 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 20 - 7 = 13. Add 13 to the number set. Current number set: [13, 39], target: 11, just two numbers left.\n     |- Try 39 + 13 = 52. Evaluate 52 != 11, drop this branch.\n     |- Try 39 - 13 = 26. Evaluate 26 != 11, drop this branch.\n     |- Try 39 * 13 = 507. Evaluate 507 != 11, drop this branch.\n     |- Try 39 \/ 13 = 3. Evaluate 3 != 11, drop this branch.\n    |- Try 20 * 7 = 140. Add 140 to the number set. Current number set: [140, 39], target: 11, just two numbers left.\n     |- Try 140 + 39 = 179. Evaluate 179 != 11, drop this branch.\n     |- Try 140 - 39 = 101. Evaluate 101 != 11, drop this branch.\n     |- Try 140 * 39 = 5460. 5460 exceeds the maximum intermediate result, drop this branch.\n     |- Try 140 \/ 39 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 20 \/ 7 = 2.9. 2.9 is a decimal, drop this branch.\n   |- Pick two numbers (20, 39) (numbers left: [7]). Try possible operations.\n    |- Try 39 + 20 = 59. Add 59 to the number set. Current number set: [59, 7], target: 11, just two numbers left.\n     |- Try 59 + 7 = 66. Evaluate 66 != 11, drop this branch.\n     |- Try 59 - 7 = 52. Evaluate 52 != 11, drop this branch.\n     |- Try 59 * 7 = 413. Evaluate 413 != 11, drop this branch.\n     |- Try 59 \/ 7 = 8.4. 8.4 is a decimal, drop this branch.\n    |- Try 39 - 20 = 19. Add 19 to the number set. Current number set: [19, 7], target: 11, just two numbers left.\n     |- Try 19 + 7 = 26. Evaluate 26 != 11, drop this branch.\n     |- Try 19 - 7 = 12. Evaluate 12 != 11, drop this branch.\n     |- Try 19 * 7 = 133. Evaluate 133 != 11, drop this branch.\n     |- Try 19 \/ 7 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 39 * 20 = 780. Add 780 to the number set. Current number set: [780, 7], target: 11, just two numbers left.\n     |- Try 780 + 7 = 787. Evaluate 787 != 11, drop this branch.\n     |- Try 780 - 7 = 773. Evaluate 773 != 11, drop this branch.\n     |- Try 780 * 7 = 5460. 5460 exceeds the maximum intermediate result, drop this branch.\n     |- Try 780 \/ 7 = 111.4. 111.4 is a decimal, drop this branch.\n    |- Try 39 \/ 20 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (7, 39) (numbers left: [20]). Try possible operations.\n    |- Try 39 + 7 = 46. Add 46 to the number set. Current number set: [46, 20], target: 11, just two numbers left.\n     |- Try 46 + 20 = 66. Evaluate 66 != 11, drop this branch.\n     |- Try 46 - 20 = 26. Evaluate 26 != 11, drop this branch.\n     |- Try 46 * 20 = 920. Evaluate 920 != 11, drop this branch.\n     |- Try 46 \/ 20 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 39 - 7 = 32. Add 32 to the number set. Current number set: [32, 20], target: 11, just two numbers left.\n     |- Try 32 + 20 = 52. Evaluate 52 != 11, drop this branch.\n     |- Try 32 - 20 = 12. Evaluate 12 != 11, drop this branch.\n     |- Try 32 * 20 = 640. Evaluate 640 != 11, drop this branch.\n     |- Try 32 \/ 20 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 39 * 7 = 273. Add 273 to the number set. Current number set: [273, 20], target: 11, just two numbers left.\n     |- Try 273 + 20 = 293. Evaluate 293 != 11, drop this branch.\n     |- Try 273 - 20 = 253. Evaluate 253 != 11, drop this branch.\n     |- Try 273 * 20 = 5460. 5460 exceeds the maximum intermediate result, drop this branch.\n     |- Try 273 \/ 20 = 13.7. 13.7 is a decimal, drop this branch.\n    |- Try 39 \/ 7 = 5.6. 5.6 is a decimal, drop this branch.\n  |- Try 17 - 3 = 14. Add 14 to the number set. Current number set: [14, 7, 39], target: 11. Options for choosing two numbers: [(14, 7), (14, 39), (7, 39)].\n   |- Pick two numbers (14, 7) (numbers left: [39]). Try possible operations.\n    |- Try 14 + 7 = 21. Add 21 to the number set. Current number set: [21, 39], target: 11, just two numbers left.\n     |- Try 39 + 21 = 60. Evaluate 60 != 11, drop this branch.\n     |- Try 39 - 21 = 18. Evaluate 18 != 11, drop this branch.\n     |- Try 39 * 21 = 819. Evaluate 819 != 11, drop this branch.\n     |- Try 39 \/ 21 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 14 - 7 = 7. Add 7 to the number set. Current number set: [7, 39], target: 11, just two numbers left.\n     |- Try 39 + 7 = 46. Evaluate 46 != 11, drop this branch.\n     |- Try 39 - 7 = 32. Evaluate 32 != 11, drop this branch.\n     |- Try 39 * 7 = 273. Evaluate 273 != 11, drop this branch.\n     |- Try 39 \/ 7 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 14 * 7 = 98. Add 98 to the number set. Current number set: [98, 39], target: 11, just two numbers left.\n     |- Try 98 + 39 = 137. Evaluate 137 != 11, drop this branch.\n     |- Try 98 - 39 = 59. Evaluate 59 != 11, drop this branch.\n     |- Try 98 * 39 = 3822. 3822 exceeds the maximum intermediate result, drop this branch.\n     |- Try 98 \/ 39 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 14 \/ 7 = 2. Add 2 to the number set. Current number set: [2, 39], target: 11, just two numbers left.\n     |- Try 39 + 2 = 41. Evaluate 41 != 11, drop this branch.\n     |- Try 39 - 2 = 37. Evaluate 37 != 11, drop this branch.\n     |- Try 39 * 2 = 78. Evaluate 78 != 11, drop this branch.\n     |- Try 39 \/ 2 = 19.5. 19.5 is a decimal, drop this branch.\n   |- Pick two numbers (14, 39) (numbers left: [7]). Try possible operations.\n    |- Try 39 + 14 = 53. Add 53 to the number set. Current number set: [53, 7], target: 11, just two numbers left.\n     |- Try 53 + 7 = 60. Evaluate 60 != 11, drop this branch.\n     |- Try 53 - 7 = 46. Evaluate 46 != 11, drop this branch.\n     |- Try 53 * 7 = 371. Evaluate 371 != 11, drop this branch.\n     |- Try 53 \/ 7 = 7.6. 7.6 is a decimal, drop this branch.\n    |- Try 39 - 14 = 25. Add 25 to the number set. Current number set: [25, 7], target: 11, just two numbers left.\n     |- Try 25 + 7 = 32. Evaluate 32 != 11, drop this branch.\n     |- Try 25 - 7 = 18. Evaluate 18 != 11, drop this branch.\n     |- Try 25 * 7 = 175. Evaluate 175 != 11, drop this branch.\n     |- Try 25 \/ 7 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 39 * 14 = 546. Add 546 to the number set. Current number set: [546, 7], target: 11, just two numbers left.\n     |- Try 546 + 7 = 553. Evaluate 553 != 11, drop this branch.\n     |- Try 546 - 7 = 539. Evaluate 539 != 11, drop this branch.\n     |- Try 546 * 7 = 3822. 3822 exceeds the maximum intermediate result, drop this branch.\n     |- Try 546 \/ 7 = 78. Evaluate 78 != 11, drop this branch.\n    |- Try 39 \/ 14 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (7, 39) (numbers left: [14]). Try possible operations.\n    |- Try 39 + 7 = 46. Add 46 to the number set. Current number set: [46, 14], target: 11, just two numbers left.\n     |- Try 46 + 14 = 60. Evaluate 60 != 11, drop this branch.\n     |- Try 46 - 14 = 32. Evaluate 32 != 11, drop this branch.\n     |- Try 46 * 14 = 644. Evaluate 644 != 11, drop this branch.\n     |- Try 46 \/ 14 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 39 - 7 = 32. Add 32 to the number set. Current number set: [32, 14], target: 11, just two numbers left.\n     |- Try 32 + 14 = 46. Evaluate 46 != 11, drop this branch.\n     |- Try 32 - 14 = 18. Evaluate 18 != 11, drop this branch.\n     |- Try 32 * 14 = 448. Evaluate 448 != 11, drop this branch.\n     |- Try 32 \/ 14 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 39 * 7 = 273. Add 273 to the number set. Current number set: [273, 14], target: 11, just two numbers left.\n     |- Try 273 + 14 = 287. Evaluate 287 != 11, drop this branch.\n     |- Try 273 - 14 = 259. Evaluate 259 != 11, drop this branch.\n     |- Try 273 * 14 = 3822. 3822 exceeds the maximum intermediate result, drop this branch.\n     |- Try 273 \/ 14 = 19.5. 19.5 is a decimal, drop this branch.\n    |- Try 39 \/ 7 = 5.6. 5.6 is a decimal, drop this branch.\n  |- Try 17 * 3 = 51. Add 51 to the number set. Current number set: [51, 7, 39], target: 11. Options for choosing two numbers: [(51, 7), (51, 39), (7, 39)].\n   |- Pick two numbers (51, 7) (numbers left: [39]). Try possible operations.\n    |- Try 51 + 7 = 58. Add 58 to the number set. Current number set: [58, 39], target: 11, just two numbers left.\n     |- Try 58 + 39 = 97. Evaluate 97 != 11, drop this branch.\n     |- Try 58 - 39 = 19. Evaluate 19 != 11, drop this branch.\n     |- Try 58 * 39 = 2262. 2262 exceeds the maximum intermediate result, drop this branch.\n     |- Try 58 \/ 39 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 51 - 7 = 44. Add 44 to the number set. Current number set: [44, 39], target: 11, just two numbers left.\n     |- Try 44 + 39 = 83. Evaluate 83 != 11, drop this branch.\n     |- Try 44 - 39 = 5. Evaluate 5 != 11, drop this branch.\n     |- Try 44 * 39 = 1716. Evaluate 1716 != 11, drop this branch.\n     |- Try 44 \/ 39 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 51 * 7 = 357. Add 357 to the number set. Current number set: [357, 39], target: 11, just two numbers left.\n     |- Try 357 + 39 = 396. Evaluate 396 != 11, drop this branch.\n     |- Try 357 - 39 = 318. Evaluate 318 != 11, drop this branch.\n     |- Try 357 * 39 = 13923. 13923 exceeds the maximum intermediate result, drop this branch.\n     |- Try 357 \/ 39 = 9.2. 9.2 is a decimal, drop this branch.\n    |- Try 51 \/ 7 = 7.3. 7.3 is a decimal, drop this branch.\n   |- Pick two numbers (51, 39) (numbers left: [7]). Try possible operations.\n    |- Try 51 + 39 = 90. Add 90 to the number set. Current number set: [90, 7], target: 11, just two numbers left.\n     |- Try 90 + 7 = 97. Evaluate 97 != 11, drop this branch.\n     |- Try 90 - 7 = 83. Evaluate 83 != 11, drop this branch.\n     |- Try 90 * 7 = 630. Evaluate 630 != 11, drop this branch.\n     |- Try 90 \/ 7 = 12.9. 12.9 is a decimal, drop this branch.\n    |- Try 51 - 39 = 12. Add 12 to the number set. Current number set: [12, 7], target: 11, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 11, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 11, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 11, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 51 * 39 = 1989. Add 1989 to the number set. Current number set: [1989, 7], target: 11, just two numbers left.\n     |- Try 1989 + 7 = 1996. Evaluate 1996 != 11, drop this branch.\n     |- Try 1989 - 7 = 1982. Evaluate 1982 != 11, drop this branch.\n     |- Try 1989 * 7 = 13923. 13923 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1989 \/ 7 = 284.1. 284.1 is a decimal, drop this branch.\n    |- Try 51 \/ 39 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (7, 39) (numbers left: [51]). Try possible operations.\n    |- Try 39 + 7 = 46. Add 46 to the number set. Current number set: [46, 51], target: 11, just two numbers left.\n     |- Try 51 + 46 = 97. Evaluate 97 != 11, drop this branch.\n     |- Try 51 - 46 = 5. Evaluate 5 != 11, drop this branch.\n     |- Try 51 * 46 = 2346. 2346 exceeds the maximum intermediate result, drop this branch.\n     |- Try 51 \/ 46 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 39 - 7 = 32. Add 32 to the number set. Current number set: [32, 51], target: 11, just two numbers left.\n     |- Try 51 + 32 = 83. Evaluate 83 != 11, drop this branch.\n     |- Try 51 - 32 = 19. Evaluate 19 != 11, drop this branch.\n     |- Try 51 * 32 = 1632. Evaluate 1632 != 11, drop this branch.\n     |- Try 51 \/ 32 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 39 * 7 = 273. Add 273 to the number set. Current number set: [273, 51], target: 11, just two numbers left.\n     |- Try 273 + 51 = 324. Evaluate 324 != 11, drop this branch.\n     |- Try 273 - 51 = 222. Evaluate 222 != 11, drop this branch.\n     |- Try 273 * 51 = 13923. 13923 exceeds the maximum intermediate result, drop this branch.\n     |- Try 273 \/ 51 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 39 \/ 7 = 5.6. 5.6 is a decimal, drop this branch.\n  |- Try 17 \/ 3 = 5.7. 5.7 is a decimal, drop this branch.\n |- Pick two numbers (17, 7) (numbers left: [3, 39]). Try possible operations.\n  |- Try 17 + 7 = 24. Add 24 to the number set. Current number set: [24, 3, 39], target: 11. Options for choosing two numbers: [(24, 3), (24, 39), (3, 39)].\n   |- Pick two numbers (24, 3) (numbers left: [39]). Try possible operations.\n    |- Try 24 + 3 = 27. Add 27 to the number set. Current number set: [27, 39], target: 11, just two numbers left.\n     |- Try 39 + 27 = 66. Evaluate 66 != 11, drop this branch.\n     |- Try 39 - 27 = 12. Evaluate 12 != 11, drop this branch.\n     |- Try 39 * 27 = 1053. Evaluate 1053 != 11, drop this branch.\n     |- Try 39 \/ 27 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 24 - 3 = 21. Add 21 to the number set. Current number set: [21, 39], target: 11, just two numbers left.\n     |- Try 39 + 21 = 60. Evaluate 60 != 11, drop this branch.\n     |- Try 39 - 21 = 18. Evaluate 18 != 11, drop this branch.\n     |- Try 39 * 21 = 819. Evaluate 819 != 11, drop this branch.\n     |- Try 39 \/ 21 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 24 * 3 = 72. Add 72 to the number set. Current number set: [72, 39], target: 11, just two numbers left.\n     |- Try 72 + 39 = 111. Evaluate 111 != 11, drop this branch.\n     |- Try 72 - 39 = 33. Evaluate 33 != 11, drop this branch.\n     |- Try 72 * 39 = 2808. 2808 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 39 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 24 \/ 3 = 8. Add 8 to the number set. Current number set: [8, 39], target: 11, just two numbers left.\n     |- Try 39 + 8 = 47. Evaluate 47 != 11, drop this branch.\n     |- Try 39 - 8 = 31. Evaluate 31 != 11, drop this branch.\n     |- Try 39 * 8 = 312. Evaluate 312 != 11, drop this branch.\n     |- Try 39 \/ 8 = 4.9. 4.9 is a decimal, drop this branch.\n   |- Pick two numbers (24, 39) (numbers left: [3]). Try possible operations.\n    |- Try 39 + 24 = 63. Add 63 to the number set. Current number set: [63, 3], target: 11, just two numbers left.\n     |- Try 63 + 3 = 66. Evaluate 66 != 11, drop this branch.\n     |- Try 63 - 3 = 60. Evaluate 60 != 11, drop this branch.\n     |- Try 63 * 3 = 189. Evaluate 189 != 11, drop this branch.\n     |- Try 63 \/ 3 = 21. Evaluate 21 != 11, drop this branch.\n    |- Try 39 - 24 = 15. Add 15 to the number set. Current number set: [15, 3], target: 11, just two numbers left.\n     |- Try 15 + 3 = 18. Evaluate 18 != 11, drop this branch.\n     |- Try 15 - 3 = 12. Evaluate 12 != 11, drop this branch.\n     |- Try 15 * 3 = 45. Evaluate 45 != 11, drop this branch.\n     |- Try 15 \/ 3 = 5. Evaluate 5 != 11, drop this branch.\n    |- Try 39 * 24 = 936. Add 936 to the number set. Current number set: [936, 3], target: 11, just two numbers left.\n     |- Try 936 + 3 = 939. Evaluate 939 != 11, drop this branch.\n     |- Try 936 - 3 = 933. Evaluate 933 != 11, drop this branch.\n     |- Try 936 * 3 = 2808. 2808 exceeds the maximum intermediate result, drop this branch.\n     |- Try 936 \/ 3 = 312. Evaluate 312 != 11, drop this branch.\n    |- Try 39 \/ 24 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (3, 39) (numbers left: [24]). Try possible operations.\n    |- Try 39 + 3 = 42. Add 42 to the number set. Current number set: [42, 24], target: 11, just two numbers left.\n     |- Try 42 + 24 = 66. Evaluate 66 != 11, drop this branch.\n     |- Try 42 - 24 = 18. Evaluate 18 != 11, drop this branch.\n     |- Try 42 * 24 = 1008. Evaluate 1008 != 11, drop this branch.\n     |- Try 42 \/ 24 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 39 - 3 = 36. Add 36 to the number set. Current number set: [36, 24], target: 11, just two numbers left.\n     |- Try 36 + 24 = 60. Evaluate 60 != 11, drop this branch.\n     |- Try 36 - 24 = 12. Evaluate 12 != 11, drop this branch.\n     |- Try 36 * 24 = 864. Evaluate 864 != 11, drop this branch.\n     |- Try 36 \/ 24 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 39 * 3 = 117. Add 117 to the number set. Current number set: [117, 24], target: 11, just two numbers left.\n     |- Try 117 + 24 = 141. Evaluate 141 != 11, drop this branch.\n     |- Try 117 - 24 = 93. Evaluate 93 != 11, drop this branch.\n     |- Try 117 * 24 = 2808. 2808 exceeds the maximum intermediate result, drop this branch.\n     |- Try 117 \/ 24 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 39 \/ 3 = 13. Add 13 to the number set. Current number set: [13, 24], target: 11, just two numbers left.\n     |- Try 24 + 13 = 37. Evaluate 37 != 11, drop this branch.\n     |- Try 24 - 13 = 11. Evaluate 11 == 11, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 24 - 13 = 11\nThe step before: 39 \/ 3 = 13\nThe first step: 17 + 7 = 24\n\nOutput the solution in the required format:\n<Solution>\n17 + 7 = 24\n39 \/ 3 = 13\n24 - 13 = 11\n<\/Solution>\n","item":{"nums":[17,3,7,39],"solution":["17 + 7 = 24","39 \/ 3 = 13","24 - 13 = 11"],"target":11}}
+{"instance_id":"countdown_8k_6","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [9, 10, 15, 25]\nTarget: 15","reference_output":"# Search Procedure\nInitial number set: [9, 10, 15, 25], target: 15. Options for choosing two numbers: [(9, 10), (9, 15), (9, 25), (10, 15), (10, 25), (15, 25)].\n |- Pick two numbers (9, 10) (numbers left: [15, 25]). Try possible operations.\n  |- Try 10 + 9 = 19. Add 19 to the number set. Current number set: [19, 15, 25], target: 15. Options for choosing two numbers: [(19, 15), (19, 25), (15, 25)].\n   |- Pick two numbers (19, 15) (numbers left: [25]). Try possible operations.\n    |- Try 19 + 15 = 34. Add 34 to the number set. Current number set: [34, 25], target: 15, just two numbers left.\n     |- Try 34 + 25 = 59. Evaluate 59 != 15, drop this branch.\n     |- Try 34 - 25 = 9. Evaluate 9 != 15, drop this branch.\n     |- Try 34 * 25 = 850. Evaluate 850 != 15, drop this branch.\n     |- Try 34 \/ 25 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 19 - 15 = 4. Add 4 to the number set. Current number set: [4, 25], target: 15, just two numbers left.\n     |- Try 25 + 4 = 29. Evaluate 29 != 15, drop this branch.\n     |- Try 25 - 4 = 21. Evaluate 21 != 15, drop this branch.\n     |- Try 25 * 4 = 100. Evaluate 100 != 15, drop this branch.\n     |- Try 25 \/ 4 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 19 * 15 = 285. Add 285 to the number set. Current number set: [285, 25], target: 15, just two numbers left.\n     |- Try 285 + 25 = 310. Evaluate 310 != 15, drop this branch.\n     |- Try 285 - 25 = 260. Evaluate 260 != 15, drop this branch.\n     |- Try 285 * 25 = 7125. 7125 exceeds the maximum intermediate result, drop this branch.\n     |- Try 285 \/ 25 = 11.4. 11.4 is a decimal, drop this branch.\n    |- Try 19 \/ 15 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (19, 25) (numbers left: [15]). Try possible operations.\n    |- Try 25 + 19 = 44. Add 44 to the number set. Current number set: [44, 15], target: 15, just two numbers left.\n     |- Try 44 + 15 = 59. Evaluate 59 != 15, drop this branch.\n     |- Try 44 - 15 = 29. Evaluate 29 != 15, drop this branch.\n     |- Try 44 * 15 = 660. Evaluate 660 != 15, drop this branch.\n     |- Try 44 \/ 15 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 25 - 19 = 6. Add 6 to the number set. Current number set: [6, 15], target: 15, just two numbers left.\n     |- Try 15 + 6 = 21. Evaluate 21 != 15, drop this branch.\n     |- Try 15 - 6 = 9. Evaluate 9 != 15, drop this branch.\n     |- Try 15 * 6 = 90. Evaluate 90 != 15, drop this branch.\n     |- Try 15 \/ 6 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 25 * 19 = 475. Add 475 to the number set. Current number set: [475, 15], target: 15, just two numbers left.\n     |- Try 475 + 15 = 490. Evaluate 490 != 15, drop this branch.\n     |- Try 475 - 15 = 460. Evaluate 460 != 15, drop this branch.\n     |- Try 475 * 15 = 7125. 7125 exceeds the maximum intermediate result, drop this branch.\n     |- Try 475 \/ 15 = 31.7. 31.7 is a decimal, drop this branch.\n    |- Try 25 \/ 19 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (15, 25) (numbers left: [19]). Try possible operations.\n    |- Try 25 + 15 = 40. Add 40 to the number set. Current number set: [40, 19], target: 15, just two numbers left.\n     |- Try 40 + 19 = 59. Evaluate 59 != 15, drop this branch.\n     |- Try 40 - 19 = 21. Evaluate 21 != 15, drop this branch.\n     |- Try 40 * 19 = 760. Evaluate 760 != 15, drop this branch.\n     |- Try 40 \/ 19 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 25 - 15 = 10. Add 10 to the number set. Current number set: [10, 19], target: 15, just two numbers left.\n     |- Try 19 + 10 = 29. Evaluate 29 != 15, drop this branch.\n     |- Try 19 - 10 = 9. Evaluate 9 != 15, drop this branch.\n     |- Try 19 * 10 = 190. Evaluate 190 != 15, drop this branch.\n     |- Try 19 \/ 10 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 25 * 15 = 375. Add 375 to the number set. Current number set: [375, 19], target: 15, just two numbers left.\n     |- Try 375 + 19 = 394. Evaluate 394 != 15, drop this branch.\n     |- Try 375 - 19 = 356. Evaluate 356 != 15, drop this branch.\n     |- Try 375 * 19 = 7125. 7125 exceeds the maximum intermediate result, drop this branch.\n     |- Try 375 \/ 19 = 19.7. 19.7 is a decimal, drop this branch.\n    |- Try 25 \/ 15 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 10 - 9 = 1. Add 1 to the number set. Current number set: [1, 15, 25], target: 15. Options for choosing two numbers: [(1, 15), (1, 25), (15, 25)].\n   |- Pick two numbers (1, 15) (numbers left: [25]). Try possible operations.\n    |- Try 15 + 1 = 16. Add 16 to the number set. Current number set: [16, 25], target: 15, just two numbers left.\n     |- Try 25 + 16 = 41. Evaluate 41 != 15, drop this branch.\n     |- Try 25 - 16 = 9. Evaluate 9 != 15, drop this branch.\n     |- Try 25 * 16 = 400. Evaluate 400 != 15, drop this branch.\n     |- Try 25 \/ 16 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 15 - 1 = 14. Add 14 to the number set. Current number set: [14, 25], target: 15, just two numbers left.\n     |- Try 25 + 14 = 39. Evaluate 39 != 15, drop this branch.\n     |- Try 25 - 14 = 11. Evaluate 11 != 15, drop this branch.\n     |- Try 25 * 14 = 350. Evaluate 350 != 15, drop this branch.\n     |- Try 25 \/ 14 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 15 * 1 = 15. Add 15 to the number set. Current number set: [15, 25], target: 15, just two numbers left.\n     |- Try 25 + 15 = 40. Evaluate 40 != 15, drop this branch.\n     |- Try 25 - 15 = 10. Evaluate 10 != 15, drop this branch.\n     |- Try 25 * 15 = 375. Evaluate 375 != 15, drop this branch.\n     |- Try 25 \/ 15 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 15 \/ 1 = 15. Add 15 to the number set. Current number set: [15, 25], target: 15, just two numbers left.\n     |- Try 25 + 15 = 40. Evaluate 40 != 15, drop this branch.\n     |- Try 25 - 15 = 10. Evaluate 10 != 15, drop this branch.\n     |- Try 25 * 15 = 375. Evaluate 375 != 15, drop this branch.\n     |- Try 25 \/ 15 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (1, 25) (numbers left: [15]). Try possible operations.\n    |- Try 25 + 1 = 26. Add 26 to the number set. Current number set: [26, 15], target: 15, just two numbers left.\n     |- Try 26 + 15 = 41. Evaluate 41 != 15, drop this branch.\n     |- Try 26 - 15 = 11. Evaluate 11 != 15, drop this branch.\n     |- Try 26 * 15 = 390. Evaluate 390 != 15, drop this branch.\n     |- Try 26 \/ 15 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 1 = 24. Add 24 to the number set. Current number set: [24, 15], target: 15, just two numbers left.\n     |- Try 24 + 15 = 39. Evaluate 39 != 15, drop this branch.\n     |- Try 24 - 15 = 9. Evaluate 9 != 15, drop this branch.\n     |- Try 24 * 15 = 360. Evaluate 360 != 15, drop this branch.\n     |- Try 24 \/ 15 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 25 * 1 = 25. Add 25 to the number set. Current number set: [25, 15], target: 15, just two numbers left.\n     |- Try 25 + 15 = 40. Evaluate 40 != 15, drop this branch.\n     |- Try 25 - 15 = 10. Evaluate 10 != 15, drop this branch.\n     |- Try 25 * 15 = 375. Evaluate 375 != 15, drop this branch.\n     |- Try 25 \/ 15 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 \/ 1 = 25. Add 25 to the number set. Current number set: [25, 15], target: 15, just two numbers left.\n     |- Try 25 + 15 = 40. Evaluate 40 != 15, drop this branch.\n     |- Try 25 - 15 = 10. Evaluate 10 != 15, drop this branch.\n     |- Try 25 * 15 = 375. Evaluate 375 != 15, drop this branch.\n     |- Try 25 \/ 15 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (15, 25) (numbers left: [1]). Try possible operations.\n    |- Try 25 + 15 = 40. Add 40 to the number set. Current number set: [40, 1], target: 15, just two numbers left.\n     |- Try 40 + 1 = 41. Evaluate 41 != 15, drop this branch.\n     |- Try 40 - 1 = 39. Evaluate 39 != 15, drop this branch.\n     |- Try 40 * 1 = 40. Evaluate 40 != 15, drop this branch.\n     |- Try 40 \/ 1 = 40. Evaluate 40 != 15, drop this branch.\n    |- Try 25 - 15 = 10. Add 10 to the number set. Current number set: [10, 1], target: 15, just two numbers left.\n     |- Try 10 + 1 = 11. Evaluate 11 != 15, drop this branch.\n     |- Try 10 - 1 = 9. Evaluate 9 != 15, drop this branch.\n     |- Try 10 * 1 = 10. Evaluate 10 != 15, drop this branch.\n     |- Try 10 \/ 1 = 10. Evaluate 10 != 15, drop this branch.\n    |- Try 25 * 15 = 375. Add 375 to the number set. Current number set: [375, 1], target: 15, just two numbers left.\n     |- Try 375 + 1 = 376. Evaluate 376 != 15, drop this branch.\n     |- Try 375 - 1 = 374. Evaluate 374 != 15, drop this branch.\n     |- Try 375 * 1 = 375. Evaluate 375 != 15, drop this branch.\n     |- Try 375 \/ 1 = 375. Evaluate 375 != 15, drop this branch.\n    |- Try 25 \/ 15 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 10 * 9 = 90. Add 90 to the number set. Current number set: [90, 15, 25], target: 15. Options for choosing two numbers: [(90, 15), (90, 25), (15, 25)].\n   |- Pick two numbers (90, 15) (numbers left: [25]). Try possible operations.\n    |- Try 90 + 15 = 105. Add 105 to the number set. Current number set: [105, 25], target: 15, just two numbers left.\n     |- Try 105 + 25 = 130. Evaluate 130 != 15, drop this branch.\n     |- Try 105 - 25 = 80. Evaluate 80 != 15, drop this branch.\n     |- Try 105 * 25 = 2625. 2625 exceeds the maximum intermediate result, drop this branch.\n     |- Try 105 \/ 25 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 90 - 15 = 75. Add 75 to the number set. Current number set: [75, 25], target: 15, just two numbers left.\n     |- Try 75 + 25 = 100. Evaluate 100 != 15, drop this branch.\n     |- Try 75 - 25 = 50. Evaluate 50 != 15, drop this branch.\n     |- Try 75 * 25 = 1875. Evaluate 1875 != 15, drop this branch.\n     |- Try 75 \/ 25 = 3. Evaluate 3 != 15, drop this branch.\n    |- Try 90 * 15 = 1350. Add 1350 to the number set. Current number set: [1350, 25], target: 15, just two numbers left.\n     |- Try 1350 + 25 = 1375. Evaluate 1375 != 15, drop this branch.\n     |- Try 1350 - 25 = 1325. Evaluate 1325 != 15, drop this branch.\n     |- Try 1350 * 25 = 33750. 33750 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1350 \/ 25 = 54. Evaluate 54 != 15, drop this branch.\n    |- Try 90 \/ 15 = 6. Add 6 to the number set. Current number set: [6, 25], target: 15, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 15, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 15, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 15, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (90, 25) (numbers left: [15]). Try possible operations.\n    |- Try 90 + 25 = 115. Add 115 to the number set. Current number set: [115, 15], target: 15, just two numbers left.\n     |- Try 115 + 15 = 130. Evaluate 130 != 15, drop this branch.\n     |- Try 115 - 15 = 100. Evaluate 100 != 15, drop this branch.\n     |- Try 115 * 15 = 1725. Evaluate 1725 != 15, drop this branch.\n     |- Try 115 \/ 15 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 90 - 25 = 65. Add 65 to the number set. Current number set: [65, 15], target: 15, just two numbers left.\n     |- Try 65 + 15 = 80. Evaluate 80 != 15, drop this branch.\n     |- Try 65 - 15 = 50. Evaluate 50 != 15, drop this branch.\n     |- Try 65 * 15 = 975. Evaluate 975 != 15, drop this branch.\n     |- Try 65 \/ 15 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 90 * 25 = 2250. 2250 exceeds the maximum intermediate result, drop this branch.\n    |- Try 90 \/ 25 = 3.6. 3.6 is a decimal, drop this branch.\n   |- Pick two numbers (15, 25) (numbers left: [90]). Try possible operations.\n    |- Try 25 + 15 = 40. Add 40 to the number set. Current number set: [40, 90], target: 15, just two numbers left.\n     |- Try 90 + 40 = 130. Evaluate 130 != 15, drop this branch.\n     |- Try 90 - 40 = 50. Evaluate 50 != 15, drop this branch.\n     |- Try 90 * 40 = 3600. 3600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 90 \/ 40 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 25 - 15 = 10. Add 10 to the number set. Current number set: [10, 90], target: 15, just two numbers left.\n     |- Try 90 + 10 = 100. Evaluate 100 != 15, drop this branch.\n     |- Try 90 - 10 = 80. Evaluate 80 != 15, drop this branch.\n     |- Try 90 * 10 = 900. Evaluate 900 != 15, drop this branch.\n     |- Try 90 \/ 10 = 9. Evaluate 9 != 15, drop this branch.\n    |- Try 25 * 15 = 375. Add 375 to the number set. Current number set: [375, 90], target: 15, just two numbers left.\n     |- Try 375 + 90 = 465. Evaluate 465 != 15, drop this branch.\n     |- Try 375 - 90 = 285. Evaluate 285 != 15, drop this branch.\n     |- Try 375 * 90 = 33750. 33750 exceeds the maximum intermediate result, drop this branch.\n     |- Try 375 \/ 90 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 25 \/ 15 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 10 \/ 9 = 1.1. 1.1 is a decimal, drop this branch.\n |- Pick two numbers (9, 15) (numbers left: [10, 25]). Try possible operations.\n  |- Try 15 + 9 = 24. Add 24 to the number set. Current number set: [24, 10, 25], target: 15. Options for choosing two numbers: [(24, 10), (24, 25), (10, 25)].\n   |- Pick two numbers (24, 10) (numbers left: [25]). Try possible operations.\n    |- Try 24 + 10 = 34. Add 34 to the number set. Current number set: [34, 25], target: 15, just two numbers left.\n     |- Try 34 + 25 = 59. Evaluate 59 != 15, drop this branch.\n     |- Try 34 - 25 = 9. Evaluate 9 != 15, drop this branch.\n     |- Try 34 * 25 = 850. Evaluate 850 != 15, drop this branch.\n     |- Try 34 \/ 25 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 24 - 10 = 14. Add 14 to the number set. Current number set: [14, 25], target: 15, just two numbers left.\n     |- Try 25 + 14 = 39. Evaluate 39 != 15, drop this branch.\n     |- Try 25 - 14 = 11. Evaluate 11 != 15, drop this branch.\n     |- Try 25 * 14 = 350. Evaluate 350 != 15, drop this branch.\n     |- Try 25 \/ 14 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 24 * 10 = 240. Add 240 to the number set. Current number set: [240, 25], target: 15, just two numbers left.\n     |- Try 240 + 25 = 265. Evaluate 265 != 15, drop this branch.\n     |- Try 240 - 25 = 215. Evaluate 215 != 15, drop this branch.\n     |- Try 240 * 25 = 6000. 6000 exceeds the maximum intermediate result, drop this branch.\n     |- Try 240 \/ 25 = 9.6. 9.6 is a decimal, drop this branch.\n    |- Try 24 \/ 10 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (24, 25) (numbers left: [10]). Try possible operations.\n    |- Try 25 + 24 = 49. Add 49 to the number set. Current number set: [49, 10], target: 15, just two numbers left.\n     |- Try 49 + 10 = 59. Evaluate 59 != 15, drop this branch.\n     |- Try 49 - 10 = 39. Evaluate 39 != 15, drop this branch.\n     |- Try 49 * 10 = 490. Evaluate 490 != 15, drop this branch.\n     |- Try 49 \/ 10 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 25 - 24 = 1. Add 1 to the number set. Current number set: [1, 10], target: 15, just two numbers left.\n     |- Try 10 + 1 = 11. Evaluate 11 != 15, drop this branch.\n     |- Try 10 - 1 = 9. Evaluate 9 != 15, drop this branch.\n     |- Try 10 * 1 = 10. Evaluate 10 != 15, drop this branch.\n     |- Try 10 \/ 1 = 10. Evaluate 10 != 15, drop this branch.\n    |- Try 25 * 24 = 600. Add 600 to the number set. Current number set: [600, 10], target: 15, just two numbers left.\n     |- Try 600 + 10 = 610. Evaluate 610 != 15, drop this branch.\n     |- Try 600 - 10 = 590. Evaluate 590 != 15, drop this branch.\n     |- Try 600 * 10 = 6000. 6000 exceeds the maximum intermediate result, drop this branch.\n     |- Try 600 \/ 10 = 60. Evaluate 60 != 15, drop this branch.\n    |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (10, 25) (numbers left: [24]). Try possible operations.\n    |- Try 25 + 10 = 35. Add 35 to the number set. Current number set: [35, 24], target: 15, just two numbers left.\n     |- Try 35 + 24 = 59. Evaluate 59 != 15, drop this branch.\n     |- Try 35 - 24 = 11. Evaluate 11 != 15, drop this branch.\n     |- Try 35 * 24 = 840. Evaluate 840 != 15, drop this branch.\n     |- Try 35 \/ 24 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 25 - 10 = 15. Add 15 to the number set. Current number set: [15, 24], target: 15, just two numbers left.\n     |- Try 24 + 15 = 39. Evaluate 39 != 15, drop this branch.\n     |- Try 24 - 15 = 9. Evaluate 9 != 15, drop this branch.\n     |- Try 24 * 15 = 360. Evaluate 360 != 15, drop this branch.\n     |- Try 24 \/ 15 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 25 * 10 = 250. Add 250 to the number set. Current number set: [250, 24], target: 15, just two numbers left.\n     |- Try 250 + 24 = 274. Evaluate 274 != 15, drop this branch.\n     |- Try 250 - 24 = 226. Evaluate 226 != 15, drop this branch.\n     |- Try 250 * 24 = 6000. 6000 exceeds the maximum intermediate result, drop this branch.\n     |- Try 250 \/ 24 = 10.4. 10.4 is a decimal, drop this branch.\n    |- Try 25 \/ 10 = 2.5. 2.5 is a decimal, drop this branch.\n  |- Try 15 - 9 = 6. Add 6 to the number set. Current number set: [6, 10, 25], target: 15. Options for choosing two numbers: [(6, 10), (6, 25), (10, 25)].\n   |- Pick two numbers (6, 10) (numbers left: [25]). Try possible operations.\n    |- Try 10 + 6 = 16. Add 16 to the number set. Current number set: [16, 25], target: 15, just two numbers left.\n     |- Try 25 + 16 = 41. Evaluate 41 != 15, drop this branch.\n     |- Try 25 - 16 = 9. Evaluate 9 != 15, drop this branch.\n     |- Try 25 * 16 = 400. Evaluate 400 != 15, drop this branch.\n     |- Try 25 \/ 16 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 10 - 6 = 4. Add 4 to the number set. Current number set: [4, 25], target: 15, just two numbers left.\n     |- Try 25 + 4 = 29. Evaluate 29 != 15, drop this branch.\n     |- Try 25 - 4 = 21. Evaluate 21 != 15, drop this branch.\n     |- Try 25 * 4 = 100. Evaluate 100 != 15, drop this branch.\n     |- Try 25 \/ 4 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 10 * 6 = 60. Add 60 to the number set. Current number set: [60, 25], target: 15, just two numbers left.\n     |- Try 60 + 25 = 85. Evaluate 85 != 15, drop this branch.\n     |- Try 60 - 25 = 35. Evaluate 35 != 15, drop this branch.\n     |- Try 60 * 25 = 1500. Evaluate 1500 != 15, drop this branch.\n     |- Try 60 \/ 25 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 10 \/ 6 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (6, 25) (numbers left: [10]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 10], target: 15, just two numbers left.\n     |- Try 31 + 10 = 41. Evaluate 41 != 15, drop this branch.\n     |- Try 31 - 10 = 21. Evaluate 21 != 15, drop this branch.\n     |- Try 31 * 10 = 310. Evaluate 310 != 15, drop this branch.\n     |- Try 31 \/ 10 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 10], target: 15, just two numbers left.\n     |- Try 19 + 10 = 29. Evaluate 29 != 15, drop this branch.\n     |- Try 19 - 10 = 9. Evaluate 9 != 15, drop this branch.\n     |- Try 19 * 10 = 190. Evaluate 190 != 15, drop this branch.\n     |- Try 19 \/ 10 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 10], target: 15, just two numbers left.\n     |- Try 150 + 10 = 160. Evaluate 160 != 15, drop this branch.\n     |- Try 150 - 10 = 140. Evaluate 140 != 15, drop this branch.\n     |- Try 150 * 10 = 1500. Evaluate 1500 != 15, drop this branch.\n     |- Try 150 \/ 10 = 15. Evaluate 15 == 15, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 150 \/ 10 = 15\nThe step before: 25 * 6 = 150\nThe first step: 15 - 9 = 6\n\nOutput the solution in the required format:\n<Solution>\n15 - 9 = 6\n25 * 6 = 150\n150 \/ 10 = 15\n<\/Solution>\n","item":{"nums":[9,10,15,25],"solution":["15 - 9 = 6","25 * 6 = 150","150 \/ 10 = 15"],"target":15}}
+{"instance_id":"countdown_8k_7","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [42, 3, 49, 2]\nTarget: 31","reference_output":"# Search Procedure\nInitial number set: [42, 3, 49, 2], target: 31. Options for choosing two numbers: [(42, 3), (42, 49), (42, 2), (3, 49), (3, 2), (49, 2)].\n |- Pick two numbers (42, 3) (numbers left: [49, 2]). Try possible operations.\n  |- Try 42 + 3 = 45. Add 45 to the number set. Current number set: [45, 49, 2], target: 31. Options for choosing two numbers: [(45, 49), (45, 2), (49, 2)].\n   |- Pick two numbers (45, 49) (numbers left: [2]). Try possible operations.\n    |- Try 49 + 45 = 94. Add 94 to the number set. Current number set: [94, 2], target: 31, just two numbers left.\n     |- Try 94 + 2 = 96. Evaluate 96 != 31, drop this branch.\n     |- Try 94 - 2 = 92. Evaluate 92 != 31, drop this branch.\n     |- Try 94 * 2 = 188. Evaluate 188 != 31, drop this branch.\n     |- Try 94 \/ 2 = 47. Evaluate 47 != 31, drop this branch.\n    |- Try 49 - 45 = 4. Add 4 to the number set. Current number set: [4, 2], target: 31, just two numbers left.\n     |- Try 4 + 2 = 6. Evaluate 6 != 31, drop this branch.\n     |- Try 4 - 2 = 2. Evaluate 2 != 31, drop this branch.\n     |- Try 4 * 2 = 8. Evaluate 8 != 31, drop this branch.\n     |- Try 4 \/ 2 = 2. Evaluate 2 != 31, drop this branch.\n    |- Try 49 * 45 = 2205. 2205 exceeds the maximum intermediate result, drop this branch.\n    |- Try 49 \/ 45 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (45, 2) (numbers left: [49]). Try possible operations.\n    |- Try 45 + 2 = 47. Add 47 to the number set. Current number set: [47, 49], target: 31, just two numbers left.\n     |- Try 49 + 47 = 96. Evaluate 96 != 31, drop this branch.\n     |- Try 49 - 47 = 2. Evaluate 2 != 31, drop this branch.\n     |- Try 49 * 47 = 2303. 2303 exceeds the maximum intermediate result, drop this branch.\n     |- Try 49 \/ 47 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 45 - 2 = 43. Add 43 to the number set. Current number set: [43, 49], target: 31, just two numbers left.\n     |- Try 49 + 43 = 92. Evaluate 92 != 31, drop this branch.\n     |- Try 49 - 43 = 6. Evaluate 6 != 31, drop this branch.\n     |- Try 49 * 43 = 2107. 2107 exceeds the maximum intermediate result, drop this branch.\n     |- Try 49 \/ 43 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 45 * 2 = 90. Add 90 to the number set. Current number set: [90, 49], target: 31, just two numbers left.\n     |- Try 90 + 49 = 139. Evaluate 139 != 31, drop this branch.\n     |- Try 90 - 49 = 41. Evaluate 41 != 31, drop this branch.\n     |- Try 90 * 49 = 4410. 4410 exceeds the maximum intermediate result, drop this branch.\n     |- Try 90 \/ 49 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 45 \/ 2 = 22.5. 22.5 is a decimal, drop this branch.\n   |- Pick two numbers (49, 2) (numbers left: [45]). Try possible operations.\n    |- Try 49 + 2 = 51. Add 51 to the number set. Current number set: [51, 45], target: 31, just two numbers left.\n     |- Try 51 + 45 = 96. Evaluate 96 != 31, drop this branch.\n     |- Try 51 - 45 = 6. Evaluate 6 != 31, drop this branch.\n     |- Try 51 * 45 = 2295. 2295 exceeds the maximum intermediate result, drop this branch.\n     |- Try 51 \/ 45 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 49 - 2 = 47. Add 47 to the number set. Current number set: [47, 45], target: 31, just two numbers left.\n     |- Try 47 + 45 = 92. Evaluate 92 != 31, drop this branch.\n     |- Try 47 - 45 = 2. Evaluate 2 != 31, drop this branch.\n     |- Try 47 * 45 = 2115. 2115 exceeds the maximum intermediate result, drop this branch.\n     |- Try 47 \/ 45 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 49 * 2 = 98. Add 98 to the number set. Current number set: [98, 45], target: 31, just two numbers left.\n     |- Try 98 + 45 = 143. Evaluate 143 != 31, drop this branch.\n     |- Try 98 - 45 = 53. Evaluate 53 != 31, drop this branch.\n     |- Try 98 * 45 = 4410. 4410 exceeds the maximum intermediate result, drop this branch.\n     |- Try 98 \/ 45 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 49 \/ 2 = 24.5. 24.5 is a decimal, drop this branch.\n  |- Try 42 - 3 = 39. Add 39 to the number set. Current number set: [39, 49, 2], target: 31. Options for choosing two numbers: [(39, 49), (39, 2), (49, 2)].\n   |- Pick two numbers (39, 49) (numbers left: [2]). Try possible operations.\n    |- Try 49 + 39 = 88. Add 88 to the number set. Current number set: [88, 2], target: 31, just two numbers left.\n     |- Try 88 + 2 = 90. Evaluate 90 != 31, drop this branch.\n     |- Try 88 - 2 = 86. Evaluate 86 != 31, drop this branch.\n     |- Try 88 * 2 = 176. Evaluate 176 != 31, drop this branch.\n     |- Try 88 \/ 2 = 44. Evaluate 44 != 31, drop this branch.\n    |- Try 49 - 39 = 10. Add 10 to the number set. Current number set: [10, 2], target: 31, just two numbers left.\n     |- Try 10 + 2 = 12. Evaluate 12 != 31, drop this branch.\n     |- Try 10 - 2 = 8. Evaluate 8 != 31, drop this branch.\n     |- Try 10 * 2 = 20. Evaluate 20 != 31, drop this branch.\n     |- Try 10 \/ 2 = 5. Evaluate 5 != 31, drop this branch.\n    |- Try 49 * 39 = 1911. Add 1911 to the number set. Current number set: [1911, 2], target: 31, just two numbers left.\n     |- Try 1911 + 2 = 1913. Evaluate 1913 != 31, drop this branch.\n     |- Try 1911 - 2 = 1909. Evaluate 1909 != 31, drop this branch.\n     |- Try 1911 * 2 = 3822. 3822 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1911 \/ 2 = 955.5. 955.5 is a decimal, drop this branch.\n    |- Try 49 \/ 39 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (39, 2) (numbers left: [49]). Try possible operations.\n    |- Try 39 + 2 = 41. Add 41 to the number set. Current number set: [41, 49], target: 31, just two numbers left.\n     |- Try 49 + 41 = 90. Evaluate 90 != 31, drop this branch.\n     |- Try 49 - 41 = 8. Evaluate 8 != 31, drop this branch.\n     |- Try 49 * 41 = 2009. 2009 exceeds the maximum intermediate result, drop this branch.\n     |- Try 49 \/ 41 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 39 - 2 = 37. Add 37 to the number set. Current number set: [37, 49], target: 31, just two numbers left.\n     |- Try 49 + 37 = 86. Evaluate 86 != 31, drop this branch.\n     |- Try 49 - 37 = 12. Evaluate 12 != 31, drop this branch.\n     |- Try 49 * 37 = 1813. Evaluate 1813 != 31, drop this branch.\n     |- Try 49 \/ 37 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 39 * 2 = 78. Add 78 to the number set. Current number set: [78, 49], target: 31, just two numbers left.\n     |- Try 78 + 49 = 127. Evaluate 127 != 31, drop this branch.\n     |- Try 78 - 49 = 29. Evaluate 29 != 31, drop this branch.\n     |- Try 78 * 49 = 3822. 3822 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 49 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 39 \/ 2 = 19.5. 19.5 is a decimal, drop this branch.\n   |- Pick two numbers (49, 2) (numbers left: [39]). Try possible operations.\n    |- Try 49 + 2 = 51. Add 51 to the number set. Current number set: [51, 39], target: 31, just two numbers left.\n     |- Try 51 + 39 = 90. Evaluate 90 != 31, drop this branch.\n     |- Try 51 - 39 = 12. Evaluate 12 != 31, drop this branch.\n     |- Try 51 * 39 = 1989. Evaluate 1989 != 31, drop this branch.\n     |- Try 51 \/ 39 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 49 - 2 = 47. Add 47 to the number set. Current number set: [47, 39], target: 31, just two numbers left.\n     |- Try 47 + 39 = 86. Evaluate 86 != 31, drop this branch.\n     |- Try 47 - 39 = 8. Evaluate 8 != 31, drop this branch.\n     |- Try 47 * 39 = 1833. Evaluate 1833 != 31, drop this branch.\n     |- Try 47 \/ 39 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 49 * 2 = 98. Add 98 to the number set. Current number set: [98, 39], target: 31, just two numbers left.\n     |- Try 98 + 39 = 137. Evaluate 137 != 31, drop this branch.\n     |- Try 98 - 39 = 59. Evaluate 59 != 31, drop this branch.\n     |- Try 98 * 39 = 3822. 3822 exceeds the maximum intermediate result, drop this branch.\n     |- Try 98 \/ 39 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 49 \/ 2 = 24.5. 24.5 is a decimal, drop this branch.\n  |- Try 42 * 3 = 126. Add 126 to the number set. Current number set: [126, 49, 2], target: 31. Options for choosing two numbers: [(126, 49), (126, 2), (49, 2)].\n   |- Pick two numbers (126, 49) (numbers left: [2]). Try possible operations.\n    |- Try 126 + 49 = 175. Add 175 to the number set. Current number set: [175, 2], target: 31, just two numbers left.\n     |- Try 175 + 2 = 177. Evaluate 177 != 31, drop this branch.\n     |- Try 175 - 2 = 173. Evaluate 173 != 31, drop this branch.\n     |- Try 175 * 2 = 350. Evaluate 350 != 31, drop this branch.\n     |- Try 175 \/ 2 = 87.5. 87.5 is a decimal, drop this branch.\n    |- Try 126 - 49 = 77. Add 77 to the number set. Current number set: [77, 2], target: 31, just two numbers left.\n     |- Try 77 + 2 = 79. Evaluate 79 != 31, drop this branch.\n     |- Try 77 - 2 = 75. Evaluate 75 != 31, drop this branch.\n     |- Try 77 * 2 = 154. Evaluate 154 != 31, drop this branch.\n     |- Try 77 \/ 2 = 38.5. 38.5 is a decimal, drop this branch.\n    |- Try 126 * 49 = 6174. 6174 exceeds the maximum intermediate result, drop this branch.\n    |- Try 126 \/ 49 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (126, 2) (numbers left: [49]). Try possible operations.\n    |- Try 126 + 2 = 128. Add 128 to the number set. Current number set: [128, 49], target: 31, just two numbers left.\n     |- Try 128 + 49 = 177. Evaluate 177 != 31, drop this branch.\n     |- Try 128 - 49 = 79. Evaluate 79 != 31, drop this branch.\n     |- Try 128 * 49 = 6272. 6272 exceeds the maximum intermediate result, drop this branch.\n     |- Try 128 \/ 49 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 126 - 2 = 124. Add 124 to the number set. Current number set: [124, 49], target: 31, just two numbers left.\n     |- Try 124 + 49 = 173. Evaluate 173 != 31, drop this branch.\n     |- Try 124 - 49 = 75. Evaluate 75 != 31, drop this branch.\n     |- Try 124 * 49 = 6076. 6076 exceeds the maximum intermediate result, drop this branch.\n     |- Try 124 \/ 49 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 126 * 2 = 252. Add 252 to the number set. Current number set: [252, 49], target: 31, just two numbers left.\n     |- Try 252 + 49 = 301. Evaluate 301 != 31, drop this branch.\n     |- Try 252 - 49 = 203. Evaluate 203 != 31, drop this branch.\n     |- Try 252 * 49 = 12348. 12348 exceeds the maximum intermediate result, drop this branch.\n     |- Try 252 \/ 49 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 126 \/ 2 = 63. Add 63 to the number set. Current number set: [63, 49], target: 31, just two numbers left.\n     |- Try 63 + 49 = 112. Evaluate 112 != 31, drop this branch.\n     |- Try 63 - 49 = 14. Evaluate 14 != 31, drop this branch.\n     |- Try 63 * 49 = 3087. 3087 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 49 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (49, 2) (numbers left: [126]). Try possible operations.\n    |- Try 49 + 2 = 51. Add 51 to the number set. Current number set: [51, 126], target: 31, just two numbers left.\n     |- Try 126 + 51 = 177. Evaluate 177 != 31, drop this branch.\n     |- Try 126 - 51 = 75. Evaluate 75 != 31, drop this branch.\n     |- Try 126 * 51 = 6426. 6426 exceeds the maximum intermediate result, drop this branch.\n     |- Try 126 \/ 51 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 49 - 2 = 47. Add 47 to the number set. Current number set: [47, 126], target: 31, just two numbers left.\n     |- Try 126 + 47 = 173. Evaluate 173 != 31, drop this branch.\n     |- Try 126 - 47 = 79. Evaluate 79 != 31, drop this branch.\n     |- Try 126 * 47 = 5922. 5922 exceeds the maximum intermediate result, drop this branch.\n     |- Try 126 \/ 47 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 49 * 2 = 98. Add 98 to the number set. Current number set: [98, 126], target: 31, just two numbers left.\n     |- Try 126 + 98 = 224. Evaluate 224 != 31, drop this branch.\n     |- Try 126 - 98 = 28. Evaluate 28 != 31, drop this branch.\n     |- Try 126 * 98 = 12348. 12348 exceeds the maximum intermediate result, drop this branch.\n     |- Try 126 \/ 98 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 49 \/ 2 = 24.5. 24.5 is a decimal, drop this branch.\n  |- Try 42 \/ 3 = 14. Add 14 to the number set. Current number set: [14, 49, 2], target: 31. Options for choosing two numbers: [(14, 49), (14, 2), (49, 2)].\n   |- Pick two numbers (14, 49) (numbers left: [2]). Try possible operations.\n    |- Try 49 + 14 = 63. Add 63 to the number set. Current number set: [63, 2], target: 31, just two numbers left.\n     |- Try 63 + 2 = 65. Evaluate 65 != 31, drop this branch.\n     |- Try 63 - 2 = 61. Evaluate 61 != 31, drop this branch.\n     |- Try 63 * 2 = 126. Evaluate 126 != 31, drop this branch.\n     |- Try 63 \/ 2 = 31.5. 31.5 is a decimal, drop this branch.\n    |- Try 49 - 14 = 35. Add 35 to the number set. Current number set: [35, 2], target: 31, just two numbers left.\n     |- Try 35 + 2 = 37. Evaluate 37 != 31, drop this branch.\n     |- Try 35 - 2 = 33. Evaluate 33 != 31, drop this branch.\n     |- Try 35 * 2 = 70. Evaluate 70 != 31, drop this branch.\n     |- Try 35 \/ 2 = 17.5. 17.5 is a decimal, drop this branch.\n    |- Try 49 * 14 = 686. Add 686 to the number set. Current number set: [686, 2], target: 31, just two numbers left.\n     |- Try 686 + 2 = 688. Evaluate 688 != 31, drop this branch.\n     |- Try 686 - 2 = 684. Evaluate 684 != 31, drop this branch.\n     |- Try 686 * 2 = 1372. Evaluate 1372 != 31, drop this branch.\n     |- Try 686 \/ 2 = 343. Evaluate 343 != 31, drop this branch.\n    |- Try 49 \/ 14 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (14, 2) (numbers left: [49]). Try possible operations.\n    |- Try 14 + 2 = 16. Add 16 to the number set. Current number set: [16, 49], target: 31, just two numbers left.\n     |- Try 49 + 16 = 65. Evaluate 65 != 31, drop this branch.\n     |- Try 49 - 16 = 33. Evaluate 33 != 31, drop this branch.\n     |- Try 49 * 16 = 784. Evaluate 784 != 31, drop this branch.\n     |- Try 49 \/ 16 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 14 - 2 = 12. Add 12 to the number set. Current number set: [12, 49], target: 31, just two numbers left.\n     |- Try 49 + 12 = 61. Evaluate 61 != 31, drop this branch.\n     |- Try 49 - 12 = 37. Evaluate 37 != 31, drop this branch.\n     |- Try 49 * 12 = 588. Evaluate 588 != 31, drop this branch.\n     |- Try 49 \/ 12 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 14 * 2 = 28. Add 28 to the number set. Current number set: [28, 49], target: 31, just two numbers left.\n     |- Try 49 + 28 = 77. Evaluate 77 != 31, drop this branch.\n     |- Try 49 - 28 = 21. Evaluate 21 != 31, drop this branch.\n     |- Try 49 * 28 = 1372. Evaluate 1372 != 31, drop this branch.\n     |- Try 49 \/ 28 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 14 \/ 2 = 7. Add 7 to the number set. Current number set: [7, 49], target: 31, just two numbers left.\n     |- Try 49 + 7 = 56. Evaluate 56 != 31, drop this branch.\n     |- Try 49 - 7 = 42. Evaluate 42 != 31, drop this branch.\n     |- Try 49 * 7 = 343. Evaluate 343 != 31, drop this branch.\n     |- Try 49 \/ 7 = 7. Evaluate 7 != 31, drop this branch.\n   |- Pick two numbers (49, 2) (numbers left: [14]). Try possible operations.\n    |- Try 49 + 2 = 51. Add 51 to the number set. Current number set: [51, 14], target: 31, just two numbers left.\n     |- Try 51 + 14 = 65. Evaluate 65 != 31, drop this branch.\n     |- Try 51 - 14 = 37. Evaluate 37 != 31, drop this branch.\n     |- Try 51 * 14 = 714. Evaluate 714 != 31, drop this branch.\n     |- Try 51 \/ 14 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 49 - 2 = 47. Add 47 to the number set. Current number set: [47, 14], target: 31, just two numbers left.\n     |- Try 47 + 14 = 61. Evaluate 61 != 31, drop this branch.\n     |- Try 47 - 14 = 33. Evaluate 33 != 31, drop this branch.\n     |- Try 47 * 14 = 658. Evaluate 658 != 31, drop this branch.\n     |- Try 47 \/ 14 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 49 * 2 = 98. Add 98 to the number set. Current number set: [98, 14], target: 31, just two numbers left.\n     |- Try 98 + 14 = 112. Evaluate 112 != 31, drop this branch.\n     |- Try 98 - 14 = 84. Evaluate 84 != 31, drop this branch.\n     |- Try 98 * 14 = 1372. Evaluate 1372 != 31, drop this branch.\n     |- Try 98 \/ 14 = 7. Evaluate 7 != 31, drop this branch.\n    |- Try 49 \/ 2 = 24.5. 24.5 is a decimal, drop this branch.\n |- Pick two numbers (42, 49) (numbers left: [3, 2]). Try possible operations.\n  |- Try 49 + 42 = 91. Add 91 to the number set. Current number set: [91, 3, 2], target: 31. Options for choosing two numbers: [(91, 3), (91, 2), (3, 2)].\n   |- Pick two numbers (91, 3) (numbers left: [2]). Try possible operations.\n    |- Try 91 + 3 = 94. Add 94 to the number set. Current number set: [94, 2], target: 31, just two numbers left.\n     |- Try 94 + 2 = 96. Evaluate 96 != 31, drop this branch.\n     |- Try 94 - 2 = 92. Evaluate 92 != 31, drop this branch.\n     |- Try 94 * 2 = 188. Evaluate 188 != 31, drop this branch.\n     |- Try 94 \/ 2 = 47. Evaluate 47 != 31, drop this branch.\n    |- Try 91 - 3 = 88. Add 88 to the number set. Current number set: [88, 2], target: 31, just two numbers left.\n     |- Try 88 + 2 = 90. Evaluate 90 != 31, drop this branch.\n     |- Try 88 - 2 = 86. Evaluate 86 != 31, drop this branch.\n     |- Try 88 * 2 = 176. Evaluate 176 != 31, drop this branch.\n     |- Try 88 \/ 2 = 44. Evaluate 44 != 31, drop this branch.\n    |- Try 91 * 3 = 273. Add 273 to the number set. Current number set: [273, 2], target: 31, just two numbers left.\n     |- Try 273 + 2 = 275. Evaluate 275 != 31, drop this branch.\n     |- Try 273 - 2 = 271. Evaluate 271 != 31, drop this branch.\n     |- Try 273 * 2 = 546. Evaluate 546 != 31, drop this branch.\n     |- Try 273 \/ 2 = 136.5. 136.5 is a decimal, drop this branch.\n    |- Try 91 \/ 3 = 30.3. 30.3 is a decimal, drop this branch.\n   |- Pick two numbers (91, 2) (numbers left: [3]). Try possible operations.\n    |- Try 91 + 2 = 93. Add 93 to the number set. Current number set: [93, 3], target: 31, just two numbers left.\n     |- Try 93 + 3 = 96. Evaluate 96 != 31, drop this branch.\n     |- Try 93 - 3 = 90. Evaluate 90 != 31, drop this branch.\n     |- Try 93 * 3 = 279. Evaluate 279 != 31, drop this branch.\n     |- Try 93 \/ 3 = 31. Evaluate 31 == 31, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 93 \/ 3 = 31\nThe step before: 91 + 2 = 93\nThe first step: 49 + 42 = 91\n\nOutput the solution in the required format:\n<Solution>\n49 + 42 = 91\n91 + 2 = 93\n93 \/ 3 = 31\n<\/Solution>\n","item":{"nums":[42,3,49,2],"solution":["49 + 42 = 91","91 + 2 = 93","93 \/ 3 = 31"],"target":31}}
+{"instance_id":"countdown_8k_8","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [18, 36, 1, 34]\nTarget: 38","reference_output":"# Search Procedure\nInitial number set: [18, 36, 1, 34], target: 38. Options for choosing two numbers: [(18, 36), (18, 1), (18, 34), (36, 1), (36, 34), (1, 34)].\n |- Pick two numbers (18, 36) (numbers left: [1, 34]). Try possible operations.\n  |- Try 36 + 18 = 54. Add 54 to the number set. Current number set: [54, 1, 34], target: 38. Options for choosing two numbers: [(54, 1), (54, 34), (1, 34)].\n   |- Pick two numbers (54, 1) (numbers left: [34]). Try possible operations.\n    |- Try 54 + 1 = 55. Add 55 to the number set. Current number set: [55, 34], target: 38, just two numbers left.\n     |- Try 55 + 34 = 89. Evaluate 89 != 38, drop this branch.\n     |- Try 55 - 34 = 21. Evaluate 21 != 38, drop this branch.\n     |- Try 55 * 34 = 1870. Evaluate 1870 != 38, drop this branch.\n     |- Try 55 \/ 34 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 54 - 1 = 53. Add 53 to the number set. Current number set: [53, 34], target: 38, just two numbers left.\n     |- Try 53 + 34 = 87. Evaluate 87 != 38, drop this branch.\n     |- Try 53 - 34 = 19. Evaluate 19 != 38, drop this branch.\n     |- Try 53 * 34 = 1802. Evaluate 1802 != 38, drop this branch.\n     |- Try 53 \/ 34 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 54 * 1 = 54. Add 54 to the number set. Current number set: [54, 34], target: 38, just two numbers left.\n     |- Try 54 + 34 = 88. Evaluate 88 != 38, drop this branch.\n     |- Try 54 - 34 = 20. Evaluate 20 != 38, drop this branch.\n     |- Try 54 * 34 = 1836. Evaluate 1836 != 38, drop this branch.\n     |- Try 54 \/ 34 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 54 \/ 1 = 54. Add 54 to the number set. Current number set: [54, 34], target: 38, just two numbers left.\n     |- Try 54 + 34 = 88. Evaluate 88 != 38, drop this branch.\n     |- Try 54 - 34 = 20. Evaluate 20 != 38, drop this branch.\n     |- Try 54 * 34 = 1836. Evaluate 1836 != 38, drop this branch.\n     |- Try 54 \/ 34 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (54, 34) (numbers left: [1]). Try possible operations.\n    |- Try 54 + 34 = 88. Add 88 to the number set. Current number set: [88, 1], target: 38, just two numbers left.\n     |- Try 88 + 1 = 89. Evaluate 89 != 38, drop this branch.\n     |- Try 88 - 1 = 87. Evaluate 87 != 38, drop this branch.\n     |- Try 88 * 1 = 88. Evaluate 88 != 38, drop this branch.\n     |- Try 88 \/ 1 = 88. Evaluate 88 != 38, drop this branch.\n    |- Try 54 - 34 = 20. Add 20 to the number set. Current number set: [20, 1], target: 38, just two numbers left.\n     |- Try 20 + 1 = 21. Evaluate 21 != 38, drop this branch.\n     |- Try 20 - 1 = 19. Evaluate 19 != 38, drop this branch.\n     |- Try 20 * 1 = 20. Evaluate 20 != 38, drop this branch.\n     |- Try 20 \/ 1 = 20. Evaluate 20 != 38, drop this branch.\n    |- Try 54 * 34 = 1836. Add 1836 to the number set. Current number set: [1836, 1], target: 38, just two numbers left.\n     |- Try 1836 + 1 = 1837. Evaluate 1837 != 38, drop this branch.\n     |- Try 1836 - 1 = 1835. Evaluate 1835 != 38, drop this branch.\n     |- Try 1836 * 1 = 1836. Evaluate 1836 != 38, drop this branch.\n     |- Try 1836 \/ 1 = 1836. Evaluate 1836 != 38, drop this branch.\n    |- Try 54 \/ 34 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (1, 34) (numbers left: [54]). Try possible operations.\n    |- Try 34 + 1 = 35. Add 35 to the number set. Current number set: [35, 54], target: 38, just two numbers left.\n     |- Try 54 + 35 = 89. Evaluate 89 != 38, drop this branch.\n     |- Try 54 - 35 = 19. Evaluate 19 != 38, drop this branch.\n     |- Try 54 * 35 = 1890. Evaluate 1890 != 38, drop this branch.\n     |- Try 54 \/ 35 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 34 - 1 = 33. Add 33 to the number set. Current number set: [33, 54], target: 38, just two numbers left.\n     |- Try 54 + 33 = 87. Evaluate 87 != 38, drop this branch.\n     |- Try 54 - 33 = 21. Evaluate 21 != 38, drop this branch.\n     |- Try 54 * 33 = 1782. Evaluate 1782 != 38, drop this branch.\n     |- Try 54 \/ 33 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 34 * 1 = 34. Add 34 to the number set. Current number set: [34, 54], target: 38, just two numbers left.\n     |- Try 54 + 34 = 88. Evaluate 88 != 38, drop this branch.\n     |- Try 54 - 34 = 20. Evaluate 20 != 38, drop this branch.\n     |- Try 54 * 34 = 1836. Evaluate 1836 != 38, drop this branch.\n     |- Try 54 \/ 34 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 34 \/ 1 = 34. Add 34 to the number set. Current number set: [34, 54], target: 38, just two numbers left.\n     |- Try 54 + 34 = 88. Evaluate 88 != 38, drop this branch.\n     |- Try 54 - 34 = 20. Evaluate 20 != 38, drop this branch.\n     |- Try 54 * 34 = 1836. Evaluate 1836 != 38, drop this branch.\n     |- Try 54 \/ 34 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 36 - 18 = 18. Add 18 to the number set. Current number set: [18, 1, 34], target: 38. Options for choosing two numbers: [(18, 1), (18, 34), (1, 34)].\n   |- Pick two numbers (18, 1) (numbers left: [34]). Try possible operations.\n    |- Try 18 + 1 = 19. Add 19 to the number set. Current number set: [19, 34], target: 38, just two numbers left.\n     |- Try 34 + 19 = 53. Evaluate 53 != 38, drop this branch.\n     |- Try 34 - 19 = 15. Evaluate 15 != 38, drop this branch.\n     |- Try 34 * 19 = 646. Evaluate 646 != 38, drop this branch.\n     |- Try 34 \/ 19 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 - 1 = 17. Add 17 to the number set. Current number set: [17, 34], target: 38, just two numbers left.\n     |- Try 34 + 17 = 51. Evaluate 51 != 38, drop this branch.\n     |- Try 34 - 17 = 17. Evaluate 17 != 38, drop this branch.\n     |- Try 34 * 17 = 578. Evaluate 578 != 38, drop this branch.\n     |- Try 34 \/ 17 = 2. Evaluate 2 != 38, drop this branch.\n    |- Try 18 * 1 = 18. Add 18 to the number set. Current number set: [18, 34], target: 38, just two numbers left.\n     |- Try 34 + 18 = 52. Evaluate 52 != 38, drop this branch.\n     |- Try 34 - 18 = 16. Evaluate 16 != 38, drop this branch.\n     |- Try 34 * 18 = 612. Evaluate 612 != 38, drop this branch.\n     |- Try 34 \/ 18 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 18 \/ 1 = 18. Add 18 to the number set. Current number set: [18, 34], target: 38, just two numbers left.\n     |- Try 34 + 18 = 52. Evaluate 52 != 38, drop this branch.\n     |- Try 34 - 18 = 16. Evaluate 16 != 38, drop this branch.\n     |- Try 34 * 18 = 612. Evaluate 612 != 38, drop this branch.\n     |- Try 34 \/ 18 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (18, 34) (numbers left: [1]). Try possible operations.\n    |- Try 34 + 18 = 52. Add 52 to the number set. Current number set: [52, 1], target: 38, just two numbers left.\n     |- Try 52 + 1 = 53. Evaluate 53 != 38, drop this branch.\n     |- Try 52 - 1 = 51. Evaluate 51 != 38, drop this branch.\n     |- Try 52 * 1 = 52. Evaluate 52 != 38, drop this branch.\n     |- Try 52 \/ 1 = 52. Evaluate 52 != 38, drop this branch.\n    |- Try 34 - 18 = 16. Add 16 to the number set. Current number set: [16, 1], target: 38, just two numbers left.\n     |- Try 16 + 1 = 17. Evaluate 17 != 38, drop this branch.\n     |- Try 16 - 1 = 15. Evaluate 15 != 38, drop this branch.\n     |- Try 16 * 1 = 16. Evaluate 16 != 38, drop this branch.\n     |- Try 16 \/ 1 = 16. Evaluate 16 != 38, drop this branch.\n    |- Try 34 * 18 = 612. Add 612 to the number set. Current number set: [612, 1], target: 38, just two numbers left.\n     |- Try 612 + 1 = 613. Evaluate 613 != 38, drop this branch.\n     |- Try 612 - 1 = 611. Evaluate 611 != 38, drop this branch.\n     |- Try 612 * 1 = 612. Evaluate 612 != 38, drop this branch.\n     |- Try 612 \/ 1 = 612. Evaluate 612 != 38, drop this branch.\n    |- Try 34 \/ 18 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (1, 34) (numbers left: [18]). Try possible operations.\n    |- Try 34 + 1 = 35. Add 35 to the number set. Current number set: [35, 18], target: 38, just two numbers left.\n     |- Try 35 + 18 = 53. Evaluate 53 != 38, drop this branch.\n     |- Try 35 - 18 = 17. Evaluate 17 != 38, drop this branch.\n     |- Try 35 * 18 = 630. Evaluate 630 != 38, drop this branch.\n     |- Try 35 \/ 18 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 34 - 1 = 33. Add 33 to the number set. Current number set: [33, 18], target: 38, just two numbers left.\n     |- Try 33 + 18 = 51. Evaluate 51 != 38, drop this branch.\n     |- Try 33 - 18 = 15. Evaluate 15 != 38, drop this branch.\n     |- Try 33 * 18 = 594. Evaluate 594 != 38, drop this branch.\n     |- Try 33 \/ 18 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 34 * 1 = 34. Add 34 to the number set. Current number set: [34, 18], target: 38, just two numbers left.\n     |- Try 34 + 18 = 52. Evaluate 52 != 38, drop this branch.\n     |- Try 34 - 18 = 16. Evaluate 16 != 38, drop this branch.\n     |- Try 34 * 18 = 612. Evaluate 612 != 38, drop this branch.\n     |- Try 34 \/ 18 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 34 \/ 1 = 34. Add 34 to the number set. Current number set: [34, 18], target: 38, just two numbers left.\n     |- Try 34 + 18 = 52. Evaluate 52 != 38, drop this branch.\n     |- Try 34 - 18 = 16. Evaluate 16 != 38, drop this branch.\n     |- Try 34 * 18 = 612. Evaluate 612 != 38, drop this branch.\n     |- Try 34 \/ 18 = 1.9. 1.9 is a decimal, drop this branch.\n  |- Try 36 * 18 = 648. Add 648 to the number set. Current number set: [648, 1, 34], target: 38. Options for choosing two numbers: [(648, 1), (648, 34), (1, 34)].\n   |- Pick two numbers (648, 1) (numbers left: [34]). Try possible operations.\n    |- Try 648 + 1 = 649. Add 649 to the number set. Current number set: [649, 34], target: 38, just two numbers left.\n     |- Try 649 + 34 = 683. Evaluate 683 != 38, drop this branch.\n     |- Try 649 - 34 = 615. Evaluate 615 != 38, drop this branch.\n     |- Try 649 * 34 = 22066. 22066 exceeds the maximum intermediate result, drop this branch.\n     |- Try 649 \/ 34 = 19.1. 19.1 is a decimal, drop this branch.\n    |- Try 648 - 1 = 647. Add 647 to the number set. Current number set: [647, 34], target: 38, just two numbers left.\n     |- Try 647 + 34 = 681. Evaluate 681 != 38, drop this branch.\n     |- Try 647 - 34 = 613. Evaluate 613 != 38, drop this branch.\n     |- Try 647 * 34 = 21998. 21998 exceeds the maximum intermediate result, drop this branch.\n     |- Try 647 \/ 34 = 19.0. 19.0 is a decimal, drop this branch.\n    |- Try 648 * 1 = 648. Add 648 to the number set. Current number set: [648, 34], target: 38, just two numbers left.\n     |- Try 648 + 34 = 682. Evaluate 682 != 38, drop this branch.\n     |- Try 648 - 34 = 614. Evaluate 614 != 38, drop this branch.\n     |- Try 648 * 34 = 22032. 22032 exceeds the maximum intermediate result, drop this branch.\n     |- Try 648 \/ 34 = 19.1. 19.1 is a decimal, drop this branch.\n    |- Try 648 \/ 1 = 648. Add 648 to the number set. Current number set: [648, 34], target: 38, just two numbers left.\n     |- Try 648 + 34 = 682. Evaluate 682 != 38, drop this branch.\n     |- Try 648 - 34 = 614. Evaluate 614 != 38, drop this branch.\n     |- Try 648 * 34 = 22032. 22032 exceeds the maximum intermediate result, drop this branch.\n     |- Try 648 \/ 34 = 19.1. 19.1 is a decimal, drop this branch.\n   |- Pick two numbers (648, 34) (numbers left: [1]). Try possible operations.\n    |- Try 648 + 34 = 682. Add 682 to the number set. Current number set: [682, 1], target: 38, just two numbers left.\n     |- Try 682 + 1 = 683. Evaluate 683 != 38, drop this branch.\n     |- Try 682 - 1 = 681. Evaluate 681 != 38, drop this branch.\n     |- Try 682 * 1 = 682. Evaluate 682 != 38, drop this branch.\n     |- Try 682 \/ 1 = 682. Evaluate 682 != 38, drop this branch.\n    |- Try 648 - 34 = 614. Add 614 to the number set. Current number set: [614, 1], target: 38, just two numbers left.\n     |- Try 614 + 1 = 615. Evaluate 615 != 38, drop this branch.\n     |- Try 614 - 1 = 613. Evaluate 613 != 38, drop this branch.\n     |- Try 614 * 1 = 614. Evaluate 614 != 38, drop this branch.\n     |- Try 614 \/ 1 = 614. Evaluate 614 != 38, drop this branch.\n    |- Try 648 * 34 = 22032. 22032 exceeds the maximum intermediate result, drop this branch.\n    |- Try 648 \/ 34 = 19.1. 19.1 is a decimal, drop this branch.\n   |- Pick two numbers (1, 34) (numbers left: [648]). Try possible operations.\n    |- Try 34 + 1 = 35. Add 35 to the number set. Current number set: [35, 648], target: 38, just two numbers left.\n     |- Try 648 + 35 = 683. Evaluate 683 != 38, drop this branch.\n     |- Try 648 - 35 = 613. Evaluate 613 != 38, drop this branch.\n     |- Try 648 * 35 = 22680. 22680 exceeds the maximum intermediate result, drop this branch.\n     |- Try 648 \/ 35 = 18.5. 18.5 is a decimal, drop this branch.\n    |- Try 34 - 1 = 33. Add 33 to the number set. Current number set: [33, 648], target: 38, just two numbers left.\n     |- Try 648 + 33 = 681. Evaluate 681 != 38, drop this branch.\n     |- Try 648 - 33 = 615. Evaluate 615 != 38, drop this branch.\n     |- Try 648 * 33 = 21384. 21384 exceeds the maximum intermediate result, drop this branch.\n     |- Try 648 \/ 33 = 19.6. 19.6 is a decimal, drop this branch.\n    |- Try 34 * 1 = 34. Add 34 to the number set. Current number set: [34, 648], target: 38, just two numbers left.\n     |- Try 648 + 34 = 682. Evaluate 682 != 38, drop this branch.\n     |- Try 648 - 34 = 614. Evaluate 614 != 38, drop this branch.\n     |- Try 648 * 34 = 22032. 22032 exceeds the maximum intermediate result, drop this branch.\n     |- Try 648 \/ 34 = 19.1. 19.1 is a decimal, drop this branch.\n    |- Try 34 \/ 1 = 34. Add 34 to the number set. Current number set: [34, 648], target: 38, just two numbers left.\n     |- Try 648 + 34 = 682. Evaluate 682 != 38, drop this branch.\n     |- Try 648 - 34 = 614. Evaluate 614 != 38, drop this branch.\n     |- Try 648 * 34 = 22032. 22032 exceeds the maximum intermediate result, drop this branch.\n     |- Try 648 \/ 34 = 19.1. 19.1 is a decimal, drop this branch.\n  |- Try 36 \/ 18 = 2. Add 2 to the number set. Current number set: [2, 1, 34], target: 38. Options for choosing two numbers: [(2, 1), (2, 34), (1, 34)].\n   |- Pick two numbers (2, 1) (numbers left: [34]). Try possible operations.\n    |- Try 2 + 1 = 3. Add 3 to the number set. Current number set: [3, 34], target: 38, just two numbers left.\n     |- Try 34 + 3 = 37. Evaluate 37 != 38, drop this branch.\n     |- Try 34 - 3 = 31. Evaluate 31 != 38, drop this branch.\n     |- Try 34 * 3 = 102. Evaluate 102 != 38, drop this branch.\n     |- Try 34 \/ 3 = 11.3. 11.3 is a decimal, drop this branch.\n    |- Try 2 - 1 = 1. Add 1 to the number set. Current number set: [1, 34], target: 38, just two numbers left.\n     |- Try 34 + 1 = 35. Evaluate 35 != 38, drop this branch.\n     |- Try 34 - 1 = 33. Evaluate 33 != 38, drop this branch.\n     |- Try 34 * 1 = 34. Evaluate 34 != 38, drop this branch.\n     |- Try 34 \/ 1 = 34. Evaluate 34 != 38, drop this branch.\n    |- Try 2 * 1 = 2. Add 2 to the number set. Current number set: [2, 34], target: 38, just two numbers left.\n     |- Try 34 + 2 = 36. Evaluate 36 != 38, drop this branch.\n     |- Try 34 - 2 = 32. Evaluate 32 != 38, drop this branch.\n     |- Try 34 * 2 = 68. Evaluate 68 != 38, drop this branch.\n     |- Try 34 \/ 2 = 17. Evaluate 17 != 38, drop this branch.\n    |- Try 2 \/ 1 = 2. Add 2 to the number set. Current number set: [2, 34], target: 38, just two numbers left.\n     |- Try 34 + 2 = 36. Evaluate 36 != 38, drop this branch.\n     |- Try 34 - 2 = 32. Evaluate 32 != 38, drop this branch.\n     |- Try 34 * 2 = 68. Evaluate 68 != 38, drop this branch.\n     |- Try 34 \/ 2 = 17. Evaluate 17 != 38, drop this branch.\n   |- Pick two numbers (2, 34) (numbers left: [1]). Try possible operations.\n    |- Try 34 + 2 = 36. Add 36 to the number set. Current number set: [36, 1], target: 38, just two numbers left.\n     |- Try 36 + 1 = 37. Evaluate 37 != 38, drop this branch.\n     |- Try 36 - 1 = 35. Evaluate 35 != 38, drop this branch.\n     |- Try 36 * 1 = 36. Evaluate 36 != 38, drop this branch.\n     |- Try 36 \/ 1 = 36. Evaluate 36 != 38, drop this branch.\n    |- Try 34 - 2 = 32. Add 32 to the number set. Current number set: [32, 1], target: 38, just two numbers left.\n     |- Try 32 + 1 = 33. Evaluate 33 != 38, drop this branch.\n     |- Try 32 - 1 = 31. Evaluate 31 != 38, drop this branch.\n     |- Try 32 * 1 = 32. Evaluate 32 != 38, drop this branch.\n     |- Try 32 \/ 1 = 32. Evaluate 32 != 38, drop this branch.\n    |- Try 34 * 2 = 68. Add 68 to the number set. Current number set: [68, 1], target: 38, just two numbers left.\n     |- Try 68 + 1 = 69. Evaluate 69 != 38, drop this branch.\n     |- Try 68 - 1 = 67. Evaluate 67 != 38, drop this branch.\n     |- Try 68 * 1 = 68. Evaluate 68 != 38, drop this branch.\n     |- Try 68 \/ 1 = 68. Evaluate 68 != 38, drop this branch.\n    |- Try 34 \/ 2 = 17. Add 17 to the number set. Current number set: [17, 1], target: 38, just two numbers left.\n     |- Try 17 + 1 = 18. Evaluate 18 != 38, drop this branch.\n     |- Try 17 - 1 = 16. Evaluate 16 != 38, drop this branch.\n     |- Try 17 * 1 = 17. Evaluate 17 != 38, drop this branch.\n     |- Try 17 \/ 1 = 17. Evaluate 17 != 38, drop this branch.\n   |- Pick two numbers (1, 34) (numbers left: [2]). Try possible operations.\n    |- Try 34 + 1 = 35. Add 35 to the number set. Current number set: [35, 2], target: 38, just two numbers left.\n     |- Try 35 + 2 = 37. Evaluate 37 != 38, drop this branch.\n     |- Try 35 - 2 = 33. Evaluate 33 != 38, drop this branch.\n     |- Try 35 * 2 = 70. Evaluate 70 != 38, drop this branch.\n     |- Try 35 \/ 2 = 17.5. 17.5 is a decimal, drop this branch.\n    |- Try 34 - 1 = 33. Add 33 to the number set. Current number set: [33, 2], target: 38, just two numbers left.\n     |- Try 33 + 2 = 35. Evaluate 35 != 38, drop this branch.\n     |- Try 33 - 2 = 31. Evaluate 31 != 38, drop this branch.\n     |- Try 33 * 2 = 66. Evaluate 66 != 38, drop this branch.\n     |- Try 33 \/ 2 = 16.5. 16.5 is a decimal, drop this branch.\n    |- Try 34 * 1 = 34. Add 34 to the number set. Current number set: [34, 2], target: 38, just two numbers left.\n     |- Try 34 + 2 = 36. Evaluate 36 != 38, drop this branch.\n     |- Try 34 - 2 = 32. Evaluate 32 != 38, drop this branch.\n     |- Try 34 * 2 = 68. Evaluate 68 != 38, drop this branch.\n     |- Try 34 \/ 2 = 17. Evaluate 17 != 38, drop this branch.\n    |- Try 34 \/ 1 = 34. Add 34 to the number set. Current number set: [34, 2], target: 38, just two numbers left.\n     |- Try 34 + 2 = 36. Evaluate 36 != 38, drop this branch.\n     |- Try 34 - 2 = 32. Evaluate 32 != 38, drop this branch.\n     |- Try 34 * 2 = 68. Evaluate 68 != 38, drop this branch.\n     |- Try 34 \/ 2 = 17. Evaluate 17 != 38, drop this branch.\n |- Pick two numbers (18, 1) (numbers left: [36, 34]). Try possible operations.\n  |- Try 18 + 1 = 19. Add 19 to the number set. Current number set: [19, 36, 34], target: 38. Options for choosing two numbers: [(19, 36), (19, 34), (36, 34)].\n   |- Pick two numbers (19, 36) (numbers left: [34]). Try possible operations.\n    |- Try 36 + 19 = 55. Add 55 to the number set. Current number set: [55, 34], target: 38, just two numbers left.\n     |- Try 55 + 34 = 89. Evaluate 89 != 38, drop this branch.\n     |- Try 55 - 34 = 21. Evaluate 21 != 38, drop this branch.\n     |- Try 55 * 34 = 1870. Evaluate 1870 != 38, drop this branch.\n     |- Try 55 \/ 34 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 36 - 19 = 17. Add 17 to the number set. Current number set: [17, 34], target: 38, just two numbers left.\n     |- Try 34 + 17 = 51. Evaluate 51 != 38, drop this branch.\n     |- Try 34 - 17 = 17. Evaluate 17 != 38, drop this branch.\n     |- Try 34 * 17 = 578. Evaluate 578 != 38, drop this branch.\n     |- Try 34 \/ 17 = 2. Evaluate 2 != 38, drop this branch.\n    |- Try 36 * 19 = 684. Add 684 to the number set. Current number set: [684, 34], target: 38, just two numbers left.\n     |- Try 684 + 34 = 718. Evaluate 718 != 38, drop this branch.\n     |- Try 684 - 34 = 650. Evaluate 650 != 38, drop this branch.\n     |- Try 684 * 34 = 23256. 23256 exceeds the maximum intermediate result, drop this branch.\n     |- Try 684 \/ 34 = 20.1. 20.1 is a decimal, drop this branch.\n    |- Try 36 \/ 19 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (19, 34) (numbers left: [36]). Try possible operations.\n    |- Try 34 + 19 = 53. Add 53 to the number set. Current number set: [53, 36], target: 38, just two numbers left.\n     |- Try 53 + 36 = 89. Evaluate 89 != 38, drop this branch.\n     |- Try 53 - 36 = 17. Evaluate 17 != 38, drop this branch.\n     |- Try 53 * 36 = 1908. Evaluate 1908 != 38, drop this branch.\n     |- Try 53 \/ 36 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 34 - 19 = 15. Add 15 to the number set. Current number set: [15, 36], target: 38, just two numbers left.\n     |- Try 36 + 15 = 51. Evaluate 51 != 38, drop this branch.\n     |- Try 36 - 15 = 21. Evaluate 21 != 38, drop this branch.\n     |- Try 36 * 15 = 540. Evaluate 540 != 38, drop this branch.\n     |- Try 36 \/ 15 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 34 * 19 = 646. Add 646 to the number set. Current number set: [646, 36], target: 38, just two numbers left.\n     |- Try 646 + 36 = 682. Evaluate 682 != 38, drop this branch.\n     |- Try 646 - 36 = 610. Evaluate 610 != 38, drop this branch.\n     |- Try 646 * 36 = 23256. 23256 exceeds the maximum intermediate result, drop this branch.\n     |- Try 646 \/ 36 = 17.9. 17.9 is a decimal, drop this branch.\n    |- Try 34 \/ 19 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (36, 34) (numbers left: [19]). Try possible operations.\n    |- Try 36 + 34 = 70. Add 70 to the number set. Current number set: [70, 19], target: 38, just two numbers left.\n     |- Try 70 + 19 = 89. Evaluate 89 != 38, drop this branch.\n     |- Try 70 - 19 = 51. Evaluate 51 != 38, drop this branch.\n     |- Try 70 * 19 = 1330. Evaluate 1330 != 38, drop this branch.\n     |- Try 70 \/ 19 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 36 - 34 = 2. Add 2 to the number set. Current number set: [2, 19], target: 38, just two numbers left.\n     |- Try 19 + 2 = 21. Evaluate 21 != 38, drop this branch.\n     |- Try 19 - 2 = 17. Evaluate 17 != 38, drop this branch.\n     |- Try 19 * 2 = 38. Evaluate 38 == 38, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 19 * 2 = 38\nThe step before: 36 - 34 = 2\nThe first step: 18 + 1 = 19\n\nOutput the solution in the required format:\n<Solution>\n18 + 1 = 19\n36 - 34 = 2\n19 * 2 = 38\n<\/Solution>\n","item":{"nums":[18,36,1,34],"solution":["18 + 1 = 19","36 - 34 = 2","19 * 2 = 38"],"target":38}}
+{"instance_id":"countdown_8k_9","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [16, 46, 11, 20]\nTarget: 42","reference_output":"# Search Procedure\nInitial number set: [16, 46, 11, 20], target: 42. Options for choosing two numbers: [(16, 46), (16, 11), (16, 20), (46, 11), (46, 20), (11, 20)].\n |- Pick two numbers (16, 46) (numbers left: [11, 20]). Try possible operations.\n  |- Try 46 + 16 = 62. Add 62 to the number set. Current number set: [62, 11, 20], target: 42. Options for choosing two numbers: [(62, 11), (62, 20), (11, 20)].\n   |- Pick two numbers (62, 11) (numbers left: [20]). Try possible operations.\n    |- Try 62 + 11 = 73. Add 73 to the number set. Current number set: [73, 20], target: 42, just two numbers left.\n     |- Try 73 + 20 = 93. Evaluate 93 != 42, drop this branch.\n     |- Try 73 - 20 = 53. Evaluate 53 != 42, drop this branch.\n     |- Try 73 * 20 = 1460. Evaluate 1460 != 42, drop this branch.\n     |- Try 73 \/ 20 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 62 - 11 = 51. Add 51 to the number set. Current number set: [51, 20], target: 42, just two numbers left.\n     |- Try 51 + 20 = 71. Evaluate 71 != 42, drop this branch.\n     |- Try 51 - 20 = 31. Evaluate 31 != 42, drop this branch.\n     |- Try 51 * 20 = 1020. Evaluate 1020 != 42, drop this branch.\n     |- Try 51 \/ 20 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 62 * 11 = 682. Add 682 to the number set. Current number set: [682, 20], target: 42, just two numbers left.\n     |- Try 682 + 20 = 702. Evaluate 702 != 42, drop this branch.\n     |- Try 682 - 20 = 662. Evaluate 662 != 42, drop this branch.\n     |- Try 682 * 20 = 13640. 13640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 682 \/ 20 = 34.1. 34.1 is a decimal, drop this branch.\n    |- Try 62 \/ 11 = 5.6. 5.6 is a decimal, drop this branch.\n   |- Pick two numbers (62, 20) (numbers left: [11]). Try possible operations.\n    |- Try 62 + 20 = 82. Add 82 to the number set. Current number set: [82, 11], target: 42, just two numbers left.\n     |- Try 82 + 11 = 93. Evaluate 93 != 42, drop this branch.\n     |- Try 82 - 11 = 71. Evaluate 71 != 42, drop this branch.\n     |- Try 82 * 11 = 902. Evaluate 902 != 42, drop this branch.\n     |- Try 82 \/ 11 = 7.5. 7.5 is a decimal, drop this branch.\n    |- Try 62 - 20 = 42. Add 42 to the number set. Current number set: [42, 11], target: 42, just two numbers left.\n     |- Try 42 + 11 = 53. Evaluate 53 != 42, drop this branch.\n     |- Try 42 - 11 = 31. Evaluate 31 != 42, drop this branch.\n     |- Try 42 * 11 = 462. Evaluate 462 != 42, drop this branch.\n     |- Try 42 \/ 11 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 62 * 20 = 1240. Add 1240 to the number set. Current number set: [1240, 11], target: 42, just two numbers left.\n     |- Try 1240 + 11 = 1251. Evaluate 1251 != 42, drop this branch.\n     |- Try 1240 - 11 = 1229. Evaluate 1229 != 42, drop this branch.\n     |- Try 1240 * 11 = 13640. 13640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1240 \/ 11 = 112.7. 112.7 is a decimal, drop this branch.\n    |- Try 62 \/ 20 = 3.1. 3.1 is a decimal, drop this branch.\n   |- Pick two numbers (11, 20) (numbers left: [62]). Try possible operations.\n    |- Try 20 + 11 = 31. Add 31 to the number set. Current number set: [31, 62], target: 42, just two numbers left.\n     |- Try 62 + 31 = 93. Evaluate 93 != 42, drop this branch.\n     |- Try 62 - 31 = 31. Evaluate 31 != 42, drop this branch.\n     |- Try 62 * 31 = 1922. Evaluate 1922 != 42, drop this branch.\n     |- Try 62 \/ 31 = 2. Evaluate 2 != 42, drop this branch.\n    |- Try 20 - 11 = 9. Add 9 to the number set. Current number set: [9, 62], target: 42, just two numbers left.\n     |- Try 62 + 9 = 71. Evaluate 71 != 42, drop this branch.\n     |- Try 62 - 9 = 53. Evaluate 53 != 42, drop this branch.\n     |- Try 62 * 9 = 558. Evaluate 558 != 42, drop this branch.\n     |- Try 62 \/ 9 = 6.9. 6.9 is a decimal, drop this branch.\n    |- Try 20 * 11 = 220. Add 220 to the number set. Current number set: [220, 62], target: 42, just two numbers left.\n     |- Try 220 + 62 = 282. Evaluate 282 != 42, drop this branch.\n     |- Try 220 - 62 = 158. Evaluate 158 != 42, drop this branch.\n     |- Try 220 * 62 = 13640. 13640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 220 \/ 62 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 20 \/ 11 = 1.8. 1.8 is a decimal, drop this branch.\n  |- Try 46 - 16 = 30. Add 30 to the number set. Current number set: [30, 11, 20], target: 42. Options for choosing two numbers: [(30, 11), (30, 20), (11, 20)].\n   |- Pick two numbers (30, 11) (numbers left: [20]). Try possible operations.\n    |- Try 30 + 11 = 41. Add 41 to the number set. Current number set: [41, 20], target: 42, just two numbers left.\n     |- Try 41 + 20 = 61. Evaluate 61 != 42, drop this branch.\n     |- Try 41 - 20 = 21. Evaluate 21 != 42, drop this branch.\n     |- Try 41 * 20 = 820. Evaluate 820 != 42, drop this branch.\n     |- Try 41 \/ 20 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 30 - 11 = 19. Add 19 to the number set. Current number set: [19, 20], target: 42, just two numbers left.\n     |- Try 20 + 19 = 39. Evaluate 39 != 42, drop this branch.\n     |- Try 20 - 19 = 1. Evaluate 1 != 42, drop this branch.\n     |- Try 20 * 19 = 380. Evaluate 380 != 42, drop this branch.\n     |- Try 20 \/ 19 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 30 * 11 = 330. Add 330 to the number set. Current number set: [330, 20], target: 42, just two numbers left.\n     |- Try 330 + 20 = 350. Evaluate 350 != 42, drop this branch.\n     |- Try 330 - 20 = 310. Evaluate 310 != 42, drop this branch.\n     |- Try 330 * 20 = 6600. 6600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 330 \/ 20 = 16.5. 16.5 is a decimal, drop this branch.\n    |- Try 30 \/ 11 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (30, 20) (numbers left: [11]). Try possible operations.\n    |- Try 30 + 20 = 50. Add 50 to the number set. Current number set: [50, 11], target: 42, just two numbers left.\n     |- Try 50 + 11 = 61. Evaluate 61 != 42, drop this branch.\n     |- Try 50 - 11 = 39. Evaluate 39 != 42, drop this branch.\n     |- Try 50 * 11 = 550. Evaluate 550 != 42, drop this branch.\n     |- Try 50 \/ 11 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 30 - 20 = 10. Add 10 to the number set. Current number set: [10, 11], target: 42, just two numbers left.\n     |- Try 11 + 10 = 21. Evaluate 21 != 42, drop this branch.\n     |- Try 11 - 10 = 1. Evaluate 1 != 42, drop this branch.\n     |- Try 11 * 10 = 110. Evaluate 110 != 42, drop this branch.\n     |- Try 11 \/ 10 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 30 * 20 = 600. Add 600 to the number set. Current number set: [600, 11], target: 42, just two numbers left.\n     |- Try 600 + 11 = 611. Evaluate 611 != 42, drop this branch.\n     |- Try 600 - 11 = 589. Evaluate 589 != 42, drop this branch.\n     |- Try 600 * 11 = 6600. 6600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 600 \/ 11 = 54.5. 54.5 is a decimal, drop this branch.\n    |- Try 30 \/ 20 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (11, 20) (numbers left: [30]). Try possible operations.\n    |- Try 20 + 11 = 31. Add 31 to the number set. Current number set: [31, 30], target: 42, just two numbers left.\n     |- Try 31 + 30 = 61. Evaluate 61 != 42, drop this branch.\n     |- Try 31 - 30 = 1. Evaluate 1 != 42, drop this branch.\n     |- Try 31 * 30 = 930. Evaluate 930 != 42, drop this branch.\n     |- Try 31 \/ 30 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 20 - 11 = 9. Add 9 to the number set. Current number set: [9, 30], target: 42, just two numbers left.\n     |- Try 30 + 9 = 39. Evaluate 39 != 42, drop this branch.\n     |- Try 30 - 9 = 21. Evaluate 21 != 42, drop this branch.\n     |- Try 30 * 9 = 270. Evaluate 270 != 42, drop this branch.\n     |- Try 30 \/ 9 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 20 * 11 = 220. Add 220 to the number set. Current number set: [220, 30], target: 42, just two numbers left.\n     |- Try 220 + 30 = 250. Evaluate 250 != 42, drop this branch.\n     |- Try 220 - 30 = 190. Evaluate 190 != 42, drop this branch.\n     |- Try 220 * 30 = 6600. 6600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 220 \/ 30 = 7.3. 7.3 is a decimal, drop this branch.\n    |- Try 20 \/ 11 = 1.8. 1.8 is a decimal, drop this branch.\n  |- Try 46 * 16 = 736. Add 736 to the number set. Current number set: [736, 11, 20], target: 42. Options for choosing two numbers: [(736, 11), (736, 20), (11, 20)].\n   |- Pick two numbers (736, 11) (numbers left: [20]). Try possible operations.\n    |- Try 736 + 11 = 747. Add 747 to the number set. Current number set: [747, 20], target: 42, just two numbers left.\n     |- Try 747 + 20 = 767. Evaluate 767 != 42, drop this branch.\n     |- Try 747 - 20 = 727. Evaluate 727 != 42, drop this branch.\n     |- Try 747 * 20 = 14940. 14940 exceeds the maximum intermediate result, drop this branch.\n     |- Try 747 \/ 20 = 37.4. 37.4 is a decimal, drop this branch.\n    |- Try 736 - 11 = 725. Add 725 to the number set. Current number set: [725, 20], target: 42, just two numbers left.\n     |- Try 725 + 20 = 745. Evaluate 745 != 42, drop this branch.\n     |- Try 725 - 20 = 705. Evaluate 705 != 42, drop this branch.\n     |- Try 725 * 20 = 14500. 14500 exceeds the maximum intermediate result, drop this branch.\n     |- Try 725 \/ 20 = 36.2. 36.2 is a decimal, drop this branch.\n    |- Try 736 * 11 = 8096. 8096 exceeds the maximum intermediate result, drop this branch.\n    |- Try 736 \/ 11 = 66.9. 66.9 is a decimal, drop this branch.\n   |- Pick two numbers (736, 20) (numbers left: [11]). Try possible operations.\n    |- Try 736 + 20 = 756. Add 756 to the number set. Current number set: [756, 11], target: 42, just two numbers left.\n     |- Try 756 + 11 = 767. Evaluate 767 != 42, drop this branch.\n     |- Try 756 - 11 = 745. Evaluate 745 != 42, drop this branch.\n     |- Try 756 * 11 = 8316. 8316 exceeds the maximum intermediate result, drop this branch.\n     |- Try 756 \/ 11 = 68.7. 68.7 is a decimal, drop this branch.\n    |- Try 736 - 20 = 716. Add 716 to the number set. Current number set: [716, 11], target: 42, just two numbers left.\n     |- Try 716 + 11 = 727. Evaluate 727 != 42, drop this branch.\n     |- Try 716 - 11 = 705. Evaluate 705 != 42, drop this branch.\n     |- Try 716 * 11 = 7876. 7876 exceeds the maximum intermediate result, drop this branch.\n     |- Try 716 \/ 11 = 65.1. 65.1 is a decimal, drop this branch.\n    |- Try 736 * 20 = 14720. 14720 exceeds the maximum intermediate result, drop this branch.\n    |- Try 736 \/ 20 = 36.8. 36.8 is a decimal, drop this branch.\n   |- Pick two numbers (11, 20) (numbers left: [736]). Try possible operations.\n    |- Try 20 + 11 = 31. Add 31 to the number set. Current number set: [31, 736], target: 42, just two numbers left.\n     |- Try 736 + 31 = 767. Evaluate 767 != 42, drop this branch.\n     |- Try 736 - 31 = 705. Evaluate 705 != 42, drop this branch.\n     |- Try 736 * 31 = 22816. 22816 exceeds the maximum intermediate result, drop this branch.\n     |- Try 736 \/ 31 = 23.7. 23.7 is a decimal, drop this branch.\n    |- Try 20 - 11 = 9. Add 9 to the number set. Current number set: [9, 736], target: 42, just two numbers left.\n     |- Try 736 + 9 = 745. Evaluate 745 != 42, drop this branch.\n     |- Try 736 - 9 = 727. Evaluate 727 != 42, drop this branch.\n     |- Try 736 * 9 = 6624. 6624 exceeds the maximum intermediate result, drop this branch.\n     |- Try 736 \/ 9 = 81.8. 81.8 is a decimal, drop this branch.\n    |- Try 20 * 11 = 220. Add 220 to the number set. Current number set: [220, 736], target: 42, just two numbers left.\n     |- Try 736 + 220 = 956. Evaluate 956 != 42, drop this branch.\n     |- Try 736 - 220 = 516. Evaluate 516 != 42, drop this branch.\n     |- Try 736 * 220 = 161920. 161920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 736 \/ 220 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 20 \/ 11 = 1.8. 1.8 is a decimal, drop this branch.\n  |- Try 46 \/ 16 = 2.9. 2.9 is a decimal, drop this branch.\n |- Pick two numbers (16, 11) (numbers left: [46, 20]). Try possible operations.\n  |- Try 16 + 11 = 27. Add 27 to the number set. Current number set: [27, 46, 20], target: 42. Options for choosing two numbers: [(27, 46), (27, 20), (46, 20)].\n   |- Pick two numbers (27, 46) (numbers left: [20]). Try possible operations.\n    |- Try 46 + 27 = 73. Add 73 to the number set. Current number set: [73, 20], target: 42, just two numbers left.\n     |- Try 73 + 20 = 93. Evaluate 93 != 42, drop this branch.\n     |- Try 73 - 20 = 53. Evaluate 53 != 42, drop this branch.\n     |- Try 73 * 20 = 1460. Evaluate 1460 != 42, drop this branch.\n     |- Try 73 \/ 20 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 46 - 27 = 19. Add 19 to the number set. Current number set: [19, 20], target: 42, just two numbers left.\n     |- Try 20 + 19 = 39. Evaluate 39 != 42, drop this branch.\n     |- Try 20 - 19 = 1. Evaluate 1 != 42, drop this branch.\n     |- Try 20 * 19 = 380. Evaluate 380 != 42, drop this branch.\n     |- Try 20 \/ 19 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 46 * 27 = 1242. Add 1242 to the number set. Current number set: [1242, 20], target: 42, just two numbers left.\n     |- Try 1242 + 20 = 1262. Evaluate 1262 != 42, drop this branch.\n     |- Try 1242 - 20 = 1222. Evaluate 1222 != 42, drop this branch.\n     |- Try 1242 * 20 = 24840. 24840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1242 \/ 20 = 62.1. 62.1 is a decimal, drop this branch.\n    |- Try 46 \/ 27 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (27, 20) (numbers left: [46]). Try possible operations.\n    |- Try 27 + 20 = 47. Add 47 to the number set. Current number set: [47, 46], target: 42, just two numbers left.\n     |- Try 47 + 46 = 93. Evaluate 93 != 42, drop this branch.\n     |- Try 47 - 46 = 1. Evaluate 1 != 42, drop this branch.\n     |- Try 47 * 46 = 2162. 2162 exceeds the maximum intermediate result, drop this branch.\n     |- Try 47 \/ 46 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 27 - 20 = 7. Add 7 to the number set. Current number set: [7, 46], target: 42, just two numbers left.\n     |- Try 46 + 7 = 53. Evaluate 53 != 42, drop this branch.\n     |- Try 46 - 7 = 39. Evaluate 39 != 42, drop this branch.\n     |- Try 46 * 7 = 322. Evaluate 322 != 42, drop this branch.\n     |- Try 46 \/ 7 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 27 * 20 = 540. Add 540 to the number set. Current number set: [540, 46], target: 42, just two numbers left.\n     |- Try 540 + 46 = 586. Evaluate 586 != 42, drop this branch.\n     |- Try 540 - 46 = 494. Evaluate 494 != 42, drop this branch.\n     |- Try 540 * 46 = 24840. 24840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 540 \/ 46 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 27 \/ 20 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (46, 20) (numbers left: [27]). Try possible operations.\n    |- Try 46 + 20 = 66. Add 66 to the number set. Current number set: [66, 27], target: 42, just two numbers left.\n     |- Try 66 + 27 = 93. Evaluate 93 != 42, drop this branch.\n     |- Try 66 - 27 = 39. Evaluate 39 != 42, drop this branch.\n     |- Try 66 * 27 = 1782. Evaluate 1782 != 42, drop this branch.\n     |- Try 66 \/ 27 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 46 - 20 = 26. Add 26 to the number set. Current number set: [26, 27], target: 42, just two numbers left.\n     |- Try 27 + 26 = 53. Evaluate 53 != 42, drop this branch.\n     |- Try 27 - 26 = 1. Evaluate 1 != 42, drop this branch.\n     |- Try 27 * 26 = 702. Evaluate 702 != 42, drop this branch.\n     |- Try 27 \/ 26 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 46 * 20 = 920. Add 920 to the number set. Current number set: [920, 27], target: 42, just two numbers left.\n     |- Try 920 + 27 = 947. Evaluate 947 != 42, drop this branch.\n     |- Try 920 - 27 = 893. Evaluate 893 != 42, drop this branch.\n     |- Try 920 * 27 = 24840. 24840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 920 \/ 27 = 34.1. 34.1 is a decimal, drop this branch.\n    |- Try 46 \/ 20 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 - 11 = 5. Add 5 to the number set. Current number set: [5, 46, 20], target: 42. Options for choosing two numbers: [(5, 46), (5, 20), (46, 20)].\n   |- Pick two numbers (5, 46) (numbers left: [20]). Try possible operations.\n    |- Try 46 + 5 = 51. Add 51 to the number set. Current number set: [51, 20], target: 42, just two numbers left.\n     |- Try 51 + 20 = 71. Evaluate 71 != 42, drop this branch.\n     |- Try 51 - 20 = 31. Evaluate 31 != 42, drop this branch.\n     |- Try 51 * 20 = 1020. Evaluate 1020 != 42, drop this branch.\n     |- Try 51 \/ 20 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 46 - 5 = 41. Add 41 to the number set. Current number set: [41, 20], target: 42, just two numbers left.\n     |- Try 41 + 20 = 61. Evaluate 61 != 42, drop this branch.\n     |- Try 41 - 20 = 21. Evaluate 21 != 42, drop this branch.\n     |- Try 41 * 20 = 820. Evaluate 820 != 42, drop this branch.\n     |- Try 41 \/ 20 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 46 * 5 = 230. Add 230 to the number set. Current number set: [230, 20], target: 42, just two numbers left.\n     |- Try 230 + 20 = 250. Evaluate 250 != 42, drop this branch.\n     |- Try 230 - 20 = 210. Evaluate 210 != 42, drop this branch.\n     |- Try 230 * 20 = 4600. 4600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 230 \/ 20 = 11.5. 11.5 is a decimal, drop this branch.\n    |- Try 46 \/ 5 = 9.2. 9.2 is a decimal, drop this branch.\n   |- Pick two numbers (5, 20) (numbers left: [46]). Try possible operations.\n    |- Try 20 + 5 = 25. Add 25 to the number set. Current number set: [25, 46], target: 42, just two numbers left.\n     |- Try 46 + 25 = 71. Evaluate 71 != 42, drop this branch.\n     |- Try 46 - 25 = 21. Evaluate 21 != 42, drop this branch.\n     |- Try 46 * 25 = 1150. Evaluate 1150 != 42, drop this branch.\n     |- Try 46 \/ 25 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 20 - 5 = 15. Add 15 to the number set. Current number set: [15, 46], target: 42, just two numbers left.\n     |- Try 46 + 15 = 61. Evaluate 61 != 42, drop this branch.\n     |- Try 46 - 15 = 31. Evaluate 31 != 42, drop this branch.\n     |- Try 46 * 15 = 690. Evaluate 690 != 42, drop this branch.\n     |- Try 46 \/ 15 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 20 * 5 = 100. Add 100 to the number set. Current number set: [100, 46], target: 42, just two numbers left.\n     |- Try 100 + 46 = 146. Evaluate 146 != 42, drop this branch.\n     |- Try 100 - 46 = 54. Evaluate 54 != 42, drop this branch.\n     |- Try 100 * 46 = 4600. 4600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 100 \/ 46 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 20 \/ 5 = 4. Add 4 to the number set. Current number set: [4, 46], target: 42, just two numbers left.\n     |- Try 46 + 4 = 50. Evaluate 50 != 42, drop this branch.\n     |- Try 46 - 4 = 42. Evaluate 42 == 42, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 46 - 4 = 42\nThe step before: 20 \/ 5 = 4\nThe first step: 16 - 11 = 5\n\nOutput the solution in the required format:\n<Solution>\n16 - 11 = 5\n20 \/ 5 = 4\n46 - 4 = 42\n<\/Solution>\n","item":{"nums":[16,46,11,20],"solution":["16 - 11 = 5","20 \/ 5 = 4","46 - 4 = 42"],"target":42}}
+{"instance_id":"countdown_8k_10","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [33, 46, 18, 27]\nTarget: 24","reference_output":"# Search Procedure\nInitial number set: [33, 46, 18, 27], target: 24. Options for choosing two numbers: [(33, 46), (33, 18), (33, 27), (46, 18), (46, 27), (18, 27)].\n |- Pick two numbers (33, 46) (numbers left: [18, 27]). Try possible operations.\n  |- Try 46 + 33 = 79. Add 79 to the number set. Current number set: [79, 18, 27], target: 24. Options for choosing two numbers: [(79, 18), (79, 27), (18, 27)].\n   |- Pick two numbers (79, 18) (numbers left: [27]). Try possible operations.\n    |- Try 79 + 18 = 97. Add 97 to the number set. Current number set: [97, 27], target: 24, just two numbers left.\n     |- Try 97 + 27 = 124. Evaluate 124 != 24, drop this branch.\n     |- Try 97 - 27 = 70. Evaluate 70 != 24, drop this branch.\n     |- Try 97 * 27 = 2619. 2619 exceeds the maximum intermediate result, drop this branch.\n     |- Try 97 \/ 27 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 79 - 18 = 61. Add 61 to the number set. Current number set: [61, 27], target: 24, just two numbers left.\n     |- Try 61 + 27 = 88. Evaluate 88 != 24, drop this branch.\n     |- Try 61 - 27 = 34. Evaluate 34 != 24, drop this branch.\n     |- Try 61 * 27 = 1647. Evaluate 1647 != 24, drop this branch.\n     |- Try 61 \/ 27 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 79 * 18 = 1422. Add 1422 to the number set. Current number set: [1422, 27], target: 24, just two numbers left.\n     |- Try 1422 + 27 = 1449. Evaluate 1449 != 24, drop this branch.\n     |- Try 1422 - 27 = 1395. Evaluate 1395 != 24, drop this branch.\n     |- Try 1422 * 27 = 38394. 38394 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1422 \/ 27 = 52.7. 52.7 is a decimal, drop this branch.\n    |- Try 79 \/ 18 = 4.4. 4.4 is a decimal, drop this branch.\n   |- Pick two numbers (79, 27) (numbers left: [18]). Try possible operations.\n    |- Try 79 + 27 = 106. Add 106 to the number set. Current number set: [106, 18], target: 24, just two numbers left.\n     |- Try 106 + 18 = 124. Evaluate 124 != 24, drop this branch.\n     |- Try 106 - 18 = 88. Evaluate 88 != 24, drop this branch.\n     |- Try 106 * 18 = 1908. Evaluate 1908 != 24, drop this branch.\n     |- Try 106 \/ 18 = 5.9. 5.9 is a decimal, drop this branch.\n    |- Try 79 - 27 = 52. Add 52 to the number set. Current number set: [52, 18], target: 24, just two numbers left.\n     |- Try 52 + 18 = 70. Evaluate 70 != 24, drop this branch.\n     |- Try 52 - 18 = 34. Evaluate 34 != 24, drop this branch.\n     |- Try 52 * 18 = 936. Evaluate 936 != 24, drop this branch.\n     |- Try 52 \/ 18 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 79 * 27 = 2133. 2133 exceeds the maximum intermediate result, drop this branch.\n    |- Try 79 \/ 27 = 2.9. 2.9 is a decimal, drop this branch.\n   |- Pick two numbers (18, 27) (numbers left: [79]). Try possible operations.\n    |- Try 27 + 18 = 45. Add 45 to the number set. Current number set: [45, 79], target: 24, just two numbers left.\n     |- Try 79 + 45 = 124. Evaluate 124 != 24, drop this branch.\n     |- Try 79 - 45 = 34. Evaluate 34 != 24, drop this branch.\n     |- Try 79 * 45 = 3555. 3555 exceeds the maximum intermediate result, drop this branch.\n     |- Try 79 \/ 45 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 27 - 18 = 9. Add 9 to the number set. Current number set: [9, 79], target: 24, just two numbers left.\n     |- Try 79 + 9 = 88. Evaluate 88 != 24, drop this branch.\n     |- Try 79 - 9 = 70. Evaluate 70 != 24, drop this branch.\n     |- Try 79 * 9 = 711. Evaluate 711 != 24, drop this branch.\n     |- Try 79 \/ 9 = 8.8. 8.8 is a decimal, drop this branch.\n    |- Try 27 * 18 = 486. Add 486 to the number set. Current number set: [486, 79], target: 24, just two numbers left.\n     |- Try 486 + 79 = 565. Evaluate 565 != 24, drop this branch.\n     |- Try 486 - 79 = 407. Evaluate 407 != 24, drop this branch.\n     |- Try 486 * 79 = 38394. 38394 exceeds the maximum intermediate result, drop this branch.\n     |- Try 486 \/ 79 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 27 \/ 18 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 46 - 33 = 13. Add 13 to the number set. Current number set: [13, 18, 27], target: 24. Options for choosing two numbers: [(13, 18), (13, 27), (18, 27)].\n   |- Pick two numbers (13, 18) (numbers left: [27]). Try possible operations.\n    |- Try 18 + 13 = 31. Add 31 to the number set. Current number set: [31, 27], target: 24, just two numbers left.\n     |- Try 31 + 27 = 58. Evaluate 58 != 24, drop this branch.\n     |- Try 31 - 27 = 4. Evaluate 4 != 24, drop this branch.\n     |- Try 31 * 27 = 837. Evaluate 837 != 24, drop this branch.\n     |- Try 31 \/ 27 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 18 - 13 = 5. Add 5 to the number set. Current number set: [5, 27], target: 24, just two numbers left.\n     |- Try 27 + 5 = 32. Evaluate 32 != 24, drop this branch.\n     |- Try 27 - 5 = 22. Evaluate 22 != 24, drop this branch.\n     |- Try 27 * 5 = 135. Evaluate 135 != 24, drop this branch.\n     |- Try 27 \/ 5 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 18 * 13 = 234. Add 234 to the number set. Current number set: [234, 27], target: 24, just two numbers left.\n     |- Try 234 + 27 = 261. Evaluate 261 != 24, drop this branch.\n     |- Try 234 - 27 = 207. Evaluate 207 != 24, drop this branch.\n     |- Try 234 * 27 = 6318. 6318 exceeds the maximum intermediate result, drop this branch.\n     |- Try 234 \/ 27 = 8.7. 8.7 is a decimal, drop this branch.\n    |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (13, 27) (numbers left: [18]). Try possible operations.\n    |- Try 27 + 13 = 40. Add 40 to the number set. Current number set: [40, 18], target: 24, just two numbers left.\n     |- Try 40 + 18 = 58. Evaluate 58 != 24, drop this branch.\n     |- Try 40 - 18 = 22. Evaluate 22 != 24, drop this branch.\n     |- Try 40 * 18 = 720. Evaluate 720 != 24, drop this branch.\n     |- Try 40 \/ 18 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 27 - 13 = 14. Add 14 to the number set. Current number set: [14, 18], target: 24, just two numbers left.\n     |- Try 18 + 14 = 32. Evaluate 32 != 24, drop this branch.\n     |- Try 18 - 14 = 4. Evaluate 4 != 24, drop this branch.\n     |- Try 18 * 14 = 252. Evaluate 252 != 24, drop this branch.\n     |- Try 18 \/ 14 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 27 * 13 = 351. Add 351 to the number set. Current number set: [351, 18], target: 24, just two numbers left.\n     |- Try 351 + 18 = 369. Evaluate 369 != 24, drop this branch.\n     |- Try 351 - 18 = 333. Evaluate 333 != 24, drop this branch.\n     |- Try 351 * 18 = 6318. 6318 exceeds the maximum intermediate result, drop this branch.\n     |- Try 351 \/ 18 = 19.5. 19.5 is a decimal, drop this branch.\n    |- Try 27 \/ 13 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (18, 27) (numbers left: [13]). Try possible operations.\n    |- Try 27 + 18 = 45. Add 45 to the number set. Current number set: [45, 13], target: 24, just two numbers left.\n     |- Try 45 + 13 = 58. Evaluate 58 != 24, drop this branch.\n     |- Try 45 - 13 = 32. Evaluate 32 != 24, drop this branch.\n     |- Try 45 * 13 = 585. Evaluate 585 != 24, drop this branch.\n     |- Try 45 \/ 13 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 27 - 18 = 9. Add 9 to the number set. Current number set: [9, 13], target: 24, just two numbers left.\n     |- Try 13 + 9 = 22. Evaluate 22 != 24, drop this branch.\n     |- Try 13 - 9 = 4. Evaluate 4 != 24, drop this branch.\n     |- Try 13 * 9 = 117. Evaluate 117 != 24, drop this branch.\n     |- Try 13 \/ 9 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 27 * 18 = 486. Add 486 to the number set. Current number set: [486, 13], target: 24, just two numbers left.\n     |- Try 486 + 13 = 499. Evaluate 499 != 24, drop this branch.\n     |- Try 486 - 13 = 473. Evaluate 473 != 24, drop this branch.\n     |- Try 486 * 13 = 6318. 6318 exceeds the maximum intermediate result, drop this branch.\n     |- Try 486 \/ 13 = 37.4. 37.4 is a decimal, drop this branch.\n    |- Try 27 \/ 18 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 46 * 33 = 1518. Add 1518 to the number set. Current number set: [1518, 18, 27], target: 24. Options for choosing two numbers: [(1518, 18), (1518, 27), (18, 27)].\n   |- Pick two numbers (1518, 18) (numbers left: [27]). Try possible operations.\n    |- Try 1518 + 18 = 1536. Add 1536 to the number set. Current number set: [1536, 27], target: 24, just two numbers left.\n     |- Try 1536 + 27 = 1563. Evaluate 1563 != 24, drop this branch.\n     |- Try 1536 - 27 = 1509. Evaluate 1509 != 24, drop this branch.\n     |- Try 1536 * 27 = 41472. 41472 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1536 \/ 27 = 56.9. 56.9 is a decimal, drop this branch.\n    |- Try 1518 - 18 = 1500. Add 1500 to the number set. Current number set: [1500, 27], target: 24, just two numbers left.\n     |- Try 1500 + 27 = 1527. Evaluate 1527 != 24, drop this branch.\n     |- Try 1500 - 27 = 1473. Evaluate 1473 != 24, drop this branch.\n     |- Try 1500 * 27 = 40500. 40500 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1500 \/ 27 = 55.6. 55.6 is a decimal, drop this branch.\n    |- Try 1518 * 18 = 27324. 27324 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1518 \/ 18 = 84.3. 84.3 is a decimal, drop this branch.\n   |- Pick two numbers (1518, 27) (numbers left: [18]). Try possible operations.\n    |- Try 1518 + 27 = 1545. Add 1545 to the number set. Current number set: [1545, 18], target: 24, just two numbers left.\n     |- Try 1545 + 18 = 1563. Evaluate 1563 != 24, drop this branch.\n     |- Try 1545 - 18 = 1527. Evaluate 1527 != 24, drop this branch.\n     |- Try 1545 * 18 = 27810. 27810 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1545 \/ 18 = 85.8. 85.8 is a decimal, drop this branch.\n    |- Try 1518 - 27 = 1491. Add 1491 to the number set. Current number set: [1491, 18], target: 24, just two numbers left.\n     |- Try 1491 + 18 = 1509. Evaluate 1509 != 24, drop this branch.\n     |- Try 1491 - 18 = 1473. Evaluate 1473 != 24, drop this branch.\n     |- Try 1491 * 18 = 26838. 26838 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1491 \/ 18 = 82.8. 82.8 is a decimal, drop this branch.\n    |- Try 1518 * 27 = 40986. 40986 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1518 \/ 27 = 56.2. 56.2 is a decimal, drop this branch.\n   |- Pick two numbers (18, 27) (numbers left: [1518]). Try possible operations.\n    |- Try 27 + 18 = 45. Add 45 to the number set. Current number set: [45, 1518], target: 24, just two numbers left.\n     |- Try 1518 + 45 = 1563. Evaluate 1563 != 24, drop this branch.\n     |- Try 1518 - 45 = 1473. Evaluate 1473 != 24, drop this branch.\n     |- Try 1518 * 45 = 68310. 68310 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1518 \/ 45 = 33.7. 33.7 is a decimal, drop this branch.\n    |- Try 27 - 18 = 9. Add 9 to the number set. Current number set: [9, 1518], target: 24, just two numbers left.\n     |- Try 1518 + 9 = 1527. Evaluate 1527 != 24, drop this branch.\n     |- Try 1518 - 9 = 1509. Evaluate 1509 != 24, drop this branch.\n     |- Try 1518 * 9 = 13662. 13662 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1518 \/ 9 = 168.7. 168.7 is a decimal, drop this branch.\n    |- Try 27 * 18 = 486. Add 486 to the number set. Current number set: [486, 1518], target: 24, just two numbers left.\n     |- Try 1518 + 486 = 2004. 2004 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1518 - 486 = 1032. Evaluate 1032 != 24, drop this branch.\n     |- Try 1518 * 486 = 737748. 737748 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1518 \/ 486 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 27 \/ 18 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 46 \/ 33 = 1.4. 1.4 is a decimal, drop this branch.\n |- Pick two numbers (33, 18) (numbers left: [46, 27]). Try possible operations.\n  |- Try 33 + 18 = 51. Add 51 to the number set. Current number set: [51, 46, 27], target: 24. Options for choosing two numbers: [(51, 46), (51, 27), (46, 27)].\n   |- Pick two numbers (51, 46) (numbers left: [27]). Try possible operations.\n    |- Try 51 + 46 = 97. Add 97 to the number set. Current number set: [97, 27], target: 24, just two numbers left.\n     |- Try 97 + 27 = 124. Evaluate 124 != 24, drop this branch.\n     |- Try 97 - 27 = 70. Evaluate 70 != 24, drop this branch.\n     |- Try 97 * 27 = 2619. 2619 exceeds the maximum intermediate result, drop this branch.\n     |- Try 97 \/ 27 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 51 - 46 = 5. Add 5 to the number set. Current number set: [5, 27], target: 24, just two numbers left.\n     |- Try 27 + 5 = 32. Evaluate 32 != 24, drop this branch.\n     |- Try 27 - 5 = 22. Evaluate 22 != 24, drop this branch.\n     |- Try 27 * 5 = 135. Evaluate 135 != 24, drop this branch.\n     |- Try 27 \/ 5 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 51 * 46 = 2346. 2346 exceeds the maximum intermediate result, drop this branch.\n    |- Try 51 \/ 46 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (51, 27) (numbers left: [46]). Try possible operations.\n    |- Try 51 + 27 = 78. Add 78 to the number set. Current number set: [78, 46], target: 24, just two numbers left.\n     |- Try 78 + 46 = 124. Evaluate 124 != 24, drop this branch.\n     |- Try 78 - 46 = 32. Evaluate 32 != 24, drop this branch.\n     |- Try 78 * 46 = 3588. 3588 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 46 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 51 - 27 = 24. Add 24 to the number set. Current number set: [24, 46], target: 24, just two numbers left.\n     |- Try 46 + 24 = 70. Evaluate 70 != 24, drop this branch.\n     |- Try 46 - 24 = 22. Evaluate 22 != 24, drop this branch.\n     |- Try 46 * 24 = 1104. Evaluate 1104 != 24, drop this branch.\n     |- Try 46 \/ 24 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 51 * 27 = 1377. Add 1377 to the number set. Current number set: [1377, 46], target: 24, just two numbers left.\n     |- Try 1377 + 46 = 1423. Evaluate 1423 != 24, drop this branch.\n     |- Try 1377 - 46 = 1331. Evaluate 1331 != 24, drop this branch.\n     |- Try 1377 * 46 = 63342. 63342 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1377 \/ 46 = 29.9. 29.9 is a decimal, drop this branch.\n    |- Try 51 \/ 27 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (46, 27) (numbers left: [51]). Try possible operations.\n    |- Try 46 + 27 = 73. Add 73 to the number set. Current number set: [73, 51], target: 24, just two numbers left.\n     |- Try 73 + 51 = 124. Evaluate 124 != 24, drop this branch.\n     |- Try 73 - 51 = 22. Evaluate 22 != 24, drop this branch.\n     |- Try 73 * 51 = 3723. 3723 exceeds the maximum intermediate result, drop this branch.\n     |- Try 73 \/ 51 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 46 - 27 = 19. Add 19 to the number set. Current number set: [19, 51], target: 24, just two numbers left.\n     |- Try 51 + 19 = 70. Evaluate 70 != 24, drop this branch.\n     |- Try 51 - 19 = 32. Evaluate 32 != 24, drop this branch.\n     |- Try 51 * 19 = 969. Evaluate 969 != 24, drop this branch.\n     |- Try 51 \/ 19 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 46 * 27 = 1242. Add 1242 to the number set. Current number set: [1242, 51], target: 24, just two numbers left.\n     |- Try 1242 + 51 = 1293. Evaluate 1293 != 24, drop this branch.\n     |- Try 1242 - 51 = 1191. Evaluate 1191 != 24, drop this branch.\n     |- Try 1242 * 51 = 63342. 63342 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1242 \/ 51 = 24.4. 24.4 is a decimal, drop this branch.\n    |- Try 46 \/ 27 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 33 - 18 = 15. Add 15 to the number set. Current number set: [15, 46, 27], target: 24. Options for choosing two numbers: [(15, 46), (15, 27), (46, 27)].\n   |- Pick two numbers (15, 46) (numbers left: [27]). Try possible operations.\n    |- Try 46 + 15 = 61. Add 61 to the number set. Current number set: [61, 27], target: 24, just two numbers left.\n     |- Try 61 + 27 = 88. Evaluate 88 != 24, drop this branch.\n     |- Try 61 - 27 = 34. Evaluate 34 != 24, drop this branch.\n     |- Try 61 * 27 = 1647. Evaluate 1647 != 24, drop this branch.\n     |- Try 61 \/ 27 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 46 - 15 = 31. Add 31 to the number set. Current number set: [31, 27], target: 24, just two numbers left.\n     |- Try 31 + 27 = 58. Evaluate 58 != 24, drop this branch.\n     |- Try 31 - 27 = 4. Evaluate 4 != 24, drop this branch.\n     |- Try 31 * 27 = 837. Evaluate 837 != 24, drop this branch.\n     |- Try 31 \/ 27 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 46 * 15 = 690. Add 690 to the number set. Current number set: [690, 27], target: 24, just two numbers left.\n     |- Try 690 + 27 = 717. Evaluate 717 != 24, drop this branch.\n     |- Try 690 - 27 = 663. Evaluate 663 != 24, drop this branch.\n     |- Try 690 * 27 = 18630. 18630 exceeds the maximum intermediate result, drop this branch.\n     |- Try 690 \/ 27 = 25.6. 25.6 is a decimal, drop this branch.\n    |- Try 46 \/ 15 = 3.1. 3.1 is a decimal, drop this branch.\n   |- Pick two numbers (15, 27) (numbers left: [46]). Try possible operations.\n    |- Try 27 + 15 = 42. Add 42 to the number set. Current number set: [42, 46], target: 24, just two numbers left.\n     |- Try 46 + 42 = 88. Evaluate 88 != 24, drop this branch.\n     |- Try 46 - 42 = 4. Evaluate 4 != 24, drop this branch.\n     |- Try 46 * 42 = 1932. Evaluate 1932 != 24, drop this branch.\n     |- Try 46 \/ 42 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 27 - 15 = 12. Add 12 to the number set. Current number set: [12, 46], target: 24, just two numbers left.\n     |- Try 46 + 12 = 58. Evaluate 58 != 24, drop this branch.\n     |- Try 46 - 12 = 34. Evaluate 34 != 24, drop this branch.\n     |- Try 46 * 12 = 552. Evaluate 552 != 24, drop this branch.\n     |- Try 46 \/ 12 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 27 * 15 = 405. Add 405 to the number set. Current number set: [405, 46], target: 24, just two numbers left.\n     |- Try 405 + 46 = 451. Evaluate 451 != 24, drop this branch.\n     |- Try 405 - 46 = 359. Evaluate 359 != 24, drop this branch.\n     |- Try 405 * 46 = 18630. 18630 exceeds the maximum intermediate result, drop this branch.\n     |- Try 405 \/ 46 = 8.8. 8.8 is a decimal, drop this branch.\n    |- Try 27 \/ 15 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (46, 27) (numbers left: [15]). Try possible operations.\n    |- Try 46 + 27 = 73. Add 73 to the number set. Current number set: [73, 15], target: 24, just two numbers left.\n     |- Try 73 + 15 = 88. Evaluate 88 != 24, drop this branch.\n     |- Try 73 - 15 = 58. Evaluate 58 != 24, drop this branch.\n     |- Try 73 * 15 = 1095. Evaluate 1095 != 24, drop this branch.\n     |- Try 73 \/ 15 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 46 - 27 = 19. Add 19 to the number set. Current number set: [19, 15], target: 24, just two numbers left.\n     |- Try 19 + 15 = 34. Evaluate 34 != 24, drop this branch.\n     |- Try 19 - 15 = 4. Evaluate 4 != 24, drop this branch.\n     |- Try 19 * 15 = 285. Evaluate 285 != 24, drop this branch.\n     |- Try 19 \/ 15 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 46 * 27 = 1242. Add 1242 to the number set. Current number set: [1242, 15], target: 24, just two numbers left.\n     |- Try 1242 + 15 = 1257. Evaluate 1257 != 24, drop this branch.\n     |- Try 1242 - 15 = 1227. Evaluate 1227 != 24, drop this branch.\n     |- Try 1242 * 15 = 18630. 18630 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1242 \/ 15 = 82.8. 82.8 is a decimal, drop this branch.\n    |- Try 46 \/ 27 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 33 * 18 = 594. Add 594 to the number set. Current number set: [594, 46, 27], target: 24. Options for choosing two numbers: [(594, 46), (594, 27), (46, 27)].\n   |- Pick two numbers (594, 46) (numbers left: [27]). Try possible operations.\n    |- Try 594 + 46 = 640. Add 640 to the number set. Current number set: [640, 27], target: 24, just two numbers left.\n     |- Try 640 + 27 = 667. Evaluate 667 != 24, drop this branch.\n     |- Try 640 - 27 = 613. Evaluate 613 != 24, drop this branch.\n     |- Try 640 * 27 = 17280. 17280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 640 \/ 27 = 23.7. 23.7 is a decimal, drop this branch.\n    |- Try 594 - 46 = 548. Add 548 to the number set. Current number set: [548, 27], target: 24, just two numbers left.\n     |- Try 548 + 27 = 575. Evaluate 575 != 24, drop this branch.\n     |- Try 548 - 27 = 521. Evaluate 521 != 24, drop this branch.\n     |- Try 548 * 27 = 14796. 14796 exceeds the maximum intermediate result, drop this branch.\n     |- Try 548 \/ 27 = 20.3. 20.3 is a decimal, drop this branch.\n    |- Try 594 * 46 = 27324. 27324 exceeds the maximum intermediate result, drop this branch.\n    |- Try 594 \/ 46 = 12.9. 12.9 is a decimal, drop this branch.\n   |- Pick two numbers (594, 27) (numbers left: [46]). Try possible operations.\n    |- Try 594 + 27 = 621. Add 621 to the number set. Current number set: [621, 46], target: 24, just two numbers left.\n     |- Try 621 + 46 = 667. Evaluate 667 != 24, drop this branch.\n     |- Try 621 - 46 = 575. Evaluate 575 != 24, drop this branch.\n     |- Try 621 * 46 = 28566. 28566 exceeds the maximum intermediate result, drop this branch.\n     |- Try 621 \/ 46 = 13.5. 13.5 is a decimal, drop this branch.\n    |- Try 594 - 27 = 567. Add 567 to the number set. Current number set: [567, 46], target: 24, just two numbers left.\n     |- Try 567 + 46 = 613. Evaluate 613 != 24, drop this branch.\n     |- Try 567 - 46 = 521. Evaluate 521 != 24, drop this branch.\n     |- Try 567 * 46 = 26082. 26082 exceeds the maximum intermediate result, drop this branch.\n     |- Try 567 \/ 46 = 12.3. 12.3 is a decimal, drop this branch.\n    |- Try 594 * 27 = 16038. 16038 exceeds the maximum intermediate result, drop this branch.\n    |- Try 594 \/ 27 = 22. Add 22 to the number set. Current number set: [22, 46], target: 24, just two numbers left.\n     |- Try 46 + 22 = 68. Evaluate 68 != 24, drop this branch.\n     |- Try 46 - 22 = 24. Evaluate 24 == 24, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 46 - 22 = 24\nThe step before: 594 \/ 27 = 22\nThe first step: 33 * 18 = 594\n\nOutput the solution in the required format:\n<Solution>\n33 * 18 = 594\n594 \/ 27 = 22\n46 - 22 = 24\n<\/Solution>\n","item":{"nums":[33,46,18,27],"solution":["33 * 18 = 594","594 \/ 27 = 22","46 - 22 = 24"],"target":24}}
+{"instance_id":"countdown_8k_11","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [42, 5, 41, 30]\nTarget: 35","reference_output":"# Search Procedure\nInitial number set: [42, 5, 41, 30], target: 35. Options for choosing two numbers: [(42, 5), (42, 41), (42, 30), (5, 41), (5, 30), (41, 30)].\n |- Pick two numbers (42, 5) (numbers left: [41, 30]). Try possible operations.\n  |- Try 42 + 5 = 47. Add 47 to the number set. Current number set: [47, 41, 30], target: 35. Options for choosing two numbers: [(47, 41), (47, 30), (41, 30)].\n   |- Pick two numbers (47, 41) (numbers left: [30]). Try possible operations.\n    |- Try 47 + 41 = 88. Add 88 to the number set. Current number set: [88, 30], target: 35, just two numbers left.\n     |- Try 88 + 30 = 118. Evaluate 118 != 35, drop this branch.\n     |- Try 88 - 30 = 58. Evaluate 58 != 35, drop this branch.\n     |- Try 88 * 30 = 2640. 2640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 88 \/ 30 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 47 - 41 = 6. Add 6 to the number set. Current number set: [6, 30], target: 35, just two numbers left.\n     |- Try 30 + 6 = 36. Evaluate 36 != 35, drop this branch.\n     |- Try 30 - 6 = 24. Evaluate 24 != 35, drop this branch.\n     |- Try 30 * 6 = 180. Evaluate 180 != 35, drop this branch.\n     |- Try 30 \/ 6 = 5. Evaluate 5 != 35, drop this branch.\n    |- Try 47 * 41 = 1927. Add 1927 to the number set. Current number set: [1927, 30], target: 35, just two numbers left.\n     |- Try 1927 + 30 = 1957. Evaluate 1957 != 35, drop this branch.\n     |- Try 1927 - 30 = 1897. Evaluate 1897 != 35, drop this branch.\n     |- Try 1927 * 30 = 57810. 57810 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1927 \/ 30 = 64.2. 64.2 is a decimal, drop this branch.\n    |- Try 47 \/ 41 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (47, 30) (numbers left: [41]). Try possible operations.\n    |- Try 47 + 30 = 77. Add 77 to the number set. Current number set: [77, 41], target: 35, just two numbers left.\n     |- Try 77 + 41 = 118. Evaluate 118 != 35, drop this branch.\n     |- Try 77 - 41 = 36. Evaluate 36 != 35, drop this branch.\n     |- Try 77 * 41 = 3157. 3157 exceeds the maximum intermediate result, drop this branch.\n     |- Try 77 \/ 41 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 47 - 30 = 17. Add 17 to the number set. Current number set: [17, 41], target: 35, just two numbers left.\n     |- Try 41 + 17 = 58. Evaluate 58 != 35, drop this branch.\n     |- Try 41 - 17 = 24. Evaluate 24 != 35, drop this branch.\n     |- Try 41 * 17 = 697. Evaluate 697 != 35, drop this branch.\n     |- Try 41 \/ 17 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 47 * 30 = 1410. Add 1410 to the number set. Current number set: [1410, 41], target: 35, just two numbers left.\n     |- Try 1410 + 41 = 1451. Evaluate 1451 != 35, drop this branch.\n     |- Try 1410 - 41 = 1369. Evaluate 1369 != 35, drop this branch.\n     |- Try 1410 * 41 = 57810. 57810 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1410 \/ 41 = 34.4. 34.4 is a decimal, drop this branch.\n    |- Try 47 \/ 30 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (41, 30) (numbers left: [47]). Try possible operations.\n    |- Try 41 + 30 = 71. Add 71 to the number set. Current number set: [71, 47], target: 35, just two numbers left.\n     |- Try 71 + 47 = 118. Evaluate 118 != 35, drop this branch.\n     |- Try 71 - 47 = 24. Evaluate 24 != 35, drop this branch.\n     |- Try 71 * 47 = 3337. 3337 exceeds the maximum intermediate result, drop this branch.\n     |- Try 71 \/ 47 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 41 - 30 = 11. Add 11 to the number set. Current number set: [11, 47], target: 35, just two numbers left.\n     |- Try 47 + 11 = 58. Evaluate 58 != 35, drop this branch.\n     |- Try 47 - 11 = 36. Evaluate 36 != 35, drop this branch.\n     |- Try 47 * 11 = 517. Evaluate 517 != 35, drop this branch.\n     |- Try 47 \/ 11 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 41 * 30 = 1230. Add 1230 to the number set. Current number set: [1230, 47], target: 35, just two numbers left.\n     |- Try 1230 + 47 = 1277. Evaluate 1277 != 35, drop this branch.\n     |- Try 1230 - 47 = 1183. Evaluate 1183 != 35, drop this branch.\n     |- Try 1230 * 47 = 57810. 57810 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1230 \/ 47 = 26.2. 26.2 is a decimal, drop this branch.\n    |- Try 41 \/ 30 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 42 - 5 = 37. Add 37 to the number set. Current number set: [37, 41, 30], target: 35. Options for choosing two numbers: [(37, 41), (37, 30), (41, 30)].\n   |- Pick two numbers (37, 41) (numbers left: [30]). Try possible operations.\n    |- Try 41 + 37 = 78. Add 78 to the number set. Current number set: [78, 30], target: 35, just two numbers left.\n     |- Try 78 + 30 = 108. Evaluate 108 != 35, drop this branch.\n     |- Try 78 - 30 = 48. Evaluate 48 != 35, drop this branch.\n     |- Try 78 * 30 = 2340. 2340 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 30 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 41 - 37 = 4. Add 4 to the number set. Current number set: [4, 30], target: 35, just two numbers left.\n     |- Try 30 + 4 = 34. Evaluate 34 != 35, drop this branch.\n     |- Try 30 - 4 = 26. Evaluate 26 != 35, drop this branch.\n     |- Try 30 * 4 = 120. Evaluate 120 != 35, drop this branch.\n     |- Try 30 \/ 4 = 7.5. 7.5 is a decimal, drop this branch.\n    |- Try 41 * 37 = 1517. Add 1517 to the number set. Current number set: [1517, 30], target: 35, just two numbers left.\n     |- Try 1517 + 30 = 1547. Evaluate 1547 != 35, drop this branch.\n     |- Try 1517 - 30 = 1487. Evaluate 1487 != 35, drop this branch.\n     |- Try 1517 * 30 = 45510. 45510 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1517 \/ 30 = 50.6. 50.6 is a decimal, drop this branch.\n    |- Try 41 \/ 37 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (37, 30) (numbers left: [41]). Try possible operations.\n    |- Try 37 + 30 = 67. Add 67 to the number set. Current number set: [67, 41], target: 35, just two numbers left.\n     |- Try 67 + 41 = 108. Evaluate 108 != 35, drop this branch.\n     |- Try 67 - 41 = 26. Evaluate 26 != 35, drop this branch.\n     |- Try 67 * 41 = 2747. 2747 exceeds the maximum intermediate result, drop this branch.\n     |- Try 67 \/ 41 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 37 - 30 = 7. Add 7 to the number set. Current number set: [7, 41], target: 35, just two numbers left.\n     |- Try 41 + 7 = 48. Evaluate 48 != 35, drop this branch.\n     |- Try 41 - 7 = 34. Evaluate 34 != 35, drop this branch.\n     |- Try 41 * 7 = 287. Evaluate 287 != 35, drop this branch.\n     |- Try 41 \/ 7 = 5.9. 5.9 is a decimal, drop this branch.\n    |- Try 37 * 30 = 1110. Add 1110 to the number set. Current number set: [1110, 41], target: 35, just two numbers left.\n     |- Try 1110 + 41 = 1151. Evaluate 1151 != 35, drop this branch.\n     |- Try 1110 - 41 = 1069. Evaluate 1069 != 35, drop this branch.\n     |- Try 1110 * 41 = 45510. 45510 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1110 \/ 41 = 27.1. 27.1 is a decimal, drop this branch.\n    |- Try 37 \/ 30 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (41, 30) (numbers left: [37]). Try possible operations.\n    |- Try 41 + 30 = 71. Add 71 to the number set. Current number set: [71, 37], target: 35, just two numbers left.\n     |- Try 71 + 37 = 108. Evaluate 108 != 35, drop this branch.\n     |- Try 71 - 37 = 34. Evaluate 34 != 35, drop this branch.\n     |- Try 71 * 37 = 2627. 2627 exceeds the maximum intermediate result, drop this branch.\n     |- Try 71 \/ 37 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 41 - 30 = 11. Add 11 to the number set. Current number set: [11, 37], target: 35, just two numbers left.\n     |- Try 37 + 11 = 48. Evaluate 48 != 35, drop this branch.\n     |- Try 37 - 11 = 26. Evaluate 26 != 35, drop this branch.\n     |- Try 37 * 11 = 407. Evaluate 407 != 35, drop this branch.\n     |- Try 37 \/ 11 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 41 * 30 = 1230. Add 1230 to the number set. Current number set: [1230, 37], target: 35, just two numbers left.\n     |- Try 1230 + 37 = 1267. Evaluate 1267 != 35, drop this branch.\n     |- Try 1230 - 37 = 1193. Evaluate 1193 != 35, drop this branch.\n     |- Try 1230 * 37 = 45510. 45510 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1230 \/ 37 = 33.2. 33.2 is a decimal, drop this branch.\n    |- Try 41 \/ 30 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 42 * 5 = 210. Add 210 to the number set. Current number set: [210, 41, 30], target: 35. Options for choosing two numbers: [(210, 41), (210, 30), (41, 30)].\n   |- Pick two numbers (210, 41) (numbers left: [30]). Try possible operations.\n    |- Try 210 + 41 = 251. Add 251 to the number set. Current number set: [251, 30], target: 35, just two numbers left.\n     |- Try 251 + 30 = 281. Evaluate 281 != 35, drop this branch.\n     |- Try 251 - 30 = 221. Evaluate 221 != 35, drop this branch.\n     |- Try 251 * 30 = 7530. 7530 exceeds the maximum intermediate result, drop this branch.\n     |- Try 251 \/ 30 = 8.4. 8.4 is a decimal, drop this branch.\n    |- Try 210 - 41 = 169. Add 169 to the number set. Current number set: [169, 30], target: 35, just two numbers left.\n     |- Try 169 + 30 = 199. Evaluate 199 != 35, drop this branch.\n     |- Try 169 - 30 = 139. Evaluate 139 != 35, drop this branch.\n     |- Try 169 * 30 = 5070. 5070 exceeds the maximum intermediate result, drop this branch.\n     |- Try 169 \/ 30 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 210 * 41 = 8610. 8610 exceeds the maximum intermediate result, drop this branch.\n    |- Try 210 \/ 41 = 5.1. 5.1 is a decimal, drop this branch.\n   |- Pick two numbers (210, 30) (numbers left: [41]). Try possible operations.\n    |- Try 210 + 30 = 240. Add 240 to the number set. Current number set: [240, 41], target: 35, just two numbers left.\n     |- Try 240 + 41 = 281. Evaluate 281 != 35, drop this branch.\n     |- Try 240 - 41 = 199. Evaluate 199 != 35, drop this branch.\n     |- Try 240 * 41 = 9840. 9840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 240 \/ 41 = 5.9. 5.9 is a decimal, drop this branch.\n    |- Try 210 - 30 = 180. Add 180 to the number set. Current number set: [180, 41], target: 35, just two numbers left.\n     |- Try 180 + 41 = 221. Evaluate 221 != 35, drop this branch.\n     |- Try 180 - 41 = 139. Evaluate 139 != 35, drop this branch.\n     |- Try 180 * 41 = 7380. 7380 exceeds the maximum intermediate result, drop this branch.\n     |- Try 180 \/ 41 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 210 * 30 = 6300. 6300 exceeds the maximum intermediate result, drop this branch.\n    |- Try 210 \/ 30 = 7. Add 7 to the number set. Current number set: [7, 41], target: 35, just two numbers left.\n     |- Try 41 + 7 = 48. Evaluate 48 != 35, drop this branch.\n     |- Try 41 - 7 = 34. Evaluate 34 != 35, drop this branch.\n     |- Try 41 * 7 = 287. Evaluate 287 != 35, drop this branch.\n     |- Try 41 \/ 7 = 5.9. 5.9 is a decimal, drop this branch.\n   |- Pick two numbers (41, 30) (numbers left: [210]). Try possible operations.\n    |- Try 41 + 30 = 71. Add 71 to the number set. Current number set: [71, 210], target: 35, just two numbers left.\n     |- Try 210 + 71 = 281. Evaluate 281 != 35, drop this branch.\n     |- Try 210 - 71 = 139. Evaluate 139 != 35, drop this branch.\n     |- Try 210 * 71 = 14910. 14910 exceeds the maximum intermediate result, drop this branch.\n     |- Try 210 \/ 71 = 3.0. 3.0 is a decimal, drop this branch.\n    |- Try 41 - 30 = 11. Add 11 to the number set. Current number set: [11, 210], target: 35, just two numbers left.\n     |- Try 210 + 11 = 221. Evaluate 221 != 35, drop this branch.\n     |- Try 210 - 11 = 199. Evaluate 199 != 35, drop this branch.\n     |- Try 210 * 11 = 2310. 2310 exceeds the maximum intermediate result, drop this branch.\n     |- Try 210 \/ 11 = 19.1. 19.1 is a decimal, drop this branch.\n    |- Try 41 * 30 = 1230. Add 1230 to the number set. Current number set: [1230, 210], target: 35, just two numbers left.\n     |- Try 1230 + 210 = 1440. Evaluate 1440 != 35, drop this branch.\n     |- Try 1230 - 210 = 1020. Evaluate 1020 != 35, drop this branch.\n     |- Try 1230 * 210 = 258300. 258300 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1230 \/ 210 = 5.9. 5.9 is a decimal, drop this branch.\n    |- Try 41 \/ 30 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 42 \/ 5 = 8.4. 8.4 is a decimal, drop this branch.\n |- Pick two numbers (42, 41) (numbers left: [5, 30]). Try possible operations.\n  |- Try 42 + 41 = 83. Add 83 to the number set. Current number set: [83, 5, 30], target: 35. Options for choosing two numbers: [(83, 5), (83, 30), (5, 30)].\n   |- Pick two numbers (83, 5) (numbers left: [30]). Try possible operations.\n    |- Try 83 + 5 = 88. Add 88 to the number set. Current number set: [88, 30], target: 35, just two numbers left.\n     |- Try 88 + 30 = 118. Evaluate 118 != 35, drop this branch.\n     |- Try 88 - 30 = 58. Evaluate 58 != 35, drop this branch.\n     |- Try 88 * 30 = 2640. 2640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 88 \/ 30 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 83 - 5 = 78. Add 78 to the number set. Current number set: [78, 30], target: 35, just two numbers left.\n     |- Try 78 + 30 = 108. Evaluate 108 != 35, drop this branch.\n     |- Try 78 - 30 = 48. Evaluate 48 != 35, drop this branch.\n     |- Try 78 * 30 = 2340. 2340 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 30 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 83 * 5 = 415. Add 415 to the number set. Current number set: [415, 30], target: 35, just two numbers left.\n     |- Try 415 + 30 = 445. Evaluate 445 != 35, drop this branch.\n     |- Try 415 - 30 = 385. Evaluate 385 != 35, drop this branch.\n     |- Try 415 * 30 = 12450. 12450 exceeds the maximum intermediate result, drop this branch.\n     |- Try 415 \/ 30 = 13.8. 13.8 is a decimal, drop this branch.\n    |- Try 83 \/ 5 = 16.6. 16.6 is a decimal, drop this branch.\n   |- Pick two numbers (83, 30) (numbers left: [5]). Try possible operations.\n    |- Try 83 + 30 = 113. Add 113 to the number set. Current number set: [113, 5], target: 35, just two numbers left.\n     |- Try 113 + 5 = 118. Evaluate 118 != 35, drop this branch.\n     |- Try 113 - 5 = 108. Evaluate 108 != 35, drop this branch.\n     |- Try 113 * 5 = 565. Evaluate 565 != 35, drop this branch.\n     |- Try 113 \/ 5 = 22.6. 22.6 is a decimal, drop this branch.\n    |- Try 83 - 30 = 53. Add 53 to the number set. Current number set: [53, 5], target: 35, just two numbers left.\n     |- Try 53 + 5 = 58. Evaluate 58 != 35, drop this branch.\n     |- Try 53 - 5 = 48. Evaluate 48 != 35, drop this branch.\n     |- Try 53 * 5 = 265. Evaluate 265 != 35, drop this branch.\n     |- Try 53 \/ 5 = 10.6. 10.6 is a decimal, drop this branch.\n    |- Try 83 * 30 = 2490. 2490 exceeds the maximum intermediate result, drop this branch.\n    |- Try 83 \/ 30 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (5, 30) (numbers left: [83]). Try possible operations.\n    |- Try 30 + 5 = 35. Add 35 to the number set. Current number set: [35, 83], target: 35, just two numbers left.\n     |- Try 83 + 35 = 118. Evaluate 118 != 35, drop this branch.\n     |- Try 83 - 35 = 48. Evaluate 48 != 35, drop this branch.\n     |- Try 83 * 35 = 2905. 2905 exceeds the maximum intermediate result, drop this branch.\n     |- Try 83 \/ 35 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 30 - 5 = 25. Add 25 to the number set. Current number set: [25, 83], target: 35, just two numbers left.\n     |- Try 83 + 25 = 108. Evaluate 108 != 35, drop this branch.\n     |- Try 83 - 25 = 58. Evaluate 58 != 35, drop this branch.\n     |- Try 83 * 25 = 2075. 2075 exceeds the maximum intermediate result, drop this branch.\n     |- Try 83 \/ 25 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 30 * 5 = 150. Add 150 to the number set. Current number set: [150, 83], target: 35, just two numbers left.\n     |- Try 150 + 83 = 233. Evaluate 233 != 35, drop this branch.\n     |- Try 150 - 83 = 67. Evaluate 67 != 35, drop this branch.\n     |- Try 150 * 83 = 12450. 12450 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 83 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 30 \/ 5 = 6. Add 6 to the number set. Current number set: [6, 83], target: 35, just two numbers left.\n     |- Try 83 + 6 = 89. Evaluate 89 != 35, drop this branch.\n     |- Try 83 - 6 = 77. Evaluate 77 != 35, drop this branch.\n     |- Try 83 * 6 = 498. Evaluate 498 != 35, drop this branch.\n     |- Try 83 \/ 6 = 13.8. 13.8 is a decimal, drop this branch.\n  |- Try 42 - 41 = 1. Add 1 to the number set. Current number set: [1, 5, 30], target: 35. Options for choosing two numbers: [(1, 5), (1, 30), (5, 30)].\n   |- Pick two numbers (1, 5) (numbers left: [30]). Try possible operations.\n    |- Try 5 + 1 = 6. Add 6 to the number set. Current number set: [6, 30], target: 35, just two numbers left.\n     |- Try 30 + 6 = 36. Evaluate 36 != 35, drop this branch.\n     |- Try 30 - 6 = 24. Evaluate 24 != 35, drop this branch.\n     |- Try 30 * 6 = 180. Evaluate 180 != 35, drop this branch.\n     |- Try 30 \/ 6 = 5. Evaluate 5 != 35, drop this branch.\n    |- Try 5 - 1 = 4. Add 4 to the number set. Current number set: [4, 30], target: 35, just two numbers left.\n     |- Try 30 + 4 = 34. Evaluate 34 != 35, drop this branch.\n     |- Try 30 - 4 = 26. Evaluate 26 != 35, drop this branch.\n     |- Try 30 * 4 = 120. Evaluate 120 != 35, drop this branch.\n     |- Try 30 \/ 4 = 7.5. 7.5 is a decimal, drop this branch.\n    |- Try 5 * 1 = 5. Add 5 to the number set. Current number set: [5, 30], target: 35, just two numbers left.\n     |- Try 30 + 5 = 35. Evaluate 35 == 35, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 30 + 5 = 35\nThe step before: 5 * 1 = 5\nThe first step: 42 - 41 = 1\n\nOutput the solution in the required format:\n<Solution>\n42 - 41 = 1\n5 * 1 = 5\n30 + 5 = 35\n<\/Solution>\n","item":{"nums":[42,5,41,30],"solution":["42 - 41 = 1","5 * 1 = 5","30 + 5 = 35"],"target":35}}
+{"instance_id":"countdown_8k_12","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [8, 7, 16, 35]\nTarget: 29","reference_output":"# Search Procedure\nInitial number set: [8, 7, 16, 35], target: 29. Options for choosing two numbers: [(8, 7), (8, 16), (8, 35), (7, 16), (7, 35), (16, 35)].\n |- Pick two numbers (8, 7) (numbers left: [16, 35]). Try possible operations.\n  |- Try 8 + 7 = 15. Add 15 to the number set. Current number set: [15, 16, 35], target: 29. Options for choosing two numbers: [(15, 16), (15, 35), (16, 35)].\n   |- Pick two numbers (15, 16) (numbers left: [35]). Try possible operations.\n    |- Try 16 + 15 = 31. Add 31 to the number set. Current number set: [31, 35], target: 29, just two numbers left.\n     |- Try 35 + 31 = 66. Evaluate 66 != 29, drop this branch.\n     |- Try 35 - 31 = 4. Evaluate 4 != 29, drop this branch.\n     |- Try 35 * 31 = 1085. Evaluate 1085 != 29, drop this branch.\n     |- Try 35 \/ 31 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 16 - 15 = 1. Add 1 to the number set. Current number set: [1, 35], target: 29, just two numbers left.\n     |- Try 35 + 1 = 36. Evaluate 36 != 29, drop this branch.\n     |- Try 35 - 1 = 34. Evaluate 34 != 29, drop this branch.\n     |- Try 35 * 1 = 35. Evaluate 35 != 29, drop this branch.\n     |- Try 35 \/ 1 = 35. Evaluate 35 != 29, drop this branch.\n    |- Try 16 * 15 = 240. Add 240 to the number set. Current number set: [240, 35], target: 29, just two numbers left.\n     |- Try 240 + 35 = 275. Evaluate 275 != 29, drop this branch.\n     |- Try 240 - 35 = 205. Evaluate 205 != 29, drop this branch.\n     |- Try 240 * 35 = 8400. 8400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 240 \/ 35 = 6.9. 6.9 is a decimal, drop this branch.\n    |- Try 16 \/ 15 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (15, 35) (numbers left: [16]). Try possible operations.\n    |- Try 35 + 15 = 50. Add 50 to the number set. Current number set: [50, 16], target: 29, just two numbers left.\n     |- Try 50 + 16 = 66. Evaluate 66 != 29, drop this branch.\n     |- Try 50 - 16 = 34. Evaluate 34 != 29, drop this branch.\n     |- Try 50 * 16 = 800. Evaluate 800 != 29, drop this branch.\n     |- Try 50 \/ 16 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 35 - 15 = 20. Add 20 to the number set. Current number set: [20, 16], target: 29, just two numbers left.\n     |- Try 20 + 16 = 36. Evaluate 36 != 29, drop this branch.\n     |- Try 20 - 16 = 4. Evaluate 4 != 29, drop this branch.\n     |- Try 20 * 16 = 320. Evaluate 320 != 29, drop this branch.\n     |- Try 20 \/ 16 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 35 * 15 = 525. Add 525 to the number set. Current number set: [525, 16], target: 29, just two numbers left.\n     |- Try 525 + 16 = 541. Evaluate 541 != 29, drop this branch.\n     |- Try 525 - 16 = 509. Evaluate 509 != 29, drop this branch.\n     |- Try 525 * 16 = 8400. 8400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 525 \/ 16 = 32.8. 32.8 is a decimal, drop this branch.\n    |- Try 35 \/ 15 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (16, 35) (numbers left: [15]). Try possible operations.\n    |- Try 35 + 16 = 51. Add 51 to the number set. Current number set: [51, 15], target: 29, just two numbers left.\n     |- Try 51 + 15 = 66. Evaluate 66 != 29, drop this branch.\n     |- Try 51 - 15 = 36. Evaluate 36 != 29, drop this branch.\n     |- Try 51 * 15 = 765. Evaluate 765 != 29, drop this branch.\n     |- Try 51 \/ 15 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 35 - 16 = 19. Add 19 to the number set. Current number set: [19, 15], target: 29, just two numbers left.\n     |- Try 19 + 15 = 34. Evaluate 34 != 29, drop this branch.\n     |- Try 19 - 15 = 4. Evaluate 4 != 29, drop this branch.\n     |- Try 19 * 15 = 285. Evaluate 285 != 29, drop this branch.\n     |- Try 19 \/ 15 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 35 * 16 = 560. Add 560 to the number set. Current number set: [560, 15], target: 29, just two numbers left.\n     |- Try 560 + 15 = 575. Evaluate 575 != 29, drop this branch.\n     |- Try 560 - 15 = 545. Evaluate 545 != 29, drop this branch.\n     |- Try 560 * 15 = 8400. 8400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 560 \/ 15 = 37.3. 37.3 is a decimal, drop this branch.\n    |- Try 35 \/ 16 = 2.2. 2.2 is a decimal, drop this branch.\n  |- Try 8 - 7 = 1. Add 1 to the number set. Current number set: [1, 16, 35], target: 29. Options for choosing two numbers: [(1, 16), (1, 35), (16, 35)].\n   |- Pick two numbers (1, 16) (numbers left: [35]). Try possible operations.\n    |- Try 16 + 1 = 17. Add 17 to the number set. Current number set: [17, 35], target: 29, just two numbers left.\n     |- Try 35 + 17 = 52. Evaluate 52 != 29, drop this branch.\n     |- Try 35 - 17 = 18. Evaluate 18 != 29, drop this branch.\n     |- Try 35 * 17 = 595. Evaluate 595 != 29, drop this branch.\n     |- Try 35 \/ 17 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 16 - 1 = 15. Add 15 to the number set. Current number set: [15, 35], target: 29, just two numbers left.\n     |- Try 35 + 15 = 50. Evaluate 50 != 29, drop this branch.\n     |- Try 35 - 15 = 20. Evaluate 20 != 29, drop this branch.\n     |- Try 35 * 15 = 525. Evaluate 525 != 29, drop this branch.\n     |- Try 35 \/ 15 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 16 * 1 = 16. Add 16 to the number set. Current number set: [16, 35], target: 29, just two numbers left.\n     |- Try 35 + 16 = 51. Evaluate 51 != 29, drop this branch.\n     |- Try 35 - 16 = 19. Evaluate 19 != 29, drop this branch.\n     |- Try 35 * 16 = 560. Evaluate 560 != 29, drop this branch.\n     |- Try 35 \/ 16 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 16 \/ 1 = 16. Add 16 to the number set. Current number set: [16, 35], target: 29, just two numbers left.\n     |- Try 35 + 16 = 51. Evaluate 51 != 29, drop this branch.\n     |- Try 35 - 16 = 19. Evaluate 19 != 29, drop this branch.\n     |- Try 35 * 16 = 560. Evaluate 560 != 29, drop this branch.\n     |- Try 35 \/ 16 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (1, 35) (numbers left: [16]). Try possible operations.\n    |- Try 35 + 1 = 36. Add 36 to the number set. Current number set: [36, 16], target: 29, just two numbers left.\n     |- Try 36 + 16 = 52. Evaluate 52 != 29, drop this branch.\n     |- Try 36 - 16 = 20. Evaluate 20 != 29, drop this branch.\n     |- Try 36 * 16 = 576. Evaluate 576 != 29, drop this branch.\n     |- Try 36 \/ 16 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 35 - 1 = 34. Add 34 to the number set. Current number set: [34, 16], target: 29, just two numbers left.\n     |- Try 34 + 16 = 50. Evaluate 50 != 29, drop this branch.\n     |- Try 34 - 16 = 18. Evaluate 18 != 29, drop this branch.\n     |- Try 34 * 16 = 544. Evaluate 544 != 29, drop this branch.\n     |- Try 34 \/ 16 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 35 * 1 = 35. Add 35 to the number set. Current number set: [35, 16], target: 29, just two numbers left.\n     |- Try 35 + 16 = 51. Evaluate 51 != 29, drop this branch.\n     |- Try 35 - 16 = 19. Evaluate 19 != 29, drop this branch.\n     |- Try 35 * 16 = 560. Evaluate 560 != 29, drop this branch.\n     |- Try 35 \/ 16 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 35 \/ 1 = 35. Add 35 to the number set. Current number set: [35, 16], target: 29, just two numbers left.\n     |- Try 35 + 16 = 51. Evaluate 51 != 29, drop this branch.\n     |- Try 35 - 16 = 19. Evaluate 19 != 29, drop this branch.\n     |- Try 35 * 16 = 560. Evaluate 560 != 29, drop this branch.\n     |- Try 35 \/ 16 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (16, 35) (numbers left: [1]). Try possible operations.\n    |- Try 35 + 16 = 51. Add 51 to the number set. Current number set: [51, 1], target: 29, just two numbers left.\n     |- Try 51 + 1 = 52. Evaluate 52 != 29, drop this branch.\n     |- Try 51 - 1 = 50. Evaluate 50 != 29, drop this branch.\n     |- Try 51 * 1 = 51. Evaluate 51 != 29, drop this branch.\n     |- Try 51 \/ 1 = 51. Evaluate 51 != 29, drop this branch.\n    |- Try 35 - 16 = 19. Add 19 to the number set. Current number set: [19, 1], target: 29, just two numbers left.\n     |- Try 19 + 1 = 20. Evaluate 20 != 29, drop this branch.\n     |- Try 19 - 1 = 18. Evaluate 18 != 29, drop this branch.\n     |- Try 19 * 1 = 19. Evaluate 19 != 29, drop this branch.\n     |- Try 19 \/ 1 = 19. Evaluate 19 != 29, drop this branch.\n    |- Try 35 * 16 = 560. Add 560 to the number set. Current number set: [560, 1], target: 29, just two numbers left.\n     |- Try 560 + 1 = 561. Evaluate 561 != 29, drop this branch.\n     |- Try 560 - 1 = 559. Evaluate 559 != 29, drop this branch.\n     |- Try 560 * 1 = 560. Evaluate 560 != 29, drop this branch.\n     |- Try 560 \/ 1 = 560. Evaluate 560 != 29, drop this branch.\n    |- Try 35 \/ 16 = 2.2. 2.2 is a decimal, drop this branch.\n  |- Try 8 * 7 = 56. Add 56 to the number set. Current number set: [56, 16, 35], target: 29. Options for choosing two numbers: [(56, 16), (56, 35), (16, 35)].\n   |- Pick two numbers (56, 16) (numbers left: [35]). Try possible operations.\n    |- Try 56 + 16 = 72. Add 72 to the number set. Current number set: [72, 35], target: 29, just two numbers left.\n     |- Try 72 + 35 = 107. Evaluate 107 != 29, drop this branch.\n     |- Try 72 - 35 = 37. Evaluate 37 != 29, drop this branch.\n     |- Try 72 * 35 = 2520. 2520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 35 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 56 - 16 = 40. Add 40 to the number set. Current number set: [40, 35], target: 29, just two numbers left.\n     |- Try 40 + 35 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 40 - 35 = 5. Evaluate 5 != 29, drop this branch.\n     |- Try 40 * 35 = 1400. Evaluate 1400 != 29, drop this branch.\n     |- Try 40 \/ 35 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 56 * 16 = 896. Add 896 to the number set. Current number set: [896, 35], target: 29, just two numbers left.\n     |- Try 896 + 35 = 931. Evaluate 931 != 29, drop this branch.\n     |- Try 896 - 35 = 861. Evaluate 861 != 29, drop this branch.\n     |- Try 896 * 35 = 31360. 31360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 896 \/ 35 = 25.6. 25.6 is a decimal, drop this branch.\n    |- Try 56 \/ 16 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (56, 35) (numbers left: [16]). Try possible operations.\n    |- Try 56 + 35 = 91. Add 91 to the number set. Current number set: [91, 16], target: 29, just two numbers left.\n     |- Try 91 + 16 = 107. Evaluate 107 != 29, drop this branch.\n     |- Try 91 - 16 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 91 * 16 = 1456. Evaluate 1456 != 29, drop this branch.\n     |- Try 91 \/ 16 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 56 - 35 = 21. Add 21 to the number set. Current number set: [21, 16], target: 29, just two numbers left.\n     |- Try 21 + 16 = 37. Evaluate 37 != 29, drop this branch.\n     |- Try 21 - 16 = 5. Evaluate 5 != 29, drop this branch.\n     |- Try 21 * 16 = 336. Evaluate 336 != 29, drop this branch.\n     |- Try 21 \/ 16 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 56 * 35 = 1960. Add 1960 to the number set. Current number set: [1960, 16], target: 29, just two numbers left.\n     |- Try 1960 + 16 = 1976. Evaluate 1976 != 29, drop this branch.\n     |- Try 1960 - 16 = 1944. Evaluate 1944 != 29, drop this branch.\n     |- Try 1960 * 16 = 31360. 31360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1960 \/ 16 = 122.5. 122.5 is a decimal, drop this branch.\n    |- Try 56 \/ 35 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (16, 35) (numbers left: [56]). Try possible operations.\n    |- Try 35 + 16 = 51. Add 51 to the number set. Current number set: [51, 56], target: 29, just two numbers left.\n     |- Try 56 + 51 = 107. Evaluate 107 != 29, drop this branch.\n     |- Try 56 - 51 = 5. Evaluate 5 != 29, drop this branch.\n     |- Try 56 * 51 = 2856. 2856 exceeds the maximum intermediate result, drop this branch.\n     |- Try 56 \/ 51 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 35 - 16 = 19. Add 19 to the number set. Current number set: [19, 56], target: 29, just two numbers left.\n     |- Try 56 + 19 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 56 - 19 = 37. Evaluate 37 != 29, drop this branch.\n     |- Try 56 * 19 = 1064. Evaluate 1064 != 29, drop this branch.\n     |- Try 56 \/ 19 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 35 * 16 = 560. Add 560 to the number set. Current number set: [560, 56], target: 29, just two numbers left.\n     |- Try 560 + 56 = 616. Evaluate 616 != 29, drop this branch.\n     |- Try 560 - 56 = 504. Evaluate 504 != 29, drop this branch.\n     |- Try 560 * 56 = 31360. 31360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 560 \/ 56 = 10. Evaluate 10 != 29, drop this branch.\n    |- Try 35 \/ 16 = 2.2. 2.2 is a decimal, drop this branch.\n  |- Try 8 \/ 7 = 1.1. 1.1 is a decimal, drop this branch.\n |- Pick two numbers (8, 16) (numbers left: [7, 35]). Try possible operations.\n  |- Try 16 + 8 = 24. Add 24 to the number set. Current number set: [24, 7, 35], target: 29. Options for choosing two numbers: [(24, 7), (24, 35), (7, 35)].\n   |- Pick two numbers (24, 7) (numbers left: [35]). Try possible operations.\n    |- Try 24 + 7 = 31. Add 31 to the number set. Current number set: [31, 35], target: 29, just two numbers left.\n     |- Try 35 + 31 = 66. Evaluate 66 != 29, drop this branch.\n     |- Try 35 - 31 = 4. Evaluate 4 != 29, drop this branch.\n     |- Try 35 * 31 = 1085. Evaluate 1085 != 29, drop this branch.\n     |- Try 35 \/ 31 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 24 - 7 = 17. Add 17 to the number set. Current number set: [17, 35], target: 29, just two numbers left.\n     |- Try 35 + 17 = 52. Evaluate 52 != 29, drop this branch.\n     |- Try 35 - 17 = 18. Evaluate 18 != 29, drop this branch.\n     |- Try 35 * 17 = 595. Evaluate 595 != 29, drop this branch.\n     |- Try 35 \/ 17 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 24 * 7 = 168. Add 168 to the number set. Current number set: [168, 35], target: 29, just two numbers left.\n     |- Try 168 + 35 = 203. Evaluate 203 != 29, drop this branch.\n     |- Try 168 - 35 = 133. Evaluate 133 != 29, drop this branch.\n     |- Try 168 * 35 = 5880. 5880 exceeds the maximum intermediate result, drop this branch.\n     |- Try 168 \/ 35 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n   |- Pick two numbers (24, 35) (numbers left: [7]). Try possible operations.\n    |- Try 35 + 24 = 59. Add 59 to the number set. Current number set: [59, 7], target: 29, just two numbers left.\n     |- Try 59 + 7 = 66. Evaluate 66 != 29, drop this branch.\n     |- Try 59 - 7 = 52. Evaluate 52 != 29, drop this branch.\n     |- Try 59 * 7 = 413. Evaluate 413 != 29, drop this branch.\n     |- Try 59 \/ 7 = 8.4. 8.4 is a decimal, drop this branch.\n    |- Try 35 - 24 = 11. Add 11 to the number set. Current number set: [11, 7], target: 29, just two numbers left.\n     |- Try 11 + 7 = 18. Evaluate 18 != 29, drop this branch.\n     |- Try 11 - 7 = 4. Evaluate 4 != 29, drop this branch.\n     |- Try 11 * 7 = 77. Evaluate 77 != 29, drop this branch.\n     |- Try 11 \/ 7 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 35 * 24 = 840. Add 840 to the number set. Current number set: [840, 7], target: 29, just two numbers left.\n     |- Try 840 + 7 = 847. Evaluate 847 != 29, drop this branch.\n     |- Try 840 - 7 = 833. Evaluate 833 != 29, drop this branch.\n     |- Try 840 * 7 = 5880. 5880 exceeds the maximum intermediate result, drop this branch.\n     |- Try 840 \/ 7 = 120. Evaluate 120 != 29, drop this branch.\n    |- Try 35 \/ 24 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (7, 35) (numbers left: [24]). Try possible operations.\n    |- Try 35 + 7 = 42. Add 42 to the number set. Current number set: [42, 24], target: 29, just two numbers left.\n     |- Try 42 + 24 = 66. Evaluate 66 != 29, drop this branch.\n     |- Try 42 - 24 = 18. Evaluate 18 != 29, drop this branch.\n     |- Try 42 * 24 = 1008. Evaluate 1008 != 29, drop this branch.\n     |- Try 42 \/ 24 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 35 - 7 = 28. Add 28 to the number set. Current number set: [28, 24], target: 29, just two numbers left.\n     |- Try 28 + 24 = 52. Evaluate 52 != 29, drop this branch.\n     |- Try 28 - 24 = 4. Evaluate 4 != 29, drop this branch.\n     |- Try 28 * 24 = 672. Evaluate 672 != 29, drop this branch.\n     |- Try 28 \/ 24 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 35 * 7 = 245. Add 245 to the number set. Current number set: [245, 24], target: 29, just two numbers left.\n     |- Try 245 + 24 = 269. Evaluate 269 != 29, drop this branch.\n     |- Try 245 - 24 = 221. Evaluate 221 != 29, drop this branch.\n     |- Try 245 * 24 = 5880. 5880 exceeds the maximum intermediate result, drop this branch.\n     |- Try 245 \/ 24 = 10.2. 10.2 is a decimal, drop this branch.\n    |- Try 35 \/ 7 = 5. Add 5 to the number set. Current number set: [5, 24], target: 29, just two numbers left.\n     |- Try 24 + 5 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 24 + 5 = 29\nThe step before: 35 \/ 7 = 5\nThe first step: 16 + 8 = 24\n\nOutput the solution in the required format:\n<Solution>\n16 + 8 = 24\n35 \/ 7 = 5\n24 + 5 = 29\n<\/Solution>\n","item":{"nums":[8,7,16,35],"solution":["16 + 8 = 24","35 \/ 7 = 5","24 + 5 = 29"],"target":29}}
+{"instance_id":"countdown_8k_13","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [10, 5, 9, 18]\nTarget: 48","reference_output":"# Search Procedure\nInitial number set: [10, 5, 9, 18], target: 48. Options for choosing two numbers: [(10, 5), (10, 9), (10, 18), (5, 9), (5, 18), (9, 18)].\n |- Pick two numbers (10, 5) (numbers left: [9, 18]). Try possible operations.\n  |- Try 10 + 5 = 15. Add 15 to the number set. Current number set: [15, 9, 18], target: 48. Options for choosing two numbers: [(15, 9), (15, 18), (9, 18)].\n   |- Pick two numbers (15, 9) (numbers left: [18]). Try possible operations.\n    |- Try 15 + 9 = 24. Add 24 to the number set. Current number set: [24, 18], target: 48, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 48, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 48, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 48, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 15 - 9 = 6. Add 6 to the number set. Current number set: [6, 18], target: 48, just two numbers left.\n     |- Try 18 + 6 = 24. Evaluate 24 != 48, drop this branch.\n     |- Try 18 - 6 = 12. Evaluate 12 != 48, drop this branch.\n     |- Try 18 * 6 = 108. Evaluate 108 != 48, drop this branch.\n     |- Try 18 \/ 6 = 3. Evaluate 3 != 48, drop this branch.\n    |- Try 15 * 9 = 135. Add 135 to the number set. Current number set: [135, 18], target: 48, just two numbers left.\n     |- Try 135 + 18 = 153. Evaluate 153 != 48, drop this branch.\n     |- Try 135 - 18 = 117. Evaluate 117 != 48, drop this branch.\n     |- Try 135 * 18 = 2430. 2430 exceeds the maximum intermediate result, drop this branch.\n     |- Try 135 \/ 18 = 7.5. 7.5 is a decimal, drop this branch.\n    |- Try 15 \/ 9 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (15, 18) (numbers left: [9]). Try possible operations.\n    |- Try 18 + 15 = 33. Add 33 to the number set. Current number set: [33, 9], target: 48, just two numbers left.\n     |- Try 33 + 9 = 42. Evaluate 42 != 48, drop this branch.\n     |- Try 33 - 9 = 24. Evaluate 24 != 48, drop this branch.\n     |- Try 33 * 9 = 297. Evaluate 297 != 48, drop this branch.\n     |- Try 33 \/ 9 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 18 - 15 = 3. Add 3 to the number set. Current number set: [3, 9], target: 48, just two numbers left.\n     |- Try 9 + 3 = 12. Evaluate 12 != 48, drop this branch.\n     |- Try 9 - 3 = 6. Evaluate 6 != 48, drop this branch.\n     |- Try 9 * 3 = 27. Evaluate 27 != 48, drop this branch.\n     |- Try 9 \/ 3 = 3. Evaluate 3 != 48, drop this branch.\n    |- Try 18 * 15 = 270. Add 270 to the number set. Current number set: [270, 9], target: 48, just two numbers left.\n     |- Try 270 + 9 = 279. Evaluate 279 != 48, drop this branch.\n     |- Try 270 - 9 = 261. Evaluate 261 != 48, drop this branch.\n     |- Try 270 * 9 = 2430. 2430 exceeds the maximum intermediate result, drop this branch.\n     |- Try 270 \/ 9 = 30. Evaluate 30 != 48, drop this branch.\n    |- Try 18 \/ 15 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (9, 18) (numbers left: [15]). Try possible operations.\n    |- Try 18 + 9 = 27. Add 27 to the number set. Current number set: [27, 15], target: 48, just two numbers left.\n     |- Try 27 + 15 = 42. Evaluate 42 != 48, drop this branch.\n     |- Try 27 - 15 = 12. Evaluate 12 != 48, drop this branch.\n     |- Try 27 * 15 = 405. Evaluate 405 != 48, drop this branch.\n     |- Try 27 \/ 15 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 - 9 = 9. Add 9 to the number set. Current number set: [9, 15], target: 48, just two numbers left.\n     |- Try 15 + 9 = 24. Evaluate 24 != 48, drop this branch.\n     |- Try 15 - 9 = 6. Evaluate 6 != 48, drop this branch.\n     |- Try 15 * 9 = 135. Evaluate 135 != 48, drop this branch.\n     |- Try 15 \/ 9 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 9 = 162. Add 162 to the number set. Current number set: [162, 15], target: 48, just two numbers left.\n     |- Try 162 + 15 = 177. Evaluate 177 != 48, drop this branch.\n     |- Try 162 - 15 = 147. Evaluate 147 != 48, drop this branch.\n     |- Try 162 * 15 = 2430. 2430 exceeds the maximum intermediate result, drop this branch.\n     |- Try 162 \/ 15 = 10.8. 10.8 is a decimal, drop this branch.\n    |- Try 18 \/ 9 = 2. Add 2 to the number set. Current number set: [2, 15], target: 48, just two numbers left.\n     |- Try 15 + 2 = 17. Evaluate 17 != 48, drop this branch.\n     |- Try 15 - 2 = 13. Evaluate 13 != 48, drop this branch.\n     |- Try 15 * 2 = 30. Evaluate 30 != 48, drop this branch.\n     |- Try 15 \/ 2 = 7.5. 7.5 is a decimal, drop this branch.\n  |- Try 10 - 5 = 5. Add 5 to the number set. Current number set: [5, 9, 18], target: 48. Options for choosing two numbers: [(5, 9), (5, 18), (9, 18)].\n   |- Pick two numbers (5, 9) (numbers left: [18]). Try possible operations.\n    |- Try 9 + 5 = 14. Add 14 to the number set. Current number set: [14, 18], target: 48, just two numbers left.\n     |- Try 18 + 14 = 32. Evaluate 32 != 48, drop this branch.\n     |- Try 18 - 14 = 4. Evaluate 4 != 48, drop this branch.\n     |- Try 18 * 14 = 252. Evaluate 252 != 48, drop this branch.\n     |- Try 18 \/ 14 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 9 - 5 = 4. Add 4 to the number set. Current number set: [4, 18], target: 48, just two numbers left.\n     |- Try 18 + 4 = 22. Evaluate 22 != 48, drop this branch.\n     |- Try 18 - 4 = 14. Evaluate 14 != 48, drop this branch.\n     |- Try 18 * 4 = 72. Evaluate 72 != 48, drop this branch.\n     |- Try 18 \/ 4 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 9 * 5 = 45. Add 45 to the number set. Current number set: [45, 18], target: 48, just two numbers left.\n     |- Try 45 + 18 = 63. Evaluate 63 != 48, drop this branch.\n     |- Try 45 - 18 = 27. Evaluate 27 != 48, drop this branch.\n     |- Try 45 * 18 = 810. Evaluate 810 != 48, drop this branch.\n     |- Try 45 \/ 18 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 9 \/ 5 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (5, 18) (numbers left: [9]). Try possible operations.\n    |- Try 18 + 5 = 23. Add 23 to the number set. Current number set: [23, 9], target: 48, just two numbers left.\n     |- Try 23 + 9 = 32. Evaluate 32 != 48, drop this branch.\n     |- Try 23 - 9 = 14. Evaluate 14 != 48, drop this branch.\n     |- Try 23 * 9 = 207. Evaluate 207 != 48, drop this branch.\n     |- Try 23 \/ 9 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 18 - 5 = 13. Add 13 to the number set. Current number set: [13, 9], target: 48, just two numbers left.\n     |- Try 13 + 9 = 22. Evaluate 22 != 48, drop this branch.\n     |- Try 13 - 9 = 4. Evaluate 4 != 48, drop this branch.\n     |- Try 13 * 9 = 117. Evaluate 117 != 48, drop this branch.\n     |- Try 13 \/ 9 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 18 * 5 = 90. Add 90 to the number set. Current number set: [90, 9], target: 48, just two numbers left.\n     |- Try 90 + 9 = 99. Evaluate 99 != 48, drop this branch.\n     |- Try 90 - 9 = 81. Evaluate 81 != 48, drop this branch.\n     |- Try 90 * 9 = 810. Evaluate 810 != 48, drop this branch.\n     |- Try 90 \/ 9 = 10. Evaluate 10 != 48, drop this branch.\n    |- Try 18 \/ 5 = 3.6. 3.6 is a decimal, drop this branch.\n   |- Pick two numbers (9, 18) (numbers left: [5]). Try possible operations.\n    |- Try 18 + 9 = 27. Add 27 to the number set. Current number set: [27, 5], target: 48, just two numbers left.\n     |- Try 27 + 5 = 32. Evaluate 32 != 48, drop this branch.\n     |- Try 27 - 5 = 22. Evaluate 22 != 48, drop this branch.\n     |- Try 27 * 5 = 135. Evaluate 135 != 48, drop this branch.\n     |- Try 27 \/ 5 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 18 - 9 = 9. Add 9 to the number set. Current number set: [9, 5], target: 48, just two numbers left.\n     |- Try 9 + 5 = 14. Evaluate 14 != 48, drop this branch.\n     |- Try 9 - 5 = 4. Evaluate 4 != 48, drop this branch.\n     |- Try 9 * 5 = 45. Evaluate 45 != 48, drop this branch.\n     |- Try 9 \/ 5 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 9 = 162. Add 162 to the number set. Current number set: [162, 5], target: 48, just two numbers left.\n     |- Try 162 + 5 = 167. Evaluate 167 != 48, drop this branch.\n     |- Try 162 - 5 = 157. Evaluate 157 != 48, drop this branch.\n     |- Try 162 * 5 = 810. Evaluate 810 != 48, drop this branch.\n     |- Try 162 \/ 5 = 32.4. 32.4 is a decimal, drop this branch.\n    |- Try 18 \/ 9 = 2. Add 2 to the number set. Current number set: [2, 5], target: 48, just two numbers left.\n     |- Try 5 + 2 = 7. Evaluate 7 != 48, drop this branch.\n     |- Try 5 - 2 = 3. Evaluate 3 != 48, drop this branch.\n     |- Try 5 * 2 = 10. Evaluate 10 != 48, drop this branch.\n     |- Try 5 \/ 2 = 2.5. 2.5 is a decimal, drop this branch.\n  |- Try 10 * 5 = 50. Add 50 to the number set. Current number set: [50, 9, 18], target: 48. Options for choosing two numbers: [(50, 9), (50, 18), (9, 18)].\n   |- Pick two numbers (50, 9) (numbers left: [18]). Try possible operations.\n    |- Try 50 + 9 = 59. Add 59 to the number set. Current number set: [59, 18], target: 48, just two numbers left.\n     |- Try 59 + 18 = 77. Evaluate 77 != 48, drop this branch.\n     |- Try 59 - 18 = 41. Evaluate 41 != 48, drop this branch.\n     |- Try 59 * 18 = 1062. Evaluate 1062 != 48, drop this branch.\n     |- Try 59 \/ 18 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 50 - 9 = 41. Add 41 to the number set. Current number set: [41, 18], target: 48, just two numbers left.\n     |- Try 41 + 18 = 59. Evaluate 59 != 48, drop this branch.\n     |- Try 41 - 18 = 23. Evaluate 23 != 48, drop this branch.\n     |- Try 41 * 18 = 738. Evaluate 738 != 48, drop this branch.\n     |- Try 41 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 50 * 9 = 450. Add 450 to the number set. Current number set: [450, 18], target: 48, just two numbers left.\n     |- Try 450 + 18 = 468. Evaluate 468 != 48, drop this branch.\n     |- Try 450 - 18 = 432. Evaluate 432 != 48, drop this branch.\n     |- Try 450 * 18 = 8100. 8100 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 18 = 25. Evaluate 25 != 48, drop this branch.\n    |- Try 50 \/ 9 = 5.6. 5.6 is a decimal, drop this branch.\n   |- Pick two numbers (50, 18) (numbers left: [9]). Try possible operations.\n    |- Try 50 + 18 = 68. Add 68 to the number set. Current number set: [68, 9], target: 48, just two numbers left.\n     |- Try 68 + 9 = 77. Evaluate 77 != 48, drop this branch.\n     |- Try 68 - 9 = 59. Evaluate 59 != 48, drop this branch.\n     |- Try 68 * 9 = 612. Evaluate 612 != 48, drop this branch.\n     |- Try 68 \/ 9 = 7.6. 7.6 is a decimal, drop this branch.\n    |- Try 50 - 18 = 32. Add 32 to the number set. Current number set: [32, 9], target: 48, just two numbers left.\n     |- Try 32 + 9 = 41. Evaluate 41 != 48, drop this branch.\n     |- Try 32 - 9 = 23. Evaluate 23 != 48, drop this branch.\n     |- Try 32 * 9 = 288. Evaluate 288 != 48, drop this branch.\n     |- Try 32 \/ 9 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 50 * 18 = 900. Add 900 to the number set. Current number set: [900, 9], target: 48, just two numbers left.\n     |- Try 900 + 9 = 909. Evaluate 909 != 48, drop this branch.\n     |- Try 900 - 9 = 891. Evaluate 891 != 48, drop this branch.\n     |- Try 900 * 9 = 8100. 8100 exceeds the maximum intermediate result, drop this branch.\n     |- Try 900 \/ 9 = 100. Evaluate 100 != 48, drop this branch.\n    |- Try 50 \/ 18 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (9, 18) (numbers left: [50]). Try possible operations.\n    |- Try 18 + 9 = 27. Add 27 to the number set. Current number set: [27, 50], target: 48, just two numbers left.\n     |- Try 50 + 27 = 77. Evaluate 77 != 48, drop this branch.\n     |- Try 50 - 27 = 23. Evaluate 23 != 48, drop this branch.\n     |- Try 50 * 27 = 1350. Evaluate 1350 != 48, drop this branch.\n     |- Try 50 \/ 27 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 18 - 9 = 9. Add 9 to the number set. Current number set: [9, 50], target: 48, just two numbers left.\n     |- Try 50 + 9 = 59. Evaluate 59 != 48, drop this branch.\n     |- Try 50 - 9 = 41. Evaluate 41 != 48, drop this branch.\n     |- Try 50 * 9 = 450. Evaluate 450 != 48, drop this branch.\n     |- Try 50 \/ 9 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 18 * 9 = 162. Add 162 to the number set. Current number set: [162, 50], target: 48, just two numbers left.\n     |- Try 162 + 50 = 212. Evaluate 212 != 48, drop this branch.\n     |- Try 162 - 50 = 112. Evaluate 112 != 48, drop this branch.\n     |- Try 162 * 50 = 8100. 8100 exceeds the maximum intermediate result, drop this branch.\n     |- Try 162 \/ 50 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 18 \/ 9 = 2. Add 2 to the number set. Current number set: [2, 50], target: 48, just two numbers left.\n     |- Try 50 + 2 = 52. Evaluate 52 != 48, drop this branch.\n     |- Try 50 - 2 = 48. Evaluate 48 == 48, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 50 - 2 = 48\nThe step before: 18 \/ 9 = 2\nThe first step: 10 * 5 = 50\n\nOutput the solution in the required format:\n<Solution>\n10 * 5 = 50\n18 \/ 9 = 2\n50 - 2 = 48\n<\/Solution>\n","item":{"nums":[10,5,9,18],"solution":["10 * 5 = 50","18 \/ 9 = 2","50 - 2 = 48"],"target":48}}
+{"instance_id":"countdown_8k_14","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [28, 7, 45, 8]\nTarget: 49","reference_output":"# Search Procedure\nInitial number set: [28, 7, 45, 8], target: 49. Options for choosing two numbers: [(28, 7), (28, 45), (28, 8), (7, 45), (7, 8), (45, 8)].\n |- Pick two numbers (28, 7) (numbers left: [45, 8]). Try possible operations.\n  |- Try 28 + 7 = 35. Add 35 to the number set. Current number set: [35, 45, 8], target: 49. Options for choosing two numbers: [(35, 45), (35, 8), (45, 8)].\n   |- Pick two numbers (35, 45) (numbers left: [8]). Try possible operations.\n    |- Try 45 + 35 = 80. Add 80 to the number set. Current number set: [80, 8], target: 49, just two numbers left.\n     |- Try 80 + 8 = 88. Evaluate 88 != 49, drop this branch.\n     |- Try 80 - 8 = 72. Evaluate 72 != 49, drop this branch.\n     |- Try 80 * 8 = 640. Evaluate 640 != 49, drop this branch.\n     |- Try 80 \/ 8 = 10. Evaluate 10 != 49, drop this branch.\n    |- Try 45 - 35 = 10. Add 10 to the number set. Current number set: [10, 8], target: 49, just two numbers left.\n     |- Try 10 + 8 = 18. Evaluate 18 != 49, drop this branch.\n     |- Try 10 - 8 = 2. Evaluate 2 != 49, drop this branch.\n     |- Try 10 * 8 = 80. Evaluate 80 != 49, drop this branch.\n     |- Try 10 \/ 8 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 45 * 35 = 1575. Add 1575 to the number set. Current number set: [1575, 8], target: 49, just two numbers left.\n     |- Try 1575 + 8 = 1583. Evaluate 1583 != 49, drop this branch.\n     |- Try 1575 - 8 = 1567. Evaluate 1567 != 49, drop this branch.\n     |- Try 1575 * 8 = 12600. 12600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1575 \/ 8 = 196.9. 196.9 is a decimal, drop this branch.\n    |- Try 45 \/ 35 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (35, 8) (numbers left: [45]). Try possible operations.\n    |- Try 35 + 8 = 43. Add 43 to the number set. Current number set: [43, 45], target: 49, just two numbers left.\n     |- Try 45 + 43 = 88. Evaluate 88 != 49, drop this branch.\n     |- Try 45 - 43 = 2. Evaluate 2 != 49, drop this branch.\n     |- Try 45 * 43 = 1935. Evaluate 1935 != 49, drop this branch.\n     |- Try 45 \/ 43 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 35 - 8 = 27. Add 27 to the number set. Current number set: [27, 45], target: 49, just two numbers left.\n     |- Try 45 + 27 = 72. Evaluate 72 != 49, drop this branch.\n     |- Try 45 - 27 = 18. Evaluate 18 != 49, drop this branch.\n     |- Try 45 * 27 = 1215. Evaluate 1215 != 49, drop this branch.\n     |- Try 45 \/ 27 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 35 * 8 = 280. Add 280 to the number set. Current number set: [280, 45], target: 49, just two numbers left.\n     |- Try 280 + 45 = 325. Evaluate 325 != 49, drop this branch.\n     |- Try 280 - 45 = 235. Evaluate 235 != 49, drop this branch.\n     |- Try 280 * 45 = 12600. 12600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 280 \/ 45 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 35 \/ 8 = 4.4. 4.4 is a decimal, drop this branch.\n   |- Pick two numbers (45, 8) (numbers left: [35]). Try possible operations.\n    |- Try 45 + 8 = 53. Add 53 to the number set. Current number set: [53, 35], target: 49, just two numbers left.\n     |- Try 53 + 35 = 88. Evaluate 88 != 49, drop this branch.\n     |- Try 53 - 35 = 18. Evaluate 18 != 49, drop this branch.\n     |- Try 53 * 35 = 1855. Evaluate 1855 != 49, drop this branch.\n     |- Try 53 \/ 35 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 45 - 8 = 37. Add 37 to the number set. Current number set: [37, 35], target: 49, just two numbers left.\n     |- Try 37 + 35 = 72. Evaluate 72 != 49, drop this branch.\n     |- Try 37 - 35 = 2. Evaluate 2 != 49, drop this branch.\n     |- Try 37 * 35 = 1295. Evaluate 1295 != 49, drop this branch.\n     |- Try 37 \/ 35 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 45 * 8 = 360. Add 360 to the number set. Current number set: [360, 35], target: 49, just two numbers left.\n     |- Try 360 + 35 = 395. Evaluate 395 != 49, drop this branch.\n     |- Try 360 - 35 = 325. Evaluate 325 != 49, drop this branch.\n     |- Try 360 * 35 = 12600. 12600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 360 \/ 35 = 10.3. 10.3 is a decimal, drop this branch.\n    |- Try 45 \/ 8 = 5.6. 5.6 is a decimal, drop this branch.\n  |- Try 28 - 7 = 21. Add 21 to the number set. Current number set: [21, 45, 8], target: 49. Options for choosing two numbers: [(21, 45), (21, 8), (45, 8)].\n   |- Pick two numbers (21, 45) (numbers left: [8]). Try possible operations.\n    |- Try 45 + 21 = 66. Add 66 to the number set. Current number set: [66, 8], target: 49, just two numbers left.\n     |- Try 66 + 8 = 74. Evaluate 74 != 49, drop this branch.\n     |- Try 66 - 8 = 58. Evaluate 58 != 49, drop this branch.\n     |- Try 66 * 8 = 528. Evaluate 528 != 49, drop this branch.\n     |- Try 66 \/ 8 = 8.2. 8.2 is a decimal, drop this branch.\n    |- Try 45 - 21 = 24. Add 24 to the number set. Current number set: [24, 8], target: 49, just two numbers left.\n     |- Try 24 + 8 = 32. Evaluate 32 != 49, drop this branch.\n     |- Try 24 - 8 = 16. Evaluate 16 != 49, drop this branch.\n     |- Try 24 * 8 = 192. Evaluate 192 != 49, drop this branch.\n     |- Try 24 \/ 8 = 3. Evaluate 3 != 49, drop this branch.\n    |- Try 45 * 21 = 945. Add 945 to the number set. Current number set: [945, 8], target: 49, just two numbers left.\n     |- Try 945 + 8 = 953. Evaluate 953 != 49, drop this branch.\n     |- Try 945 - 8 = 937. Evaluate 937 != 49, drop this branch.\n     |- Try 945 * 8 = 7560. 7560 exceeds the maximum intermediate result, drop this branch.\n     |- Try 945 \/ 8 = 118.1. 118.1 is a decimal, drop this branch.\n    |- Try 45 \/ 21 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (21, 8) (numbers left: [45]). Try possible operations.\n    |- Try 21 + 8 = 29. Add 29 to the number set. Current number set: [29, 45], target: 49, just two numbers left.\n     |- Try 45 + 29 = 74. Evaluate 74 != 49, drop this branch.\n     |- Try 45 - 29 = 16. Evaluate 16 != 49, drop this branch.\n     |- Try 45 * 29 = 1305. Evaluate 1305 != 49, drop this branch.\n     |- Try 45 \/ 29 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 21 - 8 = 13. Add 13 to the number set. Current number set: [13, 45], target: 49, just two numbers left.\n     |- Try 45 + 13 = 58. Evaluate 58 != 49, drop this branch.\n     |- Try 45 - 13 = 32. Evaluate 32 != 49, drop this branch.\n     |- Try 45 * 13 = 585. Evaluate 585 != 49, drop this branch.\n     |- Try 45 \/ 13 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 21 * 8 = 168. Add 168 to the number set. Current number set: [168, 45], target: 49, just two numbers left.\n     |- Try 168 + 45 = 213. Evaluate 213 != 49, drop this branch.\n     |- Try 168 - 45 = 123. Evaluate 123 != 49, drop this branch.\n     |- Try 168 * 45 = 7560. 7560 exceeds the maximum intermediate result, drop this branch.\n     |- Try 168 \/ 45 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 21 \/ 8 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (45, 8) (numbers left: [21]). Try possible operations.\n    |- Try 45 + 8 = 53. Add 53 to the number set. Current number set: [53, 21], target: 49, just two numbers left.\n     |- Try 53 + 21 = 74. Evaluate 74 != 49, drop this branch.\n     |- Try 53 - 21 = 32. Evaluate 32 != 49, drop this branch.\n     |- Try 53 * 21 = 1113. Evaluate 1113 != 49, drop this branch.\n     |- Try 53 \/ 21 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 45 - 8 = 37. Add 37 to the number set. Current number set: [37, 21], target: 49, just two numbers left.\n     |- Try 37 + 21 = 58. Evaluate 58 != 49, drop this branch.\n     |- Try 37 - 21 = 16. Evaluate 16 != 49, drop this branch.\n     |- Try 37 * 21 = 777. Evaluate 777 != 49, drop this branch.\n     |- Try 37 \/ 21 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 45 * 8 = 360. Add 360 to the number set. Current number set: [360, 21], target: 49, just two numbers left.\n     |- Try 360 + 21 = 381. Evaluate 381 != 49, drop this branch.\n     |- Try 360 - 21 = 339. Evaluate 339 != 49, drop this branch.\n     |- Try 360 * 21 = 7560. 7560 exceeds the maximum intermediate result, drop this branch.\n     |- Try 360 \/ 21 = 17.1. 17.1 is a decimal, drop this branch.\n    |- Try 45 \/ 8 = 5.6. 5.6 is a decimal, drop this branch.\n  |- Try 28 * 7 = 196. Add 196 to the number set. Current number set: [196, 45, 8], target: 49. Options for choosing two numbers: [(196, 45), (196, 8), (45, 8)].\n   |- Pick two numbers (196, 45) (numbers left: [8]). Try possible operations.\n    |- Try 196 + 45 = 241. Add 241 to the number set. Current number set: [241, 8], target: 49, just two numbers left.\n     |- Try 241 + 8 = 249. Evaluate 249 != 49, drop this branch.\n     |- Try 241 - 8 = 233. Evaluate 233 != 49, drop this branch.\n     |- Try 241 * 8 = 1928. Evaluate 1928 != 49, drop this branch.\n     |- Try 241 \/ 8 = 30.1. 30.1 is a decimal, drop this branch.\n    |- Try 196 - 45 = 151. Add 151 to the number set. Current number set: [151, 8], target: 49, just two numbers left.\n     |- Try 151 + 8 = 159. Evaluate 159 != 49, drop this branch.\n     |- Try 151 - 8 = 143. Evaluate 143 != 49, drop this branch.\n     |- Try 151 * 8 = 1208. Evaluate 1208 != 49, drop this branch.\n     |- Try 151 \/ 8 = 18.9. 18.9 is a decimal, drop this branch.\n    |- Try 196 * 45 = 8820. 8820 exceeds the maximum intermediate result, drop this branch.\n    |- Try 196 \/ 45 = 4.4. 4.4 is a decimal, drop this branch.\n   |- Pick two numbers (196, 8) (numbers left: [45]). Try possible operations.\n    |- Try 196 + 8 = 204. Add 204 to the number set. Current number set: [204, 45], target: 49, just two numbers left.\n     |- Try 204 + 45 = 249. Evaluate 249 != 49, drop this branch.\n     |- Try 204 - 45 = 159. Evaluate 159 != 49, drop this branch.\n     |- Try 204 * 45 = 9180. 9180 exceeds the maximum intermediate result, drop this branch.\n     |- Try 204 \/ 45 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 196 - 8 = 188. Add 188 to the number set. Current number set: [188, 45], target: 49, just two numbers left.\n     |- Try 188 + 45 = 233. Evaluate 233 != 49, drop this branch.\n     |- Try 188 - 45 = 143. Evaluate 143 != 49, drop this branch.\n     |- Try 188 * 45 = 8460. 8460 exceeds the maximum intermediate result, drop this branch.\n     |- Try 188 \/ 45 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 196 * 8 = 1568. Add 1568 to the number set. Current number set: [1568, 45], target: 49, just two numbers left.\n     |- Try 1568 + 45 = 1613. Evaluate 1613 != 49, drop this branch.\n     |- Try 1568 - 45 = 1523. Evaluate 1523 != 49, drop this branch.\n     |- Try 1568 * 45 = 70560. 70560 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1568 \/ 45 = 34.8. 34.8 is a decimal, drop this branch.\n    |- Try 196 \/ 8 = 24.5. 24.5 is a decimal, drop this branch.\n   |- Pick two numbers (45, 8) (numbers left: [196]). Try possible operations.\n    |- Try 45 + 8 = 53. Add 53 to the number set. Current number set: [53, 196], target: 49, just two numbers left.\n     |- Try 196 + 53 = 249. Evaluate 249 != 49, drop this branch.\n     |- Try 196 - 53 = 143. Evaluate 143 != 49, drop this branch.\n     |- Try 196 * 53 = 10388. 10388 exceeds the maximum intermediate result, drop this branch.\n     |- Try 196 \/ 53 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 45 - 8 = 37. Add 37 to the number set. Current number set: [37, 196], target: 49, just two numbers left.\n     |- Try 196 + 37 = 233. Evaluate 233 != 49, drop this branch.\n     |- Try 196 - 37 = 159. Evaluate 159 != 49, drop this branch.\n     |- Try 196 * 37 = 7252. 7252 exceeds the maximum intermediate result, drop this branch.\n     |- Try 196 \/ 37 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 45 * 8 = 360. Add 360 to the number set. Current number set: [360, 196], target: 49, just two numbers left.\n     |- Try 360 + 196 = 556. Evaluate 556 != 49, drop this branch.\n     |- Try 360 - 196 = 164. Evaluate 164 != 49, drop this branch.\n     |- Try 360 * 196 = 70560. 70560 exceeds the maximum intermediate result, drop this branch.\n     |- Try 360 \/ 196 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 45 \/ 8 = 5.6. 5.6 is a decimal, drop this branch.\n  |- Try 28 \/ 7 = 4. Add 4 to the number set. Current number set: [4, 45, 8], target: 49. Options for choosing two numbers: [(4, 45), (4, 8), (45, 8)].\n   |- Pick two numbers (4, 45) (numbers left: [8]). Try possible operations.\n    |- Try 45 + 4 = 49. Add 49 to the number set. Current number set: [49, 8], target: 49, just two numbers left.\n     |- Try 49 + 8 = 57. Evaluate 57 != 49, drop this branch.\n     |- Try 49 - 8 = 41. Evaluate 41 != 49, drop this branch.\n     |- Try 49 * 8 = 392. Evaluate 392 != 49, drop this branch.\n     |- Try 49 \/ 8 = 6.1. 6.1 is a decimal, drop this branch.\n    |- Try 45 - 4 = 41. Add 41 to the number set. Current number set: [41, 8], target: 49, just two numbers left.\n     |- Try 41 + 8 = 49. Evaluate 49 == 49, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 41 + 8 = 49\nThe step before: 45 - 4 = 41\nThe first step: 28 \/ 7 = 4\n\nOutput the solution in the required format:\n<Solution>\n28 \/ 7 = 4\n45 - 4 = 41\n41 + 8 = 49\n<\/Solution>\n","item":{"nums":[28,7,45,8],"solution":["28 \/ 7 = 4","45 - 4 = 41","41 + 8 = 49"],"target":49}}
+{"instance_id":"countdown_8k_15","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [9, 36, 4, 38]\nTarget: 37","reference_output":"# Search Procedure\nInitial number set: [9, 36, 4, 38], target: 37. Options for choosing two numbers: [(9, 36), (9, 4), (9, 38), (36, 4), (36, 38), (4, 38)].\n |- Pick two numbers (9, 36) (numbers left: [4, 38]). Try possible operations.\n  |- Try 36 + 9 = 45. Add 45 to the number set. Current number set: [45, 4, 38], target: 37. Options for choosing two numbers: [(45, 4), (45, 38), (4, 38)].\n   |- Pick two numbers (45, 4) (numbers left: [38]). Try possible operations.\n    |- Try 45 + 4 = 49. Add 49 to the number set. Current number set: [49, 38], target: 37, just two numbers left.\n     |- Try 49 + 38 = 87. Evaluate 87 != 37, drop this branch.\n     |- Try 49 - 38 = 11. Evaluate 11 != 37, drop this branch.\n     |- Try 49 * 38 = 1862. Evaluate 1862 != 37, drop this branch.\n     |- Try 49 \/ 38 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 45 - 4 = 41. Add 41 to the number set. Current number set: [41, 38], target: 37, just two numbers left.\n     |- Try 41 + 38 = 79. Evaluate 79 != 37, drop this branch.\n     |- Try 41 - 38 = 3. Evaluate 3 != 37, drop this branch.\n     |- Try 41 * 38 = 1558. Evaluate 1558 != 37, drop this branch.\n     |- Try 41 \/ 38 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 45 * 4 = 180. Add 180 to the number set. Current number set: [180, 38], target: 37, just two numbers left.\n     |- Try 180 + 38 = 218. Evaluate 218 != 37, drop this branch.\n     |- Try 180 - 38 = 142. Evaluate 142 != 37, drop this branch.\n     |- Try 180 * 38 = 6840. 6840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 180 \/ 38 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 45 \/ 4 = 11.2. 11.2 is a decimal, drop this branch.\n   |- Pick two numbers (45, 38) (numbers left: [4]). Try possible operations.\n    |- Try 45 + 38 = 83. Add 83 to the number set. Current number set: [83, 4], target: 37, just two numbers left.\n     |- Try 83 + 4 = 87. Evaluate 87 != 37, drop this branch.\n     |- Try 83 - 4 = 79. Evaluate 79 != 37, drop this branch.\n     |- Try 83 * 4 = 332. Evaluate 332 != 37, drop this branch.\n     |- Try 83 \/ 4 = 20.8. 20.8 is a decimal, drop this branch.\n    |- Try 45 - 38 = 7. Add 7 to the number set. Current number set: [7, 4], target: 37, just two numbers left.\n     |- Try 7 + 4 = 11. Evaluate 11 != 37, drop this branch.\n     |- Try 7 - 4 = 3. Evaluate 3 != 37, drop this branch.\n     |- Try 7 * 4 = 28. Evaluate 28 != 37, drop this branch.\n     |- Try 7 \/ 4 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 45 * 38 = 1710. Add 1710 to the number set. Current number set: [1710, 4], target: 37, just two numbers left.\n     |- Try 1710 + 4 = 1714. Evaluate 1714 != 37, drop this branch.\n     |- Try 1710 - 4 = 1706. Evaluate 1706 != 37, drop this branch.\n     |- Try 1710 * 4 = 6840. 6840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1710 \/ 4 = 427.5. 427.5 is a decimal, drop this branch.\n    |- Try 45 \/ 38 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (4, 38) (numbers left: [45]). Try possible operations.\n    |- Try 38 + 4 = 42. Add 42 to the number set. Current number set: [42, 45], target: 37, just two numbers left.\n     |- Try 45 + 42 = 87. Evaluate 87 != 37, drop this branch.\n     |- Try 45 - 42 = 3. Evaluate 3 != 37, drop this branch.\n     |- Try 45 * 42 = 1890. Evaluate 1890 != 37, drop this branch.\n     |- Try 45 \/ 42 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 38 - 4 = 34. Add 34 to the number set. Current number set: [34, 45], target: 37, just two numbers left.\n     |- Try 45 + 34 = 79. Evaluate 79 != 37, drop this branch.\n     |- Try 45 - 34 = 11. Evaluate 11 != 37, drop this branch.\n     |- Try 45 * 34 = 1530. Evaluate 1530 != 37, drop this branch.\n     |- Try 45 \/ 34 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 38 * 4 = 152. Add 152 to the number set. Current number set: [152, 45], target: 37, just two numbers left.\n     |- Try 152 + 45 = 197. Evaluate 197 != 37, drop this branch.\n     |- Try 152 - 45 = 107. Evaluate 107 != 37, drop this branch.\n     |- Try 152 * 45 = 6840. 6840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 152 \/ 45 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 38 \/ 4 = 9.5. 9.5 is a decimal, drop this branch.\n  |- Try 36 - 9 = 27. Add 27 to the number set. Current number set: [27, 4, 38], target: 37. Options for choosing two numbers: [(27, 4), (27, 38), (4, 38)].\n   |- Pick two numbers (27, 4) (numbers left: [38]). Try possible operations.\n    |- Try 27 + 4 = 31. Add 31 to the number set. Current number set: [31, 38], target: 37, just two numbers left.\n     |- Try 38 + 31 = 69. Evaluate 69 != 37, drop this branch.\n     |- Try 38 - 31 = 7. Evaluate 7 != 37, drop this branch.\n     |- Try 38 * 31 = 1178. Evaluate 1178 != 37, drop this branch.\n     |- Try 38 \/ 31 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 27 - 4 = 23. Add 23 to the number set. Current number set: [23, 38], target: 37, just two numbers left.\n     |- Try 38 + 23 = 61. Evaluate 61 != 37, drop this branch.\n     |- Try 38 - 23 = 15. Evaluate 15 != 37, drop this branch.\n     |- Try 38 * 23 = 874. Evaluate 874 != 37, drop this branch.\n     |- Try 38 \/ 23 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 27 * 4 = 108. Add 108 to the number set. Current number set: [108, 38], target: 37, just two numbers left.\n     |- Try 108 + 38 = 146. Evaluate 146 != 37, drop this branch.\n     |- Try 108 - 38 = 70. Evaluate 70 != 37, drop this branch.\n     |- Try 108 * 38 = 4104. 4104 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 38 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 27 \/ 4 = 6.8. 6.8 is a decimal, drop this branch.\n   |- Pick two numbers (27, 38) (numbers left: [4]). Try possible operations.\n    |- Try 38 + 27 = 65. Add 65 to the number set. Current number set: [65, 4], target: 37, just two numbers left.\n     |- Try 65 + 4 = 69. Evaluate 69 != 37, drop this branch.\n     |- Try 65 - 4 = 61. Evaluate 61 != 37, drop this branch.\n     |- Try 65 * 4 = 260. Evaluate 260 != 37, drop this branch.\n     |- Try 65 \/ 4 = 16.2. 16.2 is a decimal, drop this branch.\n    |- Try 38 - 27 = 11. Add 11 to the number set. Current number set: [11, 4], target: 37, just two numbers left.\n     |- Try 11 + 4 = 15. Evaluate 15 != 37, drop this branch.\n     |- Try 11 - 4 = 7. Evaluate 7 != 37, drop this branch.\n     |- Try 11 * 4 = 44. Evaluate 44 != 37, drop this branch.\n     |- Try 11 \/ 4 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 38 * 27 = 1026. Add 1026 to the number set. Current number set: [1026, 4], target: 37, just two numbers left.\n     |- Try 1026 + 4 = 1030. Evaluate 1030 != 37, drop this branch.\n     |- Try 1026 - 4 = 1022. Evaluate 1022 != 37, drop this branch.\n     |- Try 1026 * 4 = 4104. 4104 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1026 \/ 4 = 256.5. 256.5 is a decimal, drop this branch.\n    |- Try 38 \/ 27 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (4, 38) (numbers left: [27]). Try possible operations.\n    |- Try 38 + 4 = 42. Add 42 to the number set. Current number set: [42, 27], target: 37, just two numbers left.\n     |- Try 42 + 27 = 69. Evaluate 69 != 37, drop this branch.\n     |- Try 42 - 27 = 15. Evaluate 15 != 37, drop this branch.\n     |- Try 42 * 27 = 1134. Evaluate 1134 != 37, drop this branch.\n     |- Try 42 \/ 27 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 38 - 4 = 34. Add 34 to the number set. Current number set: [34, 27], target: 37, just two numbers left.\n     |- Try 34 + 27 = 61. Evaluate 61 != 37, drop this branch.\n     |- Try 34 - 27 = 7. Evaluate 7 != 37, drop this branch.\n     |- Try 34 * 27 = 918. Evaluate 918 != 37, drop this branch.\n     |- Try 34 \/ 27 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 38 * 4 = 152. Add 152 to the number set. Current number set: [152, 27], target: 37, just two numbers left.\n     |- Try 152 + 27 = 179. Evaluate 179 != 37, drop this branch.\n     |- Try 152 - 27 = 125. Evaluate 125 != 37, drop this branch.\n     |- Try 152 * 27 = 4104. 4104 exceeds the maximum intermediate result, drop this branch.\n     |- Try 152 \/ 27 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 38 \/ 4 = 9.5. 9.5 is a decimal, drop this branch.\n  |- Try 36 * 9 = 324. Add 324 to the number set. Current number set: [324, 4, 38], target: 37. Options for choosing two numbers: [(324, 4), (324, 38), (4, 38)].\n   |- Pick two numbers (324, 4) (numbers left: [38]). Try possible operations.\n    |- Try 324 + 4 = 328. Add 328 to the number set. Current number set: [328, 38], target: 37, just two numbers left.\n     |- Try 328 + 38 = 366. Evaluate 366 != 37, drop this branch.\n     |- Try 328 - 38 = 290. Evaluate 290 != 37, drop this branch.\n     |- Try 328 * 38 = 12464. 12464 exceeds the maximum intermediate result, drop this branch.\n     |- Try 328 \/ 38 = 8.6. 8.6 is a decimal, drop this branch.\n    |- Try 324 - 4 = 320. Add 320 to the number set. Current number set: [320, 38], target: 37, just two numbers left.\n     |- Try 320 + 38 = 358. Evaluate 358 != 37, drop this branch.\n     |- Try 320 - 38 = 282. Evaluate 282 != 37, drop this branch.\n     |- Try 320 * 38 = 12160. 12160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 320 \/ 38 = 8.4. 8.4 is a decimal, drop this branch.\n    |- Try 324 * 4 = 1296. Add 1296 to the number set. Current number set: [1296, 38], target: 37, just two numbers left.\n     |- Try 1296 + 38 = 1334. Evaluate 1334 != 37, drop this branch.\n     |- Try 1296 - 38 = 1258. Evaluate 1258 != 37, drop this branch.\n     |- Try 1296 * 38 = 49248. 49248 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1296 \/ 38 = 34.1. 34.1 is a decimal, drop this branch.\n    |- Try 324 \/ 4 = 81. Add 81 to the number set. Current number set: [81, 38], target: 37, just two numbers left.\n     |- Try 81 + 38 = 119. Evaluate 119 != 37, drop this branch.\n     |- Try 81 - 38 = 43. Evaluate 43 != 37, drop this branch.\n     |- Try 81 * 38 = 3078. 3078 exceeds the maximum intermediate result, drop this branch.\n     |- Try 81 \/ 38 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (324, 38) (numbers left: [4]). Try possible operations.\n    |- Try 324 + 38 = 362. Add 362 to the number set. Current number set: [362, 4], target: 37, just two numbers left.\n     |- Try 362 + 4 = 366. Evaluate 366 != 37, drop this branch.\n     |- Try 362 - 4 = 358. Evaluate 358 != 37, drop this branch.\n     |- Try 362 * 4 = 1448. Evaluate 1448 != 37, drop this branch.\n     |- Try 362 \/ 4 = 90.5. 90.5 is a decimal, drop this branch.\n    |- Try 324 - 38 = 286. Add 286 to the number set. Current number set: [286, 4], target: 37, just two numbers left.\n     |- Try 286 + 4 = 290. Evaluate 290 != 37, drop this branch.\n     |- Try 286 - 4 = 282. Evaluate 282 != 37, drop this branch.\n     |- Try 286 * 4 = 1144. Evaluate 1144 != 37, drop this branch.\n     |- Try 286 \/ 4 = 71.5. 71.5 is a decimal, drop this branch.\n    |- Try 324 * 38 = 12312. 12312 exceeds the maximum intermediate result, drop this branch.\n    |- Try 324 \/ 38 = 8.5. 8.5 is a decimal, drop this branch.\n   |- Pick two numbers (4, 38) (numbers left: [324]). Try possible operations.\n    |- Try 38 + 4 = 42. Add 42 to the number set. Current number set: [42, 324], target: 37, just two numbers left.\n     |- Try 324 + 42 = 366. Evaluate 366 != 37, drop this branch.\n     |- Try 324 - 42 = 282. Evaluate 282 != 37, drop this branch.\n     |- Try 324 * 42 = 13608. 13608 exceeds the maximum intermediate result, drop this branch.\n     |- Try 324 \/ 42 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 38 - 4 = 34. Add 34 to the number set. Current number set: [34, 324], target: 37, just two numbers left.\n     |- Try 324 + 34 = 358. Evaluate 358 != 37, drop this branch.\n     |- Try 324 - 34 = 290. Evaluate 290 != 37, drop this branch.\n     |- Try 324 * 34 = 11016. 11016 exceeds the maximum intermediate result, drop this branch.\n     |- Try 324 \/ 34 = 9.5. 9.5 is a decimal, drop this branch.\n    |- Try 38 * 4 = 152. Add 152 to the number set. Current number set: [152, 324], target: 37, just two numbers left.\n     |- Try 324 + 152 = 476. Evaluate 476 != 37, drop this branch.\n     |- Try 324 - 152 = 172. Evaluate 172 != 37, drop this branch.\n     |- Try 324 * 152 = 49248. 49248 exceeds the maximum intermediate result, drop this branch.\n     |- Try 324 \/ 152 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 38 \/ 4 = 9.5. 9.5 is a decimal, drop this branch.\n  |- Try 36 \/ 9 = 4. Add 4 to the number set. Current number set: [4, 4, 38], target: 37. Options for choosing two numbers: [(4, 4), (4, 38), (4, 38)].\n   |- Pick two numbers (4, 4) (numbers left: [38]). Try possible operations.\n    |- Try 4 + 4 = 8. Add 8 to the number set. Current number set: [8, 38], target: 37, just two numbers left.\n     |- Try 38 + 8 = 46. Evaluate 46 != 37, drop this branch.\n     |- Try 38 - 8 = 30. Evaluate 30 != 37, drop this branch.\n     |- Try 38 * 8 = 304. Evaluate 304 != 37, drop this branch.\n     |- Try 38 \/ 8 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 4 - 4 = 0. Add 0 to the number set. Current number set: [0, 38], target: 37, just two numbers left.\n     |- Try 38 + 0 = 38. Evaluate 38 != 37, drop this branch.\n     |- Try 38 - 0 = 38. Evaluate 38 != 37, drop this branch.\n     |- Try 38 * 0 = 0. Evaluate 0 != 37, drop this branch.\n     |- Try 38 \/ 0 (invalid operation). drop this branch.\n    |- Try 4 * 4 = 16. Add 16 to the number set. Current number set: [16, 38], target: 37, just two numbers left.\n     |- Try 38 + 16 = 54. Evaluate 54 != 37, drop this branch.\n     |- Try 38 - 16 = 22. Evaluate 22 != 37, drop this branch.\n     |- Try 38 * 16 = 608. Evaluate 608 != 37, drop this branch.\n     |- Try 38 \/ 16 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 4 \/ 4 = 1. Add 1 to the number set. Current number set: [1, 38], target: 37, just two numbers left.\n     |- Try 38 + 1 = 39. Evaluate 39 != 37, drop this branch.\n     |- Try 38 - 1 = 37. Evaluate 37 == 37, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 38 - 1 = 37\nThe step before: 4 \/ 4 = 1\nThe first step: 36 \/ 9 = 4\n\nOutput the solution in the required format:\n<Solution>\n36 \/ 9 = 4\n4 \/ 4 = 1\n38 - 1 = 37\n<\/Solution>\n","item":{"nums":[9,36,4,38],"solution":["36 \/ 9 = 4","4 \/ 4 = 1","38 - 1 = 37"],"target":37}}
+{"instance_id":"countdown_8k_16","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [14, 20, 14, 9]\nTarget: 24","reference_output":"# Search Procedure\nInitial number set: [14, 20, 14, 9], target: 24. Options for choosing two numbers: [(14, 20), (14, 14), (14, 9), (20, 14), (20, 9), (14, 9)].\n |- Pick two numbers (14, 20) (numbers left: [14, 9]). Try possible operations.\n  |- Try 20 + 14 = 34. Add 34 to the number set. Current number set: [34, 14, 9], target: 24. Options for choosing two numbers: [(34, 14), (34, 9), (14, 9)].\n   |- Pick two numbers (34, 14) (numbers left: [9]). Try possible operations.\n    |- Try 34 + 14 = 48. Add 48 to the number set. Current number set: [48, 9], target: 24, just two numbers left.\n     |- Try 48 + 9 = 57. Evaluate 57 != 24, drop this branch.\n     |- Try 48 - 9 = 39. Evaluate 39 != 24, drop this branch.\n     |- Try 48 * 9 = 432. Evaluate 432 != 24, drop this branch.\n     |- Try 48 \/ 9 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 34 - 14 = 20. Add 20 to the number set. Current number set: [20, 9], target: 24, just two numbers left.\n     |- Try 20 + 9 = 29. Evaluate 29 != 24, drop this branch.\n     |- Try 20 - 9 = 11. Evaluate 11 != 24, drop this branch.\n     |- Try 20 * 9 = 180. Evaluate 180 != 24, drop this branch.\n     |- Try 20 \/ 9 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 34 * 14 = 476. Add 476 to the number set. Current number set: [476, 9], target: 24, just two numbers left.\n     |- Try 476 + 9 = 485. Evaluate 485 != 24, drop this branch.\n     |- Try 476 - 9 = 467. Evaluate 467 != 24, drop this branch.\n     |- Try 476 * 9 = 4284. 4284 exceeds the maximum intermediate result, drop this branch.\n     |- Try 476 \/ 9 = 52.9. 52.9 is a decimal, drop this branch.\n    |- Try 34 \/ 14 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (34, 9) (numbers left: [14]). Try possible operations.\n    |- Try 34 + 9 = 43. Add 43 to the number set. Current number set: [43, 14], target: 24, just two numbers left.\n     |- Try 43 + 14 = 57. Evaluate 57 != 24, drop this branch.\n     |- Try 43 - 14 = 29. Evaluate 29 != 24, drop this branch.\n     |- Try 43 * 14 = 602. Evaluate 602 != 24, drop this branch.\n     |- Try 43 \/ 14 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 34 - 9 = 25. Add 25 to the number set. Current number set: [25, 14], target: 24, just two numbers left.\n     |- Try 25 + 14 = 39. Evaluate 39 != 24, drop this branch.\n     |- Try 25 - 14 = 11. Evaluate 11 != 24, drop this branch.\n     |- Try 25 * 14 = 350. Evaluate 350 != 24, drop this branch.\n     |- Try 25 \/ 14 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 34 * 9 = 306. Add 306 to the number set. Current number set: [306, 14], target: 24, just two numbers left.\n     |- Try 306 + 14 = 320. Evaluate 320 != 24, drop this branch.\n     |- Try 306 - 14 = 292. Evaluate 292 != 24, drop this branch.\n     |- Try 306 * 14 = 4284. 4284 exceeds the maximum intermediate result, drop this branch.\n     |- Try 306 \/ 14 = 21.9. 21.9 is a decimal, drop this branch.\n    |- Try 34 \/ 9 = 3.8. 3.8 is a decimal, drop this branch.\n   |- Pick two numbers (14, 9) (numbers left: [34]). Try possible operations.\n    |- Try 14 + 9 = 23. Add 23 to the number set. Current number set: [23, 34], target: 24, just two numbers left.\n     |- Try 34 + 23 = 57. Evaluate 57 != 24, drop this branch.\n     |- Try 34 - 23 = 11. Evaluate 11 != 24, drop this branch.\n     |- Try 34 * 23 = 782. Evaluate 782 != 24, drop this branch.\n     |- Try 34 \/ 23 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 14 - 9 = 5. Add 5 to the number set. Current number set: [5, 34], target: 24, just two numbers left.\n     |- Try 34 + 5 = 39. Evaluate 39 != 24, drop this branch.\n     |- Try 34 - 5 = 29. Evaluate 29 != 24, drop this branch.\n     |- Try 34 * 5 = 170. Evaluate 170 != 24, drop this branch.\n     |- Try 34 \/ 5 = 6.8. 6.8 is a decimal, drop this branch.\n    |- Try 14 * 9 = 126. Add 126 to the number set. Current number set: [126, 34], target: 24, just two numbers left.\n     |- Try 126 + 34 = 160. Evaluate 160 != 24, drop this branch.\n     |- Try 126 - 34 = 92. Evaluate 92 != 24, drop this branch.\n     |- Try 126 * 34 = 4284. 4284 exceeds the maximum intermediate result, drop this branch.\n     |- Try 126 \/ 34 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 14 \/ 9 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 20 - 14 = 6. Add 6 to the number set. Current number set: [6, 14, 9], target: 24. Options for choosing two numbers: [(6, 14), (6, 9), (14, 9)].\n   |- Pick two numbers (6, 14) (numbers left: [9]). Try possible operations.\n    |- Try 14 + 6 = 20. Add 20 to the number set. Current number set: [20, 9], target: 24, just two numbers left.\n     |- Try 20 + 9 = 29. Evaluate 29 != 24, drop this branch.\n     |- Try 20 - 9 = 11. Evaluate 11 != 24, drop this branch.\n     |- Try 20 * 9 = 180. Evaluate 180 != 24, drop this branch.\n     |- Try 20 \/ 9 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 14 - 6 = 8. Add 8 to the number set. Current number set: [8, 9], target: 24, just two numbers left.\n     |- Try 9 + 8 = 17. Evaluate 17 != 24, drop this branch.\n     |- Try 9 - 8 = 1. Evaluate 1 != 24, drop this branch.\n     |- Try 9 * 8 = 72. Evaluate 72 != 24, drop this branch.\n     |- Try 9 \/ 8 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 14 * 6 = 84. Add 84 to the number set. Current number set: [84, 9], target: 24, just two numbers left.\n     |- Try 84 + 9 = 93. Evaluate 93 != 24, drop this branch.\n     |- Try 84 - 9 = 75. Evaluate 75 != 24, drop this branch.\n     |- Try 84 * 9 = 756. Evaluate 756 != 24, drop this branch.\n     |- Try 84 \/ 9 = 9.3. 9.3 is a decimal, drop this branch.\n    |- Try 14 \/ 6 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 9) (numbers left: [14]). Try possible operations.\n    |- Try 9 + 6 = 15. Add 15 to the number set. Current number set: [15, 14], target: 24, just two numbers left.\n     |- Try 15 + 14 = 29. Evaluate 29 != 24, drop this branch.\n     |- Try 15 - 14 = 1. Evaluate 1 != 24, drop this branch.\n     |- Try 15 * 14 = 210. Evaluate 210 != 24, drop this branch.\n     |- Try 15 \/ 14 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 9 - 6 = 3. Add 3 to the number set. Current number set: [3, 14], target: 24, just two numbers left.\n     |- Try 14 + 3 = 17. Evaluate 17 != 24, drop this branch.\n     |- Try 14 - 3 = 11. Evaluate 11 != 24, drop this branch.\n     |- Try 14 * 3 = 42. Evaluate 42 != 24, drop this branch.\n     |- Try 14 \/ 3 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 9 * 6 = 54. Add 54 to the number set. Current number set: [54, 14], target: 24, just two numbers left.\n     |- Try 54 + 14 = 68. Evaluate 68 != 24, drop this branch.\n     |- Try 54 - 14 = 40. Evaluate 40 != 24, drop this branch.\n     |- Try 54 * 14 = 756. Evaluate 756 != 24, drop this branch.\n     |- Try 54 \/ 14 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 9 \/ 6 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (14, 9) (numbers left: [6]). Try possible operations.\n    |- Try 14 + 9 = 23. Add 23 to the number set. Current number set: [23, 6], target: 24, just two numbers left.\n     |- Try 23 + 6 = 29. Evaluate 29 != 24, drop this branch.\n     |- Try 23 - 6 = 17. Evaluate 17 != 24, drop this branch.\n     |- Try 23 * 6 = 138. Evaluate 138 != 24, drop this branch.\n     |- Try 23 \/ 6 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 14 - 9 = 5. Add 5 to the number set. Current number set: [5, 6], target: 24, just two numbers left.\n     |- Try 6 + 5 = 11. Evaluate 11 != 24, drop this branch.\n     |- Try 6 - 5 = 1. Evaluate 1 != 24, drop this branch.\n     |- Try 6 * 5 = 30. Evaluate 30 != 24, drop this branch.\n     |- Try 6 \/ 5 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 14 * 9 = 126. Add 126 to the number set. Current number set: [126, 6], target: 24, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 24, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 24, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 24, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 24, drop this branch.\n    |- Try 14 \/ 9 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 20 * 14 = 280. Add 280 to the number set. Current number set: [280, 14, 9], target: 24. Options for choosing two numbers: [(280, 14), (280, 9), (14, 9)].\n   |- Pick two numbers (280, 14) (numbers left: [9]). Try possible operations.\n    |- Try 280 + 14 = 294. Add 294 to the number set. Current number set: [294, 9], target: 24, just two numbers left.\n     |- Try 294 + 9 = 303. Evaluate 303 != 24, drop this branch.\n     |- Try 294 - 9 = 285. Evaluate 285 != 24, drop this branch.\n     |- Try 294 * 9 = 2646. 2646 exceeds the maximum intermediate result, drop this branch.\n     |- Try 294 \/ 9 = 32.7. 32.7 is a decimal, drop this branch.\n    |- Try 280 - 14 = 266. Add 266 to the number set. Current number set: [266, 9], target: 24, just two numbers left.\n     |- Try 266 + 9 = 275. Evaluate 275 != 24, drop this branch.\n     |- Try 266 - 9 = 257. Evaluate 257 != 24, drop this branch.\n     |- Try 266 * 9 = 2394. 2394 exceeds the maximum intermediate result, drop this branch.\n     |- Try 266 \/ 9 = 29.6. 29.6 is a decimal, drop this branch.\n    |- Try 280 * 14 = 3920. 3920 exceeds the maximum intermediate result, drop this branch.\n    |- Try 280 \/ 14 = 20. Add 20 to the number set. Current number set: [20, 9], target: 24, just two numbers left.\n     |- Try 20 + 9 = 29. Evaluate 29 != 24, drop this branch.\n     |- Try 20 - 9 = 11. Evaluate 11 != 24, drop this branch.\n     |- Try 20 * 9 = 180. Evaluate 180 != 24, drop this branch.\n     |- Try 20 \/ 9 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (280, 9) (numbers left: [14]). Try possible operations.\n    |- Try 280 + 9 = 289. Add 289 to the number set. Current number set: [289, 14], target: 24, just two numbers left.\n     |- Try 289 + 14 = 303. Evaluate 303 != 24, drop this branch.\n     |- Try 289 - 14 = 275. Evaluate 275 != 24, drop this branch.\n     |- Try 289 * 14 = 4046. 4046 exceeds the maximum intermediate result, drop this branch.\n     |- Try 289 \/ 14 = 20.6. 20.6 is a decimal, drop this branch.\n    |- Try 280 - 9 = 271. Add 271 to the number set. Current number set: [271, 14], target: 24, just two numbers left.\n     |- Try 271 + 14 = 285. Evaluate 285 != 24, drop this branch.\n     |- Try 271 - 14 = 257. Evaluate 257 != 24, drop this branch.\n     |- Try 271 * 14 = 3794. 3794 exceeds the maximum intermediate result, drop this branch.\n     |- Try 271 \/ 14 = 19.4. 19.4 is a decimal, drop this branch.\n    |- Try 280 * 9 = 2520. 2520 exceeds the maximum intermediate result, drop this branch.\n    |- Try 280 \/ 9 = 31.1. 31.1 is a decimal, drop this branch.\n   |- Pick two numbers (14, 9) (numbers left: [280]). Try possible operations.\n    |- Try 14 + 9 = 23. Add 23 to the number set. Current number set: [23, 280], target: 24, just two numbers left.\n     |- Try 280 + 23 = 303. Evaluate 303 != 24, drop this branch.\n     |- Try 280 - 23 = 257. Evaluate 257 != 24, drop this branch.\n     |- Try 280 * 23 = 6440. 6440 exceeds the maximum intermediate result, drop this branch.\n     |- Try 280 \/ 23 = 12.2. 12.2 is a decimal, drop this branch.\n    |- Try 14 - 9 = 5. Add 5 to the number set. Current number set: [5, 280], target: 24, just two numbers left.\n     |- Try 280 + 5 = 285. Evaluate 285 != 24, drop this branch.\n     |- Try 280 - 5 = 275. Evaluate 275 != 24, drop this branch.\n     |- Try 280 * 5 = 1400. Evaluate 1400 != 24, drop this branch.\n     |- Try 280 \/ 5 = 56. Evaluate 56 != 24, drop this branch.\n    |- Try 14 * 9 = 126. Add 126 to the number set. Current number set: [126, 280], target: 24, just two numbers left.\n     |- Try 280 + 126 = 406. Evaluate 406 != 24, drop this branch.\n     |- Try 280 - 126 = 154. Evaluate 154 != 24, drop this branch.\n     |- Try 280 * 126 = 35280. 35280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 280 \/ 126 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 14 \/ 9 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 20 \/ 14 = 1.4. 1.4 is a decimal, drop this branch.\n |- Pick two numbers (14, 14) (numbers left: [20, 9]). Try possible operations.\n  |- Try 14 + 14 = 28. Add 28 to the number set. Current number set: [28, 20, 9], target: 24. Options for choosing two numbers: [(28, 20), (28, 9), (20, 9)].\n   |- Pick two numbers (28, 20) (numbers left: [9]). Try possible operations.\n    |- Try 28 + 20 = 48. Add 48 to the number set. Current number set: [48, 9], target: 24, just two numbers left.\n     |- Try 48 + 9 = 57. Evaluate 57 != 24, drop this branch.\n     |- Try 48 - 9 = 39. Evaluate 39 != 24, drop this branch.\n     |- Try 48 * 9 = 432. Evaluate 432 != 24, drop this branch.\n     |- Try 48 \/ 9 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 28 - 20 = 8. Add 8 to the number set. Current number set: [8, 9], target: 24, just two numbers left.\n     |- Try 9 + 8 = 17. Evaluate 17 != 24, drop this branch.\n     |- Try 9 - 8 = 1. Evaluate 1 != 24, drop this branch.\n     |- Try 9 * 8 = 72. Evaluate 72 != 24, drop this branch.\n     |- Try 9 \/ 8 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 28 * 20 = 560. Add 560 to the number set. Current number set: [560, 9], target: 24, just two numbers left.\n     |- Try 560 + 9 = 569. Evaluate 569 != 24, drop this branch.\n     |- Try 560 - 9 = 551. Evaluate 551 != 24, drop this branch.\n     |- Try 560 * 9 = 5040. 5040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 560 \/ 9 = 62.2. 62.2 is a decimal, drop this branch.\n    |- Try 28 \/ 20 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (28, 9) (numbers left: [20]). Try possible operations.\n    |- Try 28 + 9 = 37. Add 37 to the number set. Current number set: [37, 20], target: 24, just two numbers left.\n     |- Try 37 + 20 = 57. Evaluate 57 != 24, drop this branch.\n     |- Try 37 - 20 = 17. Evaluate 17 != 24, drop this branch.\n     |- Try 37 * 20 = 740. Evaluate 740 != 24, drop this branch.\n     |- Try 37 \/ 20 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 28 - 9 = 19. Add 19 to the number set. Current number set: [19, 20], target: 24, just two numbers left.\n     |- Try 20 + 19 = 39. Evaluate 39 != 24, drop this branch.\n     |- Try 20 - 19 = 1. Evaluate 1 != 24, drop this branch.\n     |- Try 20 * 19 = 380. Evaluate 380 != 24, drop this branch.\n     |- Try 20 \/ 19 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 28 * 9 = 252. Add 252 to the number set. Current number set: [252, 20], target: 24, just two numbers left.\n     |- Try 252 + 20 = 272. Evaluate 272 != 24, drop this branch.\n     |- Try 252 - 20 = 232. Evaluate 232 != 24, drop this branch.\n     |- Try 252 * 20 = 5040. 5040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 252 \/ 20 = 12.6. 12.6 is a decimal, drop this branch.\n    |- Try 28 \/ 9 = 3.1. 3.1 is a decimal, drop this branch.\n   |- Pick two numbers (20, 9) (numbers left: [28]). Try possible operations.\n    |- Try 20 + 9 = 29. Add 29 to the number set. Current number set: [29, 28], target: 24, just two numbers left.\n     |- Try 29 + 28 = 57. Evaluate 57 != 24, drop this branch.\n     |- Try 29 - 28 = 1. Evaluate 1 != 24, drop this branch.\n     |- Try 29 * 28 = 812. Evaluate 812 != 24, drop this branch.\n     |- Try 29 \/ 28 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 20 - 9 = 11. Add 11 to the number set. Current number set: [11, 28], target: 24, just two numbers left.\n     |- Try 28 + 11 = 39. Evaluate 39 != 24, drop this branch.\n     |- Try 28 - 11 = 17. Evaluate 17 != 24, drop this branch.\n     |- Try 28 * 11 = 308. Evaluate 308 != 24, drop this branch.\n     |- Try 28 \/ 11 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 20 * 9 = 180. Add 180 to the number set. Current number set: [180, 28], target: 24, just two numbers left.\n     |- Try 180 + 28 = 208. Evaluate 208 != 24, drop this branch.\n     |- Try 180 - 28 = 152. Evaluate 152 != 24, drop this branch.\n     |- Try 180 * 28 = 5040. 5040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 180 \/ 28 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 20 \/ 9 = 2.2. 2.2 is a decimal, drop this branch.\n  |- Try 14 - 14 = 0. Add 0 to the number set. Current number set: [0, 20, 9], target: 24. Options for choosing two numbers: [(0, 20), (0, 9), (20, 9)].\n   |- Pick two numbers (0, 20) (numbers left: [9]). Try possible operations.\n    |- Try 20 + 0 = 20. Add 20 to the number set. Current number set: [20, 9], target: 24, just two numbers left.\n     |- Try 20 + 9 = 29. Evaluate 29 != 24, drop this branch.\n     |- Try 20 - 9 = 11. Evaluate 11 != 24, drop this branch.\n     |- Try 20 * 9 = 180. Evaluate 180 != 24, drop this branch.\n     |- Try 20 \/ 9 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 20 - 0 = 20. Add 20 to the number set. Current number set: [20, 9], target: 24, just two numbers left.\n     |- Try 20 + 9 = 29. Evaluate 29 != 24, drop this branch.\n     |- Try 20 - 9 = 11. Evaluate 11 != 24, drop this branch.\n     |- Try 20 * 9 = 180. Evaluate 180 != 24, drop this branch.\n     |- Try 20 \/ 9 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 20 * 0 = 0. Add 0 to the number set. Current number set: [0, 9], target: 24, just two numbers left.\n     |- Try 9 + 0 = 9. Evaluate 9 != 24, drop this branch.\n     |- Try 9 - 0 = 9. Evaluate 9 != 24, drop this branch.\n     |- Try 9 * 0 = 0. Evaluate 0 != 24, drop this branch.\n     |- Try 9 \/ 0 (invalid operation). drop this branch.\n    |- Try 20 \/ 0 (invalid operation). drop this branch.\n   |- Pick two numbers (0, 9) (numbers left: [20]). Try possible operations.\n    |- Try 9 + 0 = 9. Add 9 to the number set. Current number set: [9, 20], target: 24, just two numbers left.\n     |- Try 20 + 9 = 29. Evaluate 29 != 24, drop this branch.\n     |- Try 20 - 9 = 11. Evaluate 11 != 24, drop this branch.\n     |- Try 20 * 9 = 180. Evaluate 180 != 24, drop this branch.\n     |- Try 20 \/ 9 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 9 - 0 = 9. Add 9 to the number set. Current number set: [9, 20], target: 24, just two numbers left.\n     |- Try 20 + 9 = 29. Evaluate 29 != 24, drop this branch.\n     |- Try 20 - 9 = 11. Evaluate 11 != 24, drop this branch.\n     |- Try 20 * 9 = 180. Evaluate 180 != 24, drop this branch.\n     |- Try 20 \/ 9 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 9 * 0 = 0. Add 0 to the number set. Current number set: [0, 20], target: 24, just two numbers left.\n     |- Try 20 + 0 = 20. Evaluate 20 != 24, drop this branch.\n     |- Try 20 - 0 = 20. Evaluate 20 != 24, drop this branch.\n     |- Try 20 * 0 = 0. Evaluate 0 != 24, drop this branch.\n     |- Try 20 \/ 0 (invalid operation). drop this branch.\n    |- Try 9 \/ 0 (invalid operation). drop this branch.\n   |- Pick two numbers (20, 9) (numbers left: [0]). Try possible operations.\n    |- Try 20 + 9 = 29. Add 29 to the number set. Current number set: [29, 0], target: 24, just two numbers left.\n     |- Try 29 + 0 = 29. Evaluate 29 != 24, drop this branch.\n     |- Try 29 - 0 = 29. Evaluate 29 != 24, drop this branch.\n     |- Try 29 * 0 = 0. Evaluate 0 != 24, drop this branch.\n     |- Try 29 \/ 0 (invalid operation). drop this branch.\n    |- Try 20 - 9 = 11. Add 11 to the number set. Current number set: [11, 0], target: 24, just two numbers left.\n     |- Try 11 + 0 = 11. Evaluate 11 != 24, drop this branch.\n     |- Try 11 - 0 = 11. Evaluate 11 != 24, drop this branch.\n     |- Try 11 * 0 = 0. Evaluate 0 != 24, drop this branch.\n     |- Try 11 \/ 0 (invalid operation). drop this branch.\n    |- Try 20 * 9 = 180. Add 180 to the number set. Current number set: [180, 0], target: 24, just two numbers left.\n     |- Try 180 + 0 = 180. Evaluate 180 != 24, drop this branch.\n     |- Try 180 - 0 = 180. Evaluate 180 != 24, drop this branch.\n     |- Try 180 * 0 = 0. Evaluate 0 != 24, drop this branch.\n     |- Try 180 \/ 0 (invalid operation). drop this branch.\n    |- Try 20 \/ 9 = 2.2. 2.2 is a decimal, drop this branch.\n  |- Try 14 * 14 = 196. Add 196 to the number set. Current number set: [196, 20, 9], target: 24. Options for choosing two numbers: [(196, 20), (196, 9), (20, 9)].\n   |- Pick two numbers (196, 20) (numbers left: [9]). Try possible operations.\n    |- Try 196 + 20 = 216. Add 216 to the number set. Current number set: [216, 9], target: 24, just two numbers left.\n     |- Try 216 + 9 = 225. Evaluate 225 != 24, drop this branch.\n     |- Try 216 - 9 = 207. Evaluate 207 != 24, drop this branch.\n     |- Try 216 * 9 = 1944. Evaluate 1944 != 24, drop this branch.\n     |- Try 216 \/ 9 = 24. Evaluate 24 == 24, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 216 \/ 9 = 24\nThe step before: 196 + 20 = 216\nThe first step: 14 * 14 = 196\n\nOutput the solution in the required format:\n<Solution>\n14 * 14 = 196\n196 + 20 = 216\n216 \/ 9 = 24\n<\/Solution>\n","item":{"nums":[14,20,14,9],"solution":["14 * 14 = 196","196 + 20 = 216","216 \/ 9 = 24"],"target":24}}
+{"instance_id":"countdown_8k_17","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [5, 42, 6, 40]\nTarget: 28","reference_output":"# Search Procedure\nInitial number set: [5, 42, 6, 40], target: 28. Options for choosing two numbers: [(5, 42), (5, 6), (5, 40), (42, 6), (42, 40), (6, 40)].\n |- Pick two numbers (5, 42) (numbers left: [6, 40]). Try possible operations.\n  |- Try 42 + 5 = 47. Add 47 to the number set. Current number set: [47, 6, 40], target: 28. Options for choosing two numbers: [(47, 6), (47, 40), (6, 40)].\n   |- Pick two numbers (47, 6) (numbers left: [40]). Try possible operations.\n    |- Try 47 + 6 = 53. Add 53 to the number set. Current number set: [53, 40], target: 28, just two numbers left.\n     |- Try 53 + 40 = 93. Evaluate 93 != 28, drop this branch.\n     |- Try 53 - 40 = 13. Evaluate 13 != 28, drop this branch.\n     |- Try 53 * 40 = 2120. 2120 exceeds the maximum intermediate result, drop this branch.\n     |- Try 53 \/ 40 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 47 - 6 = 41. Add 41 to the number set. Current number set: [41, 40], target: 28, just two numbers left.\n     |- Try 41 + 40 = 81. Evaluate 81 != 28, drop this branch.\n     |- Try 41 - 40 = 1. Evaluate 1 != 28, drop this branch.\n     |- Try 41 * 40 = 1640. Evaluate 1640 != 28, drop this branch.\n     |- Try 41 \/ 40 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 47 * 6 = 282. Add 282 to the number set. Current number set: [282, 40], target: 28, just two numbers left.\n     |- Try 282 + 40 = 322. Evaluate 322 != 28, drop this branch.\n     |- Try 282 - 40 = 242. Evaluate 242 != 28, drop this branch.\n     |- Try 282 * 40 = 11280. 11280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 282 \/ 40 = 7.0. 7.0 is a decimal, drop this branch.\n    |- Try 47 \/ 6 = 7.8. 7.8 is a decimal, drop this branch.\n   |- Pick two numbers (47, 40) (numbers left: [6]). Try possible operations.\n    |- Try 47 + 40 = 87. Add 87 to the number set. Current number set: [87, 6], target: 28, just two numbers left.\n     |- Try 87 + 6 = 93. Evaluate 93 != 28, drop this branch.\n     |- Try 87 - 6 = 81. Evaluate 81 != 28, drop this branch.\n     |- Try 87 * 6 = 522. Evaluate 522 != 28, drop this branch.\n     |- Try 87 \/ 6 = 14.5. 14.5 is a decimal, drop this branch.\n    |- Try 47 - 40 = 7. Add 7 to the number set. Current number set: [7, 6], target: 28, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 28, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 28, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 28, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 47 * 40 = 1880. Add 1880 to the number set. Current number set: [1880, 6], target: 28, just two numbers left.\n     |- Try 1880 + 6 = 1886. Evaluate 1886 != 28, drop this branch.\n     |- Try 1880 - 6 = 1874. Evaluate 1874 != 28, drop this branch.\n     |- Try 1880 * 6 = 11280. 11280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1880 \/ 6 = 313.3. 313.3 is a decimal, drop this branch.\n    |- Try 47 \/ 40 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (6, 40) (numbers left: [47]). Try possible operations.\n    |- Try 40 + 6 = 46. Add 46 to the number set. Current number set: [46, 47], target: 28, just two numbers left.\n     |- Try 47 + 46 = 93. Evaluate 93 != 28, drop this branch.\n     |- Try 47 - 46 = 1. Evaluate 1 != 28, drop this branch.\n     |- Try 47 * 46 = 2162. 2162 exceeds the maximum intermediate result, drop this branch.\n     |- Try 47 \/ 46 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 40 - 6 = 34. Add 34 to the number set. Current number set: [34, 47], target: 28, just two numbers left.\n     |- Try 47 + 34 = 81. Evaluate 81 != 28, drop this branch.\n     |- Try 47 - 34 = 13. Evaluate 13 != 28, drop this branch.\n     |- Try 47 * 34 = 1598. Evaluate 1598 != 28, drop this branch.\n     |- Try 47 \/ 34 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 40 * 6 = 240. Add 240 to the number set. Current number set: [240, 47], target: 28, just two numbers left.\n     |- Try 240 + 47 = 287. Evaluate 287 != 28, drop this branch.\n     |- Try 240 - 47 = 193. Evaluate 193 != 28, drop this branch.\n     |- Try 240 * 47 = 11280. 11280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 240 \/ 47 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 40 \/ 6 = 6.7. 6.7 is a decimal, drop this branch.\n  |- Try 42 - 5 = 37. Add 37 to the number set. Current number set: [37, 6, 40], target: 28. Options for choosing two numbers: [(37, 6), (37, 40), (6, 40)].\n   |- Pick two numbers (37, 6) (numbers left: [40]). Try possible operations.\n    |- Try 37 + 6 = 43. Add 43 to the number set. Current number set: [43, 40], target: 28, just two numbers left.\n     |- Try 43 + 40 = 83. Evaluate 83 != 28, drop this branch.\n     |- Try 43 - 40 = 3. Evaluate 3 != 28, drop this branch.\n     |- Try 43 * 40 = 1720. Evaluate 1720 != 28, drop this branch.\n     |- Try 43 \/ 40 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 37 - 6 = 31. Add 31 to the number set. Current number set: [31, 40], target: 28, just two numbers left.\n     |- Try 40 + 31 = 71. Evaluate 71 != 28, drop this branch.\n     |- Try 40 - 31 = 9. Evaluate 9 != 28, drop this branch.\n     |- Try 40 * 31 = 1240. Evaluate 1240 != 28, drop this branch.\n     |- Try 40 \/ 31 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 37 * 6 = 222. Add 222 to the number set. Current number set: [222, 40], target: 28, just two numbers left.\n     |- Try 222 + 40 = 262. Evaluate 262 != 28, drop this branch.\n     |- Try 222 - 40 = 182. Evaluate 182 != 28, drop this branch.\n     |- Try 222 * 40 = 8880. 8880 exceeds the maximum intermediate result, drop this branch.\n     |- Try 222 \/ 40 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 37 \/ 6 = 6.2. 6.2 is a decimal, drop this branch.\n   |- Pick two numbers (37, 40) (numbers left: [6]). Try possible operations.\n    |- Try 40 + 37 = 77. Add 77 to the number set. Current number set: [77, 6], target: 28, just two numbers left.\n     |- Try 77 + 6 = 83. Evaluate 83 != 28, drop this branch.\n     |- Try 77 - 6 = 71. Evaluate 71 != 28, drop this branch.\n     |- Try 77 * 6 = 462. Evaluate 462 != 28, drop this branch.\n     |- Try 77 \/ 6 = 12.8. 12.8 is a decimal, drop this branch.\n    |- Try 40 - 37 = 3. Add 3 to the number set. Current number set: [3, 6], target: 28, just two numbers left.\n     |- Try 6 + 3 = 9. Evaluate 9 != 28, drop this branch.\n     |- Try 6 - 3 = 3. Evaluate 3 != 28, drop this branch.\n     |- Try 6 * 3 = 18. Evaluate 18 != 28, drop this branch.\n     |- Try 6 \/ 3 = 2. Evaluate 2 != 28, drop this branch.\n    |- Try 40 * 37 = 1480. Add 1480 to the number set. Current number set: [1480, 6], target: 28, just two numbers left.\n     |- Try 1480 + 6 = 1486. Evaluate 1486 != 28, drop this branch.\n     |- Try 1480 - 6 = 1474. Evaluate 1474 != 28, drop this branch.\n     |- Try 1480 * 6 = 8880. 8880 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1480 \/ 6 = 246.7. 246.7 is a decimal, drop this branch.\n    |- Try 40 \/ 37 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (6, 40) (numbers left: [37]). Try possible operations.\n    |- Try 40 + 6 = 46. Add 46 to the number set. Current number set: [46, 37], target: 28, just two numbers left.\n     |- Try 46 + 37 = 83. Evaluate 83 != 28, drop this branch.\n     |- Try 46 - 37 = 9. Evaluate 9 != 28, drop this branch.\n     |- Try 46 * 37 = 1702. Evaluate 1702 != 28, drop this branch.\n     |- Try 46 \/ 37 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 40 - 6 = 34. Add 34 to the number set. Current number set: [34, 37], target: 28, just two numbers left.\n     |- Try 37 + 34 = 71. Evaluate 71 != 28, drop this branch.\n     |- Try 37 - 34 = 3. Evaluate 3 != 28, drop this branch.\n     |- Try 37 * 34 = 1258. Evaluate 1258 != 28, drop this branch.\n     |- Try 37 \/ 34 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 40 * 6 = 240. Add 240 to the number set. Current number set: [240, 37], target: 28, just two numbers left.\n     |- Try 240 + 37 = 277. Evaluate 277 != 28, drop this branch.\n     |- Try 240 - 37 = 203. Evaluate 203 != 28, drop this branch.\n     |- Try 240 * 37 = 8880. 8880 exceeds the maximum intermediate result, drop this branch.\n     |- Try 240 \/ 37 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 40 \/ 6 = 6.7. 6.7 is a decimal, drop this branch.\n  |- Try 42 * 5 = 210. Add 210 to the number set. Current number set: [210, 6, 40], target: 28. Options for choosing two numbers: [(210, 6), (210, 40), (6, 40)].\n   |- Pick two numbers (210, 6) (numbers left: [40]). Try possible operations.\n    |- Try 210 + 6 = 216. Add 216 to the number set. Current number set: [216, 40], target: 28, just two numbers left.\n     |- Try 216 + 40 = 256. Evaluate 256 != 28, drop this branch.\n     |- Try 216 - 40 = 176. Evaluate 176 != 28, drop this branch.\n     |- Try 216 * 40 = 8640. 8640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 216 \/ 40 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 210 - 6 = 204. Add 204 to the number set. Current number set: [204, 40], target: 28, just two numbers left.\n     |- Try 204 + 40 = 244. Evaluate 244 != 28, drop this branch.\n     |- Try 204 - 40 = 164. Evaluate 164 != 28, drop this branch.\n     |- Try 204 * 40 = 8160. 8160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 204 \/ 40 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 210 * 6 = 1260. Add 1260 to the number set. Current number set: [1260, 40], target: 28, just two numbers left.\n     |- Try 1260 + 40 = 1300. Evaluate 1300 != 28, drop this branch.\n     |- Try 1260 - 40 = 1220. Evaluate 1220 != 28, drop this branch.\n     |- Try 1260 * 40 = 50400. 50400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1260 \/ 40 = 31.5. 31.5 is a decimal, drop this branch.\n    |- Try 210 \/ 6 = 35. Add 35 to the number set. Current number set: [35, 40], target: 28, just two numbers left.\n     |- Try 40 + 35 = 75. Evaluate 75 != 28, drop this branch.\n     |- Try 40 - 35 = 5. Evaluate 5 != 28, drop this branch.\n     |- Try 40 * 35 = 1400. Evaluate 1400 != 28, drop this branch.\n     |- Try 40 \/ 35 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (210, 40) (numbers left: [6]). Try possible operations.\n    |- Try 210 + 40 = 250. Add 250 to the number set. Current number set: [250, 6], target: 28, just two numbers left.\n     |- Try 250 + 6 = 256. Evaluate 256 != 28, drop this branch.\n     |- Try 250 - 6 = 244. Evaluate 244 != 28, drop this branch.\n     |- Try 250 * 6 = 1500. Evaluate 1500 != 28, drop this branch.\n     |- Try 250 \/ 6 = 41.7. 41.7 is a decimal, drop this branch.\n    |- Try 210 - 40 = 170. Add 170 to the number set. Current number set: [170, 6], target: 28, just two numbers left.\n     |- Try 170 + 6 = 176. Evaluate 176 != 28, drop this branch.\n     |- Try 170 - 6 = 164. Evaluate 164 != 28, drop this branch.\n     |- Try 170 * 6 = 1020. Evaluate 1020 != 28, drop this branch.\n     |- Try 170 \/ 6 = 28.3. 28.3 is a decimal, drop this branch.\n    |- Try 210 * 40 = 8400. 8400 exceeds the maximum intermediate result, drop this branch.\n    |- Try 210 \/ 40 = 5.2. 5.2 is a decimal, drop this branch.\n   |- Pick two numbers (6, 40) (numbers left: [210]). Try possible operations.\n    |- Try 40 + 6 = 46. Add 46 to the number set. Current number set: [46, 210], target: 28, just two numbers left.\n     |- Try 210 + 46 = 256. Evaluate 256 != 28, drop this branch.\n     |- Try 210 - 46 = 164. Evaluate 164 != 28, drop this branch.\n     |- Try 210 * 46 = 9660. 9660 exceeds the maximum intermediate result, drop this branch.\n     |- Try 210 \/ 46 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 40 - 6 = 34. Add 34 to the number set. Current number set: [34, 210], target: 28, just two numbers left.\n     |- Try 210 + 34 = 244. Evaluate 244 != 28, drop this branch.\n     |- Try 210 - 34 = 176. Evaluate 176 != 28, drop this branch.\n     |- Try 210 * 34 = 7140. 7140 exceeds the maximum intermediate result, drop this branch.\n     |- Try 210 \/ 34 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 40 * 6 = 240. Add 240 to the number set. Current number set: [240, 210], target: 28, just two numbers left.\n     |- Try 240 + 210 = 450. Evaluate 450 != 28, drop this branch.\n     |- Try 240 - 210 = 30. Evaluate 30 != 28, drop this branch.\n     |- Try 240 * 210 = 50400. 50400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 240 \/ 210 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 40 \/ 6 = 6.7. 6.7 is a decimal, drop this branch.\n  |- Try 42 \/ 5 = 8.4. 8.4 is a decimal, drop this branch.\n |- Pick two numbers (5, 6) (numbers left: [42, 40]). Try possible operations.\n  |- Try 6 + 5 = 11. Add 11 to the number set. Current number set: [11, 42, 40], target: 28. Options for choosing two numbers: [(11, 42), (11, 40), (42, 40)].\n   |- Pick two numbers (11, 42) (numbers left: [40]). Try possible operations.\n    |- Try 42 + 11 = 53. Add 53 to the number set. Current number set: [53, 40], target: 28, just two numbers left.\n     |- Try 53 + 40 = 93. Evaluate 93 != 28, drop this branch.\n     |- Try 53 - 40 = 13. Evaluate 13 != 28, drop this branch.\n     |- Try 53 * 40 = 2120. 2120 exceeds the maximum intermediate result, drop this branch.\n     |- Try 53 \/ 40 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 42 - 11 = 31. Add 31 to the number set. Current number set: [31, 40], target: 28, just two numbers left.\n     |- Try 40 + 31 = 71. Evaluate 71 != 28, drop this branch.\n     |- Try 40 - 31 = 9. Evaluate 9 != 28, drop this branch.\n     |- Try 40 * 31 = 1240. Evaluate 1240 != 28, drop this branch.\n     |- Try 40 \/ 31 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 42 * 11 = 462. Add 462 to the number set. Current number set: [462, 40], target: 28, just two numbers left.\n     |- Try 462 + 40 = 502. Evaluate 502 != 28, drop this branch.\n     |- Try 462 - 40 = 422. Evaluate 422 != 28, drop this branch.\n     |- Try 462 * 40 = 18480. 18480 exceeds the maximum intermediate result, drop this branch.\n     |- Try 462 \/ 40 = 11.6. 11.6 is a decimal, drop this branch.\n    |- Try 42 \/ 11 = 3.8. 3.8 is a decimal, drop this branch.\n   |- Pick two numbers (11, 40) (numbers left: [42]). Try possible operations.\n    |- Try 40 + 11 = 51. Add 51 to the number set. Current number set: [51, 42], target: 28, just two numbers left.\n     |- Try 51 + 42 = 93. Evaluate 93 != 28, drop this branch.\n     |- Try 51 - 42 = 9. Evaluate 9 != 28, drop this branch.\n     |- Try 51 * 42 = 2142. 2142 exceeds the maximum intermediate result, drop this branch.\n     |- Try 51 \/ 42 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 40 - 11 = 29. Add 29 to the number set. Current number set: [29, 42], target: 28, just two numbers left.\n     |- Try 42 + 29 = 71. Evaluate 71 != 28, drop this branch.\n     |- Try 42 - 29 = 13. Evaluate 13 != 28, drop this branch.\n     |- Try 42 * 29 = 1218. Evaluate 1218 != 28, drop this branch.\n     |- Try 42 \/ 29 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 40 * 11 = 440. Add 440 to the number set. Current number set: [440, 42], target: 28, just two numbers left.\n     |- Try 440 + 42 = 482. Evaluate 482 != 28, drop this branch.\n     |- Try 440 - 42 = 398. Evaluate 398 != 28, drop this branch.\n     |- Try 440 * 42 = 18480. 18480 exceeds the maximum intermediate result, drop this branch.\n     |- Try 440 \/ 42 = 10.5. 10.5 is a decimal, drop this branch.\n    |- Try 40 \/ 11 = 3.6. 3.6 is a decimal, drop this branch.\n   |- Pick two numbers (42, 40) (numbers left: [11]). Try possible operations.\n    |- Try 42 + 40 = 82. Add 82 to the number set. Current number set: [82, 11], target: 28, just two numbers left.\n     |- Try 82 + 11 = 93. Evaluate 93 != 28, drop this branch.\n     |- Try 82 - 11 = 71. Evaluate 71 != 28, drop this branch.\n     |- Try 82 * 11 = 902. Evaluate 902 != 28, drop this branch.\n     |- Try 82 \/ 11 = 7.5. 7.5 is a decimal, drop this branch.\n    |- Try 42 - 40 = 2. Add 2 to the number set. Current number set: [2, 11], target: 28, just two numbers left.\n     |- Try 11 + 2 = 13. Evaluate 13 != 28, drop this branch.\n     |- Try 11 - 2 = 9. Evaluate 9 != 28, drop this branch.\n     |- Try 11 * 2 = 22. Evaluate 22 != 28, drop this branch.\n     |- Try 11 \/ 2 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 42 * 40 = 1680. Add 1680 to the number set. Current number set: [1680, 11], target: 28, just two numbers left.\n     |- Try 1680 + 11 = 1691. Evaluate 1691 != 28, drop this branch.\n     |- Try 1680 - 11 = 1669. Evaluate 1669 != 28, drop this branch.\n     |- Try 1680 * 11 = 18480. 18480 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1680 \/ 11 = 152.7. 152.7 is a decimal, drop this branch.\n    |- Try 42 \/ 40 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 6 - 5 = 1. Add 1 to the number set. Current number set: [1, 42, 40], target: 28. Options for choosing two numbers: [(1, 42), (1, 40), (42, 40)].\n   |- Pick two numbers (1, 42) (numbers left: [40]). Try possible operations.\n    |- Try 42 + 1 = 43. Add 43 to the number set. Current number set: [43, 40], target: 28, just two numbers left.\n     |- Try 43 + 40 = 83. Evaluate 83 != 28, drop this branch.\n     |- Try 43 - 40 = 3. Evaluate 3 != 28, drop this branch.\n     |- Try 43 * 40 = 1720. Evaluate 1720 != 28, drop this branch.\n     |- Try 43 \/ 40 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 42 - 1 = 41. Add 41 to the number set. Current number set: [41, 40], target: 28, just two numbers left.\n     |- Try 41 + 40 = 81. Evaluate 81 != 28, drop this branch.\n     |- Try 41 - 40 = 1. Evaluate 1 != 28, drop this branch.\n     |- Try 41 * 40 = 1640. Evaluate 1640 != 28, drop this branch.\n     |- Try 41 \/ 40 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 42 * 1 = 42. Add 42 to the number set. Current number set: [42, 40], target: 28, just two numbers left.\n     |- Try 42 + 40 = 82. Evaluate 82 != 28, drop this branch.\n     |- Try 42 - 40 = 2. Evaluate 2 != 28, drop this branch.\n     |- Try 42 * 40 = 1680. Evaluate 1680 != 28, drop this branch.\n     |- Try 42 \/ 40 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 42 \/ 1 = 42. Add 42 to the number set. Current number set: [42, 40], target: 28, just two numbers left.\n     |- Try 42 + 40 = 82. Evaluate 82 != 28, drop this branch.\n     |- Try 42 - 40 = 2. Evaluate 2 != 28, drop this branch.\n     |- Try 42 * 40 = 1680. Evaluate 1680 != 28, drop this branch.\n     |- Try 42 \/ 40 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (1, 40) (numbers left: [42]). Try possible operations.\n    |- Try 40 + 1 = 41. Add 41 to the number set. Current number set: [41, 42], target: 28, just two numbers left.\n     |- Try 42 + 41 = 83. Evaluate 83 != 28, drop this branch.\n     |- Try 42 - 41 = 1. Evaluate 1 != 28, drop this branch.\n     |- Try 42 * 41 = 1722. Evaluate 1722 != 28, drop this branch.\n     |- Try 42 \/ 41 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 40 - 1 = 39. Add 39 to the number set. Current number set: [39, 42], target: 28, just two numbers left.\n     |- Try 42 + 39 = 81. Evaluate 81 != 28, drop this branch.\n     |- Try 42 - 39 = 3. Evaluate 3 != 28, drop this branch.\n     |- Try 42 * 39 = 1638. Evaluate 1638 != 28, drop this branch.\n     |- Try 42 \/ 39 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 40 * 1 = 40. Add 40 to the number set. Current number set: [40, 42], target: 28, just two numbers left.\n     |- Try 42 + 40 = 82. Evaluate 82 != 28, drop this branch.\n     |- Try 42 - 40 = 2. Evaluate 2 != 28, drop this branch.\n     |- Try 42 * 40 = 1680. Evaluate 1680 != 28, drop this branch.\n     |- Try 42 \/ 40 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 40 \/ 1 = 40. Add 40 to the number set. Current number set: [40, 42], target: 28, just two numbers left.\n     |- Try 42 + 40 = 82. Evaluate 82 != 28, drop this branch.\n     |- Try 42 - 40 = 2. Evaluate 2 != 28, drop this branch.\n     |- Try 42 * 40 = 1680. Evaluate 1680 != 28, drop this branch.\n     |- Try 42 \/ 40 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (42, 40) (numbers left: [1]). Try possible operations.\n    |- Try 42 + 40 = 82. Add 82 to the number set. Current number set: [82, 1], target: 28, just two numbers left.\n     |- Try 82 + 1 = 83. Evaluate 83 != 28, drop this branch.\n     |- Try 82 - 1 = 81. Evaluate 81 != 28, drop this branch.\n     |- Try 82 * 1 = 82. Evaluate 82 != 28, drop this branch.\n     |- Try 82 \/ 1 = 82. Evaluate 82 != 28, drop this branch.\n    |- Try 42 - 40 = 2. Add 2 to the number set. Current number set: [2, 1], target: 28, just two numbers left.\n     |- Try 2 + 1 = 3. Evaluate 3 != 28, drop this branch.\n     |- Try 2 - 1 = 1. Evaluate 1 != 28, drop this branch.\n     |- Try 2 * 1 = 2. Evaluate 2 != 28, drop this branch.\n     |- Try 2 \/ 1 = 2. Evaluate 2 != 28, drop this branch.\n    |- Try 42 * 40 = 1680. Add 1680 to the number set. Current number set: [1680, 1], target: 28, just two numbers left.\n     |- Try 1680 + 1 = 1681. Evaluate 1681 != 28, drop this branch.\n     |- Try 1680 - 1 = 1679. Evaluate 1679 != 28, drop this branch.\n     |- Try 1680 * 1 = 1680. Evaluate 1680 != 28, drop this branch.\n     |- Try 1680 \/ 1 = 1680. Evaluate 1680 != 28, drop this branch.\n    |- Try 42 \/ 40 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 6 * 5 = 30. Add 30 to the number set. Current number set: [30, 42, 40], target: 28. Options for choosing two numbers: [(30, 42), (30, 40), (42, 40)].\n   |- Pick two numbers (30, 42) (numbers left: [40]). Try possible operations.\n    |- Try 42 + 30 = 72. Add 72 to the number set. Current number set: [72, 40], target: 28, just two numbers left.\n     |- Try 72 + 40 = 112. Evaluate 112 != 28, drop this branch.\n     |- Try 72 - 40 = 32. Evaluate 32 != 28, drop this branch.\n     |- Try 72 * 40 = 2880. 2880 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 40 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 42 - 30 = 12. Add 12 to the number set. Current number set: [12, 40], target: 28, just two numbers left.\n     |- Try 40 + 12 = 52. Evaluate 52 != 28, drop this branch.\n     |- Try 40 - 12 = 28. Evaluate 28 == 28, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 40 - 12 = 28\nThe step before: 42 - 30 = 12\nThe first step: 6 * 5 = 30\n\nOutput the solution in the required format:\n<Solution>\n6 * 5 = 30\n42 - 30 = 12\n40 - 12 = 28\n<\/Solution>\n","item":{"nums":[5,42,6,40],"solution":["6 * 5 = 30","42 - 30 = 12","40 - 12 = 28"],"target":28}}
+{"instance_id":"countdown_8k_18","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [37, 42, 13, 21]\nTarget: 48","reference_output":"# Search Procedure\nInitial number set: [37, 42, 13, 21], target: 48. Options for choosing two numbers: [(37, 42), (37, 13), (37, 21), (42, 13), (42, 21), (13, 21)].\n |- Pick two numbers (37, 42) (numbers left: [13, 21]). Try possible operations.\n  |- Try 42 + 37 = 79. Add 79 to the number set. Current number set: [79, 13, 21], target: 48. Options for choosing two numbers: [(79, 13), (79, 21), (13, 21)].\n   |- Pick two numbers (79, 13) (numbers left: [21]). Try possible operations.\n    |- Try 79 + 13 = 92. Add 92 to the number set. Current number set: [92, 21], target: 48, just two numbers left.\n     |- Try 92 + 21 = 113. Evaluate 113 != 48, drop this branch.\n     |- Try 92 - 21 = 71. Evaluate 71 != 48, drop this branch.\n     |- Try 92 * 21 = 1932. Evaluate 1932 != 48, drop this branch.\n     |- Try 92 \/ 21 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 79 - 13 = 66. Add 66 to the number set. Current number set: [66, 21], target: 48, just two numbers left.\n     |- Try 66 + 21 = 87. Evaluate 87 != 48, drop this branch.\n     |- Try 66 - 21 = 45. Evaluate 45 != 48, drop this branch.\n     |- Try 66 * 21 = 1386. Evaluate 1386 != 48, drop this branch.\n     |- Try 66 \/ 21 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 79 * 13 = 1027. Add 1027 to the number set. Current number set: [1027, 21], target: 48, just two numbers left.\n     |- Try 1027 + 21 = 1048. Evaluate 1048 != 48, drop this branch.\n     |- Try 1027 - 21 = 1006. Evaluate 1006 != 48, drop this branch.\n     |- Try 1027 * 21 = 21567. 21567 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1027 \/ 21 = 48.9. 48.9 is a decimal, drop this branch.\n    |- Try 79 \/ 13 = 6.1. 6.1 is a decimal, drop this branch.\n   |- Pick two numbers (79, 21) (numbers left: [13]). Try possible operations.\n    |- Try 79 + 21 = 100. Add 100 to the number set. Current number set: [100, 13], target: 48, just two numbers left.\n     |- Try 100 + 13 = 113. Evaluate 113 != 48, drop this branch.\n     |- Try 100 - 13 = 87. Evaluate 87 != 48, drop this branch.\n     |- Try 100 * 13 = 1300. Evaluate 1300 != 48, drop this branch.\n     |- Try 100 \/ 13 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 79 - 21 = 58. Add 58 to the number set. Current number set: [58, 13], target: 48, just two numbers left.\n     |- Try 58 + 13 = 71. Evaluate 71 != 48, drop this branch.\n     |- Try 58 - 13 = 45. Evaluate 45 != 48, drop this branch.\n     |- Try 58 * 13 = 754. Evaluate 754 != 48, drop this branch.\n     |- Try 58 \/ 13 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 79 * 21 = 1659. Add 1659 to the number set. Current number set: [1659, 13], target: 48, just two numbers left.\n     |- Try 1659 + 13 = 1672. Evaluate 1672 != 48, drop this branch.\n     |- Try 1659 - 13 = 1646. Evaluate 1646 != 48, drop this branch.\n     |- Try 1659 * 13 = 21567. 21567 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1659 \/ 13 = 127.6. 127.6 is a decimal, drop this branch.\n    |- Try 79 \/ 21 = 3.8. 3.8 is a decimal, drop this branch.\n   |- Pick two numbers (13, 21) (numbers left: [79]). Try possible operations.\n    |- Try 21 + 13 = 34. Add 34 to the number set. Current number set: [34, 79], target: 48, just two numbers left.\n     |- Try 79 + 34 = 113. Evaluate 113 != 48, drop this branch.\n     |- Try 79 - 34 = 45. Evaluate 45 != 48, drop this branch.\n     |- Try 79 * 34 = 2686. 2686 exceeds the maximum intermediate result, drop this branch.\n     |- Try 79 \/ 34 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 21 - 13 = 8. Add 8 to the number set. Current number set: [8, 79], target: 48, just two numbers left.\n     |- Try 79 + 8 = 87. Evaluate 87 != 48, drop this branch.\n     |- Try 79 - 8 = 71. Evaluate 71 != 48, drop this branch.\n     |- Try 79 * 8 = 632. Evaluate 632 != 48, drop this branch.\n     |- Try 79 \/ 8 = 9.9. 9.9 is a decimal, drop this branch.\n    |- Try 21 * 13 = 273. Add 273 to the number set. Current number set: [273, 79], target: 48, just two numbers left.\n     |- Try 273 + 79 = 352. Evaluate 352 != 48, drop this branch.\n     |- Try 273 - 79 = 194. Evaluate 194 != 48, drop this branch.\n     |- Try 273 * 79 = 21567. 21567 exceeds the maximum intermediate result, drop this branch.\n     |- Try 273 \/ 79 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 21 \/ 13 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 42 - 37 = 5. Add 5 to the number set. Current number set: [5, 13, 21], target: 48. Options for choosing two numbers: [(5, 13), (5, 21), (13, 21)].\n   |- Pick two numbers (5, 13) (numbers left: [21]). Try possible operations.\n    |- Try 13 + 5 = 18. Add 18 to the number set. Current number set: [18, 21], target: 48, just two numbers left.\n     |- Try 21 + 18 = 39. Evaluate 39 != 48, drop this branch.\n     |- Try 21 - 18 = 3. Evaluate 3 != 48, drop this branch.\n     |- Try 21 * 18 = 378. Evaluate 378 != 48, drop this branch.\n     |- Try 21 \/ 18 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 13 - 5 = 8. Add 8 to the number set. Current number set: [8, 21], target: 48, just two numbers left.\n     |- Try 21 + 8 = 29. Evaluate 29 != 48, drop this branch.\n     |- Try 21 - 8 = 13. Evaluate 13 != 48, drop this branch.\n     |- Try 21 * 8 = 168. Evaluate 168 != 48, drop this branch.\n     |- Try 21 \/ 8 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 13 * 5 = 65. Add 65 to the number set. Current number set: [65, 21], target: 48, just two numbers left.\n     |- Try 65 + 21 = 86. Evaluate 86 != 48, drop this branch.\n     |- Try 65 - 21 = 44. Evaluate 44 != 48, drop this branch.\n     |- Try 65 * 21 = 1365. Evaluate 1365 != 48, drop this branch.\n     |- Try 65 \/ 21 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 13 \/ 5 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (5, 21) (numbers left: [13]). Try possible operations.\n    |- Try 21 + 5 = 26. Add 26 to the number set. Current number set: [26, 13], target: 48, just two numbers left.\n     |- Try 26 + 13 = 39. Evaluate 39 != 48, drop this branch.\n     |- Try 26 - 13 = 13. Evaluate 13 != 48, drop this branch.\n     |- Try 26 * 13 = 338. Evaluate 338 != 48, drop this branch.\n     |- Try 26 \/ 13 = 2. Evaluate 2 != 48, drop this branch.\n    |- Try 21 - 5 = 16. Add 16 to the number set. Current number set: [16, 13], target: 48, just two numbers left.\n     |- Try 16 + 13 = 29. Evaluate 29 != 48, drop this branch.\n     |- Try 16 - 13 = 3. Evaluate 3 != 48, drop this branch.\n     |- Try 16 * 13 = 208. Evaluate 208 != 48, drop this branch.\n     |- Try 16 \/ 13 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 21 * 5 = 105. Add 105 to the number set. Current number set: [105, 13], target: 48, just two numbers left.\n     |- Try 105 + 13 = 118. Evaluate 118 != 48, drop this branch.\n     |- Try 105 - 13 = 92. Evaluate 92 != 48, drop this branch.\n     |- Try 105 * 13 = 1365. Evaluate 1365 != 48, drop this branch.\n     |- Try 105 \/ 13 = 8.1. 8.1 is a decimal, drop this branch.\n    |- Try 21 \/ 5 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (13, 21) (numbers left: [5]). Try possible operations.\n    |- Try 21 + 13 = 34. Add 34 to the number set. Current number set: [34, 5], target: 48, just two numbers left.\n     |- Try 34 + 5 = 39. Evaluate 39 != 48, drop this branch.\n     |- Try 34 - 5 = 29. Evaluate 29 != 48, drop this branch.\n     |- Try 34 * 5 = 170. Evaluate 170 != 48, drop this branch.\n     |- Try 34 \/ 5 = 6.8. 6.8 is a decimal, drop this branch.\n    |- Try 21 - 13 = 8. Add 8 to the number set. Current number set: [8, 5], target: 48, just two numbers left.\n     |- Try 8 + 5 = 13. Evaluate 13 != 48, drop this branch.\n     |- Try 8 - 5 = 3. Evaluate 3 != 48, drop this branch.\n     |- Try 8 * 5 = 40. Evaluate 40 != 48, drop this branch.\n     |- Try 8 \/ 5 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 21 * 13 = 273. Add 273 to the number set. Current number set: [273, 5], target: 48, just two numbers left.\n     |- Try 273 + 5 = 278. Evaluate 278 != 48, drop this branch.\n     |- Try 273 - 5 = 268. Evaluate 268 != 48, drop this branch.\n     |- Try 273 * 5 = 1365. Evaluate 1365 != 48, drop this branch.\n     |- Try 273 \/ 5 = 54.6. 54.6 is a decimal, drop this branch.\n    |- Try 21 \/ 13 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 42 * 37 = 1554. Add 1554 to the number set. Current number set: [1554, 13, 21], target: 48. Options for choosing two numbers: [(1554, 13), (1554, 21), (13, 21)].\n   |- Pick two numbers (1554, 13) (numbers left: [21]). Try possible operations.\n    |- Try 1554 + 13 = 1567. Add 1567 to the number set. Current number set: [1567, 21], target: 48, just two numbers left.\n     |- Try 1567 + 21 = 1588. Evaluate 1588 != 48, drop this branch.\n     |- Try 1567 - 21 = 1546. Evaluate 1546 != 48, drop this branch.\n     |- Try 1567 * 21 = 32907. 32907 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1567 \/ 21 = 74.6. 74.6 is a decimal, drop this branch.\n    |- Try 1554 - 13 = 1541. Add 1541 to the number set. Current number set: [1541, 21], target: 48, just two numbers left.\n     |- Try 1541 + 21 = 1562. Evaluate 1562 != 48, drop this branch.\n     |- Try 1541 - 21 = 1520. Evaluate 1520 != 48, drop this branch.\n     |- Try 1541 * 21 = 32361. 32361 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1541 \/ 21 = 73.4. 73.4 is a decimal, drop this branch.\n    |- Try 1554 * 13 = 20202. 20202 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1554 \/ 13 = 119.5. 119.5 is a decimal, drop this branch.\n   |- Pick two numbers (1554, 21) (numbers left: [13]). Try possible operations.\n    |- Try 1554 + 21 = 1575. Add 1575 to the number set. Current number set: [1575, 13], target: 48, just two numbers left.\n     |- Try 1575 + 13 = 1588. Evaluate 1588 != 48, drop this branch.\n     |- Try 1575 - 13 = 1562. Evaluate 1562 != 48, drop this branch.\n     |- Try 1575 * 13 = 20475. 20475 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1575 \/ 13 = 121.2. 121.2 is a decimal, drop this branch.\n    |- Try 1554 - 21 = 1533. Add 1533 to the number set. Current number set: [1533, 13], target: 48, just two numbers left.\n     |- Try 1533 + 13 = 1546. Evaluate 1546 != 48, drop this branch.\n     |- Try 1533 - 13 = 1520. Evaluate 1520 != 48, drop this branch.\n     |- Try 1533 * 13 = 19929. 19929 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1533 \/ 13 = 117.9. 117.9 is a decimal, drop this branch.\n    |- Try 1554 * 21 = 32634. 32634 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1554 \/ 21 = 74. Add 74 to the number set. Current number set: [74, 13], target: 48, just two numbers left.\n     |- Try 74 + 13 = 87. Evaluate 87 != 48, drop this branch.\n     |- Try 74 - 13 = 61. Evaluate 61 != 48, drop this branch.\n     |- Try 74 * 13 = 962. Evaluate 962 != 48, drop this branch.\n     |- Try 74 \/ 13 = 5.7. 5.7 is a decimal, drop this branch.\n   |- Pick two numbers (13, 21) (numbers left: [1554]). Try possible operations.\n    |- Try 21 + 13 = 34. Add 34 to the number set. Current number set: [34, 1554], target: 48, just two numbers left.\n     |- Try 1554 + 34 = 1588. Evaluate 1588 != 48, drop this branch.\n     |- Try 1554 - 34 = 1520. Evaluate 1520 != 48, drop this branch.\n     |- Try 1554 * 34 = 52836. 52836 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1554 \/ 34 = 45.7. 45.7 is a decimal, drop this branch.\n    |- Try 21 - 13 = 8. Add 8 to the number set. Current number set: [8, 1554], target: 48, just two numbers left.\n     |- Try 1554 + 8 = 1562. Evaluate 1562 != 48, drop this branch.\n     |- Try 1554 - 8 = 1546. Evaluate 1546 != 48, drop this branch.\n     |- Try 1554 * 8 = 12432. 12432 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1554 \/ 8 = 194.2. 194.2 is a decimal, drop this branch.\n    |- Try 21 * 13 = 273. Add 273 to the number set. Current number set: [273, 1554], target: 48, just two numbers left.\n     |- Try 1554 + 273 = 1827. Evaluate 1827 != 48, drop this branch.\n     |- Try 1554 - 273 = 1281. Evaluate 1281 != 48, drop this branch.\n     |- Try 1554 * 273 = 424242. 424242 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1554 \/ 273 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 21 \/ 13 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 42 \/ 37 = 1.1. 1.1 is a decimal, drop this branch.\n |- Pick two numbers (37, 13) (numbers left: [42, 21]). Try possible operations.\n  |- Try 37 + 13 = 50. Add 50 to the number set. Current number set: [50, 42, 21], target: 48. Options for choosing two numbers: [(50, 42), (50, 21), (42, 21)].\n   |- Pick two numbers (50, 42) (numbers left: [21]). Try possible operations.\n    |- Try 50 + 42 = 92. Add 92 to the number set. Current number set: [92, 21], target: 48, just two numbers left.\n     |- Try 92 + 21 = 113. Evaluate 113 != 48, drop this branch.\n     |- Try 92 - 21 = 71. Evaluate 71 != 48, drop this branch.\n     |- Try 92 * 21 = 1932. Evaluate 1932 != 48, drop this branch.\n     |- Try 92 \/ 21 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 50 - 42 = 8. Add 8 to the number set. Current number set: [8, 21], target: 48, just two numbers left.\n     |- Try 21 + 8 = 29. Evaluate 29 != 48, drop this branch.\n     |- Try 21 - 8 = 13. Evaluate 13 != 48, drop this branch.\n     |- Try 21 * 8 = 168. Evaluate 168 != 48, drop this branch.\n     |- Try 21 \/ 8 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 50 * 42 = 2100. 2100 exceeds the maximum intermediate result, drop this branch.\n    |- Try 50 \/ 42 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (50, 21) (numbers left: [42]). Try possible operations.\n    |- Try 50 + 21 = 71. Add 71 to the number set. Current number set: [71, 42], target: 48, just two numbers left.\n     |- Try 71 + 42 = 113. Evaluate 113 != 48, drop this branch.\n     |- Try 71 - 42 = 29. Evaluate 29 != 48, drop this branch.\n     |- Try 71 * 42 = 2982. 2982 exceeds the maximum intermediate result, drop this branch.\n     |- Try 71 \/ 42 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 50 - 21 = 29. Add 29 to the number set. Current number set: [29, 42], target: 48, just two numbers left.\n     |- Try 42 + 29 = 71. Evaluate 71 != 48, drop this branch.\n     |- Try 42 - 29 = 13. Evaluate 13 != 48, drop this branch.\n     |- Try 42 * 29 = 1218. Evaluate 1218 != 48, drop this branch.\n     |- Try 42 \/ 29 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 50 * 21 = 1050. Add 1050 to the number set. Current number set: [1050, 42], target: 48, just two numbers left.\n     |- Try 1050 + 42 = 1092. Evaluate 1092 != 48, drop this branch.\n     |- Try 1050 - 42 = 1008. Evaluate 1008 != 48, drop this branch.\n     |- Try 1050 * 42 = 44100. 44100 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1050 \/ 42 = 25. Evaluate 25 != 48, drop this branch.\n    |- Try 50 \/ 21 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (42, 21) (numbers left: [50]). Try possible operations.\n    |- Try 42 + 21 = 63. Add 63 to the number set. Current number set: [63, 50], target: 48, just two numbers left.\n     |- Try 63 + 50 = 113. Evaluate 113 != 48, drop this branch.\n     |- Try 63 - 50 = 13. Evaluate 13 != 48, drop this branch.\n     |- Try 63 * 50 = 3150. 3150 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 50 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 42 - 21 = 21. Add 21 to the number set. Current number set: [21, 50], target: 48, just two numbers left.\n     |- Try 50 + 21 = 71. Evaluate 71 != 48, drop this branch.\n     |- Try 50 - 21 = 29. Evaluate 29 != 48, drop this branch.\n     |- Try 50 * 21 = 1050. Evaluate 1050 != 48, drop this branch.\n     |- Try 50 \/ 21 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 42 * 21 = 882. Add 882 to the number set. Current number set: [882, 50], target: 48, just two numbers left.\n     |- Try 882 + 50 = 932. Evaluate 932 != 48, drop this branch.\n     |- Try 882 - 50 = 832. Evaluate 832 != 48, drop this branch.\n     |- Try 882 * 50 = 44100. 44100 exceeds the maximum intermediate result, drop this branch.\n     |- Try 882 \/ 50 = 17.6. 17.6 is a decimal, drop this branch.\n    |- Try 42 \/ 21 = 2. Add 2 to the number set. Current number set: [2, 50], target: 48, just two numbers left.\n     |- Try 50 + 2 = 52. Evaluate 52 != 48, drop this branch.\n     |- Try 50 - 2 = 48. Evaluate 48 == 48, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 50 - 2 = 48\nThe step before: 42 \/ 21 = 2\nThe first step: 37 + 13 = 50\n\nOutput the solution in the required format:\n<Solution>\n37 + 13 = 50\n42 \/ 21 = 2\n50 - 2 = 48\n<\/Solution>\n","item":{"nums":[37,42,13,21],"solution":["37 + 13 = 50","42 \/ 21 = 2","50 - 2 = 48"],"target":48}}
+{"instance_id":"countdown_8k_19","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [2, 27, 4, 26]\nTarget: 25","reference_output":"# Search Procedure\nInitial number set: [2, 27, 4, 26], target: 25. Options for choosing two numbers: [(2, 27), (2, 4), (2, 26), (27, 4), (27, 26), (4, 26)].\n |- Pick two numbers (2, 27) (numbers left: [4, 26]). Try possible operations.\n  |- Try 27 + 2 = 29. Add 29 to the number set. Current number set: [29, 4, 26], target: 25. Options for choosing two numbers: [(29, 4), (29, 26), (4, 26)].\n   |- Pick two numbers (29, 4) (numbers left: [26]). Try possible operations.\n    |- Try 29 + 4 = 33. Add 33 to the number set. Current number set: [33, 26], target: 25, just two numbers left.\n     |- Try 33 + 26 = 59. Evaluate 59 != 25, drop this branch.\n     |- Try 33 - 26 = 7. Evaluate 7 != 25, drop this branch.\n     |- Try 33 * 26 = 858. Evaluate 858 != 25, drop this branch.\n     |- Try 33 \/ 26 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 29 - 4 = 25. Add 25 to the number set. Current number set: [25, 26], target: 25, just two numbers left.\n     |- Try 26 + 25 = 51. Evaluate 51 != 25, drop this branch.\n     |- Try 26 - 25 = 1. Evaluate 1 != 25, drop this branch.\n     |- Try 26 * 25 = 650. Evaluate 650 != 25, drop this branch.\n     |- Try 26 \/ 25 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 29 * 4 = 116. Add 116 to the number set. Current number set: [116, 26], target: 25, just two numbers left.\n     |- Try 116 + 26 = 142. Evaluate 142 != 25, drop this branch.\n     |- Try 116 - 26 = 90. Evaluate 90 != 25, drop this branch.\n     |- Try 116 * 26 = 3016. 3016 exceeds the maximum intermediate result, drop this branch.\n     |- Try 116 \/ 26 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 29 \/ 4 = 7.2. 7.2 is a decimal, drop this branch.\n   |- Pick two numbers (29, 26) (numbers left: [4]). Try possible operations.\n    |- Try 29 + 26 = 55. Add 55 to the number set. Current number set: [55, 4], target: 25, just two numbers left.\n     |- Try 55 + 4 = 59. Evaluate 59 != 25, drop this branch.\n     |- Try 55 - 4 = 51. Evaluate 51 != 25, drop this branch.\n     |- Try 55 * 4 = 220. Evaluate 220 != 25, drop this branch.\n     |- Try 55 \/ 4 = 13.8. 13.8 is a decimal, drop this branch.\n    |- Try 29 - 26 = 3. Add 3 to the number set. Current number set: [3, 4], target: 25, just two numbers left.\n     |- Try 4 + 3 = 7. Evaluate 7 != 25, drop this branch.\n     |- Try 4 - 3 = 1. Evaluate 1 != 25, drop this branch.\n     |- Try 4 * 3 = 12. Evaluate 12 != 25, drop this branch.\n     |- Try 4 \/ 3 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 29 * 26 = 754. Add 754 to the number set. Current number set: [754, 4], target: 25, just two numbers left.\n     |- Try 754 + 4 = 758. Evaluate 758 != 25, drop this branch.\n     |- Try 754 - 4 = 750. Evaluate 750 != 25, drop this branch.\n     |- Try 754 * 4 = 3016. 3016 exceeds the maximum intermediate result, drop this branch.\n     |- Try 754 \/ 4 = 188.5. 188.5 is a decimal, drop this branch.\n    |- Try 29 \/ 26 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (4, 26) (numbers left: [29]). Try possible operations.\n    |- Try 26 + 4 = 30. Add 30 to the number set. Current number set: [30, 29], target: 25, just two numbers left.\n     |- Try 30 + 29 = 59. Evaluate 59 != 25, drop this branch.\n     |- Try 30 - 29 = 1. Evaluate 1 != 25, drop this branch.\n     |- Try 30 * 29 = 870. Evaluate 870 != 25, drop this branch.\n     |- Try 30 \/ 29 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 26 - 4 = 22. Add 22 to the number set. Current number set: [22, 29], target: 25, just two numbers left.\n     |- Try 29 + 22 = 51. Evaluate 51 != 25, drop this branch.\n     |- Try 29 - 22 = 7. Evaluate 7 != 25, drop this branch.\n     |- Try 29 * 22 = 638. Evaluate 638 != 25, drop this branch.\n     |- Try 29 \/ 22 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 26 * 4 = 104. Add 104 to the number set. Current number set: [104, 29], target: 25, just two numbers left.\n     |- Try 104 + 29 = 133. Evaluate 133 != 25, drop this branch.\n     |- Try 104 - 29 = 75. Evaluate 75 != 25, drop this branch.\n     |- Try 104 * 29 = 3016. 3016 exceeds the maximum intermediate result, drop this branch.\n     |- Try 104 \/ 29 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 26 \/ 4 = 6.5. 6.5 is a decimal, drop this branch.\n  |- Try 27 - 2 = 25. Add 25 to the number set. Current number set: [25, 4, 26], target: 25. Options for choosing two numbers: [(25, 4), (25, 26), (4, 26)].\n   |- Pick two numbers (25, 4) (numbers left: [26]). Try possible operations.\n    |- Try 25 + 4 = 29. Add 29 to the number set. Current number set: [29, 26], target: 25, just two numbers left.\n     |- Try 29 + 26 = 55. Evaluate 55 != 25, drop this branch.\n     |- Try 29 - 26 = 3. Evaluate 3 != 25, drop this branch.\n     |- Try 29 * 26 = 754. Evaluate 754 != 25, drop this branch.\n     |- Try 29 \/ 26 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 - 4 = 21. Add 21 to the number set. Current number set: [21, 26], target: 25, just two numbers left.\n     |- Try 26 + 21 = 47. Evaluate 47 != 25, drop this branch.\n     |- Try 26 - 21 = 5. Evaluate 5 != 25, drop this branch.\n     |- Try 26 * 21 = 546. Evaluate 546 != 25, drop this branch.\n     |- Try 26 \/ 21 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 4 = 100. Add 100 to the number set. Current number set: [100, 26], target: 25, just two numbers left.\n     |- Try 100 + 26 = 126. Evaluate 126 != 25, drop this branch.\n     |- Try 100 - 26 = 74. Evaluate 74 != 25, drop this branch.\n     |- Try 100 * 26 = 2600. 2600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 100 \/ 26 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 25 \/ 4 = 6.2. 6.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 26) (numbers left: [4]). Try possible operations.\n    |- Try 26 + 25 = 51. Add 51 to the number set. Current number set: [51, 4], target: 25, just two numbers left.\n     |- Try 51 + 4 = 55. Evaluate 55 != 25, drop this branch.\n     |- Try 51 - 4 = 47. Evaluate 47 != 25, drop this branch.\n     |- Try 51 * 4 = 204. Evaluate 204 != 25, drop this branch.\n     |- Try 51 \/ 4 = 12.8. 12.8 is a decimal, drop this branch.\n    |- Try 26 - 25 = 1. Add 1 to the number set. Current number set: [1, 4], target: 25, just two numbers left.\n     |- Try 4 + 1 = 5. Evaluate 5 != 25, drop this branch.\n     |- Try 4 - 1 = 3. Evaluate 3 != 25, drop this branch.\n     |- Try 4 * 1 = 4. Evaluate 4 != 25, drop this branch.\n     |- Try 4 \/ 1 = 4. Evaluate 4 != 25, drop this branch.\n    |- Try 26 * 25 = 650. Add 650 to the number set. Current number set: [650, 4], target: 25, just two numbers left.\n     |- Try 650 + 4 = 654. Evaluate 654 != 25, drop this branch.\n     |- Try 650 - 4 = 646. Evaluate 646 != 25, drop this branch.\n     |- Try 650 * 4 = 2600. 2600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 650 \/ 4 = 162.5. 162.5 is a decimal, drop this branch.\n    |- Try 26 \/ 25 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (4, 26) (numbers left: [25]). Try possible operations.\n    |- Try 26 + 4 = 30. Add 30 to the number set. Current number set: [30, 25], target: 25, just two numbers left.\n     |- Try 30 + 25 = 55. Evaluate 55 != 25, drop this branch.\n     |- Try 30 - 25 = 5. Evaluate 5 != 25, drop this branch.\n     |- Try 30 * 25 = 750. Evaluate 750 != 25, drop this branch.\n     |- Try 30 \/ 25 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 26 - 4 = 22. Add 22 to the number set. Current number set: [22, 25], target: 25, just two numbers left.\n     |- Try 25 + 22 = 47. Evaluate 47 != 25, drop this branch.\n     |- Try 25 - 22 = 3. Evaluate 3 != 25, drop this branch.\n     |- Try 25 * 22 = 550. Evaluate 550 != 25, drop this branch.\n     |- Try 25 \/ 22 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 26 * 4 = 104. Add 104 to the number set. Current number set: [104, 25], target: 25, just two numbers left.\n     |- Try 104 + 25 = 129. Evaluate 129 != 25, drop this branch.\n     |- Try 104 - 25 = 79. Evaluate 79 != 25, drop this branch.\n     |- Try 104 * 25 = 2600. 2600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 104 \/ 25 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 26 \/ 4 = 6.5. 6.5 is a decimal, drop this branch.\n  |- Try 27 * 2 = 54. Add 54 to the number set. Current number set: [54, 4, 26], target: 25. Options for choosing two numbers: [(54, 4), (54, 26), (4, 26)].\n   |- Pick two numbers (54, 4) (numbers left: [26]). Try possible operations.\n    |- Try 54 + 4 = 58. Add 58 to the number set. Current number set: [58, 26], target: 25, just two numbers left.\n     |- Try 58 + 26 = 84. Evaluate 84 != 25, drop this branch.\n     |- Try 58 - 26 = 32. Evaluate 32 != 25, drop this branch.\n     |- Try 58 * 26 = 1508. Evaluate 1508 != 25, drop this branch.\n     |- Try 58 \/ 26 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 54 - 4 = 50. Add 50 to the number set. Current number set: [50, 26], target: 25, just two numbers left.\n     |- Try 50 + 26 = 76. Evaluate 76 != 25, drop this branch.\n     |- Try 50 - 26 = 24. Evaluate 24 != 25, drop this branch.\n     |- Try 50 * 26 = 1300. Evaluate 1300 != 25, drop this branch.\n     |- Try 50 \/ 26 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 54 * 4 = 216. Add 216 to the number set. Current number set: [216, 26], target: 25, just two numbers left.\n     |- Try 216 + 26 = 242. Evaluate 242 != 25, drop this branch.\n     |- Try 216 - 26 = 190. Evaluate 190 != 25, drop this branch.\n     |- Try 216 * 26 = 5616. 5616 exceeds the maximum intermediate result, drop this branch.\n     |- Try 216 \/ 26 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 54 \/ 4 = 13.5. 13.5 is a decimal, drop this branch.\n   |- Pick two numbers (54, 26) (numbers left: [4]). Try possible operations.\n    |- Try 54 + 26 = 80. Add 80 to the number set. Current number set: [80, 4], target: 25, just two numbers left.\n     |- Try 80 + 4 = 84. Evaluate 84 != 25, drop this branch.\n     |- Try 80 - 4 = 76. Evaluate 76 != 25, drop this branch.\n     |- Try 80 * 4 = 320. Evaluate 320 != 25, drop this branch.\n     |- Try 80 \/ 4 = 20. Evaluate 20 != 25, drop this branch.\n    |- Try 54 - 26 = 28. Add 28 to the number set. Current number set: [28, 4], target: 25, just two numbers left.\n     |- Try 28 + 4 = 32. Evaluate 32 != 25, drop this branch.\n     |- Try 28 - 4 = 24. Evaluate 24 != 25, drop this branch.\n     |- Try 28 * 4 = 112. Evaluate 112 != 25, drop this branch.\n     |- Try 28 \/ 4 = 7. Evaluate 7 != 25, drop this branch.\n    |- Try 54 * 26 = 1404. Add 1404 to the number set. Current number set: [1404, 4], target: 25, just two numbers left.\n     |- Try 1404 + 4 = 1408. Evaluate 1408 != 25, drop this branch.\n     |- Try 1404 - 4 = 1400. Evaluate 1400 != 25, drop this branch.\n     |- Try 1404 * 4 = 5616. 5616 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1404 \/ 4 = 351. Evaluate 351 != 25, drop this branch.\n    |- Try 54 \/ 26 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (4, 26) (numbers left: [54]). Try possible operations.\n    |- Try 26 + 4 = 30. Add 30 to the number set. Current number set: [30, 54], target: 25, just two numbers left.\n     |- Try 54 + 30 = 84. Evaluate 84 != 25, drop this branch.\n     |- Try 54 - 30 = 24. Evaluate 24 != 25, drop this branch.\n     |- Try 54 * 30 = 1620. Evaluate 1620 != 25, drop this branch.\n     |- Try 54 \/ 30 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 26 - 4 = 22. Add 22 to the number set. Current number set: [22, 54], target: 25, just two numbers left.\n     |- Try 54 + 22 = 76. Evaluate 76 != 25, drop this branch.\n     |- Try 54 - 22 = 32. Evaluate 32 != 25, drop this branch.\n     |- Try 54 * 22 = 1188. Evaluate 1188 != 25, drop this branch.\n     |- Try 54 \/ 22 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 26 * 4 = 104. Add 104 to the number set. Current number set: [104, 54], target: 25, just two numbers left.\n     |- Try 104 + 54 = 158. Evaluate 158 != 25, drop this branch.\n     |- Try 104 - 54 = 50. Evaluate 50 != 25, drop this branch.\n     |- Try 104 * 54 = 5616. 5616 exceeds the maximum intermediate result, drop this branch.\n     |- Try 104 \/ 54 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 26 \/ 4 = 6.5. 6.5 is a decimal, drop this branch.\n  |- Try 27 \/ 2 = 13.5. 13.5 is a decimal, drop this branch.\n |- Pick two numbers (2, 4) (numbers left: [27, 26]). Try possible operations.\n  |- Try 4 + 2 = 6. Add 6 to the number set. Current number set: [6, 27, 26], target: 25. Options for choosing two numbers: [(6, 27), (6, 26), (27, 26)].\n   |- Pick two numbers (6, 27) (numbers left: [26]). Try possible operations.\n    |- Try 27 + 6 = 33. Add 33 to the number set. Current number set: [33, 26], target: 25, just two numbers left.\n     |- Try 33 + 26 = 59. Evaluate 59 != 25, drop this branch.\n     |- Try 33 - 26 = 7. Evaluate 7 != 25, drop this branch.\n     |- Try 33 * 26 = 858. Evaluate 858 != 25, drop this branch.\n     |- Try 33 \/ 26 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 27 - 6 = 21. Add 21 to the number set. Current number set: [21, 26], target: 25, just two numbers left.\n     |- Try 26 + 21 = 47. Evaluate 47 != 25, drop this branch.\n     |- Try 26 - 21 = 5. Evaluate 5 != 25, drop this branch.\n     |- Try 26 * 21 = 546. Evaluate 546 != 25, drop this branch.\n     |- Try 26 \/ 21 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 27 * 6 = 162. Add 162 to the number set. Current number set: [162, 26], target: 25, just two numbers left.\n     |- Try 162 + 26 = 188. Evaluate 188 != 25, drop this branch.\n     |- Try 162 - 26 = 136. Evaluate 136 != 25, drop this branch.\n     |- Try 162 * 26 = 4212. 4212 exceeds the maximum intermediate result, drop this branch.\n     |- Try 162 \/ 26 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 27 \/ 6 = 4.5. 4.5 is a decimal, drop this branch.\n   |- Pick two numbers (6, 26) (numbers left: [27]). Try possible operations.\n    |- Try 26 + 6 = 32. Add 32 to the number set. Current number set: [32, 27], target: 25, just two numbers left.\n     |- Try 32 + 27 = 59. Evaluate 59 != 25, drop this branch.\n     |- Try 32 - 27 = 5. Evaluate 5 != 25, drop this branch.\n     |- Try 32 * 27 = 864. Evaluate 864 != 25, drop this branch.\n     |- Try 32 \/ 27 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 26 - 6 = 20. Add 20 to the number set. Current number set: [20, 27], target: 25, just two numbers left.\n     |- Try 27 + 20 = 47. Evaluate 47 != 25, drop this branch.\n     |- Try 27 - 20 = 7. Evaluate 7 != 25, drop this branch.\n     |- Try 27 * 20 = 540. Evaluate 540 != 25, drop this branch.\n     |- Try 27 \/ 20 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 26 * 6 = 156. Add 156 to the number set. Current number set: [156, 27], target: 25, just two numbers left.\n     |- Try 156 + 27 = 183. Evaluate 183 != 25, drop this branch.\n     |- Try 156 - 27 = 129. Evaluate 129 != 25, drop this branch.\n     |- Try 156 * 27 = 4212. 4212 exceeds the maximum intermediate result, drop this branch.\n     |- Try 156 \/ 27 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 26 \/ 6 = 4.3. 4.3 is a decimal, drop this branch.\n   |- Pick two numbers (27, 26) (numbers left: [6]). Try possible operations.\n    |- Try 27 + 26 = 53. Add 53 to the number set. Current number set: [53, 6], target: 25, just two numbers left.\n     |- Try 53 + 6 = 59. Evaluate 59 != 25, drop this branch.\n     |- Try 53 - 6 = 47. Evaluate 47 != 25, drop this branch.\n     |- Try 53 * 6 = 318. Evaluate 318 != 25, drop this branch.\n     |- Try 53 \/ 6 = 8.8. 8.8 is a decimal, drop this branch.\n    |- Try 27 - 26 = 1. Add 1 to the number set. Current number set: [1, 6], target: 25, just two numbers left.\n     |- Try 6 + 1 = 7. Evaluate 7 != 25, drop this branch.\n     |- Try 6 - 1 = 5. Evaluate 5 != 25, drop this branch.\n     |- Try 6 * 1 = 6. Evaluate 6 != 25, drop this branch.\n     |- Try 6 \/ 1 = 6. Evaluate 6 != 25, drop this branch.\n    |- Try 27 * 26 = 702. Add 702 to the number set. Current number set: [702, 6], target: 25, just two numbers left.\n     |- Try 702 + 6 = 708. Evaluate 708 != 25, drop this branch.\n     |- Try 702 - 6 = 696. Evaluate 696 != 25, drop this branch.\n     |- Try 702 * 6 = 4212. 4212 exceeds the maximum intermediate result, drop this branch.\n     |- Try 702 \/ 6 = 117. Evaluate 117 != 25, drop this branch.\n    |- Try 27 \/ 26 = 1.0. 1.0 is a decimal, drop this branch.\n  |- Try 4 - 2 = 2. Add 2 to the number set. Current number set: [2, 27, 26], target: 25. Options for choosing two numbers: [(2, 27), (2, 26), (27, 26)].\n   |- Pick two numbers (2, 27) (numbers left: [26]). Try possible operations.\n    |- Try 27 + 2 = 29. Add 29 to the number set. Current number set: [29, 26], target: 25, just two numbers left.\n     |- Try 29 + 26 = 55. Evaluate 55 != 25, drop this branch.\n     |- Try 29 - 26 = 3. Evaluate 3 != 25, drop this branch.\n     |- Try 29 * 26 = 754. Evaluate 754 != 25, drop this branch.\n     |- Try 29 \/ 26 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 27 - 2 = 25. Add 25 to the number set. Current number set: [25, 26], target: 25, just two numbers left.\n     |- Try 26 + 25 = 51. Evaluate 51 != 25, drop this branch.\n     |- Try 26 - 25 = 1. Evaluate 1 != 25, drop this branch.\n     |- Try 26 * 25 = 650. Evaluate 650 != 25, drop this branch.\n     |- Try 26 \/ 25 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 27 * 2 = 54. Add 54 to the number set. Current number set: [54, 26], target: 25, just two numbers left.\n     |- Try 54 + 26 = 80. Evaluate 80 != 25, drop this branch.\n     |- Try 54 - 26 = 28. Evaluate 28 != 25, drop this branch.\n     |- Try 54 * 26 = 1404. Evaluate 1404 != 25, drop this branch.\n     |- Try 54 \/ 26 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 27 \/ 2 = 13.5. 13.5 is a decimal, drop this branch.\n   |- Pick two numbers (2, 26) (numbers left: [27]). Try possible operations.\n    |- Try 26 + 2 = 28. Add 28 to the number set. Current number set: [28, 27], target: 25, just two numbers left.\n     |- Try 28 + 27 = 55. Evaluate 55 != 25, drop this branch.\n     |- Try 28 - 27 = 1. Evaluate 1 != 25, drop this branch.\n     |- Try 28 * 27 = 756. Evaluate 756 != 25, drop this branch.\n     |- Try 28 \/ 27 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 26 - 2 = 24. Add 24 to the number set. Current number set: [24, 27], target: 25, just two numbers left.\n     |- Try 27 + 24 = 51. Evaluate 51 != 25, drop this branch.\n     |- Try 27 - 24 = 3. Evaluate 3 != 25, drop this branch.\n     |- Try 27 * 24 = 648. Evaluate 648 != 25, drop this branch.\n     |- Try 27 \/ 24 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 26 * 2 = 52. Add 52 to the number set. Current number set: [52, 27], target: 25, just two numbers left.\n     |- Try 52 + 27 = 79. Evaluate 79 != 25, drop this branch.\n     |- Try 52 - 27 = 25. Evaluate 25 == 25, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 52 - 27 = 25\nThe step before: 26 * 2 = 52\nThe first step: 4 - 2 = 2\n\nOutput the solution in the required format:\n<Solution>\n4 - 2 = 2\n26 * 2 = 52\n52 - 27 = 25\n<\/Solution>\n","item":{"nums":[2,27,4,26],"solution":["4 - 2 = 2","26 * 2 = 52","52 - 27 = 25"],"target":25}}
+{"instance_id":"countdown_8k_20","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [24, 15, 2, 21]\nTarget: 42","reference_output":"# Search Procedure\nInitial number set: [24, 15, 2, 21], target: 42. Options for choosing two numbers: [(24, 15), (24, 2), (24, 21), (15, 2), (15, 21), (2, 21)].\n |- Pick two numbers (24, 15) (numbers left: [2, 21]). Try possible operations.\n  |- Try 24 + 15 = 39. Add 39 to the number set. Current number set: [39, 2, 21], target: 42. Options for choosing two numbers: [(39, 2), (39, 21), (2, 21)].\n   |- Pick two numbers (39, 2) (numbers left: [21]). Try possible operations.\n    |- Try 39 + 2 = 41. Add 41 to the number set. Current number set: [41, 21], target: 42, just two numbers left.\n     |- Try 41 + 21 = 62. Evaluate 62 != 42, drop this branch.\n     |- Try 41 - 21 = 20. Evaluate 20 != 42, drop this branch.\n     |- Try 41 * 21 = 861. Evaluate 861 != 42, drop this branch.\n     |- Try 41 \/ 21 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 39 - 2 = 37. Add 37 to the number set. Current number set: [37, 21], target: 42, just two numbers left.\n     |- Try 37 + 21 = 58. Evaluate 58 != 42, drop this branch.\n     |- Try 37 - 21 = 16. Evaluate 16 != 42, drop this branch.\n     |- Try 37 * 21 = 777. Evaluate 777 != 42, drop this branch.\n     |- Try 37 \/ 21 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 39 * 2 = 78. Add 78 to the number set. Current number set: [78, 21], target: 42, just two numbers left.\n     |- Try 78 + 21 = 99. Evaluate 99 != 42, drop this branch.\n     |- Try 78 - 21 = 57. Evaluate 57 != 42, drop this branch.\n     |- Try 78 * 21 = 1638. Evaluate 1638 != 42, drop this branch.\n     |- Try 78 \/ 21 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 39 \/ 2 = 19.5. 19.5 is a decimal, drop this branch.\n   |- Pick two numbers (39, 21) (numbers left: [2]). Try possible operations.\n    |- Try 39 + 21 = 60. Add 60 to the number set. Current number set: [60, 2], target: 42, just two numbers left.\n     |- Try 60 + 2 = 62. Evaluate 62 != 42, drop this branch.\n     |- Try 60 - 2 = 58. Evaluate 58 != 42, drop this branch.\n     |- Try 60 * 2 = 120. Evaluate 120 != 42, drop this branch.\n     |- Try 60 \/ 2 = 30. Evaluate 30 != 42, drop this branch.\n    |- Try 39 - 21 = 18. Add 18 to the number set. Current number set: [18, 2], target: 42, just two numbers left.\n     |- Try 18 + 2 = 20. Evaluate 20 != 42, drop this branch.\n     |- Try 18 - 2 = 16. Evaluate 16 != 42, drop this branch.\n     |- Try 18 * 2 = 36. Evaluate 36 != 42, drop this branch.\n     |- Try 18 \/ 2 = 9. Evaluate 9 != 42, drop this branch.\n    |- Try 39 * 21 = 819. Add 819 to the number set. Current number set: [819, 2], target: 42, just two numbers left.\n     |- Try 819 + 2 = 821. Evaluate 821 != 42, drop this branch.\n     |- Try 819 - 2 = 817. Evaluate 817 != 42, drop this branch.\n     |- Try 819 * 2 = 1638. Evaluate 1638 != 42, drop this branch.\n     |- Try 819 \/ 2 = 409.5. 409.5 is a decimal, drop this branch.\n    |- Try 39 \/ 21 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (2, 21) (numbers left: [39]). Try possible operations.\n    |- Try 21 + 2 = 23. Add 23 to the number set. Current number set: [23, 39], target: 42, just two numbers left.\n     |- Try 39 + 23 = 62. Evaluate 62 != 42, drop this branch.\n     |- Try 39 - 23 = 16. Evaluate 16 != 42, drop this branch.\n     |- Try 39 * 23 = 897. Evaluate 897 != 42, drop this branch.\n     |- Try 39 \/ 23 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 21 - 2 = 19. Add 19 to the number set. Current number set: [19, 39], target: 42, just two numbers left.\n     |- Try 39 + 19 = 58. Evaluate 58 != 42, drop this branch.\n     |- Try 39 - 19 = 20. Evaluate 20 != 42, drop this branch.\n     |- Try 39 * 19 = 741. Evaluate 741 != 42, drop this branch.\n     |- Try 39 \/ 19 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 21 * 2 = 42. Add 42 to the number set. Current number set: [42, 39], target: 42, just two numbers left.\n     |- Try 42 + 39 = 81. Evaluate 81 != 42, drop this branch.\n     |- Try 42 - 39 = 3. Evaluate 3 != 42, drop this branch.\n     |- Try 42 * 39 = 1638. Evaluate 1638 != 42, drop this branch.\n     |- Try 42 \/ 39 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 21 \/ 2 = 10.5. 10.5 is a decimal, drop this branch.\n  |- Try 24 - 15 = 9. Add 9 to the number set. Current number set: [9, 2, 21], target: 42. Options for choosing two numbers: [(9, 2), (9, 21), (2, 21)].\n   |- Pick two numbers (9, 2) (numbers left: [21]). Try possible operations.\n    |- Try 9 + 2 = 11. Add 11 to the number set. Current number set: [11, 21], target: 42, just two numbers left.\n     |- Try 21 + 11 = 32. Evaluate 32 != 42, drop this branch.\n     |- Try 21 - 11 = 10. Evaluate 10 != 42, drop this branch.\n     |- Try 21 * 11 = 231. Evaluate 231 != 42, drop this branch.\n     |- Try 21 \/ 11 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 9 - 2 = 7. Add 7 to the number set. Current number set: [7, 21], target: 42, just two numbers left.\n     |- Try 21 + 7 = 28. Evaluate 28 != 42, drop this branch.\n     |- Try 21 - 7 = 14. Evaluate 14 != 42, drop this branch.\n     |- Try 21 * 7 = 147. Evaluate 147 != 42, drop this branch.\n     |- Try 21 \/ 7 = 3. Evaluate 3 != 42, drop this branch.\n    |- Try 9 * 2 = 18. Add 18 to the number set. Current number set: [18, 21], target: 42, just two numbers left.\n     |- Try 21 + 18 = 39. Evaluate 39 != 42, drop this branch.\n     |- Try 21 - 18 = 3. Evaluate 3 != 42, drop this branch.\n     |- Try 21 * 18 = 378. Evaluate 378 != 42, drop this branch.\n     |- Try 21 \/ 18 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 9 \/ 2 = 4.5. 4.5 is a decimal, drop this branch.\n   |- Pick two numbers (9, 21) (numbers left: [2]). Try possible operations.\n    |- Try 21 + 9 = 30. Add 30 to the number set. Current number set: [30, 2], target: 42, just two numbers left.\n     |- Try 30 + 2 = 32. Evaluate 32 != 42, drop this branch.\n     |- Try 30 - 2 = 28. Evaluate 28 != 42, drop this branch.\n     |- Try 30 * 2 = 60. Evaluate 60 != 42, drop this branch.\n     |- Try 30 \/ 2 = 15. Evaluate 15 != 42, drop this branch.\n    |- Try 21 - 9 = 12. Add 12 to the number set. Current number set: [12, 2], target: 42, just two numbers left.\n     |- Try 12 + 2 = 14. Evaluate 14 != 42, drop this branch.\n     |- Try 12 - 2 = 10. Evaluate 10 != 42, drop this branch.\n     |- Try 12 * 2 = 24. Evaluate 24 != 42, drop this branch.\n     |- Try 12 \/ 2 = 6. Evaluate 6 != 42, drop this branch.\n    |- Try 21 * 9 = 189. Add 189 to the number set. Current number set: [189, 2], target: 42, just two numbers left.\n     |- Try 189 + 2 = 191. Evaluate 191 != 42, drop this branch.\n     |- Try 189 - 2 = 187. Evaluate 187 != 42, drop this branch.\n     |- Try 189 * 2 = 378. Evaluate 378 != 42, drop this branch.\n     |- Try 189 \/ 2 = 94.5. 94.5 is a decimal, drop this branch.\n    |- Try 21 \/ 9 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (2, 21) (numbers left: [9]). Try possible operations.\n    |- Try 21 + 2 = 23. Add 23 to the number set. Current number set: [23, 9], target: 42, just two numbers left.\n     |- Try 23 + 9 = 32. Evaluate 32 != 42, drop this branch.\n     |- Try 23 - 9 = 14. Evaluate 14 != 42, drop this branch.\n     |- Try 23 * 9 = 207. Evaluate 207 != 42, drop this branch.\n     |- Try 23 \/ 9 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 21 - 2 = 19. Add 19 to the number set. Current number set: [19, 9], target: 42, just two numbers left.\n     |- Try 19 + 9 = 28. Evaluate 28 != 42, drop this branch.\n     |- Try 19 - 9 = 10. Evaluate 10 != 42, drop this branch.\n     |- Try 19 * 9 = 171. Evaluate 171 != 42, drop this branch.\n     |- Try 19 \/ 9 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 21 * 2 = 42. Add 42 to the number set. Current number set: [42, 9], target: 42, just two numbers left.\n     |- Try 42 + 9 = 51. Evaluate 51 != 42, drop this branch.\n     |- Try 42 - 9 = 33. Evaluate 33 != 42, drop this branch.\n     |- Try 42 * 9 = 378. Evaluate 378 != 42, drop this branch.\n     |- Try 42 \/ 9 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 21 \/ 2 = 10.5. 10.5 is a decimal, drop this branch.\n  |- Try 24 * 15 = 360. Add 360 to the number set. Current number set: [360, 2, 21], target: 42. Options for choosing two numbers: [(360, 2), (360, 21), (2, 21)].\n   |- Pick two numbers (360, 2) (numbers left: [21]). Try possible operations.\n    |- Try 360 + 2 = 362. Add 362 to the number set. Current number set: [362, 21], target: 42, just two numbers left.\n     |- Try 362 + 21 = 383. Evaluate 383 != 42, drop this branch.\n     |- Try 362 - 21 = 341. Evaluate 341 != 42, drop this branch.\n     |- Try 362 * 21 = 7602. 7602 exceeds the maximum intermediate result, drop this branch.\n     |- Try 362 \/ 21 = 17.2. 17.2 is a decimal, drop this branch.\n    |- Try 360 - 2 = 358. Add 358 to the number set. Current number set: [358, 21], target: 42, just two numbers left.\n     |- Try 358 + 21 = 379. Evaluate 379 != 42, drop this branch.\n     |- Try 358 - 21 = 337. Evaluate 337 != 42, drop this branch.\n     |- Try 358 * 21 = 7518. 7518 exceeds the maximum intermediate result, drop this branch.\n     |- Try 358 \/ 21 = 17.0. 17.0 is a decimal, drop this branch.\n    |- Try 360 * 2 = 720. Add 720 to the number set. Current number set: [720, 21], target: 42, just two numbers left.\n     |- Try 720 + 21 = 741. Evaluate 741 != 42, drop this branch.\n     |- Try 720 - 21 = 699. Evaluate 699 != 42, drop this branch.\n     |- Try 720 * 21 = 15120. 15120 exceeds the maximum intermediate result, drop this branch.\n     |- Try 720 \/ 21 = 34.3. 34.3 is a decimal, drop this branch.\n    |- Try 360 \/ 2 = 180. Add 180 to the number set. Current number set: [180, 21], target: 42, just two numbers left.\n     |- Try 180 + 21 = 201. Evaluate 201 != 42, drop this branch.\n     |- Try 180 - 21 = 159. Evaluate 159 != 42, drop this branch.\n     |- Try 180 * 21 = 3780. 3780 exceeds the maximum intermediate result, drop this branch.\n     |- Try 180 \/ 21 = 8.6. 8.6 is a decimal, drop this branch.\n   |- Pick two numbers (360, 21) (numbers left: [2]). Try possible operations.\n    |- Try 360 + 21 = 381. Add 381 to the number set. Current number set: [381, 2], target: 42, just two numbers left.\n     |- Try 381 + 2 = 383. Evaluate 383 != 42, drop this branch.\n     |- Try 381 - 2 = 379. Evaluate 379 != 42, drop this branch.\n     |- Try 381 * 2 = 762. Evaluate 762 != 42, drop this branch.\n     |- Try 381 \/ 2 = 190.5. 190.5 is a decimal, drop this branch.\n    |- Try 360 - 21 = 339. Add 339 to the number set. Current number set: [339, 2], target: 42, just two numbers left.\n     |- Try 339 + 2 = 341. Evaluate 341 != 42, drop this branch.\n     |- Try 339 - 2 = 337. Evaluate 337 != 42, drop this branch.\n     |- Try 339 * 2 = 678. Evaluate 678 != 42, drop this branch.\n     |- Try 339 \/ 2 = 169.5. 169.5 is a decimal, drop this branch.\n    |- Try 360 * 21 = 7560. 7560 exceeds the maximum intermediate result, drop this branch.\n    |- Try 360 \/ 21 = 17.1. 17.1 is a decimal, drop this branch.\n   |- Pick two numbers (2, 21) (numbers left: [360]). Try possible operations.\n    |- Try 21 + 2 = 23. Add 23 to the number set. Current number set: [23, 360], target: 42, just two numbers left.\n     |- Try 360 + 23 = 383. Evaluate 383 != 42, drop this branch.\n     |- Try 360 - 23 = 337. Evaluate 337 != 42, drop this branch.\n     |- Try 360 * 23 = 8280. 8280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 360 \/ 23 = 15.7. 15.7 is a decimal, drop this branch.\n    |- Try 21 - 2 = 19. Add 19 to the number set. Current number set: [19, 360], target: 42, just two numbers left.\n     |- Try 360 + 19 = 379. Evaluate 379 != 42, drop this branch.\n     |- Try 360 - 19 = 341. Evaluate 341 != 42, drop this branch.\n     |- Try 360 * 19 = 6840. 6840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 360 \/ 19 = 18.9. 18.9 is a decimal, drop this branch.\n    |- Try 21 * 2 = 42. Add 42 to the number set. Current number set: [42, 360], target: 42, just two numbers left.\n     |- Try 360 + 42 = 402. Evaluate 402 != 42, drop this branch.\n     |- Try 360 - 42 = 318. Evaluate 318 != 42, drop this branch.\n     |- Try 360 * 42 = 15120. 15120 exceeds the maximum intermediate result, drop this branch.\n     |- Try 360 \/ 42 = 8.6. 8.6 is a decimal, drop this branch.\n    |- Try 21 \/ 2 = 10.5. 10.5 is a decimal, drop this branch.\n  |- Try 24 \/ 15 = 1.6. 1.6 is a decimal, drop this branch.\n |- Pick two numbers (24, 2) (numbers left: [15, 21]). Try possible operations.\n  |- Try 24 + 2 = 26. Add 26 to the number set. Current number set: [26, 15, 21], target: 42. Options for choosing two numbers: [(26, 15), (26, 21), (15, 21)].\n   |- Pick two numbers (26, 15) (numbers left: [21]). Try possible operations.\n    |- Try 26 + 15 = 41. Add 41 to the number set. Current number set: [41, 21], target: 42, just two numbers left.\n     |- Try 41 + 21 = 62. Evaluate 62 != 42, drop this branch.\n     |- Try 41 - 21 = 20. Evaluate 20 != 42, drop this branch.\n     |- Try 41 * 21 = 861. Evaluate 861 != 42, drop this branch.\n     |- Try 41 \/ 21 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 26 - 15 = 11. Add 11 to the number set. Current number set: [11, 21], target: 42, just two numbers left.\n     |- Try 21 + 11 = 32. Evaluate 32 != 42, drop this branch.\n     |- Try 21 - 11 = 10. Evaluate 10 != 42, drop this branch.\n     |- Try 21 * 11 = 231. Evaluate 231 != 42, drop this branch.\n     |- Try 21 \/ 11 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 26 * 15 = 390. Add 390 to the number set. Current number set: [390, 21], target: 42, just two numbers left.\n     |- Try 390 + 21 = 411. Evaluate 411 != 42, drop this branch.\n     |- Try 390 - 21 = 369. Evaluate 369 != 42, drop this branch.\n     |- Try 390 * 21 = 8190. 8190 exceeds the maximum intermediate result, drop this branch.\n     |- Try 390 \/ 21 = 18.6. 18.6 is a decimal, drop this branch.\n    |- Try 26 \/ 15 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (26, 21) (numbers left: [15]). Try possible operations.\n    |- Try 26 + 21 = 47. Add 47 to the number set. Current number set: [47, 15], target: 42, just two numbers left.\n     |- Try 47 + 15 = 62. Evaluate 62 != 42, drop this branch.\n     |- Try 47 - 15 = 32. Evaluate 32 != 42, drop this branch.\n     |- Try 47 * 15 = 705. Evaluate 705 != 42, drop this branch.\n     |- Try 47 \/ 15 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 26 - 21 = 5. Add 5 to the number set. Current number set: [5, 15], target: 42, just two numbers left.\n     |- Try 15 + 5 = 20. Evaluate 20 != 42, drop this branch.\n     |- Try 15 - 5 = 10. Evaluate 10 != 42, drop this branch.\n     |- Try 15 * 5 = 75. Evaluate 75 != 42, drop this branch.\n     |- Try 15 \/ 5 = 3. Evaluate 3 != 42, drop this branch.\n    |- Try 26 * 21 = 546. Add 546 to the number set. Current number set: [546, 15], target: 42, just two numbers left.\n     |- Try 546 + 15 = 561. Evaluate 561 != 42, drop this branch.\n     |- Try 546 - 15 = 531. Evaluate 531 != 42, drop this branch.\n     |- Try 546 * 15 = 8190. 8190 exceeds the maximum intermediate result, drop this branch.\n     |- Try 546 \/ 15 = 36.4. 36.4 is a decimal, drop this branch.\n    |- Try 26 \/ 21 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (15, 21) (numbers left: [26]). Try possible operations.\n    |- Try 21 + 15 = 36. Add 36 to the number set. Current number set: [36, 26], target: 42, just two numbers left.\n     |- Try 36 + 26 = 62. Evaluate 62 != 42, drop this branch.\n     |- Try 36 - 26 = 10. Evaluate 10 != 42, drop this branch.\n     |- Try 36 * 26 = 936. Evaluate 936 != 42, drop this branch.\n     |- Try 36 \/ 26 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 21 - 15 = 6. Add 6 to the number set. Current number set: [6, 26], target: 42, just two numbers left.\n     |- Try 26 + 6 = 32. Evaluate 32 != 42, drop this branch.\n     |- Try 26 - 6 = 20. Evaluate 20 != 42, drop this branch.\n     |- Try 26 * 6 = 156. Evaluate 156 != 42, drop this branch.\n     |- Try 26 \/ 6 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 21 * 15 = 315. Add 315 to the number set. Current number set: [315, 26], target: 42, just two numbers left.\n     |- Try 315 + 26 = 341. Evaluate 341 != 42, drop this branch.\n     |- Try 315 - 26 = 289. Evaluate 289 != 42, drop this branch.\n     |- Try 315 * 26 = 8190. 8190 exceeds the maximum intermediate result, drop this branch.\n     |- Try 315 \/ 26 = 12.1. 12.1 is a decimal, drop this branch.\n    |- Try 21 \/ 15 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 24 - 2 = 22. Add 22 to the number set. Current number set: [22, 15, 21], target: 42. Options for choosing two numbers: [(22, 15), (22, 21), (15, 21)].\n   |- Pick two numbers (22, 15) (numbers left: [21]). Try possible operations.\n    |- Try 22 + 15 = 37. Add 37 to the number set. Current number set: [37, 21], target: 42, just two numbers left.\n     |- Try 37 + 21 = 58. Evaluate 58 != 42, drop this branch.\n     |- Try 37 - 21 = 16. Evaluate 16 != 42, drop this branch.\n     |- Try 37 * 21 = 777. Evaluate 777 != 42, drop this branch.\n     |- Try 37 \/ 21 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 22 - 15 = 7. Add 7 to the number set. Current number set: [7, 21], target: 42, just two numbers left.\n     |- Try 21 + 7 = 28. Evaluate 28 != 42, drop this branch.\n     |- Try 21 - 7 = 14. Evaluate 14 != 42, drop this branch.\n     |- Try 21 * 7 = 147. Evaluate 147 != 42, drop this branch.\n     |- Try 21 \/ 7 = 3. Evaluate 3 != 42, drop this branch.\n    |- Try 22 * 15 = 330. Add 330 to the number set. Current number set: [330, 21], target: 42, just two numbers left.\n     |- Try 330 + 21 = 351. Evaluate 351 != 42, drop this branch.\n     |- Try 330 - 21 = 309. Evaluate 309 != 42, drop this branch.\n     |- Try 330 * 21 = 6930. 6930 exceeds the maximum intermediate result, drop this branch.\n     |- Try 330 \/ 21 = 15.7. 15.7 is a decimal, drop this branch.\n    |- Try 22 \/ 15 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (22, 21) (numbers left: [15]). Try possible operations.\n    |- Try 22 + 21 = 43. Add 43 to the number set. Current number set: [43, 15], target: 42, just two numbers left.\n     |- Try 43 + 15 = 58. Evaluate 58 != 42, drop this branch.\n     |- Try 43 - 15 = 28. Evaluate 28 != 42, drop this branch.\n     |- Try 43 * 15 = 645. Evaluate 645 != 42, drop this branch.\n     |- Try 43 \/ 15 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 22 - 21 = 1. Add 1 to the number set. Current number set: [1, 15], target: 42, just two numbers left.\n     |- Try 15 + 1 = 16. Evaluate 16 != 42, drop this branch.\n     |- Try 15 - 1 = 14. Evaluate 14 != 42, drop this branch.\n     |- Try 15 * 1 = 15. Evaluate 15 != 42, drop this branch.\n     |- Try 15 \/ 1 = 15. Evaluate 15 != 42, drop this branch.\n    |- Try 22 * 21 = 462. Add 462 to the number set. Current number set: [462, 15], target: 42, just two numbers left.\n     |- Try 462 + 15 = 477. Evaluate 477 != 42, drop this branch.\n     |- Try 462 - 15 = 447. Evaluate 447 != 42, drop this branch.\n     |- Try 462 * 15 = 6930. 6930 exceeds the maximum intermediate result, drop this branch.\n     |- Try 462 \/ 15 = 30.8. 30.8 is a decimal, drop this branch.\n    |- Try 22 \/ 21 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (15, 21) (numbers left: [22]). Try possible operations.\n    |- Try 21 + 15 = 36. Add 36 to the number set. Current number set: [36, 22], target: 42, just two numbers left.\n     |- Try 36 + 22 = 58. Evaluate 58 != 42, drop this branch.\n     |- Try 36 - 22 = 14. Evaluate 14 != 42, drop this branch.\n     |- Try 36 * 22 = 792. Evaluate 792 != 42, drop this branch.\n     |- Try 36 \/ 22 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 21 - 15 = 6. Add 6 to the number set. Current number set: [6, 22], target: 42, just two numbers left.\n     |- Try 22 + 6 = 28. Evaluate 28 != 42, drop this branch.\n     |- Try 22 - 6 = 16. Evaluate 16 != 42, drop this branch.\n     |- Try 22 * 6 = 132. Evaluate 132 != 42, drop this branch.\n     |- Try 22 \/ 6 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 21 * 15 = 315. Add 315 to the number set. Current number set: [315, 22], target: 42, just two numbers left.\n     |- Try 315 + 22 = 337. Evaluate 337 != 42, drop this branch.\n     |- Try 315 - 22 = 293. Evaluate 293 != 42, drop this branch.\n     |- Try 315 * 22 = 6930. 6930 exceeds the maximum intermediate result, drop this branch.\n     |- Try 315 \/ 22 = 14.3. 14.3 is a decimal, drop this branch.\n    |- Try 21 \/ 15 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 24 * 2 = 48. Add 48 to the number set. Current number set: [48, 15, 21], target: 42. Options for choosing two numbers: [(48, 15), (48, 21), (15, 21)].\n   |- Pick two numbers (48, 15) (numbers left: [21]). Try possible operations.\n    |- Try 48 + 15 = 63. Add 63 to the number set. Current number set: [63, 21], target: 42, just two numbers left.\n     |- Try 63 + 21 = 84. Evaluate 84 != 42, drop this branch.\n     |- Try 63 - 21 = 42. Evaluate 42 == 42, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 63 - 21 = 42\nThe step before: 48 + 15 = 63\nThe first step: 24 * 2 = 48\n\nOutput the solution in the required format:\n<Solution>\n24 * 2 = 48\n48 + 15 = 63\n63 - 21 = 42\n<\/Solution>\n","item":{"nums":[24,15,2,21],"solution":["24 * 2 = 48","48 + 15 = 63","63 - 21 = 42"],"target":42}}
+{"instance_id":"countdown_8k_21","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [9, 5, 46, 30]\nTarget: 41","reference_output":"# Search Procedure\nInitial number set: [9, 5, 46, 30], target: 41. Options for choosing two numbers: [(9, 5), (9, 46), (9, 30), (5, 46), (5, 30), (46, 30)].\n |- Pick two numbers (9, 5) (numbers left: [46, 30]). Try possible operations.\n  |- Try 9 + 5 = 14. Add 14 to the number set. Current number set: [14, 46, 30], target: 41. Options for choosing two numbers: [(14, 46), (14, 30), (46, 30)].\n   |- Pick two numbers (14, 46) (numbers left: [30]). Try possible operations.\n    |- Try 46 + 14 = 60. Add 60 to the number set. Current number set: [60, 30], target: 41, just two numbers left.\n     |- Try 60 + 30 = 90. Evaluate 90 != 41, drop this branch.\n     |- Try 60 - 30 = 30. Evaluate 30 != 41, drop this branch.\n     |- Try 60 * 30 = 1800. Evaluate 1800 != 41, drop this branch.\n     |- Try 60 \/ 30 = 2. Evaluate 2 != 41, drop this branch.\n    |- Try 46 - 14 = 32. Add 32 to the number set. Current number set: [32, 30], target: 41, just two numbers left.\n     |- Try 32 + 30 = 62. Evaluate 62 != 41, drop this branch.\n     |- Try 32 - 30 = 2. Evaluate 2 != 41, drop this branch.\n     |- Try 32 * 30 = 960. Evaluate 960 != 41, drop this branch.\n     |- Try 32 \/ 30 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 46 * 14 = 644. Add 644 to the number set. Current number set: [644, 30], target: 41, just two numbers left.\n     |- Try 644 + 30 = 674. Evaluate 674 != 41, drop this branch.\n     |- Try 644 - 30 = 614. Evaluate 614 != 41, drop this branch.\n     |- Try 644 * 30 = 19320. 19320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 644 \/ 30 = 21.5. 21.5 is a decimal, drop this branch.\n    |- Try 46 \/ 14 = 3.3. 3.3 is a decimal, drop this branch.\n   |- Pick two numbers (14, 30) (numbers left: [46]). Try possible operations.\n    |- Try 30 + 14 = 44. Add 44 to the number set. Current number set: [44, 46], target: 41, just two numbers left.\n     |- Try 46 + 44 = 90. Evaluate 90 != 41, drop this branch.\n     |- Try 46 - 44 = 2. Evaluate 2 != 41, drop this branch.\n     |- Try 46 * 44 = 2024. 2024 exceeds the maximum intermediate result, drop this branch.\n     |- Try 46 \/ 44 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 30 - 14 = 16. Add 16 to the number set. Current number set: [16, 46], target: 41, just two numbers left.\n     |- Try 46 + 16 = 62. Evaluate 62 != 41, drop this branch.\n     |- Try 46 - 16 = 30. Evaluate 30 != 41, drop this branch.\n     |- Try 46 * 16 = 736. Evaluate 736 != 41, drop this branch.\n     |- Try 46 \/ 16 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 30 * 14 = 420. Add 420 to the number set. Current number set: [420, 46], target: 41, just two numbers left.\n     |- Try 420 + 46 = 466. Evaluate 466 != 41, drop this branch.\n     |- Try 420 - 46 = 374. Evaluate 374 != 41, drop this branch.\n     |- Try 420 * 46 = 19320. 19320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 420 \/ 46 = 9.1. 9.1 is a decimal, drop this branch.\n    |- Try 30 \/ 14 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (46, 30) (numbers left: [14]). Try possible operations.\n    |- Try 46 + 30 = 76. Add 76 to the number set. Current number set: [76, 14], target: 41, just two numbers left.\n     |- Try 76 + 14 = 90. Evaluate 90 != 41, drop this branch.\n     |- Try 76 - 14 = 62. Evaluate 62 != 41, drop this branch.\n     |- Try 76 * 14 = 1064. Evaluate 1064 != 41, drop this branch.\n     |- Try 76 \/ 14 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 46 - 30 = 16. Add 16 to the number set. Current number set: [16, 14], target: 41, just two numbers left.\n     |- Try 16 + 14 = 30. Evaluate 30 != 41, drop this branch.\n     |- Try 16 - 14 = 2. Evaluate 2 != 41, drop this branch.\n     |- Try 16 * 14 = 224. Evaluate 224 != 41, drop this branch.\n     |- Try 16 \/ 14 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 46 * 30 = 1380. Add 1380 to the number set. Current number set: [1380, 14], target: 41, just two numbers left.\n     |- Try 1380 + 14 = 1394. Evaluate 1394 != 41, drop this branch.\n     |- Try 1380 - 14 = 1366. Evaluate 1366 != 41, drop this branch.\n     |- Try 1380 * 14 = 19320. 19320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1380 \/ 14 = 98.6. 98.6 is a decimal, drop this branch.\n    |- Try 46 \/ 30 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 9 - 5 = 4. Add 4 to the number set. Current number set: [4, 46, 30], target: 41. Options for choosing two numbers: [(4, 46), (4, 30), (46, 30)].\n   |- Pick two numbers (4, 46) (numbers left: [30]). Try possible operations.\n    |- Try 46 + 4 = 50. Add 50 to the number set. Current number set: [50, 30], target: 41, just two numbers left.\n     |- Try 50 + 30 = 80. Evaluate 80 != 41, drop this branch.\n     |- Try 50 - 30 = 20. Evaluate 20 != 41, drop this branch.\n     |- Try 50 * 30 = 1500. Evaluate 1500 != 41, drop this branch.\n     |- Try 50 \/ 30 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 46 - 4 = 42. Add 42 to the number set. Current number set: [42, 30], target: 41, just two numbers left.\n     |- Try 42 + 30 = 72. Evaluate 72 != 41, drop this branch.\n     |- Try 42 - 30 = 12. Evaluate 12 != 41, drop this branch.\n     |- Try 42 * 30 = 1260. Evaluate 1260 != 41, drop this branch.\n     |- Try 42 \/ 30 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 46 * 4 = 184. Add 184 to the number set. Current number set: [184, 30], target: 41, just two numbers left.\n     |- Try 184 + 30 = 214. Evaluate 214 != 41, drop this branch.\n     |- Try 184 - 30 = 154. Evaluate 154 != 41, drop this branch.\n     |- Try 184 * 30 = 5520. 5520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 184 \/ 30 = 6.1. 6.1 is a decimal, drop this branch.\n    |- Try 46 \/ 4 = 11.5. 11.5 is a decimal, drop this branch.\n   |- Pick two numbers (4, 30) (numbers left: [46]). Try possible operations.\n    |- Try 30 + 4 = 34. Add 34 to the number set. Current number set: [34, 46], target: 41, just two numbers left.\n     |- Try 46 + 34 = 80. Evaluate 80 != 41, drop this branch.\n     |- Try 46 - 34 = 12. Evaluate 12 != 41, drop this branch.\n     |- Try 46 * 34 = 1564. Evaluate 1564 != 41, drop this branch.\n     |- Try 46 \/ 34 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 30 - 4 = 26. Add 26 to the number set. Current number set: [26, 46], target: 41, just two numbers left.\n     |- Try 46 + 26 = 72. Evaluate 72 != 41, drop this branch.\n     |- Try 46 - 26 = 20. Evaluate 20 != 41, drop this branch.\n     |- Try 46 * 26 = 1196. Evaluate 1196 != 41, drop this branch.\n     |- Try 46 \/ 26 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 30 * 4 = 120. Add 120 to the number set. Current number set: [120, 46], target: 41, just two numbers left.\n     |- Try 120 + 46 = 166. Evaluate 166 != 41, drop this branch.\n     |- Try 120 - 46 = 74. Evaluate 74 != 41, drop this branch.\n     |- Try 120 * 46 = 5520. 5520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 120 \/ 46 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 30 \/ 4 = 7.5. 7.5 is a decimal, drop this branch.\n   |- Pick two numbers (46, 30) (numbers left: [4]). Try possible operations.\n    |- Try 46 + 30 = 76. Add 76 to the number set. Current number set: [76, 4], target: 41, just two numbers left.\n     |- Try 76 + 4 = 80. Evaluate 80 != 41, drop this branch.\n     |- Try 76 - 4 = 72. Evaluate 72 != 41, drop this branch.\n     |- Try 76 * 4 = 304. Evaluate 304 != 41, drop this branch.\n     |- Try 76 \/ 4 = 19. Evaluate 19 != 41, drop this branch.\n    |- Try 46 - 30 = 16. Add 16 to the number set. Current number set: [16, 4], target: 41, just two numbers left.\n     |- Try 16 + 4 = 20. Evaluate 20 != 41, drop this branch.\n     |- Try 16 - 4 = 12. Evaluate 12 != 41, drop this branch.\n     |- Try 16 * 4 = 64. Evaluate 64 != 41, drop this branch.\n     |- Try 16 \/ 4 = 4. Evaluate 4 != 41, drop this branch.\n    |- Try 46 * 30 = 1380. Add 1380 to the number set. Current number set: [1380, 4], target: 41, just two numbers left.\n     |- Try 1380 + 4 = 1384. Evaluate 1384 != 41, drop this branch.\n     |- Try 1380 - 4 = 1376. Evaluate 1376 != 41, drop this branch.\n     |- Try 1380 * 4 = 5520. 5520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1380 \/ 4 = 345. Evaluate 345 != 41, drop this branch.\n    |- Try 46 \/ 30 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 9 * 5 = 45. Add 45 to the number set. Current number set: [45, 46, 30], target: 41. Options for choosing two numbers: [(45, 46), (45, 30), (46, 30)].\n   |- Pick two numbers (45, 46) (numbers left: [30]). Try possible operations.\n    |- Try 46 + 45 = 91. Add 91 to the number set. Current number set: [91, 30], target: 41, just two numbers left.\n     |- Try 91 + 30 = 121. Evaluate 121 != 41, drop this branch.\n     |- Try 91 - 30 = 61. Evaluate 61 != 41, drop this branch.\n     |- Try 91 * 30 = 2730. 2730 exceeds the maximum intermediate result, drop this branch.\n     |- Try 91 \/ 30 = 3.0. 3.0 is a decimal, drop this branch.\n    |- Try 46 - 45 = 1. Add 1 to the number set. Current number set: [1, 30], target: 41, just two numbers left.\n     |- Try 30 + 1 = 31. Evaluate 31 != 41, drop this branch.\n     |- Try 30 - 1 = 29. Evaluate 29 != 41, drop this branch.\n     |- Try 30 * 1 = 30. Evaluate 30 != 41, drop this branch.\n     |- Try 30 \/ 1 = 30. Evaluate 30 != 41, drop this branch.\n    |- Try 46 * 45 = 2070. 2070 exceeds the maximum intermediate result, drop this branch.\n    |- Try 46 \/ 45 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (45, 30) (numbers left: [46]). Try possible operations.\n    |- Try 45 + 30 = 75. Add 75 to the number set. Current number set: [75, 46], target: 41, just two numbers left.\n     |- Try 75 + 46 = 121. Evaluate 121 != 41, drop this branch.\n     |- Try 75 - 46 = 29. Evaluate 29 != 41, drop this branch.\n     |- Try 75 * 46 = 3450. 3450 exceeds the maximum intermediate result, drop this branch.\n     |- Try 75 \/ 46 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 45 - 30 = 15. Add 15 to the number set. Current number set: [15, 46], target: 41, just two numbers left.\n     |- Try 46 + 15 = 61. Evaluate 61 != 41, drop this branch.\n     |- Try 46 - 15 = 31. Evaluate 31 != 41, drop this branch.\n     |- Try 46 * 15 = 690. Evaluate 690 != 41, drop this branch.\n     |- Try 46 \/ 15 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 45 * 30 = 1350. Add 1350 to the number set. Current number set: [1350, 46], target: 41, just two numbers left.\n     |- Try 1350 + 46 = 1396. Evaluate 1396 != 41, drop this branch.\n     |- Try 1350 - 46 = 1304. Evaluate 1304 != 41, drop this branch.\n     |- Try 1350 * 46 = 62100. 62100 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1350 \/ 46 = 29.3. 29.3 is a decimal, drop this branch.\n    |- Try 45 \/ 30 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (46, 30) (numbers left: [45]). Try possible operations.\n    |- Try 46 + 30 = 76. Add 76 to the number set. Current number set: [76, 45], target: 41, just two numbers left.\n     |- Try 76 + 45 = 121. Evaluate 121 != 41, drop this branch.\n     |- Try 76 - 45 = 31. Evaluate 31 != 41, drop this branch.\n     |- Try 76 * 45 = 3420. 3420 exceeds the maximum intermediate result, drop this branch.\n     |- Try 76 \/ 45 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 46 - 30 = 16. Add 16 to the number set. Current number set: [16, 45], target: 41, just two numbers left.\n     |- Try 45 + 16 = 61. Evaluate 61 != 41, drop this branch.\n     |- Try 45 - 16 = 29. Evaluate 29 != 41, drop this branch.\n     |- Try 45 * 16 = 720. Evaluate 720 != 41, drop this branch.\n     |- Try 45 \/ 16 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 46 * 30 = 1380. Add 1380 to the number set. Current number set: [1380, 45], target: 41, just two numbers left.\n     |- Try 1380 + 45 = 1425. Evaluate 1425 != 41, drop this branch.\n     |- Try 1380 - 45 = 1335. Evaluate 1335 != 41, drop this branch.\n     |- Try 1380 * 45 = 62100. 62100 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1380 \/ 45 = 30.7. 30.7 is a decimal, drop this branch.\n    |- Try 46 \/ 30 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 9 \/ 5 = 1.8. 1.8 is a decimal, drop this branch.\n |- Pick two numbers (9, 46) (numbers left: [5, 30]). Try possible operations.\n  |- Try 46 + 9 = 55. Add 55 to the number set. Current number set: [55, 5, 30], target: 41. Options for choosing two numbers: [(55, 5), (55, 30), (5, 30)].\n   |- Pick two numbers (55, 5) (numbers left: [30]). Try possible operations.\n    |- Try 55 + 5 = 60. Add 60 to the number set. Current number set: [60, 30], target: 41, just two numbers left.\n     |- Try 60 + 30 = 90. Evaluate 90 != 41, drop this branch.\n     |- Try 60 - 30 = 30. Evaluate 30 != 41, drop this branch.\n     |- Try 60 * 30 = 1800. Evaluate 1800 != 41, drop this branch.\n     |- Try 60 \/ 30 = 2. Evaluate 2 != 41, drop this branch.\n    |- Try 55 - 5 = 50. Add 50 to the number set. Current number set: [50, 30], target: 41, just two numbers left.\n     |- Try 50 + 30 = 80. Evaluate 80 != 41, drop this branch.\n     |- Try 50 - 30 = 20. Evaluate 20 != 41, drop this branch.\n     |- Try 50 * 30 = 1500. Evaluate 1500 != 41, drop this branch.\n     |- Try 50 \/ 30 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 55 * 5 = 275. Add 275 to the number set. Current number set: [275, 30], target: 41, just two numbers left.\n     |- Try 275 + 30 = 305. Evaluate 305 != 41, drop this branch.\n     |- Try 275 - 30 = 245. Evaluate 245 != 41, drop this branch.\n     |- Try 275 * 30 = 8250. 8250 exceeds the maximum intermediate result, drop this branch.\n     |- Try 275 \/ 30 = 9.2. 9.2 is a decimal, drop this branch.\n    |- Try 55 \/ 5 = 11. Add 11 to the number set. Current number set: [11, 30], target: 41, just two numbers left.\n     |- Try 30 + 11 = 41. Evaluate 41 == 41, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 30 + 11 = 41\nThe step before: 55 \/ 5 = 11\nThe first step: 46 + 9 = 55\n\nOutput the solution in the required format:\n<Solution>\n46 + 9 = 55\n55 \/ 5 = 11\n30 + 11 = 41\n<\/Solution>\n","item":{"nums":[9,5,46,30],"solution":["46 + 9 = 55","55 \/ 5 = 11","30 + 11 = 41"],"target":41}}
+{"instance_id":"countdown_8k_22","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [45, 32, 13, 8]\nTarget: 28","reference_output":"# Search Procedure\nInitial number set: [45, 32, 13, 8], target: 28. Options for choosing two numbers: [(45, 32), (45, 13), (45, 8), (32, 13), (32, 8), (13, 8)].\n |- Pick two numbers (45, 32) (numbers left: [13, 8]). Try possible operations.\n  |- Try 45 + 32 = 77. Add 77 to the number set. Current number set: [77, 13, 8], target: 28. Options for choosing two numbers: [(77, 13), (77, 8), (13, 8)].\n   |- Pick two numbers (77, 13) (numbers left: [8]). Try possible operations.\n    |- Try 77 + 13 = 90. Add 90 to the number set. Current number set: [90, 8], target: 28, just two numbers left.\n     |- Try 90 + 8 = 98. Evaluate 98 != 28, drop this branch.\n     |- Try 90 - 8 = 82. Evaluate 82 != 28, drop this branch.\n     |- Try 90 * 8 = 720. Evaluate 720 != 28, drop this branch.\n     |- Try 90 \/ 8 = 11.2. 11.2 is a decimal, drop this branch.\n    |- Try 77 - 13 = 64. Add 64 to the number set. Current number set: [64, 8], target: 28, just two numbers left.\n     |- Try 64 + 8 = 72. Evaluate 72 != 28, drop this branch.\n     |- Try 64 - 8 = 56. Evaluate 56 != 28, drop this branch.\n     |- Try 64 * 8 = 512. Evaluate 512 != 28, drop this branch.\n     |- Try 64 \/ 8 = 8. Evaluate 8 != 28, drop this branch.\n    |- Try 77 * 13 = 1001. Add 1001 to the number set. Current number set: [1001, 8], target: 28, just two numbers left.\n     |- Try 1001 + 8 = 1009. Evaluate 1009 != 28, drop this branch.\n     |- Try 1001 - 8 = 993. Evaluate 993 != 28, drop this branch.\n     |- Try 1001 * 8 = 8008. 8008 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1001 \/ 8 = 125.1. 125.1 is a decimal, drop this branch.\n    |- Try 77 \/ 13 = 5.9. 5.9 is a decimal, drop this branch.\n   |- Pick two numbers (77, 8) (numbers left: [13]). Try possible operations.\n    |- Try 77 + 8 = 85. Add 85 to the number set. Current number set: [85, 13], target: 28, just two numbers left.\n     |- Try 85 + 13 = 98. Evaluate 98 != 28, drop this branch.\n     |- Try 85 - 13 = 72. Evaluate 72 != 28, drop this branch.\n     |- Try 85 * 13 = 1105. Evaluate 1105 != 28, drop this branch.\n     |- Try 85 \/ 13 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 77 - 8 = 69. Add 69 to the number set. Current number set: [69, 13], target: 28, just two numbers left.\n     |- Try 69 + 13 = 82. Evaluate 82 != 28, drop this branch.\n     |- Try 69 - 13 = 56. Evaluate 56 != 28, drop this branch.\n     |- Try 69 * 13 = 897. Evaluate 897 != 28, drop this branch.\n     |- Try 69 \/ 13 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 77 * 8 = 616. Add 616 to the number set. Current number set: [616, 13], target: 28, just two numbers left.\n     |- Try 616 + 13 = 629. Evaluate 629 != 28, drop this branch.\n     |- Try 616 - 13 = 603. Evaluate 603 != 28, drop this branch.\n     |- Try 616 * 13 = 8008. 8008 exceeds the maximum intermediate result, drop this branch.\n     |- Try 616 \/ 13 = 47.4. 47.4 is a decimal, drop this branch.\n    |- Try 77 \/ 8 = 9.6. 9.6 is a decimal, drop this branch.\n   |- Pick two numbers (13, 8) (numbers left: [77]). Try possible operations.\n    |- Try 13 + 8 = 21. Add 21 to the number set. Current number set: [21, 77], target: 28, just two numbers left.\n     |- Try 77 + 21 = 98. Evaluate 98 != 28, drop this branch.\n     |- Try 77 - 21 = 56. Evaluate 56 != 28, drop this branch.\n     |- Try 77 * 21 = 1617. Evaluate 1617 != 28, drop this branch.\n     |- Try 77 \/ 21 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 13 - 8 = 5. Add 5 to the number set. Current number set: [5, 77], target: 28, just two numbers left.\n     |- Try 77 + 5 = 82. Evaluate 82 != 28, drop this branch.\n     |- Try 77 - 5 = 72. Evaluate 72 != 28, drop this branch.\n     |- Try 77 * 5 = 385. Evaluate 385 != 28, drop this branch.\n     |- Try 77 \/ 5 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 13 * 8 = 104. Add 104 to the number set. Current number set: [104, 77], target: 28, just two numbers left.\n     |- Try 104 + 77 = 181. Evaluate 181 != 28, drop this branch.\n     |- Try 104 - 77 = 27. Evaluate 27 != 28, drop this branch.\n     |- Try 104 * 77 = 8008. 8008 exceeds the maximum intermediate result, drop this branch.\n     |- Try 104 \/ 77 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 13 \/ 8 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 45 - 32 = 13. Add 13 to the number set. Current number set: [13, 13, 8], target: 28. Options for choosing two numbers: [(13, 13), (13, 8), (13, 8)].\n   |- Pick two numbers (13, 13) (numbers left: [8]). Try possible operations.\n    |- Try 13 + 13 = 26. Add 26 to the number set. Current number set: [26, 8], target: 28, just two numbers left.\n     |- Try 26 + 8 = 34. Evaluate 34 != 28, drop this branch.\n     |- Try 26 - 8 = 18. Evaluate 18 != 28, drop this branch.\n     |- Try 26 * 8 = 208. Evaluate 208 != 28, drop this branch.\n     |- Try 26 \/ 8 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 13 - 13 = 0. Add 0 to the number set. Current number set: [0, 8], target: 28, just two numbers left.\n     |- Try 8 + 0 = 8. Evaluate 8 != 28, drop this branch.\n     |- Try 8 - 0 = 8. Evaluate 8 != 28, drop this branch.\n     |- Try 8 * 0 = 0. Evaluate 0 != 28, drop this branch.\n     |- Try 8 \/ 0 (invalid operation). drop this branch.\n    |- Try 13 * 13 = 169. Add 169 to the number set. Current number set: [169, 8], target: 28, just two numbers left.\n     |- Try 169 + 8 = 177. Evaluate 177 != 28, drop this branch.\n     |- Try 169 - 8 = 161. Evaluate 161 != 28, drop this branch.\n     |- Try 169 * 8 = 1352. Evaluate 1352 != 28, drop this branch.\n     |- Try 169 \/ 8 = 21.1. 21.1 is a decimal, drop this branch.\n    |- Try 13 \/ 13 = 1. Add 1 to the number set. Current number set: [1, 8], target: 28, just two numbers left.\n     |- Try 8 + 1 = 9. Evaluate 9 != 28, drop this branch.\n     |- Try 8 - 1 = 7. Evaluate 7 != 28, drop this branch.\n     |- Try 8 * 1 = 8. Evaluate 8 != 28, drop this branch.\n     |- Try 8 \/ 1 = 8. Evaluate 8 != 28, drop this branch.\n   |- Pick two numbers (13, 8) (numbers left: [13]). Try possible operations.\n    |- Try 13 + 8 = 21. Add 21 to the number set. Current number set: [21, 13], target: 28, just two numbers left.\n     |- Try 21 + 13 = 34. Evaluate 34 != 28, drop this branch.\n     |- Try 21 - 13 = 8. Evaluate 8 != 28, drop this branch.\n     |- Try 21 * 13 = 273. Evaluate 273 != 28, drop this branch.\n     |- Try 21 \/ 13 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 13 - 8 = 5. Add 5 to the number set. Current number set: [5, 13], target: 28, just two numbers left.\n     |- Try 13 + 5 = 18. Evaluate 18 != 28, drop this branch.\n     |- Try 13 - 5 = 8. Evaluate 8 != 28, drop this branch.\n     |- Try 13 * 5 = 65. Evaluate 65 != 28, drop this branch.\n     |- Try 13 \/ 5 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 13 * 8 = 104. Add 104 to the number set. Current number set: [104, 13], target: 28, just two numbers left.\n     |- Try 104 + 13 = 117. Evaluate 117 != 28, drop this branch.\n     |- Try 104 - 13 = 91. Evaluate 91 != 28, drop this branch.\n     |- Try 104 * 13 = 1352. Evaluate 1352 != 28, drop this branch.\n     |- Try 104 \/ 13 = 8. Evaluate 8 != 28, drop this branch.\n    |- Try 13 \/ 8 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (13, 8) (numbers left: [13]). Try possible operations.\n    |- Try 13 + 8 = 21. Add 21 to the number set. Current number set: [21, 13], target: 28, just two numbers left.\n     |- Try 21 + 13 = 34. Evaluate 34 != 28, drop this branch.\n     |- Try 21 - 13 = 8. Evaluate 8 != 28, drop this branch.\n     |- Try 21 * 13 = 273. Evaluate 273 != 28, drop this branch.\n     |- Try 21 \/ 13 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 13 - 8 = 5. Add 5 to the number set. Current number set: [5, 13], target: 28, just two numbers left.\n     |- Try 13 + 5 = 18. Evaluate 18 != 28, drop this branch.\n     |- Try 13 - 5 = 8. Evaluate 8 != 28, drop this branch.\n     |- Try 13 * 5 = 65. Evaluate 65 != 28, drop this branch.\n     |- Try 13 \/ 5 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 13 * 8 = 104. Add 104 to the number set. Current number set: [104, 13], target: 28, just two numbers left.\n     |- Try 104 + 13 = 117. Evaluate 117 != 28, drop this branch.\n     |- Try 104 - 13 = 91. Evaluate 91 != 28, drop this branch.\n     |- Try 104 * 13 = 1352. Evaluate 1352 != 28, drop this branch.\n     |- Try 104 \/ 13 = 8. Evaluate 8 != 28, drop this branch.\n    |- Try 13 \/ 8 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 45 * 32 = 1440. Add 1440 to the number set. Current number set: [1440, 13, 8], target: 28. Options for choosing two numbers: [(1440, 13), (1440, 8), (13, 8)].\n   |- Pick two numbers (1440, 13) (numbers left: [8]). Try possible operations.\n    |- Try 1440 + 13 = 1453. Add 1453 to the number set. Current number set: [1453, 8], target: 28, just two numbers left.\n     |- Try 1453 + 8 = 1461. Evaluate 1461 != 28, drop this branch.\n     |- Try 1453 - 8 = 1445. Evaluate 1445 != 28, drop this branch.\n     |- Try 1453 * 8 = 11624. 11624 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1453 \/ 8 = 181.6. 181.6 is a decimal, drop this branch.\n    |- Try 1440 - 13 = 1427. Add 1427 to the number set. Current number set: [1427, 8], target: 28, just two numbers left.\n     |- Try 1427 + 8 = 1435. Evaluate 1435 != 28, drop this branch.\n     |- Try 1427 - 8 = 1419. Evaluate 1419 != 28, drop this branch.\n     |- Try 1427 * 8 = 11416. 11416 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1427 \/ 8 = 178.4. 178.4 is a decimal, drop this branch.\n    |- Try 1440 * 13 = 18720. 18720 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1440 \/ 13 = 110.8. 110.8 is a decimal, drop this branch.\n   |- Pick two numbers (1440, 8) (numbers left: [13]). Try possible operations.\n    |- Try 1440 + 8 = 1448. Add 1448 to the number set. Current number set: [1448, 13], target: 28, just two numbers left.\n     |- Try 1448 + 13 = 1461. Evaluate 1461 != 28, drop this branch.\n     |- Try 1448 - 13 = 1435. Evaluate 1435 != 28, drop this branch.\n     |- Try 1448 * 13 = 18824. 18824 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1448 \/ 13 = 111.4. 111.4 is a decimal, drop this branch.\n    |- Try 1440 - 8 = 1432. Add 1432 to the number set. Current number set: [1432, 13], target: 28, just two numbers left.\n     |- Try 1432 + 13 = 1445. Evaluate 1445 != 28, drop this branch.\n     |- Try 1432 - 13 = 1419. Evaluate 1419 != 28, drop this branch.\n     |- Try 1432 * 13 = 18616. 18616 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1432 \/ 13 = 110.2. 110.2 is a decimal, drop this branch.\n    |- Try 1440 * 8 = 11520. 11520 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1440 \/ 8 = 180. Add 180 to the number set. Current number set: [180, 13], target: 28, just two numbers left.\n     |- Try 180 + 13 = 193. Evaluate 193 != 28, drop this branch.\n     |- Try 180 - 13 = 167. Evaluate 167 != 28, drop this branch.\n     |- Try 180 * 13 = 2340. 2340 exceeds the maximum intermediate result, drop this branch.\n     |- Try 180 \/ 13 = 13.8. 13.8 is a decimal, drop this branch.\n   |- Pick two numbers (13, 8) (numbers left: [1440]). Try possible operations.\n    |- Try 13 + 8 = 21. Add 21 to the number set. Current number set: [21, 1440], target: 28, just two numbers left.\n     |- Try 1440 + 21 = 1461. Evaluate 1461 != 28, drop this branch.\n     |- Try 1440 - 21 = 1419. Evaluate 1419 != 28, drop this branch.\n     |- Try 1440 * 21 = 30240. 30240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1440 \/ 21 = 68.6. 68.6 is a decimal, drop this branch.\n    |- Try 13 - 8 = 5. Add 5 to the number set. Current number set: [5, 1440], target: 28, just two numbers left.\n     |- Try 1440 + 5 = 1445. Evaluate 1445 != 28, drop this branch.\n     |- Try 1440 - 5 = 1435. Evaluate 1435 != 28, drop this branch.\n     |- Try 1440 * 5 = 7200. 7200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1440 \/ 5 = 288. Evaluate 288 != 28, drop this branch.\n    |- Try 13 * 8 = 104. Add 104 to the number set. Current number set: [104, 1440], target: 28, just two numbers left.\n     |- Try 1440 + 104 = 1544. Evaluate 1544 != 28, drop this branch.\n     |- Try 1440 - 104 = 1336. Evaluate 1336 != 28, drop this branch.\n     |- Try 1440 * 104 = 149760. 149760 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1440 \/ 104 = 13.8. 13.8 is a decimal, drop this branch.\n    |- Try 13 \/ 8 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 45 \/ 32 = 1.4. 1.4 is a decimal, drop this branch.\n |- Pick two numbers (45, 13) (numbers left: [32, 8]). Try possible operations.\n  |- Try 45 + 13 = 58. Add 58 to the number set. Current number set: [58, 32, 8], target: 28. Options for choosing two numbers: [(58, 32), (58, 8), (32, 8)].\n   |- Pick two numbers (58, 32) (numbers left: [8]). Try possible operations.\n    |- Try 58 + 32 = 90. Add 90 to the number set. Current number set: [90, 8], target: 28, just two numbers left.\n     |- Try 90 + 8 = 98. Evaluate 98 != 28, drop this branch.\n     |- Try 90 - 8 = 82. Evaluate 82 != 28, drop this branch.\n     |- Try 90 * 8 = 720. Evaluate 720 != 28, drop this branch.\n     |- Try 90 \/ 8 = 11.2. 11.2 is a decimal, drop this branch.\n    |- Try 58 - 32 = 26. Add 26 to the number set. Current number set: [26, 8], target: 28, just two numbers left.\n     |- Try 26 + 8 = 34. Evaluate 34 != 28, drop this branch.\n     |- Try 26 - 8 = 18. Evaluate 18 != 28, drop this branch.\n     |- Try 26 * 8 = 208. Evaluate 208 != 28, drop this branch.\n     |- Try 26 \/ 8 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 58 * 32 = 1856. Add 1856 to the number set. Current number set: [1856, 8], target: 28, just two numbers left.\n     |- Try 1856 + 8 = 1864. Evaluate 1864 != 28, drop this branch.\n     |- Try 1856 - 8 = 1848. Evaluate 1848 != 28, drop this branch.\n     |- Try 1856 * 8 = 14848. 14848 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1856 \/ 8 = 232. Evaluate 232 != 28, drop this branch.\n    |- Try 58 \/ 32 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (58, 8) (numbers left: [32]). Try possible operations.\n    |- Try 58 + 8 = 66. Add 66 to the number set. Current number set: [66, 32], target: 28, just two numbers left.\n     |- Try 66 + 32 = 98. Evaluate 98 != 28, drop this branch.\n     |- Try 66 - 32 = 34. Evaluate 34 != 28, drop this branch.\n     |- Try 66 * 32 = 2112. 2112 exceeds the maximum intermediate result, drop this branch.\n     |- Try 66 \/ 32 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 58 - 8 = 50. Add 50 to the number set. Current number set: [50, 32], target: 28, just two numbers left.\n     |- Try 50 + 32 = 82. Evaluate 82 != 28, drop this branch.\n     |- Try 50 - 32 = 18. Evaluate 18 != 28, drop this branch.\n     |- Try 50 * 32 = 1600. Evaluate 1600 != 28, drop this branch.\n     |- Try 50 \/ 32 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 58 * 8 = 464. Add 464 to the number set. Current number set: [464, 32], target: 28, just two numbers left.\n     |- Try 464 + 32 = 496. Evaluate 496 != 28, drop this branch.\n     |- Try 464 - 32 = 432. Evaluate 432 != 28, drop this branch.\n     |- Try 464 * 32 = 14848. 14848 exceeds the maximum intermediate result, drop this branch.\n     |- Try 464 \/ 32 = 14.5. 14.5 is a decimal, drop this branch.\n    |- Try 58 \/ 8 = 7.2. 7.2 is a decimal, drop this branch.\n   |- Pick two numbers (32, 8) (numbers left: [58]). Try possible operations.\n    |- Try 32 + 8 = 40. Add 40 to the number set. Current number set: [40, 58], target: 28, just two numbers left.\n     |- Try 58 + 40 = 98. Evaluate 98 != 28, drop this branch.\n     |- Try 58 - 40 = 18. Evaluate 18 != 28, drop this branch.\n     |- Try 58 * 40 = 2320. 2320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 58 \/ 40 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 32 - 8 = 24. Add 24 to the number set. Current number set: [24, 58], target: 28, just two numbers left.\n     |- Try 58 + 24 = 82. Evaluate 82 != 28, drop this branch.\n     |- Try 58 - 24 = 34. Evaluate 34 != 28, drop this branch.\n     |- Try 58 * 24 = 1392. Evaluate 1392 != 28, drop this branch.\n     |- Try 58 \/ 24 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 32 * 8 = 256. Add 256 to the number set. Current number set: [256, 58], target: 28, just two numbers left.\n     |- Try 256 + 58 = 314. Evaluate 314 != 28, drop this branch.\n     |- Try 256 - 58 = 198. Evaluate 198 != 28, drop this branch.\n     |- Try 256 * 58 = 14848. 14848 exceeds the maximum intermediate result, drop this branch.\n     |- Try 256 \/ 58 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 32 \/ 8 = 4. Add 4 to the number set. Current number set: [4, 58], target: 28, just two numbers left.\n     |- Try 58 + 4 = 62. Evaluate 62 != 28, drop this branch.\n     |- Try 58 - 4 = 54. Evaluate 54 != 28, drop this branch.\n     |- Try 58 * 4 = 232. Evaluate 232 != 28, drop this branch.\n     |- Try 58 \/ 4 = 14.5. 14.5 is a decimal, drop this branch.\n  |- Try 45 - 13 = 32. Add 32 to the number set. Current number set: [32, 32, 8], target: 28. Options for choosing two numbers: [(32, 32), (32, 8), (32, 8)].\n   |- Pick two numbers (32, 32) (numbers left: [8]). Try possible operations.\n    |- Try 32 + 32 = 64. Add 64 to the number set. Current number set: [64, 8], target: 28, just two numbers left.\n     |- Try 64 + 8 = 72. Evaluate 72 != 28, drop this branch.\n     |- Try 64 - 8 = 56. Evaluate 56 != 28, drop this branch.\n     |- Try 64 * 8 = 512. Evaluate 512 != 28, drop this branch.\n     |- Try 64 \/ 8 = 8. Evaluate 8 != 28, drop this branch.\n    |- Try 32 - 32 = 0. Add 0 to the number set. Current number set: [0, 8], target: 28, just two numbers left.\n     |- Try 8 + 0 = 8. Evaluate 8 != 28, drop this branch.\n     |- Try 8 - 0 = 8. Evaluate 8 != 28, drop this branch.\n     |- Try 8 * 0 = 0. Evaluate 0 != 28, drop this branch.\n     |- Try 8 \/ 0 (invalid operation). drop this branch.\n    |- Try 32 * 32 = 1024. Add 1024 to the number set. Current number set: [1024, 8], target: 28, just two numbers left.\n     |- Try 1024 + 8 = 1032. Evaluate 1032 != 28, drop this branch.\n     |- Try 1024 - 8 = 1016. Evaluate 1016 != 28, drop this branch.\n     |- Try 1024 * 8 = 8192. 8192 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1024 \/ 8 = 128. Evaluate 128 != 28, drop this branch.\n    |- Try 32 \/ 32 = 1. Add 1 to the number set. Current number set: [1, 8], target: 28, just two numbers left.\n     |- Try 8 + 1 = 9. Evaluate 9 != 28, drop this branch.\n     |- Try 8 - 1 = 7. Evaluate 7 != 28, drop this branch.\n     |- Try 8 * 1 = 8. Evaluate 8 != 28, drop this branch.\n     |- Try 8 \/ 1 = 8. Evaluate 8 != 28, drop this branch.\n   |- Pick two numbers (32, 8) (numbers left: [32]). Try possible operations.\n    |- Try 32 + 8 = 40. Add 40 to the number set. Current number set: [40, 32], target: 28, just two numbers left.\n     |- Try 40 + 32 = 72. Evaluate 72 != 28, drop this branch.\n     |- Try 40 - 32 = 8. Evaluate 8 != 28, drop this branch.\n     |- Try 40 * 32 = 1280. Evaluate 1280 != 28, drop this branch.\n     |- Try 40 \/ 32 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 32 - 8 = 24. Add 24 to the number set. Current number set: [24, 32], target: 28, just two numbers left.\n     |- Try 32 + 24 = 56. Evaluate 56 != 28, drop this branch.\n     |- Try 32 - 24 = 8. Evaluate 8 != 28, drop this branch.\n     |- Try 32 * 24 = 768. Evaluate 768 != 28, drop this branch.\n     |- Try 32 \/ 24 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 32 * 8 = 256. Add 256 to the number set. Current number set: [256, 32], target: 28, just two numbers left.\n     |- Try 256 + 32 = 288. Evaluate 288 != 28, drop this branch.\n     |- Try 256 - 32 = 224. Evaluate 224 != 28, drop this branch.\n     |- Try 256 * 32 = 8192. 8192 exceeds the maximum intermediate result, drop this branch.\n     |- Try 256 \/ 32 = 8. Evaluate 8 != 28, drop this branch.\n    |- Try 32 \/ 8 = 4. Add 4 to the number set. Current number set: [4, 32], target: 28, just two numbers left.\n     |- Try 32 + 4 = 36. Evaluate 36 != 28, drop this branch.\n     |- Try 32 - 4 = 28. Evaluate 28 == 28, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 32 - 4 = 28\nThe step before: 32 \/ 8 = 4\nThe first step: 45 - 13 = 32\n\nOutput the solution in the required format:\n<Solution>\n45 - 13 = 32\n32 \/ 8 = 4\n32 - 4 = 28\n<\/Solution>\n","item":{"nums":[45,32,13,8],"solution":["45 - 13 = 32","32 \/ 8 = 4","32 - 4 = 28"],"target":28}}
+{"instance_id":"countdown_8k_23","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [47, 39, 22, 37]\nTarget: 29","reference_output":"# Search Procedure\nInitial number set: [47, 39, 22, 37], target: 29. Options for choosing two numbers: [(47, 39), (47, 22), (47, 37), (39, 22), (39, 37), (22, 37)].\n |- Pick two numbers (47, 39) (numbers left: [22, 37]). Try possible operations.\n  |- Try 47 + 39 = 86. Add 86 to the number set. Current number set: [86, 22, 37], target: 29. Options for choosing two numbers: [(86, 22), (86, 37), (22, 37)].\n   |- Pick two numbers (86, 22) (numbers left: [37]). Try possible operations.\n    |- Try 86 + 22 = 108. Add 108 to the number set. Current number set: [108, 37], target: 29, just two numbers left.\n     |- Try 108 + 37 = 145. Evaluate 145 != 29, drop this branch.\n     |- Try 108 - 37 = 71. Evaluate 71 != 29, drop this branch.\n     |- Try 108 * 37 = 3996. 3996 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 37 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 86 - 22 = 64. Add 64 to the number set. Current number set: [64, 37], target: 29, just two numbers left.\n     |- Try 64 + 37 = 101. Evaluate 101 != 29, drop this branch.\n     |- Try 64 - 37 = 27. Evaluate 27 != 29, drop this branch.\n     |- Try 64 * 37 = 2368. 2368 exceeds the maximum intermediate result, drop this branch.\n     |- Try 64 \/ 37 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 86 * 22 = 1892. Add 1892 to the number set. Current number set: [1892, 37], target: 29, just two numbers left.\n     |- Try 1892 + 37 = 1929. Evaluate 1929 != 29, drop this branch.\n     |- Try 1892 - 37 = 1855. Evaluate 1855 != 29, drop this branch.\n     |- Try 1892 * 37 = 70004. 70004 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1892 \/ 37 = 51.1. 51.1 is a decimal, drop this branch.\n    |- Try 86 \/ 22 = 3.9. 3.9 is a decimal, drop this branch.\n   |- Pick two numbers (86, 37) (numbers left: [22]). Try possible operations.\n    |- Try 86 + 37 = 123. Add 123 to the number set. Current number set: [123, 22], target: 29, just two numbers left.\n     |- Try 123 + 22 = 145. Evaluate 145 != 29, drop this branch.\n     |- Try 123 - 22 = 101. Evaluate 101 != 29, drop this branch.\n     |- Try 123 * 22 = 2706. 2706 exceeds the maximum intermediate result, drop this branch.\n     |- Try 123 \/ 22 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 86 - 37 = 49. Add 49 to the number set. Current number set: [49, 22], target: 29, just two numbers left.\n     |- Try 49 + 22 = 71. Evaluate 71 != 29, drop this branch.\n     |- Try 49 - 22 = 27. Evaluate 27 != 29, drop this branch.\n     |- Try 49 * 22 = 1078. Evaluate 1078 != 29, drop this branch.\n     |- Try 49 \/ 22 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 86 * 37 = 3182. 3182 exceeds the maximum intermediate result, drop this branch.\n    |- Try 86 \/ 37 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (22, 37) (numbers left: [86]). Try possible operations.\n    |- Try 37 + 22 = 59. Add 59 to the number set. Current number set: [59, 86], target: 29, just two numbers left.\n     |- Try 86 + 59 = 145. Evaluate 145 != 29, drop this branch.\n     |- Try 86 - 59 = 27. Evaluate 27 != 29, drop this branch.\n     |- Try 86 * 59 = 5074. 5074 exceeds the maximum intermediate result, drop this branch.\n     |- Try 86 \/ 59 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 37 - 22 = 15. Add 15 to the number set. Current number set: [15, 86], target: 29, just two numbers left.\n     |- Try 86 + 15 = 101. Evaluate 101 != 29, drop this branch.\n     |- Try 86 - 15 = 71. Evaluate 71 != 29, drop this branch.\n     |- Try 86 * 15 = 1290. Evaluate 1290 != 29, drop this branch.\n     |- Try 86 \/ 15 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 37 * 22 = 814. Add 814 to the number set. Current number set: [814, 86], target: 29, just two numbers left.\n     |- Try 814 + 86 = 900. Evaluate 900 != 29, drop this branch.\n     |- Try 814 - 86 = 728. Evaluate 728 != 29, drop this branch.\n     |- Try 814 * 86 = 70004. 70004 exceeds the maximum intermediate result, drop this branch.\n     |- Try 814 \/ 86 = 9.5. 9.5 is a decimal, drop this branch.\n    |- Try 37 \/ 22 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 47 - 39 = 8. Add 8 to the number set. Current number set: [8, 22, 37], target: 29. Options for choosing two numbers: [(8, 22), (8, 37), (22, 37)].\n   |- Pick two numbers (8, 22) (numbers left: [37]). Try possible operations.\n    |- Try 22 + 8 = 30. Add 30 to the number set. Current number set: [30, 37], target: 29, just two numbers left.\n     |- Try 37 + 30 = 67. Evaluate 67 != 29, drop this branch.\n     |- Try 37 - 30 = 7. Evaluate 7 != 29, drop this branch.\n     |- Try 37 * 30 = 1110. Evaluate 1110 != 29, drop this branch.\n     |- Try 37 \/ 30 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 22 - 8 = 14. Add 14 to the number set. Current number set: [14, 37], target: 29, just two numbers left.\n     |- Try 37 + 14 = 51. Evaluate 51 != 29, drop this branch.\n     |- Try 37 - 14 = 23. Evaluate 23 != 29, drop this branch.\n     |- Try 37 * 14 = 518. Evaluate 518 != 29, drop this branch.\n     |- Try 37 \/ 14 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 22 * 8 = 176. Add 176 to the number set. Current number set: [176, 37], target: 29, just two numbers left.\n     |- Try 176 + 37 = 213. Evaluate 213 != 29, drop this branch.\n     |- Try 176 - 37 = 139. Evaluate 139 != 29, drop this branch.\n     |- Try 176 * 37 = 6512. 6512 exceeds the maximum intermediate result, drop this branch.\n     |- Try 176 \/ 37 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 22 \/ 8 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (8, 37) (numbers left: [22]). Try possible operations.\n    |- Try 37 + 8 = 45. Add 45 to the number set. Current number set: [45, 22], target: 29, just two numbers left.\n     |- Try 45 + 22 = 67. Evaluate 67 != 29, drop this branch.\n     |- Try 45 - 22 = 23. Evaluate 23 != 29, drop this branch.\n     |- Try 45 * 22 = 990. Evaluate 990 != 29, drop this branch.\n     |- Try 45 \/ 22 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 37 - 8 = 29. Add 29 to the number set. Current number set: [29, 22], target: 29, just two numbers left.\n     |- Try 29 + 22 = 51. Evaluate 51 != 29, drop this branch.\n     |- Try 29 - 22 = 7. Evaluate 7 != 29, drop this branch.\n     |- Try 29 * 22 = 638. Evaluate 638 != 29, drop this branch.\n     |- Try 29 \/ 22 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 37 * 8 = 296. Add 296 to the number set. Current number set: [296, 22], target: 29, just two numbers left.\n     |- Try 296 + 22 = 318. Evaluate 318 != 29, drop this branch.\n     |- Try 296 - 22 = 274. Evaluate 274 != 29, drop this branch.\n     |- Try 296 * 22 = 6512. 6512 exceeds the maximum intermediate result, drop this branch.\n     |- Try 296 \/ 22 = 13.5. 13.5 is a decimal, drop this branch.\n    |- Try 37 \/ 8 = 4.6. 4.6 is a decimal, drop this branch.\n   |- Pick two numbers (22, 37) (numbers left: [8]). Try possible operations.\n    |- Try 37 + 22 = 59. Add 59 to the number set. Current number set: [59, 8], target: 29, just two numbers left.\n     |- Try 59 + 8 = 67. Evaluate 67 != 29, drop this branch.\n     |- Try 59 - 8 = 51. Evaluate 51 != 29, drop this branch.\n     |- Try 59 * 8 = 472. Evaluate 472 != 29, drop this branch.\n     |- Try 59 \/ 8 = 7.4. 7.4 is a decimal, drop this branch.\n    |- Try 37 - 22 = 15. Add 15 to the number set. Current number set: [15, 8], target: 29, just two numbers left.\n     |- Try 15 + 8 = 23. Evaluate 23 != 29, drop this branch.\n     |- Try 15 - 8 = 7. Evaluate 7 != 29, drop this branch.\n     |- Try 15 * 8 = 120. Evaluate 120 != 29, drop this branch.\n     |- Try 15 \/ 8 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 37 * 22 = 814. Add 814 to the number set. Current number set: [814, 8], target: 29, just two numbers left.\n     |- Try 814 + 8 = 822. Evaluate 822 != 29, drop this branch.\n     |- Try 814 - 8 = 806. Evaluate 806 != 29, drop this branch.\n     |- Try 814 * 8 = 6512. 6512 exceeds the maximum intermediate result, drop this branch.\n     |- Try 814 \/ 8 = 101.8. 101.8 is a decimal, drop this branch.\n    |- Try 37 \/ 22 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 47 * 39 = 1833. Add 1833 to the number set. Current number set: [1833, 22, 37], target: 29. Options for choosing two numbers: [(1833, 22), (1833, 37), (22, 37)].\n   |- Pick two numbers (1833, 22) (numbers left: [37]). Try possible operations.\n    |- Try 1833 + 22 = 1855. Add 1855 to the number set. Current number set: [1855, 37], target: 29, just two numbers left.\n     |- Try 1855 + 37 = 1892. Evaluate 1892 != 29, drop this branch.\n     |- Try 1855 - 37 = 1818. Evaluate 1818 != 29, drop this branch.\n     |- Try 1855 * 37 = 68635. 68635 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1855 \/ 37 = 50.1. 50.1 is a decimal, drop this branch.\n    |- Try 1833 - 22 = 1811. Add 1811 to the number set. Current number set: [1811, 37], target: 29, just two numbers left.\n     |- Try 1811 + 37 = 1848. Evaluate 1848 != 29, drop this branch.\n     |- Try 1811 - 37 = 1774. Evaluate 1774 != 29, drop this branch.\n     |- Try 1811 * 37 = 67007. 67007 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1811 \/ 37 = 48.9. 48.9 is a decimal, drop this branch.\n    |- Try 1833 * 22 = 40326. 40326 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1833 \/ 22 = 83.3. 83.3 is a decimal, drop this branch.\n   |- Pick two numbers (1833, 37) (numbers left: [22]). Try possible operations.\n    |- Try 1833 + 37 = 1870. Add 1870 to the number set. Current number set: [1870, 22], target: 29, just two numbers left.\n     |- Try 1870 + 22 = 1892. Evaluate 1892 != 29, drop this branch.\n     |- Try 1870 - 22 = 1848. Evaluate 1848 != 29, drop this branch.\n     |- Try 1870 * 22 = 41140. 41140 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1870 \/ 22 = 85. Evaluate 85 != 29, drop this branch.\n    |- Try 1833 - 37 = 1796. Add 1796 to the number set. Current number set: [1796, 22], target: 29, just two numbers left.\n     |- Try 1796 + 22 = 1818. Evaluate 1818 != 29, drop this branch.\n     |- Try 1796 - 22 = 1774. Evaluate 1774 != 29, drop this branch.\n     |- Try 1796 * 22 = 39512. 39512 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1796 \/ 22 = 81.6. 81.6 is a decimal, drop this branch.\n    |- Try 1833 * 37 = 67821. 67821 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1833 \/ 37 = 49.5. 49.5 is a decimal, drop this branch.\n   |- Pick two numbers (22, 37) (numbers left: [1833]). Try possible operations.\n    |- Try 37 + 22 = 59. Add 59 to the number set. Current number set: [59, 1833], target: 29, just two numbers left.\n     |- Try 1833 + 59 = 1892. Evaluate 1892 != 29, drop this branch.\n     |- Try 1833 - 59 = 1774. Evaluate 1774 != 29, drop this branch.\n     |- Try 1833 * 59 = 108147. 108147 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1833 \/ 59 = 31.1. 31.1 is a decimal, drop this branch.\n    |- Try 37 - 22 = 15. Add 15 to the number set. Current number set: [15, 1833], target: 29, just two numbers left.\n     |- Try 1833 + 15 = 1848. Evaluate 1848 != 29, drop this branch.\n     |- Try 1833 - 15 = 1818. Evaluate 1818 != 29, drop this branch.\n     |- Try 1833 * 15 = 27495. 27495 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1833 \/ 15 = 122.2. 122.2 is a decimal, drop this branch.\n    |- Try 37 * 22 = 814. Add 814 to the number set. Current number set: [814, 1833], target: 29, just two numbers left.\n     |- Try 1833 + 814 = 2647. 2647 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1833 - 814 = 1019. Evaluate 1019 != 29, drop this branch.\n     |- Try 1833 * 814 = 1492062. 1492062 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1833 \/ 814 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 37 \/ 22 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 47 \/ 39 = 1.2. 1.2 is a decimal, drop this branch.\n |- Pick two numbers (47, 22) (numbers left: [39, 37]). Try possible operations.\n  |- Try 47 + 22 = 69. Add 69 to the number set. Current number set: [69, 39, 37], target: 29. Options for choosing two numbers: [(69, 39), (69, 37), (39, 37)].\n   |- Pick two numbers (69, 39) (numbers left: [37]). Try possible operations.\n    |- Try 69 + 39 = 108. Add 108 to the number set. Current number set: [108, 37], target: 29, just two numbers left.\n     |- Try 108 + 37 = 145. Evaluate 145 != 29, drop this branch.\n     |- Try 108 - 37 = 71. Evaluate 71 != 29, drop this branch.\n     |- Try 108 * 37 = 3996. 3996 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 37 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 69 - 39 = 30. Add 30 to the number set. Current number set: [30, 37], target: 29, just two numbers left.\n     |- Try 37 + 30 = 67. Evaluate 67 != 29, drop this branch.\n     |- Try 37 - 30 = 7. Evaluate 7 != 29, drop this branch.\n     |- Try 37 * 30 = 1110. Evaluate 1110 != 29, drop this branch.\n     |- Try 37 \/ 30 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 69 * 39 = 2691. 2691 exceeds the maximum intermediate result, drop this branch.\n    |- Try 69 \/ 39 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (69, 37) (numbers left: [39]). Try possible operations.\n    |- Try 69 + 37 = 106. Add 106 to the number set. Current number set: [106, 39], target: 29, just two numbers left.\n     |- Try 106 + 39 = 145. Evaluate 145 != 29, drop this branch.\n     |- Try 106 - 39 = 67. Evaluate 67 != 29, drop this branch.\n     |- Try 106 * 39 = 4134. 4134 exceeds the maximum intermediate result, drop this branch.\n     |- Try 106 \/ 39 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 69 - 37 = 32. Add 32 to the number set. Current number set: [32, 39], target: 29, just two numbers left.\n     |- Try 39 + 32 = 71. Evaluate 71 != 29, drop this branch.\n     |- Try 39 - 32 = 7. Evaluate 7 != 29, drop this branch.\n     |- Try 39 * 32 = 1248. Evaluate 1248 != 29, drop this branch.\n     |- Try 39 \/ 32 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 69 * 37 = 2553. 2553 exceeds the maximum intermediate result, drop this branch.\n    |- Try 69 \/ 37 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (39, 37) (numbers left: [69]). Try possible operations.\n    |- Try 39 + 37 = 76. Add 76 to the number set. Current number set: [76, 69], target: 29, just two numbers left.\n     |- Try 76 + 69 = 145. Evaluate 145 != 29, drop this branch.\n     |- Try 76 - 69 = 7. Evaluate 7 != 29, drop this branch.\n     |- Try 76 * 69 = 5244. 5244 exceeds the maximum intermediate result, drop this branch.\n     |- Try 76 \/ 69 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 39 - 37 = 2. Add 2 to the number set. Current number set: [2, 69], target: 29, just two numbers left.\n     |- Try 69 + 2 = 71. Evaluate 71 != 29, drop this branch.\n     |- Try 69 - 2 = 67. Evaluate 67 != 29, drop this branch.\n     |- Try 69 * 2 = 138. Evaluate 138 != 29, drop this branch.\n     |- Try 69 \/ 2 = 34.5. 34.5 is a decimal, drop this branch.\n    |- Try 39 * 37 = 1443. Add 1443 to the number set. Current number set: [1443, 69], target: 29, just two numbers left.\n     |- Try 1443 + 69 = 1512. Evaluate 1512 != 29, drop this branch.\n     |- Try 1443 - 69 = 1374. Evaluate 1374 != 29, drop this branch.\n     |- Try 1443 * 69 = 99567. 99567 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1443 \/ 69 = 20.9. 20.9 is a decimal, drop this branch.\n    |- Try 39 \/ 37 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 47 - 22 = 25. Add 25 to the number set. Current number set: [25, 39, 37], target: 29. Options for choosing two numbers: [(25, 39), (25, 37), (39, 37)].\n   |- Pick two numbers (25, 39) (numbers left: [37]). Try possible operations.\n    |- Try 39 + 25 = 64. Add 64 to the number set. Current number set: [64, 37], target: 29, just two numbers left.\n     |- Try 64 + 37 = 101. Evaluate 101 != 29, drop this branch.\n     |- Try 64 - 37 = 27. Evaluate 27 != 29, drop this branch.\n     |- Try 64 * 37 = 2368. 2368 exceeds the maximum intermediate result, drop this branch.\n     |- Try 64 \/ 37 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 39 - 25 = 14. Add 14 to the number set. Current number set: [14, 37], target: 29, just two numbers left.\n     |- Try 37 + 14 = 51. Evaluate 51 != 29, drop this branch.\n     |- Try 37 - 14 = 23. Evaluate 23 != 29, drop this branch.\n     |- Try 37 * 14 = 518. Evaluate 518 != 29, drop this branch.\n     |- Try 37 \/ 14 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 39 * 25 = 975. Add 975 to the number set. Current number set: [975, 37], target: 29, just two numbers left.\n     |- Try 975 + 37 = 1012. Evaluate 1012 != 29, drop this branch.\n     |- Try 975 - 37 = 938. Evaluate 938 != 29, drop this branch.\n     |- Try 975 * 37 = 36075. 36075 exceeds the maximum intermediate result, drop this branch.\n     |- Try 975 \/ 37 = 26.4. 26.4 is a decimal, drop this branch.\n    |- Try 39 \/ 25 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (25, 37) (numbers left: [39]). Try possible operations.\n    |- Try 37 + 25 = 62. Add 62 to the number set. Current number set: [62, 39], target: 29, just two numbers left.\n     |- Try 62 + 39 = 101. Evaluate 101 != 29, drop this branch.\n     |- Try 62 - 39 = 23. Evaluate 23 != 29, drop this branch.\n     |- Try 62 * 39 = 2418. 2418 exceeds the maximum intermediate result, drop this branch.\n     |- Try 62 \/ 39 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 37 - 25 = 12. Add 12 to the number set. Current number set: [12, 39], target: 29, just two numbers left.\n     |- Try 39 + 12 = 51. Evaluate 51 != 29, drop this branch.\n     |- Try 39 - 12 = 27. Evaluate 27 != 29, drop this branch.\n     |- Try 39 * 12 = 468. Evaluate 468 != 29, drop this branch.\n     |- Try 39 \/ 12 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 37 * 25 = 925. Add 925 to the number set. Current number set: [925, 39], target: 29, just two numbers left.\n     |- Try 925 + 39 = 964. Evaluate 964 != 29, drop this branch.\n     |- Try 925 - 39 = 886. Evaluate 886 != 29, drop this branch.\n     |- Try 925 * 39 = 36075. 36075 exceeds the maximum intermediate result, drop this branch.\n     |- Try 925 \/ 39 = 23.7. 23.7 is a decimal, drop this branch.\n    |- Try 37 \/ 25 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (39, 37) (numbers left: [25]). Try possible operations.\n    |- Try 39 + 37 = 76. Add 76 to the number set. Current number set: [76, 25], target: 29, just two numbers left.\n     |- Try 76 + 25 = 101. Evaluate 101 != 29, drop this branch.\n     |- Try 76 - 25 = 51. Evaluate 51 != 29, drop this branch.\n     |- Try 76 * 25 = 1900. Evaluate 1900 != 29, drop this branch.\n     |- Try 76 \/ 25 = 3.0. 3.0 is a decimal, drop this branch.\n    |- Try 39 - 37 = 2. Add 2 to the number set. Current number set: [2, 25], target: 29, just two numbers left.\n     |- Try 25 + 2 = 27. Evaluate 27 != 29, drop this branch.\n     |- Try 25 - 2 = 23. Evaluate 23 != 29, drop this branch.\n     |- Try 25 * 2 = 50. Evaluate 50 != 29, drop this branch.\n     |- Try 25 \/ 2 = 12.5. 12.5 is a decimal, drop this branch.\n    |- Try 39 * 37 = 1443. Add 1443 to the number set. Current number set: [1443, 25], target: 29, just two numbers left.\n     |- Try 1443 + 25 = 1468. Evaluate 1468 != 29, drop this branch.\n     |- Try 1443 - 25 = 1418. Evaluate 1418 != 29, drop this branch.\n     |- Try 1443 * 25 = 36075. 36075 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1443 \/ 25 = 57.7. 57.7 is a decimal, drop this branch.\n    |- Try 39 \/ 37 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 47 * 22 = 1034. Add 1034 to the number set. Current number set: [1034, 39, 37], target: 29. Options for choosing two numbers: [(1034, 39), (1034, 37), (39, 37)].\n   |- Pick two numbers (1034, 39) (numbers left: [37]). Try possible operations.\n    |- Try 1034 + 39 = 1073. Add 1073 to the number set. Current number set: [1073, 37], target: 29, just two numbers left.\n     |- Try 1073 + 37 = 1110. Evaluate 1110 != 29, drop this branch.\n     |- Try 1073 - 37 = 1036. Evaluate 1036 != 29, drop this branch.\n     |- Try 1073 * 37 = 39701. 39701 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1073 \/ 37 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 1073 \/ 37 = 29\nThe step before: 1034 + 39 = 1073\nThe first step: 47 * 22 = 1034\n\nOutput the solution in the required format:\n<Solution>\n47 * 22 = 1034\n1034 + 39 = 1073\n1073 \/ 37 = 29\n<\/Solution>\n","item":{"nums":[47,39,22,37],"solution":["47 * 22 = 1034","1034 + 39 = 1073","1073 \/ 37 = 29"],"target":29}}
+{"instance_id":"countdown_8k_24","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [2, 6, 3, 42]\nTarget: 12","reference_output":"# Search Procedure\nInitial number set: [2, 6, 3, 42], target: 12. Options for choosing two numbers: [(2, 6), (2, 3), (2, 42), (6, 3), (6, 42), (3, 42)].\n |- Pick two numbers (2, 6) (numbers left: [3, 42]). Try possible operations.\n  |- Try 6 + 2 = 8. Add 8 to the number set. Current number set: [8, 3, 42], target: 12. Options for choosing two numbers: [(8, 3), (8, 42), (3, 42)].\n   |- Pick two numbers (8, 3) (numbers left: [42]). Try possible operations.\n    |- Try 8 + 3 = 11. Add 11 to the number set. Current number set: [11, 42], target: 12, just two numbers left.\n     |- Try 42 + 11 = 53. Evaluate 53 != 12, drop this branch.\n     |- Try 42 - 11 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 42 * 11 = 462. Evaluate 462 != 12, drop this branch.\n     |- Try 42 \/ 11 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 8 - 3 = 5. Add 5 to the number set. Current number set: [5, 42], target: 12, just two numbers left.\n     |- Try 42 + 5 = 47. Evaluate 47 != 12, drop this branch.\n     |- Try 42 - 5 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 42 * 5 = 210. Evaluate 210 != 12, drop this branch.\n     |- Try 42 \/ 5 = 8.4. 8.4 is a decimal, drop this branch.\n    |- Try 8 * 3 = 24. Add 24 to the number set. Current number set: [24, 42], target: 12, just two numbers left.\n     |- Try 42 + 24 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 42 - 24 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 42 * 24 = 1008. Evaluate 1008 != 12, drop this branch.\n     |- Try 42 \/ 24 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 8 \/ 3 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (8, 42) (numbers left: [3]). Try possible operations.\n    |- Try 42 + 8 = 50. Add 50 to the number set. Current number set: [50, 3], target: 12, just two numbers left.\n     |- Try 50 + 3 = 53. Evaluate 53 != 12, drop this branch.\n     |- Try 50 - 3 = 47. Evaluate 47 != 12, drop this branch.\n     |- Try 50 * 3 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 50 \/ 3 = 16.7. 16.7 is a decimal, drop this branch.\n    |- Try 42 - 8 = 34. Add 34 to the number set. Current number set: [34, 3], target: 12, just two numbers left.\n     |- Try 34 + 3 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 34 - 3 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 34 * 3 = 102. Evaluate 102 != 12, drop this branch.\n     |- Try 34 \/ 3 = 11.3. 11.3 is a decimal, drop this branch.\n    |- Try 42 * 8 = 336. Add 336 to the number set. Current number set: [336, 3], target: 12, just two numbers left.\n     |- Try 336 + 3 = 339. Evaluate 339 != 12, drop this branch.\n     |- Try 336 - 3 = 333. Evaluate 333 != 12, drop this branch.\n     |- Try 336 * 3 = 1008. Evaluate 1008 != 12, drop this branch.\n     |- Try 336 \/ 3 = 112. Evaluate 112 != 12, drop this branch.\n    |- Try 42 \/ 8 = 5.2. 5.2 is a decimal, drop this branch.\n   |- Pick two numbers (3, 42) (numbers left: [8]). Try possible operations.\n    |- Try 42 + 3 = 45. Add 45 to the number set. Current number set: [45, 8], target: 12, just two numbers left.\n     |- Try 45 + 8 = 53. Evaluate 53 != 12, drop this branch.\n     |- Try 45 - 8 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 45 * 8 = 360. Evaluate 360 != 12, drop this branch.\n     |- Try 45 \/ 8 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 42 - 3 = 39. Add 39 to the number set. Current number set: [39, 8], target: 12, just two numbers left.\n     |- Try 39 + 8 = 47. Evaluate 47 != 12, drop this branch.\n     |- Try 39 - 8 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 39 * 8 = 312. Evaluate 312 != 12, drop this branch.\n     |- Try 39 \/ 8 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 42 * 3 = 126. Add 126 to the number set. Current number set: [126, 8], target: 12, just two numbers left.\n     |- Try 126 + 8 = 134. Evaluate 134 != 12, drop this branch.\n     |- Try 126 - 8 = 118. Evaluate 118 != 12, drop this branch.\n     |- Try 126 * 8 = 1008. Evaluate 1008 != 12, drop this branch.\n     |- Try 126 \/ 8 = 15.8. 15.8 is a decimal, drop this branch.\n    |- Try 42 \/ 3 = 14. Add 14 to the number set. Current number set: [14, 8], target: 12, just two numbers left.\n     |- Try 14 + 8 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 14 - 8 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 14 * 8 = 112. Evaluate 112 != 12, drop this branch.\n     |- Try 14 \/ 8 = 1.8. 1.8 is a decimal, drop this branch.\n  |- Try 6 - 2 = 4. Add 4 to the number set. Current number set: [4, 3, 42], target: 12. Options for choosing two numbers: [(4, 3), (4, 42), (3, 42)].\n   |- Pick two numbers (4, 3) (numbers left: [42]). Try possible operations.\n    |- Try 4 + 3 = 7. Add 7 to the number set. Current number set: [7, 42], target: 12, just two numbers left.\n     |- Try 42 + 7 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 42 - 7 = 35. Evaluate 35 != 12, drop this branch.\n     |- Try 42 * 7 = 294. Evaluate 294 != 12, drop this branch.\n     |- Try 42 \/ 7 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 4 - 3 = 1. Add 1 to the number set. Current number set: [1, 42], target: 12, just two numbers left.\n     |- Try 42 + 1 = 43. Evaluate 43 != 12, drop this branch.\n     |- Try 42 - 1 = 41. Evaluate 41 != 12, drop this branch.\n     |- Try 42 * 1 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 42 \/ 1 = 42. Evaluate 42 != 12, drop this branch.\n    |- Try 4 * 3 = 12. Add 12 to the number set. Current number set: [12, 42], target: 12, just two numbers left.\n     |- Try 42 + 12 = 54. Evaluate 54 != 12, drop this branch.\n     |- Try 42 - 12 = 30. Evaluate 30 != 12, drop this branch.\n     |- Try 42 * 12 = 504. Evaluate 504 != 12, drop this branch.\n     |- Try 42 \/ 12 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 4 \/ 3 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (4, 42) (numbers left: [3]). Try possible operations.\n    |- Try 42 + 4 = 46. Add 46 to the number set. Current number set: [46, 3], target: 12, just two numbers left.\n     |- Try 46 + 3 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 46 - 3 = 43. Evaluate 43 != 12, drop this branch.\n     |- Try 46 * 3 = 138. Evaluate 138 != 12, drop this branch.\n     |- Try 46 \/ 3 = 15.3. 15.3 is a decimal, drop this branch.\n    |- Try 42 - 4 = 38. Add 38 to the number set. Current number set: [38, 3], target: 12, just two numbers left.\n     |- Try 38 + 3 = 41. Evaluate 41 != 12, drop this branch.\n     |- Try 38 - 3 = 35. Evaluate 35 != 12, drop this branch.\n     |- Try 38 * 3 = 114. Evaluate 114 != 12, drop this branch.\n     |- Try 38 \/ 3 = 12.7. 12.7 is a decimal, drop this branch.\n    |- Try 42 * 4 = 168. Add 168 to the number set. Current number set: [168, 3], target: 12, just two numbers left.\n     |- Try 168 + 3 = 171. Evaluate 171 != 12, drop this branch.\n     |- Try 168 - 3 = 165. Evaluate 165 != 12, drop this branch.\n     |- Try 168 * 3 = 504. Evaluate 504 != 12, drop this branch.\n     |- Try 168 \/ 3 = 56. Evaluate 56 != 12, drop this branch.\n    |- Try 42 \/ 4 = 10.5. 10.5 is a decimal, drop this branch.\n   |- Pick two numbers (3, 42) (numbers left: [4]). Try possible operations.\n    |- Try 42 + 3 = 45. Add 45 to the number set. Current number set: [45, 4], target: 12, just two numbers left.\n     |- Try 45 + 4 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 45 - 4 = 41. Evaluate 41 != 12, drop this branch.\n     |- Try 45 * 4 = 180. Evaluate 180 != 12, drop this branch.\n     |- Try 45 \/ 4 = 11.2. 11.2 is a decimal, drop this branch.\n    |- Try 42 - 3 = 39. Add 39 to the number set. Current number set: [39, 4], target: 12, just two numbers left.\n     |- Try 39 + 4 = 43. Evaluate 43 != 12, drop this branch.\n     |- Try 39 - 4 = 35. Evaluate 35 != 12, drop this branch.\n     |- Try 39 * 4 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 39 \/ 4 = 9.8. 9.8 is a decimal, drop this branch.\n    |- Try 42 * 3 = 126. Add 126 to the number set. Current number set: [126, 4], target: 12, just two numbers left.\n     |- Try 126 + 4 = 130. Evaluate 130 != 12, drop this branch.\n     |- Try 126 - 4 = 122. Evaluate 122 != 12, drop this branch.\n     |- Try 126 * 4 = 504. Evaluate 504 != 12, drop this branch.\n     |- Try 126 \/ 4 = 31.5. 31.5 is a decimal, drop this branch.\n    |- Try 42 \/ 3 = 14. Add 14 to the number set. Current number set: [14, 4], target: 12, just two numbers left.\n     |- Try 14 + 4 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 14 - 4 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 14 * 4 = 56. Evaluate 56 != 12, drop this branch.\n     |- Try 14 \/ 4 = 3.5. 3.5 is a decimal, drop this branch.\n  |- Try 6 * 2 = 12. Add 12 to the number set. Current number set: [12, 3, 42], target: 12. Options for choosing two numbers: [(12, 3), (12, 42), (3, 42)].\n   |- Pick two numbers (12, 3) (numbers left: [42]). Try possible operations.\n    |- Try 12 + 3 = 15. Add 15 to the number set. Current number set: [15, 42], target: 12, just two numbers left.\n     |- Try 42 + 15 = 57. Evaluate 57 != 12, drop this branch.\n     |- Try 42 - 15 = 27. Evaluate 27 != 12, drop this branch.\n     |- Try 42 * 15 = 630. Evaluate 630 != 12, drop this branch.\n     |- Try 42 \/ 15 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 12 - 3 = 9. Add 9 to the number set. Current number set: [9, 42], target: 12, just two numbers left.\n     |- Try 42 + 9 = 51. Evaluate 51 != 12, drop this branch.\n     |- Try 42 - 9 = 33. Evaluate 33 != 12, drop this branch.\n     |- Try 42 * 9 = 378. Evaluate 378 != 12, drop this branch.\n     |- Try 42 \/ 9 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 12 * 3 = 36. Add 36 to the number set. Current number set: [36, 42], target: 12, just two numbers left.\n     |- Try 42 + 36 = 78. Evaluate 78 != 12, drop this branch.\n     |- Try 42 - 36 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 42 * 36 = 1512. Evaluate 1512 != 12, drop this branch.\n     |- Try 42 \/ 36 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 12 \/ 3 = 4. Add 4 to the number set. Current number set: [4, 42], target: 12, just two numbers left.\n     |- Try 42 + 4 = 46. Evaluate 46 != 12, drop this branch.\n     |- Try 42 - 4 = 38. Evaluate 38 != 12, drop this branch.\n     |- Try 42 * 4 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 42 \/ 4 = 10.5. 10.5 is a decimal, drop this branch.\n   |- Pick two numbers (12, 42) (numbers left: [3]). Try possible operations.\n    |- Try 42 + 12 = 54. Add 54 to the number set. Current number set: [54, 3], target: 12, just two numbers left.\n     |- Try 54 + 3 = 57. Evaluate 57 != 12, drop this branch.\n     |- Try 54 - 3 = 51. Evaluate 51 != 12, drop this branch.\n     |- Try 54 * 3 = 162. Evaluate 162 != 12, drop this branch.\n     |- Try 54 \/ 3 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 42 - 12 = 30. Add 30 to the number set. Current number set: [30, 3], target: 12, just two numbers left.\n     |- Try 30 + 3 = 33. Evaluate 33 != 12, drop this branch.\n     |- Try 30 - 3 = 27. Evaluate 27 != 12, drop this branch.\n     |- Try 30 * 3 = 90. Evaluate 90 != 12, drop this branch.\n     |- Try 30 \/ 3 = 10. Evaluate 10 != 12, drop this branch.\n    |- Try 42 * 12 = 504. Add 504 to the number set. Current number set: [504, 3], target: 12, just two numbers left.\n     |- Try 504 + 3 = 507. Evaluate 507 != 12, drop this branch.\n     |- Try 504 - 3 = 501. Evaluate 501 != 12, drop this branch.\n     |- Try 504 * 3 = 1512. Evaluate 1512 != 12, drop this branch.\n     |- Try 504 \/ 3 = 168. Evaluate 168 != 12, drop this branch.\n    |- Try 42 \/ 12 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (3, 42) (numbers left: [12]). Try possible operations.\n    |- Try 42 + 3 = 45. Add 45 to the number set. Current number set: [45, 12], target: 12, just two numbers left.\n     |- Try 45 + 12 = 57. Evaluate 57 != 12, drop this branch.\n     |- Try 45 - 12 = 33. Evaluate 33 != 12, drop this branch.\n     |- Try 45 * 12 = 540. Evaluate 540 != 12, drop this branch.\n     |- Try 45 \/ 12 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 42 - 3 = 39. Add 39 to the number set. Current number set: [39, 12], target: 12, just two numbers left.\n     |- Try 39 + 12 = 51. Evaluate 51 != 12, drop this branch.\n     |- Try 39 - 12 = 27. Evaluate 27 != 12, drop this branch.\n     |- Try 39 * 12 = 468. Evaluate 468 != 12, drop this branch.\n     |- Try 39 \/ 12 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 42 * 3 = 126. Add 126 to the number set. Current number set: [126, 12], target: 12, just two numbers left.\n     |- Try 126 + 12 = 138. Evaluate 138 != 12, drop this branch.\n     |- Try 126 - 12 = 114. Evaluate 114 != 12, drop this branch.\n     |- Try 126 * 12 = 1512. Evaluate 1512 != 12, drop this branch.\n     |- Try 126 \/ 12 = 10.5. 10.5 is a decimal, drop this branch.\n    |- Try 42 \/ 3 = 14. Add 14 to the number set. Current number set: [14, 12], target: 12, just two numbers left.\n     |- Try 14 + 12 = 26. Evaluate 26 != 12, drop this branch.\n     |- Try 14 - 12 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 14 * 12 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 14 \/ 12 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 6 \/ 2 = 3. Add 3 to the number set. Current number set: [3, 3, 42], target: 12. Options for choosing two numbers: [(3, 3), (3, 42), (3, 42)].\n   |- Pick two numbers (3, 3) (numbers left: [42]). Try possible operations.\n    |- Try 3 + 3 = 6. Add 6 to the number set. Current number set: [6, 42], target: 12, just two numbers left.\n     |- Try 42 + 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 42 - 6 = 36. Evaluate 36 != 12, drop this branch.\n     |- Try 42 * 6 = 252. Evaluate 252 != 12, drop this branch.\n     |- Try 42 \/ 6 = 7. Evaluate 7 != 12, drop this branch.\n    |- Try 3 - 3 = 0. Add 0 to the number set. Current number set: [0, 42], target: 12, just two numbers left.\n     |- Try 42 + 0 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 42 - 0 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 42 * 0 = 0. Evaluate 0 != 12, drop this branch.\n     |- Try 42 \/ 0 (invalid operation). drop this branch.\n    |- Try 3 * 3 = 9. Add 9 to the number set. Current number set: [9, 42], target: 12, just two numbers left.\n     |- Try 42 + 9 = 51. Evaluate 51 != 12, drop this branch.\n     |- Try 42 - 9 = 33. Evaluate 33 != 12, drop this branch.\n     |- Try 42 * 9 = 378. Evaluate 378 != 12, drop this branch.\n     |- Try 42 \/ 9 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 3 \/ 3 = 1. Add 1 to the number set. Current number set: [1, 42], target: 12, just two numbers left.\n     |- Try 42 + 1 = 43. Evaluate 43 != 12, drop this branch.\n     |- Try 42 - 1 = 41. Evaluate 41 != 12, drop this branch.\n     |- Try 42 * 1 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 42 \/ 1 = 42. Evaluate 42 != 12, drop this branch.\n   |- Pick two numbers (3, 42) (numbers left: [3]). Try possible operations.\n    |- Try 42 + 3 = 45. Add 45 to the number set. Current number set: [45, 3], target: 12, just two numbers left.\n     |- Try 45 + 3 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 45 - 3 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 45 * 3 = 135. Evaluate 135 != 12, drop this branch.\n     |- Try 45 \/ 3 = 15. Evaluate 15 != 12, drop this branch.\n    |- Try 42 - 3 = 39. Add 39 to the number set. Current number set: [39, 3], target: 12, just two numbers left.\n     |- Try 39 + 3 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 39 - 3 = 36. Evaluate 36 != 12, drop this branch.\n     |- Try 39 * 3 = 117. Evaluate 117 != 12, drop this branch.\n     |- Try 39 \/ 3 = 13. Evaluate 13 != 12, drop this branch.\n    |- Try 42 * 3 = 126. Add 126 to the number set. Current number set: [126, 3], target: 12, just two numbers left.\n     |- Try 126 + 3 = 129. Evaluate 129 != 12, drop this branch.\n     |- Try 126 - 3 = 123. Evaluate 123 != 12, drop this branch.\n     |- Try 126 * 3 = 378. Evaluate 378 != 12, drop this branch.\n     |- Try 126 \/ 3 = 42. Evaluate 42 != 12, drop this branch.\n    |- Try 42 \/ 3 = 14. Add 14 to the number set. Current number set: [14, 3], target: 12, just two numbers left.\n     |- Try 14 + 3 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 14 - 3 = 11. Evaluate 11 != 12, drop this branch.\n     |- Try 14 * 3 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 14 \/ 3 = 4.7. 4.7 is a decimal, drop this branch.\n   |- Pick two numbers (3, 42) (numbers left: [3]). Try possible operations.\n    |- Try 42 + 3 = 45. Add 45 to the number set. Current number set: [45, 3], target: 12, just two numbers left.\n     |- Try 45 + 3 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 45 - 3 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 45 * 3 = 135. Evaluate 135 != 12, drop this branch.\n     |- Try 45 \/ 3 = 15. Evaluate 15 != 12, drop this branch.\n    |- Try 42 - 3 = 39. Add 39 to the number set. Current number set: [39, 3], target: 12, just two numbers left.\n     |- Try 39 + 3 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 39 - 3 = 36. Evaluate 36 != 12, drop this branch.\n     |- Try 39 * 3 = 117. Evaluate 117 != 12, drop this branch.\n     |- Try 39 \/ 3 = 13. Evaluate 13 != 12, drop this branch.\n    |- Try 42 * 3 = 126. Add 126 to the number set. Current number set: [126, 3], target: 12, just two numbers left.\n     |- Try 126 + 3 = 129. Evaluate 129 != 12, drop this branch.\n     |- Try 126 - 3 = 123. Evaluate 123 != 12, drop this branch.\n     |- Try 126 * 3 = 378. Evaluate 378 != 12, drop this branch.\n     |- Try 126 \/ 3 = 42. Evaluate 42 != 12, drop this branch.\n    |- Try 42 \/ 3 = 14. Add 14 to the number set. Current number set: [14, 3], target: 12, just two numbers left.\n     |- Try 14 + 3 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 14 - 3 = 11. Evaluate 11 != 12, drop this branch.\n     |- Try 14 * 3 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 14 \/ 3 = 4.7. 4.7 is a decimal, drop this branch.\n |- Pick two numbers (2, 3) (numbers left: [6, 42]). Try possible operations.\n  |- Try 3 + 2 = 5. Add 5 to the number set. Current number set: [5, 6, 42], target: 12. Options for choosing two numbers: [(5, 6), (5, 42), (6, 42)].\n   |- Pick two numbers (5, 6) (numbers left: [42]). Try possible operations.\n    |- Try 6 + 5 = 11. Add 11 to the number set. Current number set: [11, 42], target: 12, just two numbers left.\n     |- Try 42 + 11 = 53. Evaluate 53 != 12, drop this branch.\n     |- Try 42 - 11 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 42 * 11 = 462. Evaluate 462 != 12, drop this branch.\n     |- Try 42 \/ 11 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 6 - 5 = 1. Add 1 to the number set. Current number set: [1, 42], target: 12, just two numbers left.\n     |- Try 42 + 1 = 43. Evaluate 43 != 12, drop this branch.\n     |- Try 42 - 1 = 41. Evaluate 41 != 12, drop this branch.\n     |- Try 42 * 1 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 42 \/ 1 = 42. Evaluate 42 != 12, drop this branch.\n    |- Try 6 * 5 = 30. Add 30 to the number set. Current number set: [30, 42], target: 12, just two numbers left.\n     |- Try 42 + 30 = 72. Evaluate 72 != 12, drop this branch.\n     |- Try 42 - 30 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 42 - 30 = 12\nThe step before: 6 * 5 = 30\nThe first step: 3 + 2 = 5\n\nOutput the solution in the required format:\n<Solution>\n3 + 2 = 5\n6 * 5 = 30\n42 - 30 = 12\n<\/Solution>\n","item":{"nums":[2,6,3,42],"solution":["3 + 2 = 5","6 * 5 = 30","42 - 30 = 12"],"target":12}}
+{"instance_id":"countdown_8k_25","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [3, 9, 46, 22]\nTarget: 27","reference_output":"# Search Procedure\nInitial number set: [3, 9, 46, 22], target: 27. Options for choosing two numbers: [(3, 9), (3, 46), (3, 22), (9, 46), (9, 22), (46, 22)].\n |- Pick two numbers (3, 9) (numbers left: [46, 22]). Try possible operations.\n  |- Try 9 + 3 = 12. Add 12 to the number set. Current number set: [12, 46, 22], target: 27. Options for choosing two numbers: [(12, 46), (12, 22), (46, 22)].\n   |- Pick two numbers (12, 46) (numbers left: [22]). Try possible operations.\n    |- Try 46 + 12 = 58. Add 58 to the number set. Current number set: [58, 22], target: 27, just two numbers left.\n     |- Try 58 + 22 = 80. Evaluate 80 != 27, drop this branch.\n     |- Try 58 - 22 = 36. Evaluate 36 != 27, drop this branch.\n     |- Try 58 * 22 = 1276. Evaluate 1276 != 27, drop this branch.\n     |- Try 58 \/ 22 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 46 - 12 = 34. Add 34 to the number set. Current number set: [34, 22], target: 27, just two numbers left.\n     |- Try 34 + 22 = 56. Evaluate 56 != 27, drop this branch.\n     |- Try 34 - 22 = 12. Evaluate 12 != 27, drop this branch.\n     |- Try 34 * 22 = 748. Evaluate 748 != 27, drop this branch.\n     |- Try 34 \/ 22 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 46 * 12 = 552. Add 552 to the number set. Current number set: [552, 22], target: 27, just two numbers left.\n     |- Try 552 + 22 = 574. Evaluate 574 != 27, drop this branch.\n     |- Try 552 - 22 = 530. Evaluate 530 != 27, drop this branch.\n     |- Try 552 * 22 = 12144. 12144 exceeds the maximum intermediate result, drop this branch.\n     |- Try 552 \/ 22 = 25.1. 25.1 is a decimal, drop this branch.\n    |- Try 46 \/ 12 = 3.8. 3.8 is a decimal, drop this branch.\n   |- Pick two numbers (12, 22) (numbers left: [46]). Try possible operations.\n    |- Try 22 + 12 = 34. Add 34 to the number set. Current number set: [34, 46], target: 27, just two numbers left.\n     |- Try 46 + 34 = 80. Evaluate 80 != 27, drop this branch.\n     |- Try 46 - 34 = 12. Evaluate 12 != 27, drop this branch.\n     |- Try 46 * 34 = 1564. Evaluate 1564 != 27, drop this branch.\n     |- Try 46 \/ 34 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 22 - 12 = 10. Add 10 to the number set. Current number set: [10, 46], target: 27, just two numbers left.\n     |- Try 46 + 10 = 56. Evaluate 56 != 27, drop this branch.\n     |- Try 46 - 10 = 36. Evaluate 36 != 27, drop this branch.\n     |- Try 46 * 10 = 460. Evaluate 460 != 27, drop this branch.\n     |- Try 46 \/ 10 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 22 * 12 = 264. Add 264 to the number set. Current number set: [264, 46], target: 27, just two numbers left.\n     |- Try 264 + 46 = 310. Evaluate 310 != 27, drop this branch.\n     |- Try 264 - 46 = 218. Evaluate 218 != 27, drop this branch.\n     |- Try 264 * 46 = 12144. 12144 exceeds the maximum intermediate result, drop this branch.\n     |- Try 264 \/ 46 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 22 \/ 12 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (46, 22) (numbers left: [12]). Try possible operations.\n    |- Try 46 + 22 = 68. Add 68 to the number set. Current number set: [68, 12], target: 27, just two numbers left.\n     |- Try 68 + 12 = 80. Evaluate 80 != 27, drop this branch.\n     |- Try 68 - 12 = 56. Evaluate 56 != 27, drop this branch.\n     |- Try 68 * 12 = 816. Evaluate 816 != 27, drop this branch.\n     |- Try 68 \/ 12 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 46 - 22 = 24. Add 24 to the number set. Current number set: [24, 12], target: 27, just two numbers left.\n     |- Try 24 + 12 = 36. Evaluate 36 != 27, drop this branch.\n     |- Try 24 - 12 = 12. Evaluate 12 != 27, drop this branch.\n     |- Try 24 * 12 = 288. Evaluate 288 != 27, drop this branch.\n     |- Try 24 \/ 12 = 2. Evaluate 2 != 27, drop this branch.\n    |- Try 46 * 22 = 1012. Add 1012 to the number set. Current number set: [1012, 12], target: 27, just two numbers left.\n     |- Try 1012 + 12 = 1024. Evaluate 1024 != 27, drop this branch.\n     |- Try 1012 - 12 = 1000. Evaluate 1000 != 27, drop this branch.\n     |- Try 1012 * 12 = 12144. 12144 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1012 \/ 12 = 84.3. 84.3 is a decimal, drop this branch.\n    |- Try 46 \/ 22 = 2.1. 2.1 is a decimal, drop this branch.\n  |- Try 9 - 3 = 6. Add 6 to the number set. Current number set: [6, 46, 22], target: 27. Options for choosing two numbers: [(6, 46), (6, 22), (46, 22)].\n   |- Pick two numbers (6, 46) (numbers left: [22]). Try possible operations.\n    |- Try 46 + 6 = 52. Add 52 to the number set. Current number set: [52, 22], target: 27, just two numbers left.\n     |- Try 52 + 22 = 74. Evaluate 74 != 27, drop this branch.\n     |- Try 52 - 22 = 30. Evaluate 30 != 27, drop this branch.\n     |- Try 52 * 22 = 1144. Evaluate 1144 != 27, drop this branch.\n     |- Try 52 \/ 22 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 46 - 6 = 40. Add 40 to the number set. Current number set: [40, 22], target: 27, just two numbers left.\n     |- Try 40 + 22 = 62. Evaluate 62 != 27, drop this branch.\n     |- Try 40 - 22 = 18. Evaluate 18 != 27, drop this branch.\n     |- Try 40 * 22 = 880. Evaluate 880 != 27, drop this branch.\n     |- Try 40 \/ 22 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 46 * 6 = 276. Add 276 to the number set. Current number set: [276, 22], target: 27, just two numbers left.\n     |- Try 276 + 22 = 298. Evaluate 298 != 27, drop this branch.\n     |- Try 276 - 22 = 254. Evaluate 254 != 27, drop this branch.\n     |- Try 276 * 22 = 6072. 6072 exceeds the maximum intermediate result, drop this branch.\n     |- Try 276 \/ 22 = 12.5. 12.5 is a decimal, drop this branch.\n    |- Try 46 \/ 6 = 7.7. 7.7 is a decimal, drop this branch.\n   |- Pick two numbers (6, 22) (numbers left: [46]). Try possible operations.\n    |- Try 22 + 6 = 28. Add 28 to the number set. Current number set: [28, 46], target: 27, just two numbers left.\n     |- Try 46 + 28 = 74. Evaluate 74 != 27, drop this branch.\n     |- Try 46 - 28 = 18. Evaluate 18 != 27, drop this branch.\n     |- Try 46 * 28 = 1288. Evaluate 1288 != 27, drop this branch.\n     |- Try 46 \/ 28 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 22 - 6 = 16. Add 16 to the number set. Current number set: [16, 46], target: 27, just two numbers left.\n     |- Try 46 + 16 = 62. Evaluate 62 != 27, drop this branch.\n     |- Try 46 - 16 = 30. Evaluate 30 != 27, drop this branch.\n     |- Try 46 * 16 = 736. Evaluate 736 != 27, drop this branch.\n     |- Try 46 \/ 16 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 22 * 6 = 132. Add 132 to the number set. Current number set: [132, 46], target: 27, just two numbers left.\n     |- Try 132 + 46 = 178. Evaluate 178 != 27, drop this branch.\n     |- Try 132 - 46 = 86. Evaluate 86 != 27, drop this branch.\n     |- Try 132 * 46 = 6072. 6072 exceeds the maximum intermediate result, drop this branch.\n     |- Try 132 \/ 46 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 22 \/ 6 = 3.7. 3.7 is a decimal, drop this branch.\n   |- Pick two numbers (46, 22) (numbers left: [6]). Try possible operations.\n    |- Try 46 + 22 = 68. Add 68 to the number set. Current number set: [68, 6], target: 27, just two numbers left.\n     |- Try 68 + 6 = 74. Evaluate 74 != 27, drop this branch.\n     |- Try 68 - 6 = 62. Evaluate 62 != 27, drop this branch.\n     |- Try 68 * 6 = 408. Evaluate 408 != 27, drop this branch.\n     |- Try 68 \/ 6 = 11.3. 11.3 is a decimal, drop this branch.\n    |- Try 46 - 22 = 24. Add 24 to the number set. Current number set: [24, 6], target: 27, just two numbers left.\n     |- Try 24 + 6 = 30. Evaluate 30 != 27, drop this branch.\n     |- Try 24 - 6 = 18. Evaluate 18 != 27, drop this branch.\n     |- Try 24 * 6 = 144. Evaluate 144 != 27, drop this branch.\n     |- Try 24 \/ 6 = 4. Evaluate 4 != 27, drop this branch.\n    |- Try 46 * 22 = 1012. Add 1012 to the number set. Current number set: [1012, 6], target: 27, just two numbers left.\n     |- Try 1012 + 6 = 1018. Evaluate 1018 != 27, drop this branch.\n     |- Try 1012 - 6 = 1006. Evaluate 1006 != 27, drop this branch.\n     |- Try 1012 * 6 = 6072. 6072 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1012 \/ 6 = 168.7. 168.7 is a decimal, drop this branch.\n    |- Try 46 \/ 22 = 2.1. 2.1 is a decimal, drop this branch.\n  |- Try 9 * 3 = 27. Add 27 to the number set. Current number set: [27, 46, 22], target: 27. Options for choosing two numbers: [(27, 46), (27, 22), (46, 22)].\n   |- Pick two numbers (27, 46) (numbers left: [22]). Try possible operations.\n    |- Try 46 + 27 = 73. Add 73 to the number set. Current number set: [73, 22], target: 27, just two numbers left.\n     |- Try 73 + 22 = 95. Evaluate 95 != 27, drop this branch.\n     |- Try 73 - 22 = 51. Evaluate 51 != 27, drop this branch.\n     |- Try 73 * 22 = 1606. Evaluate 1606 != 27, drop this branch.\n     |- Try 73 \/ 22 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 46 - 27 = 19. Add 19 to the number set. Current number set: [19, 22], target: 27, just two numbers left.\n     |- Try 22 + 19 = 41. Evaluate 41 != 27, drop this branch.\n     |- Try 22 - 19 = 3. Evaluate 3 != 27, drop this branch.\n     |- Try 22 * 19 = 418. Evaluate 418 != 27, drop this branch.\n     |- Try 22 \/ 19 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 46 * 27 = 1242. Add 1242 to the number set. Current number set: [1242, 22], target: 27, just two numbers left.\n     |- Try 1242 + 22 = 1264. Evaluate 1264 != 27, drop this branch.\n     |- Try 1242 - 22 = 1220. Evaluate 1220 != 27, drop this branch.\n     |- Try 1242 * 22 = 27324. 27324 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1242 \/ 22 = 56.5. 56.5 is a decimal, drop this branch.\n    |- Try 46 \/ 27 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (27, 22) (numbers left: [46]). Try possible operations.\n    |- Try 27 + 22 = 49. Add 49 to the number set. Current number set: [49, 46], target: 27, just two numbers left.\n     |- Try 49 + 46 = 95. Evaluate 95 != 27, drop this branch.\n     |- Try 49 - 46 = 3. Evaluate 3 != 27, drop this branch.\n     |- Try 49 * 46 = 2254. 2254 exceeds the maximum intermediate result, drop this branch.\n     |- Try 49 \/ 46 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 27 - 22 = 5. Add 5 to the number set. Current number set: [5, 46], target: 27, just two numbers left.\n     |- Try 46 + 5 = 51. Evaluate 51 != 27, drop this branch.\n     |- Try 46 - 5 = 41. Evaluate 41 != 27, drop this branch.\n     |- Try 46 * 5 = 230. Evaluate 230 != 27, drop this branch.\n     |- Try 46 \/ 5 = 9.2. 9.2 is a decimal, drop this branch.\n    |- Try 27 * 22 = 594. Add 594 to the number set. Current number set: [594, 46], target: 27, just two numbers left.\n     |- Try 594 + 46 = 640. Evaluate 640 != 27, drop this branch.\n     |- Try 594 - 46 = 548. Evaluate 548 != 27, drop this branch.\n     |- Try 594 * 46 = 27324. 27324 exceeds the maximum intermediate result, drop this branch.\n     |- Try 594 \/ 46 = 12.9. 12.9 is a decimal, drop this branch.\n    |- Try 27 \/ 22 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (46, 22) (numbers left: [27]). Try possible operations.\n    |- Try 46 + 22 = 68. Add 68 to the number set. Current number set: [68, 27], target: 27, just two numbers left.\n     |- Try 68 + 27 = 95. Evaluate 95 != 27, drop this branch.\n     |- Try 68 - 27 = 41. Evaluate 41 != 27, drop this branch.\n     |- Try 68 * 27 = 1836. Evaluate 1836 != 27, drop this branch.\n     |- Try 68 \/ 27 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 46 - 22 = 24. Add 24 to the number set. Current number set: [24, 27], target: 27, just two numbers left.\n     |- Try 27 + 24 = 51. Evaluate 51 != 27, drop this branch.\n     |- Try 27 - 24 = 3. Evaluate 3 != 27, drop this branch.\n     |- Try 27 * 24 = 648. Evaluate 648 != 27, drop this branch.\n     |- Try 27 \/ 24 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 46 * 22 = 1012. Add 1012 to the number set. Current number set: [1012, 27], target: 27, just two numbers left.\n     |- Try 1012 + 27 = 1039. Evaluate 1039 != 27, drop this branch.\n     |- Try 1012 - 27 = 985. Evaluate 985 != 27, drop this branch.\n     |- Try 1012 * 27 = 27324. 27324 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1012 \/ 27 = 37.5. 37.5 is a decimal, drop this branch.\n    |- Try 46 \/ 22 = 2.1. 2.1 is a decimal, drop this branch.\n  |- Try 9 \/ 3 = 3. Add 3 to the number set. Current number set: [3, 46, 22], target: 27. Options for choosing two numbers: [(3, 46), (3, 22), (46, 22)].\n   |- Pick two numbers (3, 46) (numbers left: [22]). Try possible operations.\n    |- Try 46 + 3 = 49. Add 49 to the number set. Current number set: [49, 22], target: 27, just two numbers left.\n     |- Try 49 + 22 = 71. Evaluate 71 != 27, drop this branch.\n     |- Try 49 - 22 = 27. Evaluate 27 == 27, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 49 - 22 = 27\nThe step before: 46 + 3 = 49\nThe first step: 9 \/ 3 = 3\n\nOutput the solution in the required format:\n<Solution>\n9 \/ 3 = 3\n46 + 3 = 49\n49 - 22 = 27\n<\/Solution>\n","item":{"nums":[3,9,46,22],"solution":["9 \/ 3 = 3","46 + 3 = 49","49 - 22 = 27"],"target":27}}
+{"instance_id":"countdown_8k_26","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [47, 44, 42, 45]\nTarget: 46","reference_output":"# Search Procedure\nInitial number set: [47, 44, 42, 45], target: 46. Options for choosing two numbers: [(47, 44), (47, 42), (47, 45), (44, 42), (44, 45), (42, 45)].\n |- Pick two numbers (47, 44) (numbers left: [42, 45]). Try possible operations.\n  |- Try 47 + 44 = 91. Add 91 to the number set. Current number set: [91, 42, 45], target: 46. Options for choosing two numbers: [(91, 42), (91, 45), (42, 45)].\n   |- Pick two numbers (91, 42) (numbers left: [45]). Try possible operations.\n    |- Try 91 + 42 = 133. Add 133 to the number set. Current number set: [133, 45], target: 46, just two numbers left.\n     |- Try 133 + 45 = 178. Evaluate 178 != 46, drop this branch.\n     |- Try 133 - 45 = 88. Evaluate 88 != 46, drop this branch.\n     |- Try 133 * 45 = 5985. 5985 exceeds the maximum intermediate result, drop this branch.\n     |- Try 133 \/ 45 = 3.0. 3.0 is a decimal, drop this branch.\n    |- Try 91 - 42 = 49. Add 49 to the number set. Current number set: [49, 45], target: 46, just two numbers left.\n     |- Try 49 + 45 = 94. Evaluate 94 != 46, drop this branch.\n     |- Try 49 - 45 = 4. Evaluate 4 != 46, drop this branch.\n     |- Try 49 * 45 = 2205. 2205 exceeds the maximum intermediate result, drop this branch.\n     |- Try 49 \/ 45 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 91 * 42 = 3822. 3822 exceeds the maximum intermediate result, drop this branch.\n    |- Try 91 \/ 42 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (91, 45) (numbers left: [42]). Try possible operations.\n    |- Try 91 + 45 = 136. Add 136 to the number set. Current number set: [136, 42], target: 46, just two numbers left.\n     |- Try 136 + 42 = 178. Evaluate 178 != 46, drop this branch.\n     |- Try 136 - 42 = 94. Evaluate 94 != 46, drop this branch.\n     |- Try 136 * 42 = 5712. 5712 exceeds the maximum intermediate result, drop this branch.\n     |- Try 136 \/ 42 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 91 - 45 = 46. Add 46 to the number set. Current number set: [46, 42], target: 46, just two numbers left.\n     |- Try 46 + 42 = 88. Evaluate 88 != 46, drop this branch.\n     |- Try 46 - 42 = 4. Evaluate 4 != 46, drop this branch.\n     |- Try 46 * 42 = 1932. Evaluate 1932 != 46, drop this branch.\n     |- Try 46 \/ 42 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 91 * 45 = 4095. 4095 exceeds the maximum intermediate result, drop this branch.\n    |- Try 91 \/ 45 = 2.0. 2.0 is a decimal, drop this branch.\n   |- Pick two numbers (42, 45) (numbers left: [91]). Try possible operations.\n    |- Try 45 + 42 = 87. Add 87 to the number set. Current number set: [87, 91], target: 46, just two numbers left.\n     |- Try 91 + 87 = 178. Evaluate 178 != 46, drop this branch.\n     |- Try 91 - 87 = 4. Evaluate 4 != 46, drop this branch.\n     |- Try 91 * 87 = 7917. 7917 exceeds the maximum intermediate result, drop this branch.\n     |- Try 91 \/ 87 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 45 - 42 = 3. Add 3 to the number set. Current number set: [3, 91], target: 46, just two numbers left.\n     |- Try 91 + 3 = 94. Evaluate 94 != 46, drop this branch.\n     |- Try 91 - 3 = 88. Evaluate 88 != 46, drop this branch.\n     |- Try 91 * 3 = 273. Evaluate 273 != 46, drop this branch.\n     |- Try 91 \/ 3 = 30.3. 30.3 is a decimal, drop this branch.\n    |- Try 45 * 42 = 1890. Add 1890 to the number set. Current number set: [1890, 91], target: 46, just two numbers left.\n     |- Try 1890 + 91 = 1981. Evaluate 1981 != 46, drop this branch.\n     |- Try 1890 - 91 = 1799. Evaluate 1799 != 46, drop this branch.\n     |- Try 1890 * 91 = 171990. 171990 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1890 \/ 91 = 20.8. 20.8 is a decimal, drop this branch.\n    |- Try 45 \/ 42 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 47 - 44 = 3. Add 3 to the number set. Current number set: [3, 42, 45], target: 46. Options for choosing two numbers: [(3, 42), (3, 45), (42, 45)].\n   |- Pick two numbers (3, 42) (numbers left: [45]). Try possible operations.\n    |- Try 42 + 3 = 45. Add 45 to the number set. Current number set: [45, 45], target: 46, just two numbers left.\n     |- Try 45 + 45 = 90. Evaluate 90 != 46, drop this branch.\n     |- Try 45 - 45 = 0. Evaluate 0 != 46, drop this branch.\n     |- Try 45 * 45 = 2025. 2025 exceeds the maximum intermediate result, drop this branch.\n     |- Try 45 \/ 45 = 1. Evaluate 1 != 46, drop this branch.\n    |- Try 42 - 3 = 39. Add 39 to the number set. Current number set: [39, 45], target: 46, just two numbers left.\n     |- Try 45 + 39 = 84. Evaluate 84 != 46, drop this branch.\n     |- Try 45 - 39 = 6. Evaluate 6 != 46, drop this branch.\n     |- Try 45 * 39 = 1755. Evaluate 1755 != 46, drop this branch.\n     |- Try 45 \/ 39 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 42 * 3 = 126. Add 126 to the number set. Current number set: [126, 45], target: 46, just two numbers left.\n     |- Try 126 + 45 = 171. Evaluate 171 != 46, drop this branch.\n     |- Try 126 - 45 = 81. Evaluate 81 != 46, drop this branch.\n     |- Try 126 * 45 = 5670. 5670 exceeds the maximum intermediate result, drop this branch.\n     |- Try 126 \/ 45 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 42 \/ 3 = 14. Add 14 to the number set. Current number set: [14, 45], target: 46, just two numbers left.\n     |- Try 45 + 14 = 59. Evaluate 59 != 46, drop this branch.\n     |- Try 45 - 14 = 31. Evaluate 31 != 46, drop this branch.\n     |- Try 45 * 14 = 630. Evaluate 630 != 46, drop this branch.\n     |- Try 45 \/ 14 = 3.2. 3.2 is a decimal, drop this branch.\n   |- Pick two numbers (3, 45) (numbers left: [42]). Try possible operations.\n    |- Try 45 + 3 = 48. Add 48 to the number set. Current number set: [48, 42], target: 46, just two numbers left.\n     |- Try 48 + 42 = 90. Evaluate 90 != 46, drop this branch.\n     |- Try 48 - 42 = 6. Evaluate 6 != 46, drop this branch.\n     |- Try 48 * 42 = 2016. 2016 exceeds the maximum intermediate result, drop this branch.\n     |- Try 48 \/ 42 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 45 - 3 = 42. Add 42 to the number set. Current number set: [42, 42], target: 46, just two numbers left.\n     |- Try 42 + 42 = 84. Evaluate 84 != 46, drop this branch.\n     |- Try 42 - 42 = 0. Evaluate 0 != 46, drop this branch.\n     |- Try 42 * 42 = 1764. Evaluate 1764 != 46, drop this branch.\n     |- Try 42 \/ 42 = 1. Evaluate 1 != 46, drop this branch.\n    |- Try 45 * 3 = 135. Add 135 to the number set. Current number set: [135, 42], target: 46, just two numbers left.\n     |- Try 135 + 42 = 177. Evaluate 177 != 46, drop this branch.\n     |- Try 135 - 42 = 93. Evaluate 93 != 46, drop this branch.\n     |- Try 135 * 42 = 5670. 5670 exceeds the maximum intermediate result, drop this branch.\n     |- Try 135 \/ 42 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 45 \/ 3 = 15. Add 15 to the number set. Current number set: [15, 42], target: 46, just two numbers left.\n     |- Try 42 + 15 = 57. Evaluate 57 != 46, drop this branch.\n     |- Try 42 - 15 = 27. Evaluate 27 != 46, drop this branch.\n     |- Try 42 * 15 = 630. Evaluate 630 != 46, drop this branch.\n     |- Try 42 \/ 15 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (42, 45) (numbers left: [3]). Try possible operations.\n    |- Try 45 + 42 = 87. Add 87 to the number set. Current number set: [87, 3], target: 46, just two numbers left.\n     |- Try 87 + 3 = 90. Evaluate 90 != 46, drop this branch.\n     |- Try 87 - 3 = 84. Evaluate 84 != 46, drop this branch.\n     |- Try 87 * 3 = 261. Evaluate 261 != 46, drop this branch.\n     |- Try 87 \/ 3 = 29. Evaluate 29 != 46, drop this branch.\n    |- Try 45 - 42 = 3. Add 3 to the number set. Current number set: [3, 3], target: 46, just two numbers left.\n     |- Try 3 + 3 = 6. Evaluate 6 != 46, drop this branch.\n     |- Try 3 - 3 = 0. Evaluate 0 != 46, drop this branch.\n     |- Try 3 * 3 = 9. Evaluate 9 != 46, drop this branch.\n     |- Try 3 \/ 3 = 1. Evaluate 1 != 46, drop this branch.\n    |- Try 45 * 42 = 1890. Add 1890 to the number set. Current number set: [1890, 3], target: 46, just two numbers left.\n     |- Try 1890 + 3 = 1893. Evaluate 1893 != 46, drop this branch.\n     |- Try 1890 - 3 = 1887. Evaluate 1887 != 46, drop this branch.\n     |- Try 1890 * 3 = 5670. 5670 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1890 \/ 3 = 630. Evaluate 630 != 46, drop this branch.\n    |- Try 45 \/ 42 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 47 * 44 = 2068. 2068 exceeds the maximum intermediate result, drop this branch.\n  |- Try 47 \/ 44 = 1.1. 1.1 is a decimal, drop this branch.\n |- Pick two numbers (47, 42) (numbers left: [44, 45]). Try possible operations.\n  |- Try 47 + 42 = 89. Add 89 to the number set. Current number set: [89, 44, 45], target: 46. Options for choosing two numbers: [(89, 44), (89, 45), (44, 45)].\n   |- Pick two numbers (89, 44) (numbers left: [45]). Try possible operations.\n    |- Try 89 + 44 = 133. Add 133 to the number set. Current number set: [133, 45], target: 46, just two numbers left.\n     |- Try 133 + 45 = 178. Evaluate 178 != 46, drop this branch.\n     |- Try 133 - 45 = 88. Evaluate 88 != 46, drop this branch.\n     |- Try 133 * 45 = 5985. 5985 exceeds the maximum intermediate result, drop this branch.\n     |- Try 133 \/ 45 = 3.0. 3.0 is a decimal, drop this branch.\n    |- Try 89 - 44 = 45. Add 45 to the number set. Current number set: [45, 45], target: 46, just two numbers left.\n     |- Try 45 + 45 = 90. Evaluate 90 != 46, drop this branch.\n     |- Try 45 - 45 = 0. Evaluate 0 != 46, drop this branch.\n     |- Try 45 * 45 = 2025. 2025 exceeds the maximum intermediate result, drop this branch.\n     |- Try 45 \/ 45 = 1. Evaluate 1 != 46, drop this branch.\n    |- Try 89 * 44 = 3916. 3916 exceeds the maximum intermediate result, drop this branch.\n    |- Try 89 \/ 44 = 2.0. 2.0 is a decimal, drop this branch.\n   |- Pick two numbers (89, 45) (numbers left: [44]). Try possible operations.\n    |- Try 89 + 45 = 134. Add 134 to the number set. Current number set: [134, 44], target: 46, just two numbers left.\n     |- Try 134 + 44 = 178. Evaluate 178 != 46, drop this branch.\n     |- Try 134 - 44 = 90. Evaluate 90 != 46, drop this branch.\n     |- Try 134 * 44 = 5896. 5896 exceeds the maximum intermediate result, drop this branch.\n     |- Try 134 \/ 44 = 3.0. 3.0 is a decimal, drop this branch.\n    |- Try 89 - 45 = 44. Add 44 to the number set. Current number set: [44, 44], target: 46, just two numbers left.\n     |- Try 44 + 44 = 88. Evaluate 88 != 46, drop this branch.\n     |- Try 44 - 44 = 0. Evaluate 0 != 46, drop this branch.\n     |- Try 44 * 44 = 1936. Evaluate 1936 != 46, drop this branch.\n     |- Try 44 \/ 44 = 1. Evaluate 1 != 46, drop this branch.\n    |- Try 89 * 45 = 4005. 4005 exceeds the maximum intermediate result, drop this branch.\n    |- Try 89 \/ 45 = 2.0. 2.0 is a decimal, drop this branch.\n   |- Pick two numbers (44, 45) (numbers left: [89]). Try possible operations.\n    |- Try 45 + 44 = 89. Add 89 to the number set. Current number set: [89, 89], target: 46, just two numbers left.\n     |- Try 89 + 89 = 178. Evaluate 178 != 46, drop this branch.\n     |- Try 89 - 89 = 0. Evaluate 0 != 46, drop this branch.\n     |- Try 89 * 89 = 7921. 7921 exceeds the maximum intermediate result, drop this branch.\n     |- Try 89 \/ 89 = 1. Evaluate 1 != 46, drop this branch.\n    |- Try 45 - 44 = 1. Add 1 to the number set. Current number set: [1, 89], target: 46, just two numbers left.\n     |- Try 89 + 1 = 90. Evaluate 90 != 46, drop this branch.\n     |- Try 89 - 1 = 88. Evaluate 88 != 46, drop this branch.\n     |- Try 89 * 1 = 89. Evaluate 89 != 46, drop this branch.\n     |- Try 89 \/ 1 = 89. Evaluate 89 != 46, drop this branch.\n    |- Try 45 * 44 = 1980. Add 1980 to the number set. Current number set: [1980, 89], target: 46, just two numbers left.\n     |- Try 1980 + 89 = 2069. 2069 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1980 - 89 = 1891. Evaluate 1891 != 46, drop this branch.\n     |- Try 1980 * 89 = 176220. 176220 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1980 \/ 89 = 22.2. 22.2 is a decimal, drop this branch.\n    |- Try 45 \/ 44 = 1.0. 1.0 is a decimal, drop this branch.\n  |- Try 47 - 42 = 5. Add 5 to the number set. Current number set: [5, 44, 45], target: 46. Options for choosing two numbers: [(5, 44), (5, 45), (44, 45)].\n   |- Pick two numbers (5, 44) (numbers left: [45]). Try possible operations.\n    |- Try 44 + 5 = 49. Add 49 to the number set. Current number set: [49, 45], target: 46, just two numbers left.\n     |- Try 49 + 45 = 94. Evaluate 94 != 46, drop this branch.\n     |- Try 49 - 45 = 4. Evaluate 4 != 46, drop this branch.\n     |- Try 49 * 45 = 2205. 2205 exceeds the maximum intermediate result, drop this branch.\n     |- Try 49 \/ 45 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 44 - 5 = 39. Add 39 to the number set. Current number set: [39, 45], target: 46, just two numbers left.\n     |- Try 45 + 39 = 84. Evaluate 84 != 46, drop this branch.\n     |- Try 45 - 39 = 6. Evaluate 6 != 46, drop this branch.\n     |- Try 45 * 39 = 1755. Evaluate 1755 != 46, drop this branch.\n     |- Try 45 \/ 39 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 44 * 5 = 220. Add 220 to the number set. Current number set: [220, 45], target: 46, just two numbers left.\n     |- Try 220 + 45 = 265. Evaluate 265 != 46, drop this branch.\n     |- Try 220 - 45 = 175. Evaluate 175 != 46, drop this branch.\n     |- Try 220 * 45 = 9900. 9900 exceeds the maximum intermediate result, drop this branch.\n     |- Try 220 \/ 45 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 44 \/ 5 = 8.8. 8.8 is a decimal, drop this branch.\n   |- Pick two numbers (5, 45) (numbers left: [44]). Try possible operations.\n    |- Try 45 + 5 = 50. Add 50 to the number set. Current number set: [50, 44], target: 46, just two numbers left.\n     |- Try 50 + 44 = 94. Evaluate 94 != 46, drop this branch.\n     |- Try 50 - 44 = 6. Evaluate 6 != 46, drop this branch.\n     |- Try 50 * 44 = 2200. 2200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 50 \/ 44 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 45 - 5 = 40. Add 40 to the number set. Current number set: [40, 44], target: 46, just two numbers left.\n     |- Try 44 + 40 = 84. Evaluate 84 != 46, drop this branch.\n     |- Try 44 - 40 = 4. Evaluate 4 != 46, drop this branch.\n     |- Try 44 * 40 = 1760. Evaluate 1760 != 46, drop this branch.\n     |- Try 44 \/ 40 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 45 * 5 = 225. Add 225 to the number set. Current number set: [225, 44], target: 46, just two numbers left.\n     |- Try 225 + 44 = 269. Evaluate 269 != 46, drop this branch.\n     |- Try 225 - 44 = 181. Evaluate 181 != 46, drop this branch.\n     |- Try 225 * 44 = 9900. 9900 exceeds the maximum intermediate result, drop this branch.\n     |- Try 225 \/ 44 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 45 \/ 5 = 9. Add 9 to the number set. Current number set: [9, 44], target: 46, just two numbers left.\n     |- Try 44 + 9 = 53. Evaluate 53 != 46, drop this branch.\n     |- Try 44 - 9 = 35. Evaluate 35 != 46, drop this branch.\n     |- Try 44 * 9 = 396. Evaluate 396 != 46, drop this branch.\n     |- Try 44 \/ 9 = 4.9. 4.9 is a decimal, drop this branch.\n   |- Pick two numbers (44, 45) (numbers left: [5]). Try possible operations.\n    |- Try 45 + 44 = 89. Add 89 to the number set. Current number set: [89, 5], target: 46, just two numbers left.\n     |- Try 89 + 5 = 94. Evaluate 94 != 46, drop this branch.\n     |- Try 89 - 5 = 84. Evaluate 84 != 46, drop this branch.\n     |- Try 89 * 5 = 445. Evaluate 445 != 46, drop this branch.\n     |- Try 89 \/ 5 = 17.8. 17.8 is a decimal, drop this branch.\n    |- Try 45 - 44 = 1. Add 1 to the number set. Current number set: [1, 5], target: 46, just two numbers left.\n     |- Try 5 + 1 = 6. Evaluate 6 != 46, drop this branch.\n     |- Try 5 - 1 = 4. Evaluate 4 != 46, drop this branch.\n     |- Try 5 * 1 = 5. Evaluate 5 != 46, drop this branch.\n     |- Try 5 \/ 1 = 5. Evaluate 5 != 46, drop this branch.\n    |- Try 45 * 44 = 1980. Add 1980 to the number set. Current number set: [1980, 5], target: 46, just two numbers left.\n     |- Try 1980 + 5 = 1985. Evaluate 1985 != 46, drop this branch.\n     |- Try 1980 - 5 = 1975. Evaluate 1975 != 46, drop this branch.\n     |- Try 1980 * 5 = 9900. 9900 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1980 \/ 5 = 396. Evaluate 396 != 46, drop this branch.\n    |- Try 45 \/ 44 = 1.0. 1.0 is a decimal, drop this branch.\n  |- Try 47 * 42 = 1974. Add 1974 to the number set. Current number set: [1974, 44, 45], target: 46. Options for choosing two numbers: [(1974, 44), (1974, 45), (44, 45)].\n   |- Pick two numbers (1974, 44) (numbers left: [45]). Try possible operations.\n    |- Try 1974 + 44 = 2018. 2018 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1974 - 44 = 1930. Add 1930 to the number set. Current number set: [1930, 45], target: 46, just two numbers left.\n     |- Try 1930 + 45 = 1975. Evaluate 1975 != 46, drop this branch.\n     |- Try 1930 - 45 = 1885. Evaluate 1885 != 46, drop this branch.\n     |- Try 1930 * 45 = 86850. 86850 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1930 \/ 45 = 42.9. 42.9 is a decimal, drop this branch.\n    |- Try 1974 * 44 = 86856. 86856 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1974 \/ 44 = 44.9. 44.9 is a decimal, drop this branch.\n   |- Pick two numbers (1974, 45) (numbers left: [44]). Try possible operations.\n    |- Try 1974 + 45 = 2019. 2019 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1974 - 45 = 1929. Add 1929 to the number set. Current number set: [1929, 44], target: 46, just two numbers left.\n     |- Try 1929 + 44 = 1973. Evaluate 1973 != 46, drop this branch.\n     |- Try 1929 - 44 = 1885. Evaluate 1885 != 46, drop this branch.\n     |- Try 1929 * 44 = 84876. 84876 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1929 \/ 44 = 43.8. 43.8 is a decimal, drop this branch.\n    |- Try 1974 * 45 = 88830. 88830 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1974 \/ 45 = 43.9. 43.9 is a decimal, drop this branch.\n   |- Pick two numbers (44, 45) (numbers left: [1974]). Try possible operations.\n    |- Try 45 + 44 = 89. Add 89 to the number set. Current number set: [89, 1974], target: 46, just two numbers left.\n     |- Try 1974 + 89 = 2063. 2063 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1974 - 89 = 1885. Evaluate 1885 != 46, drop this branch.\n     |- Try 1974 * 89 = 175686. 175686 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1974 \/ 89 = 22.2. 22.2 is a decimal, drop this branch.\n    |- Try 45 - 44 = 1. Add 1 to the number set. Current number set: [1, 1974], target: 46, just two numbers left.\n     |- Try 1974 + 1 = 1975. Evaluate 1975 != 46, drop this branch.\n     |- Try 1974 - 1 = 1973. Evaluate 1973 != 46, drop this branch.\n     |- Try 1974 * 1 = 1974. Evaluate 1974 != 46, drop this branch.\n     |- Try 1974 \/ 1 = 1974. Evaluate 1974 != 46, drop this branch.\n    |- Try 45 * 44 = 1980. Add 1980 to the number set. Current number set: [1980, 1974], target: 46, just two numbers left.\n     |- Try 1980 + 1974 = 3954. 3954 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1980 - 1974 = 6. Evaluate 6 != 46, drop this branch.\n     |- Try 1980 * 1974 = 3908520. 3908520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1980 \/ 1974 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 45 \/ 44 = 1.0. 1.0 is a decimal, drop this branch.\n  |- Try 47 \/ 42 = 1.1. 1.1 is a decimal, drop this branch.\n |- Pick two numbers (47, 45) (numbers left: [44, 42]). Try possible operations.\n  |- Try 47 + 45 = 92. Add 92 to the number set. Current number set: [92, 44, 42], target: 46. Options for choosing two numbers: [(92, 44), (92, 42), (44, 42)].\n   |- Pick two numbers (92, 44) (numbers left: [42]). Try possible operations.\n    |- Try 92 + 44 = 136. Add 136 to the number set. Current number set: [136, 42], target: 46, just two numbers left.\n     |- Try 136 + 42 = 178. Evaluate 178 != 46, drop this branch.\n     |- Try 136 - 42 = 94. Evaluate 94 != 46, drop this branch.\n     |- Try 136 * 42 = 5712. 5712 exceeds the maximum intermediate result, drop this branch.\n     |- Try 136 \/ 42 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 92 - 44 = 48. Add 48 to the number set. Current number set: [48, 42], target: 46, just two numbers left.\n     |- Try 48 + 42 = 90. Evaluate 90 != 46, drop this branch.\n     |- Try 48 - 42 = 6. Evaluate 6 != 46, drop this branch.\n     |- Try 48 * 42 = 2016. 2016 exceeds the maximum intermediate result, drop this branch.\n     |- Try 48 \/ 42 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 92 * 44 = 4048. 4048 exceeds the maximum intermediate result, drop this branch.\n    |- Try 92 \/ 44 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (92, 42) (numbers left: [44]). Try possible operations.\n    |- Try 92 + 42 = 134. Add 134 to the number set. Current number set: [134, 44], target: 46, just two numbers left.\n     |- Try 134 + 44 = 178. Evaluate 178 != 46, drop this branch.\n     |- Try 134 - 44 = 90. Evaluate 90 != 46, drop this branch.\n     |- Try 134 * 44 = 5896. 5896 exceeds the maximum intermediate result, drop this branch.\n     |- Try 134 \/ 44 = 3.0. 3.0 is a decimal, drop this branch.\n    |- Try 92 - 42 = 50. Add 50 to the number set. Current number set: [50, 44], target: 46, just two numbers left.\n     |- Try 50 + 44 = 94. Evaluate 94 != 46, drop this branch.\n     |- Try 50 - 44 = 6. Evaluate 6 != 46, drop this branch.\n     |- Try 50 * 44 = 2200. 2200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 50 \/ 44 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 92 * 42 = 3864. 3864 exceeds the maximum intermediate result, drop this branch.\n    |- Try 92 \/ 42 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (44, 42) (numbers left: [92]). Try possible operations.\n    |- Try 44 + 42 = 86. Add 86 to the number set. Current number set: [86, 92], target: 46, just two numbers left.\n     |- Try 92 + 86 = 178. Evaluate 178 != 46, drop this branch.\n     |- Try 92 - 86 = 6. Evaluate 6 != 46, drop this branch.\n     |- Try 92 * 86 = 7912. 7912 exceeds the maximum intermediate result, drop this branch.\n     |- Try 92 \/ 86 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 44 - 42 = 2. Add 2 to the number set. Current number set: [2, 92], target: 46, just two numbers left.\n     |- Try 92 + 2 = 94. Evaluate 94 != 46, drop this branch.\n     |- Try 92 - 2 = 90. Evaluate 90 != 46, drop this branch.\n     |- Try 92 * 2 = 184. Evaluate 184 != 46, drop this branch.\n     |- Try 92 \/ 2 = 46. Evaluate 46 == 46, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 92 \/ 2 = 46\nThe step before: 44 - 42 = 2\nThe first step: 47 + 45 = 92\n\nOutput the solution in the required format:\n<Solution>\n47 + 45 = 92\n44 - 42 = 2\n92 \/ 2 = 46\n<\/Solution>\n","item":{"nums":[47,44,42,45],"solution":["47 + 45 = 92","44 - 42 = 2","92 \/ 2 = 46"],"target":46}}
+{"instance_id":"countdown_8k_27","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [23, 10, 19, 3]\nTarget: 26","reference_output":"# Search Procedure\nInitial number set: [23, 10, 19, 3], target: 26. Options for choosing two numbers: [(23, 10), (23, 19), (23, 3), (10, 19), (10, 3), (19, 3)].\n |- Pick two numbers (23, 10) (numbers left: [19, 3]). Try possible operations.\n  |- Try 23 + 10 = 33. Add 33 to the number set. Current number set: [33, 19, 3], target: 26. Options for choosing two numbers: [(33, 19), (33, 3), (19, 3)].\n   |- Pick two numbers (33, 19) (numbers left: [3]). Try possible operations.\n    |- Try 33 + 19 = 52. Add 52 to the number set. Current number set: [52, 3], target: 26, just two numbers left.\n     |- Try 52 + 3 = 55. Evaluate 55 != 26, drop this branch.\n     |- Try 52 - 3 = 49. Evaluate 49 != 26, drop this branch.\n     |- Try 52 * 3 = 156. Evaluate 156 != 26, drop this branch.\n     |- Try 52 \/ 3 = 17.3. 17.3 is a decimal, drop this branch.\n    |- Try 33 - 19 = 14. Add 14 to the number set. Current number set: [14, 3], target: 26, just two numbers left.\n     |- Try 14 + 3 = 17. Evaluate 17 != 26, drop this branch.\n     |- Try 14 - 3 = 11. Evaluate 11 != 26, drop this branch.\n     |- Try 14 * 3 = 42. Evaluate 42 != 26, drop this branch.\n     |- Try 14 \/ 3 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 33 * 19 = 627. Add 627 to the number set. Current number set: [627, 3], target: 26, just two numbers left.\n     |- Try 627 + 3 = 630. Evaluate 630 != 26, drop this branch.\n     |- Try 627 - 3 = 624. Evaluate 624 != 26, drop this branch.\n     |- Try 627 * 3 = 1881. Evaluate 1881 != 26, drop this branch.\n     |- Try 627 \/ 3 = 209. Evaluate 209 != 26, drop this branch.\n    |- Try 33 \/ 19 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (33, 3) (numbers left: [19]). Try possible operations.\n    |- Try 33 + 3 = 36. Add 36 to the number set. Current number set: [36, 19], target: 26, just two numbers left.\n     |- Try 36 + 19 = 55. Evaluate 55 != 26, drop this branch.\n     |- Try 36 - 19 = 17. Evaluate 17 != 26, drop this branch.\n     |- Try 36 * 19 = 684. Evaluate 684 != 26, drop this branch.\n     |- Try 36 \/ 19 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 33 - 3 = 30. Add 30 to the number set. Current number set: [30, 19], target: 26, just two numbers left.\n     |- Try 30 + 19 = 49. Evaluate 49 != 26, drop this branch.\n     |- Try 30 - 19 = 11. Evaluate 11 != 26, drop this branch.\n     |- Try 30 * 19 = 570. Evaluate 570 != 26, drop this branch.\n     |- Try 30 \/ 19 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 33 * 3 = 99. Add 99 to the number set. Current number set: [99, 19], target: 26, just two numbers left.\n     |- Try 99 + 19 = 118. Evaluate 118 != 26, drop this branch.\n     |- Try 99 - 19 = 80. Evaluate 80 != 26, drop this branch.\n     |- Try 99 * 19 = 1881. Evaluate 1881 != 26, drop this branch.\n     |- Try 99 \/ 19 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 33 \/ 3 = 11. Add 11 to the number set. Current number set: [11, 19], target: 26, just two numbers left.\n     |- Try 19 + 11 = 30. Evaluate 30 != 26, drop this branch.\n     |- Try 19 - 11 = 8. Evaluate 8 != 26, drop this branch.\n     |- Try 19 * 11 = 209. Evaluate 209 != 26, drop this branch.\n     |- Try 19 \/ 11 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (19, 3) (numbers left: [33]). Try possible operations.\n    |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 33], target: 26, just two numbers left.\n     |- Try 33 + 22 = 55. Evaluate 55 != 26, drop this branch.\n     |- Try 33 - 22 = 11. Evaluate 11 != 26, drop this branch.\n     |- Try 33 * 22 = 726. Evaluate 726 != 26, drop this branch.\n     |- Try 33 \/ 22 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 33], target: 26, just two numbers left.\n     |- Try 33 + 16 = 49. Evaluate 49 != 26, drop this branch.\n     |- Try 33 - 16 = 17. Evaluate 17 != 26, drop this branch.\n     |- Try 33 * 16 = 528. Evaluate 528 != 26, drop this branch.\n     |- Try 33 \/ 16 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 19 * 3 = 57. Add 57 to the number set. Current number set: [57, 33], target: 26, just two numbers left.\n     |- Try 57 + 33 = 90. Evaluate 90 != 26, drop this branch.\n     |- Try 57 - 33 = 24. Evaluate 24 != 26, drop this branch.\n     |- Try 57 * 33 = 1881. Evaluate 1881 != 26, drop this branch.\n     |- Try 57 \/ 33 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 19 \/ 3 = 6.3. 6.3 is a decimal, drop this branch.\n  |- Try 23 - 10 = 13. Add 13 to the number set. Current number set: [13, 19, 3], target: 26. Options for choosing two numbers: [(13, 19), (13, 3), (19, 3)].\n   |- Pick two numbers (13, 19) (numbers left: [3]). Try possible operations.\n    |- Try 19 + 13 = 32. Add 32 to the number set. Current number set: [32, 3], target: 26, just two numbers left.\n     |- Try 32 + 3 = 35. Evaluate 35 != 26, drop this branch.\n     |- Try 32 - 3 = 29. Evaluate 29 != 26, drop this branch.\n     |- Try 32 * 3 = 96. Evaluate 96 != 26, drop this branch.\n     |- Try 32 \/ 3 = 10.7. 10.7 is a decimal, drop this branch.\n    |- Try 19 - 13 = 6. Add 6 to the number set. Current number set: [6, 3], target: 26, just two numbers left.\n     |- Try 6 + 3 = 9. Evaluate 9 != 26, drop this branch.\n     |- Try 6 - 3 = 3. Evaluate 3 != 26, drop this branch.\n     |- Try 6 * 3 = 18. Evaluate 18 != 26, drop this branch.\n     |- Try 6 \/ 3 = 2. Evaluate 2 != 26, drop this branch.\n    |- Try 19 * 13 = 247. Add 247 to the number set. Current number set: [247, 3], target: 26, just two numbers left.\n     |- Try 247 + 3 = 250. Evaluate 250 != 26, drop this branch.\n     |- Try 247 - 3 = 244. Evaluate 244 != 26, drop this branch.\n     |- Try 247 * 3 = 741. Evaluate 741 != 26, drop this branch.\n     |- Try 247 \/ 3 = 82.3. 82.3 is a decimal, drop this branch.\n    |- Try 19 \/ 13 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (13, 3) (numbers left: [19]). Try possible operations.\n    |- Try 13 + 3 = 16. Add 16 to the number set. Current number set: [16, 19], target: 26, just two numbers left.\n     |- Try 19 + 16 = 35. Evaluate 35 != 26, drop this branch.\n     |- Try 19 - 16 = 3. Evaluate 3 != 26, drop this branch.\n     |- Try 19 * 16 = 304. Evaluate 304 != 26, drop this branch.\n     |- Try 19 \/ 16 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 13 - 3 = 10. Add 10 to the number set. Current number set: [10, 19], target: 26, just two numbers left.\n     |- Try 19 + 10 = 29. Evaluate 29 != 26, drop this branch.\n     |- Try 19 - 10 = 9. Evaluate 9 != 26, drop this branch.\n     |- Try 19 * 10 = 190. Evaluate 190 != 26, drop this branch.\n     |- Try 19 \/ 10 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 13 * 3 = 39. Add 39 to the number set. Current number set: [39, 19], target: 26, just two numbers left.\n     |- Try 39 + 19 = 58. Evaluate 58 != 26, drop this branch.\n     |- Try 39 - 19 = 20. Evaluate 20 != 26, drop this branch.\n     |- Try 39 * 19 = 741. Evaluate 741 != 26, drop this branch.\n     |- Try 39 \/ 19 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 13 \/ 3 = 4.3. 4.3 is a decimal, drop this branch.\n   |- Pick two numbers (19, 3) (numbers left: [13]). Try possible operations.\n    |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 13], target: 26, just two numbers left.\n     |- Try 22 + 13 = 35. Evaluate 35 != 26, drop this branch.\n     |- Try 22 - 13 = 9. Evaluate 9 != 26, drop this branch.\n     |- Try 22 * 13 = 286. Evaluate 286 != 26, drop this branch.\n     |- Try 22 \/ 13 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 13], target: 26, just two numbers left.\n     |- Try 16 + 13 = 29. Evaluate 29 != 26, drop this branch.\n     |- Try 16 - 13 = 3. Evaluate 3 != 26, drop this branch.\n     |- Try 16 * 13 = 208. Evaluate 208 != 26, drop this branch.\n     |- Try 16 \/ 13 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 19 * 3 = 57. Add 57 to the number set. Current number set: [57, 13], target: 26, just two numbers left.\n     |- Try 57 + 13 = 70. Evaluate 70 != 26, drop this branch.\n     |- Try 57 - 13 = 44. Evaluate 44 != 26, drop this branch.\n     |- Try 57 * 13 = 741. Evaluate 741 != 26, drop this branch.\n     |- Try 57 \/ 13 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 19 \/ 3 = 6.3. 6.3 is a decimal, drop this branch.\n  |- Try 23 * 10 = 230. Add 230 to the number set. Current number set: [230, 19, 3], target: 26. Options for choosing two numbers: [(230, 19), (230, 3), (19, 3)].\n   |- Pick two numbers (230, 19) (numbers left: [3]). Try possible operations.\n    |- Try 230 + 19 = 249. Add 249 to the number set. Current number set: [249, 3], target: 26, just two numbers left.\n     |- Try 249 + 3 = 252. Evaluate 252 != 26, drop this branch.\n     |- Try 249 - 3 = 246. Evaluate 246 != 26, drop this branch.\n     |- Try 249 * 3 = 747. Evaluate 747 != 26, drop this branch.\n     |- Try 249 \/ 3 = 83. Evaluate 83 != 26, drop this branch.\n    |- Try 230 - 19 = 211. Add 211 to the number set. Current number set: [211, 3], target: 26, just two numbers left.\n     |- Try 211 + 3 = 214. Evaluate 214 != 26, drop this branch.\n     |- Try 211 - 3 = 208. Evaluate 208 != 26, drop this branch.\n     |- Try 211 * 3 = 633. Evaluate 633 != 26, drop this branch.\n     |- Try 211 \/ 3 = 70.3. 70.3 is a decimal, drop this branch.\n    |- Try 230 * 19 = 4370. 4370 exceeds the maximum intermediate result, drop this branch.\n    |- Try 230 \/ 19 = 12.1. 12.1 is a decimal, drop this branch.\n   |- Pick two numbers (230, 3) (numbers left: [19]). Try possible operations.\n    |- Try 230 + 3 = 233. Add 233 to the number set. Current number set: [233, 19], target: 26, just two numbers left.\n     |- Try 233 + 19 = 252. Evaluate 252 != 26, drop this branch.\n     |- Try 233 - 19 = 214. Evaluate 214 != 26, drop this branch.\n     |- Try 233 * 19 = 4427. 4427 exceeds the maximum intermediate result, drop this branch.\n     |- Try 233 \/ 19 = 12.3. 12.3 is a decimal, drop this branch.\n    |- Try 230 - 3 = 227. Add 227 to the number set. Current number set: [227, 19], target: 26, just two numbers left.\n     |- Try 227 + 19 = 246. Evaluate 246 != 26, drop this branch.\n     |- Try 227 - 19 = 208. Evaluate 208 != 26, drop this branch.\n     |- Try 227 * 19 = 4313. 4313 exceeds the maximum intermediate result, drop this branch.\n     |- Try 227 \/ 19 = 11.9. 11.9 is a decimal, drop this branch.\n    |- Try 230 * 3 = 690. Add 690 to the number set. Current number set: [690, 19], target: 26, just two numbers left.\n     |- Try 690 + 19 = 709. Evaluate 709 != 26, drop this branch.\n     |- Try 690 - 19 = 671. Evaluate 671 != 26, drop this branch.\n     |- Try 690 * 19 = 13110. 13110 exceeds the maximum intermediate result, drop this branch.\n     |- Try 690 \/ 19 = 36.3. 36.3 is a decimal, drop this branch.\n    |- Try 230 \/ 3 = 76.7. 76.7 is a decimal, drop this branch.\n   |- Pick two numbers (19, 3) (numbers left: [230]). Try possible operations.\n    |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 230], target: 26, just two numbers left.\n     |- Try 230 + 22 = 252. Evaluate 252 != 26, drop this branch.\n     |- Try 230 - 22 = 208. Evaluate 208 != 26, drop this branch.\n     |- Try 230 * 22 = 5060. 5060 exceeds the maximum intermediate result, drop this branch.\n     |- Try 230 \/ 22 = 10.5. 10.5 is a decimal, drop this branch.\n    |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 230], target: 26, just two numbers left.\n     |- Try 230 + 16 = 246. Evaluate 246 != 26, drop this branch.\n     |- Try 230 - 16 = 214. Evaluate 214 != 26, drop this branch.\n     |- Try 230 * 16 = 3680. 3680 exceeds the maximum intermediate result, drop this branch.\n     |- Try 230 \/ 16 = 14.4. 14.4 is a decimal, drop this branch.\n    |- Try 19 * 3 = 57. Add 57 to the number set. Current number set: [57, 230], target: 26, just two numbers left.\n     |- Try 230 + 57 = 287. Evaluate 287 != 26, drop this branch.\n     |- Try 230 - 57 = 173. Evaluate 173 != 26, drop this branch.\n     |- Try 230 * 57 = 13110. 13110 exceeds the maximum intermediate result, drop this branch.\n     |- Try 230 \/ 57 = 4.0. 4.0 is a decimal, drop this branch.\n    |- Try 19 \/ 3 = 6.3. 6.3 is a decimal, drop this branch.\n  |- Try 23 \/ 10 = 2.3. 2.3 is a decimal, drop this branch.\n |- Pick two numbers (23, 19) (numbers left: [10, 3]). Try possible operations.\n  |- Try 23 + 19 = 42. Add 42 to the number set. Current number set: [42, 10, 3], target: 26. Options for choosing two numbers: [(42, 10), (42, 3), (10, 3)].\n   |- Pick two numbers (42, 10) (numbers left: [3]). Try possible operations.\n    |- Try 42 + 10 = 52. Add 52 to the number set. Current number set: [52, 3], target: 26, just two numbers left.\n     |- Try 52 + 3 = 55. Evaluate 55 != 26, drop this branch.\n     |- Try 52 - 3 = 49. Evaluate 49 != 26, drop this branch.\n     |- Try 52 * 3 = 156. Evaluate 156 != 26, drop this branch.\n     |- Try 52 \/ 3 = 17.3. 17.3 is a decimal, drop this branch.\n    |- Try 42 - 10 = 32. Add 32 to the number set. Current number set: [32, 3], target: 26, just two numbers left.\n     |- Try 32 + 3 = 35. Evaluate 35 != 26, drop this branch.\n     |- Try 32 - 3 = 29. Evaluate 29 != 26, drop this branch.\n     |- Try 32 * 3 = 96. Evaluate 96 != 26, drop this branch.\n     |- Try 32 \/ 3 = 10.7. 10.7 is a decimal, drop this branch.\n    |- Try 42 * 10 = 420. Add 420 to the number set. Current number set: [420, 3], target: 26, just two numbers left.\n     |- Try 420 + 3 = 423. Evaluate 423 != 26, drop this branch.\n     |- Try 420 - 3 = 417. Evaluate 417 != 26, drop this branch.\n     |- Try 420 * 3 = 1260. Evaluate 1260 != 26, drop this branch.\n     |- Try 420 \/ 3 = 140. Evaluate 140 != 26, drop this branch.\n    |- Try 42 \/ 10 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (42, 3) (numbers left: [10]). Try possible operations.\n    |- Try 42 + 3 = 45. Add 45 to the number set. Current number set: [45, 10], target: 26, just two numbers left.\n     |- Try 45 + 10 = 55. Evaluate 55 != 26, drop this branch.\n     |- Try 45 - 10 = 35. Evaluate 35 != 26, drop this branch.\n     |- Try 45 * 10 = 450. Evaluate 450 != 26, drop this branch.\n     |- Try 45 \/ 10 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 42 - 3 = 39. Add 39 to the number set. Current number set: [39, 10], target: 26, just two numbers left.\n     |- Try 39 + 10 = 49. Evaluate 49 != 26, drop this branch.\n     |- Try 39 - 10 = 29. Evaluate 29 != 26, drop this branch.\n     |- Try 39 * 10 = 390. Evaluate 390 != 26, drop this branch.\n     |- Try 39 \/ 10 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 42 * 3 = 126. Add 126 to the number set. Current number set: [126, 10], target: 26, just two numbers left.\n     |- Try 126 + 10 = 136. Evaluate 136 != 26, drop this branch.\n     |- Try 126 - 10 = 116. Evaluate 116 != 26, drop this branch.\n     |- Try 126 * 10 = 1260. Evaluate 1260 != 26, drop this branch.\n     |- Try 126 \/ 10 = 12.6. 12.6 is a decimal, drop this branch.\n    |- Try 42 \/ 3 = 14. Add 14 to the number set. Current number set: [14, 10], target: 26, just two numbers left.\n     |- Try 14 + 10 = 24. Evaluate 24 != 26, drop this branch.\n     |- Try 14 - 10 = 4. Evaluate 4 != 26, drop this branch.\n     |- Try 14 * 10 = 140. Evaluate 140 != 26, drop this branch.\n     |- Try 14 \/ 10 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (10, 3) (numbers left: [42]). Try possible operations.\n    |- Try 10 + 3 = 13. Add 13 to the number set. Current number set: [13, 42], target: 26, just two numbers left.\n     |- Try 42 + 13 = 55. Evaluate 55 != 26, drop this branch.\n     |- Try 42 - 13 = 29. Evaluate 29 != 26, drop this branch.\n     |- Try 42 * 13 = 546. Evaluate 546 != 26, drop this branch.\n     |- Try 42 \/ 13 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 10 - 3 = 7. Add 7 to the number set. Current number set: [7, 42], target: 26, just two numbers left.\n     |- Try 42 + 7 = 49. Evaluate 49 != 26, drop this branch.\n     |- Try 42 - 7 = 35. Evaluate 35 != 26, drop this branch.\n     |- Try 42 * 7 = 294. Evaluate 294 != 26, drop this branch.\n     |- Try 42 \/ 7 = 6. Evaluate 6 != 26, drop this branch.\n    |- Try 10 * 3 = 30. Add 30 to the number set. Current number set: [30, 42], target: 26, just two numbers left.\n     |- Try 42 + 30 = 72. Evaluate 72 != 26, drop this branch.\n     |- Try 42 - 30 = 12. Evaluate 12 != 26, drop this branch.\n     |- Try 42 * 30 = 1260. Evaluate 1260 != 26, drop this branch.\n     |- Try 42 \/ 30 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 10 \/ 3 = 3.3. 3.3 is a decimal, drop this branch.\n  |- Try 23 - 19 = 4. Add 4 to the number set. Current number set: [4, 10, 3], target: 26. Options for choosing two numbers: [(4, 10), (4, 3), (10, 3)].\n   |- Pick two numbers (4, 10) (numbers left: [3]). Try possible operations.\n    |- Try 10 + 4 = 14. Add 14 to the number set. Current number set: [14, 3], target: 26, just two numbers left.\n     |- Try 14 + 3 = 17. Evaluate 17 != 26, drop this branch.\n     |- Try 14 - 3 = 11. Evaluate 11 != 26, drop this branch.\n     |- Try 14 * 3 = 42. Evaluate 42 != 26, drop this branch.\n     |- Try 14 \/ 3 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 10 - 4 = 6. Add 6 to the number set. Current number set: [6, 3], target: 26, just two numbers left.\n     |- Try 6 + 3 = 9. Evaluate 9 != 26, drop this branch.\n     |- Try 6 - 3 = 3. Evaluate 3 != 26, drop this branch.\n     |- Try 6 * 3 = 18. Evaluate 18 != 26, drop this branch.\n     |- Try 6 \/ 3 = 2. Evaluate 2 != 26, drop this branch.\n    |- Try 10 * 4 = 40. Add 40 to the number set. Current number set: [40, 3], target: 26, just two numbers left.\n     |- Try 40 + 3 = 43. Evaluate 43 != 26, drop this branch.\n     |- Try 40 - 3 = 37. Evaluate 37 != 26, drop this branch.\n     |- Try 40 * 3 = 120. Evaluate 120 != 26, drop this branch.\n     |- Try 40 \/ 3 = 13.3. 13.3 is a decimal, drop this branch.\n    |- Try 10 \/ 4 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (4, 3) (numbers left: [10]). Try possible operations.\n    |- Try 4 + 3 = 7. Add 7 to the number set. Current number set: [7, 10], target: 26, just two numbers left.\n     |- Try 10 + 7 = 17. Evaluate 17 != 26, drop this branch.\n     |- Try 10 - 7 = 3. Evaluate 3 != 26, drop this branch.\n     |- Try 10 * 7 = 70. Evaluate 70 != 26, drop this branch.\n     |- Try 10 \/ 7 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 4 - 3 = 1. Add 1 to the number set. Current number set: [1, 10], target: 26, just two numbers left.\n     |- Try 10 + 1 = 11. Evaluate 11 != 26, drop this branch.\n     |- Try 10 - 1 = 9. Evaluate 9 != 26, drop this branch.\n     |- Try 10 * 1 = 10. Evaluate 10 != 26, drop this branch.\n     |- Try 10 \/ 1 = 10. Evaluate 10 != 26, drop this branch.\n    |- Try 4 * 3 = 12. Add 12 to the number set. Current number set: [12, 10], target: 26, just two numbers left.\n     |- Try 12 + 10 = 22. Evaluate 22 != 26, drop this branch.\n     |- Try 12 - 10 = 2. Evaluate 2 != 26, drop this branch.\n     |- Try 12 * 10 = 120. Evaluate 120 != 26, drop this branch.\n     |- Try 12 \/ 10 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 4 \/ 3 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (10, 3) (numbers left: [4]). Try possible operations.\n    |- Try 10 + 3 = 13. Add 13 to the number set. Current number set: [13, 4], target: 26, just two numbers left.\n     |- Try 13 + 4 = 17. Evaluate 17 != 26, drop this branch.\n     |- Try 13 - 4 = 9. Evaluate 9 != 26, drop this branch.\n     |- Try 13 * 4 = 52. Evaluate 52 != 26, drop this branch.\n     |- Try 13 \/ 4 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 10 - 3 = 7. Add 7 to the number set. Current number set: [7, 4], target: 26, just two numbers left.\n     |- Try 7 + 4 = 11. Evaluate 11 != 26, drop this branch.\n     |- Try 7 - 4 = 3. Evaluate 3 != 26, drop this branch.\n     |- Try 7 * 4 = 28. Evaluate 28 != 26, drop this branch.\n     |- Try 7 \/ 4 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 10 * 3 = 30. Add 30 to the number set. Current number set: [30, 4], target: 26, just two numbers left.\n     |- Try 30 + 4 = 34. Evaluate 34 != 26, drop this branch.\n     |- Try 30 - 4 = 26. Evaluate 26 == 26, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 30 - 4 = 26\nThe step before: 10 * 3 = 30\nThe first step: 23 - 19 = 4\n\nOutput the solution in the required format:\n<Solution>\n23 - 19 = 4\n10 * 3 = 30\n30 - 4 = 26\n<\/Solution>\n","item":{"nums":[23,10,19,3],"solution":["23 - 19 = 4","10 * 3 = 30","30 - 4 = 26"],"target":26}}
+{"instance_id":"countdown_8k_28","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [6, 34, 29, 34]\nTarget: 36","reference_output":"# Search Procedure\nInitial number set: [6, 34, 29, 34], target: 36. Options for choosing two numbers: [(6, 34), (6, 29), (6, 34), (34, 29), (34, 34), (29, 34)].\n |- Pick two numbers (6, 34) (numbers left: [29, 34]). Try possible operations.\n  |- Try 34 + 6 = 40. Add 40 to the number set. Current number set: [40, 29, 34], target: 36. Options for choosing two numbers: [(40, 29), (40, 34), (29, 34)].\n   |- Pick two numbers (40, 29) (numbers left: [34]). Try possible operations.\n    |- Try 40 + 29 = 69. Add 69 to the number set. Current number set: [69, 34], target: 36, just two numbers left.\n     |- Try 69 + 34 = 103. Evaluate 103 != 36, drop this branch.\n     |- Try 69 - 34 = 35. Evaluate 35 != 36, drop this branch.\n     |- Try 69 * 34 = 2346. 2346 exceeds the maximum intermediate result, drop this branch.\n     |- Try 69 \/ 34 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 40 - 29 = 11. Add 11 to the number set. Current number set: [11, 34], target: 36, just two numbers left.\n     |- Try 34 + 11 = 45. Evaluate 45 != 36, drop this branch.\n     |- Try 34 - 11 = 23. Evaluate 23 != 36, drop this branch.\n     |- Try 34 * 11 = 374. Evaluate 374 != 36, drop this branch.\n     |- Try 34 \/ 11 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 40 * 29 = 1160. Add 1160 to the number set. Current number set: [1160, 34], target: 36, just two numbers left.\n     |- Try 1160 + 34 = 1194. Evaluate 1194 != 36, drop this branch.\n     |- Try 1160 - 34 = 1126. Evaluate 1126 != 36, drop this branch.\n     |- Try 1160 * 34 = 39440. 39440 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1160 \/ 34 = 34.1. 34.1 is a decimal, drop this branch.\n    |- Try 40 \/ 29 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (40, 34) (numbers left: [29]). Try possible operations.\n    |- Try 40 + 34 = 74. Add 74 to the number set. Current number set: [74, 29], target: 36, just two numbers left.\n     |- Try 74 + 29 = 103. Evaluate 103 != 36, drop this branch.\n     |- Try 74 - 29 = 45. Evaluate 45 != 36, drop this branch.\n     |- Try 74 * 29 = 2146. 2146 exceeds the maximum intermediate result, drop this branch.\n     |- Try 74 \/ 29 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 40 - 34 = 6. Add 6 to the number set. Current number set: [6, 29], target: 36, just two numbers left.\n     |- Try 29 + 6 = 35. Evaluate 35 != 36, drop this branch.\n     |- Try 29 - 6 = 23. Evaluate 23 != 36, drop this branch.\n     |- Try 29 * 6 = 174. Evaluate 174 != 36, drop this branch.\n     |- Try 29 \/ 6 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 40 * 34 = 1360. Add 1360 to the number set. Current number set: [1360, 29], target: 36, just two numbers left.\n     |- Try 1360 + 29 = 1389. Evaluate 1389 != 36, drop this branch.\n     |- Try 1360 - 29 = 1331. Evaluate 1331 != 36, drop this branch.\n     |- Try 1360 * 29 = 39440. 39440 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1360 \/ 29 = 46.9. 46.9 is a decimal, drop this branch.\n    |- Try 40 \/ 34 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (29, 34) (numbers left: [40]). Try possible operations.\n    |- Try 34 + 29 = 63. Add 63 to the number set. Current number set: [63, 40], target: 36, just two numbers left.\n     |- Try 63 + 40 = 103. Evaluate 103 != 36, drop this branch.\n     |- Try 63 - 40 = 23. Evaluate 23 != 36, drop this branch.\n     |- Try 63 * 40 = 2520. 2520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 40 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 34 - 29 = 5. Add 5 to the number set. Current number set: [5, 40], target: 36, just two numbers left.\n     |- Try 40 + 5 = 45. Evaluate 45 != 36, drop this branch.\n     |- Try 40 - 5 = 35. Evaluate 35 != 36, drop this branch.\n     |- Try 40 * 5 = 200. Evaluate 200 != 36, drop this branch.\n     |- Try 40 \/ 5 = 8. Evaluate 8 != 36, drop this branch.\n    |- Try 34 * 29 = 986. Add 986 to the number set. Current number set: [986, 40], target: 36, just two numbers left.\n     |- Try 986 + 40 = 1026. Evaluate 1026 != 36, drop this branch.\n     |- Try 986 - 40 = 946. Evaluate 946 != 36, drop this branch.\n     |- Try 986 * 40 = 39440. 39440 exceeds the maximum intermediate result, drop this branch.\n     |- Try 986 \/ 40 = 24.6. 24.6 is a decimal, drop this branch.\n    |- Try 34 \/ 29 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 34 - 6 = 28. Add 28 to the number set. Current number set: [28, 29, 34], target: 36. Options for choosing two numbers: [(28, 29), (28, 34), (29, 34)].\n   |- Pick two numbers (28, 29) (numbers left: [34]). Try possible operations.\n    |- Try 29 + 28 = 57. Add 57 to the number set. Current number set: [57, 34], target: 36, just two numbers left.\n     |- Try 57 + 34 = 91. Evaluate 91 != 36, drop this branch.\n     |- Try 57 - 34 = 23. Evaluate 23 != 36, drop this branch.\n     |- Try 57 * 34 = 1938. Evaluate 1938 != 36, drop this branch.\n     |- Try 57 \/ 34 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 29 - 28 = 1. Add 1 to the number set. Current number set: [1, 34], target: 36, just two numbers left.\n     |- Try 34 + 1 = 35. Evaluate 35 != 36, drop this branch.\n     |- Try 34 - 1 = 33. Evaluate 33 != 36, drop this branch.\n     |- Try 34 * 1 = 34. Evaluate 34 != 36, drop this branch.\n     |- Try 34 \/ 1 = 34. Evaluate 34 != 36, drop this branch.\n    |- Try 29 * 28 = 812. Add 812 to the number set. Current number set: [812, 34], target: 36, just two numbers left.\n     |- Try 812 + 34 = 846. Evaluate 846 != 36, drop this branch.\n     |- Try 812 - 34 = 778. Evaluate 778 != 36, drop this branch.\n     |- Try 812 * 34 = 27608. 27608 exceeds the maximum intermediate result, drop this branch.\n     |- Try 812 \/ 34 = 23.9. 23.9 is a decimal, drop this branch.\n    |- Try 29 \/ 28 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (28, 34) (numbers left: [29]). Try possible operations.\n    |- Try 34 + 28 = 62. Add 62 to the number set. Current number set: [62, 29], target: 36, just two numbers left.\n     |- Try 62 + 29 = 91. Evaluate 91 != 36, drop this branch.\n     |- Try 62 - 29 = 33. Evaluate 33 != 36, drop this branch.\n     |- Try 62 * 29 = 1798. Evaluate 1798 != 36, drop this branch.\n     |- Try 62 \/ 29 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 34 - 28 = 6. Add 6 to the number set. Current number set: [6, 29], target: 36, just two numbers left.\n     |- Try 29 + 6 = 35. Evaluate 35 != 36, drop this branch.\n     |- Try 29 - 6 = 23. Evaluate 23 != 36, drop this branch.\n     |- Try 29 * 6 = 174. Evaluate 174 != 36, drop this branch.\n     |- Try 29 \/ 6 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 34 * 28 = 952. Add 952 to the number set. Current number set: [952, 29], target: 36, just two numbers left.\n     |- Try 952 + 29 = 981. Evaluate 981 != 36, drop this branch.\n     |- Try 952 - 29 = 923. Evaluate 923 != 36, drop this branch.\n     |- Try 952 * 29 = 27608. 27608 exceeds the maximum intermediate result, drop this branch.\n     |- Try 952 \/ 29 = 32.8. 32.8 is a decimal, drop this branch.\n    |- Try 34 \/ 28 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (29, 34) (numbers left: [28]). Try possible operations.\n    |- Try 34 + 29 = 63. Add 63 to the number set. Current number set: [63, 28], target: 36, just two numbers left.\n     |- Try 63 + 28 = 91. Evaluate 91 != 36, drop this branch.\n     |- Try 63 - 28 = 35. Evaluate 35 != 36, drop this branch.\n     |- Try 63 * 28 = 1764. Evaluate 1764 != 36, drop this branch.\n     |- Try 63 \/ 28 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 34 - 29 = 5. Add 5 to the number set. Current number set: [5, 28], target: 36, just two numbers left.\n     |- Try 28 + 5 = 33. Evaluate 33 != 36, drop this branch.\n     |- Try 28 - 5 = 23. Evaluate 23 != 36, drop this branch.\n     |- Try 28 * 5 = 140. Evaluate 140 != 36, drop this branch.\n     |- Try 28 \/ 5 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 34 * 29 = 986. Add 986 to the number set. Current number set: [986, 28], target: 36, just two numbers left.\n     |- Try 986 + 28 = 1014. Evaluate 1014 != 36, drop this branch.\n     |- Try 986 - 28 = 958. Evaluate 958 != 36, drop this branch.\n     |- Try 986 * 28 = 27608. 27608 exceeds the maximum intermediate result, drop this branch.\n     |- Try 986 \/ 28 = 35.2. 35.2 is a decimal, drop this branch.\n    |- Try 34 \/ 29 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 34 * 6 = 204. Add 204 to the number set. Current number set: [204, 29, 34], target: 36. Options for choosing two numbers: [(204, 29), (204, 34), (29, 34)].\n   |- Pick two numbers (204, 29) (numbers left: [34]). Try possible operations.\n    |- Try 204 + 29 = 233. Add 233 to the number set. Current number set: [233, 34], target: 36, just two numbers left.\n     |- Try 233 + 34 = 267. Evaluate 267 != 36, drop this branch.\n     |- Try 233 - 34 = 199. Evaluate 199 != 36, drop this branch.\n     |- Try 233 * 34 = 7922. 7922 exceeds the maximum intermediate result, drop this branch.\n     |- Try 233 \/ 34 = 6.9. 6.9 is a decimal, drop this branch.\n    |- Try 204 - 29 = 175. Add 175 to the number set. Current number set: [175, 34], target: 36, just two numbers left.\n     |- Try 175 + 34 = 209. Evaluate 209 != 36, drop this branch.\n     |- Try 175 - 34 = 141. Evaluate 141 != 36, drop this branch.\n     |- Try 175 * 34 = 5950. 5950 exceeds the maximum intermediate result, drop this branch.\n     |- Try 175 \/ 34 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 204 * 29 = 5916. 5916 exceeds the maximum intermediate result, drop this branch.\n    |- Try 204 \/ 29 = 7.0. 7.0 is a decimal, drop this branch.\n   |- Pick two numbers (204, 34) (numbers left: [29]). Try possible operations.\n    |- Try 204 + 34 = 238. Add 238 to the number set. Current number set: [238, 29], target: 36, just two numbers left.\n     |- Try 238 + 29 = 267. Evaluate 267 != 36, drop this branch.\n     |- Try 238 - 29 = 209. Evaluate 209 != 36, drop this branch.\n     |- Try 238 * 29 = 6902. 6902 exceeds the maximum intermediate result, drop this branch.\n     |- Try 238 \/ 29 = 8.2. 8.2 is a decimal, drop this branch.\n    |- Try 204 - 34 = 170. Add 170 to the number set. Current number set: [170, 29], target: 36, just two numbers left.\n     |- Try 170 + 29 = 199. Evaluate 199 != 36, drop this branch.\n     |- Try 170 - 29 = 141. Evaluate 141 != 36, drop this branch.\n     |- Try 170 * 29 = 4930. 4930 exceeds the maximum intermediate result, drop this branch.\n     |- Try 170 \/ 29 = 5.9. 5.9 is a decimal, drop this branch.\n    |- Try 204 * 34 = 6936. 6936 exceeds the maximum intermediate result, drop this branch.\n    |- Try 204 \/ 34 = 6. Add 6 to the number set. Current number set: [6, 29], target: 36, just two numbers left.\n     |- Try 29 + 6 = 35. Evaluate 35 != 36, drop this branch.\n     |- Try 29 - 6 = 23. Evaluate 23 != 36, drop this branch.\n     |- Try 29 * 6 = 174. Evaluate 174 != 36, drop this branch.\n     |- Try 29 \/ 6 = 4.8. 4.8 is a decimal, drop this branch.\n   |- Pick two numbers (29, 34) (numbers left: [204]). Try possible operations.\n    |- Try 34 + 29 = 63. Add 63 to the number set. Current number set: [63, 204], target: 36, just two numbers left.\n     |- Try 204 + 63 = 267. Evaluate 267 != 36, drop this branch.\n     |- Try 204 - 63 = 141. Evaluate 141 != 36, drop this branch.\n     |- Try 204 * 63 = 12852. 12852 exceeds the maximum intermediate result, drop this branch.\n     |- Try 204 \/ 63 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 34 - 29 = 5. Add 5 to the number set. Current number set: [5, 204], target: 36, just two numbers left.\n     |- Try 204 + 5 = 209. Evaluate 209 != 36, drop this branch.\n     |- Try 204 - 5 = 199. Evaluate 199 != 36, drop this branch.\n     |- Try 204 * 5 = 1020. Evaluate 1020 != 36, drop this branch.\n     |- Try 204 \/ 5 = 40.8. 40.8 is a decimal, drop this branch.\n    |- Try 34 * 29 = 986. Add 986 to the number set. Current number set: [986, 204], target: 36, just two numbers left.\n     |- Try 986 + 204 = 1190. Evaluate 1190 != 36, drop this branch.\n     |- Try 986 - 204 = 782. Evaluate 782 != 36, drop this branch.\n     |- Try 986 * 204 = 201144. 201144 exceeds the maximum intermediate result, drop this branch.\n     |- Try 986 \/ 204 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 34 \/ 29 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 34 \/ 6 = 5.7. 5.7 is a decimal, drop this branch.\n |- Pick two numbers (6, 29) (numbers left: [34, 34]). Try possible operations.\n  |- Try 29 + 6 = 35. Add 35 to the number set. Current number set: [35, 34, 34], target: 36. Options for choosing two numbers: [(35, 34), (35, 34), (34, 34)].\n   |- Pick two numbers (35, 34) (numbers left: [34]). Try possible operations.\n    |- Try 35 + 34 = 69. Add 69 to the number set. Current number set: [69, 34], target: 36, just two numbers left.\n     |- Try 69 + 34 = 103. Evaluate 103 != 36, drop this branch.\n     |- Try 69 - 34 = 35. Evaluate 35 != 36, drop this branch.\n     |- Try 69 * 34 = 2346. 2346 exceeds the maximum intermediate result, drop this branch.\n     |- Try 69 \/ 34 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 35 - 34 = 1. Add 1 to the number set. Current number set: [1, 34], target: 36, just two numbers left.\n     |- Try 34 + 1 = 35. Evaluate 35 != 36, drop this branch.\n     |- Try 34 - 1 = 33. Evaluate 33 != 36, drop this branch.\n     |- Try 34 * 1 = 34. Evaluate 34 != 36, drop this branch.\n     |- Try 34 \/ 1 = 34. Evaluate 34 != 36, drop this branch.\n    |- Try 35 * 34 = 1190. Add 1190 to the number set. Current number set: [1190, 34], target: 36, just two numbers left.\n     |- Try 1190 + 34 = 1224. Evaluate 1224 != 36, drop this branch.\n     |- Try 1190 - 34 = 1156. Evaluate 1156 != 36, drop this branch.\n     |- Try 1190 * 34 = 40460. 40460 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1190 \/ 34 = 35. Evaluate 35 != 36, drop this branch.\n    |- Try 35 \/ 34 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (35, 34) (numbers left: [34]). Try possible operations.\n    |- Try 35 + 34 = 69. Add 69 to the number set. Current number set: [69, 34], target: 36, just two numbers left.\n     |- Try 69 + 34 = 103. Evaluate 103 != 36, drop this branch.\n     |- Try 69 - 34 = 35. Evaluate 35 != 36, drop this branch.\n     |- Try 69 * 34 = 2346. 2346 exceeds the maximum intermediate result, drop this branch.\n     |- Try 69 \/ 34 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 35 - 34 = 1. Add 1 to the number set. Current number set: [1, 34], target: 36, just two numbers left.\n     |- Try 34 + 1 = 35. Evaluate 35 != 36, drop this branch.\n     |- Try 34 - 1 = 33. Evaluate 33 != 36, drop this branch.\n     |- Try 34 * 1 = 34. Evaluate 34 != 36, drop this branch.\n     |- Try 34 \/ 1 = 34. Evaluate 34 != 36, drop this branch.\n    |- Try 35 * 34 = 1190. Add 1190 to the number set. Current number set: [1190, 34], target: 36, just two numbers left.\n     |- Try 1190 + 34 = 1224. Evaluate 1224 != 36, drop this branch.\n     |- Try 1190 - 34 = 1156. Evaluate 1156 != 36, drop this branch.\n     |- Try 1190 * 34 = 40460. 40460 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1190 \/ 34 = 35. Evaluate 35 != 36, drop this branch.\n    |- Try 35 \/ 34 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (34, 34) (numbers left: [35]). Try possible operations.\n    |- Try 34 + 34 = 68. Add 68 to the number set. Current number set: [68, 35], target: 36, just two numbers left.\n     |- Try 68 + 35 = 103. Evaluate 103 != 36, drop this branch.\n     |- Try 68 - 35 = 33. Evaluate 33 != 36, drop this branch.\n     |- Try 68 * 35 = 2380. 2380 exceeds the maximum intermediate result, drop this branch.\n     |- Try 68 \/ 35 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 34 - 34 = 0. Add 0 to the number set. Current number set: [0, 35], target: 36, just two numbers left.\n     |- Try 35 + 0 = 35. Evaluate 35 != 36, drop this branch.\n     |- Try 35 - 0 = 35. Evaluate 35 != 36, drop this branch.\n     |- Try 35 * 0 = 0. Evaluate 0 != 36, drop this branch.\n     |- Try 35 \/ 0 (invalid operation). drop this branch.\n    |- Try 34 * 34 = 1156. Add 1156 to the number set. Current number set: [1156, 35], target: 36, just two numbers left.\n     |- Try 1156 + 35 = 1191. Evaluate 1191 != 36, drop this branch.\n     |- Try 1156 - 35 = 1121. Evaluate 1121 != 36, drop this branch.\n     |- Try 1156 * 35 = 40460. 40460 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1156 \/ 35 = 33.0. 33.0 is a decimal, drop this branch.\n    |- Try 34 \/ 34 = 1. Add 1 to the number set. Current number set: [1, 35], target: 36, just two numbers left.\n     |- Try 35 + 1 = 36. Evaluate 36 == 36, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 35 + 1 = 36\nThe step before: 34 \/ 34 = 1\nThe first step: 29 + 6 = 35\n\nOutput the solution in the required format:\n<Solution>\n29 + 6 = 35\n34 \/ 34 = 1\n35 + 1 = 36\n<\/Solution>\n","item":{"nums":[6,34,29,34],"solution":["29 + 6 = 35","34 \/ 34 = 1","35 + 1 = 36"],"target":36}}
+{"instance_id":"countdown_8k_29","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [49, 2, 20, 30]\nTarget: 44","reference_output":"# Search Procedure\nInitial number set: [49, 2, 20, 30], target: 44. Options for choosing two numbers: [(49, 2), (49, 20), (49, 30), (2, 20), (2, 30), (20, 30)].\n |- Pick two numbers (49, 2) (numbers left: [20, 30]). Try possible operations.\n  |- Try 49 + 2 = 51. Add 51 to the number set. Current number set: [51, 20, 30], target: 44. Options for choosing two numbers: [(51, 20), (51, 30), (20, 30)].\n   |- Pick two numbers (51, 20) (numbers left: [30]). Try possible operations.\n    |- Try 51 + 20 = 71. Add 71 to the number set. Current number set: [71, 30], target: 44, just two numbers left.\n     |- Try 71 + 30 = 101. Evaluate 101 != 44, drop this branch.\n     |- Try 71 - 30 = 41. Evaluate 41 != 44, drop this branch.\n     |- Try 71 * 30 = 2130. 2130 exceeds the maximum intermediate result, drop this branch.\n     |- Try 71 \/ 30 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 51 - 20 = 31. Add 31 to the number set. Current number set: [31, 30], target: 44, just two numbers left.\n     |- Try 31 + 30 = 61. Evaluate 61 != 44, drop this branch.\n     |- Try 31 - 30 = 1. Evaluate 1 != 44, drop this branch.\n     |- Try 31 * 30 = 930. Evaluate 930 != 44, drop this branch.\n     |- Try 31 \/ 30 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 51 * 20 = 1020. Add 1020 to the number set. Current number set: [1020, 30], target: 44, just two numbers left.\n     |- Try 1020 + 30 = 1050. Evaluate 1050 != 44, drop this branch.\n     |- Try 1020 - 30 = 990. Evaluate 990 != 44, drop this branch.\n     |- Try 1020 * 30 = 30600. 30600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1020 \/ 30 = 34. Evaluate 34 != 44, drop this branch.\n    |- Try 51 \/ 20 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (51, 30) (numbers left: [20]). Try possible operations.\n    |- Try 51 + 30 = 81. Add 81 to the number set. Current number set: [81, 20], target: 44, just two numbers left.\n     |- Try 81 + 20 = 101. Evaluate 101 != 44, drop this branch.\n     |- Try 81 - 20 = 61. Evaluate 61 != 44, drop this branch.\n     |- Try 81 * 20 = 1620. Evaluate 1620 != 44, drop this branch.\n     |- Try 81 \/ 20 = 4.0. 4.0 is a decimal, drop this branch.\n    |- Try 51 - 30 = 21. Add 21 to the number set. Current number set: [21, 20], target: 44, just two numbers left.\n     |- Try 21 + 20 = 41. Evaluate 41 != 44, drop this branch.\n     |- Try 21 - 20 = 1. Evaluate 1 != 44, drop this branch.\n     |- Try 21 * 20 = 420. Evaluate 420 != 44, drop this branch.\n     |- Try 21 \/ 20 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 51 * 30 = 1530. Add 1530 to the number set. Current number set: [1530, 20], target: 44, just two numbers left.\n     |- Try 1530 + 20 = 1550. Evaluate 1550 != 44, drop this branch.\n     |- Try 1530 - 20 = 1510. Evaluate 1510 != 44, drop this branch.\n     |- Try 1530 * 20 = 30600. 30600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1530 \/ 20 = 76.5. 76.5 is a decimal, drop this branch.\n    |- Try 51 \/ 30 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (20, 30) (numbers left: [51]). Try possible operations.\n    |- Try 30 + 20 = 50. Add 50 to the number set. Current number set: [50, 51], target: 44, just two numbers left.\n     |- Try 51 + 50 = 101. Evaluate 101 != 44, drop this branch.\n     |- Try 51 - 50 = 1. Evaluate 1 != 44, drop this branch.\n     |- Try 51 * 50 = 2550. 2550 exceeds the maximum intermediate result, drop this branch.\n     |- Try 51 \/ 50 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 30 - 20 = 10. Add 10 to the number set. Current number set: [10, 51], target: 44, just two numbers left.\n     |- Try 51 + 10 = 61. Evaluate 61 != 44, drop this branch.\n     |- Try 51 - 10 = 41. Evaluate 41 != 44, drop this branch.\n     |- Try 51 * 10 = 510. Evaluate 510 != 44, drop this branch.\n     |- Try 51 \/ 10 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 30 * 20 = 600. Add 600 to the number set. Current number set: [600, 51], target: 44, just two numbers left.\n     |- Try 600 + 51 = 651. Evaluate 651 != 44, drop this branch.\n     |- Try 600 - 51 = 549. Evaluate 549 != 44, drop this branch.\n     |- Try 600 * 51 = 30600. 30600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 600 \/ 51 = 11.8. 11.8 is a decimal, drop this branch.\n    |- Try 30 \/ 20 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 49 - 2 = 47. Add 47 to the number set. Current number set: [47, 20, 30], target: 44. Options for choosing two numbers: [(47, 20), (47, 30), (20, 30)].\n   |- Pick two numbers (47, 20) (numbers left: [30]). Try possible operations.\n    |- Try 47 + 20 = 67. Add 67 to the number set. Current number set: [67, 30], target: 44, just two numbers left.\n     |- Try 67 + 30 = 97. Evaluate 97 != 44, drop this branch.\n     |- Try 67 - 30 = 37. Evaluate 37 != 44, drop this branch.\n     |- Try 67 * 30 = 2010. 2010 exceeds the maximum intermediate result, drop this branch.\n     |- Try 67 \/ 30 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 47 - 20 = 27. Add 27 to the number set. Current number set: [27, 30], target: 44, just two numbers left.\n     |- Try 30 + 27 = 57. Evaluate 57 != 44, drop this branch.\n     |- Try 30 - 27 = 3. Evaluate 3 != 44, drop this branch.\n     |- Try 30 * 27 = 810. Evaluate 810 != 44, drop this branch.\n     |- Try 30 \/ 27 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 47 * 20 = 940. Add 940 to the number set. Current number set: [940, 30], target: 44, just two numbers left.\n     |- Try 940 + 30 = 970. Evaluate 970 != 44, drop this branch.\n     |- Try 940 - 30 = 910. Evaluate 910 != 44, drop this branch.\n     |- Try 940 * 30 = 28200. 28200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 940 \/ 30 = 31.3. 31.3 is a decimal, drop this branch.\n    |- Try 47 \/ 20 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (47, 30) (numbers left: [20]). Try possible operations.\n    |- Try 47 + 30 = 77. Add 77 to the number set. Current number set: [77, 20], target: 44, just two numbers left.\n     |- Try 77 + 20 = 97. Evaluate 97 != 44, drop this branch.\n     |- Try 77 - 20 = 57. Evaluate 57 != 44, drop this branch.\n     |- Try 77 * 20 = 1540. Evaluate 1540 != 44, drop this branch.\n     |- Try 77 \/ 20 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 47 - 30 = 17. Add 17 to the number set. Current number set: [17, 20], target: 44, just two numbers left.\n     |- Try 20 + 17 = 37. Evaluate 37 != 44, drop this branch.\n     |- Try 20 - 17 = 3. Evaluate 3 != 44, drop this branch.\n     |- Try 20 * 17 = 340. Evaluate 340 != 44, drop this branch.\n     |- Try 20 \/ 17 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 47 * 30 = 1410. Add 1410 to the number set. Current number set: [1410, 20], target: 44, just two numbers left.\n     |- Try 1410 + 20 = 1430. Evaluate 1430 != 44, drop this branch.\n     |- Try 1410 - 20 = 1390. Evaluate 1390 != 44, drop this branch.\n     |- Try 1410 * 20 = 28200. 28200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1410 \/ 20 = 70.5. 70.5 is a decimal, drop this branch.\n    |- Try 47 \/ 30 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (20, 30) (numbers left: [47]). Try possible operations.\n    |- Try 30 + 20 = 50. Add 50 to the number set. Current number set: [50, 47], target: 44, just two numbers left.\n     |- Try 50 + 47 = 97. Evaluate 97 != 44, drop this branch.\n     |- Try 50 - 47 = 3. Evaluate 3 != 44, drop this branch.\n     |- Try 50 * 47 = 2350. 2350 exceeds the maximum intermediate result, drop this branch.\n     |- Try 50 \/ 47 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 30 - 20 = 10. Add 10 to the number set. Current number set: [10, 47], target: 44, just two numbers left.\n     |- Try 47 + 10 = 57. Evaluate 57 != 44, drop this branch.\n     |- Try 47 - 10 = 37. Evaluate 37 != 44, drop this branch.\n     |- Try 47 * 10 = 470. Evaluate 470 != 44, drop this branch.\n     |- Try 47 \/ 10 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 30 * 20 = 600. Add 600 to the number set. Current number set: [600, 47], target: 44, just two numbers left.\n     |- Try 600 + 47 = 647. Evaluate 647 != 44, drop this branch.\n     |- Try 600 - 47 = 553. Evaluate 553 != 44, drop this branch.\n     |- Try 600 * 47 = 28200. 28200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 600 \/ 47 = 12.8. 12.8 is a decimal, drop this branch.\n    |- Try 30 \/ 20 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 49 * 2 = 98. Add 98 to the number set. Current number set: [98, 20, 30], target: 44. Options for choosing two numbers: [(98, 20), (98, 30), (20, 30)].\n   |- Pick two numbers (98, 20) (numbers left: [30]). Try possible operations.\n    |- Try 98 + 20 = 118. Add 118 to the number set. Current number set: [118, 30], target: 44, just two numbers left.\n     |- Try 118 + 30 = 148. Evaluate 148 != 44, drop this branch.\n     |- Try 118 - 30 = 88. Evaluate 88 != 44, drop this branch.\n     |- Try 118 * 30 = 3540. 3540 exceeds the maximum intermediate result, drop this branch.\n     |- Try 118 \/ 30 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 98 - 20 = 78. Add 78 to the number set. Current number set: [78, 30], target: 44, just two numbers left.\n     |- Try 78 + 30 = 108. Evaluate 108 != 44, drop this branch.\n     |- Try 78 - 30 = 48. Evaluate 48 != 44, drop this branch.\n     |- Try 78 * 30 = 2340. 2340 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 30 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 98 * 20 = 1960. Add 1960 to the number set. Current number set: [1960, 30], target: 44, just two numbers left.\n     |- Try 1960 + 30 = 1990. Evaluate 1990 != 44, drop this branch.\n     |- Try 1960 - 30 = 1930. Evaluate 1930 != 44, drop this branch.\n     |- Try 1960 * 30 = 58800. 58800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1960 \/ 30 = 65.3. 65.3 is a decimal, drop this branch.\n    |- Try 98 \/ 20 = 4.9. 4.9 is a decimal, drop this branch.\n   |- Pick two numbers (98, 30) (numbers left: [20]). Try possible operations.\n    |- Try 98 + 30 = 128. Add 128 to the number set. Current number set: [128, 20], target: 44, just two numbers left.\n     |- Try 128 + 20 = 148. Evaluate 148 != 44, drop this branch.\n     |- Try 128 - 20 = 108. Evaluate 108 != 44, drop this branch.\n     |- Try 128 * 20 = 2560. 2560 exceeds the maximum intermediate result, drop this branch.\n     |- Try 128 \/ 20 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 98 - 30 = 68. Add 68 to the number set. Current number set: [68, 20], target: 44, just two numbers left.\n     |- Try 68 + 20 = 88. Evaluate 88 != 44, drop this branch.\n     |- Try 68 - 20 = 48. Evaluate 48 != 44, drop this branch.\n     |- Try 68 * 20 = 1360. Evaluate 1360 != 44, drop this branch.\n     |- Try 68 \/ 20 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 98 * 30 = 2940. 2940 exceeds the maximum intermediate result, drop this branch.\n    |- Try 98 \/ 30 = 3.3. 3.3 is a decimal, drop this branch.\n   |- Pick two numbers (20, 30) (numbers left: [98]). Try possible operations.\n    |- Try 30 + 20 = 50. Add 50 to the number set. Current number set: [50, 98], target: 44, just two numbers left.\n     |- Try 98 + 50 = 148. Evaluate 148 != 44, drop this branch.\n     |- Try 98 - 50 = 48. Evaluate 48 != 44, drop this branch.\n     |- Try 98 * 50 = 4900. 4900 exceeds the maximum intermediate result, drop this branch.\n     |- Try 98 \/ 50 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 30 - 20 = 10. Add 10 to the number set. Current number set: [10, 98], target: 44, just two numbers left.\n     |- Try 98 + 10 = 108. Evaluate 108 != 44, drop this branch.\n     |- Try 98 - 10 = 88. Evaluate 88 != 44, drop this branch.\n     |- Try 98 * 10 = 980. Evaluate 980 != 44, drop this branch.\n     |- Try 98 \/ 10 = 9.8. 9.8 is a decimal, drop this branch.\n    |- Try 30 * 20 = 600. Add 600 to the number set. Current number set: [600, 98], target: 44, just two numbers left.\n     |- Try 600 + 98 = 698. Evaluate 698 != 44, drop this branch.\n     |- Try 600 - 98 = 502. Evaluate 502 != 44, drop this branch.\n     |- Try 600 * 98 = 58800. 58800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 600 \/ 98 = 6.1. 6.1 is a decimal, drop this branch.\n    |- Try 30 \/ 20 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 49 \/ 2 = 24.5. 24.5 is a decimal, drop this branch.\n |- Pick two numbers (49, 20) (numbers left: [2, 30]). Try possible operations.\n  |- Try 49 + 20 = 69. Add 69 to the number set. Current number set: [69, 2, 30], target: 44. Options for choosing two numbers: [(69, 2), (69, 30), (2, 30)].\n   |- Pick two numbers (69, 2) (numbers left: [30]). Try possible operations.\n    |- Try 69 + 2 = 71. Add 71 to the number set. Current number set: [71, 30], target: 44, just two numbers left.\n     |- Try 71 + 30 = 101. Evaluate 101 != 44, drop this branch.\n     |- Try 71 - 30 = 41. Evaluate 41 != 44, drop this branch.\n     |- Try 71 * 30 = 2130. 2130 exceeds the maximum intermediate result, drop this branch.\n     |- Try 71 \/ 30 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 69 - 2 = 67. Add 67 to the number set. Current number set: [67, 30], target: 44, just two numbers left.\n     |- Try 67 + 30 = 97. Evaluate 97 != 44, drop this branch.\n     |- Try 67 - 30 = 37. Evaluate 37 != 44, drop this branch.\n     |- Try 67 * 30 = 2010. 2010 exceeds the maximum intermediate result, drop this branch.\n     |- Try 67 \/ 30 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 69 * 2 = 138. Add 138 to the number set. Current number set: [138, 30], target: 44, just two numbers left.\n     |- Try 138 + 30 = 168. Evaluate 168 != 44, drop this branch.\n     |- Try 138 - 30 = 108. Evaluate 108 != 44, drop this branch.\n     |- Try 138 * 30 = 4140. 4140 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 30 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 69 \/ 2 = 34.5. 34.5 is a decimal, drop this branch.\n   |- Pick two numbers (69, 30) (numbers left: [2]). Try possible operations.\n    |- Try 69 + 30 = 99. Add 99 to the number set. Current number set: [99, 2], target: 44, just two numbers left.\n     |- Try 99 + 2 = 101. Evaluate 101 != 44, drop this branch.\n     |- Try 99 - 2 = 97. Evaluate 97 != 44, drop this branch.\n     |- Try 99 * 2 = 198. Evaluate 198 != 44, drop this branch.\n     |- Try 99 \/ 2 = 49.5. 49.5 is a decimal, drop this branch.\n    |- Try 69 - 30 = 39. Add 39 to the number set. Current number set: [39, 2], target: 44, just two numbers left.\n     |- Try 39 + 2 = 41. Evaluate 41 != 44, drop this branch.\n     |- Try 39 - 2 = 37. Evaluate 37 != 44, drop this branch.\n     |- Try 39 * 2 = 78. Evaluate 78 != 44, drop this branch.\n     |- Try 39 \/ 2 = 19.5. 19.5 is a decimal, drop this branch.\n    |- Try 69 * 30 = 2070. 2070 exceeds the maximum intermediate result, drop this branch.\n    |- Try 69 \/ 30 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (2, 30) (numbers left: [69]). Try possible operations.\n    |- Try 30 + 2 = 32. Add 32 to the number set. Current number set: [32, 69], target: 44, just two numbers left.\n     |- Try 69 + 32 = 101. Evaluate 101 != 44, drop this branch.\n     |- Try 69 - 32 = 37. Evaluate 37 != 44, drop this branch.\n     |- Try 69 * 32 = 2208. 2208 exceeds the maximum intermediate result, drop this branch.\n     |- Try 69 \/ 32 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 30 - 2 = 28. Add 28 to the number set. Current number set: [28, 69], target: 44, just two numbers left.\n     |- Try 69 + 28 = 97. Evaluate 97 != 44, drop this branch.\n     |- Try 69 - 28 = 41. Evaluate 41 != 44, drop this branch.\n     |- Try 69 * 28 = 1932. Evaluate 1932 != 44, drop this branch.\n     |- Try 69 \/ 28 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 30 * 2 = 60. Add 60 to the number set. Current number set: [60, 69], target: 44, just two numbers left.\n     |- Try 69 + 60 = 129. Evaluate 129 != 44, drop this branch.\n     |- Try 69 - 60 = 9. Evaluate 9 != 44, drop this branch.\n     |- Try 69 * 60 = 4140. 4140 exceeds the maximum intermediate result, drop this branch.\n     |- Try 69 \/ 60 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 30 \/ 2 = 15. Add 15 to the number set. Current number set: [15, 69], target: 44, just two numbers left.\n     |- Try 69 + 15 = 84. Evaluate 84 != 44, drop this branch.\n     |- Try 69 - 15 = 54. Evaluate 54 != 44, drop this branch.\n     |- Try 69 * 15 = 1035. Evaluate 1035 != 44, drop this branch.\n     |- Try 69 \/ 15 = 4.6. 4.6 is a decimal, drop this branch.\n  |- Try 49 - 20 = 29. Add 29 to the number set. Current number set: [29, 2, 30], target: 44. Options for choosing two numbers: [(29, 2), (29, 30), (2, 30)].\n   |- Pick two numbers (29, 2) (numbers left: [30]). Try possible operations.\n    |- Try 29 + 2 = 31. Add 31 to the number set. Current number set: [31, 30], target: 44, just two numbers left.\n     |- Try 31 + 30 = 61. Evaluate 61 != 44, drop this branch.\n     |- Try 31 - 30 = 1. Evaluate 1 != 44, drop this branch.\n     |- Try 31 * 30 = 930. Evaluate 930 != 44, drop this branch.\n     |- Try 31 \/ 30 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 29 - 2 = 27. Add 27 to the number set. Current number set: [27, 30], target: 44, just two numbers left.\n     |- Try 30 + 27 = 57. Evaluate 57 != 44, drop this branch.\n     |- Try 30 - 27 = 3. Evaluate 3 != 44, drop this branch.\n     |- Try 30 * 27 = 810. Evaluate 810 != 44, drop this branch.\n     |- Try 30 \/ 27 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 29 * 2 = 58. Add 58 to the number set. Current number set: [58, 30], target: 44, just two numbers left.\n     |- Try 58 + 30 = 88. Evaluate 88 != 44, drop this branch.\n     |- Try 58 - 30 = 28. Evaluate 28 != 44, drop this branch.\n     |- Try 58 * 30 = 1740. Evaluate 1740 != 44, drop this branch.\n     |- Try 58 \/ 30 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 29 \/ 2 = 14.5. 14.5 is a decimal, drop this branch.\n   |- Pick two numbers (29, 30) (numbers left: [2]). Try possible operations.\n    |- Try 30 + 29 = 59. Add 59 to the number set. Current number set: [59, 2], target: 44, just two numbers left.\n     |- Try 59 + 2 = 61. Evaluate 61 != 44, drop this branch.\n     |- Try 59 - 2 = 57. Evaluate 57 != 44, drop this branch.\n     |- Try 59 * 2 = 118. Evaluate 118 != 44, drop this branch.\n     |- Try 59 \/ 2 = 29.5. 29.5 is a decimal, drop this branch.\n    |- Try 30 - 29 = 1. Add 1 to the number set. Current number set: [1, 2], target: 44, just two numbers left.\n     |- Try 2 + 1 = 3. Evaluate 3 != 44, drop this branch.\n     |- Try 2 - 1 = 1. Evaluate 1 != 44, drop this branch.\n     |- Try 2 * 1 = 2. Evaluate 2 != 44, drop this branch.\n     |- Try 2 \/ 1 = 2. Evaluate 2 != 44, drop this branch.\n    |- Try 30 * 29 = 870. Add 870 to the number set. Current number set: [870, 2], target: 44, just two numbers left.\n     |- Try 870 + 2 = 872. Evaluate 872 != 44, drop this branch.\n     |- Try 870 - 2 = 868. Evaluate 868 != 44, drop this branch.\n     |- Try 870 * 2 = 1740. Evaluate 1740 != 44, drop this branch.\n     |- Try 870 \/ 2 = 435. Evaluate 435 != 44, drop this branch.\n    |- Try 30 \/ 29 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (2, 30) (numbers left: [29]). Try possible operations.\n    |- Try 30 + 2 = 32. Add 32 to the number set. Current number set: [32, 29], target: 44, just two numbers left.\n     |- Try 32 + 29 = 61. Evaluate 61 != 44, drop this branch.\n     |- Try 32 - 29 = 3. Evaluate 3 != 44, drop this branch.\n     |- Try 32 * 29 = 928. Evaluate 928 != 44, drop this branch.\n     |- Try 32 \/ 29 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 30 - 2 = 28. Add 28 to the number set. Current number set: [28, 29], target: 44, just two numbers left.\n     |- Try 29 + 28 = 57. Evaluate 57 != 44, drop this branch.\n     |- Try 29 - 28 = 1. Evaluate 1 != 44, drop this branch.\n     |- Try 29 * 28 = 812. Evaluate 812 != 44, drop this branch.\n     |- Try 29 \/ 28 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 30 * 2 = 60. Add 60 to the number set. Current number set: [60, 29], target: 44, just two numbers left.\n     |- Try 60 + 29 = 89. Evaluate 89 != 44, drop this branch.\n     |- Try 60 - 29 = 31. Evaluate 31 != 44, drop this branch.\n     |- Try 60 * 29 = 1740. Evaluate 1740 != 44, drop this branch.\n     |- Try 60 \/ 29 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 30 \/ 2 = 15. Add 15 to the number set. Current number set: [15, 29], target: 44, just two numbers left.\n     |- Try 29 + 15 = 44. Evaluate 44 == 44, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 29 + 15 = 44\nThe step before: 30 \/ 2 = 15\nThe first step: 49 - 20 = 29\n\nOutput the solution in the required format:\n<Solution>\n49 - 20 = 29\n30 \/ 2 = 15\n29 + 15 = 44\n<\/Solution>\n","item":{"nums":[49,2,20,30],"solution":["49 - 20 = 29","30 \/ 2 = 15","29 + 15 = 44"],"target":44}}
+{"instance_id":"countdown_8k_30","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [18, 13, 47, 49]\nTarget: 44","reference_output":"# Search Procedure\nInitial number set: [18, 13, 47, 49], target: 44. Options for choosing two numbers: [(18, 13), (18, 47), (18, 49), (13, 47), (13, 49), (47, 49)].\n |- Pick two numbers (18, 13) (numbers left: [47, 49]). Try possible operations.\n  |- Try 18 + 13 = 31. Add 31 to the number set. Current number set: [31, 47, 49], target: 44. Options for choosing two numbers: [(31, 47), (31, 49), (47, 49)].\n   |- Pick two numbers (31, 47) (numbers left: [49]). Try possible operations.\n    |- Try 47 + 31 = 78. Add 78 to the number set. Current number set: [78, 49], target: 44, just two numbers left.\n     |- Try 78 + 49 = 127. Evaluate 127 != 44, drop this branch.\n     |- Try 78 - 49 = 29. Evaluate 29 != 44, drop this branch.\n     |- Try 78 * 49 = 3822. 3822 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 49 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 47 - 31 = 16. Add 16 to the number set. Current number set: [16, 49], target: 44, just two numbers left.\n     |- Try 49 + 16 = 65. Evaluate 65 != 44, drop this branch.\n     |- Try 49 - 16 = 33. Evaluate 33 != 44, drop this branch.\n     |- Try 49 * 16 = 784. Evaluate 784 != 44, drop this branch.\n     |- Try 49 \/ 16 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 47 * 31 = 1457. Add 1457 to the number set. Current number set: [1457, 49], target: 44, just two numbers left.\n     |- Try 1457 + 49 = 1506. Evaluate 1506 != 44, drop this branch.\n     |- Try 1457 - 49 = 1408. Evaluate 1408 != 44, drop this branch.\n     |- Try 1457 * 49 = 71393. 71393 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1457 \/ 49 = 29.7. 29.7 is a decimal, drop this branch.\n    |- Try 47 \/ 31 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (31, 49) (numbers left: [47]). Try possible operations.\n    |- Try 49 + 31 = 80. Add 80 to the number set. Current number set: [80, 47], target: 44, just two numbers left.\n     |- Try 80 + 47 = 127. Evaluate 127 != 44, drop this branch.\n     |- Try 80 - 47 = 33. Evaluate 33 != 44, drop this branch.\n     |- Try 80 * 47 = 3760. 3760 exceeds the maximum intermediate result, drop this branch.\n     |- Try 80 \/ 47 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 49 - 31 = 18. Add 18 to the number set. Current number set: [18, 47], target: 44, just two numbers left.\n     |- Try 47 + 18 = 65. Evaluate 65 != 44, drop this branch.\n     |- Try 47 - 18 = 29. Evaluate 29 != 44, drop this branch.\n     |- Try 47 * 18 = 846. Evaluate 846 != 44, drop this branch.\n     |- Try 47 \/ 18 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 49 * 31 = 1519. Add 1519 to the number set. Current number set: [1519, 47], target: 44, just two numbers left.\n     |- Try 1519 + 47 = 1566. Evaluate 1566 != 44, drop this branch.\n     |- Try 1519 - 47 = 1472. Evaluate 1472 != 44, drop this branch.\n     |- Try 1519 * 47 = 71393. 71393 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1519 \/ 47 = 32.3. 32.3 is a decimal, drop this branch.\n    |- Try 49 \/ 31 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (47, 49) (numbers left: [31]). Try possible operations.\n    |- Try 49 + 47 = 96. Add 96 to the number set. Current number set: [96, 31], target: 44, just two numbers left.\n     |- Try 96 + 31 = 127. Evaluate 127 != 44, drop this branch.\n     |- Try 96 - 31 = 65. Evaluate 65 != 44, drop this branch.\n     |- Try 96 * 31 = 2976. 2976 exceeds the maximum intermediate result, drop this branch.\n     |- Try 96 \/ 31 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 49 - 47 = 2. Add 2 to the number set. Current number set: [2, 31], target: 44, just two numbers left.\n     |- Try 31 + 2 = 33. Evaluate 33 != 44, drop this branch.\n     |- Try 31 - 2 = 29. Evaluate 29 != 44, drop this branch.\n     |- Try 31 * 2 = 62. Evaluate 62 != 44, drop this branch.\n     |- Try 31 \/ 2 = 15.5. 15.5 is a decimal, drop this branch.\n    |- Try 49 * 47 = 2303. 2303 exceeds the maximum intermediate result, drop this branch.\n    |- Try 49 \/ 47 = 1.0. 1.0 is a decimal, drop this branch.\n  |- Try 18 - 13 = 5. Add 5 to the number set. Current number set: [5, 47, 49], target: 44. Options for choosing two numbers: [(5, 47), (5, 49), (47, 49)].\n   |- Pick two numbers (5, 47) (numbers left: [49]). Try possible operations.\n    |- Try 47 + 5 = 52. Add 52 to the number set. Current number set: [52, 49], target: 44, just two numbers left.\n     |- Try 52 + 49 = 101. Evaluate 101 != 44, drop this branch.\n     |- Try 52 - 49 = 3. Evaluate 3 != 44, drop this branch.\n     |- Try 52 * 49 = 2548. 2548 exceeds the maximum intermediate result, drop this branch.\n     |- Try 52 \/ 49 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 47 - 5 = 42. Add 42 to the number set. Current number set: [42, 49], target: 44, just two numbers left.\n     |- Try 49 + 42 = 91. Evaluate 91 != 44, drop this branch.\n     |- Try 49 - 42 = 7. Evaluate 7 != 44, drop this branch.\n     |- Try 49 * 42 = 2058. 2058 exceeds the maximum intermediate result, drop this branch.\n     |- Try 49 \/ 42 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 47 * 5 = 235. Add 235 to the number set. Current number set: [235, 49], target: 44, just two numbers left.\n     |- Try 235 + 49 = 284. Evaluate 284 != 44, drop this branch.\n     |- Try 235 - 49 = 186. Evaluate 186 != 44, drop this branch.\n     |- Try 235 * 49 = 11515. 11515 exceeds the maximum intermediate result, drop this branch.\n     |- Try 235 \/ 49 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 47 \/ 5 = 9.4. 9.4 is a decimal, drop this branch.\n   |- Pick two numbers (5, 49) (numbers left: [47]). Try possible operations.\n    |- Try 49 + 5 = 54. Add 54 to the number set. Current number set: [54, 47], target: 44, just two numbers left.\n     |- Try 54 + 47 = 101. Evaluate 101 != 44, drop this branch.\n     |- Try 54 - 47 = 7. Evaluate 7 != 44, drop this branch.\n     |- Try 54 * 47 = 2538. 2538 exceeds the maximum intermediate result, drop this branch.\n     |- Try 54 \/ 47 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 49 - 5 = 44. Add 44 to the number set. Current number set: [44, 47], target: 44, just two numbers left.\n     |- Try 47 + 44 = 91. Evaluate 91 != 44, drop this branch.\n     |- Try 47 - 44 = 3. Evaluate 3 != 44, drop this branch.\n     |- Try 47 * 44 = 2068. 2068 exceeds the maximum intermediate result, drop this branch.\n     |- Try 47 \/ 44 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 49 * 5 = 245. Add 245 to the number set. Current number set: [245, 47], target: 44, just two numbers left.\n     |- Try 245 + 47 = 292. Evaluate 292 != 44, drop this branch.\n     |- Try 245 - 47 = 198. Evaluate 198 != 44, drop this branch.\n     |- Try 245 * 47 = 11515. 11515 exceeds the maximum intermediate result, drop this branch.\n     |- Try 245 \/ 47 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 49 \/ 5 = 9.8. 9.8 is a decimal, drop this branch.\n   |- Pick two numbers (47, 49) (numbers left: [5]). Try possible operations.\n    |- Try 49 + 47 = 96. Add 96 to the number set. Current number set: [96, 5], target: 44, just two numbers left.\n     |- Try 96 + 5 = 101. Evaluate 101 != 44, drop this branch.\n     |- Try 96 - 5 = 91. Evaluate 91 != 44, drop this branch.\n     |- Try 96 * 5 = 480. Evaluate 480 != 44, drop this branch.\n     |- Try 96 \/ 5 = 19.2. 19.2 is a decimal, drop this branch.\n    |- Try 49 - 47 = 2. Add 2 to the number set. Current number set: [2, 5], target: 44, just two numbers left.\n     |- Try 5 + 2 = 7. Evaluate 7 != 44, drop this branch.\n     |- Try 5 - 2 = 3. Evaluate 3 != 44, drop this branch.\n     |- Try 5 * 2 = 10. Evaluate 10 != 44, drop this branch.\n     |- Try 5 \/ 2 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 49 * 47 = 2303. 2303 exceeds the maximum intermediate result, drop this branch.\n    |- Try 49 \/ 47 = 1.0. 1.0 is a decimal, drop this branch.\n  |- Try 18 * 13 = 234. Add 234 to the number set. Current number set: [234, 47, 49], target: 44. Options for choosing two numbers: [(234, 47), (234, 49), (47, 49)].\n   |- Pick two numbers (234, 47) (numbers left: [49]). Try possible operations.\n    |- Try 234 + 47 = 281. Add 281 to the number set. Current number set: [281, 49], target: 44, just two numbers left.\n     |- Try 281 + 49 = 330. Evaluate 330 != 44, drop this branch.\n     |- Try 281 - 49 = 232. Evaluate 232 != 44, drop this branch.\n     |- Try 281 * 49 = 13769. 13769 exceeds the maximum intermediate result, drop this branch.\n     |- Try 281 \/ 49 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 234 - 47 = 187. Add 187 to the number set. Current number set: [187, 49], target: 44, just two numbers left.\n     |- Try 187 + 49 = 236. Evaluate 236 != 44, drop this branch.\n     |- Try 187 - 49 = 138. Evaluate 138 != 44, drop this branch.\n     |- Try 187 * 49 = 9163. 9163 exceeds the maximum intermediate result, drop this branch.\n     |- Try 187 \/ 49 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 234 * 47 = 10998. 10998 exceeds the maximum intermediate result, drop this branch.\n    |- Try 234 \/ 47 = 5.0. 5.0 is a decimal, drop this branch.\n   |- Pick two numbers (234, 49) (numbers left: [47]). Try possible operations.\n    |- Try 234 + 49 = 283. Add 283 to the number set. Current number set: [283, 47], target: 44, just two numbers left.\n     |- Try 283 + 47 = 330. Evaluate 330 != 44, drop this branch.\n     |- Try 283 - 47 = 236. Evaluate 236 != 44, drop this branch.\n     |- Try 283 * 47 = 13301. 13301 exceeds the maximum intermediate result, drop this branch.\n     |- Try 283 \/ 47 = 6.0. 6.0 is a decimal, drop this branch.\n    |- Try 234 - 49 = 185. Add 185 to the number set. Current number set: [185, 47], target: 44, just two numbers left.\n     |- Try 185 + 47 = 232. Evaluate 232 != 44, drop this branch.\n     |- Try 185 - 47 = 138. Evaluate 138 != 44, drop this branch.\n     |- Try 185 * 47 = 8695. 8695 exceeds the maximum intermediate result, drop this branch.\n     |- Try 185 \/ 47 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 234 * 49 = 11466. 11466 exceeds the maximum intermediate result, drop this branch.\n    |- Try 234 \/ 49 = 4.8. 4.8 is a decimal, drop this branch.\n   |- Pick two numbers (47, 49) (numbers left: [234]). Try possible operations.\n    |- Try 49 + 47 = 96. Add 96 to the number set. Current number set: [96, 234], target: 44, just two numbers left.\n     |- Try 234 + 96 = 330. Evaluate 330 != 44, drop this branch.\n     |- Try 234 - 96 = 138. Evaluate 138 != 44, drop this branch.\n     |- Try 234 * 96 = 22464. 22464 exceeds the maximum intermediate result, drop this branch.\n     |- Try 234 \/ 96 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 49 - 47 = 2. Add 2 to the number set. Current number set: [2, 234], target: 44, just two numbers left.\n     |- Try 234 + 2 = 236. Evaluate 236 != 44, drop this branch.\n     |- Try 234 - 2 = 232. Evaluate 232 != 44, drop this branch.\n     |- Try 234 * 2 = 468. Evaluate 468 != 44, drop this branch.\n     |- Try 234 \/ 2 = 117. Evaluate 117 != 44, drop this branch.\n    |- Try 49 * 47 = 2303. 2303 exceeds the maximum intermediate result, drop this branch.\n    |- Try 49 \/ 47 = 1.0. 1.0 is a decimal, drop this branch.\n  |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n |- Pick two numbers (18, 47) (numbers left: [13, 49]). Try possible operations.\n  |- Try 47 + 18 = 65. Add 65 to the number set. Current number set: [65, 13, 49], target: 44. Options for choosing two numbers: [(65, 13), (65, 49), (13, 49)].\n   |- Pick two numbers (65, 13) (numbers left: [49]). Try possible operations.\n    |- Try 65 + 13 = 78. Add 78 to the number set. Current number set: [78, 49], target: 44, just two numbers left.\n     |- Try 78 + 49 = 127. Evaluate 127 != 44, drop this branch.\n     |- Try 78 - 49 = 29. Evaluate 29 != 44, drop this branch.\n     |- Try 78 * 49 = 3822. 3822 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 49 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 65 - 13 = 52. Add 52 to the number set. Current number set: [52, 49], target: 44, just two numbers left.\n     |- Try 52 + 49 = 101. Evaluate 101 != 44, drop this branch.\n     |- Try 52 - 49 = 3. Evaluate 3 != 44, drop this branch.\n     |- Try 52 * 49 = 2548. 2548 exceeds the maximum intermediate result, drop this branch.\n     |- Try 52 \/ 49 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 65 * 13 = 845. Add 845 to the number set. Current number set: [845, 49], target: 44, just two numbers left.\n     |- Try 845 + 49 = 894. Evaluate 894 != 44, drop this branch.\n     |- Try 845 - 49 = 796. Evaluate 796 != 44, drop this branch.\n     |- Try 845 * 49 = 41405. 41405 exceeds the maximum intermediate result, drop this branch.\n     |- Try 845 \/ 49 = 17.2. 17.2 is a decimal, drop this branch.\n    |- Try 65 \/ 13 = 5. Add 5 to the number set. Current number set: [5, 49], target: 44, just two numbers left.\n     |- Try 49 + 5 = 54. Evaluate 54 != 44, drop this branch.\n     |- Try 49 - 5 = 44. Evaluate 44 == 44, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 49 - 5 = 44\nThe step before: 65 \/ 13 = 5\nThe first step: 47 + 18 = 65\n\nOutput the solution in the required format:\n<Solution>\n47 + 18 = 65\n65 \/ 13 = 5\n49 - 5 = 44\n<\/Solution>\n","item":{"nums":[18,13,47,49],"solution":["47 + 18 = 65","65 \/ 13 = 5","49 - 5 = 44"],"target":44}}
+{"instance_id":"countdown_8k_31","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [2, 16, 14, 5]\nTarget: 17","reference_output":"# Search Procedure\nInitial number set: [2, 16, 14, 5], target: 17. Options for choosing two numbers: [(2, 16), (2, 14), (2, 5), (16, 14), (16, 5), (14, 5)].\n |- Pick two numbers (2, 16) (numbers left: [14, 5]). Try possible operations.\n  |- Try 16 + 2 = 18. Add 18 to the number set. Current number set: [18, 14, 5], target: 17. Options for choosing two numbers: [(18, 14), (18, 5), (14, 5)].\n   |- Pick two numbers (18, 14) (numbers left: [5]). Try possible operations.\n    |- Try 18 + 14 = 32. Add 32 to the number set. Current number set: [32, 5], target: 17, just two numbers left.\n     |- Try 32 + 5 = 37. Evaluate 37 != 17, drop this branch.\n     |- Try 32 - 5 = 27. Evaluate 27 != 17, drop this branch.\n     |- Try 32 * 5 = 160. Evaluate 160 != 17, drop this branch.\n     |- Try 32 \/ 5 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 18 - 14 = 4. Add 4 to the number set. Current number set: [4, 5], target: 17, just two numbers left.\n     |- Try 5 + 4 = 9. Evaluate 9 != 17, drop this branch.\n     |- Try 5 - 4 = 1. Evaluate 1 != 17, drop this branch.\n     |- Try 5 * 4 = 20. Evaluate 20 != 17, drop this branch.\n     |- Try 5 \/ 4 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 18 * 14 = 252. Add 252 to the number set. Current number set: [252, 5], target: 17, just two numbers left.\n     |- Try 252 + 5 = 257. Evaluate 257 != 17, drop this branch.\n     |- Try 252 - 5 = 247. Evaluate 247 != 17, drop this branch.\n     |- Try 252 * 5 = 1260. Evaluate 1260 != 17, drop this branch.\n     |- Try 252 \/ 5 = 50.4. 50.4 is a decimal, drop this branch.\n    |- Try 18 \/ 14 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (18, 5) (numbers left: [14]). Try possible operations.\n    |- Try 18 + 5 = 23. Add 23 to the number set. Current number set: [23, 14], target: 17, just two numbers left.\n     |- Try 23 + 14 = 37. Evaluate 37 != 17, drop this branch.\n     |- Try 23 - 14 = 9. Evaluate 9 != 17, drop this branch.\n     |- Try 23 * 14 = 322. Evaluate 322 != 17, drop this branch.\n     |- Try 23 \/ 14 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 18 - 5 = 13. Add 13 to the number set. Current number set: [13, 14], target: 17, just two numbers left.\n     |- Try 14 + 13 = 27. Evaluate 27 != 17, drop this branch.\n     |- Try 14 - 13 = 1. Evaluate 1 != 17, drop this branch.\n     |- Try 14 * 13 = 182. Evaluate 182 != 17, drop this branch.\n     |- Try 14 \/ 13 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 18 * 5 = 90. Add 90 to the number set. Current number set: [90, 14], target: 17, just two numbers left.\n     |- Try 90 + 14 = 104. Evaluate 104 != 17, drop this branch.\n     |- Try 90 - 14 = 76. Evaluate 76 != 17, drop this branch.\n     |- Try 90 * 14 = 1260. Evaluate 1260 != 17, drop this branch.\n     |- Try 90 \/ 14 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 18 \/ 5 = 3.6. 3.6 is a decimal, drop this branch.\n   |- Pick two numbers (14, 5) (numbers left: [18]). Try possible operations.\n    |- Try 14 + 5 = 19. Add 19 to the number set. Current number set: [19, 18], target: 17, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 17, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 17, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 17, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 14 - 5 = 9. Add 9 to the number set. Current number set: [9, 18], target: 17, just two numbers left.\n     |- Try 18 + 9 = 27. Evaluate 27 != 17, drop this branch.\n     |- Try 18 - 9 = 9. Evaluate 9 != 17, drop this branch.\n     |- Try 18 * 9 = 162. Evaluate 162 != 17, drop this branch.\n     |- Try 18 \/ 9 = 2. Evaluate 2 != 17, drop this branch.\n    |- Try 14 * 5 = 70. Add 70 to the number set. Current number set: [70, 18], target: 17, just two numbers left.\n     |- Try 70 + 18 = 88. Evaluate 88 != 17, drop this branch.\n     |- Try 70 - 18 = 52. Evaluate 52 != 17, drop this branch.\n     |- Try 70 * 18 = 1260. Evaluate 1260 != 17, drop this branch.\n     |- Try 70 \/ 18 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 14 \/ 5 = 2.8. 2.8 is a decimal, drop this branch.\n  |- Try 16 - 2 = 14. Add 14 to the number set. Current number set: [14, 14, 5], target: 17. Options for choosing two numbers: [(14, 14), (14, 5), (14, 5)].\n   |- Pick two numbers (14, 14) (numbers left: [5]). Try possible operations.\n    |- Try 14 + 14 = 28. Add 28 to the number set. Current number set: [28, 5], target: 17, just two numbers left.\n     |- Try 28 + 5 = 33. Evaluate 33 != 17, drop this branch.\n     |- Try 28 - 5 = 23. Evaluate 23 != 17, drop this branch.\n     |- Try 28 * 5 = 140. Evaluate 140 != 17, drop this branch.\n     |- Try 28 \/ 5 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 14 - 14 = 0. Add 0 to the number set. Current number set: [0, 5], target: 17, just two numbers left.\n     |- Try 5 + 0 = 5. Evaluate 5 != 17, drop this branch.\n     |- Try 5 - 0 = 5. Evaluate 5 != 17, drop this branch.\n     |- Try 5 * 0 = 0. Evaluate 0 != 17, drop this branch.\n     |- Try 5 \/ 0 (invalid operation). drop this branch.\n    |- Try 14 * 14 = 196. Add 196 to the number set. Current number set: [196, 5], target: 17, just two numbers left.\n     |- Try 196 + 5 = 201. Evaluate 201 != 17, drop this branch.\n     |- Try 196 - 5 = 191. Evaluate 191 != 17, drop this branch.\n     |- Try 196 * 5 = 980. Evaluate 980 != 17, drop this branch.\n     |- Try 196 \/ 5 = 39.2. 39.2 is a decimal, drop this branch.\n    |- Try 14 \/ 14 = 1. Add 1 to the number set. Current number set: [1, 5], target: 17, just two numbers left.\n     |- Try 5 + 1 = 6. Evaluate 6 != 17, drop this branch.\n     |- Try 5 - 1 = 4. Evaluate 4 != 17, drop this branch.\n     |- Try 5 * 1 = 5. Evaluate 5 != 17, drop this branch.\n     |- Try 5 \/ 1 = 5. Evaluate 5 != 17, drop this branch.\n   |- Pick two numbers (14, 5) (numbers left: [14]). Try possible operations.\n    |- Try 14 + 5 = 19. Add 19 to the number set. Current number set: [19, 14], target: 17, just two numbers left.\n     |- Try 19 + 14 = 33. Evaluate 33 != 17, drop this branch.\n     |- Try 19 - 14 = 5. Evaluate 5 != 17, drop this branch.\n     |- Try 19 * 14 = 266. Evaluate 266 != 17, drop this branch.\n     |- Try 19 \/ 14 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 14 - 5 = 9. Add 9 to the number set. Current number set: [9, 14], target: 17, just two numbers left.\n     |- Try 14 + 9 = 23. Evaluate 23 != 17, drop this branch.\n     |- Try 14 - 9 = 5. Evaluate 5 != 17, drop this branch.\n     |- Try 14 * 9 = 126. Evaluate 126 != 17, drop this branch.\n     |- Try 14 \/ 9 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 14 * 5 = 70. Add 70 to the number set. Current number set: [70, 14], target: 17, just two numbers left.\n     |- Try 70 + 14 = 84. Evaluate 84 != 17, drop this branch.\n     |- Try 70 - 14 = 56. Evaluate 56 != 17, drop this branch.\n     |- Try 70 * 14 = 980. Evaluate 980 != 17, drop this branch.\n     |- Try 70 \/ 14 = 5. Evaluate 5 != 17, drop this branch.\n    |- Try 14 \/ 5 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (14, 5) (numbers left: [14]). Try possible operations.\n    |- Try 14 + 5 = 19. Add 19 to the number set. Current number set: [19, 14], target: 17, just two numbers left.\n     |- Try 19 + 14 = 33. Evaluate 33 != 17, drop this branch.\n     |- Try 19 - 14 = 5. Evaluate 5 != 17, drop this branch.\n     |- Try 19 * 14 = 266. Evaluate 266 != 17, drop this branch.\n     |- Try 19 \/ 14 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 14 - 5 = 9. Add 9 to the number set. Current number set: [9, 14], target: 17, just two numbers left.\n     |- Try 14 + 9 = 23. Evaluate 23 != 17, drop this branch.\n     |- Try 14 - 9 = 5. Evaluate 5 != 17, drop this branch.\n     |- Try 14 * 9 = 126. Evaluate 126 != 17, drop this branch.\n     |- Try 14 \/ 9 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 14 * 5 = 70. Add 70 to the number set. Current number set: [70, 14], target: 17, just two numbers left.\n     |- Try 70 + 14 = 84. Evaluate 84 != 17, drop this branch.\n     |- Try 70 - 14 = 56. Evaluate 56 != 17, drop this branch.\n     |- Try 70 * 14 = 980. Evaluate 980 != 17, drop this branch.\n     |- Try 70 \/ 14 = 5. Evaluate 5 != 17, drop this branch.\n    |- Try 14 \/ 5 = 2.8. 2.8 is a decimal, drop this branch.\n  |- Try 16 * 2 = 32. Add 32 to the number set. Current number set: [32, 14, 5], target: 17. Options for choosing two numbers: [(32, 14), (32, 5), (14, 5)].\n   |- Pick two numbers (32, 14) (numbers left: [5]). Try possible operations.\n    |- Try 32 + 14 = 46. Add 46 to the number set. Current number set: [46, 5], target: 17, just two numbers left.\n     |- Try 46 + 5 = 51. Evaluate 51 != 17, drop this branch.\n     |- Try 46 - 5 = 41. Evaluate 41 != 17, drop this branch.\n     |- Try 46 * 5 = 230. Evaluate 230 != 17, drop this branch.\n     |- Try 46 \/ 5 = 9.2. 9.2 is a decimal, drop this branch.\n    |- Try 32 - 14 = 18. Add 18 to the number set. Current number set: [18, 5], target: 17, just two numbers left.\n     |- Try 18 + 5 = 23. Evaluate 23 != 17, drop this branch.\n     |- Try 18 - 5 = 13. Evaluate 13 != 17, drop this branch.\n     |- Try 18 * 5 = 90. Evaluate 90 != 17, drop this branch.\n     |- Try 18 \/ 5 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 32 * 14 = 448. Add 448 to the number set. Current number set: [448, 5], target: 17, just two numbers left.\n     |- Try 448 + 5 = 453. Evaluate 453 != 17, drop this branch.\n     |- Try 448 - 5 = 443. Evaluate 443 != 17, drop this branch.\n     |- Try 448 * 5 = 2240. 2240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 448 \/ 5 = 89.6. 89.6 is a decimal, drop this branch.\n    |- Try 32 \/ 14 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (32, 5) (numbers left: [14]). Try possible operations.\n    |- Try 32 + 5 = 37. Add 37 to the number set. Current number set: [37, 14], target: 17, just two numbers left.\n     |- Try 37 + 14 = 51. Evaluate 51 != 17, drop this branch.\n     |- Try 37 - 14 = 23. Evaluate 23 != 17, drop this branch.\n     |- Try 37 * 14 = 518. Evaluate 518 != 17, drop this branch.\n     |- Try 37 \/ 14 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 32 - 5 = 27. Add 27 to the number set. Current number set: [27, 14], target: 17, just two numbers left.\n     |- Try 27 + 14 = 41. Evaluate 41 != 17, drop this branch.\n     |- Try 27 - 14 = 13. Evaluate 13 != 17, drop this branch.\n     |- Try 27 * 14 = 378. Evaluate 378 != 17, drop this branch.\n     |- Try 27 \/ 14 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 32 * 5 = 160. Add 160 to the number set. Current number set: [160, 14], target: 17, just two numbers left.\n     |- Try 160 + 14 = 174. Evaluate 174 != 17, drop this branch.\n     |- Try 160 - 14 = 146. Evaluate 146 != 17, drop this branch.\n     |- Try 160 * 14 = 2240. 2240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 160 \/ 14 = 11.4. 11.4 is a decimal, drop this branch.\n    |- Try 32 \/ 5 = 6.4. 6.4 is a decimal, drop this branch.\n   |- Pick two numbers (14, 5) (numbers left: [32]). Try possible operations.\n    |- Try 14 + 5 = 19. Add 19 to the number set. Current number set: [19, 32], target: 17, just two numbers left.\n     |- Try 32 + 19 = 51. Evaluate 51 != 17, drop this branch.\n     |- Try 32 - 19 = 13. Evaluate 13 != 17, drop this branch.\n     |- Try 32 * 19 = 608. Evaluate 608 != 17, drop this branch.\n     |- Try 32 \/ 19 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 14 - 5 = 9. Add 9 to the number set. Current number set: [9, 32], target: 17, just two numbers left.\n     |- Try 32 + 9 = 41. Evaluate 41 != 17, drop this branch.\n     |- Try 32 - 9 = 23. Evaluate 23 != 17, drop this branch.\n     |- Try 32 * 9 = 288. Evaluate 288 != 17, drop this branch.\n     |- Try 32 \/ 9 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 14 * 5 = 70. Add 70 to the number set. Current number set: [70, 32], target: 17, just two numbers left.\n     |- Try 70 + 32 = 102. Evaluate 102 != 17, drop this branch.\n     |- Try 70 - 32 = 38. Evaluate 38 != 17, drop this branch.\n     |- Try 70 * 32 = 2240. 2240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 70 \/ 32 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 14 \/ 5 = 2.8. 2.8 is a decimal, drop this branch.\n  |- Try 16 \/ 2 = 8. Add 8 to the number set. Current number set: [8, 14, 5], target: 17. Options for choosing two numbers: [(8, 14), (8, 5), (14, 5)].\n   |- Pick two numbers (8, 14) (numbers left: [5]). Try possible operations.\n    |- Try 14 + 8 = 22. Add 22 to the number set. Current number set: [22, 5], target: 17, just two numbers left.\n     |- Try 22 + 5 = 27. Evaluate 27 != 17, drop this branch.\n     |- Try 22 - 5 = 17. Evaluate 17 == 17, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 22 - 5 = 17\nThe step before: 14 + 8 = 22\nThe first step: 16 \/ 2 = 8\n\nOutput the solution in the required format:\n<Solution>\n16 \/ 2 = 8\n14 + 8 = 22\n22 - 5 = 17\n<\/Solution>\n","item":{"nums":[2,16,14,5],"solution":["16 \/ 2 = 8","14 + 8 = 22","22 - 5 = 17"],"target":17}}
+{"instance_id":"countdown_8k_32","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [25, 16, 17, 14]\nTarget: 19","reference_output":"# Search Procedure\nInitial number set: [25, 16, 17, 14], target: 19. Options for choosing two numbers: [(25, 16), (25, 17), (25, 14), (16, 17), (16, 14), (17, 14)].\n |- Pick two numbers (25, 16) (numbers left: [17, 14]). Try possible operations.\n  |- Try 25 + 16 = 41. Add 41 to the number set. Current number set: [41, 17, 14], target: 19. Options for choosing two numbers: [(41, 17), (41, 14), (17, 14)].\n   |- Pick two numbers (41, 17) (numbers left: [14]). Try possible operations.\n    |- Try 41 + 17 = 58. Add 58 to the number set. Current number set: [58, 14], target: 19, just two numbers left.\n     |- Try 58 + 14 = 72. Evaluate 72 != 19, drop this branch.\n     |- Try 58 - 14 = 44. Evaluate 44 != 19, drop this branch.\n     |- Try 58 * 14 = 812. Evaluate 812 != 19, drop this branch.\n     |- Try 58 \/ 14 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 41 - 17 = 24. Add 24 to the number set. Current number set: [24, 14], target: 19, just two numbers left.\n     |- Try 24 + 14 = 38. Evaluate 38 != 19, drop this branch.\n     |- Try 24 - 14 = 10. Evaluate 10 != 19, drop this branch.\n     |- Try 24 * 14 = 336. Evaluate 336 != 19, drop this branch.\n     |- Try 24 \/ 14 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 41 * 17 = 697. Add 697 to the number set. Current number set: [697, 14], target: 19, just two numbers left.\n     |- Try 697 + 14 = 711. Evaluate 711 != 19, drop this branch.\n     |- Try 697 - 14 = 683. Evaluate 683 != 19, drop this branch.\n     |- Try 697 * 14 = 9758. 9758 exceeds the maximum intermediate result, drop this branch.\n     |- Try 697 \/ 14 = 49.8. 49.8 is a decimal, drop this branch.\n    |- Try 41 \/ 17 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (41, 14) (numbers left: [17]). Try possible operations.\n    |- Try 41 + 14 = 55. Add 55 to the number set. Current number set: [55, 17], target: 19, just two numbers left.\n     |- Try 55 + 17 = 72. Evaluate 72 != 19, drop this branch.\n     |- Try 55 - 17 = 38. Evaluate 38 != 19, drop this branch.\n     |- Try 55 * 17 = 935. Evaluate 935 != 19, drop this branch.\n     |- Try 55 \/ 17 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 41 - 14 = 27. Add 27 to the number set. Current number set: [27, 17], target: 19, just two numbers left.\n     |- Try 27 + 17 = 44. Evaluate 44 != 19, drop this branch.\n     |- Try 27 - 17 = 10. Evaluate 10 != 19, drop this branch.\n     |- Try 27 * 17 = 459. Evaluate 459 != 19, drop this branch.\n     |- Try 27 \/ 17 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 41 * 14 = 574. Add 574 to the number set. Current number set: [574, 17], target: 19, just two numbers left.\n     |- Try 574 + 17 = 591. Evaluate 591 != 19, drop this branch.\n     |- Try 574 - 17 = 557. Evaluate 557 != 19, drop this branch.\n     |- Try 574 * 17 = 9758. 9758 exceeds the maximum intermediate result, drop this branch.\n     |- Try 574 \/ 17 = 33.8. 33.8 is a decimal, drop this branch.\n    |- Try 41 \/ 14 = 2.9. 2.9 is a decimal, drop this branch.\n   |- Pick two numbers (17, 14) (numbers left: [41]). Try possible operations.\n    |- Try 17 + 14 = 31. Add 31 to the number set. Current number set: [31, 41], target: 19, just two numbers left.\n     |- Try 41 + 31 = 72. Evaluate 72 != 19, drop this branch.\n     |- Try 41 - 31 = 10. Evaluate 10 != 19, drop this branch.\n     |- Try 41 * 31 = 1271. Evaluate 1271 != 19, drop this branch.\n     |- Try 41 \/ 31 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 17 - 14 = 3. Add 3 to the number set. Current number set: [3, 41], target: 19, just two numbers left.\n     |- Try 41 + 3 = 44. Evaluate 44 != 19, drop this branch.\n     |- Try 41 - 3 = 38. Evaluate 38 != 19, drop this branch.\n     |- Try 41 * 3 = 123. Evaluate 123 != 19, drop this branch.\n     |- Try 41 \/ 3 = 13.7. 13.7 is a decimal, drop this branch.\n    |- Try 17 * 14 = 238. Add 238 to the number set. Current number set: [238, 41], target: 19, just two numbers left.\n     |- Try 238 + 41 = 279. Evaluate 279 != 19, drop this branch.\n     |- Try 238 - 41 = 197. Evaluate 197 != 19, drop this branch.\n     |- Try 238 * 41 = 9758. 9758 exceeds the maximum intermediate result, drop this branch.\n     |- Try 238 \/ 41 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 17 \/ 14 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 25 - 16 = 9. Add 9 to the number set. Current number set: [9, 17, 14], target: 19. Options for choosing two numbers: [(9, 17), (9, 14), (17, 14)].\n   |- Pick two numbers (9, 17) (numbers left: [14]). Try possible operations.\n    |- Try 17 + 9 = 26. Add 26 to the number set. Current number set: [26, 14], target: 19, just two numbers left.\n     |- Try 26 + 14 = 40. Evaluate 40 != 19, drop this branch.\n     |- Try 26 - 14 = 12. Evaluate 12 != 19, drop this branch.\n     |- Try 26 * 14 = 364. Evaluate 364 != 19, drop this branch.\n     |- Try 26 \/ 14 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 17 - 9 = 8. Add 8 to the number set. Current number set: [8, 14], target: 19, just two numbers left.\n     |- Try 14 + 8 = 22. Evaluate 22 != 19, drop this branch.\n     |- Try 14 - 8 = 6. Evaluate 6 != 19, drop this branch.\n     |- Try 14 * 8 = 112. Evaluate 112 != 19, drop this branch.\n     |- Try 14 \/ 8 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 17 * 9 = 153. Add 153 to the number set. Current number set: [153, 14], target: 19, just two numbers left.\n     |- Try 153 + 14 = 167. Evaluate 167 != 19, drop this branch.\n     |- Try 153 - 14 = 139. Evaluate 139 != 19, drop this branch.\n     |- Try 153 * 14 = 2142. 2142 exceeds the maximum intermediate result, drop this branch.\n     |- Try 153 \/ 14 = 10.9. 10.9 is a decimal, drop this branch.\n    |- Try 17 \/ 9 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (9, 14) (numbers left: [17]). Try possible operations.\n    |- Try 14 + 9 = 23. Add 23 to the number set. Current number set: [23, 17], target: 19, just two numbers left.\n     |- Try 23 + 17 = 40. Evaluate 40 != 19, drop this branch.\n     |- Try 23 - 17 = 6. Evaluate 6 != 19, drop this branch.\n     |- Try 23 * 17 = 391. Evaluate 391 != 19, drop this branch.\n     |- Try 23 \/ 17 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 14 - 9 = 5. Add 5 to the number set. Current number set: [5, 17], target: 19, just two numbers left.\n     |- Try 17 + 5 = 22. Evaluate 22 != 19, drop this branch.\n     |- Try 17 - 5 = 12. Evaluate 12 != 19, drop this branch.\n     |- Try 17 * 5 = 85. Evaluate 85 != 19, drop this branch.\n     |- Try 17 \/ 5 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 14 * 9 = 126. Add 126 to the number set. Current number set: [126, 17], target: 19, just two numbers left.\n     |- Try 126 + 17 = 143. Evaluate 143 != 19, drop this branch.\n     |- Try 126 - 17 = 109. Evaluate 109 != 19, drop this branch.\n     |- Try 126 * 17 = 2142. 2142 exceeds the maximum intermediate result, drop this branch.\n     |- Try 126 \/ 17 = 7.4. 7.4 is a decimal, drop this branch.\n    |- Try 14 \/ 9 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (17, 14) (numbers left: [9]). Try possible operations.\n    |- Try 17 + 14 = 31. Add 31 to the number set. Current number set: [31, 9], target: 19, just two numbers left.\n     |- Try 31 + 9 = 40. Evaluate 40 != 19, drop this branch.\n     |- Try 31 - 9 = 22. Evaluate 22 != 19, drop this branch.\n     |- Try 31 * 9 = 279. Evaluate 279 != 19, drop this branch.\n     |- Try 31 \/ 9 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 17 - 14 = 3. Add 3 to the number set. Current number set: [3, 9], target: 19, just two numbers left.\n     |- Try 9 + 3 = 12. Evaluate 12 != 19, drop this branch.\n     |- Try 9 - 3 = 6. Evaluate 6 != 19, drop this branch.\n     |- Try 9 * 3 = 27. Evaluate 27 != 19, drop this branch.\n     |- Try 9 \/ 3 = 3. Evaluate 3 != 19, drop this branch.\n    |- Try 17 * 14 = 238. Add 238 to the number set. Current number set: [238, 9], target: 19, just two numbers left.\n     |- Try 238 + 9 = 247. Evaluate 247 != 19, drop this branch.\n     |- Try 238 - 9 = 229. Evaluate 229 != 19, drop this branch.\n     |- Try 238 * 9 = 2142. 2142 exceeds the maximum intermediate result, drop this branch.\n     |- Try 238 \/ 9 = 26.4. 26.4 is a decimal, drop this branch.\n    |- Try 17 \/ 14 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 25 * 16 = 400. Add 400 to the number set. Current number set: [400, 17, 14], target: 19. Options for choosing two numbers: [(400, 17), (400, 14), (17, 14)].\n   |- Pick two numbers (400, 17) (numbers left: [14]). Try possible operations.\n    |- Try 400 + 17 = 417. Add 417 to the number set. Current number set: [417, 14], target: 19, just two numbers left.\n     |- Try 417 + 14 = 431. Evaluate 431 != 19, drop this branch.\n     |- Try 417 - 14 = 403. Evaluate 403 != 19, drop this branch.\n     |- Try 417 * 14 = 5838. 5838 exceeds the maximum intermediate result, drop this branch.\n     |- Try 417 \/ 14 = 29.8. 29.8 is a decimal, drop this branch.\n    |- Try 400 - 17 = 383. Add 383 to the number set. Current number set: [383, 14], target: 19, just two numbers left.\n     |- Try 383 + 14 = 397. Evaluate 397 != 19, drop this branch.\n     |- Try 383 - 14 = 369. Evaluate 369 != 19, drop this branch.\n     |- Try 383 * 14 = 5362. 5362 exceeds the maximum intermediate result, drop this branch.\n     |- Try 383 \/ 14 = 27.4. 27.4 is a decimal, drop this branch.\n    |- Try 400 * 17 = 6800. 6800 exceeds the maximum intermediate result, drop this branch.\n    |- Try 400 \/ 17 = 23.5. 23.5 is a decimal, drop this branch.\n   |- Pick two numbers (400, 14) (numbers left: [17]). Try possible operations.\n    |- Try 400 + 14 = 414. Add 414 to the number set. Current number set: [414, 17], target: 19, just two numbers left.\n     |- Try 414 + 17 = 431. Evaluate 431 != 19, drop this branch.\n     |- Try 414 - 17 = 397. Evaluate 397 != 19, drop this branch.\n     |- Try 414 * 17 = 7038. 7038 exceeds the maximum intermediate result, drop this branch.\n     |- Try 414 \/ 17 = 24.4. 24.4 is a decimal, drop this branch.\n    |- Try 400 - 14 = 386. Add 386 to the number set. Current number set: [386, 17], target: 19, just two numbers left.\n     |- Try 386 + 17 = 403. Evaluate 403 != 19, drop this branch.\n     |- Try 386 - 17 = 369. Evaluate 369 != 19, drop this branch.\n     |- Try 386 * 17 = 6562. 6562 exceeds the maximum intermediate result, drop this branch.\n     |- Try 386 \/ 17 = 22.7. 22.7 is a decimal, drop this branch.\n    |- Try 400 * 14 = 5600. 5600 exceeds the maximum intermediate result, drop this branch.\n    |- Try 400 \/ 14 = 28.6. 28.6 is a decimal, drop this branch.\n   |- Pick two numbers (17, 14) (numbers left: [400]). Try possible operations.\n    |- Try 17 + 14 = 31. Add 31 to the number set. Current number set: [31, 400], target: 19, just two numbers left.\n     |- Try 400 + 31 = 431. Evaluate 431 != 19, drop this branch.\n     |- Try 400 - 31 = 369. Evaluate 369 != 19, drop this branch.\n     |- Try 400 * 31 = 12400. 12400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 400 \/ 31 = 12.9. 12.9 is a decimal, drop this branch.\n    |- Try 17 - 14 = 3. Add 3 to the number set. Current number set: [3, 400], target: 19, just two numbers left.\n     |- Try 400 + 3 = 403. Evaluate 403 != 19, drop this branch.\n     |- Try 400 - 3 = 397. Evaluate 397 != 19, drop this branch.\n     |- Try 400 * 3 = 1200. Evaluate 1200 != 19, drop this branch.\n     |- Try 400 \/ 3 = 133.3. 133.3 is a decimal, drop this branch.\n    |- Try 17 * 14 = 238. Add 238 to the number set. Current number set: [238, 400], target: 19, just two numbers left.\n     |- Try 400 + 238 = 638. Evaluate 638 != 19, drop this branch.\n     |- Try 400 - 238 = 162. Evaluate 162 != 19, drop this branch.\n     |- Try 400 * 238 = 95200. 95200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 400 \/ 238 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 17 \/ 14 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 25 \/ 16 = 1.6. 1.6 is a decimal, drop this branch.\n |- Pick two numbers (25, 17) (numbers left: [16, 14]). Try possible operations.\n  |- Try 25 + 17 = 42. Add 42 to the number set. Current number set: [42, 16, 14], target: 19. Options for choosing two numbers: [(42, 16), (42, 14), (16, 14)].\n   |- Pick two numbers (42, 16) (numbers left: [14]). Try possible operations.\n    |- Try 42 + 16 = 58. Add 58 to the number set. Current number set: [58, 14], target: 19, just two numbers left.\n     |- Try 58 + 14 = 72. Evaluate 72 != 19, drop this branch.\n     |- Try 58 - 14 = 44. Evaluate 44 != 19, drop this branch.\n     |- Try 58 * 14 = 812. Evaluate 812 != 19, drop this branch.\n     |- Try 58 \/ 14 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 42 - 16 = 26. Add 26 to the number set. Current number set: [26, 14], target: 19, just two numbers left.\n     |- Try 26 + 14 = 40. Evaluate 40 != 19, drop this branch.\n     |- Try 26 - 14 = 12. Evaluate 12 != 19, drop this branch.\n     |- Try 26 * 14 = 364. Evaluate 364 != 19, drop this branch.\n     |- Try 26 \/ 14 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 42 * 16 = 672. Add 672 to the number set. Current number set: [672, 14], target: 19, just two numbers left.\n     |- Try 672 + 14 = 686. Evaluate 686 != 19, drop this branch.\n     |- Try 672 - 14 = 658. Evaluate 658 != 19, drop this branch.\n     |- Try 672 * 14 = 9408. 9408 exceeds the maximum intermediate result, drop this branch.\n     |- Try 672 \/ 14 = 48. Evaluate 48 != 19, drop this branch.\n    |- Try 42 \/ 16 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (42, 14) (numbers left: [16]). Try possible operations.\n    |- Try 42 + 14 = 56. Add 56 to the number set. Current number set: [56, 16], target: 19, just two numbers left.\n     |- Try 56 + 16 = 72. Evaluate 72 != 19, drop this branch.\n     |- Try 56 - 16 = 40. Evaluate 40 != 19, drop this branch.\n     |- Try 56 * 16 = 896. Evaluate 896 != 19, drop this branch.\n     |- Try 56 \/ 16 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 42 - 14 = 28. Add 28 to the number set. Current number set: [28, 16], target: 19, just two numbers left.\n     |- Try 28 + 16 = 44. Evaluate 44 != 19, drop this branch.\n     |- Try 28 - 16 = 12. Evaluate 12 != 19, drop this branch.\n     |- Try 28 * 16 = 448. Evaluate 448 != 19, drop this branch.\n     |- Try 28 \/ 16 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 42 * 14 = 588. Add 588 to the number set. Current number set: [588, 16], target: 19, just two numbers left.\n     |- Try 588 + 16 = 604. Evaluate 604 != 19, drop this branch.\n     |- Try 588 - 16 = 572. Evaluate 572 != 19, drop this branch.\n     |- Try 588 * 16 = 9408. 9408 exceeds the maximum intermediate result, drop this branch.\n     |- Try 588 \/ 16 = 36.8. 36.8 is a decimal, drop this branch.\n    |- Try 42 \/ 14 = 3. Add 3 to the number set. Current number set: [3, 16], target: 19, just two numbers left.\n     |- Try 16 + 3 = 19. Evaluate 19 == 19, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 16 + 3 = 19\nThe step before: 42 \/ 14 = 3\nThe first step: 25 + 17 = 42\n\nOutput the solution in the required format:\n<Solution>\n25 + 17 = 42\n42 \/ 14 = 3\n16 + 3 = 19\n<\/Solution>\n","item":{"nums":[25,16,17,14],"solution":["25 + 17 = 42","42 \/ 14 = 3","16 + 3 = 19"],"target":19}}
+{"instance_id":"countdown_8k_33","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [27, 1, 2, 34]\nTarget: 41","reference_output":"# Search Procedure\nInitial number set: [27, 1, 2, 34], target: 41. Options for choosing two numbers: [(27, 1), (27, 2), (27, 34), (1, 2), (1, 34), (2, 34)].\n |- Pick two numbers (27, 1) (numbers left: [2, 34]). Try possible operations.\n  |- Try 27 + 1 = 28. Add 28 to the number set. Current number set: [28, 2, 34], target: 41. Options for choosing two numbers: [(28, 2), (28, 34), (2, 34)].\n   |- Pick two numbers (28, 2) (numbers left: [34]). Try possible operations.\n    |- Try 28 + 2 = 30. Add 30 to the number set. Current number set: [30, 34], target: 41, just two numbers left.\n     |- Try 34 + 30 = 64. Evaluate 64 != 41, drop this branch.\n     |- Try 34 - 30 = 4. Evaluate 4 != 41, drop this branch.\n     |- Try 34 * 30 = 1020. Evaluate 1020 != 41, drop this branch.\n     |- Try 34 \/ 30 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 28 - 2 = 26. Add 26 to the number set. Current number set: [26, 34], target: 41, just two numbers left.\n     |- Try 34 + 26 = 60. Evaluate 60 != 41, drop this branch.\n     |- Try 34 - 26 = 8. Evaluate 8 != 41, drop this branch.\n     |- Try 34 * 26 = 884. Evaluate 884 != 41, drop this branch.\n     |- Try 34 \/ 26 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 28 * 2 = 56. Add 56 to the number set. Current number set: [56, 34], target: 41, just two numbers left.\n     |- Try 56 + 34 = 90. Evaluate 90 != 41, drop this branch.\n     |- Try 56 - 34 = 22. Evaluate 22 != 41, drop this branch.\n     |- Try 56 * 34 = 1904. Evaluate 1904 != 41, drop this branch.\n     |- Try 56 \/ 34 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 28 \/ 2 = 14. Add 14 to the number set. Current number set: [14, 34], target: 41, just two numbers left.\n     |- Try 34 + 14 = 48. Evaluate 48 != 41, drop this branch.\n     |- Try 34 - 14 = 20. Evaluate 20 != 41, drop this branch.\n     |- Try 34 * 14 = 476. Evaluate 476 != 41, drop this branch.\n     |- Try 34 \/ 14 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (28, 34) (numbers left: [2]). Try possible operations.\n    |- Try 34 + 28 = 62. Add 62 to the number set. Current number set: [62, 2], target: 41, just two numbers left.\n     |- Try 62 + 2 = 64. Evaluate 64 != 41, drop this branch.\n     |- Try 62 - 2 = 60. Evaluate 60 != 41, drop this branch.\n     |- Try 62 * 2 = 124. Evaluate 124 != 41, drop this branch.\n     |- Try 62 \/ 2 = 31. Evaluate 31 != 41, drop this branch.\n    |- Try 34 - 28 = 6. Add 6 to the number set. Current number set: [6, 2], target: 41, just two numbers left.\n     |- Try 6 + 2 = 8. Evaluate 8 != 41, drop this branch.\n     |- Try 6 - 2 = 4. Evaluate 4 != 41, drop this branch.\n     |- Try 6 * 2 = 12. Evaluate 12 != 41, drop this branch.\n     |- Try 6 \/ 2 = 3. Evaluate 3 != 41, drop this branch.\n    |- Try 34 * 28 = 952. Add 952 to the number set. Current number set: [952, 2], target: 41, just two numbers left.\n     |- Try 952 + 2 = 954. Evaluate 954 != 41, drop this branch.\n     |- Try 952 - 2 = 950. Evaluate 950 != 41, drop this branch.\n     |- Try 952 * 2 = 1904. Evaluate 1904 != 41, drop this branch.\n     |- Try 952 \/ 2 = 476. Evaluate 476 != 41, drop this branch.\n    |- Try 34 \/ 28 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (2, 34) (numbers left: [28]). Try possible operations.\n    |- Try 34 + 2 = 36. Add 36 to the number set. Current number set: [36, 28], target: 41, just two numbers left.\n     |- Try 36 + 28 = 64. Evaluate 64 != 41, drop this branch.\n     |- Try 36 - 28 = 8. Evaluate 8 != 41, drop this branch.\n     |- Try 36 * 28 = 1008. Evaluate 1008 != 41, drop this branch.\n     |- Try 36 \/ 28 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 34 - 2 = 32. Add 32 to the number set. Current number set: [32, 28], target: 41, just two numbers left.\n     |- Try 32 + 28 = 60. Evaluate 60 != 41, drop this branch.\n     |- Try 32 - 28 = 4. Evaluate 4 != 41, drop this branch.\n     |- Try 32 * 28 = 896. Evaluate 896 != 41, drop this branch.\n     |- Try 32 \/ 28 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 34 * 2 = 68. Add 68 to the number set. Current number set: [68, 28], target: 41, just two numbers left.\n     |- Try 68 + 28 = 96. Evaluate 96 != 41, drop this branch.\n     |- Try 68 - 28 = 40. Evaluate 40 != 41, drop this branch.\n     |- Try 68 * 28 = 1904. Evaluate 1904 != 41, drop this branch.\n     |- Try 68 \/ 28 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 34 \/ 2 = 17. Add 17 to the number set. Current number set: [17, 28], target: 41, just two numbers left.\n     |- Try 28 + 17 = 45. Evaluate 45 != 41, drop this branch.\n     |- Try 28 - 17 = 11. Evaluate 11 != 41, drop this branch.\n     |- Try 28 * 17 = 476. Evaluate 476 != 41, drop this branch.\n     |- Try 28 \/ 17 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 27 - 1 = 26. Add 26 to the number set. Current number set: [26, 2, 34], target: 41. Options for choosing two numbers: [(26, 2), (26, 34), (2, 34)].\n   |- Pick two numbers (26, 2) (numbers left: [34]). Try possible operations.\n    |- Try 26 + 2 = 28. Add 28 to the number set. Current number set: [28, 34], target: 41, just two numbers left.\n     |- Try 34 + 28 = 62. Evaluate 62 != 41, drop this branch.\n     |- Try 34 - 28 = 6. Evaluate 6 != 41, drop this branch.\n     |- Try 34 * 28 = 952. Evaluate 952 != 41, drop this branch.\n     |- Try 34 \/ 28 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 26 - 2 = 24. Add 24 to the number set. Current number set: [24, 34], target: 41, just two numbers left.\n     |- Try 34 + 24 = 58. Evaluate 58 != 41, drop this branch.\n     |- Try 34 - 24 = 10. Evaluate 10 != 41, drop this branch.\n     |- Try 34 * 24 = 816. Evaluate 816 != 41, drop this branch.\n     |- Try 34 \/ 24 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 26 * 2 = 52. Add 52 to the number set. Current number set: [52, 34], target: 41, just two numbers left.\n     |- Try 52 + 34 = 86. Evaluate 86 != 41, drop this branch.\n     |- Try 52 - 34 = 18. Evaluate 18 != 41, drop this branch.\n     |- Try 52 * 34 = 1768. Evaluate 1768 != 41, drop this branch.\n     |- Try 52 \/ 34 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 26 \/ 2 = 13. Add 13 to the number set. Current number set: [13, 34], target: 41, just two numbers left.\n     |- Try 34 + 13 = 47. Evaluate 47 != 41, drop this branch.\n     |- Try 34 - 13 = 21. Evaluate 21 != 41, drop this branch.\n     |- Try 34 * 13 = 442. Evaluate 442 != 41, drop this branch.\n     |- Try 34 \/ 13 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (26, 34) (numbers left: [2]). Try possible operations.\n    |- Try 34 + 26 = 60. Add 60 to the number set. Current number set: [60, 2], target: 41, just two numbers left.\n     |- Try 60 + 2 = 62. Evaluate 62 != 41, drop this branch.\n     |- Try 60 - 2 = 58. Evaluate 58 != 41, drop this branch.\n     |- Try 60 * 2 = 120. Evaluate 120 != 41, drop this branch.\n     |- Try 60 \/ 2 = 30. Evaluate 30 != 41, drop this branch.\n    |- Try 34 - 26 = 8. Add 8 to the number set. Current number set: [8, 2], target: 41, just two numbers left.\n     |- Try 8 + 2 = 10. Evaluate 10 != 41, drop this branch.\n     |- Try 8 - 2 = 6. Evaluate 6 != 41, drop this branch.\n     |- Try 8 * 2 = 16. Evaluate 16 != 41, drop this branch.\n     |- Try 8 \/ 2 = 4. Evaluate 4 != 41, drop this branch.\n    |- Try 34 * 26 = 884. Add 884 to the number set. Current number set: [884, 2], target: 41, just two numbers left.\n     |- Try 884 + 2 = 886. Evaluate 886 != 41, drop this branch.\n     |- Try 884 - 2 = 882. Evaluate 882 != 41, drop this branch.\n     |- Try 884 * 2 = 1768. Evaluate 1768 != 41, drop this branch.\n     |- Try 884 \/ 2 = 442. Evaluate 442 != 41, drop this branch.\n    |- Try 34 \/ 26 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (2, 34) (numbers left: [26]). Try possible operations.\n    |- Try 34 + 2 = 36. Add 36 to the number set. Current number set: [36, 26], target: 41, just two numbers left.\n     |- Try 36 + 26 = 62. Evaluate 62 != 41, drop this branch.\n     |- Try 36 - 26 = 10. Evaluate 10 != 41, drop this branch.\n     |- Try 36 * 26 = 936. Evaluate 936 != 41, drop this branch.\n     |- Try 36 \/ 26 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 34 - 2 = 32. Add 32 to the number set. Current number set: [32, 26], target: 41, just two numbers left.\n     |- Try 32 + 26 = 58. Evaluate 58 != 41, drop this branch.\n     |- Try 32 - 26 = 6. Evaluate 6 != 41, drop this branch.\n     |- Try 32 * 26 = 832. Evaluate 832 != 41, drop this branch.\n     |- Try 32 \/ 26 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 34 * 2 = 68. Add 68 to the number set. Current number set: [68, 26], target: 41, just two numbers left.\n     |- Try 68 + 26 = 94. Evaluate 94 != 41, drop this branch.\n     |- Try 68 - 26 = 42. Evaluate 42 != 41, drop this branch.\n     |- Try 68 * 26 = 1768. Evaluate 1768 != 41, drop this branch.\n     |- Try 68 \/ 26 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 34 \/ 2 = 17. Add 17 to the number set. Current number set: [17, 26], target: 41, just two numbers left.\n     |- Try 26 + 17 = 43. Evaluate 43 != 41, drop this branch.\n     |- Try 26 - 17 = 9. Evaluate 9 != 41, drop this branch.\n     |- Try 26 * 17 = 442. Evaluate 442 != 41, drop this branch.\n     |- Try 26 \/ 17 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 27 * 1 = 27. Add 27 to the number set. Current number set: [27, 2, 34], target: 41. Options for choosing two numbers: [(27, 2), (27, 34), (2, 34)].\n   |- Pick two numbers (27, 2) (numbers left: [34]). Try possible operations.\n    |- Try 27 + 2 = 29. Add 29 to the number set. Current number set: [29, 34], target: 41, just two numbers left.\n     |- Try 34 + 29 = 63. Evaluate 63 != 41, drop this branch.\n     |- Try 34 - 29 = 5. Evaluate 5 != 41, drop this branch.\n     |- Try 34 * 29 = 986. Evaluate 986 != 41, drop this branch.\n     |- Try 34 \/ 29 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 27 - 2 = 25. Add 25 to the number set. Current number set: [25, 34], target: 41, just two numbers left.\n     |- Try 34 + 25 = 59. Evaluate 59 != 41, drop this branch.\n     |- Try 34 - 25 = 9. Evaluate 9 != 41, drop this branch.\n     |- Try 34 * 25 = 850. Evaluate 850 != 41, drop this branch.\n     |- Try 34 \/ 25 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 27 * 2 = 54. Add 54 to the number set. Current number set: [54, 34], target: 41, just two numbers left.\n     |- Try 54 + 34 = 88. Evaluate 88 != 41, drop this branch.\n     |- Try 54 - 34 = 20. Evaluate 20 != 41, drop this branch.\n     |- Try 54 * 34 = 1836. Evaluate 1836 != 41, drop this branch.\n     |- Try 54 \/ 34 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 27 \/ 2 = 13.5. 13.5 is a decimal, drop this branch.\n   |- Pick two numbers (27, 34) (numbers left: [2]). Try possible operations.\n    |- Try 34 + 27 = 61. Add 61 to the number set. Current number set: [61, 2], target: 41, just two numbers left.\n     |- Try 61 + 2 = 63. Evaluate 63 != 41, drop this branch.\n     |- Try 61 - 2 = 59. Evaluate 59 != 41, drop this branch.\n     |- Try 61 * 2 = 122. Evaluate 122 != 41, drop this branch.\n     |- Try 61 \/ 2 = 30.5. 30.5 is a decimal, drop this branch.\n    |- Try 34 - 27 = 7. Add 7 to the number set. Current number set: [7, 2], target: 41, just two numbers left.\n     |- Try 7 + 2 = 9. Evaluate 9 != 41, drop this branch.\n     |- Try 7 - 2 = 5. Evaluate 5 != 41, drop this branch.\n     |- Try 7 * 2 = 14. Evaluate 14 != 41, drop this branch.\n     |- Try 7 \/ 2 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 34 * 27 = 918. Add 918 to the number set. Current number set: [918, 2], target: 41, just two numbers left.\n     |- Try 918 + 2 = 920. Evaluate 920 != 41, drop this branch.\n     |- Try 918 - 2 = 916. Evaluate 916 != 41, drop this branch.\n     |- Try 918 * 2 = 1836. Evaluate 1836 != 41, drop this branch.\n     |- Try 918 \/ 2 = 459. Evaluate 459 != 41, drop this branch.\n    |- Try 34 \/ 27 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (2, 34) (numbers left: [27]). Try possible operations.\n    |- Try 34 + 2 = 36. Add 36 to the number set. Current number set: [36, 27], target: 41, just two numbers left.\n     |- Try 36 + 27 = 63. Evaluate 63 != 41, drop this branch.\n     |- Try 36 - 27 = 9. Evaluate 9 != 41, drop this branch.\n     |- Try 36 * 27 = 972. Evaluate 972 != 41, drop this branch.\n     |- Try 36 \/ 27 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 34 - 2 = 32. Add 32 to the number set. Current number set: [32, 27], target: 41, just two numbers left.\n     |- Try 32 + 27 = 59. Evaluate 59 != 41, drop this branch.\n     |- Try 32 - 27 = 5. Evaluate 5 != 41, drop this branch.\n     |- Try 32 * 27 = 864. Evaluate 864 != 41, drop this branch.\n     |- Try 32 \/ 27 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 34 * 2 = 68. Add 68 to the number set. Current number set: [68, 27], target: 41, just two numbers left.\n     |- Try 68 + 27 = 95. Evaluate 95 != 41, drop this branch.\n     |- Try 68 - 27 = 41. Evaluate 41 == 41, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 68 - 27 = 41\nThe step before: 34 * 2 = 68\nThe first step: 27 * 1 = 27\n\nOutput the solution in the required format:\n<Solution>\n27 * 1 = 27\n34 * 2 = 68\n68 - 27 = 41\n<\/Solution>\n","item":{"nums":[27,1,2,34],"solution":["27 * 1 = 27","34 * 2 = 68","68 - 27 = 41"],"target":41}}
+{"instance_id":"countdown_8k_34","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [23, 36, 25, 28]\nTarget: 50","reference_output":"# Search Procedure\nInitial number set: [23, 36, 25, 28], target: 50. Options for choosing two numbers: [(23, 36), (23, 25), (23, 28), (36, 25), (36, 28), (25, 28)].\n |- Pick two numbers (23, 36) (numbers left: [25, 28]). Try possible operations.\n  |- Try 36 + 23 = 59. Add 59 to the number set. Current number set: [59, 25, 28], target: 50. Options for choosing two numbers: [(59, 25), (59, 28), (25, 28)].\n   |- Pick two numbers (59, 25) (numbers left: [28]). Try possible operations.\n    |- Try 59 + 25 = 84. Add 84 to the number set. Current number set: [84, 28], target: 50, just two numbers left.\n     |- Try 84 + 28 = 112. Evaluate 112 != 50, drop this branch.\n     |- Try 84 - 28 = 56. Evaluate 56 != 50, drop this branch.\n     |- Try 84 * 28 = 2352. 2352 exceeds the maximum intermediate result, drop this branch.\n     |- Try 84 \/ 28 = 3. Evaluate 3 != 50, drop this branch.\n    |- Try 59 - 25 = 34. Add 34 to the number set. Current number set: [34, 28], target: 50, just two numbers left.\n     |- Try 34 + 28 = 62. Evaluate 62 != 50, drop this branch.\n     |- Try 34 - 28 = 6. Evaluate 6 != 50, drop this branch.\n     |- Try 34 * 28 = 952. Evaluate 952 != 50, drop this branch.\n     |- Try 34 \/ 28 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 59 * 25 = 1475. Add 1475 to the number set. Current number set: [1475, 28], target: 50, just two numbers left.\n     |- Try 1475 + 28 = 1503. Evaluate 1503 != 50, drop this branch.\n     |- Try 1475 - 28 = 1447. Evaluate 1447 != 50, drop this branch.\n     |- Try 1475 * 28 = 41300. 41300 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1475 \/ 28 = 52.7. 52.7 is a decimal, drop this branch.\n    |- Try 59 \/ 25 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (59, 28) (numbers left: [25]). Try possible operations.\n    |- Try 59 + 28 = 87. Add 87 to the number set. Current number set: [87, 25], target: 50, just two numbers left.\n     |- Try 87 + 25 = 112. Evaluate 112 != 50, drop this branch.\n     |- Try 87 - 25 = 62. Evaluate 62 != 50, drop this branch.\n     |- Try 87 * 25 = 2175. 2175 exceeds the maximum intermediate result, drop this branch.\n     |- Try 87 \/ 25 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 59 - 28 = 31. Add 31 to the number set. Current number set: [31, 25], target: 50, just two numbers left.\n     |- Try 31 + 25 = 56. Evaluate 56 != 50, drop this branch.\n     |- Try 31 - 25 = 6. Evaluate 6 != 50, drop this branch.\n     |- Try 31 * 25 = 775. Evaluate 775 != 50, drop this branch.\n     |- Try 31 \/ 25 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 59 * 28 = 1652. Add 1652 to the number set. Current number set: [1652, 25], target: 50, just two numbers left.\n     |- Try 1652 + 25 = 1677. Evaluate 1677 != 50, drop this branch.\n     |- Try 1652 - 25 = 1627. Evaluate 1627 != 50, drop this branch.\n     |- Try 1652 * 25 = 41300. 41300 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1652 \/ 25 = 66.1. 66.1 is a decimal, drop this branch.\n    |- Try 59 \/ 28 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (25, 28) (numbers left: [59]). Try possible operations.\n    |- Try 28 + 25 = 53. Add 53 to the number set. Current number set: [53, 59], target: 50, just two numbers left.\n     |- Try 59 + 53 = 112. Evaluate 112 != 50, drop this branch.\n     |- Try 59 - 53 = 6. Evaluate 6 != 50, drop this branch.\n     |- Try 59 * 53 = 3127. 3127 exceeds the maximum intermediate result, drop this branch.\n     |- Try 59 \/ 53 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 28 - 25 = 3. Add 3 to the number set. Current number set: [3, 59], target: 50, just two numbers left.\n     |- Try 59 + 3 = 62. Evaluate 62 != 50, drop this branch.\n     |- Try 59 - 3 = 56. Evaluate 56 != 50, drop this branch.\n     |- Try 59 * 3 = 177. Evaluate 177 != 50, drop this branch.\n     |- Try 59 \/ 3 = 19.7. 19.7 is a decimal, drop this branch.\n    |- Try 28 * 25 = 700. Add 700 to the number set. Current number set: [700, 59], target: 50, just two numbers left.\n     |- Try 700 + 59 = 759. Evaluate 759 != 50, drop this branch.\n     |- Try 700 - 59 = 641. Evaluate 641 != 50, drop this branch.\n     |- Try 700 * 59 = 41300. 41300 exceeds the maximum intermediate result, drop this branch.\n     |- Try 700 \/ 59 = 11.9. 11.9 is a decimal, drop this branch.\n    |- Try 28 \/ 25 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 36 - 23 = 13. Add 13 to the number set. Current number set: [13, 25, 28], target: 50. Options for choosing two numbers: [(13, 25), (13, 28), (25, 28)].\n   |- Pick two numbers (13, 25) (numbers left: [28]). Try possible operations.\n    |- Try 25 + 13 = 38. Add 38 to the number set. Current number set: [38, 28], target: 50, just two numbers left.\n     |- Try 38 + 28 = 66. Evaluate 66 != 50, drop this branch.\n     |- Try 38 - 28 = 10. Evaluate 10 != 50, drop this branch.\n     |- Try 38 * 28 = 1064. Evaluate 1064 != 50, drop this branch.\n     |- Try 38 \/ 28 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 25 - 13 = 12. Add 12 to the number set. Current number set: [12, 28], target: 50, just two numbers left.\n     |- Try 28 + 12 = 40. Evaluate 40 != 50, drop this branch.\n     |- Try 28 - 12 = 16. Evaluate 16 != 50, drop this branch.\n     |- Try 28 * 12 = 336. Evaluate 336 != 50, drop this branch.\n     |- Try 28 \/ 12 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 25 * 13 = 325. Add 325 to the number set. Current number set: [325, 28], target: 50, just two numbers left.\n     |- Try 325 + 28 = 353. Evaluate 353 != 50, drop this branch.\n     |- Try 325 - 28 = 297. Evaluate 297 != 50, drop this branch.\n     |- Try 325 * 28 = 9100. 9100 exceeds the maximum intermediate result, drop this branch.\n     |- Try 325 \/ 28 = 11.6. 11.6 is a decimal, drop this branch.\n    |- Try 25 \/ 13 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (13, 28) (numbers left: [25]). Try possible operations.\n    |- Try 28 + 13 = 41. Add 41 to the number set. Current number set: [41, 25], target: 50, just two numbers left.\n     |- Try 41 + 25 = 66. Evaluate 66 != 50, drop this branch.\n     |- Try 41 - 25 = 16. Evaluate 16 != 50, drop this branch.\n     |- Try 41 * 25 = 1025. Evaluate 1025 != 50, drop this branch.\n     |- Try 41 \/ 25 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 28 - 13 = 15. Add 15 to the number set. Current number set: [15, 25], target: 50, just two numbers left.\n     |- Try 25 + 15 = 40. Evaluate 40 != 50, drop this branch.\n     |- Try 25 - 15 = 10. Evaluate 10 != 50, drop this branch.\n     |- Try 25 * 15 = 375. Evaluate 375 != 50, drop this branch.\n     |- Try 25 \/ 15 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 28 * 13 = 364. Add 364 to the number set. Current number set: [364, 25], target: 50, just two numbers left.\n     |- Try 364 + 25 = 389. Evaluate 389 != 50, drop this branch.\n     |- Try 364 - 25 = 339. Evaluate 339 != 50, drop this branch.\n     |- Try 364 * 25 = 9100. 9100 exceeds the maximum intermediate result, drop this branch.\n     |- Try 364 \/ 25 = 14.6. 14.6 is a decimal, drop this branch.\n    |- Try 28 \/ 13 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 28) (numbers left: [13]). Try possible operations.\n    |- Try 28 + 25 = 53. Add 53 to the number set. Current number set: [53, 13], target: 50, just two numbers left.\n     |- Try 53 + 13 = 66. Evaluate 66 != 50, drop this branch.\n     |- Try 53 - 13 = 40. Evaluate 40 != 50, drop this branch.\n     |- Try 53 * 13 = 689. Evaluate 689 != 50, drop this branch.\n     |- Try 53 \/ 13 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 28 - 25 = 3. Add 3 to the number set. Current number set: [3, 13], target: 50, just two numbers left.\n     |- Try 13 + 3 = 16. Evaluate 16 != 50, drop this branch.\n     |- Try 13 - 3 = 10. Evaluate 10 != 50, drop this branch.\n     |- Try 13 * 3 = 39. Evaluate 39 != 50, drop this branch.\n     |- Try 13 \/ 3 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 28 * 25 = 700. Add 700 to the number set. Current number set: [700, 13], target: 50, just two numbers left.\n     |- Try 700 + 13 = 713. Evaluate 713 != 50, drop this branch.\n     |- Try 700 - 13 = 687. Evaluate 687 != 50, drop this branch.\n     |- Try 700 * 13 = 9100. 9100 exceeds the maximum intermediate result, drop this branch.\n     |- Try 700 \/ 13 = 53.8. 53.8 is a decimal, drop this branch.\n    |- Try 28 \/ 25 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 36 * 23 = 828. Add 828 to the number set. Current number set: [828, 25, 28], target: 50. Options for choosing two numbers: [(828, 25), (828, 28), (25, 28)].\n   |- Pick two numbers (828, 25) (numbers left: [28]). Try possible operations.\n    |- Try 828 + 25 = 853. Add 853 to the number set. Current number set: [853, 28], target: 50, just two numbers left.\n     |- Try 853 + 28 = 881. Evaluate 881 != 50, drop this branch.\n     |- Try 853 - 28 = 825. Evaluate 825 != 50, drop this branch.\n     |- Try 853 * 28 = 23884. 23884 exceeds the maximum intermediate result, drop this branch.\n     |- Try 853 \/ 28 = 30.5. 30.5 is a decimal, drop this branch.\n    |- Try 828 - 25 = 803. Add 803 to the number set. Current number set: [803, 28], target: 50, just two numbers left.\n     |- Try 803 + 28 = 831. Evaluate 831 != 50, drop this branch.\n     |- Try 803 - 28 = 775. Evaluate 775 != 50, drop this branch.\n     |- Try 803 * 28 = 22484. 22484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 803 \/ 28 = 28.7. 28.7 is a decimal, drop this branch.\n    |- Try 828 * 25 = 20700. 20700 exceeds the maximum intermediate result, drop this branch.\n    |- Try 828 \/ 25 = 33.1. 33.1 is a decimal, drop this branch.\n   |- Pick two numbers (828, 28) (numbers left: [25]). Try possible operations.\n    |- Try 828 + 28 = 856. Add 856 to the number set. Current number set: [856, 25], target: 50, just two numbers left.\n     |- Try 856 + 25 = 881. Evaluate 881 != 50, drop this branch.\n     |- Try 856 - 25 = 831. Evaluate 831 != 50, drop this branch.\n     |- Try 856 * 25 = 21400. 21400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 856 \/ 25 = 34.2. 34.2 is a decimal, drop this branch.\n    |- Try 828 - 28 = 800. Add 800 to the number set. Current number set: [800, 25], target: 50, just two numbers left.\n     |- Try 800 + 25 = 825. Evaluate 825 != 50, drop this branch.\n     |- Try 800 - 25 = 775. Evaluate 775 != 50, drop this branch.\n     |- Try 800 * 25 = 20000. 20000 exceeds the maximum intermediate result, drop this branch.\n     |- Try 800 \/ 25 = 32. Evaluate 32 != 50, drop this branch.\n    |- Try 828 * 28 = 23184. 23184 exceeds the maximum intermediate result, drop this branch.\n    |- Try 828 \/ 28 = 29.6. 29.6 is a decimal, drop this branch.\n   |- Pick two numbers (25, 28) (numbers left: [828]). Try possible operations.\n    |- Try 28 + 25 = 53. Add 53 to the number set. Current number set: [53, 828], target: 50, just two numbers left.\n     |- Try 828 + 53 = 881. Evaluate 881 != 50, drop this branch.\n     |- Try 828 - 53 = 775. Evaluate 775 != 50, drop this branch.\n     |- Try 828 * 53 = 43884. 43884 exceeds the maximum intermediate result, drop this branch.\n     |- Try 828 \/ 53 = 15.6. 15.6 is a decimal, drop this branch.\n    |- Try 28 - 25 = 3. Add 3 to the number set. Current number set: [3, 828], target: 50, just two numbers left.\n     |- Try 828 + 3 = 831. Evaluate 831 != 50, drop this branch.\n     |- Try 828 - 3 = 825. Evaluate 825 != 50, drop this branch.\n     |- Try 828 * 3 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 828 \/ 3 = 276. Evaluate 276 != 50, drop this branch.\n    |- Try 28 * 25 = 700. Add 700 to the number set. Current number set: [700, 828], target: 50, just two numbers left.\n     |- Try 828 + 700 = 1528. Evaluate 1528 != 50, drop this branch.\n     |- Try 828 - 700 = 128. Evaluate 128 != 50, drop this branch.\n     |- Try 828 * 700 = 579600. 579600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 828 \/ 700 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 28 \/ 25 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 36 \/ 23 = 1.6. 1.6 is a decimal, drop this branch.\n |- Pick two numbers (23, 25) (numbers left: [36, 28]). Try possible operations.\n  |- Try 25 + 23 = 48. Add 48 to the number set. Current number set: [48, 36, 28], target: 50. Options for choosing two numbers: [(48, 36), (48, 28), (36, 28)].\n   |- Pick two numbers (48, 36) (numbers left: [28]). Try possible operations.\n    |- Try 48 + 36 = 84. Add 84 to the number set. Current number set: [84, 28], target: 50, just two numbers left.\n     |- Try 84 + 28 = 112. Evaluate 112 != 50, drop this branch.\n     |- Try 84 - 28 = 56. Evaluate 56 != 50, drop this branch.\n     |- Try 84 * 28 = 2352. 2352 exceeds the maximum intermediate result, drop this branch.\n     |- Try 84 \/ 28 = 3. Evaluate 3 != 50, drop this branch.\n    |- Try 48 - 36 = 12. Add 12 to the number set. Current number set: [12, 28], target: 50, just two numbers left.\n     |- Try 28 + 12 = 40. Evaluate 40 != 50, drop this branch.\n     |- Try 28 - 12 = 16. Evaluate 16 != 50, drop this branch.\n     |- Try 28 * 12 = 336. Evaluate 336 != 50, drop this branch.\n     |- Try 28 \/ 12 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 48 * 36 = 1728. Add 1728 to the number set. Current number set: [1728, 28], target: 50, just two numbers left.\n     |- Try 1728 + 28 = 1756. Evaluate 1756 != 50, drop this branch.\n     |- Try 1728 - 28 = 1700. Evaluate 1700 != 50, drop this branch.\n     |- Try 1728 * 28 = 48384. 48384 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1728 \/ 28 = 61.7. 61.7 is a decimal, drop this branch.\n    |- Try 48 \/ 36 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (48, 28) (numbers left: [36]). Try possible operations.\n    |- Try 48 + 28 = 76. Add 76 to the number set. Current number set: [76, 36], target: 50, just two numbers left.\n     |- Try 76 + 36 = 112. Evaluate 112 != 50, drop this branch.\n     |- Try 76 - 36 = 40. Evaluate 40 != 50, drop this branch.\n     |- Try 76 * 36 = 2736. 2736 exceeds the maximum intermediate result, drop this branch.\n     |- Try 76 \/ 36 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 48 - 28 = 20. Add 20 to the number set. Current number set: [20, 36], target: 50, just two numbers left.\n     |- Try 36 + 20 = 56. Evaluate 56 != 50, drop this branch.\n     |- Try 36 - 20 = 16. Evaluate 16 != 50, drop this branch.\n     |- Try 36 * 20 = 720. Evaluate 720 != 50, drop this branch.\n     |- Try 36 \/ 20 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 48 * 28 = 1344. Add 1344 to the number set. Current number set: [1344, 36], target: 50, just two numbers left.\n     |- Try 1344 + 36 = 1380. Evaluate 1380 != 50, drop this branch.\n     |- Try 1344 - 36 = 1308. Evaluate 1308 != 50, drop this branch.\n     |- Try 1344 * 36 = 48384. 48384 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1344 \/ 36 = 37.3. 37.3 is a decimal, drop this branch.\n    |- Try 48 \/ 28 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (36, 28) (numbers left: [48]). Try possible operations.\n    |- Try 36 + 28 = 64. Add 64 to the number set. Current number set: [64, 48], target: 50, just two numbers left.\n     |- Try 64 + 48 = 112. Evaluate 112 != 50, drop this branch.\n     |- Try 64 - 48 = 16. Evaluate 16 != 50, drop this branch.\n     |- Try 64 * 48 = 3072. 3072 exceeds the maximum intermediate result, drop this branch.\n     |- Try 64 \/ 48 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 36 - 28 = 8. Add 8 to the number set. Current number set: [8, 48], target: 50, just two numbers left.\n     |- Try 48 + 8 = 56. Evaluate 56 != 50, drop this branch.\n     |- Try 48 - 8 = 40. Evaluate 40 != 50, drop this branch.\n     |- Try 48 * 8 = 384. Evaluate 384 != 50, drop this branch.\n     |- Try 48 \/ 8 = 6. Evaluate 6 != 50, drop this branch.\n    |- Try 36 * 28 = 1008. Add 1008 to the number set. Current number set: [1008, 48], target: 50, just two numbers left.\n     |- Try 1008 + 48 = 1056. Evaluate 1056 != 50, drop this branch.\n     |- Try 1008 - 48 = 960. Evaluate 960 != 50, drop this branch.\n     |- Try 1008 * 48 = 48384. 48384 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1008 \/ 48 = 21. Evaluate 21 != 50, drop this branch.\n    |- Try 36 \/ 28 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 25 - 23 = 2. Add 2 to the number set. Current number set: [2, 36, 28], target: 50. Options for choosing two numbers: [(2, 36), (2, 28), (36, 28)].\n   |- Pick two numbers (2, 36) (numbers left: [28]). Try possible operations.\n    |- Try 36 + 2 = 38. Add 38 to the number set. Current number set: [38, 28], target: 50, just two numbers left.\n     |- Try 38 + 28 = 66. Evaluate 66 != 50, drop this branch.\n     |- Try 38 - 28 = 10. Evaluate 10 != 50, drop this branch.\n     |- Try 38 * 28 = 1064. Evaluate 1064 != 50, drop this branch.\n     |- Try 38 \/ 28 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 36 - 2 = 34. Add 34 to the number set. Current number set: [34, 28], target: 50, just two numbers left.\n     |- Try 34 + 28 = 62. Evaluate 62 != 50, drop this branch.\n     |- Try 34 - 28 = 6. Evaluate 6 != 50, drop this branch.\n     |- Try 34 * 28 = 952. Evaluate 952 != 50, drop this branch.\n     |- Try 34 \/ 28 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 36 * 2 = 72. Add 72 to the number set. Current number set: [72, 28], target: 50, just two numbers left.\n     |- Try 72 + 28 = 100. Evaluate 100 != 50, drop this branch.\n     |- Try 72 - 28 = 44. Evaluate 44 != 50, drop this branch.\n     |- Try 72 * 28 = 2016. 2016 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 28 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 36 \/ 2 = 18. Add 18 to the number set. Current number set: [18, 28], target: 50, just two numbers left.\n     |- Try 28 + 18 = 46. Evaluate 46 != 50, drop this branch.\n     |- Try 28 - 18 = 10. Evaluate 10 != 50, drop this branch.\n     |- Try 28 * 18 = 504. Evaluate 504 != 50, drop this branch.\n     |- Try 28 \/ 18 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (2, 28) (numbers left: [36]). Try possible operations.\n    |- Try 28 + 2 = 30. Add 30 to the number set. Current number set: [30, 36], target: 50, just two numbers left.\n     |- Try 36 + 30 = 66. Evaluate 66 != 50, drop this branch.\n     |- Try 36 - 30 = 6. Evaluate 6 != 50, drop this branch.\n     |- Try 36 * 30 = 1080. Evaluate 1080 != 50, drop this branch.\n     |- Try 36 \/ 30 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 28 - 2 = 26. Add 26 to the number set. Current number set: [26, 36], target: 50, just two numbers left.\n     |- Try 36 + 26 = 62. Evaluate 62 != 50, drop this branch.\n     |- Try 36 - 26 = 10. Evaluate 10 != 50, drop this branch.\n     |- Try 36 * 26 = 936. Evaluate 936 != 50, drop this branch.\n     |- Try 36 \/ 26 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 28 * 2 = 56. Add 56 to the number set. Current number set: [56, 36], target: 50, just two numbers left.\n     |- Try 56 + 36 = 92. Evaluate 92 != 50, drop this branch.\n     |- Try 56 - 36 = 20. Evaluate 20 != 50, drop this branch.\n     |- Try 56 * 36 = 2016. 2016 exceeds the maximum intermediate result, drop this branch.\n     |- Try 56 \/ 36 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 28 \/ 2 = 14. Add 14 to the number set. Current number set: [14, 36], target: 50, just two numbers left.\n     |- Try 36 + 14 = 50. Evaluate 50 == 50, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 + 14 = 50\nThe step before: 28 \/ 2 = 14\nThe first step: 25 - 23 = 2\n\nOutput the solution in the required format:\n<Solution>\n25 - 23 = 2\n28 \/ 2 = 14\n36 + 14 = 50\n<\/Solution>\n","item":{"nums":[23,36,25,28],"solution":["25 - 23 = 2","28 \/ 2 = 14","36 + 14 = 50"],"target":50}}
+{"instance_id":"countdown_8k_35","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [11, 44, 25, 11]\nTarget: 32","reference_output":"# Search Procedure\nInitial number set: [11, 44, 25, 11], target: 32. Options for choosing two numbers: [(11, 44), (11, 25), (11, 11), (44, 25), (44, 11), (25, 11)].\n |- Pick two numbers (11, 44) (numbers left: [25, 11]). Try possible operations.\n  |- Try 44 + 11 = 55. Add 55 to the number set. Current number set: [55, 25, 11], target: 32. Options for choosing two numbers: [(55, 25), (55, 11), (25, 11)].\n   |- Pick two numbers (55, 25) (numbers left: [11]). Try possible operations.\n    |- Try 55 + 25 = 80. Add 80 to the number set. Current number set: [80, 11], target: 32, just two numbers left.\n     |- Try 80 + 11 = 91. Evaluate 91 != 32, drop this branch.\n     |- Try 80 - 11 = 69. Evaluate 69 != 32, drop this branch.\n     |- Try 80 * 11 = 880. Evaluate 880 != 32, drop this branch.\n     |- Try 80 \/ 11 = 7.3. 7.3 is a decimal, drop this branch.\n    |- Try 55 - 25 = 30. Add 30 to the number set. Current number set: [30, 11], target: 32, just two numbers left.\n     |- Try 30 + 11 = 41. Evaluate 41 != 32, drop this branch.\n     |- Try 30 - 11 = 19. Evaluate 19 != 32, drop this branch.\n     |- Try 30 * 11 = 330. Evaluate 330 != 32, drop this branch.\n     |- Try 30 \/ 11 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 55 * 25 = 1375. Add 1375 to the number set. Current number set: [1375, 11], target: 32, just two numbers left.\n     |- Try 1375 + 11 = 1386. Evaluate 1386 != 32, drop this branch.\n     |- Try 1375 - 11 = 1364. Evaluate 1364 != 32, drop this branch.\n     |- Try 1375 * 11 = 15125. 15125 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1375 \/ 11 = 125. Evaluate 125 != 32, drop this branch.\n    |- Try 55 \/ 25 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (55, 11) (numbers left: [25]). Try possible operations.\n    |- Try 55 + 11 = 66. Add 66 to the number set. Current number set: [66, 25], target: 32, just two numbers left.\n     |- Try 66 + 25 = 91. Evaluate 91 != 32, drop this branch.\n     |- Try 66 - 25 = 41. Evaluate 41 != 32, drop this branch.\n     |- Try 66 * 25 = 1650. Evaluate 1650 != 32, drop this branch.\n     |- Try 66 \/ 25 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 55 - 11 = 44. Add 44 to the number set. Current number set: [44, 25], target: 32, just two numbers left.\n     |- Try 44 + 25 = 69. Evaluate 69 != 32, drop this branch.\n     |- Try 44 - 25 = 19. Evaluate 19 != 32, drop this branch.\n     |- Try 44 * 25 = 1100. Evaluate 1100 != 32, drop this branch.\n     |- Try 44 \/ 25 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 55 * 11 = 605. Add 605 to the number set. Current number set: [605, 25], target: 32, just two numbers left.\n     |- Try 605 + 25 = 630. Evaluate 630 != 32, drop this branch.\n     |- Try 605 - 25 = 580. Evaluate 580 != 32, drop this branch.\n     |- Try 605 * 25 = 15125. 15125 exceeds the maximum intermediate result, drop this branch.\n     |- Try 605 \/ 25 = 24.2. 24.2 is a decimal, drop this branch.\n    |- Try 55 \/ 11 = 5. Add 5 to the number set. Current number set: [5, 25], target: 32, just two numbers left.\n     |- Try 25 + 5 = 30. Evaluate 30 != 32, drop this branch.\n     |- Try 25 - 5 = 20. Evaluate 20 != 32, drop this branch.\n     |- Try 25 * 5 = 125. Evaluate 125 != 32, drop this branch.\n     |- Try 25 \/ 5 = 5. Evaluate 5 != 32, drop this branch.\n   |- Pick two numbers (25, 11) (numbers left: [55]). Try possible operations.\n    |- Try 25 + 11 = 36. Add 36 to the number set. Current number set: [36, 55], target: 32, just two numbers left.\n     |- Try 55 + 36 = 91. Evaluate 91 != 32, drop this branch.\n     |- Try 55 - 36 = 19. Evaluate 19 != 32, drop this branch.\n     |- Try 55 * 36 = 1980. Evaluate 1980 != 32, drop this branch.\n     |- Try 55 \/ 36 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 25 - 11 = 14. Add 14 to the number set. Current number set: [14, 55], target: 32, just two numbers left.\n     |- Try 55 + 14 = 69. Evaluate 69 != 32, drop this branch.\n     |- Try 55 - 14 = 41. Evaluate 41 != 32, drop this branch.\n     |- Try 55 * 14 = 770. Evaluate 770 != 32, drop this branch.\n     |- Try 55 \/ 14 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 25 * 11 = 275. Add 275 to the number set. Current number set: [275, 55], target: 32, just two numbers left.\n     |- Try 275 + 55 = 330. Evaluate 330 != 32, drop this branch.\n     |- Try 275 - 55 = 220. Evaluate 220 != 32, drop this branch.\n     |- Try 275 * 55 = 15125. 15125 exceeds the maximum intermediate result, drop this branch.\n     |- Try 275 \/ 55 = 5. Evaluate 5 != 32, drop this branch.\n    |- Try 25 \/ 11 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 44 - 11 = 33. Add 33 to the number set. Current number set: [33, 25, 11], target: 32. Options for choosing two numbers: [(33, 25), (33, 11), (25, 11)].\n   |- Pick two numbers (33, 25) (numbers left: [11]). Try possible operations.\n    |- Try 33 + 25 = 58. Add 58 to the number set. Current number set: [58, 11], target: 32, just two numbers left.\n     |- Try 58 + 11 = 69. Evaluate 69 != 32, drop this branch.\n     |- Try 58 - 11 = 47. Evaluate 47 != 32, drop this branch.\n     |- Try 58 * 11 = 638. Evaluate 638 != 32, drop this branch.\n     |- Try 58 \/ 11 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 33 - 25 = 8. Add 8 to the number set. Current number set: [8, 11], target: 32, just two numbers left.\n     |- Try 11 + 8 = 19. Evaluate 19 != 32, drop this branch.\n     |- Try 11 - 8 = 3. Evaluate 3 != 32, drop this branch.\n     |- Try 11 * 8 = 88. Evaluate 88 != 32, drop this branch.\n     |- Try 11 \/ 8 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 33 * 25 = 825. Add 825 to the number set. Current number set: [825, 11], target: 32, just two numbers left.\n     |- Try 825 + 11 = 836. Evaluate 836 != 32, drop this branch.\n     |- Try 825 - 11 = 814. Evaluate 814 != 32, drop this branch.\n     |- Try 825 * 11 = 9075. 9075 exceeds the maximum intermediate result, drop this branch.\n     |- Try 825 \/ 11 = 75. Evaluate 75 != 32, drop this branch.\n    |- Try 33 \/ 25 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (33, 11) (numbers left: [25]). Try possible operations.\n    |- Try 33 + 11 = 44. Add 44 to the number set. Current number set: [44, 25], target: 32, just two numbers left.\n     |- Try 44 + 25 = 69. Evaluate 69 != 32, drop this branch.\n     |- Try 44 - 25 = 19. Evaluate 19 != 32, drop this branch.\n     |- Try 44 * 25 = 1100. Evaluate 1100 != 32, drop this branch.\n     |- Try 44 \/ 25 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 33 - 11 = 22. Add 22 to the number set. Current number set: [22, 25], target: 32, just two numbers left.\n     |- Try 25 + 22 = 47. Evaluate 47 != 32, drop this branch.\n     |- Try 25 - 22 = 3. Evaluate 3 != 32, drop this branch.\n     |- Try 25 * 22 = 550. Evaluate 550 != 32, drop this branch.\n     |- Try 25 \/ 22 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 33 * 11 = 363. Add 363 to the number set. Current number set: [363, 25], target: 32, just two numbers left.\n     |- Try 363 + 25 = 388. Evaluate 388 != 32, drop this branch.\n     |- Try 363 - 25 = 338. Evaluate 338 != 32, drop this branch.\n     |- Try 363 * 25 = 9075. 9075 exceeds the maximum intermediate result, drop this branch.\n     |- Try 363 \/ 25 = 14.5. 14.5 is a decimal, drop this branch.\n    |- Try 33 \/ 11 = 3. Add 3 to the number set. Current number set: [3, 25], target: 32, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 32, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 32, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 32, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n   |- Pick two numbers (25, 11) (numbers left: [33]). Try possible operations.\n    |- Try 25 + 11 = 36. Add 36 to the number set. Current number set: [36, 33], target: 32, just two numbers left.\n     |- Try 36 + 33 = 69. Evaluate 69 != 32, drop this branch.\n     |- Try 36 - 33 = 3. Evaluate 3 != 32, drop this branch.\n     |- Try 36 * 33 = 1188. Evaluate 1188 != 32, drop this branch.\n     |- Try 36 \/ 33 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 - 11 = 14. Add 14 to the number set. Current number set: [14, 33], target: 32, just two numbers left.\n     |- Try 33 + 14 = 47. Evaluate 47 != 32, drop this branch.\n     |- Try 33 - 14 = 19. Evaluate 19 != 32, drop this branch.\n     |- Try 33 * 14 = 462. Evaluate 462 != 32, drop this branch.\n     |- Try 33 \/ 14 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 25 * 11 = 275. Add 275 to the number set. Current number set: [275, 33], target: 32, just two numbers left.\n     |- Try 275 + 33 = 308. Evaluate 308 != 32, drop this branch.\n     |- Try 275 - 33 = 242. Evaluate 242 != 32, drop this branch.\n     |- Try 275 * 33 = 9075. 9075 exceeds the maximum intermediate result, drop this branch.\n     |- Try 275 \/ 33 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 11 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 44 * 11 = 484. Add 484 to the number set. Current number set: [484, 25, 11], target: 32. Options for choosing two numbers: [(484, 25), (484, 11), (25, 11)].\n   |- Pick two numbers (484, 25) (numbers left: [11]). Try possible operations.\n    |- Try 484 + 25 = 509. Add 509 to the number set. Current number set: [509, 11], target: 32, just two numbers left.\n     |- Try 509 + 11 = 520. Evaluate 520 != 32, drop this branch.\n     |- Try 509 - 11 = 498. Evaluate 498 != 32, drop this branch.\n     |- Try 509 * 11 = 5599. 5599 exceeds the maximum intermediate result, drop this branch.\n     |- Try 509 \/ 11 = 46.3. 46.3 is a decimal, drop this branch.\n    |- Try 484 - 25 = 459. Add 459 to the number set. Current number set: [459, 11], target: 32, just two numbers left.\n     |- Try 459 + 11 = 470. Evaluate 470 != 32, drop this branch.\n     |- Try 459 - 11 = 448. Evaluate 448 != 32, drop this branch.\n     |- Try 459 * 11 = 5049. 5049 exceeds the maximum intermediate result, drop this branch.\n     |- Try 459 \/ 11 = 41.7. 41.7 is a decimal, drop this branch.\n    |- Try 484 * 25 = 12100. 12100 exceeds the maximum intermediate result, drop this branch.\n    |- Try 484 \/ 25 = 19.4. 19.4 is a decimal, drop this branch.\n   |- Pick two numbers (484, 11) (numbers left: [25]). Try possible operations.\n    |- Try 484 + 11 = 495. Add 495 to the number set. Current number set: [495, 25], target: 32, just two numbers left.\n     |- Try 495 + 25 = 520. Evaluate 520 != 32, drop this branch.\n     |- Try 495 - 25 = 470. Evaluate 470 != 32, drop this branch.\n     |- Try 495 * 25 = 12375. 12375 exceeds the maximum intermediate result, drop this branch.\n     |- Try 495 \/ 25 = 19.8. 19.8 is a decimal, drop this branch.\n    |- Try 484 - 11 = 473. Add 473 to the number set. Current number set: [473, 25], target: 32, just two numbers left.\n     |- Try 473 + 25 = 498. Evaluate 498 != 32, drop this branch.\n     |- Try 473 - 25 = 448. Evaluate 448 != 32, drop this branch.\n     |- Try 473 * 25 = 11825. 11825 exceeds the maximum intermediate result, drop this branch.\n     |- Try 473 \/ 25 = 18.9. 18.9 is a decimal, drop this branch.\n    |- Try 484 * 11 = 5324. 5324 exceeds the maximum intermediate result, drop this branch.\n    |- Try 484 \/ 11 = 44. Add 44 to the number set. Current number set: [44, 25], target: 32, just two numbers left.\n     |- Try 44 + 25 = 69. Evaluate 69 != 32, drop this branch.\n     |- Try 44 - 25 = 19. Evaluate 19 != 32, drop this branch.\n     |- Try 44 * 25 = 1100. Evaluate 1100 != 32, drop this branch.\n     |- Try 44 \/ 25 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (25, 11) (numbers left: [484]). Try possible operations.\n    |- Try 25 + 11 = 36. Add 36 to the number set. Current number set: [36, 484], target: 32, just two numbers left.\n     |- Try 484 + 36 = 520. Evaluate 520 != 32, drop this branch.\n     |- Try 484 - 36 = 448. Evaluate 448 != 32, drop this branch.\n     |- Try 484 * 36 = 17424. 17424 exceeds the maximum intermediate result, drop this branch.\n     |- Try 484 \/ 36 = 13.4. 13.4 is a decimal, drop this branch.\n    |- Try 25 - 11 = 14. Add 14 to the number set. Current number set: [14, 484], target: 32, just two numbers left.\n     |- Try 484 + 14 = 498. Evaluate 498 != 32, drop this branch.\n     |- Try 484 - 14 = 470. Evaluate 470 != 32, drop this branch.\n     |- Try 484 * 14 = 6776. 6776 exceeds the maximum intermediate result, drop this branch.\n     |- Try 484 \/ 14 = 34.6. 34.6 is a decimal, drop this branch.\n    |- Try 25 * 11 = 275. Add 275 to the number set. Current number set: [275, 484], target: 32, just two numbers left.\n     |- Try 484 + 275 = 759. Evaluate 759 != 32, drop this branch.\n     |- Try 484 - 275 = 209. Evaluate 209 != 32, drop this branch.\n     |- Try 484 * 275 = 133100. 133100 exceeds the maximum intermediate result, drop this branch.\n     |- Try 484 \/ 275 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 25 \/ 11 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 44 \/ 11 = 4. Add 4 to the number set. Current number set: [4, 25, 11], target: 32. Options for choosing two numbers: [(4, 25), (4, 11), (25, 11)].\n   |- Pick two numbers (4, 25) (numbers left: [11]). Try possible operations.\n    |- Try 25 + 4 = 29. Add 29 to the number set. Current number set: [29, 11], target: 32, just two numbers left.\n     |- Try 29 + 11 = 40. Evaluate 40 != 32, drop this branch.\n     |- Try 29 - 11 = 18. Evaluate 18 != 32, drop this branch.\n     |- Try 29 * 11 = 319. Evaluate 319 != 32, drop this branch.\n     |- Try 29 \/ 11 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 25 - 4 = 21. Add 21 to the number set. Current number set: [21, 11], target: 32, just two numbers left.\n     |- Try 21 + 11 = 32. Evaluate 32 == 32, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 21 + 11 = 32\nThe step before: 25 - 4 = 21\nThe first step: 44 \/ 11 = 4\n\nOutput the solution in the required format:\n<Solution>\n44 \/ 11 = 4\n25 - 4 = 21\n21 + 11 = 32\n<\/Solution>\n","item":{"nums":[11,44,25,11],"solution":["44 \/ 11 = 4","25 - 4 = 21","21 + 11 = 32"],"target":32}}
+{"instance_id":"countdown_8k_36","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [13, 30, 7, 9]\nTarget: 14","reference_output":"# Search Procedure\nInitial number set: [13, 30, 7, 9], target: 14. Options for choosing two numbers: [(13, 30), (13, 7), (13, 9), (30, 7), (30, 9), (7, 9)].\n |- Pick two numbers (13, 30) (numbers left: [7, 9]). Try possible operations.\n  |- Try 30 + 13 = 43. Add 43 to the number set. Current number set: [43, 7, 9], target: 14. Options for choosing two numbers: [(43, 7), (43, 9), (7, 9)].\n   |- Pick two numbers (43, 7) (numbers left: [9]). Try possible operations.\n    |- Try 43 + 7 = 50. Add 50 to the number set. Current number set: [50, 9], target: 14, just two numbers left.\n     |- Try 50 + 9 = 59. Evaluate 59 != 14, drop this branch.\n     |- Try 50 - 9 = 41. Evaluate 41 != 14, drop this branch.\n     |- Try 50 * 9 = 450. Evaluate 450 != 14, drop this branch.\n     |- Try 50 \/ 9 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 43 - 7 = 36. Add 36 to the number set. Current number set: [36, 9], target: 14, just two numbers left.\n     |- Try 36 + 9 = 45. Evaluate 45 != 14, drop this branch.\n     |- Try 36 - 9 = 27. Evaluate 27 != 14, drop this branch.\n     |- Try 36 * 9 = 324. Evaluate 324 != 14, drop this branch.\n     |- Try 36 \/ 9 = 4. Evaluate 4 != 14, drop this branch.\n    |- Try 43 * 7 = 301. Add 301 to the number set. Current number set: [301, 9], target: 14, just two numbers left.\n     |- Try 301 + 9 = 310. Evaluate 310 != 14, drop this branch.\n     |- Try 301 - 9 = 292. Evaluate 292 != 14, drop this branch.\n     |- Try 301 * 9 = 2709. 2709 exceeds the maximum intermediate result, drop this branch.\n     |- Try 301 \/ 9 = 33.4. 33.4 is a decimal, drop this branch.\n    |- Try 43 \/ 7 = 6.1. 6.1 is a decimal, drop this branch.\n   |- Pick two numbers (43, 9) (numbers left: [7]). Try possible operations.\n    |- Try 43 + 9 = 52. Add 52 to the number set. Current number set: [52, 7], target: 14, just two numbers left.\n     |- Try 52 + 7 = 59. Evaluate 59 != 14, drop this branch.\n     |- Try 52 - 7 = 45. Evaluate 45 != 14, drop this branch.\n     |- Try 52 * 7 = 364. Evaluate 364 != 14, drop this branch.\n     |- Try 52 \/ 7 = 7.4. 7.4 is a decimal, drop this branch.\n    |- Try 43 - 9 = 34. Add 34 to the number set. Current number set: [34, 7], target: 14, just two numbers left.\n     |- Try 34 + 7 = 41. Evaluate 41 != 14, drop this branch.\n     |- Try 34 - 7 = 27. Evaluate 27 != 14, drop this branch.\n     |- Try 34 * 7 = 238. Evaluate 238 != 14, drop this branch.\n     |- Try 34 \/ 7 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 43 * 9 = 387. Add 387 to the number set. Current number set: [387, 7], target: 14, just two numbers left.\n     |- Try 387 + 7 = 394. Evaluate 394 != 14, drop this branch.\n     |- Try 387 - 7 = 380. Evaluate 380 != 14, drop this branch.\n     |- Try 387 * 7 = 2709. 2709 exceeds the maximum intermediate result, drop this branch.\n     |- Try 387 \/ 7 = 55.3. 55.3 is a decimal, drop this branch.\n    |- Try 43 \/ 9 = 4.8. 4.8 is a decimal, drop this branch.\n   |- Pick two numbers (7, 9) (numbers left: [43]). Try possible operations.\n    |- Try 9 + 7 = 16. Add 16 to the number set. Current number set: [16, 43], target: 14, just two numbers left.\n     |- Try 43 + 16 = 59. Evaluate 59 != 14, drop this branch.\n     |- Try 43 - 16 = 27. Evaluate 27 != 14, drop this branch.\n     |- Try 43 * 16 = 688. Evaluate 688 != 14, drop this branch.\n     |- Try 43 \/ 16 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 9 - 7 = 2. Add 2 to the number set. Current number set: [2, 43], target: 14, just two numbers left.\n     |- Try 43 + 2 = 45. Evaluate 45 != 14, drop this branch.\n     |- Try 43 - 2 = 41. Evaluate 41 != 14, drop this branch.\n     |- Try 43 * 2 = 86. Evaluate 86 != 14, drop this branch.\n     |- Try 43 \/ 2 = 21.5. 21.5 is a decimal, drop this branch.\n    |- Try 9 * 7 = 63. Add 63 to the number set. Current number set: [63, 43], target: 14, just two numbers left.\n     |- Try 63 + 43 = 106. Evaluate 106 != 14, drop this branch.\n     |- Try 63 - 43 = 20. Evaluate 20 != 14, drop this branch.\n     |- Try 63 * 43 = 2709. 2709 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 43 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 9 \/ 7 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 30 - 13 = 17. Add 17 to the number set. Current number set: [17, 7, 9], target: 14. Options for choosing two numbers: [(17, 7), (17, 9), (7, 9)].\n   |- Pick two numbers (17, 7) (numbers left: [9]). Try possible operations.\n    |- Try 17 + 7 = 24. Add 24 to the number set. Current number set: [24, 9], target: 14, just two numbers left.\n     |- Try 24 + 9 = 33. Evaluate 33 != 14, drop this branch.\n     |- Try 24 - 9 = 15. Evaluate 15 != 14, drop this branch.\n     |- Try 24 * 9 = 216. Evaluate 216 != 14, drop this branch.\n     |- Try 24 \/ 9 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 17 - 7 = 10. Add 10 to the number set. Current number set: [10, 9], target: 14, just two numbers left.\n     |- Try 10 + 9 = 19. Evaluate 19 != 14, drop this branch.\n     |- Try 10 - 9 = 1. Evaluate 1 != 14, drop this branch.\n     |- Try 10 * 9 = 90. Evaluate 90 != 14, drop this branch.\n     |- Try 10 \/ 9 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 17 * 7 = 119. Add 119 to the number set. Current number set: [119, 9], target: 14, just two numbers left.\n     |- Try 119 + 9 = 128. Evaluate 128 != 14, drop this branch.\n     |- Try 119 - 9 = 110. Evaluate 110 != 14, drop this branch.\n     |- Try 119 * 9 = 1071. Evaluate 1071 != 14, drop this branch.\n     |- Try 119 \/ 9 = 13.2. 13.2 is a decimal, drop this branch.\n    |- Try 17 \/ 7 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (17, 9) (numbers left: [7]). Try possible operations.\n    |- Try 17 + 9 = 26. Add 26 to the number set. Current number set: [26, 7], target: 14, just two numbers left.\n     |- Try 26 + 7 = 33. Evaluate 33 != 14, drop this branch.\n     |- Try 26 - 7 = 19. Evaluate 19 != 14, drop this branch.\n     |- Try 26 * 7 = 182. Evaluate 182 != 14, drop this branch.\n     |- Try 26 \/ 7 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 17 - 9 = 8. Add 8 to the number set. Current number set: [8, 7], target: 14, just two numbers left.\n     |- Try 8 + 7 = 15. Evaluate 15 != 14, drop this branch.\n     |- Try 8 - 7 = 1. Evaluate 1 != 14, drop this branch.\n     |- Try 8 * 7 = 56. Evaluate 56 != 14, drop this branch.\n     |- Try 8 \/ 7 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 17 * 9 = 153. Add 153 to the number set. Current number set: [153, 7], target: 14, just two numbers left.\n     |- Try 153 + 7 = 160. Evaluate 160 != 14, drop this branch.\n     |- Try 153 - 7 = 146. Evaluate 146 != 14, drop this branch.\n     |- Try 153 * 7 = 1071. Evaluate 1071 != 14, drop this branch.\n     |- Try 153 \/ 7 = 21.9. 21.9 is a decimal, drop this branch.\n    |- Try 17 \/ 9 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (7, 9) (numbers left: [17]). Try possible operations.\n    |- Try 9 + 7 = 16. Add 16 to the number set. Current number set: [16, 17], target: 14, just two numbers left.\n     |- Try 17 + 16 = 33. Evaluate 33 != 14, drop this branch.\n     |- Try 17 - 16 = 1. Evaluate 1 != 14, drop this branch.\n     |- Try 17 * 16 = 272. Evaluate 272 != 14, drop this branch.\n     |- Try 17 \/ 16 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 9 - 7 = 2. Add 2 to the number set. Current number set: [2, 17], target: 14, just two numbers left.\n     |- Try 17 + 2 = 19. Evaluate 19 != 14, drop this branch.\n     |- Try 17 - 2 = 15. Evaluate 15 != 14, drop this branch.\n     |- Try 17 * 2 = 34. Evaluate 34 != 14, drop this branch.\n     |- Try 17 \/ 2 = 8.5. 8.5 is a decimal, drop this branch.\n    |- Try 9 * 7 = 63. Add 63 to the number set. Current number set: [63, 17], target: 14, just two numbers left.\n     |- Try 63 + 17 = 80. Evaluate 80 != 14, drop this branch.\n     |- Try 63 - 17 = 46. Evaluate 46 != 14, drop this branch.\n     |- Try 63 * 17 = 1071. Evaluate 1071 != 14, drop this branch.\n     |- Try 63 \/ 17 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 9 \/ 7 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 30 * 13 = 390. Add 390 to the number set. Current number set: [390, 7, 9], target: 14. Options for choosing two numbers: [(390, 7), (390, 9), (7, 9)].\n   |- Pick two numbers (390, 7) (numbers left: [9]). Try possible operations.\n    |- Try 390 + 7 = 397. Add 397 to the number set. Current number set: [397, 9], target: 14, just two numbers left.\n     |- Try 397 + 9 = 406. Evaluate 406 != 14, drop this branch.\n     |- Try 397 - 9 = 388. Evaluate 388 != 14, drop this branch.\n     |- Try 397 * 9 = 3573. 3573 exceeds the maximum intermediate result, drop this branch.\n     |- Try 397 \/ 9 = 44.1. 44.1 is a decimal, drop this branch.\n    |- Try 390 - 7 = 383. Add 383 to the number set. Current number set: [383, 9], target: 14, just two numbers left.\n     |- Try 383 + 9 = 392. Evaluate 392 != 14, drop this branch.\n     |- Try 383 - 9 = 374. Evaluate 374 != 14, drop this branch.\n     |- Try 383 * 9 = 3447. 3447 exceeds the maximum intermediate result, drop this branch.\n     |- Try 383 \/ 9 = 42.6. 42.6 is a decimal, drop this branch.\n    |- Try 390 * 7 = 2730. 2730 exceeds the maximum intermediate result, drop this branch.\n    |- Try 390 \/ 7 = 55.7. 55.7 is a decimal, drop this branch.\n   |- Pick two numbers (390, 9) (numbers left: [7]). Try possible operations.\n    |- Try 390 + 9 = 399. Add 399 to the number set. Current number set: [399, 7], target: 14, just two numbers left.\n     |- Try 399 + 7 = 406. Evaluate 406 != 14, drop this branch.\n     |- Try 399 - 7 = 392. Evaluate 392 != 14, drop this branch.\n     |- Try 399 * 7 = 2793. 2793 exceeds the maximum intermediate result, drop this branch.\n     |- Try 399 \/ 7 = 57. Evaluate 57 != 14, drop this branch.\n    |- Try 390 - 9 = 381. Add 381 to the number set. Current number set: [381, 7], target: 14, just two numbers left.\n     |- Try 381 + 7 = 388. Evaluate 388 != 14, drop this branch.\n     |- Try 381 - 7 = 374. Evaluate 374 != 14, drop this branch.\n     |- Try 381 * 7 = 2667. 2667 exceeds the maximum intermediate result, drop this branch.\n     |- Try 381 \/ 7 = 54.4. 54.4 is a decimal, drop this branch.\n    |- Try 390 * 9 = 3510. 3510 exceeds the maximum intermediate result, drop this branch.\n    |- Try 390 \/ 9 = 43.3. 43.3 is a decimal, drop this branch.\n   |- Pick two numbers (7, 9) (numbers left: [390]). Try possible operations.\n    |- Try 9 + 7 = 16. Add 16 to the number set. Current number set: [16, 390], target: 14, just two numbers left.\n     |- Try 390 + 16 = 406. Evaluate 406 != 14, drop this branch.\n     |- Try 390 - 16 = 374. Evaluate 374 != 14, drop this branch.\n     |- Try 390 * 16 = 6240. 6240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 390 \/ 16 = 24.4. 24.4 is a decimal, drop this branch.\n    |- Try 9 - 7 = 2. Add 2 to the number set. Current number set: [2, 390], target: 14, just two numbers left.\n     |- Try 390 + 2 = 392. Evaluate 392 != 14, drop this branch.\n     |- Try 390 - 2 = 388. Evaluate 388 != 14, drop this branch.\n     |- Try 390 * 2 = 780. Evaluate 780 != 14, drop this branch.\n     |- Try 390 \/ 2 = 195. Evaluate 195 != 14, drop this branch.\n    |- Try 9 * 7 = 63. Add 63 to the number set. Current number set: [63, 390], target: 14, just two numbers left.\n     |- Try 390 + 63 = 453. Evaluate 453 != 14, drop this branch.\n     |- Try 390 - 63 = 327. Evaluate 327 != 14, drop this branch.\n     |- Try 390 * 63 = 24570. 24570 exceeds the maximum intermediate result, drop this branch.\n     |- Try 390 \/ 63 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 9 \/ 7 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 30 \/ 13 = 2.3. 2.3 is a decimal, drop this branch.\n |- Pick two numbers (13, 7) (numbers left: [30, 9]). Try possible operations.\n  |- Try 13 + 7 = 20. Add 20 to the number set. Current number set: [20, 30, 9], target: 14. Options for choosing two numbers: [(20, 30), (20, 9), (30, 9)].\n   |- Pick two numbers (20, 30) (numbers left: [9]). Try possible operations.\n    |- Try 30 + 20 = 50. Add 50 to the number set. Current number set: [50, 9], target: 14, just two numbers left.\n     |- Try 50 + 9 = 59. Evaluate 59 != 14, drop this branch.\n     |- Try 50 - 9 = 41. Evaluate 41 != 14, drop this branch.\n     |- Try 50 * 9 = 450. Evaluate 450 != 14, drop this branch.\n     |- Try 50 \/ 9 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 30 - 20 = 10. Add 10 to the number set. Current number set: [10, 9], target: 14, just two numbers left.\n     |- Try 10 + 9 = 19. Evaluate 19 != 14, drop this branch.\n     |- Try 10 - 9 = 1. Evaluate 1 != 14, drop this branch.\n     |- Try 10 * 9 = 90. Evaluate 90 != 14, drop this branch.\n     |- Try 10 \/ 9 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 30 * 20 = 600. Add 600 to the number set. Current number set: [600, 9], target: 14, just two numbers left.\n     |- Try 600 + 9 = 609. Evaluate 609 != 14, drop this branch.\n     |- Try 600 - 9 = 591. Evaluate 591 != 14, drop this branch.\n     |- Try 600 * 9 = 5400. 5400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 600 \/ 9 = 66.7. 66.7 is a decimal, drop this branch.\n    |- Try 30 \/ 20 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (20, 9) (numbers left: [30]). Try possible operations.\n    |- Try 20 + 9 = 29. Add 29 to the number set. Current number set: [29, 30], target: 14, just two numbers left.\n     |- Try 30 + 29 = 59. Evaluate 59 != 14, drop this branch.\n     |- Try 30 - 29 = 1. Evaluate 1 != 14, drop this branch.\n     |- Try 30 * 29 = 870. Evaluate 870 != 14, drop this branch.\n     |- Try 30 \/ 29 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 20 - 9 = 11. Add 11 to the number set. Current number set: [11, 30], target: 14, just two numbers left.\n     |- Try 30 + 11 = 41. Evaluate 41 != 14, drop this branch.\n     |- Try 30 - 11 = 19. Evaluate 19 != 14, drop this branch.\n     |- Try 30 * 11 = 330. Evaluate 330 != 14, drop this branch.\n     |- Try 30 \/ 11 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 20 * 9 = 180. Add 180 to the number set. Current number set: [180, 30], target: 14, just two numbers left.\n     |- Try 180 + 30 = 210. Evaluate 210 != 14, drop this branch.\n     |- Try 180 - 30 = 150. Evaluate 150 != 14, drop this branch.\n     |- Try 180 * 30 = 5400. 5400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 180 \/ 30 = 6. Evaluate 6 != 14, drop this branch.\n    |- Try 20 \/ 9 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (30, 9) (numbers left: [20]). Try possible operations.\n    |- Try 30 + 9 = 39. Add 39 to the number set. Current number set: [39, 20], target: 14, just two numbers left.\n     |- Try 39 + 20 = 59. Evaluate 59 != 14, drop this branch.\n     |- Try 39 - 20 = 19. Evaluate 19 != 14, drop this branch.\n     |- Try 39 * 20 = 780. Evaluate 780 != 14, drop this branch.\n     |- Try 39 \/ 20 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 30 - 9 = 21. Add 21 to the number set. Current number set: [21, 20], target: 14, just two numbers left.\n     |- Try 21 + 20 = 41. Evaluate 41 != 14, drop this branch.\n     |- Try 21 - 20 = 1. Evaluate 1 != 14, drop this branch.\n     |- Try 21 * 20 = 420. Evaluate 420 != 14, drop this branch.\n     |- Try 21 \/ 20 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 30 * 9 = 270. Add 270 to the number set. Current number set: [270, 20], target: 14, just two numbers left.\n     |- Try 270 + 20 = 290. Evaluate 290 != 14, drop this branch.\n     |- Try 270 - 20 = 250. Evaluate 250 != 14, drop this branch.\n     |- Try 270 * 20 = 5400. 5400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 270 \/ 20 = 13.5. 13.5 is a decimal, drop this branch.\n    |- Try 30 \/ 9 = 3.3. 3.3 is a decimal, drop this branch.\n  |- Try 13 - 7 = 6. Add 6 to the number set. Current number set: [6, 30, 9], target: 14. Options for choosing two numbers: [(6, 30), (6, 9), (30, 9)].\n   |- Pick two numbers (6, 30) (numbers left: [9]). Try possible operations.\n    |- Try 30 + 6 = 36. Add 36 to the number set. Current number set: [36, 9], target: 14, just two numbers left.\n     |- Try 36 + 9 = 45. Evaluate 45 != 14, drop this branch.\n     |- Try 36 - 9 = 27. Evaluate 27 != 14, drop this branch.\n     |- Try 36 * 9 = 324. Evaluate 324 != 14, drop this branch.\n     |- Try 36 \/ 9 = 4. Evaluate 4 != 14, drop this branch.\n    |- Try 30 - 6 = 24. Add 24 to the number set. Current number set: [24, 9], target: 14, just two numbers left.\n     |- Try 24 + 9 = 33. Evaluate 33 != 14, drop this branch.\n     |- Try 24 - 9 = 15. Evaluate 15 != 14, drop this branch.\n     |- Try 24 * 9 = 216. Evaluate 216 != 14, drop this branch.\n     |- Try 24 \/ 9 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 30 * 6 = 180. Add 180 to the number set. Current number set: [180, 9], target: 14, just two numbers left.\n     |- Try 180 + 9 = 189. Evaluate 189 != 14, drop this branch.\n     |- Try 180 - 9 = 171. Evaluate 171 != 14, drop this branch.\n     |- Try 180 * 9 = 1620. Evaluate 1620 != 14, drop this branch.\n     |- Try 180 \/ 9 = 20. Evaluate 20 != 14, drop this branch.\n    |- Try 30 \/ 6 = 5. Add 5 to the number set. Current number set: [5, 9], target: 14, just two numbers left.\n     |- Try 9 + 5 = 14. Evaluate 14 == 14, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 9 + 5 = 14\nThe step before: 30 \/ 6 = 5\nThe first step: 13 - 7 = 6\n\nOutput the solution in the required format:\n<Solution>\n13 - 7 = 6\n30 \/ 6 = 5\n9 + 5 = 14\n<\/Solution>\n","item":{"nums":[13,30,7,9],"solution":["13 - 7 = 6","30 \/ 6 = 5","9 + 5 = 14"],"target":14}}
+{"instance_id":"countdown_8k_37","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [41, 6, 7, 16]\nTarget: 48","reference_output":"# Search Procedure\nInitial number set: [41, 6, 7, 16], target: 48. Options for choosing two numbers: [(41, 6), (41, 7), (41, 16), (6, 7), (6, 16), (7, 16)].\n |- Pick two numbers (41, 6) (numbers left: [7, 16]). Try possible operations.\n  |- Try 41 + 6 = 47. Add 47 to the number set. Current number set: [47, 7, 16], target: 48. Options for choosing two numbers: [(47, 7), (47, 16), (7, 16)].\n   |- Pick two numbers (47, 7) (numbers left: [16]). Try possible operations.\n    |- Try 47 + 7 = 54. Add 54 to the number set. Current number set: [54, 16], target: 48, just two numbers left.\n     |- Try 54 + 16 = 70. Evaluate 70 != 48, drop this branch.\n     |- Try 54 - 16 = 38. Evaluate 38 != 48, drop this branch.\n     |- Try 54 * 16 = 864. Evaluate 864 != 48, drop this branch.\n     |- Try 54 \/ 16 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 47 - 7 = 40. Add 40 to the number set. Current number set: [40, 16], target: 48, just two numbers left.\n     |- Try 40 + 16 = 56. Evaluate 56 != 48, drop this branch.\n     |- Try 40 - 16 = 24. Evaluate 24 != 48, drop this branch.\n     |- Try 40 * 16 = 640. Evaluate 640 != 48, drop this branch.\n     |- Try 40 \/ 16 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 47 * 7 = 329. Add 329 to the number set. Current number set: [329, 16], target: 48, just two numbers left.\n     |- Try 329 + 16 = 345. Evaluate 345 != 48, drop this branch.\n     |- Try 329 - 16 = 313. Evaluate 313 != 48, drop this branch.\n     |- Try 329 * 16 = 5264. 5264 exceeds the maximum intermediate result, drop this branch.\n     |- Try 329 \/ 16 = 20.6. 20.6 is a decimal, drop this branch.\n    |- Try 47 \/ 7 = 6.7. 6.7 is a decimal, drop this branch.\n   |- Pick two numbers (47, 16) (numbers left: [7]). Try possible operations.\n    |- Try 47 + 16 = 63. Add 63 to the number set. Current number set: [63, 7], target: 48, just two numbers left.\n     |- Try 63 + 7 = 70. Evaluate 70 != 48, drop this branch.\n     |- Try 63 - 7 = 56. Evaluate 56 != 48, drop this branch.\n     |- Try 63 * 7 = 441. Evaluate 441 != 48, drop this branch.\n     |- Try 63 \/ 7 = 9. Evaluate 9 != 48, drop this branch.\n    |- Try 47 - 16 = 31. Add 31 to the number set. Current number set: [31, 7], target: 48, just two numbers left.\n     |- Try 31 + 7 = 38. Evaluate 38 != 48, drop this branch.\n     |- Try 31 - 7 = 24. Evaluate 24 != 48, drop this branch.\n     |- Try 31 * 7 = 217. Evaluate 217 != 48, drop this branch.\n     |- Try 31 \/ 7 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 47 * 16 = 752. Add 752 to the number set. Current number set: [752, 7], target: 48, just two numbers left.\n     |- Try 752 + 7 = 759. Evaluate 759 != 48, drop this branch.\n     |- Try 752 - 7 = 745. Evaluate 745 != 48, drop this branch.\n     |- Try 752 * 7 = 5264. 5264 exceeds the maximum intermediate result, drop this branch.\n     |- Try 752 \/ 7 = 107.4. 107.4 is a decimal, drop this branch.\n    |- Try 47 \/ 16 = 2.9. 2.9 is a decimal, drop this branch.\n   |- Pick two numbers (7, 16) (numbers left: [47]). Try possible operations.\n    |- Try 16 + 7 = 23. Add 23 to the number set. Current number set: [23, 47], target: 48, just two numbers left.\n     |- Try 47 + 23 = 70. Evaluate 70 != 48, drop this branch.\n     |- Try 47 - 23 = 24. Evaluate 24 != 48, drop this branch.\n     |- Try 47 * 23 = 1081. Evaluate 1081 != 48, drop this branch.\n     |- Try 47 \/ 23 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 16 - 7 = 9. Add 9 to the number set. Current number set: [9, 47], target: 48, just two numbers left.\n     |- Try 47 + 9 = 56. Evaluate 56 != 48, drop this branch.\n     |- Try 47 - 9 = 38. Evaluate 38 != 48, drop this branch.\n     |- Try 47 * 9 = 423. Evaluate 423 != 48, drop this branch.\n     |- Try 47 \/ 9 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 16 * 7 = 112. Add 112 to the number set. Current number set: [112, 47], target: 48, just two numbers left.\n     |- Try 112 + 47 = 159. Evaluate 159 != 48, drop this branch.\n     |- Try 112 - 47 = 65. Evaluate 65 != 48, drop this branch.\n     |- Try 112 * 47 = 5264. 5264 exceeds the maximum intermediate result, drop this branch.\n     |- Try 112 \/ 47 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 16 \/ 7 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 41 - 6 = 35. Add 35 to the number set. Current number set: [35, 7, 16], target: 48. Options for choosing two numbers: [(35, 7), (35, 16), (7, 16)].\n   |- Pick two numbers (35, 7) (numbers left: [16]). Try possible operations.\n    |- Try 35 + 7 = 42. Add 42 to the number set. Current number set: [42, 16], target: 48, just two numbers left.\n     |- Try 42 + 16 = 58. Evaluate 58 != 48, drop this branch.\n     |- Try 42 - 16 = 26. Evaluate 26 != 48, drop this branch.\n     |- Try 42 * 16 = 672. Evaluate 672 != 48, drop this branch.\n     |- Try 42 \/ 16 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 35 - 7 = 28. Add 28 to the number set. Current number set: [28, 16], target: 48, just two numbers left.\n     |- Try 28 + 16 = 44. Evaluate 44 != 48, drop this branch.\n     |- Try 28 - 16 = 12. Evaluate 12 != 48, drop this branch.\n     |- Try 28 * 16 = 448. Evaluate 448 != 48, drop this branch.\n     |- Try 28 \/ 16 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 35 * 7 = 245. Add 245 to the number set. Current number set: [245, 16], target: 48, just two numbers left.\n     |- Try 245 + 16 = 261. Evaluate 261 != 48, drop this branch.\n     |- Try 245 - 16 = 229. Evaluate 229 != 48, drop this branch.\n     |- Try 245 * 16 = 3920. 3920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 245 \/ 16 = 15.3. 15.3 is a decimal, drop this branch.\n    |- Try 35 \/ 7 = 5. Add 5 to the number set. Current number set: [5, 16], target: 48, just two numbers left.\n     |- Try 16 + 5 = 21. Evaluate 21 != 48, drop this branch.\n     |- Try 16 - 5 = 11. Evaluate 11 != 48, drop this branch.\n     |- Try 16 * 5 = 80. Evaluate 80 != 48, drop this branch.\n     |- Try 16 \/ 5 = 3.2. 3.2 is a decimal, drop this branch.\n   |- Pick two numbers (35, 16) (numbers left: [7]). Try possible operations.\n    |- Try 35 + 16 = 51. Add 51 to the number set. Current number set: [51, 7], target: 48, just two numbers left.\n     |- Try 51 + 7 = 58. Evaluate 58 != 48, drop this branch.\n     |- Try 51 - 7 = 44. Evaluate 44 != 48, drop this branch.\n     |- Try 51 * 7 = 357. Evaluate 357 != 48, drop this branch.\n     |- Try 51 \/ 7 = 7.3. 7.3 is a decimal, drop this branch.\n    |- Try 35 - 16 = 19. Add 19 to the number set. Current number set: [19, 7], target: 48, just two numbers left.\n     |- Try 19 + 7 = 26. Evaluate 26 != 48, drop this branch.\n     |- Try 19 - 7 = 12. Evaluate 12 != 48, drop this branch.\n     |- Try 19 * 7 = 133. Evaluate 133 != 48, drop this branch.\n     |- Try 19 \/ 7 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 35 * 16 = 560. Add 560 to the number set. Current number set: [560, 7], target: 48, just two numbers left.\n     |- Try 560 + 7 = 567. Evaluate 567 != 48, drop this branch.\n     |- Try 560 - 7 = 553. Evaluate 553 != 48, drop this branch.\n     |- Try 560 * 7 = 3920. 3920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 560 \/ 7 = 80. Evaluate 80 != 48, drop this branch.\n    |- Try 35 \/ 16 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 16) (numbers left: [35]). Try possible operations.\n    |- Try 16 + 7 = 23. Add 23 to the number set. Current number set: [23, 35], target: 48, just two numbers left.\n     |- Try 35 + 23 = 58. Evaluate 58 != 48, drop this branch.\n     |- Try 35 - 23 = 12. Evaluate 12 != 48, drop this branch.\n     |- Try 35 * 23 = 805. Evaluate 805 != 48, drop this branch.\n     |- Try 35 \/ 23 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 16 - 7 = 9. Add 9 to the number set. Current number set: [9, 35], target: 48, just two numbers left.\n     |- Try 35 + 9 = 44. Evaluate 44 != 48, drop this branch.\n     |- Try 35 - 9 = 26. Evaluate 26 != 48, drop this branch.\n     |- Try 35 * 9 = 315. Evaluate 315 != 48, drop this branch.\n     |- Try 35 \/ 9 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 16 * 7 = 112. Add 112 to the number set. Current number set: [112, 35], target: 48, just two numbers left.\n     |- Try 112 + 35 = 147. Evaluate 147 != 48, drop this branch.\n     |- Try 112 - 35 = 77. Evaluate 77 != 48, drop this branch.\n     |- Try 112 * 35 = 3920. 3920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 112 \/ 35 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 16 \/ 7 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 41 * 6 = 246. Add 246 to the number set. Current number set: [246, 7, 16], target: 48. Options for choosing two numbers: [(246, 7), (246, 16), (7, 16)].\n   |- Pick two numbers (246, 7) (numbers left: [16]). Try possible operations.\n    |- Try 246 + 7 = 253. Add 253 to the number set. Current number set: [253, 16], target: 48, just two numbers left.\n     |- Try 253 + 16 = 269. Evaluate 269 != 48, drop this branch.\n     |- Try 253 - 16 = 237. Evaluate 237 != 48, drop this branch.\n     |- Try 253 * 16 = 4048. 4048 exceeds the maximum intermediate result, drop this branch.\n     |- Try 253 \/ 16 = 15.8. 15.8 is a decimal, drop this branch.\n    |- Try 246 - 7 = 239. Add 239 to the number set. Current number set: [239, 16], target: 48, just two numbers left.\n     |- Try 239 + 16 = 255. Evaluate 255 != 48, drop this branch.\n     |- Try 239 - 16 = 223. Evaluate 223 != 48, drop this branch.\n     |- Try 239 * 16 = 3824. 3824 exceeds the maximum intermediate result, drop this branch.\n     |- Try 239 \/ 16 = 14.9. 14.9 is a decimal, drop this branch.\n    |- Try 246 * 7 = 1722. Add 1722 to the number set. Current number set: [1722, 16], target: 48, just two numbers left.\n     |- Try 1722 + 16 = 1738. Evaluate 1738 != 48, drop this branch.\n     |- Try 1722 - 16 = 1706. Evaluate 1706 != 48, drop this branch.\n     |- Try 1722 * 16 = 27552. 27552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1722 \/ 16 = 107.6. 107.6 is a decimal, drop this branch.\n    |- Try 246 \/ 7 = 35.1. 35.1 is a decimal, drop this branch.\n   |- Pick two numbers (246, 16) (numbers left: [7]). Try possible operations.\n    |- Try 246 + 16 = 262. Add 262 to the number set. Current number set: [262, 7], target: 48, just two numbers left.\n     |- Try 262 + 7 = 269. Evaluate 269 != 48, drop this branch.\n     |- Try 262 - 7 = 255. Evaluate 255 != 48, drop this branch.\n     |- Try 262 * 7 = 1834. Evaluate 1834 != 48, drop this branch.\n     |- Try 262 \/ 7 = 37.4. 37.4 is a decimal, drop this branch.\n    |- Try 246 - 16 = 230. Add 230 to the number set. Current number set: [230, 7], target: 48, just two numbers left.\n     |- Try 230 + 7 = 237. Evaluate 237 != 48, drop this branch.\n     |- Try 230 - 7 = 223. Evaluate 223 != 48, drop this branch.\n     |- Try 230 * 7 = 1610. Evaluate 1610 != 48, drop this branch.\n     |- Try 230 \/ 7 = 32.9. 32.9 is a decimal, drop this branch.\n    |- Try 246 * 16 = 3936. 3936 exceeds the maximum intermediate result, drop this branch.\n    |- Try 246 \/ 16 = 15.4. 15.4 is a decimal, drop this branch.\n   |- Pick two numbers (7, 16) (numbers left: [246]). Try possible operations.\n    |- Try 16 + 7 = 23. Add 23 to the number set. Current number set: [23, 246], target: 48, just two numbers left.\n     |- Try 246 + 23 = 269. Evaluate 269 != 48, drop this branch.\n     |- Try 246 - 23 = 223. Evaluate 223 != 48, drop this branch.\n     |- Try 246 * 23 = 5658. 5658 exceeds the maximum intermediate result, drop this branch.\n     |- Try 246 \/ 23 = 10.7. 10.7 is a decimal, drop this branch.\n    |- Try 16 - 7 = 9. Add 9 to the number set. Current number set: [9, 246], target: 48, just two numbers left.\n     |- Try 246 + 9 = 255. Evaluate 255 != 48, drop this branch.\n     |- Try 246 - 9 = 237. Evaluate 237 != 48, drop this branch.\n     |- Try 246 * 9 = 2214. 2214 exceeds the maximum intermediate result, drop this branch.\n     |- Try 246 \/ 9 = 27.3. 27.3 is a decimal, drop this branch.\n    |- Try 16 * 7 = 112. Add 112 to the number set. Current number set: [112, 246], target: 48, just two numbers left.\n     |- Try 246 + 112 = 358. Evaluate 358 != 48, drop this branch.\n     |- Try 246 - 112 = 134. Evaluate 134 != 48, drop this branch.\n     |- Try 246 * 112 = 27552. 27552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 246 \/ 112 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 16 \/ 7 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 41 \/ 6 = 6.8. 6.8 is a decimal, drop this branch.\n |- Pick two numbers (41, 7) (numbers left: [6, 16]). Try possible operations.\n  |- Try 41 + 7 = 48. Add 48 to the number set. Current number set: [48, 6, 16], target: 48. Options for choosing two numbers: [(48, 6), (48, 16), (6, 16)].\n   |- Pick two numbers (48, 6) (numbers left: [16]). Try possible operations.\n    |- Try 48 + 6 = 54. Add 54 to the number set. Current number set: [54, 16], target: 48, just two numbers left.\n     |- Try 54 + 16 = 70. Evaluate 70 != 48, drop this branch.\n     |- Try 54 - 16 = 38. Evaluate 38 != 48, drop this branch.\n     |- Try 54 * 16 = 864. Evaluate 864 != 48, drop this branch.\n     |- Try 54 \/ 16 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 48 - 6 = 42. Add 42 to the number set. Current number set: [42, 16], target: 48, just two numbers left.\n     |- Try 42 + 16 = 58. Evaluate 58 != 48, drop this branch.\n     |- Try 42 - 16 = 26. Evaluate 26 != 48, drop this branch.\n     |- Try 42 * 16 = 672. Evaluate 672 != 48, drop this branch.\n     |- Try 42 \/ 16 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 48 * 6 = 288. Add 288 to the number set. Current number set: [288, 16], target: 48, just two numbers left.\n     |- Try 288 + 16 = 304. Evaluate 304 != 48, drop this branch.\n     |- Try 288 - 16 = 272. Evaluate 272 != 48, drop this branch.\n     |- Try 288 * 16 = 4608. 4608 exceeds the maximum intermediate result, drop this branch.\n     |- Try 288 \/ 16 = 18. Evaluate 18 != 48, drop this branch.\n    |- Try 48 \/ 6 = 8. Add 8 to the number set. Current number set: [8, 16], target: 48, just two numbers left.\n     |- Try 16 + 8 = 24. Evaluate 24 != 48, drop this branch.\n     |- Try 16 - 8 = 8. Evaluate 8 != 48, drop this branch.\n     |- Try 16 * 8 = 128. Evaluate 128 != 48, drop this branch.\n     |- Try 16 \/ 8 = 2. Evaluate 2 != 48, drop this branch.\n   |- Pick two numbers (48, 16) (numbers left: [6]). Try possible operations.\n    |- Try 48 + 16 = 64. Add 64 to the number set. Current number set: [64, 6], target: 48, just two numbers left.\n     |- Try 64 + 6 = 70. Evaluate 70 != 48, drop this branch.\n     |- Try 64 - 6 = 58. Evaluate 58 != 48, drop this branch.\n     |- Try 64 * 6 = 384. Evaluate 384 != 48, drop this branch.\n     |- Try 64 \/ 6 = 10.7. 10.7 is a decimal, drop this branch.\n    |- Try 48 - 16 = 32. Add 32 to the number set. Current number set: [32, 6], target: 48, just two numbers left.\n     |- Try 32 + 6 = 38. Evaluate 38 != 48, drop this branch.\n     |- Try 32 - 6 = 26. Evaluate 26 != 48, drop this branch.\n     |- Try 32 * 6 = 192. Evaluate 192 != 48, drop this branch.\n     |- Try 32 \/ 6 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 48 * 16 = 768. Add 768 to the number set. Current number set: [768, 6], target: 48, just two numbers left.\n     |- Try 768 + 6 = 774. Evaluate 774 != 48, drop this branch.\n     |- Try 768 - 6 = 762. Evaluate 762 != 48, drop this branch.\n     |- Try 768 * 6 = 4608. 4608 exceeds the maximum intermediate result, drop this branch.\n     |- Try 768 \/ 6 = 128. Evaluate 128 != 48, drop this branch.\n    |- Try 48 \/ 16 = 3. Add 3 to the number set. Current number set: [3, 6], target: 48, just two numbers left.\n     |- Try 6 + 3 = 9. Evaluate 9 != 48, drop this branch.\n     |- Try 6 - 3 = 3. Evaluate 3 != 48, drop this branch.\n     |- Try 6 * 3 = 18. Evaluate 18 != 48, drop this branch.\n     |- Try 6 \/ 3 = 2. Evaluate 2 != 48, drop this branch.\n   |- Pick two numbers (6, 16) (numbers left: [48]). Try possible operations.\n    |- Try 16 + 6 = 22. Add 22 to the number set. Current number set: [22, 48], target: 48, just two numbers left.\n     |- Try 48 + 22 = 70. Evaluate 70 != 48, drop this branch.\n     |- Try 48 - 22 = 26. Evaluate 26 != 48, drop this branch.\n     |- Try 48 * 22 = 1056. Evaluate 1056 != 48, drop this branch.\n     |- Try 48 \/ 22 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 16 - 6 = 10. Add 10 to the number set. Current number set: [10, 48], target: 48, just two numbers left.\n     |- Try 48 + 10 = 58. Evaluate 58 != 48, drop this branch.\n     |- Try 48 - 10 = 38. Evaluate 38 != 48, drop this branch.\n     |- Try 48 * 10 = 480. Evaluate 480 != 48, drop this branch.\n     |- Try 48 \/ 10 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 16 * 6 = 96. Add 96 to the number set. Current number set: [96, 48], target: 48, just two numbers left.\n     |- Try 96 + 48 = 144. Evaluate 144 != 48, drop this branch.\n     |- Try 96 - 48 = 48. Evaluate 48 == 48, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 96 - 48 = 48\nThe step before: 16 * 6 = 96\nThe first step: 41 + 7 = 48\n\nOutput the solution in the required format:\n<Solution>\n41 + 7 = 48\n16 * 6 = 96\n96 - 48 = 48\n<\/Solution>\n","item":{"nums":[41,6,7,16],"solution":["41 + 7 = 48","16 * 6 = 96","96 - 48 = 48"],"target":48}}
+{"instance_id":"countdown_8k_38","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [41, 21, 39, 25]\nTarget: 20","reference_output":"# Search Procedure\nInitial number set: [41, 21, 39, 25], target: 20. Options for choosing two numbers: [(41, 21), (41, 39), (41, 25), (21, 39), (21, 25), (39, 25)].\n |- Pick two numbers (41, 21) (numbers left: [39, 25]). Try possible operations.\n  |- Try 41 + 21 = 62. Add 62 to the number set. Current number set: [62, 39, 25], target: 20. Options for choosing two numbers: [(62, 39), (62, 25), (39, 25)].\n   |- Pick two numbers (62, 39) (numbers left: [25]). Try possible operations.\n    |- Try 62 + 39 = 101. Add 101 to the number set. Current number set: [101, 25], target: 20, just two numbers left.\n     |- Try 101 + 25 = 126. Evaluate 126 != 20, drop this branch.\n     |- Try 101 - 25 = 76. Evaluate 76 != 20, drop this branch.\n     |- Try 101 * 25 = 2525. 2525 exceeds the maximum intermediate result, drop this branch.\n     |- Try 101 \/ 25 = 4.0. 4.0 is a decimal, drop this branch.\n    |- Try 62 - 39 = 23. Add 23 to the number set. Current number set: [23, 25], target: 20, just two numbers left.\n     |- Try 25 + 23 = 48. Evaluate 48 != 20, drop this branch.\n     |- Try 25 - 23 = 2. Evaluate 2 != 20, drop this branch.\n     |- Try 25 * 23 = 575. Evaluate 575 != 20, drop this branch.\n     |- Try 25 \/ 23 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 62 * 39 = 2418. 2418 exceeds the maximum intermediate result, drop this branch.\n    |- Try 62 \/ 39 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (62, 25) (numbers left: [39]). Try possible operations.\n    |- Try 62 + 25 = 87. Add 87 to the number set. Current number set: [87, 39], target: 20, just two numbers left.\n     |- Try 87 + 39 = 126. Evaluate 126 != 20, drop this branch.\n     |- Try 87 - 39 = 48. Evaluate 48 != 20, drop this branch.\n     |- Try 87 * 39 = 3393. 3393 exceeds the maximum intermediate result, drop this branch.\n     |- Try 87 \/ 39 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 62 - 25 = 37. Add 37 to the number set. Current number set: [37, 39], target: 20, just two numbers left.\n     |- Try 39 + 37 = 76. Evaluate 76 != 20, drop this branch.\n     |- Try 39 - 37 = 2. Evaluate 2 != 20, drop this branch.\n     |- Try 39 * 37 = 1443. Evaluate 1443 != 20, drop this branch.\n     |- Try 39 \/ 37 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 62 * 25 = 1550. Add 1550 to the number set. Current number set: [1550, 39], target: 20, just two numbers left.\n     |- Try 1550 + 39 = 1589. Evaluate 1589 != 20, drop this branch.\n     |- Try 1550 - 39 = 1511. Evaluate 1511 != 20, drop this branch.\n     |- Try 1550 * 39 = 60450. 60450 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1550 \/ 39 = 39.7. 39.7 is a decimal, drop this branch.\n    |- Try 62 \/ 25 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (39, 25) (numbers left: [62]). Try possible operations.\n    |- Try 39 + 25 = 64. Add 64 to the number set. Current number set: [64, 62], target: 20, just two numbers left.\n     |- Try 64 + 62 = 126. Evaluate 126 != 20, drop this branch.\n     |- Try 64 - 62 = 2. Evaluate 2 != 20, drop this branch.\n     |- Try 64 * 62 = 3968. 3968 exceeds the maximum intermediate result, drop this branch.\n     |- Try 64 \/ 62 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 39 - 25 = 14. Add 14 to the number set. Current number set: [14, 62], target: 20, just two numbers left.\n     |- Try 62 + 14 = 76. Evaluate 76 != 20, drop this branch.\n     |- Try 62 - 14 = 48. Evaluate 48 != 20, drop this branch.\n     |- Try 62 * 14 = 868. Evaluate 868 != 20, drop this branch.\n     |- Try 62 \/ 14 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 39 * 25 = 975. Add 975 to the number set. Current number set: [975, 62], target: 20, just two numbers left.\n     |- Try 975 + 62 = 1037. Evaluate 1037 != 20, drop this branch.\n     |- Try 975 - 62 = 913. Evaluate 913 != 20, drop this branch.\n     |- Try 975 * 62 = 60450. 60450 exceeds the maximum intermediate result, drop this branch.\n     |- Try 975 \/ 62 = 15.7. 15.7 is a decimal, drop this branch.\n    |- Try 39 \/ 25 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 41 - 21 = 20. Add 20 to the number set. Current number set: [20, 39, 25], target: 20. Options for choosing two numbers: [(20, 39), (20, 25), (39, 25)].\n   |- Pick two numbers (20, 39) (numbers left: [25]). Try possible operations.\n    |- Try 39 + 20 = 59. Add 59 to the number set. Current number set: [59, 25], target: 20, just two numbers left.\n     |- Try 59 + 25 = 84. Evaluate 84 != 20, drop this branch.\n     |- Try 59 - 25 = 34. Evaluate 34 != 20, drop this branch.\n     |- Try 59 * 25 = 1475. Evaluate 1475 != 20, drop this branch.\n     |- Try 59 \/ 25 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 39 - 20 = 19. Add 19 to the number set. Current number set: [19, 25], target: 20, just two numbers left.\n     |- Try 25 + 19 = 44. Evaluate 44 != 20, drop this branch.\n     |- Try 25 - 19 = 6. Evaluate 6 != 20, drop this branch.\n     |- Try 25 * 19 = 475. Evaluate 475 != 20, drop this branch.\n     |- Try 25 \/ 19 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 39 * 20 = 780. Add 780 to the number set. Current number set: [780, 25], target: 20, just two numbers left.\n     |- Try 780 + 25 = 805. Evaluate 805 != 20, drop this branch.\n     |- Try 780 - 25 = 755. Evaluate 755 != 20, drop this branch.\n     |- Try 780 * 25 = 19500. 19500 exceeds the maximum intermediate result, drop this branch.\n     |- Try 780 \/ 25 = 31.2. 31.2 is a decimal, drop this branch.\n    |- Try 39 \/ 20 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (20, 25) (numbers left: [39]). Try possible operations.\n    |- Try 25 + 20 = 45. Add 45 to the number set. Current number set: [45, 39], target: 20, just two numbers left.\n     |- Try 45 + 39 = 84. Evaluate 84 != 20, drop this branch.\n     |- Try 45 - 39 = 6. Evaluate 6 != 20, drop this branch.\n     |- Try 45 * 39 = 1755. Evaluate 1755 != 20, drop this branch.\n     |- Try 45 \/ 39 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 - 20 = 5. Add 5 to the number set. Current number set: [5, 39], target: 20, just two numbers left.\n     |- Try 39 + 5 = 44. Evaluate 44 != 20, drop this branch.\n     |- Try 39 - 5 = 34. Evaluate 34 != 20, drop this branch.\n     |- Try 39 * 5 = 195. Evaluate 195 != 20, drop this branch.\n     |- Try 39 \/ 5 = 7.8. 7.8 is a decimal, drop this branch.\n    |- Try 25 * 20 = 500. Add 500 to the number set. Current number set: [500, 39], target: 20, just two numbers left.\n     |- Try 500 + 39 = 539. Evaluate 539 != 20, drop this branch.\n     |- Try 500 - 39 = 461. Evaluate 461 != 20, drop this branch.\n     |- Try 500 * 39 = 19500. 19500 exceeds the maximum intermediate result, drop this branch.\n     |- Try 500 \/ 39 = 12.8. 12.8 is a decimal, drop this branch.\n    |- Try 25 \/ 20 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (39, 25) (numbers left: [20]). Try possible operations.\n    |- Try 39 + 25 = 64. Add 64 to the number set. Current number set: [64, 20], target: 20, just two numbers left.\n     |- Try 64 + 20 = 84. Evaluate 84 != 20, drop this branch.\n     |- Try 64 - 20 = 44. Evaluate 44 != 20, drop this branch.\n     |- Try 64 * 20 = 1280. Evaluate 1280 != 20, drop this branch.\n     |- Try 64 \/ 20 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 39 - 25 = 14. Add 14 to the number set. Current number set: [14, 20], target: 20, just two numbers left.\n     |- Try 20 + 14 = 34. Evaluate 34 != 20, drop this branch.\n     |- Try 20 - 14 = 6. Evaluate 6 != 20, drop this branch.\n     |- Try 20 * 14 = 280. Evaluate 280 != 20, drop this branch.\n     |- Try 20 \/ 14 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 39 * 25 = 975. Add 975 to the number set. Current number set: [975, 20], target: 20, just two numbers left.\n     |- Try 975 + 20 = 995. Evaluate 995 != 20, drop this branch.\n     |- Try 975 - 20 = 955. Evaluate 955 != 20, drop this branch.\n     |- Try 975 * 20 = 19500. 19500 exceeds the maximum intermediate result, drop this branch.\n     |- Try 975 \/ 20 = 48.8. 48.8 is a decimal, drop this branch.\n    |- Try 39 \/ 25 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 41 * 21 = 861. Add 861 to the number set. Current number set: [861, 39, 25], target: 20. Options for choosing two numbers: [(861, 39), (861, 25), (39, 25)].\n   |- Pick two numbers (861, 39) (numbers left: [25]). Try possible operations.\n    |- Try 861 + 39 = 900. Add 900 to the number set. Current number set: [900, 25], target: 20, just two numbers left.\n     |- Try 900 + 25 = 925. Evaluate 925 != 20, drop this branch.\n     |- Try 900 - 25 = 875. Evaluate 875 != 20, drop this branch.\n     |- Try 900 * 25 = 22500. 22500 exceeds the maximum intermediate result, drop this branch.\n     |- Try 900 \/ 25 = 36. Evaluate 36 != 20, drop this branch.\n    |- Try 861 - 39 = 822. Add 822 to the number set. Current number set: [822, 25], target: 20, just two numbers left.\n     |- Try 822 + 25 = 847. Evaluate 847 != 20, drop this branch.\n     |- Try 822 - 25 = 797. Evaluate 797 != 20, drop this branch.\n     |- Try 822 * 25 = 20550. 20550 exceeds the maximum intermediate result, drop this branch.\n     |- Try 822 \/ 25 = 32.9. 32.9 is a decimal, drop this branch.\n    |- Try 861 * 39 = 33579. 33579 exceeds the maximum intermediate result, drop this branch.\n    |- Try 861 \/ 39 = 22.1. 22.1 is a decimal, drop this branch.\n   |- Pick two numbers (861, 25) (numbers left: [39]). Try possible operations.\n    |- Try 861 + 25 = 886. Add 886 to the number set. Current number set: [886, 39], target: 20, just two numbers left.\n     |- Try 886 + 39 = 925. Evaluate 925 != 20, drop this branch.\n     |- Try 886 - 39 = 847. Evaluate 847 != 20, drop this branch.\n     |- Try 886 * 39 = 34554. 34554 exceeds the maximum intermediate result, drop this branch.\n     |- Try 886 \/ 39 = 22.7. 22.7 is a decimal, drop this branch.\n    |- Try 861 - 25 = 836. Add 836 to the number set. Current number set: [836, 39], target: 20, just two numbers left.\n     |- Try 836 + 39 = 875. Evaluate 875 != 20, drop this branch.\n     |- Try 836 - 39 = 797. Evaluate 797 != 20, drop this branch.\n     |- Try 836 * 39 = 32604. 32604 exceeds the maximum intermediate result, drop this branch.\n     |- Try 836 \/ 39 = 21.4. 21.4 is a decimal, drop this branch.\n    |- Try 861 * 25 = 21525. 21525 exceeds the maximum intermediate result, drop this branch.\n    |- Try 861 \/ 25 = 34.4. 34.4 is a decimal, drop this branch.\n   |- Pick two numbers (39, 25) (numbers left: [861]). Try possible operations.\n    |- Try 39 + 25 = 64. Add 64 to the number set. Current number set: [64, 861], target: 20, just two numbers left.\n     |- Try 861 + 64 = 925. Evaluate 925 != 20, drop this branch.\n     |- Try 861 - 64 = 797. Evaluate 797 != 20, drop this branch.\n     |- Try 861 * 64 = 55104. 55104 exceeds the maximum intermediate result, drop this branch.\n     |- Try 861 \/ 64 = 13.5. 13.5 is a decimal, drop this branch.\n    |- Try 39 - 25 = 14. Add 14 to the number set. Current number set: [14, 861], target: 20, just two numbers left.\n     |- Try 861 + 14 = 875. Evaluate 875 != 20, drop this branch.\n     |- Try 861 - 14 = 847. Evaluate 847 != 20, drop this branch.\n     |- Try 861 * 14 = 12054. 12054 exceeds the maximum intermediate result, drop this branch.\n     |- Try 861 \/ 14 = 61.5. 61.5 is a decimal, drop this branch.\n    |- Try 39 * 25 = 975. Add 975 to the number set. Current number set: [975, 861], target: 20, just two numbers left.\n     |- Try 975 + 861 = 1836. Evaluate 1836 != 20, drop this branch.\n     |- Try 975 - 861 = 114. Evaluate 114 != 20, drop this branch.\n     |- Try 975 * 861 = 839475. 839475 exceeds the maximum intermediate result, drop this branch.\n     |- Try 975 \/ 861 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 39 \/ 25 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 41 \/ 21 = 2.0. 2.0 is a decimal, drop this branch.\n |- Pick two numbers (41, 39) (numbers left: [21, 25]). Try possible operations.\n  |- Try 41 + 39 = 80. Add 80 to the number set. Current number set: [80, 21, 25], target: 20. Options for choosing two numbers: [(80, 21), (80, 25), (21, 25)].\n   |- Pick two numbers (80, 21) (numbers left: [25]). Try possible operations.\n    |- Try 80 + 21 = 101. Add 101 to the number set. Current number set: [101, 25], target: 20, just two numbers left.\n     |- Try 101 + 25 = 126. Evaluate 126 != 20, drop this branch.\n     |- Try 101 - 25 = 76. Evaluate 76 != 20, drop this branch.\n     |- Try 101 * 25 = 2525. 2525 exceeds the maximum intermediate result, drop this branch.\n     |- Try 101 \/ 25 = 4.0. 4.0 is a decimal, drop this branch.\n    |- Try 80 - 21 = 59. Add 59 to the number set. Current number set: [59, 25], target: 20, just two numbers left.\n     |- Try 59 + 25 = 84. Evaluate 84 != 20, drop this branch.\n     |- Try 59 - 25 = 34. Evaluate 34 != 20, drop this branch.\n     |- Try 59 * 25 = 1475. Evaluate 1475 != 20, drop this branch.\n     |- Try 59 \/ 25 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 80 * 21 = 1680. Add 1680 to the number set. Current number set: [1680, 25], target: 20, just two numbers left.\n     |- Try 1680 + 25 = 1705. Evaluate 1705 != 20, drop this branch.\n     |- Try 1680 - 25 = 1655. Evaluate 1655 != 20, drop this branch.\n     |- Try 1680 * 25 = 42000. 42000 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1680 \/ 25 = 67.2. 67.2 is a decimal, drop this branch.\n    |- Try 80 \/ 21 = 3.8. 3.8 is a decimal, drop this branch.\n   |- Pick two numbers (80, 25) (numbers left: [21]). Try possible operations.\n    |- Try 80 + 25 = 105. Add 105 to the number set. Current number set: [105, 21], target: 20, just two numbers left.\n     |- Try 105 + 21 = 126. Evaluate 126 != 20, drop this branch.\n     |- Try 105 - 21 = 84. Evaluate 84 != 20, drop this branch.\n     |- Try 105 * 21 = 2205. 2205 exceeds the maximum intermediate result, drop this branch.\n     |- Try 105 \/ 21 = 5. Evaluate 5 != 20, drop this branch.\n    |- Try 80 - 25 = 55. Add 55 to the number set. Current number set: [55, 21], target: 20, just two numbers left.\n     |- Try 55 + 21 = 76. Evaluate 76 != 20, drop this branch.\n     |- Try 55 - 21 = 34. Evaluate 34 != 20, drop this branch.\n     |- Try 55 * 21 = 1155. Evaluate 1155 != 20, drop this branch.\n     |- Try 55 \/ 21 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 80 * 25 = 2000. 2000 exceeds the maximum intermediate result, drop this branch.\n    |- Try 80 \/ 25 = 3.2. 3.2 is a decimal, drop this branch.\n   |- Pick two numbers (21, 25) (numbers left: [80]). Try possible operations.\n    |- Try 25 + 21 = 46. Add 46 to the number set. Current number set: [46, 80], target: 20, just two numbers left.\n     |- Try 80 + 46 = 126. Evaluate 126 != 20, drop this branch.\n     |- Try 80 - 46 = 34. Evaluate 34 != 20, drop this branch.\n     |- Try 80 * 46 = 3680. 3680 exceeds the maximum intermediate result, drop this branch.\n     |- Try 80 \/ 46 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 21 = 4. Add 4 to the number set. Current number set: [4, 80], target: 20, just two numbers left.\n     |- Try 80 + 4 = 84. Evaluate 84 != 20, drop this branch.\n     |- Try 80 - 4 = 76. Evaluate 76 != 20, drop this branch.\n     |- Try 80 * 4 = 320. Evaluate 320 != 20, drop this branch.\n     |- Try 80 \/ 4 = 20. Evaluate 20 == 20, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 80 \/ 4 = 20\nThe step before: 25 - 21 = 4\nThe first step: 41 + 39 = 80\n\nOutput the solution in the required format:\n<Solution>\n41 + 39 = 80\n25 - 21 = 4\n80 \/ 4 = 20\n<\/Solution>\n","item":{"nums":[41,21,39,25],"solution":["41 + 39 = 80","25 - 21 = 4","80 \/ 4 = 20"],"target":20}}
+{"instance_id":"countdown_8k_39","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [12, 36, 11, 32]\nTarget: 46","reference_output":"# Search Procedure\nInitial number set: [12, 36, 11, 32], target: 46. Options for choosing two numbers: [(12, 36), (12, 11), (12, 32), (36, 11), (36, 32), (11, 32)].\n |- Pick two numbers (12, 36) (numbers left: [11, 32]). Try possible operations.\n  |- Try 36 + 12 = 48. Add 48 to the number set. Current number set: [48, 11, 32], target: 46. Options for choosing two numbers: [(48, 11), (48, 32), (11, 32)].\n   |- Pick two numbers (48, 11) (numbers left: [32]). Try possible operations.\n    |- Try 48 + 11 = 59. Add 59 to the number set. Current number set: [59, 32], target: 46, just two numbers left.\n     |- Try 59 + 32 = 91. Evaluate 91 != 46, drop this branch.\n     |- Try 59 - 32 = 27. Evaluate 27 != 46, drop this branch.\n     |- Try 59 * 32 = 1888. Evaluate 1888 != 46, drop this branch.\n     |- Try 59 \/ 32 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 48 - 11 = 37. Add 37 to the number set. Current number set: [37, 32], target: 46, just two numbers left.\n     |- Try 37 + 32 = 69. Evaluate 69 != 46, drop this branch.\n     |- Try 37 - 32 = 5. Evaluate 5 != 46, drop this branch.\n     |- Try 37 * 32 = 1184. Evaluate 1184 != 46, drop this branch.\n     |- Try 37 \/ 32 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 48 * 11 = 528. Add 528 to the number set. Current number set: [528, 32], target: 46, just two numbers left.\n     |- Try 528 + 32 = 560. Evaluate 560 != 46, drop this branch.\n     |- Try 528 - 32 = 496. Evaluate 496 != 46, drop this branch.\n     |- Try 528 * 32 = 16896. 16896 exceeds the maximum intermediate result, drop this branch.\n     |- Try 528 \/ 32 = 16.5. 16.5 is a decimal, drop this branch.\n    |- Try 48 \/ 11 = 4.4. 4.4 is a decimal, drop this branch.\n   |- Pick two numbers (48, 32) (numbers left: [11]). Try possible operations.\n    |- Try 48 + 32 = 80. Add 80 to the number set. Current number set: [80, 11], target: 46, just two numbers left.\n     |- Try 80 + 11 = 91. Evaluate 91 != 46, drop this branch.\n     |- Try 80 - 11 = 69. Evaluate 69 != 46, drop this branch.\n     |- Try 80 * 11 = 880. Evaluate 880 != 46, drop this branch.\n     |- Try 80 \/ 11 = 7.3. 7.3 is a decimal, drop this branch.\n    |- Try 48 - 32 = 16. Add 16 to the number set. Current number set: [16, 11], target: 46, just two numbers left.\n     |- Try 16 + 11 = 27. Evaluate 27 != 46, drop this branch.\n     |- Try 16 - 11 = 5. Evaluate 5 != 46, drop this branch.\n     |- Try 16 * 11 = 176. Evaluate 176 != 46, drop this branch.\n     |- Try 16 \/ 11 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 48 * 32 = 1536. Add 1536 to the number set. Current number set: [1536, 11], target: 46, just two numbers left.\n     |- Try 1536 + 11 = 1547. Evaluate 1547 != 46, drop this branch.\n     |- Try 1536 - 11 = 1525. Evaluate 1525 != 46, drop this branch.\n     |- Try 1536 * 11 = 16896. 16896 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1536 \/ 11 = 139.6. 139.6 is a decimal, drop this branch.\n    |- Try 48 \/ 32 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (11, 32) (numbers left: [48]). Try possible operations.\n    |- Try 32 + 11 = 43. Add 43 to the number set. Current number set: [43, 48], target: 46, just two numbers left.\n     |- Try 48 + 43 = 91. Evaluate 91 != 46, drop this branch.\n     |- Try 48 - 43 = 5. Evaluate 5 != 46, drop this branch.\n     |- Try 48 * 43 = 2064. 2064 exceeds the maximum intermediate result, drop this branch.\n     |- Try 48 \/ 43 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 32 - 11 = 21. Add 21 to the number set. Current number set: [21, 48], target: 46, just two numbers left.\n     |- Try 48 + 21 = 69. Evaluate 69 != 46, drop this branch.\n     |- Try 48 - 21 = 27. Evaluate 27 != 46, drop this branch.\n     |- Try 48 * 21 = 1008. Evaluate 1008 != 46, drop this branch.\n     |- Try 48 \/ 21 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 32 * 11 = 352. Add 352 to the number set. Current number set: [352, 48], target: 46, just two numbers left.\n     |- Try 352 + 48 = 400. Evaluate 400 != 46, drop this branch.\n     |- Try 352 - 48 = 304. Evaluate 304 != 46, drop this branch.\n     |- Try 352 * 48 = 16896. 16896 exceeds the maximum intermediate result, drop this branch.\n     |- Try 352 \/ 48 = 7.3. 7.3 is a decimal, drop this branch.\n    |- Try 32 \/ 11 = 2.9. 2.9 is a decimal, drop this branch.\n  |- Try 36 - 12 = 24. Add 24 to the number set. Current number set: [24, 11, 32], target: 46. Options for choosing two numbers: [(24, 11), (24, 32), (11, 32)].\n   |- Pick two numbers (24, 11) (numbers left: [32]). Try possible operations.\n    |- Try 24 + 11 = 35. Add 35 to the number set. Current number set: [35, 32], target: 46, just two numbers left.\n     |- Try 35 + 32 = 67. Evaluate 67 != 46, drop this branch.\n     |- Try 35 - 32 = 3. Evaluate 3 != 46, drop this branch.\n     |- Try 35 * 32 = 1120. Evaluate 1120 != 46, drop this branch.\n     |- Try 35 \/ 32 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 24 - 11 = 13. Add 13 to the number set. Current number set: [13, 32], target: 46, just two numbers left.\n     |- Try 32 + 13 = 45. Evaluate 45 != 46, drop this branch.\n     |- Try 32 - 13 = 19. Evaluate 19 != 46, drop this branch.\n     |- Try 32 * 13 = 416. Evaluate 416 != 46, drop this branch.\n     |- Try 32 \/ 13 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 24 * 11 = 264. Add 264 to the number set. Current number set: [264, 32], target: 46, just two numbers left.\n     |- Try 264 + 32 = 296. Evaluate 296 != 46, drop this branch.\n     |- Try 264 - 32 = 232. Evaluate 232 != 46, drop this branch.\n     |- Try 264 * 32 = 8448. 8448 exceeds the maximum intermediate result, drop this branch.\n     |- Try 264 \/ 32 = 8.2. 8.2 is a decimal, drop this branch.\n    |- Try 24 \/ 11 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (24, 32) (numbers left: [11]). Try possible operations.\n    |- Try 32 + 24 = 56. Add 56 to the number set. Current number set: [56, 11], target: 46, just two numbers left.\n     |- Try 56 + 11 = 67. Evaluate 67 != 46, drop this branch.\n     |- Try 56 - 11 = 45. Evaluate 45 != 46, drop this branch.\n     |- Try 56 * 11 = 616. Evaluate 616 != 46, drop this branch.\n     |- Try 56 \/ 11 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 32 - 24 = 8. Add 8 to the number set. Current number set: [8, 11], target: 46, just two numbers left.\n     |- Try 11 + 8 = 19. Evaluate 19 != 46, drop this branch.\n     |- Try 11 - 8 = 3. Evaluate 3 != 46, drop this branch.\n     |- Try 11 * 8 = 88. Evaluate 88 != 46, drop this branch.\n     |- Try 11 \/ 8 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 32 * 24 = 768. Add 768 to the number set. Current number set: [768, 11], target: 46, just two numbers left.\n     |- Try 768 + 11 = 779. Evaluate 779 != 46, drop this branch.\n     |- Try 768 - 11 = 757. Evaluate 757 != 46, drop this branch.\n     |- Try 768 * 11 = 8448. 8448 exceeds the maximum intermediate result, drop this branch.\n     |- Try 768 \/ 11 = 69.8. 69.8 is a decimal, drop this branch.\n    |- Try 32 \/ 24 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (11, 32) (numbers left: [24]). Try possible operations.\n    |- Try 32 + 11 = 43. Add 43 to the number set. Current number set: [43, 24], target: 46, just two numbers left.\n     |- Try 43 + 24 = 67. Evaluate 67 != 46, drop this branch.\n     |- Try 43 - 24 = 19. Evaluate 19 != 46, drop this branch.\n     |- Try 43 * 24 = 1032. Evaluate 1032 != 46, drop this branch.\n     |- Try 43 \/ 24 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 32 - 11 = 21. Add 21 to the number set. Current number set: [21, 24], target: 46, just two numbers left.\n     |- Try 24 + 21 = 45. Evaluate 45 != 46, drop this branch.\n     |- Try 24 - 21 = 3. Evaluate 3 != 46, drop this branch.\n     |- Try 24 * 21 = 504. Evaluate 504 != 46, drop this branch.\n     |- Try 24 \/ 21 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 32 * 11 = 352. Add 352 to the number set. Current number set: [352, 24], target: 46, just two numbers left.\n     |- Try 352 + 24 = 376. Evaluate 376 != 46, drop this branch.\n     |- Try 352 - 24 = 328. Evaluate 328 != 46, drop this branch.\n     |- Try 352 * 24 = 8448. 8448 exceeds the maximum intermediate result, drop this branch.\n     |- Try 352 \/ 24 = 14.7. 14.7 is a decimal, drop this branch.\n    |- Try 32 \/ 11 = 2.9. 2.9 is a decimal, drop this branch.\n  |- Try 36 * 12 = 432. Add 432 to the number set. Current number set: [432, 11, 32], target: 46. Options for choosing two numbers: [(432, 11), (432, 32), (11, 32)].\n   |- Pick two numbers (432, 11) (numbers left: [32]). Try possible operations.\n    |- Try 432 + 11 = 443. Add 443 to the number set. Current number set: [443, 32], target: 46, just two numbers left.\n     |- Try 443 + 32 = 475. Evaluate 475 != 46, drop this branch.\n     |- Try 443 - 32 = 411. Evaluate 411 != 46, drop this branch.\n     |- Try 443 * 32 = 14176. 14176 exceeds the maximum intermediate result, drop this branch.\n     |- Try 443 \/ 32 = 13.8. 13.8 is a decimal, drop this branch.\n    |- Try 432 - 11 = 421. Add 421 to the number set. Current number set: [421, 32], target: 46, just two numbers left.\n     |- Try 421 + 32 = 453. Evaluate 453 != 46, drop this branch.\n     |- Try 421 - 32 = 389. Evaluate 389 != 46, drop this branch.\n     |- Try 421 * 32 = 13472. 13472 exceeds the maximum intermediate result, drop this branch.\n     |- Try 421 \/ 32 = 13.2. 13.2 is a decimal, drop this branch.\n    |- Try 432 * 11 = 4752. 4752 exceeds the maximum intermediate result, drop this branch.\n    |- Try 432 \/ 11 = 39.3. 39.3 is a decimal, drop this branch.\n   |- Pick two numbers (432, 32) (numbers left: [11]). Try possible operations.\n    |- Try 432 + 32 = 464. Add 464 to the number set. Current number set: [464, 11], target: 46, just two numbers left.\n     |- Try 464 + 11 = 475. Evaluate 475 != 46, drop this branch.\n     |- Try 464 - 11 = 453. Evaluate 453 != 46, drop this branch.\n     |- Try 464 * 11 = 5104. 5104 exceeds the maximum intermediate result, drop this branch.\n     |- Try 464 \/ 11 = 42.2. 42.2 is a decimal, drop this branch.\n    |- Try 432 - 32 = 400. Add 400 to the number set. Current number set: [400, 11], target: 46, just two numbers left.\n     |- Try 400 + 11 = 411. Evaluate 411 != 46, drop this branch.\n     |- Try 400 - 11 = 389. Evaluate 389 != 46, drop this branch.\n     |- Try 400 * 11 = 4400. 4400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 400 \/ 11 = 36.4. 36.4 is a decimal, drop this branch.\n    |- Try 432 * 32 = 13824. 13824 exceeds the maximum intermediate result, drop this branch.\n    |- Try 432 \/ 32 = 13.5. 13.5 is a decimal, drop this branch.\n   |- Pick two numbers (11, 32) (numbers left: [432]). Try possible operations.\n    |- Try 32 + 11 = 43. Add 43 to the number set. Current number set: [43, 432], target: 46, just two numbers left.\n     |- Try 432 + 43 = 475. Evaluate 475 != 46, drop this branch.\n     |- Try 432 - 43 = 389. Evaluate 389 != 46, drop this branch.\n     |- Try 432 * 43 = 18576. 18576 exceeds the maximum intermediate result, drop this branch.\n     |- Try 432 \/ 43 = 10.0. 10.0 is a decimal, drop this branch.\n    |- Try 32 - 11 = 21. Add 21 to the number set. Current number set: [21, 432], target: 46, just two numbers left.\n     |- Try 432 + 21 = 453. Evaluate 453 != 46, drop this branch.\n     |- Try 432 - 21 = 411. Evaluate 411 != 46, drop this branch.\n     |- Try 432 * 21 = 9072. 9072 exceeds the maximum intermediate result, drop this branch.\n     |- Try 432 \/ 21 = 20.6. 20.6 is a decimal, drop this branch.\n    |- Try 32 * 11 = 352. Add 352 to the number set. Current number set: [352, 432], target: 46, just two numbers left.\n     |- Try 432 + 352 = 784. Evaluate 784 != 46, drop this branch.\n     |- Try 432 - 352 = 80. Evaluate 80 != 46, drop this branch.\n     |- Try 432 * 352 = 152064. 152064 exceeds the maximum intermediate result, drop this branch.\n     |- Try 432 \/ 352 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 32 \/ 11 = 2.9. 2.9 is a decimal, drop this branch.\n  |- Try 36 \/ 12 = 3. Add 3 to the number set. Current number set: [3, 11, 32], target: 46. Options for choosing two numbers: [(3, 11), (3, 32), (11, 32)].\n   |- Pick two numbers (3, 11) (numbers left: [32]). Try possible operations.\n    |- Try 11 + 3 = 14. Add 14 to the number set. Current number set: [14, 32], target: 46, just two numbers left.\n     |- Try 32 + 14 = 46. Evaluate 46 == 46, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 32 + 14 = 46\nThe step before: 11 + 3 = 14\nThe first step: 36 \/ 12 = 3\n\nOutput the solution in the required format:\n<Solution>\n36 \/ 12 = 3\n11 + 3 = 14\n32 + 14 = 46\n<\/Solution>\n","item":{"nums":[12,36,11,32],"solution":["36 \/ 12 = 3","11 + 3 = 14","32 + 14 = 46"],"target":46}}
+{"instance_id":"countdown_8k_40","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [4, 18, 42, 9]\nTarget: 36","reference_output":"# Search Procedure\nInitial number set: [4, 18, 42, 9], target: 36. Options for choosing two numbers: [(4, 18), (4, 42), (4, 9), (18, 42), (18, 9), (42, 9)].\n |- Pick two numbers (4, 18) (numbers left: [42, 9]). Try possible operations.\n  |- Try 18 + 4 = 22. Add 22 to the number set. Current number set: [22, 42, 9], target: 36. Options for choosing two numbers: [(22, 42), (22, 9), (42, 9)].\n   |- Pick two numbers (22, 42) (numbers left: [9]). Try possible operations.\n    |- Try 42 + 22 = 64. Add 64 to the number set. Current number set: [64, 9], target: 36, just two numbers left.\n     |- Try 64 + 9 = 73. Evaluate 73 != 36, drop this branch.\n     |- Try 64 - 9 = 55. Evaluate 55 != 36, drop this branch.\n     |- Try 64 * 9 = 576. Evaluate 576 != 36, drop this branch.\n     |- Try 64 \/ 9 = 7.1. 7.1 is a decimal, drop this branch.\n    |- Try 42 - 22 = 20. Add 20 to the number set. Current number set: [20, 9], target: 36, just two numbers left.\n     |- Try 20 + 9 = 29. Evaluate 29 != 36, drop this branch.\n     |- Try 20 - 9 = 11. Evaluate 11 != 36, drop this branch.\n     |- Try 20 * 9 = 180. Evaluate 180 != 36, drop this branch.\n     |- Try 20 \/ 9 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 42 * 22 = 924. Add 924 to the number set. Current number set: [924, 9], target: 36, just two numbers left.\n     |- Try 924 + 9 = 933. Evaluate 933 != 36, drop this branch.\n     |- Try 924 - 9 = 915. Evaluate 915 != 36, drop this branch.\n     |- Try 924 * 9 = 8316. 8316 exceeds the maximum intermediate result, drop this branch.\n     |- Try 924 \/ 9 = 102.7. 102.7 is a decimal, drop this branch.\n    |- Try 42 \/ 22 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (22, 9) (numbers left: [42]). Try possible operations.\n    |- Try 22 + 9 = 31. Add 31 to the number set. Current number set: [31, 42], target: 36, just two numbers left.\n     |- Try 42 + 31 = 73. Evaluate 73 != 36, drop this branch.\n     |- Try 42 - 31 = 11. Evaluate 11 != 36, drop this branch.\n     |- Try 42 * 31 = 1302. Evaluate 1302 != 36, drop this branch.\n     |- Try 42 \/ 31 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 22 - 9 = 13. Add 13 to the number set. Current number set: [13, 42], target: 36, just two numbers left.\n     |- Try 42 + 13 = 55. Evaluate 55 != 36, drop this branch.\n     |- Try 42 - 13 = 29. Evaluate 29 != 36, drop this branch.\n     |- Try 42 * 13 = 546. Evaluate 546 != 36, drop this branch.\n     |- Try 42 \/ 13 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 22 * 9 = 198. Add 198 to the number set. Current number set: [198, 42], target: 36, just two numbers left.\n     |- Try 198 + 42 = 240. Evaluate 240 != 36, drop this branch.\n     |- Try 198 - 42 = 156. Evaluate 156 != 36, drop this branch.\n     |- Try 198 * 42 = 8316. 8316 exceeds the maximum intermediate result, drop this branch.\n     |- Try 198 \/ 42 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 22 \/ 9 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (42, 9) (numbers left: [22]). Try possible operations.\n    |- Try 42 + 9 = 51. Add 51 to the number set. Current number set: [51, 22], target: 36, just two numbers left.\n     |- Try 51 + 22 = 73. Evaluate 73 != 36, drop this branch.\n     |- Try 51 - 22 = 29. Evaluate 29 != 36, drop this branch.\n     |- Try 51 * 22 = 1122. Evaluate 1122 != 36, drop this branch.\n     |- Try 51 \/ 22 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 42 - 9 = 33. Add 33 to the number set. Current number set: [33, 22], target: 36, just two numbers left.\n     |- Try 33 + 22 = 55. Evaluate 55 != 36, drop this branch.\n     |- Try 33 - 22 = 11. Evaluate 11 != 36, drop this branch.\n     |- Try 33 * 22 = 726. Evaluate 726 != 36, drop this branch.\n     |- Try 33 \/ 22 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 42 * 9 = 378. Add 378 to the number set. Current number set: [378, 22], target: 36, just two numbers left.\n     |- Try 378 + 22 = 400. Evaluate 400 != 36, drop this branch.\n     |- Try 378 - 22 = 356. Evaluate 356 != 36, drop this branch.\n     |- Try 378 * 22 = 8316. 8316 exceeds the maximum intermediate result, drop this branch.\n     |- Try 378 \/ 22 = 17.2. 17.2 is a decimal, drop this branch.\n    |- Try 42 \/ 9 = 4.7. 4.7 is a decimal, drop this branch.\n  |- Try 18 - 4 = 14. Add 14 to the number set. Current number set: [14, 42, 9], target: 36. Options for choosing two numbers: [(14, 42), (14, 9), (42, 9)].\n   |- Pick two numbers (14, 42) (numbers left: [9]). Try possible operations.\n    |- Try 42 + 14 = 56. Add 56 to the number set. Current number set: [56, 9], target: 36, just two numbers left.\n     |- Try 56 + 9 = 65. Evaluate 65 != 36, drop this branch.\n     |- Try 56 - 9 = 47. Evaluate 47 != 36, drop this branch.\n     |- Try 56 * 9 = 504. Evaluate 504 != 36, drop this branch.\n     |- Try 56 \/ 9 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 42 - 14 = 28. Add 28 to the number set. Current number set: [28, 9], target: 36, just two numbers left.\n     |- Try 28 + 9 = 37. Evaluate 37 != 36, drop this branch.\n     |- Try 28 - 9 = 19. Evaluate 19 != 36, drop this branch.\n     |- Try 28 * 9 = 252. Evaluate 252 != 36, drop this branch.\n     |- Try 28 \/ 9 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 42 * 14 = 588. Add 588 to the number set. Current number set: [588, 9], target: 36, just two numbers left.\n     |- Try 588 + 9 = 597. Evaluate 597 != 36, drop this branch.\n     |- Try 588 - 9 = 579. Evaluate 579 != 36, drop this branch.\n     |- Try 588 * 9 = 5292. 5292 exceeds the maximum intermediate result, drop this branch.\n     |- Try 588 \/ 9 = 65.3. 65.3 is a decimal, drop this branch.\n    |- Try 42 \/ 14 = 3. Add 3 to the number set. Current number set: [3, 9], target: 36, just two numbers left.\n     |- Try 9 + 3 = 12. Evaluate 12 != 36, drop this branch.\n     |- Try 9 - 3 = 6. Evaluate 6 != 36, drop this branch.\n     |- Try 9 * 3 = 27. Evaluate 27 != 36, drop this branch.\n     |- Try 9 \/ 3 = 3. Evaluate 3 != 36, drop this branch.\n   |- Pick two numbers (14, 9) (numbers left: [42]). Try possible operations.\n    |- Try 14 + 9 = 23. Add 23 to the number set. Current number set: [23, 42], target: 36, just two numbers left.\n     |- Try 42 + 23 = 65. Evaluate 65 != 36, drop this branch.\n     |- Try 42 - 23 = 19. Evaluate 19 != 36, drop this branch.\n     |- Try 42 * 23 = 966. Evaluate 966 != 36, drop this branch.\n     |- Try 42 \/ 23 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 14 - 9 = 5. Add 5 to the number set. Current number set: [5, 42], target: 36, just two numbers left.\n     |- Try 42 + 5 = 47. Evaluate 47 != 36, drop this branch.\n     |- Try 42 - 5 = 37. Evaluate 37 != 36, drop this branch.\n     |- Try 42 * 5 = 210. Evaluate 210 != 36, drop this branch.\n     |- Try 42 \/ 5 = 8.4. 8.4 is a decimal, drop this branch.\n    |- Try 14 * 9 = 126. Add 126 to the number set. Current number set: [126, 42], target: 36, just two numbers left.\n     |- Try 126 + 42 = 168. Evaluate 168 != 36, drop this branch.\n     |- Try 126 - 42 = 84. Evaluate 84 != 36, drop this branch.\n     |- Try 126 * 42 = 5292. 5292 exceeds the maximum intermediate result, drop this branch.\n     |- Try 126 \/ 42 = 3. Evaluate 3 != 36, drop this branch.\n    |- Try 14 \/ 9 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (42, 9) (numbers left: [14]). Try possible operations.\n    |- Try 42 + 9 = 51. Add 51 to the number set. Current number set: [51, 14], target: 36, just two numbers left.\n     |- Try 51 + 14 = 65. Evaluate 65 != 36, drop this branch.\n     |- Try 51 - 14 = 37. Evaluate 37 != 36, drop this branch.\n     |- Try 51 * 14 = 714. Evaluate 714 != 36, drop this branch.\n     |- Try 51 \/ 14 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 42 - 9 = 33. Add 33 to the number set. Current number set: [33, 14], target: 36, just two numbers left.\n     |- Try 33 + 14 = 47. Evaluate 47 != 36, drop this branch.\n     |- Try 33 - 14 = 19. Evaluate 19 != 36, drop this branch.\n     |- Try 33 * 14 = 462. Evaluate 462 != 36, drop this branch.\n     |- Try 33 \/ 14 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 42 * 9 = 378. Add 378 to the number set. Current number set: [378, 14], target: 36, just two numbers left.\n     |- Try 378 + 14 = 392. Evaluate 392 != 36, drop this branch.\n     |- Try 378 - 14 = 364. Evaluate 364 != 36, drop this branch.\n     |- Try 378 * 14 = 5292. 5292 exceeds the maximum intermediate result, drop this branch.\n     |- Try 378 \/ 14 = 27. Evaluate 27 != 36, drop this branch.\n    |- Try 42 \/ 9 = 4.7. 4.7 is a decimal, drop this branch.\n  |- Try 18 * 4 = 72. Add 72 to the number set. Current number set: [72, 42, 9], target: 36. Options for choosing two numbers: [(72, 42), (72, 9), (42, 9)].\n   |- Pick two numbers (72, 42) (numbers left: [9]). Try possible operations.\n    |- Try 72 + 42 = 114. Add 114 to the number set. Current number set: [114, 9], target: 36, just two numbers left.\n     |- Try 114 + 9 = 123. Evaluate 123 != 36, drop this branch.\n     |- Try 114 - 9 = 105. Evaluate 105 != 36, drop this branch.\n     |- Try 114 * 9 = 1026. Evaluate 1026 != 36, drop this branch.\n     |- Try 114 \/ 9 = 12.7. 12.7 is a decimal, drop this branch.\n    |- Try 72 - 42 = 30. Add 30 to the number set. Current number set: [30, 9], target: 36, just two numbers left.\n     |- Try 30 + 9 = 39. Evaluate 39 != 36, drop this branch.\n     |- Try 30 - 9 = 21. Evaluate 21 != 36, drop this branch.\n     |- Try 30 * 9 = 270. Evaluate 270 != 36, drop this branch.\n     |- Try 30 \/ 9 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 72 * 42 = 3024. 3024 exceeds the maximum intermediate result, drop this branch.\n    |- Try 72 \/ 42 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (72, 9) (numbers left: [42]). Try possible operations.\n    |- Try 72 + 9 = 81. Add 81 to the number set. Current number set: [81, 42], target: 36, just two numbers left.\n     |- Try 81 + 42 = 123. Evaluate 123 != 36, drop this branch.\n     |- Try 81 - 42 = 39. Evaluate 39 != 36, drop this branch.\n     |- Try 81 * 42 = 3402. 3402 exceeds the maximum intermediate result, drop this branch.\n     |- Try 81 \/ 42 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 72 - 9 = 63. Add 63 to the number set. Current number set: [63, 42], target: 36, just two numbers left.\n     |- Try 63 + 42 = 105. Evaluate 105 != 36, drop this branch.\n     |- Try 63 - 42 = 21. Evaluate 21 != 36, drop this branch.\n     |- Try 63 * 42 = 2646. 2646 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 42 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 72 * 9 = 648. Add 648 to the number set. Current number set: [648, 42], target: 36, just two numbers left.\n     |- Try 648 + 42 = 690. Evaluate 690 != 36, drop this branch.\n     |- Try 648 - 42 = 606. Evaluate 606 != 36, drop this branch.\n     |- Try 648 * 42 = 27216. 27216 exceeds the maximum intermediate result, drop this branch.\n     |- Try 648 \/ 42 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 72 \/ 9 = 8. Add 8 to the number set. Current number set: [8, 42], target: 36, just two numbers left.\n     |- Try 42 + 8 = 50. Evaluate 50 != 36, drop this branch.\n     |- Try 42 - 8 = 34. Evaluate 34 != 36, drop this branch.\n     |- Try 42 * 8 = 336. Evaluate 336 != 36, drop this branch.\n     |- Try 42 \/ 8 = 5.2. 5.2 is a decimal, drop this branch.\n   |- Pick two numbers (42, 9) (numbers left: [72]). Try possible operations.\n    |- Try 42 + 9 = 51. Add 51 to the number set. Current number set: [51, 72], target: 36, just two numbers left.\n     |- Try 72 + 51 = 123. Evaluate 123 != 36, drop this branch.\n     |- Try 72 - 51 = 21. Evaluate 21 != 36, drop this branch.\n     |- Try 72 * 51 = 3672. 3672 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 51 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 42 - 9 = 33. Add 33 to the number set. Current number set: [33, 72], target: 36, just two numbers left.\n     |- Try 72 + 33 = 105. Evaluate 105 != 36, drop this branch.\n     |- Try 72 - 33 = 39. Evaluate 39 != 36, drop this branch.\n     |- Try 72 * 33 = 2376. 2376 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 33 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 42 * 9 = 378. Add 378 to the number set. Current number set: [378, 72], target: 36, just two numbers left.\n     |- Try 378 + 72 = 450. Evaluate 450 != 36, drop this branch.\n     |- Try 378 - 72 = 306. Evaluate 306 != 36, drop this branch.\n     |- Try 378 * 72 = 27216. 27216 exceeds the maximum intermediate result, drop this branch.\n     |- Try 378 \/ 72 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 42 \/ 9 = 4.7. 4.7 is a decimal, drop this branch.\n  |- Try 18 \/ 4 = 4.5. 4.5 is a decimal, drop this branch.\n |- Pick two numbers (4, 42) (numbers left: [18, 9]). Try possible operations.\n  |- Try 42 + 4 = 46. Add 46 to the number set. Current number set: [46, 18, 9], target: 36. Options for choosing two numbers: [(46, 18), (46, 9), (18, 9)].\n   |- Pick two numbers (46, 18) (numbers left: [9]). Try possible operations.\n    |- Try 46 + 18 = 64. Add 64 to the number set. Current number set: [64, 9], target: 36, just two numbers left.\n     |- Try 64 + 9 = 73. Evaluate 73 != 36, drop this branch.\n     |- Try 64 - 9 = 55. Evaluate 55 != 36, drop this branch.\n     |- Try 64 * 9 = 576. Evaluate 576 != 36, drop this branch.\n     |- Try 64 \/ 9 = 7.1. 7.1 is a decimal, drop this branch.\n    |- Try 46 - 18 = 28. Add 28 to the number set. Current number set: [28, 9], target: 36, just two numbers left.\n     |- Try 28 + 9 = 37. Evaluate 37 != 36, drop this branch.\n     |- Try 28 - 9 = 19. Evaluate 19 != 36, drop this branch.\n     |- Try 28 * 9 = 252. Evaluate 252 != 36, drop this branch.\n     |- Try 28 \/ 9 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 46 * 18 = 828. Add 828 to the number set. Current number set: [828, 9], target: 36, just two numbers left.\n     |- Try 828 + 9 = 837. Evaluate 837 != 36, drop this branch.\n     |- Try 828 - 9 = 819. Evaluate 819 != 36, drop this branch.\n     |- Try 828 * 9 = 7452. 7452 exceeds the maximum intermediate result, drop this branch.\n     |- Try 828 \/ 9 = 92. Evaluate 92 != 36, drop this branch.\n    |- Try 46 \/ 18 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (46, 9) (numbers left: [18]). Try possible operations.\n    |- Try 46 + 9 = 55. Add 55 to the number set. Current number set: [55, 18], target: 36, just two numbers left.\n     |- Try 55 + 18 = 73. Evaluate 73 != 36, drop this branch.\n     |- Try 55 - 18 = 37. Evaluate 37 != 36, drop this branch.\n     |- Try 55 * 18 = 990. Evaluate 990 != 36, drop this branch.\n     |- Try 55 \/ 18 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 46 - 9 = 37. Add 37 to the number set. Current number set: [37, 18], target: 36, just two numbers left.\n     |- Try 37 + 18 = 55. Evaluate 55 != 36, drop this branch.\n     |- Try 37 - 18 = 19. Evaluate 19 != 36, drop this branch.\n     |- Try 37 * 18 = 666. Evaluate 666 != 36, drop this branch.\n     |- Try 37 \/ 18 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 46 * 9 = 414. Add 414 to the number set. Current number set: [414, 18], target: 36, just two numbers left.\n     |- Try 414 + 18 = 432. Evaluate 432 != 36, drop this branch.\n     |- Try 414 - 18 = 396. Evaluate 396 != 36, drop this branch.\n     |- Try 414 * 18 = 7452. 7452 exceeds the maximum intermediate result, drop this branch.\n     |- Try 414 \/ 18 = 23. Evaluate 23 != 36, drop this branch.\n    |- Try 46 \/ 9 = 5.1. 5.1 is a decimal, drop this branch.\n   |- Pick two numbers (18, 9) (numbers left: [46]). Try possible operations.\n    |- Try 18 + 9 = 27. Add 27 to the number set. Current number set: [27, 46], target: 36, just two numbers left.\n     |- Try 46 + 27 = 73. Evaluate 73 != 36, drop this branch.\n     |- Try 46 - 27 = 19. Evaluate 19 != 36, drop this branch.\n     |- Try 46 * 27 = 1242. Evaluate 1242 != 36, drop this branch.\n     |- Try 46 \/ 27 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 - 9 = 9. Add 9 to the number set. Current number set: [9, 46], target: 36, just two numbers left.\n     |- Try 46 + 9 = 55. Evaluate 55 != 36, drop this branch.\n     |- Try 46 - 9 = 37. Evaluate 37 != 36, drop this branch.\n     |- Try 46 * 9 = 414. Evaluate 414 != 36, drop this branch.\n     |- Try 46 \/ 9 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 18 * 9 = 162. Add 162 to the number set. Current number set: [162, 46], target: 36, just two numbers left.\n     |- Try 162 + 46 = 208. Evaluate 208 != 36, drop this branch.\n     |- Try 162 - 46 = 116. Evaluate 116 != 36, drop this branch.\n     |- Try 162 * 46 = 7452. 7452 exceeds the maximum intermediate result, drop this branch.\n     |- Try 162 \/ 46 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 18 \/ 9 = 2. Add 2 to the number set. Current number set: [2, 46], target: 36, just two numbers left.\n     |- Try 46 + 2 = 48. Evaluate 48 != 36, drop this branch.\n     |- Try 46 - 2 = 44. Evaluate 44 != 36, drop this branch.\n     |- Try 46 * 2 = 92. Evaluate 92 != 36, drop this branch.\n     |- Try 46 \/ 2 = 23. Evaluate 23 != 36, drop this branch.\n  |- Try 42 - 4 = 38. Add 38 to the number set. Current number set: [38, 18, 9], target: 36. Options for choosing two numbers: [(38, 18), (38, 9), (18, 9)].\n   |- Pick two numbers (38, 18) (numbers left: [9]). Try possible operations.\n    |- Try 38 + 18 = 56. Add 56 to the number set. Current number set: [56, 9], target: 36, just two numbers left.\n     |- Try 56 + 9 = 65. Evaluate 65 != 36, drop this branch.\n     |- Try 56 - 9 = 47. Evaluate 47 != 36, drop this branch.\n     |- Try 56 * 9 = 504. Evaluate 504 != 36, drop this branch.\n     |- Try 56 \/ 9 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 38 - 18 = 20. Add 20 to the number set. Current number set: [20, 9], target: 36, just two numbers left.\n     |- Try 20 + 9 = 29. Evaluate 29 != 36, drop this branch.\n     |- Try 20 - 9 = 11. Evaluate 11 != 36, drop this branch.\n     |- Try 20 * 9 = 180. Evaluate 180 != 36, drop this branch.\n     |- Try 20 \/ 9 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 38 * 18 = 684. Add 684 to the number set. Current number set: [684, 9], target: 36, just two numbers left.\n     |- Try 684 + 9 = 693. Evaluate 693 != 36, drop this branch.\n     |- Try 684 - 9 = 675. Evaluate 675 != 36, drop this branch.\n     |- Try 684 * 9 = 6156. 6156 exceeds the maximum intermediate result, drop this branch.\n     |- Try 684 \/ 9 = 76. Evaluate 76 != 36, drop this branch.\n    |- Try 38 \/ 18 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (38, 9) (numbers left: [18]). Try possible operations.\n    |- Try 38 + 9 = 47. Add 47 to the number set. Current number set: [47, 18], target: 36, just two numbers left.\n     |- Try 47 + 18 = 65. Evaluate 65 != 36, drop this branch.\n     |- Try 47 - 18 = 29. Evaluate 29 != 36, drop this branch.\n     |- Try 47 * 18 = 846. Evaluate 846 != 36, drop this branch.\n     |- Try 47 \/ 18 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 38 - 9 = 29. Add 29 to the number set. Current number set: [29, 18], target: 36, just two numbers left.\n     |- Try 29 + 18 = 47. Evaluate 47 != 36, drop this branch.\n     |- Try 29 - 18 = 11. Evaluate 11 != 36, drop this branch.\n     |- Try 29 * 18 = 522. Evaluate 522 != 36, drop this branch.\n     |- Try 29 \/ 18 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 38 * 9 = 342. Add 342 to the number set. Current number set: [342, 18], target: 36, just two numbers left.\n     |- Try 342 + 18 = 360. Evaluate 360 != 36, drop this branch.\n     |- Try 342 - 18 = 324. Evaluate 324 != 36, drop this branch.\n     |- Try 342 * 18 = 6156. 6156 exceeds the maximum intermediate result, drop this branch.\n     |- Try 342 \/ 18 = 19. Evaluate 19 != 36, drop this branch.\n    |- Try 38 \/ 9 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (18, 9) (numbers left: [38]). Try possible operations.\n    |- Try 18 + 9 = 27. Add 27 to the number set. Current number set: [27, 38], target: 36, just two numbers left.\n     |- Try 38 + 27 = 65. Evaluate 65 != 36, drop this branch.\n     |- Try 38 - 27 = 11. Evaluate 11 != 36, drop this branch.\n     |- Try 38 * 27 = 1026. Evaluate 1026 != 36, drop this branch.\n     |- Try 38 \/ 27 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 18 - 9 = 9. Add 9 to the number set. Current number set: [9, 38], target: 36, just two numbers left.\n     |- Try 38 + 9 = 47. Evaluate 47 != 36, drop this branch.\n     |- Try 38 - 9 = 29. Evaluate 29 != 36, drop this branch.\n     |- Try 38 * 9 = 342. Evaluate 342 != 36, drop this branch.\n     |- Try 38 \/ 9 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 * 9 = 162. Add 162 to the number set. Current number set: [162, 38], target: 36, just two numbers left.\n     |- Try 162 + 38 = 200. Evaluate 200 != 36, drop this branch.\n     |- Try 162 - 38 = 124. Evaluate 124 != 36, drop this branch.\n     |- Try 162 * 38 = 6156. 6156 exceeds the maximum intermediate result, drop this branch.\n     |- Try 162 \/ 38 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 9 = 2. Add 2 to the number set. Current number set: [2, 38], target: 36, just two numbers left.\n     |- Try 38 + 2 = 40. Evaluate 40 != 36, drop this branch.\n     |- Try 38 - 2 = 36. Evaluate 36 == 36, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 38 - 2 = 36\nThe step before: 18 \/ 9 = 2\nThe first step: 42 - 4 = 38\n\nOutput the solution in the required format:\n<Solution>\n42 - 4 = 38\n18 \/ 9 = 2\n38 - 2 = 36\n<\/Solution>\n","item":{"nums":[4,18,42,9],"solution":["42 - 4 = 38","18 \/ 9 = 2","38 - 2 = 36"],"target":36}}
+{"instance_id":"countdown_8k_41","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [16, 10, 46, 21]\nTarget: 18","reference_output":"# Search Procedure\nInitial number set: [16, 10, 46, 21], target: 18. Options for choosing two numbers: [(16, 10), (16, 46), (16, 21), (10, 46), (10, 21), (46, 21)].\n |- Pick two numbers (16, 10) (numbers left: [46, 21]). Try possible operations.\n  |- Try 16 + 10 = 26. Add 26 to the number set. Current number set: [26, 46, 21], target: 18. Options for choosing two numbers: [(26, 46), (26, 21), (46, 21)].\n   |- Pick two numbers (26, 46) (numbers left: [21]). Try possible operations.\n    |- Try 46 + 26 = 72. Add 72 to the number set. Current number set: [72, 21], target: 18, just two numbers left.\n     |- Try 72 + 21 = 93. Evaluate 93 != 18, drop this branch.\n     |- Try 72 - 21 = 51. Evaluate 51 != 18, drop this branch.\n     |- Try 72 * 21 = 1512. Evaluate 1512 != 18, drop this branch.\n     |- Try 72 \/ 21 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 46 - 26 = 20. Add 20 to the number set. Current number set: [20, 21], target: 18, just two numbers left.\n     |- Try 21 + 20 = 41. Evaluate 41 != 18, drop this branch.\n     |- Try 21 - 20 = 1. Evaluate 1 != 18, drop this branch.\n     |- Try 21 * 20 = 420. Evaluate 420 != 18, drop this branch.\n     |- Try 21 \/ 20 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 46 * 26 = 1196. Add 1196 to the number set. Current number set: [1196, 21], target: 18, just two numbers left.\n     |- Try 1196 + 21 = 1217. Evaluate 1217 != 18, drop this branch.\n     |- Try 1196 - 21 = 1175. Evaluate 1175 != 18, drop this branch.\n     |- Try 1196 * 21 = 25116. 25116 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1196 \/ 21 = 57.0. 57.0 is a decimal, drop this branch.\n    |- Try 46 \/ 26 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (26, 21) (numbers left: [46]). Try possible operations.\n    |- Try 26 + 21 = 47. Add 47 to the number set. Current number set: [47, 46], target: 18, just two numbers left.\n     |- Try 47 + 46 = 93. Evaluate 93 != 18, drop this branch.\n     |- Try 47 - 46 = 1. Evaluate 1 != 18, drop this branch.\n     |- Try 47 * 46 = 2162. 2162 exceeds the maximum intermediate result, drop this branch.\n     |- Try 47 \/ 46 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 26 - 21 = 5. Add 5 to the number set. Current number set: [5, 46], target: 18, just two numbers left.\n     |- Try 46 + 5 = 51. Evaluate 51 != 18, drop this branch.\n     |- Try 46 - 5 = 41. Evaluate 41 != 18, drop this branch.\n     |- Try 46 * 5 = 230. Evaluate 230 != 18, drop this branch.\n     |- Try 46 \/ 5 = 9.2. 9.2 is a decimal, drop this branch.\n    |- Try 26 * 21 = 546. Add 546 to the number set. Current number set: [546, 46], target: 18, just two numbers left.\n     |- Try 546 + 46 = 592. Evaluate 592 != 18, drop this branch.\n     |- Try 546 - 46 = 500. Evaluate 500 != 18, drop this branch.\n     |- Try 546 * 46 = 25116. 25116 exceeds the maximum intermediate result, drop this branch.\n     |- Try 546 \/ 46 = 11.9. 11.9 is a decimal, drop this branch.\n    |- Try 26 \/ 21 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (46, 21) (numbers left: [26]). Try possible operations.\n    |- Try 46 + 21 = 67. Add 67 to the number set. Current number set: [67, 26], target: 18, just two numbers left.\n     |- Try 67 + 26 = 93. Evaluate 93 != 18, drop this branch.\n     |- Try 67 - 26 = 41. Evaluate 41 != 18, drop this branch.\n     |- Try 67 * 26 = 1742. Evaluate 1742 != 18, drop this branch.\n     |- Try 67 \/ 26 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 46 - 21 = 25. Add 25 to the number set. Current number set: [25, 26], target: 18, just two numbers left.\n     |- Try 26 + 25 = 51. Evaluate 51 != 18, drop this branch.\n     |- Try 26 - 25 = 1. Evaluate 1 != 18, drop this branch.\n     |- Try 26 * 25 = 650. Evaluate 650 != 18, drop this branch.\n     |- Try 26 \/ 25 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 46 * 21 = 966. Add 966 to the number set. Current number set: [966, 26], target: 18, just two numbers left.\n     |- Try 966 + 26 = 992. Evaluate 992 != 18, drop this branch.\n     |- Try 966 - 26 = 940. Evaluate 940 != 18, drop this branch.\n     |- Try 966 * 26 = 25116. 25116 exceeds the maximum intermediate result, drop this branch.\n     |- Try 966 \/ 26 = 37.2. 37.2 is a decimal, drop this branch.\n    |- Try 46 \/ 21 = 2.2. 2.2 is a decimal, drop this branch.\n  |- Try 16 - 10 = 6. Add 6 to the number set. Current number set: [6, 46, 21], target: 18. Options for choosing two numbers: [(6, 46), (6, 21), (46, 21)].\n   |- Pick two numbers (6, 46) (numbers left: [21]). Try possible operations.\n    |- Try 46 + 6 = 52. Add 52 to the number set. Current number set: [52, 21], target: 18, just two numbers left.\n     |- Try 52 + 21 = 73. Evaluate 73 != 18, drop this branch.\n     |- Try 52 - 21 = 31. Evaluate 31 != 18, drop this branch.\n     |- Try 52 * 21 = 1092. Evaluate 1092 != 18, drop this branch.\n     |- Try 52 \/ 21 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 46 - 6 = 40. Add 40 to the number set. Current number set: [40, 21], target: 18, just two numbers left.\n     |- Try 40 + 21 = 61. Evaluate 61 != 18, drop this branch.\n     |- Try 40 - 21 = 19. Evaluate 19 != 18, drop this branch.\n     |- Try 40 * 21 = 840. Evaluate 840 != 18, drop this branch.\n     |- Try 40 \/ 21 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 46 * 6 = 276. Add 276 to the number set. Current number set: [276, 21], target: 18, just two numbers left.\n     |- Try 276 + 21 = 297. Evaluate 297 != 18, drop this branch.\n     |- Try 276 - 21 = 255. Evaluate 255 != 18, drop this branch.\n     |- Try 276 * 21 = 5796. 5796 exceeds the maximum intermediate result, drop this branch.\n     |- Try 276 \/ 21 = 13.1. 13.1 is a decimal, drop this branch.\n    |- Try 46 \/ 6 = 7.7. 7.7 is a decimal, drop this branch.\n   |- Pick two numbers (6, 21) (numbers left: [46]). Try possible operations.\n    |- Try 21 + 6 = 27. Add 27 to the number set. Current number set: [27, 46], target: 18, just two numbers left.\n     |- Try 46 + 27 = 73. Evaluate 73 != 18, drop this branch.\n     |- Try 46 - 27 = 19. Evaluate 19 != 18, drop this branch.\n     |- Try 46 * 27 = 1242. Evaluate 1242 != 18, drop this branch.\n     |- Try 46 \/ 27 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 21 - 6 = 15. Add 15 to the number set. Current number set: [15, 46], target: 18, just two numbers left.\n     |- Try 46 + 15 = 61. Evaluate 61 != 18, drop this branch.\n     |- Try 46 - 15 = 31. Evaluate 31 != 18, drop this branch.\n     |- Try 46 * 15 = 690. Evaluate 690 != 18, drop this branch.\n     |- Try 46 \/ 15 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 21 * 6 = 126. Add 126 to the number set. Current number set: [126, 46], target: 18, just two numbers left.\n     |- Try 126 + 46 = 172. Evaluate 172 != 18, drop this branch.\n     |- Try 126 - 46 = 80. Evaluate 80 != 18, drop this branch.\n     |- Try 126 * 46 = 5796. 5796 exceeds the maximum intermediate result, drop this branch.\n     |- Try 126 \/ 46 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 21 \/ 6 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (46, 21) (numbers left: [6]). Try possible operations.\n    |- Try 46 + 21 = 67. Add 67 to the number set. Current number set: [67, 6], target: 18, just two numbers left.\n     |- Try 67 + 6 = 73. Evaluate 73 != 18, drop this branch.\n     |- Try 67 - 6 = 61. Evaluate 61 != 18, drop this branch.\n     |- Try 67 * 6 = 402. Evaluate 402 != 18, drop this branch.\n     |- Try 67 \/ 6 = 11.2. 11.2 is a decimal, drop this branch.\n    |- Try 46 - 21 = 25. Add 25 to the number set. Current number set: [25, 6], target: 18, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 18, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 18, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 18, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 46 * 21 = 966. Add 966 to the number set. Current number set: [966, 6], target: 18, just two numbers left.\n     |- Try 966 + 6 = 972. Evaluate 972 != 18, drop this branch.\n     |- Try 966 - 6 = 960. Evaluate 960 != 18, drop this branch.\n     |- Try 966 * 6 = 5796. 5796 exceeds the maximum intermediate result, drop this branch.\n     |- Try 966 \/ 6 = 161. Evaluate 161 != 18, drop this branch.\n    |- Try 46 \/ 21 = 2.2. 2.2 is a decimal, drop this branch.\n  |- Try 16 * 10 = 160. Add 160 to the number set. Current number set: [160, 46, 21], target: 18. Options for choosing two numbers: [(160, 46), (160, 21), (46, 21)].\n   |- Pick two numbers (160, 46) (numbers left: [21]). Try possible operations.\n    |- Try 160 + 46 = 206. Add 206 to the number set. Current number set: [206, 21], target: 18, just two numbers left.\n     |- Try 206 + 21 = 227. Evaluate 227 != 18, drop this branch.\n     |- Try 206 - 21 = 185. Evaluate 185 != 18, drop this branch.\n     |- Try 206 * 21 = 4326. 4326 exceeds the maximum intermediate result, drop this branch.\n     |- Try 206 \/ 21 = 9.8. 9.8 is a decimal, drop this branch.\n    |- Try 160 - 46 = 114. Add 114 to the number set. Current number set: [114, 21], target: 18, just two numbers left.\n     |- Try 114 + 21 = 135. Evaluate 135 != 18, drop this branch.\n     |- Try 114 - 21 = 93. Evaluate 93 != 18, drop this branch.\n     |- Try 114 * 21 = 2394. 2394 exceeds the maximum intermediate result, drop this branch.\n     |- Try 114 \/ 21 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 160 * 46 = 7360. 7360 exceeds the maximum intermediate result, drop this branch.\n    |- Try 160 \/ 46 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (160, 21) (numbers left: [46]). Try possible operations.\n    |- Try 160 + 21 = 181. Add 181 to the number set. Current number set: [181, 46], target: 18, just two numbers left.\n     |- Try 181 + 46 = 227. Evaluate 227 != 18, drop this branch.\n     |- Try 181 - 46 = 135. Evaluate 135 != 18, drop this branch.\n     |- Try 181 * 46 = 8326. 8326 exceeds the maximum intermediate result, drop this branch.\n     |- Try 181 \/ 46 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 160 - 21 = 139. Add 139 to the number set. Current number set: [139, 46], target: 18, just two numbers left.\n     |- Try 139 + 46 = 185. Evaluate 185 != 18, drop this branch.\n     |- Try 139 - 46 = 93. Evaluate 93 != 18, drop this branch.\n     |- Try 139 * 46 = 6394. 6394 exceeds the maximum intermediate result, drop this branch.\n     |- Try 139 \/ 46 = 3.0. 3.0 is a decimal, drop this branch.\n    |- Try 160 * 21 = 3360. 3360 exceeds the maximum intermediate result, drop this branch.\n    |- Try 160 \/ 21 = 7.6. 7.6 is a decimal, drop this branch.\n   |- Pick two numbers (46, 21) (numbers left: [160]). Try possible operations.\n    |- Try 46 + 21 = 67. Add 67 to the number set. Current number set: [67, 160], target: 18, just two numbers left.\n     |- Try 160 + 67 = 227. Evaluate 227 != 18, drop this branch.\n     |- Try 160 - 67 = 93. Evaluate 93 != 18, drop this branch.\n     |- Try 160 * 67 = 10720. 10720 exceeds the maximum intermediate result, drop this branch.\n     |- Try 160 \/ 67 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 46 - 21 = 25. Add 25 to the number set. Current number set: [25, 160], target: 18, just two numbers left.\n     |- Try 160 + 25 = 185. Evaluate 185 != 18, drop this branch.\n     |- Try 160 - 25 = 135. Evaluate 135 != 18, drop this branch.\n     |- Try 160 * 25 = 4000. 4000 exceeds the maximum intermediate result, drop this branch.\n     |- Try 160 \/ 25 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 46 * 21 = 966. Add 966 to the number set. Current number set: [966, 160], target: 18, just two numbers left.\n     |- Try 966 + 160 = 1126. Evaluate 1126 != 18, drop this branch.\n     |- Try 966 - 160 = 806. Evaluate 806 != 18, drop this branch.\n     |- Try 966 * 160 = 154560. 154560 exceeds the maximum intermediate result, drop this branch.\n     |- Try 966 \/ 160 = 6.0. 6.0 is a decimal, drop this branch.\n    |- Try 46 \/ 21 = 2.2. 2.2 is a decimal, drop this branch.\n  |- Try 16 \/ 10 = 1.6. 1.6 is a decimal, drop this branch.\n |- Pick two numbers (16, 46) (numbers left: [10, 21]). Try possible operations.\n  |- Try 46 + 16 = 62. Add 62 to the number set. Current number set: [62, 10, 21], target: 18. Options for choosing two numbers: [(62, 10), (62, 21), (10, 21)].\n   |- Pick two numbers (62, 10) (numbers left: [21]). Try possible operations.\n    |- Try 62 + 10 = 72. Add 72 to the number set. Current number set: [72, 21], target: 18, just two numbers left.\n     |- Try 72 + 21 = 93. Evaluate 93 != 18, drop this branch.\n     |- Try 72 - 21 = 51. Evaluate 51 != 18, drop this branch.\n     |- Try 72 * 21 = 1512. Evaluate 1512 != 18, drop this branch.\n     |- Try 72 \/ 21 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 62 - 10 = 52. Add 52 to the number set. Current number set: [52, 21], target: 18, just two numbers left.\n     |- Try 52 + 21 = 73. Evaluate 73 != 18, drop this branch.\n     |- Try 52 - 21 = 31. Evaluate 31 != 18, drop this branch.\n     |- Try 52 * 21 = 1092. Evaluate 1092 != 18, drop this branch.\n     |- Try 52 \/ 21 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 62 * 10 = 620. Add 620 to the number set. Current number set: [620, 21], target: 18, just two numbers left.\n     |- Try 620 + 21 = 641. Evaluate 641 != 18, drop this branch.\n     |- Try 620 - 21 = 599. Evaluate 599 != 18, drop this branch.\n     |- Try 620 * 21 = 13020. 13020 exceeds the maximum intermediate result, drop this branch.\n     |- Try 620 \/ 21 = 29.5. 29.5 is a decimal, drop this branch.\n    |- Try 62 \/ 10 = 6.2. 6.2 is a decimal, drop this branch.\n   |- Pick two numbers (62, 21) (numbers left: [10]). Try possible operations.\n    |- Try 62 + 21 = 83. Add 83 to the number set. Current number set: [83, 10], target: 18, just two numbers left.\n     |- Try 83 + 10 = 93. Evaluate 93 != 18, drop this branch.\n     |- Try 83 - 10 = 73. Evaluate 73 != 18, drop this branch.\n     |- Try 83 * 10 = 830. Evaluate 830 != 18, drop this branch.\n     |- Try 83 \/ 10 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 62 - 21 = 41. Add 41 to the number set. Current number set: [41, 10], target: 18, just two numbers left.\n     |- Try 41 + 10 = 51. Evaluate 51 != 18, drop this branch.\n     |- Try 41 - 10 = 31. Evaluate 31 != 18, drop this branch.\n     |- Try 41 * 10 = 410. Evaluate 410 != 18, drop this branch.\n     |- Try 41 \/ 10 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 62 * 21 = 1302. Add 1302 to the number set. Current number set: [1302, 10], target: 18, just two numbers left.\n     |- Try 1302 + 10 = 1312. Evaluate 1312 != 18, drop this branch.\n     |- Try 1302 - 10 = 1292. Evaluate 1292 != 18, drop this branch.\n     |- Try 1302 * 10 = 13020. 13020 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1302 \/ 10 = 130.2. 130.2 is a decimal, drop this branch.\n    |- Try 62 \/ 21 = 3.0. 3.0 is a decimal, drop this branch.\n   |- Pick two numbers (10, 21) (numbers left: [62]). Try possible operations.\n    |- Try 21 + 10 = 31. Add 31 to the number set. Current number set: [31, 62], target: 18, just two numbers left.\n     |- Try 62 + 31 = 93. Evaluate 93 != 18, drop this branch.\n     |- Try 62 - 31 = 31. Evaluate 31 != 18, drop this branch.\n     |- Try 62 * 31 = 1922. Evaluate 1922 != 18, drop this branch.\n     |- Try 62 \/ 31 = 2. Evaluate 2 != 18, drop this branch.\n    |- Try 21 - 10 = 11. Add 11 to the number set. Current number set: [11, 62], target: 18, just two numbers left.\n     |- Try 62 + 11 = 73. Evaluate 73 != 18, drop this branch.\n     |- Try 62 - 11 = 51. Evaluate 51 != 18, drop this branch.\n     |- Try 62 * 11 = 682. Evaluate 682 != 18, drop this branch.\n     |- Try 62 \/ 11 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 21 * 10 = 210. Add 210 to the number set. Current number set: [210, 62], target: 18, just two numbers left.\n     |- Try 210 + 62 = 272. Evaluate 272 != 18, drop this branch.\n     |- Try 210 - 62 = 148. Evaluate 148 != 18, drop this branch.\n     |- Try 210 * 62 = 13020. 13020 exceeds the maximum intermediate result, drop this branch.\n     |- Try 210 \/ 62 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 21 \/ 10 = 2.1. 2.1 is a decimal, drop this branch.\n  |- Try 46 - 16 = 30. Add 30 to the number set. Current number set: [30, 10, 21], target: 18. Options for choosing two numbers: [(30, 10), (30, 21), (10, 21)].\n   |- Pick two numbers (30, 10) (numbers left: [21]). Try possible operations.\n    |- Try 30 + 10 = 40. Add 40 to the number set. Current number set: [40, 21], target: 18, just two numbers left.\n     |- Try 40 + 21 = 61. Evaluate 61 != 18, drop this branch.\n     |- Try 40 - 21 = 19. Evaluate 19 != 18, drop this branch.\n     |- Try 40 * 21 = 840. Evaluate 840 != 18, drop this branch.\n     |- Try 40 \/ 21 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 30 - 10 = 20. Add 20 to the number set. Current number set: [20, 21], target: 18, just two numbers left.\n     |- Try 21 + 20 = 41. Evaluate 41 != 18, drop this branch.\n     |- Try 21 - 20 = 1. Evaluate 1 != 18, drop this branch.\n     |- Try 21 * 20 = 420. Evaluate 420 != 18, drop this branch.\n     |- Try 21 \/ 20 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 30 * 10 = 300. Add 300 to the number set. Current number set: [300, 21], target: 18, just two numbers left.\n     |- Try 300 + 21 = 321. Evaluate 321 != 18, drop this branch.\n     |- Try 300 - 21 = 279. Evaluate 279 != 18, drop this branch.\n     |- Try 300 * 21 = 6300. 6300 exceeds the maximum intermediate result, drop this branch.\n     |- Try 300 \/ 21 = 14.3. 14.3 is a decimal, drop this branch.\n    |- Try 30 \/ 10 = 3. Add 3 to the number set. Current number set: [3, 21], target: 18, just two numbers left.\n     |- Try 21 + 3 = 24. Evaluate 24 != 18, drop this branch.\n     |- Try 21 - 3 = 18. Evaluate 18 == 18, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 21 - 3 = 18\nThe step before: 30 \/ 10 = 3\nThe first step: 46 - 16 = 30\n\nOutput the solution in the required format:\n<Solution>\n46 - 16 = 30\n30 \/ 10 = 3\n21 - 3 = 18\n<\/Solution>\n","item":{"nums":[16,10,46,21],"solution":["46 - 16 = 30","30 \/ 10 = 3","21 - 3 = 18"],"target":18}}
+{"instance_id":"countdown_8k_42","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [48, 12, 8, 1]\nTarget: 13","reference_output":"# Search Procedure\nInitial number set: [48, 12, 8, 1], target: 13. Options for choosing two numbers: [(48, 12), (48, 8), (48, 1), (12, 8), (12, 1), (8, 1)].\n |- Pick two numbers (48, 12) (numbers left: [8, 1]). Try possible operations.\n  |- Try 48 + 12 = 60. Add 60 to the number set. Current number set: [60, 8, 1], target: 13. Options for choosing two numbers: [(60, 8), (60, 1), (8, 1)].\n   |- Pick two numbers (60, 8) (numbers left: [1]). Try possible operations.\n    |- Try 60 + 8 = 68. Add 68 to the number set. Current number set: [68, 1], target: 13, just two numbers left.\n     |- Try 68 + 1 = 69. Evaluate 69 != 13, drop this branch.\n     |- Try 68 - 1 = 67. Evaluate 67 != 13, drop this branch.\n     |- Try 68 * 1 = 68. Evaluate 68 != 13, drop this branch.\n     |- Try 68 \/ 1 = 68. Evaluate 68 != 13, drop this branch.\n    |- Try 60 - 8 = 52. Add 52 to the number set. Current number set: [52, 1], target: 13, just two numbers left.\n     |- Try 52 + 1 = 53. Evaluate 53 != 13, drop this branch.\n     |- Try 52 - 1 = 51. Evaluate 51 != 13, drop this branch.\n     |- Try 52 * 1 = 52. Evaluate 52 != 13, drop this branch.\n     |- Try 52 \/ 1 = 52. Evaluate 52 != 13, drop this branch.\n    |- Try 60 * 8 = 480. Add 480 to the number set. Current number set: [480, 1], target: 13, just two numbers left.\n     |- Try 480 + 1 = 481. Evaluate 481 != 13, drop this branch.\n     |- Try 480 - 1 = 479. Evaluate 479 != 13, drop this branch.\n     |- Try 480 * 1 = 480. Evaluate 480 != 13, drop this branch.\n     |- Try 480 \/ 1 = 480. Evaluate 480 != 13, drop this branch.\n    |- Try 60 \/ 8 = 7.5. 7.5 is a decimal, drop this branch.\n   |- Pick two numbers (60, 1) (numbers left: [8]). Try possible operations.\n    |- Try 60 + 1 = 61. Add 61 to the number set. Current number set: [61, 8], target: 13, just two numbers left.\n     |- Try 61 + 8 = 69. Evaluate 69 != 13, drop this branch.\n     |- Try 61 - 8 = 53. Evaluate 53 != 13, drop this branch.\n     |- Try 61 * 8 = 488. Evaluate 488 != 13, drop this branch.\n     |- Try 61 \/ 8 = 7.6. 7.6 is a decimal, drop this branch.\n    |- Try 60 - 1 = 59. Add 59 to the number set. Current number set: [59, 8], target: 13, just two numbers left.\n     |- Try 59 + 8 = 67. Evaluate 67 != 13, drop this branch.\n     |- Try 59 - 8 = 51. Evaluate 51 != 13, drop this branch.\n     |- Try 59 * 8 = 472. Evaluate 472 != 13, drop this branch.\n     |- Try 59 \/ 8 = 7.4. 7.4 is a decimal, drop this branch.\n    |- Try 60 * 1 = 60. Add 60 to the number set. Current number set: [60, 8], target: 13, just two numbers left.\n     |- Try 60 + 8 = 68. Evaluate 68 != 13, drop this branch.\n     |- Try 60 - 8 = 52. Evaluate 52 != 13, drop this branch.\n     |- Try 60 * 8 = 480. Evaluate 480 != 13, drop this branch.\n     |- Try 60 \/ 8 = 7.5. 7.5 is a decimal, drop this branch.\n    |- Try 60 \/ 1 = 60. Add 60 to the number set. Current number set: [60, 8], target: 13, just two numbers left.\n     |- Try 60 + 8 = 68. Evaluate 68 != 13, drop this branch.\n     |- Try 60 - 8 = 52. Evaluate 52 != 13, drop this branch.\n     |- Try 60 * 8 = 480. Evaluate 480 != 13, drop this branch.\n     |- Try 60 \/ 8 = 7.5. 7.5 is a decimal, drop this branch.\n   |- Pick two numbers (8, 1) (numbers left: [60]). Try possible operations.\n    |- Try 8 + 1 = 9. Add 9 to the number set. Current number set: [9, 60], target: 13, just two numbers left.\n     |- Try 60 + 9 = 69. Evaluate 69 != 13, drop this branch.\n     |- Try 60 - 9 = 51. Evaluate 51 != 13, drop this branch.\n     |- Try 60 * 9 = 540. Evaluate 540 != 13, drop this branch.\n     |- Try 60 \/ 9 = 6.7. 6.7 is a decimal, drop this branch.\n    |- Try 8 - 1 = 7. Add 7 to the number set. Current number set: [7, 60], target: 13, just two numbers left.\n     |- Try 60 + 7 = 67. Evaluate 67 != 13, drop this branch.\n     |- Try 60 - 7 = 53. Evaluate 53 != 13, drop this branch.\n     |- Try 60 * 7 = 420. Evaluate 420 != 13, drop this branch.\n     |- Try 60 \/ 7 = 8.6. 8.6 is a decimal, drop this branch.\n    |- Try 8 * 1 = 8. Add 8 to the number set. Current number set: [8, 60], target: 13, just two numbers left.\n     |- Try 60 + 8 = 68. Evaluate 68 != 13, drop this branch.\n     |- Try 60 - 8 = 52. Evaluate 52 != 13, drop this branch.\n     |- Try 60 * 8 = 480. Evaluate 480 != 13, drop this branch.\n     |- Try 60 \/ 8 = 7.5. 7.5 is a decimal, drop this branch.\n    |- Try 8 \/ 1 = 8. Add 8 to the number set. Current number set: [8, 60], target: 13, just two numbers left.\n     |- Try 60 + 8 = 68. Evaluate 68 != 13, drop this branch.\n     |- Try 60 - 8 = 52. Evaluate 52 != 13, drop this branch.\n     |- Try 60 * 8 = 480. Evaluate 480 != 13, drop this branch.\n     |- Try 60 \/ 8 = 7.5. 7.5 is a decimal, drop this branch.\n  |- Try 48 - 12 = 36. Add 36 to the number set. Current number set: [36, 8, 1], target: 13. Options for choosing two numbers: [(36, 8), (36, 1), (8, 1)].\n   |- Pick two numbers (36, 8) (numbers left: [1]). Try possible operations.\n    |- Try 36 + 8 = 44. Add 44 to the number set. Current number set: [44, 1], target: 13, just two numbers left.\n     |- Try 44 + 1 = 45. Evaluate 45 != 13, drop this branch.\n     |- Try 44 - 1 = 43. Evaluate 43 != 13, drop this branch.\n     |- Try 44 * 1 = 44. Evaluate 44 != 13, drop this branch.\n     |- Try 44 \/ 1 = 44. Evaluate 44 != 13, drop this branch.\n    |- Try 36 - 8 = 28. Add 28 to the number set. Current number set: [28, 1], target: 13, just two numbers left.\n     |- Try 28 + 1 = 29. Evaluate 29 != 13, drop this branch.\n     |- Try 28 - 1 = 27. Evaluate 27 != 13, drop this branch.\n     |- Try 28 * 1 = 28. Evaluate 28 != 13, drop this branch.\n     |- Try 28 \/ 1 = 28. Evaluate 28 != 13, drop this branch.\n    |- Try 36 * 8 = 288. Add 288 to the number set. Current number set: [288, 1], target: 13, just two numbers left.\n     |- Try 288 + 1 = 289. Evaluate 289 != 13, drop this branch.\n     |- Try 288 - 1 = 287. Evaluate 287 != 13, drop this branch.\n     |- Try 288 * 1 = 288. Evaluate 288 != 13, drop this branch.\n     |- Try 288 \/ 1 = 288. Evaluate 288 != 13, drop this branch.\n    |- Try 36 \/ 8 = 4.5. 4.5 is a decimal, drop this branch.\n   |- Pick two numbers (36, 1) (numbers left: [8]). Try possible operations.\n    |- Try 36 + 1 = 37. Add 37 to the number set. Current number set: [37, 8], target: 13, just two numbers left.\n     |- Try 37 + 8 = 45. Evaluate 45 != 13, drop this branch.\n     |- Try 37 - 8 = 29. Evaluate 29 != 13, drop this branch.\n     |- Try 37 * 8 = 296. Evaluate 296 != 13, drop this branch.\n     |- Try 37 \/ 8 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 36 - 1 = 35. Add 35 to the number set. Current number set: [35, 8], target: 13, just two numbers left.\n     |- Try 35 + 8 = 43. Evaluate 43 != 13, drop this branch.\n     |- Try 35 - 8 = 27. Evaluate 27 != 13, drop this branch.\n     |- Try 35 * 8 = 280. Evaluate 280 != 13, drop this branch.\n     |- Try 35 \/ 8 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 36 * 1 = 36. Add 36 to the number set. Current number set: [36, 8], target: 13, just two numbers left.\n     |- Try 36 + 8 = 44. Evaluate 44 != 13, drop this branch.\n     |- Try 36 - 8 = 28. Evaluate 28 != 13, drop this branch.\n     |- Try 36 * 8 = 288. Evaluate 288 != 13, drop this branch.\n     |- Try 36 \/ 8 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 36 \/ 1 = 36. Add 36 to the number set. Current number set: [36, 8], target: 13, just two numbers left.\n     |- Try 36 + 8 = 44. Evaluate 44 != 13, drop this branch.\n     |- Try 36 - 8 = 28. Evaluate 28 != 13, drop this branch.\n     |- Try 36 * 8 = 288. Evaluate 288 != 13, drop this branch.\n     |- Try 36 \/ 8 = 4.5. 4.5 is a decimal, drop this branch.\n   |- Pick two numbers (8, 1) (numbers left: [36]). Try possible operations.\n    |- Try 8 + 1 = 9. Add 9 to the number set. Current number set: [9, 36], target: 13, just two numbers left.\n     |- Try 36 + 9 = 45. Evaluate 45 != 13, drop this branch.\n     |- Try 36 - 9 = 27. Evaluate 27 != 13, drop this branch.\n     |- Try 36 * 9 = 324. Evaluate 324 != 13, drop this branch.\n     |- Try 36 \/ 9 = 4. Evaluate 4 != 13, drop this branch.\n    |- Try 8 - 1 = 7. Add 7 to the number set. Current number set: [7, 36], target: 13, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 13, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 != 13, drop this branch.\n     |- Try 36 * 7 = 252. Evaluate 252 != 13, drop this branch.\n     |- Try 36 \/ 7 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 8 * 1 = 8. Add 8 to the number set. Current number set: [8, 36], target: 13, just two numbers left.\n     |- Try 36 + 8 = 44. Evaluate 44 != 13, drop this branch.\n     |- Try 36 - 8 = 28. Evaluate 28 != 13, drop this branch.\n     |- Try 36 * 8 = 288. Evaluate 288 != 13, drop this branch.\n     |- Try 36 \/ 8 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 8 \/ 1 = 8. Add 8 to the number set. Current number set: [8, 36], target: 13, just two numbers left.\n     |- Try 36 + 8 = 44. Evaluate 44 != 13, drop this branch.\n     |- Try 36 - 8 = 28. Evaluate 28 != 13, drop this branch.\n     |- Try 36 * 8 = 288. Evaluate 288 != 13, drop this branch.\n     |- Try 36 \/ 8 = 4.5. 4.5 is a decimal, drop this branch.\n  |- Try 48 * 12 = 576. Add 576 to the number set. Current number set: [576, 8, 1], target: 13. Options for choosing two numbers: [(576, 8), (576, 1), (8, 1)].\n   |- Pick two numbers (576, 8) (numbers left: [1]). Try possible operations.\n    |- Try 576 + 8 = 584. Add 584 to the number set. Current number set: [584, 1], target: 13, just two numbers left.\n     |- Try 584 + 1 = 585. Evaluate 585 != 13, drop this branch.\n     |- Try 584 - 1 = 583. Evaluate 583 != 13, drop this branch.\n     |- Try 584 * 1 = 584. Evaluate 584 != 13, drop this branch.\n     |- Try 584 \/ 1 = 584. Evaluate 584 != 13, drop this branch.\n    |- Try 576 - 8 = 568. Add 568 to the number set. Current number set: [568, 1], target: 13, just two numbers left.\n     |- Try 568 + 1 = 569. Evaluate 569 != 13, drop this branch.\n     |- Try 568 - 1 = 567. Evaluate 567 != 13, drop this branch.\n     |- Try 568 * 1 = 568. Evaluate 568 != 13, drop this branch.\n     |- Try 568 \/ 1 = 568. Evaluate 568 != 13, drop this branch.\n    |- Try 576 * 8 = 4608. 4608 exceeds the maximum intermediate result, drop this branch.\n    |- Try 576 \/ 8 = 72. Add 72 to the number set. Current number set: [72, 1], target: 13, just two numbers left.\n     |- Try 72 + 1 = 73. Evaluate 73 != 13, drop this branch.\n     |- Try 72 - 1 = 71. Evaluate 71 != 13, drop this branch.\n     |- Try 72 * 1 = 72. Evaluate 72 != 13, drop this branch.\n     |- Try 72 \/ 1 = 72. Evaluate 72 != 13, drop this branch.\n   |- Pick two numbers (576, 1) (numbers left: [8]). Try possible operations.\n    |- Try 576 + 1 = 577. Add 577 to the number set. Current number set: [577, 8], target: 13, just two numbers left.\n     |- Try 577 + 8 = 585. Evaluate 585 != 13, drop this branch.\n     |- Try 577 - 8 = 569. Evaluate 569 != 13, drop this branch.\n     |- Try 577 * 8 = 4616. 4616 exceeds the maximum intermediate result, drop this branch.\n     |- Try 577 \/ 8 = 72.1. 72.1 is a decimal, drop this branch.\n    |- Try 576 - 1 = 575. Add 575 to the number set. Current number set: [575, 8], target: 13, just two numbers left.\n     |- Try 575 + 8 = 583. Evaluate 583 != 13, drop this branch.\n     |- Try 575 - 8 = 567. Evaluate 567 != 13, drop this branch.\n     |- Try 575 * 8 = 4600. 4600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 575 \/ 8 = 71.9. 71.9 is a decimal, drop this branch.\n    |- Try 576 * 1 = 576. Add 576 to the number set. Current number set: [576, 8], target: 13, just two numbers left.\n     |- Try 576 + 8 = 584. Evaluate 584 != 13, drop this branch.\n     |- Try 576 - 8 = 568. Evaluate 568 != 13, drop this branch.\n     |- Try 576 * 8 = 4608. 4608 exceeds the maximum intermediate result, drop this branch.\n     |- Try 576 \/ 8 = 72. Evaluate 72 != 13, drop this branch.\n    |- Try 576 \/ 1 = 576. Add 576 to the number set. Current number set: [576, 8], target: 13, just two numbers left.\n     |- Try 576 + 8 = 584. Evaluate 584 != 13, drop this branch.\n     |- Try 576 - 8 = 568. Evaluate 568 != 13, drop this branch.\n     |- Try 576 * 8 = 4608. 4608 exceeds the maximum intermediate result, drop this branch.\n     |- Try 576 \/ 8 = 72. Evaluate 72 != 13, drop this branch.\n   |- Pick two numbers (8, 1) (numbers left: [576]). Try possible operations.\n    |- Try 8 + 1 = 9. Add 9 to the number set. Current number set: [9, 576], target: 13, just two numbers left.\n     |- Try 576 + 9 = 585. Evaluate 585 != 13, drop this branch.\n     |- Try 576 - 9 = 567. Evaluate 567 != 13, drop this branch.\n     |- Try 576 * 9 = 5184. 5184 exceeds the maximum intermediate result, drop this branch.\n     |- Try 576 \/ 9 = 64. Evaluate 64 != 13, drop this branch.\n    |- Try 8 - 1 = 7. Add 7 to the number set. Current number set: [7, 576], target: 13, just two numbers left.\n     |- Try 576 + 7 = 583. Evaluate 583 != 13, drop this branch.\n     |- Try 576 - 7 = 569. Evaluate 569 != 13, drop this branch.\n     |- Try 576 * 7 = 4032. 4032 exceeds the maximum intermediate result, drop this branch.\n     |- Try 576 \/ 7 = 82.3. 82.3 is a decimal, drop this branch.\n    |- Try 8 * 1 = 8. Add 8 to the number set. Current number set: [8, 576], target: 13, just two numbers left.\n     |- Try 576 + 8 = 584. Evaluate 584 != 13, drop this branch.\n     |- Try 576 - 8 = 568. Evaluate 568 != 13, drop this branch.\n     |- Try 576 * 8 = 4608. 4608 exceeds the maximum intermediate result, drop this branch.\n     |- Try 576 \/ 8 = 72. Evaluate 72 != 13, drop this branch.\n    |- Try 8 \/ 1 = 8. Add 8 to the number set. Current number set: [8, 576], target: 13, just two numbers left.\n     |- Try 576 + 8 = 584. Evaluate 584 != 13, drop this branch.\n     |- Try 576 - 8 = 568. Evaluate 568 != 13, drop this branch.\n     |- Try 576 * 8 = 4608. 4608 exceeds the maximum intermediate result, drop this branch.\n     |- Try 576 \/ 8 = 72. Evaluate 72 != 13, drop this branch.\n  |- Try 48 \/ 12 = 4. Add 4 to the number set. Current number set: [4, 8, 1], target: 13. Options for choosing two numbers: [(4, 8), (4, 1), (8, 1)].\n   |- Pick two numbers (4, 8) (numbers left: [1]). Try possible operations.\n    |- Try 8 + 4 = 12. Add 12 to the number set. Current number set: [12, 1], target: 13, just two numbers left.\n     |- Try 12 + 1 = 13. Evaluate 13 == 13, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 12 + 1 = 13\nThe step before: 8 + 4 = 12\nThe first step: 48 \/ 12 = 4\n\nOutput the solution in the required format:\n<Solution>\n48 \/ 12 = 4\n8 + 4 = 12\n12 + 1 = 13\n<\/Solution>\n","item":{"nums":[48,12,8,1],"solution":["48 \/ 12 = 4","8 + 4 = 12","12 + 1 = 13"],"target":13}}
+{"instance_id":"countdown_8k_43","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [1, 3, 1, 16]\nTarget: 42","reference_output":"# Search Procedure\nInitial number set: [1, 3, 1, 16], target: 42. Options for choosing two numbers: [(1, 3), (1, 1), (1, 16), (3, 1), (3, 16), (1, 16)].\n |- Pick two numbers (1, 3) (numbers left: [1, 16]). Try possible operations.\n  |- Try 3 + 1 = 4. Add 4 to the number set. Current number set: [4, 1, 16], target: 42. Options for choosing two numbers: [(4, 1), (4, 16), (1, 16)].\n   |- Pick two numbers (4, 1) (numbers left: [16]). Try possible operations.\n    |- Try 4 + 1 = 5. Add 5 to the number set. Current number set: [5, 16], target: 42, just two numbers left.\n     |- Try 16 + 5 = 21. Evaluate 21 != 42, drop this branch.\n     |- Try 16 - 5 = 11. Evaluate 11 != 42, drop this branch.\n     |- Try 16 * 5 = 80. Evaluate 80 != 42, drop this branch.\n     |- Try 16 \/ 5 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 4 - 1 = 3. Add 3 to the number set. Current number set: [3, 16], target: 42, just two numbers left.\n     |- Try 16 + 3 = 19. Evaluate 19 != 42, drop this branch.\n     |- Try 16 - 3 = 13. Evaluate 13 != 42, drop this branch.\n     |- Try 16 * 3 = 48. Evaluate 48 != 42, drop this branch.\n     |- Try 16 \/ 3 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 4 * 1 = 4. Add 4 to the number set. Current number set: [4, 16], target: 42, just two numbers left.\n     |- Try 16 + 4 = 20. Evaluate 20 != 42, drop this branch.\n     |- Try 16 - 4 = 12. Evaluate 12 != 42, drop this branch.\n     |- Try 16 * 4 = 64. Evaluate 64 != 42, drop this branch.\n     |- Try 16 \/ 4 = 4. Evaluate 4 != 42, drop this branch.\n    |- Try 4 \/ 1 = 4. Add 4 to the number set. Current number set: [4, 16], target: 42, just two numbers left.\n     |- Try 16 + 4 = 20. Evaluate 20 != 42, drop this branch.\n     |- Try 16 - 4 = 12. Evaluate 12 != 42, drop this branch.\n     |- Try 16 * 4 = 64. Evaluate 64 != 42, drop this branch.\n     |- Try 16 \/ 4 = 4. Evaluate 4 != 42, drop this branch.\n   |- Pick two numbers (4, 16) (numbers left: [1]). Try possible operations.\n    |- Try 16 + 4 = 20. Add 20 to the number set. Current number set: [20, 1], target: 42, just two numbers left.\n     |- Try 20 + 1 = 21. Evaluate 21 != 42, drop this branch.\n     |- Try 20 - 1 = 19. Evaluate 19 != 42, drop this branch.\n     |- Try 20 * 1 = 20. Evaluate 20 != 42, drop this branch.\n     |- Try 20 \/ 1 = 20. Evaluate 20 != 42, drop this branch.\n    |- Try 16 - 4 = 12. Add 12 to the number set. Current number set: [12, 1], target: 42, just two numbers left.\n     |- Try 12 + 1 = 13. Evaluate 13 != 42, drop this branch.\n     |- Try 12 - 1 = 11. Evaluate 11 != 42, drop this branch.\n     |- Try 12 * 1 = 12. Evaluate 12 != 42, drop this branch.\n     |- Try 12 \/ 1 = 12. Evaluate 12 != 42, drop this branch.\n    |- Try 16 * 4 = 64. Add 64 to the number set. Current number set: [64, 1], target: 42, just two numbers left.\n     |- Try 64 + 1 = 65. Evaluate 65 != 42, drop this branch.\n     |- Try 64 - 1 = 63. Evaluate 63 != 42, drop this branch.\n     |- Try 64 * 1 = 64. Evaluate 64 != 42, drop this branch.\n     |- Try 64 \/ 1 = 64. Evaluate 64 != 42, drop this branch.\n    |- Try 16 \/ 4 = 4. Add 4 to the number set. Current number set: [4, 1], target: 42, just two numbers left.\n     |- Try 4 + 1 = 5. Evaluate 5 != 42, drop this branch.\n     |- Try 4 - 1 = 3. Evaluate 3 != 42, drop this branch.\n     |- Try 4 * 1 = 4. Evaluate 4 != 42, drop this branch.\n     |- Try 4 \/ 1 = 4. Evaluate 4 != 42, drop this branch.\n   |- Pick two numbers (1, 16) (numbers left: [4]). Try possible operations.\n    |- Try 16 + 1 = 17. Add 17 to the number set. Current number set: [17, 4], target: 42, just two numbers left.\n     |- Try 17 + 4 = 21. Evaluate 21 != 42, drop this branch.\n     |- Try 17 - 4 = 13. Evaluate 13 != 42, drop this branch.\n     |- Try 17 * 4 = 68. Evaluate 68 != 42, drop this branch.\n     |- Try 17 \/ 4 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 16 - 1 = 15. Add 15 to the number set. Current number set: [15, 4], target: 42, just two numbers left.\n     |- Try 15 + 4 = 19. Evaluate 19 != 42, drop this branch.\n     |- Try 15 - 4 = 11. Evaluate 11 != 42, drop this branch.\n     |- Try 15 * 4 = 60. Evaluate 60 != 42, drop this branch.\n     |- Try 15 \/ 4 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 16 * 1 = 16. Add 16 to the number set. Current number set: [16, 4], target: 42, just two numbers left.\n     |- Try 16 + 4 = 20. Evaluate 20 != 42, drop this branch.\n     |- Try 16 - 4 = 12. Evaluate 12 != 42, drop this branch.\n     |- Try 16 * 4 = 64. Evaluate 64 != 42, drop this branch.\n     |- Try 16 \/ 4 = 4. Evaluate 4 != 42, drop this branch.\n    |- Try 16 \/ 1 = 16. Add 16 to the number set. Current number set: [16, 4], target: 42, just two numbers left.\n     |- Try 16 + 4 = 20. Evaluate 20 != 42, drop this branch.\n     |- Try 16 - 4 = 12. Evaluate 12 != 42, drop this branch.\n     |- Try 16 * 4 = 64. Evaluate 64 != 42, drop this branch.\n     |- Try 16 \/ 4 = 4. Evaluate 4 != 42, drop this branch.\n  |- Try 3 - 1 = 2. Add 2 to the number set. Current number set: [2, 1, 16], target: 42. Options for choosing two numbers: [(2, 1), (2, 16), (1, 16)].\n   |- Pick two numbers (2, 1) (numbers left: [16]). Try possible operations.\n    |- Try 2 + 1 = 3. Add 3 to the number set. Current number set: [3, 16], target: 42, just two numbers left.\n     |- Try 16 + 3 = 19. Evaluate 19 != 42, drop this branch.\n     |- Try 16 - 3 = 13. Evaluate 13 != 42, drop this branch.\n     |- Try 16 * 3 = 48. Evaluate 48 != 42, drop this branch.\n     |- Try 16 \/ 3 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 2 - 1 = 1. Add 1 to the number set. Current number set: [1, 16], target: 42, just two numbers left.\n     |- Try 16 + 1 = 17. Evaluate 17 != 42, drop this branch.\n     |- Try 16 - 1 = 15. Evaluate 15 != 42, drop this branch.\n     |- Try 16 * 1 = 16. Evaluate 16 != 42, drop this branch.\n     |- Try 16 \/ 1 = 16. Evaluate 16 != 42, drop this branch.\n    |- Try 2 * 1 = 2. Add 2 to the number set. Current number set: [2, 16], target: 42, just two numbers left.\n     |- Try 16 + 2 = 18. Evaluate 18 != 42, drop this branch.\n     |- Try 16 - 2 = 14. Evaluate 14 != 42, drop this branch.\n     |- Try 16 * 2 = 32. Evaluate 32 != 42, drop this branch.\n     |- Try 16 \/ 2 = 8. Evaluate 8 != 42, drop this branch.\n    |- Try 2 \/ 1 = 2. Add 2 to the number set. Current number set: [2, 16], target: 42, just two numbers left.\n     |- Try 16 + 2 = 18. Evaluate 18 != 42, drop this branch.\n     |- Try 16 - 2 = 14. Evaluate 14 != 42, drop this branch.\n     |- Try 16 * 2 = 32. Evaluate 32 != 42, drop this branch.\n     |- Try 16 \/ 2 = 8. Evaluate 8 != 42, drop this branch.\n   |- Pick two numbers (2, 16) (numbers left: [1]). Try possible operations.\n    |- Try 16 + 2 = 18. Add 18 to the number set. Current number set: [18, 1], target: 42, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 42, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 42, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 42, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 42, drop this branch.\n    |- Try 16 - 2 = 14. Add 14 to the number set. Current number set: [14, 1], target: 42, just two numbers left.\n     |- Try 14 + 1 = 15. Evaluate 15 != 42, drop this branch.\n     |- Try 14 - 1 = 13. Evaluate 13 != 42, drop this branch.\n     |- Try 14 * 1 = 14. Evaluate 14 != 42, drop this branch.\n     |- Try 14 \/ 1 = 14. Evaluate 14 != 42, drop this branch.\n    |- Try 16 * 2 = 32. Add 32 to the number set. Current number set: [32, 1], target: 42, just two numbers left.\n     |- Try 32 + 1 = 33. Evaluate 33 != 42, drop this branch.\n     |- Try 32 - 1 = 31. Evaluate 31 != 42, drop this branch.\n     |- Try 32 * 1 = 32. Evaluate 32 != 42, drop this branch.\n     |- Try 32 \/ 1 = 32. Evaluate 32 != 42, drop this branch.\n    |- Try 16 \/ 2 = 8. Add 8 to the number set. Current number set: [8, 1], target: 42, just two numbers left.\n     |- Try 8 + 1 = 9. Evaluate 9 != 42, drop this branch.\n     |- Try 8 - 1 = 7. Evaluate 7 != 42, drop this branch.\n     |- Try 8 * 1 = 8. Evaluate 8 != 42, drop this branch.\n     |- Try 8 \/ 1 = 8. Evaluate 8 != 42, drop this branch.\n   |- Pick two numbers (1, 16) (numbers left: [2]). Try possible operations.\n    |- Try 16 + 1 = 17. Add 17 to the number set. Current number set: [17, 2], target: 42, just two numbers left.\n     |- Try 17 + 2 = 19. Evaluate 19 != 42, drop this branch.\n     |- Try 17 - 2 = 15. Evaluate 15 != 42, drop this branch.\n     |- Try 17 * 2 = 34. Evaluate 34 != 42, drop this branch.\n     |- Try 17 \/ 2 = 8.5. 8.5 is a decimal, drop this branch.\n    |- Try 16 - 1 = 15. Add 15 to the number set. Current number set: [15, 2], target: 42, just two numbers left.\n     |- Try 15 + 2 = 17. Evaluate 17 != 42, drop this branch.\n     |- Try 15 - 2 = 13. Evaluate 13 != 42, drop this branch.\n     |- Try 15 * 2 = 30. Evaluate 30 != 42, drop this branch.\n     |- Try 15 \/ 2 = 7.5. 7.5 is a decimal, drop this branch.\n    |- Try 16 * 1 = 16. Add 16 to the number set. Current number set: [16, 2], target: 42, just two numbers left.\n     |- Try 16 + 2 = 18. Evaluate 18 != 42, drop this branch.\n     |- Try 16 - 2 = 14. Evaluate 14 != 42, drop this branch.\n     |- Try 16 * 2 = 32. Evaluate 32 != 42, drop this branch.\n     |- Try 16 \/ 2 = 8. Evaluate 8 != 42, drop this branch.\n    |- Try 16 \/ 1 = 16. Add 16 to the number set. Current number set: [16, 2], target: 42, just two numbers left.\n     |- Try 16 + 2 = 18. Evaluate 18 != 42, drop this branch.\n     |- Try 16 - 2 = 14. Evaluate 14 != 42, drop this branch.\n     |- Try 16 * 2 = 32. Evaluate 32 != 42, drop this branch.\n     |- Try 16 \/ 2 = 8. Evaluate 8 != 42, drop this branch.\n  |- Try 3 * 1 = 3. Add 3 to the number set. Current number set: [3, 1, 16], target: 42. Options for choosing two numbers: [(3, 1), (3, 16), (1, 16)].\n   |- Pick two numbers (3, 1) (numbers left: [16]). Try possible operations.\n    |- Try 3 + 1 = 4. Add 4 to the number set. Current number set: [4, 16], target: 42, just two numbers left.\n     |- Try 16 + 4 = 20. Evaluate 20 != 42, drop this branch.\n     |- Try 16 - 4 = 12. Evaluate 12 != 42, drop this branch.\n     |- Try 16 * 4 = 64. Evaluate 64 != 42, drop this branch.\n     |- Try 16 \/ 4 = 4. Evaluate 4 != 42, drop this branch.\n    |- Try 3 - 1 = 2. Add 2 to the number set. Current number set: [2, 16], target: 42, just two numbers left.\n     |- Try 16 + 2 = 18. Evaluate 18 != 42, drop this branch.\n     |- Try 16 - 2 = 14. Evaluate 14 != 42, drop this branch.\n     |- Try 16 * 2 = 32. Evaluate 32 != 42, drop this branch.\n     |- Try 16 \/ 2 = 8. Evaluate 8 != 42, drop this branch.\n    |- Try 3 * 1 = 3. Add 3 to the number set. Current number set: [3, 16], target: 42, just two numbers left.\n     |- Try 16 + 3 = 19. Evaluate 19 != 42, drop this branch.\n     |- Try 16 - 3 = 13. Evaluate 13 != 42, drop this branch.\n     |- Try 16 * 3 = 48. Evaluate 48 != 42, drop this branch.\n     |- Try 16 \/ 3 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 3 \/ 1 = 3. Add 3 to the number set. Current number set: [3, 16], target: 42, just two numbers left.\n     |- Try 16 + 3 = 19. Evaluate 19 != 42, drop this branch.\n     |- Try 16 - 3 = 13. Evaluate 13 != 42, drop this branch.\n     |- Try 16 * 3 = 48. Evaluate 48 != 42, drop this branch.\n     |- Try 16 \/ 3 = 5.3. 5.3 is a decimal, drop this branch.\n   |- Pick two numbers (3, 16) (numbers left: [1]). Try possible operations.\n    |- Try 16 + 3 = 19. Add 19 to the number set. Current number set: [19, 1], target: 42, just two numbers left.\n     |- Try 19 + 1 = 20. Evaluate 20 != 42, drop this branch.\n     |- Try 19 - 1 = 18. Evaluate 18 != 42, drop this branch.\n     |- Try 19 * 1 = 19. Evaluate 19 != 42, drop this branch.\n     |- Try 19 \/ 1 = 19. Evaluate 19 != 42, drop this branch.\n    |- Try 16 - 3 = 13. Add 13 to the number set. Current number set: [13, 1], target: 42, just two numbers left.\n     |- Try 13 + 1 = 14. Evaluate 14 != 42, drop this branch.\n     |- Try 13 - 1 = 12. Evaluate 12 != 42, drop this branch.\n     |- Try 13 * 1 = 13. Evaluate 13 != 42, drop this branch.\n     |- Try 13 \/ 1 = 13. Evaluate 13 != 42, drop this branch.\n    |- Try 16 * 3 = 48. Add 48 to the number set. Current number set: [48, 1], target: 42, just two numbers left.\n     |- Try 48 + 1 = 49. Evaluate 49 != 42, drop this branch.\n     |- Try 48 - 1 = 47. Evaluate 47 != 42, drop this branch.\n     |- Try 48 * 1 = 48. Evaluate 48 != 42, drop this branch.\n     |- Try 48 \/ 1 = 48. Evaluate 48 != 42, drop this branch.\n    |- Try 16 \/ 3 = 5.3. 5.3 is a decimal, drop this branch.\n   |- Pick two numbers (1, 16) (numbers left: [3]). Try possible operations.\n    |- Try 16 + 1 = 17. Add 17 to the number set. Current number set: [17, 3], target: 42, just two numbers left.\n     |- Try 17 + 3 = 20. Evaluate 20 != 42, drop this branch.\n     |- Try 17 - 3 = 14. Evaluate 14 != 42, drop this branch.\n     |- Try 17 * 3 = 51. Evaluate 51 != 42, drop this branch.\n     |- Try 17 \/ 3 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 16 - 1 = 15. Add 15 to the number set. Current number set: [15, 3], target: 42, just two numbers left.\n     |- Try 15 + 3 = 18. Evaluate 18 != 42, drop this branch.\n     |- Try 15 - 3 = 12. Evaluate 12 != 42, drop this branch.\n     |- Try 15 * 3 = 45. Evaluate 45 != 42, drop this branch.\n     |- Try 15 \/ 3 = 5. Evaluate 5 != 42, drop this branch.\n    |- Try 16 * 1 = 16. Add 16 to the number set. Current number set: [16, 3], target: 42, just two numbers left.\n     |- Try 16 + 3 = 19. Evaluate 19 != 42, drop this branch.\n     |- Try 16 - 3 = 13. Evaluate 13 != 42, drop this branch.\n     |- Try 16 * 3 = 48. Evaluate 48 != 42, drop this branch.\n     |- Try 16 \/ 3 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 16 \/ 1 = 16. Add 16 to the number set. Current number set: [16, 3], target: 42, just two numbers left.\n     |- Try 16 + 3 = 19. Evaluate 19 != 42, drop this branch.\n     |- Try 16 - 3 = 13. Evaluate 13 != 42, drop this branch.\n     |- Try 16 * 3 = 48. Evaluate 48 != 42, drop this branch.\n     |- Try 16 \/ 3 = 5.3. 5.3 is a decimal, drop this branch.\n  |- Try 3 \/ 1 = 3. Add 3 to the number set. Current number set: [3, 1, 16], target: 42. Options for choosing two numbers: [(3, 1), (3, 16), (1, 16)].\n   |- Pick two numbers (3, 1) (numbers left: [16]). Try possible operations.\n    |- Try 3 + 1 = 4. Add 4 to the number set. Current number set: [4, 16], target: 42, just two numbers left.\n     |- Try 16 + 4 = 20. Evaluate 20 != 42, drop this branch.\n     |- Try 16 - 4 = 12. Evaluate 12 != 42, drop this branch.\n     |- Try 16 * 4 = 64. Evaluate 64 != 42, drop this branch.\n     |- Try 16 \/ 4 = 4. Evaluate 4 != 42, drop this branch.\n    |- Try 3 - 1 = 2. Add 2 to the number set. Current number set: [2, 16], target: 42, just two numbers left.\n     |- Try 16 + 2 = 18. Evaluate 18 != 42, drop this branch.\n     |- Try 16 - 2 = 14. Evaluate 14 != 42, drop this branch.\n     |- Try 16 * 2 = 32. Evaluate 32 != 42, drop this branch.\n     |- Try 16 \/ 2 = 8. Evaluate 8 != 42, drop this branch.\n    |- Try 3 * 1 = 3. Add 3 to the number set. Current number set: [3, 16], target: 42, just two numbers left.\n     |- Try 16 + 3 = 19. Evaluate 19 != 42, drop this branch.\n     |- Try 16 - 3 = 13. Evaluate 13 != 42, drop this branch.\n     |- Try 16 * 3 = 48. Evaluate 48 != 42, drop this branch.\n     |- Try 16 \/ 3 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 3 \/ 1 = 3. Add 3 to the number set. Current number set: [3, 16], target: 42, just two numbers left.\n     |- Try 16 + 3 = 19. Evaluate 19 != 42, drop this branch.\n     |- Try 16 - 3 = 13. Evaluate 13 != 42, drop this branch.\n     |- Try 16 * 3 = 48. Evaluate 48 != 42, drop this branch.\n     |- Try 16 \/ 3 = 5.3. 5.3 is a decimal, drop this branch.\n   |- Pick two numbers (3, 16) (numbers left: [1]). Try possible operations.\n    |- Try 16 + 3 = 19. Add 19 to the number set. Current number set: [19, 1], target: 42, just two numbers left.\n     |- Try 19 + 1 = 20. Evaluate 20 != 42, drop this branch.\n     |- Try 19 - 1 = 18. Evaluate 18 != 42, drop this branch.\n     |- Try 19 * 1 = 19. Evaluate 19 != 42, drop this branch.\n     |- Try 19 \/ 1 = 19. Evaluate 19 != 42, drop this branch.\n    |- Try 16 - 3 = 13. Add 13 to the number set. Current number set: [13, 1], target: 42, just two numbers left.\n     |- Try 13 + 1 = 14. Evaluate 14 != 42, drop this branch.\n     |- Try 13 - 1 = 12. Evaluate 12 != 42, drop this branch.\n     |- Try 13 * 1 = 13. Evaluate 13 != 42, drop this branch.\n     |- Try 13 \/ 1 = 13. Evaluate 13 != 42, drop this branch.\n    |- Try 16 * 3 = 48. Add 48 to the number set. Current number set: [48, 1], target: 42, just two numbers left.\n     |- Try 48 + 1 = 49. Evaluate 49 != 42, drop this branch.\n     |- Try 48 - 1 = 47. Evaluate 47 != 42, drop this branch.\n     |- Try 48 * 1 = 48. Evaluate 48 != 42, drop this branch.\n     |- Try 48 \/ 1 = 48. Evaluate 48 != 42, drop this branch.\n    |- Try 16 \/ 3 = 5.3. 5.3 is a decimal, drop this branch.\n   |- Pick two numbers (1, 16) (numbers left: [3]). Try possible operations.\n    |- Try 16 + 1 = 17. Add 17 to the number set. Current number set: [17, 3], target: 42, just two numbers left.\n     |- Try 17 + 3 = 20. Evaluate 20 != 42, drop this branch.\n     |- Try 17 - 3 = 14. Evaluate 14 != 42, drop this branch.\n     |- Try 17 * 3 = 51. Evaluate 51 != 42, drop this branch.\n     |- Try 17 \/ 3 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 16 - 1 = 15. Add 15 to the number set. Current number set: [15, 3], target: 42, just two numbers left.\n     |- Try 15 + 3 = 18. Evaluate 18 != 42, drop this branch.\n     |- Try 15 - 3 = 12. Evaluate 12 != 42, drop this branch.\n     |- Try 15 * 3 = 45. Evaluate 45 != 42, drop this branch.\n     |- Try 15 \/ 3 = 5. Evaluate 5 != 42, drop this branch.\n    |- Try 16 * 1 = 16. Add 16 to the number set. Current number set: [16, 3], target: 42, just two numbers left.\n     |- Try 16 + 3 = 19. Evaluate 19 != 42, drop this branch.\n     |- Try 16 - 3 = 13. Evaluate 13 != 42, drop this branch.\n     |- Try 16 * 3 = 48. Evaluate 48 != 42, drop this branch.\n     |- Try 16 \/ 3 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 16 \/ 1 = 16. Add 16 to the number set. Current number set: [16, 3], target: 42, just two numbers left.\n     |- Try 16 + 3 = 19. Evaluate 19 != 42, drop this branch.\n     |- Try 16 - 3 = 13. Evaluate 13 != 42, drop this branch.\n     |- Try 16 * 3 = 48. Evaluate 48 != 42, drop this branch.\n     |- Try 16 \/ 3 = 5.3. 5.3 is a decimal, drop this branch.\n |- Pick two numbers (1, 1) (numbers left: [3, 16]). Try possible operations.\n  |- Try 1 + 1 = 2. Add 2 to the number set. Current number set: [2, 3, 16], target: 42. Options for choosing two numbers: [(2, 3), (2, 16), (3, 16)].\n   |- Pick two numbers (2, 3) (numbers left: [16]). Try possible operations.\n    |- Try 3 + 2 = 5. Add 5 to the number set. Current number set: [5, 16], target: 42, just two numbers left.\n     |- Try 16 + 5 = 21. Evaluate 21 != 42, drop this branch.\n     |- Try 16 - 5 = 11. Evaluate 11 != 42, drop this branch.\n     |- Try 16 * 5 = 80. Evaluate 80 != 42, drop this branch.\n     |- Try 16 \/ 5 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 3 - 2 = 1. Add 1 to the number set. Current number set: [1, 16], target: 42, just two numbers left.\n     |- Try 16 + 1 = 17. Evaluate 17 != 42, drop this branch.\n     |- Try 16 - 1 = 15. Evaluate 15 != 42, drop this branch.\n     |- Try 16 * 1 = 16. Evaluate 16 != 42, drop this branch.\n     |- Try 16 \/ 1 = 16. Evaluate 16 != 42, drop this branch.\n    |- Try 3 * 2 = 6. Add 6 to the number set. Current number set: [6, 16], target: 42, just two numbers left.\n     |- Try 16 + 6 = 22. Evaluate 22 != 42, drop this branch.\n     |- Try 16 - 6 = 10. Evaluate 10 != 42, drop this branch.\n     |- Try 16 * 6 = 96. Evaluate 96 != 42, drop this branch.\n     |- Try 16 \/ 6 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 3 \/ 2 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (2, 16) (numbers left: [3]). Try possible operations.\n    |- Try 16 + 2 = 18. Add 18 to the number set. Current number set: [18, 3], target: 42, just two numbers left.\n     |- Try 18 + 3 = 21. Evaluate 21 != 42, drop this branch.\n     |- Try 18 - 3 = 15. Evaluate 15 != 42, drop this branch.\n     |- Try 18 * 3 = 54. Evaluate 54 != 42, drop this branch.\n     |- Try 18 \/ 3 = 6. Evaluate 6 != 42, drop this branch.\n    |- Try 16 - 2 = 14. Add 14 to the number set. Current number set: [14, 3], target: 42, just two numbers left.\n     |- Try 14 + 3 = 17. Evaluate 17 != 42, drop this branch.\n     |- Try 14 - 3 = 11. Evaluate 11 != 42, drop this branch.\n     |- Try 14 * 3 = 42. Evaluate 42 == 42, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 14 * 3 = 42\nThe step before: 16 - 2 = 14\nThe first step: 1 + 1 = 2\n\nOutput the solution in the required format:\n<Solution>\n1 + 1 = 2\n16 - 2 = 14\n14 * 3 = 42\n<\/Solution>\n","item":{"nums":[1,3,1,16],"solution":["1 + 1 = 2","16 - 2 = 14","14 * 3 = 42"],"target":42}}
+{"instance_id":"countdown_8k_44","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [7, 10, 7, 11]\nTarget: 30","reference_output":"# Search Procedure\nInitial number set: [7, 10, 7, 11], target: 30. Options for choosing two numbers: [(7, 10), (7, 7), (7, 11), (10, 7), (10, 11), (7, 11)].\n |- Pick two numbers (7, 10) (numbers left: [7, 11]). Try possible operations.\n  |- Try 10 + 7 = 17. Add 17 to the number set. Current number set: [17, 7, 11], target: 30. Options for choosing two numbers: [(17, 7), (17, 11), (7, 11)].\n   |- Pick two numbers (17, 7) (numbers left: [11]). Try possible operations.\n    |- Try 17 + 7 = 24. Add 24 to the number set. Current number set: [24, 11], target: 30, just two numbers left.\n     |- Try 24 + 11 = 35. Evaluate 35 != 30, drop this branch.\n     |- Try 24 - 11 = 13. Evaluate 13 != 30, drop this branch.\n     |- Try 24 * 11 = 264. Evaluate 264 != 30, drop this branch.\n     |- Try 24 \/ 11 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 17 - 7 = 10. Add 10 to the number set. Current number set: [10, 11], target: 30, just two numbers left.\n     |- Try 11 + 10 = 21. Evaluate 21 != 30, drop this branch.\n     |- Try 11 - 10 = 1. Evaluate 1 != 30, drop this branch.\n     |- Try 11 * 10 = 110. Evaluate 110 != 30, drop this branch.\n     |- Try 11 \/ 10 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 17 * 7 = 119. Add 119 to the number set. Current number set: [119, 11], target: 30, just two numbers left.\n     |- Try 119 + 11 = 130. Evaluate 130 != 30, drop this branch.\n     |- Try 119 - 11 = 108. Evaluate 108 != 30, drop this branch.\n     |- Try 119 * 11 = 1309. Evaluate 1309 != 30, drop this branch.\n     |- Try 119 \/ 11 = 10.8. 10.8 is a decimal, drop this branch.\n    |- Try 17 \/ 7 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (17, 11) (numbers left: [7]). Try possible operations.\n    |- Try 17 + 11 = 28. Add 28 to the number set. Current number set: [28, 7], target: 30, just two numbers left.\n     |- Try 28 + 7 = 35. Evaluate 35 != 30, drop this branch.\n     |- Try 28 - 7 = 21. Evaluate 21 != 30, drop this branch.\n     |- Try 28 * 7 = 196. Evaluate 196 != 30, drop this branch.\n     |- Try 28 \/ 7 = 4. Evaluate 4 != 30, drop this branch.\n    |- Try 17 - 11 = 6. Add 6 to the number set. Current number set: [6, 7], target: 30, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 30, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 30, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 30, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 17 * 11 = 187. Add 187 to the number set. Current number set: [187, 7], target: 30, just two numbers left.\n     |- Try 187 + 7 = 194. Evaluate 194 != 30, drop this branch.\n     |- Try 187 - 7 = 180. Evaluate 180 != 30, drop this branch.\n     |- Try 187 * 7 = 1309. Evaluate 1309 != 30, drop this branch.\n     |- Try 187 \/ 7 = 26.7. 26.7 is a decimal, drop this branch.\n    |- Try 17 \/ 11 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (7, 11) (numbers left: [17]). Try possible operations.\n    |- Try 11 + 7 = 18. Add 18 to the number set. Current number set: [18, 17], target: 30, just two numbers left.\n     |- Try 18 + 17 = 35. Evaluate 35 != 30, drop this branch.\n     |- Try 18 - 17 = 1. Evaluate 1 != 30, drop this branch.\n     |- Try 18 * 17 = 306. Evaluate 306 != 30, drop this branch.\n     |- Try 18 \/ 17 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 11 - 7 = 4. Add 4 to the number set. Current number set: [4, 17], target: 30, just two numbers left.\n     |- Try 17 + 4 = 21. Evaluate 21 != 30, drop this branch.\n     |- Try 17 - 4 = 13. Evaluate 13 != 30, drop this branch.\n     |- Try 17 * 4 = 68. Evaluate 68 != 30, drop this branch.\n     |- Try 17 \/ 4 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 11 * 7 = 77. Add 77 to the number set. Current number set: [77, 17], target: 30, just two numbers left.\n     |- Try 77 + 17 = 94. Evaluate 94 != 30, drop this branch.\n     |- Try 77 - 17 = 60. Evaluate 60 != 30, drop this branch.\n     |- Try 77 * 17 = 1309. Evaluate 1309 != 30, drop this branch.\n     |- Try 77 \/ 17 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 11 \/ 7 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 10 - 7 = 3. Add 3 to the number set. Current number set: [3, 7, 11], target: 30. Options for choosing two numbers: [(3, 7), (3, 11), (7, 11)].\n   |- Pick two numbers (3, 7) (numbers left: [11]). Try possible operations.\n    |- Try 7 + 3 = 10. Add 10 to the number set. Current number set: [10, 11], target: 30, just two numbers left.\n     |- Try 11 + 10 = 21. Evaluate 21 != 30, drop this branch.\n     |- Try 11 - 10 = 1. Evaluate 1 != 30, drop this branch.\n     |- Try 11 * 10 = 110. Evaluate 110 != 30, drop this branch.\n     |- Try 11 \/ 10 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 7 - 3 = 4. Add 4 to the number set. Current number set: [4, 11], target: 30, just two numbers left.\n     |- Try 11 + 4 = 15. Evaluate 15 != 30, drop this branch.\n     |- Try 11 - 4 = 7. Evaluate 7 != 30, drop this branch.\n     |- Try 11 * 4 = 44. Evaluate 44 != 30, drop this branch.\n     |- Try 11 \/ 4 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 7 * 3 = 21. Add 21 to the number set. Current number set: [21, 11], target: 30, just two numbers left.\n     |- Try 21 + 11 = 32. Evaluate 32 != 30, drop this branch.\n     |- Try 21 - 11 = 10. Evaluate 10 != 30, drop this branch.\n     |- Try 21 * 11 = 231. Evaluate 231 != 30, drop this branch.\n     |- Try 21 \/ 11 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (3, 11) (numbers left: [7]). Try possible operations.\n    |- Try 11 + 3 = 14. Add 14 to the number set. Current number set: [14, 7], target: 30, just two numbers left.\n     |- Try 14 + 7 = 21. Evaluate 21 != 30, drop this branch.\n     |- Try 14 - 7 = 7. Evaluate 7 != 30, drop this branch.\n     |- Try 14 * 7 = 98. Evaluate 98 != 30, drop this branch.\n     |- Try 14 \/ 7 = 2. Evaluate 2 != 30, drop this branch.\n    |- Try 11 - 3 = 8. Add 8 to the number set. Current number set: [8, 7], target: 30, just two numbers left.\n     |- Try 8 + 7 = 15. Evaluate 15 != 30, drop this branch.\n     |- Try 8 - 7 = 1. Evaluate 1 != 30, drop this branch.\n     |- Try 8 * 7 = 56. Evaluate 56 != 30, drop this branch.\n     |- Try 8 \/ 7 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 11 * 3 = 33. Add 33 to the number set. Current number set: [33, 7], target: 30, just two numbers left.\n     |- Try 33 + 7 = 40. Evaluate 40 != 30, drop this branch.\n     |- Try 33 - 7 = 26. Evaluate 26 != 30, drop this branch.\n     |- Try 33 * 7 = 231. Evaluate 231 != 30, drop this branch.\n     |- Try 33 \/ 7 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 11 \/ 3 = 3.7. 3.7 is a decimal, drop this branch.\n   |- Pick two numbers (7, 11) (numbers left: [3]). Try possible operations.\n    |- Try 11 + 7 = 18. Add 18 to the number set. Current number set: [18, 3], target: 30, just two numbers left.\n     |- Try 18 + 3 = 21. Evaluate 21 != 30, drop this branch.\n     |- Try 18 - 3 = 15. Evaluate 15 != 30, drop this branch.\n     |- Try 18 * 3 = 54. Evaluate 54 != 30, drop this branch.\n     |- Try 18 \/ 3 = 6. Evaluate 6 != 30, drop this branch.\n    |- Try 11 - 7 = 4. Add 4 to the number set. Current number set: [4, 3], target: 30, just two numbers left.\n     |- Try 4 + 3 = 7. Evaluate 7 != 30, drop this branch.\n     |- Try 4 - 3 = 1. Evaluate 1 != 30, drop this branch.\n     |- Try 4 * 3 = 12. Evaluate 12 != 30, drop this branch.\n     |- Try 4 \/ 3 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 11 * 7 = 77. Add 77 to the number set. Current number set: [77, 3], target: 30, just two numbers left.\n     |- Try 77 + 3 = 80. Evaluate 80 != 30, drop this branch.\n     |- Try 77 - 3 = 74. Evaluate 74 != 30, drop this branch.\n     |- Try 77 * 3 = 231. Evaluate 231 != 30, drop this branch.\n     |- Try 77 \/ 3 = 25.7. 25.7 is a decimal, drop this branch.\n    |- Try 11 \/ 7 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 10 * 7 = 70. Add 70 to the number set. Current number set: [70, 7, 11], target: 30. Options for choosing two numbers: [(70, 7), (70, 11), (7, 11)].\n   |- Pick two numbers (70, 7) (numbers left: [11]). Try possible operations.\n    |- Try 70 + 7 = 77. Add 77 to the number set. Current number set: [77, 11], target: 30, just two numbers left.\n     |- Try 77 + 11 = 88. Evaluate 88 != 30, drop this branch.\n     |- Try 77 - 11 = 66. Evaluate 66 != 30, drop this branch.\n     |- Try 77 * 11 = 847. Evaluate 847 != 30, drop this branch.\n     |- Try 77 \/ 11 = 7. Evaluate 7 != 30, drop this branch.\n    |- Try 70 - 7 = 63. Add 63 to the number set. Current number set: [63, 11], target: 30, just two numbers left.\n     |- Try 63 + 11 = 74. Evaluate 74 != 30, drop this branch.\n     |- Try 63 - 11 = 52. Evaluate 52 != 30, drop this branch.\n     |- Try 63 * 11 = 693. Evaluate 693 != 30, drop this branch.\n     |- Try 63 \/ 11 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 70 * 7 = 490. Add 490 to the number set. Current number set: [490, 11], target: 30, just two numbers left.\n     |- Try 490 + 11 = 501. Evaluate 501 != 30, drop this branch.\n     |- Try 490 - 11 = 479. Evaluate 479 != 30, drop this branch.\n     |- Try 490 * 11 = 5390. 5390 exceeds the maximum intermediate result, drop this branch.\n     |- Try 490 \/ 11 = 44.5. 44.5 is a decimal, drop this branch.\n    |- Try 70 \/ 7 = 10. Add 10 to the number set. Current number set: [10, 11], target: 30, just two numbers left.\n     |- Try 11 + 10 = 21. Evaluate 21 != 30, drop this branch.\n     |- Try 11 - 10 = 1. Evaluate 1 != 30, drop this branch.\n     |- Try 11 * 10 = 110. Evaluate 110 != 30, drop this branch.\n     |- Try 11 \/ 10 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (70, 11) (numbers left: [7]). Try possible operations.\n    |- Try 70 + 11 = 81. Add 81 to the number set. Current number set: [81, 7], target: 30, just two numbers left.\n     |- Try 81 + 7 = 88. Evaluate 88 != 30, drop this branch.\n     |- Try 81 - 7 = 74. Evaluate 74 != 30, drop this branch.\n     |- Try 81 * 7 = 567. Evaluate 567 != 30, drop this branch.\n     |- Try 81 \/ 7 = 11.6. 11.6 is a decimal, drop this branch.\n    |- Try 70 - 11 = 59. Add 59 to the number set. Current number set: [59, 7], target: 30, just two numbers left.\n     |- Try 59 + 7 = 66. Evaluate 66 != 30, drop this branch.\n     |- Try 59 - 7 = 52. Evaluate 52 != 30, drop this branch.\n     |- Try 59 * 7 = 413. Evaluate 413 != 30, drop this branch.\n     |- Try 59 \/ 7 = 8.4. 8.4 is a decimal, drop this branch.\n    |- Try 70 * 11 = 770. Add 770 to the number set. Current number set: [770, 7], target: 30, just two numbers left.\n     |- Try 770 + 7 = 777. Evaluate 777 != 30, drop this branch.\n     |- Try 770 - 7 = 763. Evaluate 763 != 30, drop this branch.\n     |- Try 770 * 7 = 5390. 5390 exceeds the maximum intermediate result, drop this branch.\n     |- Try 770 \/ 7 = 110. Evaluate 110 != 30, drop this branch.\n    |- Try 70 \/ 11 = 6.4. 6.4 is a decimal, drop this branch.\n   |- Pick two numbers (7, 11) (numbers left: [70]). Try possible operations.\n    |- Try 11 + 7 = 18. Add 18 to the number set. Current number set: [18, 70], target: 30, just two numbers left.\n     |- Try 70 + 18 = 88. Evaluate 88 != 30, drop this branch.\n     |- Try 70 - 18 = 52. Evaluate 52 != 30, drop this branch.\n     |- Try 70 * 18 = 1260. Evaluate 1260 != 30, drop this branch.\n     |- Try 70 \/ 18 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 11 - 7 = 4. Add 4 to the number set. Current number set: [4, 70], target: 30, just two numbers left.\n     |- Try 70 + 4 = 74. Evaluate 74 != 30, drop this branch.\n     |- Try 70 - 4 = 66. Evaluate 66 != 30, drop this branch.\n     |- Try 70 * 4 = 280. Evaluate 280 != 30, drop this branch.\n     |- Try 70 \/ 4 = 17.5. 17.5 is a decimal, drop this branch.\n    |- Try 11 * 7 = 77. Add 77 to the number set. Current number set: [77, 70], target: 30, just two numbers left.\n     |- Try 77 + 70 = 147. Evaluate 147 != 30, drop this branch.\n     |- Try 77 - 70 = 7. Evaluate 7 != 30, drop this branch.\n     |- Try 77 * 70 = 5390. 5390 exceeds the maximum intermediate result, drop this branch.\n     |- Try 77 \/ 70 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 11 \/ 7 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 10 \/ 7 = 1.4. 1.4 is a decimal, drop this branch.\n |- Pick two numbers (7, 7) (numbers left: [10, 11]). Try possible operations.\n  |- Try 7 + 7 = 14. Add 14 to the number set. Current number set: [14, 10, 11], target: 30. Options for choosing two numbers: [(14, 10), (14, 11), (10, 11)].\n   |- Pick two numbers (14, 10) (numbers left: [11]). Try possible operations.\n    |- Try 14 + 10 = 24. Add 24 to the number set. Current number set: [24, 11], target: 30, just two numbers left.\n     |- Try 24 + 11 = 35. Evaluate 35 != 30, drop this branch.\n     |- Try 24 - 11 = 13. Evaluate 13 != 30, drop this branch.\n     |- Try 24 * 11 = 264. Evaluate 264 != 30, drop this branch.\n     |- Try 24 \/ 11 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 14 - 10 = 4. Add 4 to the number set. Current number set: [4, 11], target: 30, just two numbers left.\n     |- Try 11 + 4 = 15. Evaluate 15 != 30, drop this branch.\n     |- Try 11 - 4 = 7. Evaluate 7 != 30, drop this branch.\n     |- Try 11 * 4 = 44. Evaluate 44 != 30, drop this branch.\n     |- Try 11 \/ 4 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 14 * 10 = 140. Add 140 to the number set. Current number set: [140, 11], target: 30, just two numbers left.\n     |- Try 140 + 11 = 151. Evaluate 151 != 30, drop this branch.\n     |- Try 140 - 11 = 129. Evaluate 129 != 30, drop this branch.\n     |- Try 140 * 11 = 1540. Evaluate 1540 != 30, drop this branch.\n     |- Try 140 \/ 11 = 12.7. 12.7 is a decimal, drop this branch.\n    |- Try 14 \/ 10 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (14, 11) (numbers left: [10]). Try possible operations.\n    |- Try 14 + 11 = 25. Add 25 to the number set. Current number set: [25, 10], target: 30, just two numbers left.\n     |- Try 25 + 10 = 35. Evaluate 35 != 30, drop this branch.\n     |- Try 25 - 10 = 15. Evaluate 15 != 30, drop this branch.\n     |- Try 25 * 10 = 250. Evaluate 250 != 30, drop this branch.\n     |- Try 25 \/ 10 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 14 - 11 = 3. Add 3 to the number set. Current number set: [3, 10], target: 30, just two numbers left.\n     |- Try 10 + 3 = 13. Evaluate 13 != 30, drop this branch.\n     |- Try 10 - 3 = 7. Evaluate 7 != 30, drop this branch.\n     |- Try 10 * 3 = 30. Evaluate 30 == 30, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 10 * 3 = 30\nThe step before: 14 - 11 = 3\nThe first step: 7 + 7 = 14\n\nOutput the solution in the required format:\n<Solution>\n7 + 7 = 14\n14 - 11 = 3\n10 * 3 = 30\n<\/Solution>\n","item":{"nums":[7,10,7,11],"solution":["7 + 7 = 14","14 - 11 = 3","10 * 3 = 30"],"target":30}}
+{"instance_id":"countdown_8k_45","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [37, 28, 47, 26]\nTarget: 20","reference_output":"# Search Procedure\nInitial number set: [37, 28, 47, 26], target: 20. Options for choosing two numbers: [(37, 28), (37, 47), (37, 26), (28, 47), (28, 26), (47, 26)].\n |- Pick two numbers (37, 28) (numbers left: [47, 26]). Try possible operations.\n  |- Try 37 + 28 = 65. Add 65 to the number set. Current number set: [65, 47, 26], target: 20. Options for choosing two numbers: [(65, 47), (65, 26), (47, 26)].\n   |- Pick two numbers (65, 47) (numbers left: [26]). Try possible operations.\n    |- Try 65 + 47 = 112. Add 112 to the number set. Current number set: [112, 26], target: 20, just two numbers left.\n     |- Try 112 + 26 = 138. Evaluate 138 != 20, drop this branch.\n     |- Try 112 - 26 = 86. Evaluate 86 != 20, drop this branch.\n     |- Try 112 * 26 = 2912. 2912 exceeds the maximum intermediate result, drop this branch.\n     |- Try 112 \/ 26 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 65 - 47 = 18. Add 18 to the number set. Current number set: [18, 26], target: 20, just two numbers left.\n     |- Try 26 + 18 = 44. Evaluate 44 != 20, drop this branch.\n     |- Try 26 - 18 = 8. Evaluate 8 != 20, drop this branch.\n     |- Try 26 * 18 = 468. Evaluate 468 != 20, drop this branch.\n     |- Try 26 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 65 * 47 = 3055. 3055 exceeds the maximum intermediate result, drop this branch.\n    |- Try 65 \/ 47 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (65, 26) (numbers left: [47]). Try possible operations.\n    |- Try 65 + 26 = 91. Add 91 to the number set. Current number set: [91, 47], target: 20, just two numbers left.\n     |- Try 91 + 47 = 138. Evaluate 138 != 20, drop this branch.\n     |- Try 91 - 47 = 44. Evaluate 44 != 20, drop this branch.\n     |- Try 91 * 47 = 4277. 4277 exceeds the maximum intermediate result, drop this branch.\n     |- Try 91 \/ 47 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 65 - 26 = 39. Add 39 to the number set. Current number set: [39, 47], target: 20, just two numbers left.\n     |- Try 47 + 39 = 86. Evaluate 86 != 20, drop this branch.\n     |- Try 47 - 39 = 8. Evaluate 8 != 20, drop this branch.\n     |- Try 47 * 39 = 1833. Evaluate 1833 != 20, drop this branch.\n     |- Try 47 \/ 39 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 65 * 26 = 1690. Add 1690 to the number set. Current number set: [1690, 47], target: 20, just two numbers left.\n     |- Try 1690 + 47 = 1737. Evaluate 1737 != 20, drop this branch.\n     |- Try 1690 - 47 = 1643. Evaluate 1643 != 20, drop this branch.\n     |- Try 1690 * 47 = 79430. 79430 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1690 \/ 47 = 36.0. 36.0 is a decimal, drop this branch.\n    |- Try 65 \/ 26 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (47, 26) (numbers left: [65]). Try possible operations.\n    |- Try 47 + 26 = 73. Add 73 to the number set. Current number set: [73, 65], target: 20, just two numbers left.\n     |- Try 73 + 65 = 138. Evaluate 138 != 20, drop this branch.\n     |- Try 73 - 65 = 8. Evaluate 8 != 20, drop this branch.\n     |- Try 73 * 65 = 4745. 4745 exceeds the maximum intermediate result, drop this branch.\n     |- Try 73 \/ 65 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 47 - 26 = 21. Add 21 to the number set. Current number set: [21, 65], target: 20, just two numbers left.\n     |- Try 65 + 21 = 86. Evaluate 86 != 20, drop this branch.\n     |- Try 65 - 21 = 44. Evaluate 44 != 20, drop this branch.\n     |- Try 65 * 21 = 1365. Evaluate 1365 != 20, drop this branch.\n     |- Try 65 \/ 21 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 47 * 26 = 1222. Add 1222 to the number set. Current number set: [1222, 65], target: 20, just two numbers left.\n     |- Try 1222 + 65 = 1287. Evaluate 1287 != 20, drop this branch.\n     |- Try 1222 - 65 = 1157. Evaluate 1157 != 20, drop this branch.\n     |- Try 1222 * 65 = 79430. 79430 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1222 \/ 65 = 18.8. 18.8 is a decimal, drop this branch.\n    |- Try 47 \/ 26 = 1.8. 1.8 is a decimal, drop this branch.\n  |- Try 37 - 28 = 9. Add 9 to the number set. Current number set: [9, 47, 26], target: 20. Options for choosing two numbers: [(9, 47), (9, 26), (47, 26)].\n   |- Pick two numbers (9, 47) (numbers left: [26]). Try possible operations.\n    |- Try 47 + 9 = 56. Add 56 to the number set. Current number set: [56, 26], target: 20, just two numbers left.\n     |- Try 56 + 26 = 82. Evaluate 82 != 20, drop this branch.\n     |- Try 56 - 26 = 30. Evaluate 30 != 20, drop this branch.\n     |- Try 56 * 26 = 1456. Evaluate 1456 != 20, drop this branch.\n     |- Try 56 \/ 26 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 47 - 9 = 38. Add 38 to the number set. Current number set: [38, 26], target: 20, just two numbers left.\n     |- Try 38 + 26 = 64. Evaluate 64 != 20, drop this branch.\n     |- Try 38 - 26 = 12. Evaluate 12 != 20, drop this branch.\n     |- Try 38 * 26 = 988. Evaluate 988 != 20, drop this branch.\n     |- Try 38 \/ 26 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 47 * 9 = 423. Add 423 to the number set. Current number set: [423, 26], target: 20, just two numbers left.\n     |- Try 423 + 26 = 449. Evaluate 449 != 20, drop this branch.\n     |- Try 423 - 26 = 397. Evaluate 397 != 20, drop this branch.\n     |- Try 423 * 26 = 10998. 10998 exceeds the maximum intermediate result, drop this branch.\n     |- Try 423 \/ 26 = 16.3. 16.3 is a decimal, drop this branch.\n    |- Try 47 \/ 9 = 5.2. 5.2 is a decimal, drop this branch.\n   |- Pick two numbers (9, 26) (numbers left: [47]). Try possible operations.\n    |- Try 26 + 9 = 35. Add 35 to the number set. Current number set: [35, 47], target: 20, just two numbers left.\n     |- Try 47 + 35 = 82. Evaluate 82 != 20, drop this branch.\n     |- Try 47 - 35 = 12. Evaluate 12 != 20, drop this branch.\n     |- Try 47 * 35 = 1645. Evaluate 1645 != 20, drop this branch.\n     |- Try 47 \/ 35 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 26 - 9 = 17. Add 17 to the number set. Current number set: [17, 47], target: 20, just two numbers left.\n     |- Try 47 + 17 = 64. Evaluate 64 != 20, drop this branch.\n     |- Try 47 - 17 = 30. Evaluate 30 != 20, drop this branch.\n     |- Try 47 * 17 = 799. Evaluate 799 != 20, drop this branch.\n     |- Try 47 \/ 17 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 26 * 9 = 234. Add 234 to the number set. Current number set: [234, 47], target: 20, just two numbers left.\n     |- Try 234 + 47 = 281. Evaluate 281 != 20, drop this branch.\n     |- Try 234 - 47 = 187. Evaluate 187 != 20, drop this branch.\n     |- Try 234 * 47 = 10998. 10998 exceeds the maximum intermediate result, drop this branch.\n     |- Try 234 \/ 47 = 5.0. 5.0 is a decimal, drop this branch.\n    |- Try 26 \/ 9 = 2.9. 2.9 is a decimal, drop this branch.\n   |- Pick two numbers (47, 26) (numbers left: [9]). Try possible operations.\n    |- Try 47 + 26 = 73. Add 73 to the number set. Current number set: [73, 9], target: 20, just two numbers left.\n     |- Try 73 + 9 = 82. Evaluate 82 != 20, drop this branch.\n     |- Try 73 - 9 = 64. Evaluate 64 != 20, drop this branch.\n     |- Try 73 * 9 = 657. Evaluate 657 != 20, drop this branch.\n     |- Try 73 \/ 9 = 8.1. 8.1 is a decimal, drop this branch.\n    |- Try 47 - 26 = 21. Add 21 to the number set. Current number set: [21, 9], target: 20, just two numbers left.\n     |- Try 21 + 9 = 30. Evaluate 30 != 20, drop this branch.\n     |- Try 21 - 9 = 12. Evaluate 12 != 20, drop this branch.\n     |- Try 21 * 9 = 189. Evaluate 189 != 20, drop this branch.\n     |- Try 21 \/ 9 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 47 * 26 = 1222. Add 1222 to the number set. Current number set: [1222, 9], target: 20, just two numbers left.\n     |- Try 1222 + 9 = 1231. Evaluate 1231 != 20, drop this branch.\n     |- Try 1222 - 9 = 1213. Evaluate 1213 != 20, drop this branch.\n     |- Try 1222 * 9 = 10998. 10998 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1222 \/ 9 = 135.8. 135.8 is a decimal, drop this branch.\n    |- Try 47 \/ 26 = 1.8. 1.8 is a decimal, drop this branch.\n  |- Try 37 * 28 = 1036. Add 1036 to the number set. Current number set: [1036, 47, 26], target: 20. Options for choosing two numbers: [(1036, 47), (1036, 26), (47, 26)].\n   |- Pick two numbers (1036, 47) (numbers left: [26]). Try possible operations.\n    |- Try 1036 + 47 = 1083. Add 1083 to the number set. Current number set: [1083, 26], target: 20, just two numbers left.\n     |- Try 1083 + 26 = 1109. Evaluate 1109 != 20, drop this branch.\n     |- Try 1083 - 26 = 1057. Evaluate 1057 != 20, drop this branch.\n     |- Try 1083 * 26 = 28158. 28158 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1083 \/ 26 = 41.7. 41.7 is a decimal, drop this branch.\n    |- Try 1036 - 47 = 989. Add 989 to the number set. Current number set: [989, 26], target: 20, just two numbers left.\n     |- Try 989 + 26 = 1015. Evaluate 1015 != 20, drop this branch.\n     |- Try 989 - 26 = 963. Evaluate 963 != 20, drop this branch.\n     |- Try 989 * 26 = 25714. 25714 exceeds the maximum intermediate result, drop this branch.\n     |- Try 989 \/ 26 = 38.0. 38.0 is a decimal, drop this branch.\n    |- Try 1036 * 47 = 48692. 48692 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1036 \/ 47 = 22.0. 22.0 is a decimal, drop this branch.\n   |- Pick two numbers (1036, 26) (numbers left: [47]). Try possible operations.\n    |- Try 1036 + 26 = 1062. Add 1062 to the number set. Current number set: [1062, 47], target: 20, just two numbers left.\n     |- Try 1062 + 47 = 1109. Evaluate 1109 != 20, drop this branch.\n     |- Try 1062 - 47 = 1015. Evaluate 1015 != 20, drop this branch.\n     |- Try 1062 * 47 = 49914. 49914 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1062 \/ 47 = 22.6. 22.6 is a decimal, drop this branch.\n    |- Try 1036 - 26 = 1010. Add 1010 to the number set. Current number set: [1010, 47], target: 20, just two numbers left.\n     |- Try 1010 + 47 = 1057. Evaluate 1057 != 20, drop this branch.\n     |- Try 1010 - 47 = 963. Evaluate 963 != 20, drop this branch.\n     |- Try 1010 * 47 = 47470. 47470 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1010 \/ 47 = 21.5. 21.5 is a decimal, drop this branch.\n    |- Try 1036 * 26 = 26936. 26936 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1036 \/ 26 = 39.8. 39.8 is a decimal, drop this branch.\n   |- Pick two numbers (47, 26) (numbers left: [1036]). Try possible operations.\n    |- Try 47 + 26 = 73. Add 73 to the number set. Current number set: [73, 1036], target: 20, just two numbers left.\n     |- Try 1036 + 73 = 1109. Evaluate 1109 != 20, drop this branch.\n     |- Try 1036 - 73 = 963. Evaluate 963 != 20, drop this branch.\n     |- Try 1036 * 73 = 75628. 75628 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1036 \/ 73 = 14.2. 14.2 is a decimal, drop this branch.\n    |- Try 47 - 26 = 21. Add 21 to the number set. Current number set: [21, 1036], target: 20, just two numbers left.\n     |- Try 1036 + 21 = 1057. Evaluate 1057 != 20, drop this branch.\n     |- Try 1036 - 21 = 1015. Evaluate 1015 != 20, drop this branch.\n     |- Try 1036 * 21 = 21756. 21756 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1036 \/ 21 = 49.3. 49.3 is a decimal, drop this branch.\n    |- Try 47 * 26 = 1222. Add 1222 to the number set. Current number set: [1222, 1036], target: 20, just two numbers left.\n     |- Try 1222 + 1036 = 2258. 2258 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1222 - 1036 = 186. Evaluate 186 != 20, drop this branch.\n     |- Try 1222 * 1036 = 1265992. 1265992 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1222 \/ 1036 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 47 \/ 26 = 1.8. 1.8 is a decimal, drop this branch.\n  |- Try 37 \/ 28 = 1.3. 1.3 is a decimal, drop this branch.\n |- Pick two numbers (37, 47) (numbers left: [28, 26]). Try possible operations.\n  |- Try 47 + 37 = 84. Add 84 to the number set. Current number set: [84, 28, 26], target: 20. Options for choosing two numbers: [(84, 28), (84, 26), (28, 26)].\n   |- Pick two numbers (84, 28) (numbers left: [26]). Try possible operations.\n    |- Try 84 + 28 = 112. Add 112 to the number set. Current number set: [112, 26], target: 20, just two numbers left.\n     |- Try 112 + 26 = 138. Evaluate 138 != 20, drop this branch.\n     |- Try 112 - 26 = 86. Evaluate 86 != 20, drop this branch.\n     |- Try 112 * 26 = 2912. 2912 exceeds the maximum intermediate result, drop this branch.\n     |- Try 112 \/ 26 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 84 - 28 = 56. Add 56 to the number set. Current number set: [56, 26], target: 20, just two numbers left.\n     |- Try 56 + 26 = 82. Evaluate 82 != 20, drop this branch.\n     |- Try 56 - 26 = 30. Evaluate 30 != 20, drop this branch.\n     |- Try 56 * 26 = 1456. Evaluate 1456 != 20, drop this branch.\n     |- Try 56 \/ 26 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 84 * 28 = 2352. 2352 exceeds the maximum intermediate result, drop this branch.\n    |- Try 84 \/ 28 = 3. Add 3 to the number set. Current number set: [3, 26], target: 20, just two numbers left.\n     |- Try 26 + 3 = 29. Evaluate 29 != 20, drop this branch.\n     |- Try 26 - 3 = 23. Evaluate 23 != 20, drop this branch.\n     |- Try 26 * 3 = 78. Evaluate 78 != 20, drop this branch.\n     |- Try 26 \/ 3 = 8.7. 8.7 is a decimal, drop this branch.\n   |- Pick two numbers (84, 26) (numbers left: [28]). Try possible operations.\n    |- Try 84 + 26 = 110. Add 110 to the number set. Current number set: [110, 28], target: 20, just two numbers left.\n     |- Try 110 + 28 = 138. Evaluate 138 != 20, drop this branch.\n     |- Try 110 - 28 = 82. Evaluate 82 != 20, drop this branch.\n     |- Try 110 * 28 = 3080. 3080 exceeds the maximum intermediate result, drop this branch.\n     |- Try 110 \/ 28 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 84 - 26 = 58. Add 58 to the number set. Current number set: [58, 28], target: 20, just two numbers left.\n     |- Try 58 + 28 = 86. Evaluate 86 != 20, drop this branch.\n     |- Try 58 - 28 = 30. Evaluate 30 != 20, drop this branch.\n     |- Try 58 * 28 = 1624. Evaluate 1624 != 20, drop this branch.\n     |- Try 58 \/ 28 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 84 * 26 = 2184. 2184 exceeds the maximum intermediate result, drop this branch.\n    |- Try 84 \/ 26 = 3.2. 3.2 is a decimal, drop this branch.\n   |- Pick two numbers (28, 26) (numbers left: [84]). Try possible operations.\n    |- Try 28 + 26 = 54. Add 54 to the number set. Current number set: [54, 84], target: 20, just two numbers left.\n     |- Try 84 + 54 = 138. Evaluate 138 != 20, drop this branch.\n     |- Try 84 - 54 = 30. Evaluate 30 != 20, drop this branch.\n     |- Try 84 * 54 = 4536. 4536 exceeds the maximum intermediate result, drop this branch.\n     |- Try 84 \/ 54 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 28 - 26 = 2. Add 2 to the number set. Current number set: [2, 84], target: 20, just two numbers left.\n     |- Try 84 + 2 = 86. Evaluate 86 != 20, drop this branch.\n     |- Try 84 - 2 = 82. Evaluate 82 != 20, drop this branch.\n     |- Try 84 * 2 = 168. Evaluate 168 != 20, drop this branch.\n     |- Try 84 \/ 2 = 42. Evaluate 42 != 20, drop this branch.\n    |- Try 28 * 26 = 728. Add 728 to the number set. Current number set: [728, 84], target: 20, just two numbers left.\n     |- Try 728 + 84 = 812. Evaluate 812 != 20, drop this branch.\n     |- Try 728 - 84 = 644. Evaluate 644 != 20, drop this branch.\n     |- Try 728 * 84 = 61152. 61152 exceeds the maximum intermediate result, drop this branch.\n     |- Try 728 \/ 84 = 8.7. 8.7 is a decimal, drop this branch.\n    |- Try 28 \/ 26 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 47 - 37 = 10. Add 10 to the number set. Current number set: [10, 28, 26], target: 20. Options for choosing two numbers: [(10, 28), (10, 26), (28, 26)].\n   |- Pick two numbers (10, 28) (numbers left: [26]). Try possible operations.\n    |- Try 28 + 10 = 38. Add 38 to the number set. Current number set: [38, 26], target: 20, just two numbers left.\n     |- Try 38 + 26 = 64. Evaluate 64 != 20, drop this branch.\n     |- Try 38 - 26 = 12. Evaluate 12 != 20, drop this branch.\n     |- Try 38 * 26 = 988. Evaluate 988 != 20, drop this branch.\n     |- Try 38 \/ 26 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 28 - 10 = 18. Add 18 to the number set. Current number set: [18, 26], target: 20, just two numbers left.\n     |- Try 26 + 18 = 44. Evaluate 44 != 20, drop this branch.\n     |- Try 26 - 18 = 8. Evaluate 8 != 20, drop this branch.\n     |- Try 26 * 18 = 468. Evaluate 468 != 20, drop this branch.\n     |- Try 26 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 28 * 10 = 280. Add 280 to the number set. Current number set: [280, 26], target: 20, just two numbers left.\n     |- Try 280 + 26 = 306. Evaluate 306 != 20, drop this branch.\n     |- Try 280 - 26 = 254. Evaluate 254 != 20, drop this branch.\n     |- Try 280 * 26 = 7280. 7280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 280 \/ 26 = 10.8. 10.8 is a decimal, drop this branch.\n    |- Try 28 \/ 10 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (10, 26) (numbers left: [28]). Try possible operations.\n    |- Try 26 + 10 = 36. Add 36 to the number set. Current number set: [36, 28], target: 20, just two numbers left.\n     |- Try 36 + 28 = 64. Evaluate 64 != 20, drop this branch.\n     |- Try 36 - 28 = 8. Evaluate 8 != 20, drop this branch.\n     |- Try 36 * 28 = 1008. Evaluate 1008 != 20, drop this branch.\n     |- Try 36 \/ 28 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 26 - 10 = 16. Add 16 to the number set. Current number set: [16, 28], target: 20, just two numbers left.\n     |- Try 28 + 16 = 44. Evaluate 44 != 20, drop this branch.\n     |- Try 28 - 16 = 12. Evaluate 12 != 20, drop this branch.\n     |- Try 28 * 16 = 448. Evaluate 448 != 20, drop this branch.\n     |- Try 28 \/ 16 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 26 * 10 = 260. Add 260 to the number set. Current number set: [260, 28], target: 20, just two numbers left.\n     |- Try 260 + 28 = 288. Evaluate 288 != 20, drop this branch.\n     |- Try 260 - 28 = 232. Evaluate 232 != 20, drop this branch.\n     |- Try 260 * 28 = 7280. 7280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 260 \/ 28 = 9.3. 9.3 is a decimal, drop this branch.\n    |- Try 26 \/ 10 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (28, 26) (numbers left: [10]). Try possible operations.\n    |- Try 28 + 26 = 54. Add 54 to the number set. Current number set: [54, 10], target: 20, just two numbers left.\n     |- Try 54 + 10 = 64. Evaluate 64 != 20, drop this branch.\n     |- Try 54 - 10 = 44. Evaluate 44 != 20, drop this branch.\n     |- Try 54 * 10 = 540. Evaluate 540 != 20, drop this branch.\n     |- Try 54 \/ 10 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 28 - 26 = 2. Add 2 to the number set. Current number set: [2, 10], target: 20, just two numbers left.\n     |- Try 10 + 2 = 12. Evaluate 12 != 20, drop this branch.\n     |- Try 10 - 2 = 8. Evaluate 8 != 20, drop this branch.\n     |- Try 10 * 2 = 20. Evaluate 20 == 20, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 10 * 2 = 20\nThe step before: 28 - 26 = 2\nThe first step: 47 - 37 = 10\n\nOutput the solution in the required format:\n<Solution>\n47 - 37 = 10\n28 - 26 = 2\n10 * 2 = 20\n<\/Solution>\n","item":{"nums":[37,28,47,26],"solution":["47 - 37 = 10","28 - 26 = 2","10 * 2 = 20"],"target":20}}
+{"instance_id":"countdown_8k_46","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [15, 39, 15, 2]\nTarget: 21","reference_output":"# Search Procedure\nInitial number set: [15, 39, 15, 2], target: 21. Options for choosing two numbers: [(15, 39), (15, 15), (15, 2), (39, 15), (39, 2), (15, 2)].\n |- Pick two numbers (15, 39) (numbers left: [15, 2]). Try possible operations.\n  |- Try 39 + 15 = 54. Add 54 to the number set. Current number set: [54, 15, 2], target: 21. Options for choosing two numbers: [(54, 15), (54, 2), (15, 2)].\n   |- Pick two numbers (54, 15) (numbers left: [2]). Try possible operations.\n    |- Try 54 + 15 = 69. Add 69 to the number set. Current number set: [69, 2], target: 21, just two numbers left.\n     |- Try 69 + 2 = 71. Evaluate 71 != 21, drop this branch.\n     |- Try 69 - 2 = 67. Evaluate 67 != 21, drop this branch.\n     |- Try 69 * 2 = 138. Evaluate 138 != 21, drop this branch.\n     |- Try 69 \/ 2 = 34.5. 34.5 is a decimal, drop this branch.\n    |- Try 54 - 15 = 39. Add 39 to the number set. Current number set: [39, 2], target: 21, just two numbers left.\n     |- Try 39 + 2 = 41. Evaluate 41 != 21, drop this branch.\n     |- Try 39 - 2 = 37. Evaluate 37 != 21, drop this branch.\n     |- Try 39 * 2 = 78. Evaluate 78 != 21, drop this branch.\n     |- Try 39 \/ 2 = 19.5. 19.5 is a decimal, drop this branch.\n    |- Try 54 * 15 = 810. Add 810 to the number set. Current number set: [810, 2], target: 21, just two numbers left.\n     |- Try 810 + 2 = 812. Evaluate 812 != 21, drop this branch.\n     |- Try 810 - 2 = 808. Evaluate 808 != 21, drop this branch.\n     |- Try 810 * 2 = 1620. Evaluate 1620 != 21, drop this branch.\n     |- Try 810 \/ 2 = 405. Evaluate 405 != 21, drop this branch.\n    |- Try 54 \/ 15 = 3.6. 3.6 is a decimal, drop this branch.\n   |- Pick two numbers (54, 2) (numbers left: [15]). Try possible operations.\n    |- Try 54 + 2 = 56. Add 56 to the number set. Current number set: [56, 15], target: 21, just two numbers left.\n     |- Try 56 + 15 = 71. Evaluate 71 != 21, drop this branch.\n     |- Try 56 - 15 = 41. Evaluate 41 != 21, drop this branch.\n     |- Try 56 * 15 = 840. Evaluate 840 != 21, drop this branch.\n     |- Try 56 \/ 15 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 54 - 2 = 52. Add 52 to the number set. Current number set: [52, 15], target: 21, just two numbers left.\n     |- Try 52 + 15 = 67. Evaluate 67 != 21, drop this branch.\n     |- Try 52 - 15 = 37. Evaluate 37 != 21, drop this branch.\n     |- Try 52 * 15 = 780. Evaluate 780 != 21, drop this branch.\n     |- Try 52 \/ 15 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 54 * 2 = 108. Add 108 to the number set. Current number set: [108, 15], target: 21, just two numbers left.\n     |- Try 108 + 15 = 123. Evaluate 123 != 21, drop this branch.\n     |- Try 108 - 15 = 93. Evaluate 93 != 21, drop this branch.\n     |- Try 108 * 15 = 1620. Evaluate 1620 != 21, drop this branch.\n     |- Try 108 \/ 15 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 54 \/ 2 = 27. Add 27 to the number set. Current number set: [27, 15], target: 21, just two numbers left.\n     |- Try 27 + 15 = 42. Evaluate 42 != 21, drop this branch.\n     |- Try 27 - 15 = 12. Evaluate 12 != 21, drop this branch.\n     |- Try 27 * 15 = 405. Evaluate 405 != 21, drop this branch.\n     |- Try 27 \/ 15 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (15, 2) (numbers left: [54]). Try possible operations.\n    |- Try 15 + 2 = 17. Add 17 to the number set. Current number set: [17, 54], target: 21, just two numbers left.\n     |- Try 54 + 17 = 71. Evaluate 71 != 21, drop this branch.\n     |- Try 54 - 17 = 37. Evaluate 37 != 21, drop this branch.\n     |- Try 54 * 17 = 918. Evaluate 918 != 21, drop this branch.\n     |- Try 54 \/ 17 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 15 - 2 = 13. Add 13 to the number set. Current number set: [13, 54], target: 21, just two numbers left.\n     |- Try 54 + 13 = 67. Evaluate 67 != 21, drop this branch.\n     |- Try 54 - 13 = 41. Evaluate 41 != 21, drop this branch.\n     |- Try 54 * 13 = 702. Evaluate 702 != 21, drop this branch.\n     |- Try 54 \/ 13 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 15 * 2 = 30. Add 30 to the number set. Current number set: [30, 54], target: 21, just two numbers left.\n     |- Try 54 + 30 = 84. Evaluate 84 != 21, drop this branch.\n     |- Try 54 - 30 = 24. Evaluate 24 != 21, drop this branch.\n     |- Try 54 * 30 = 1620. Evaluate 1620 != 21, drop this branch.\n     |- Try 54 \/ 30 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 15 \/ 2 = 7.5. 7.5 is a decimal, drop this branch.\n  |- Try 39 - 15 = 24. Add 24 to the number set. Current number set: [24, 15, 2], target: 21. Options for choosing two numbers: [(24, 15), (24, 2), (15, 2)].\n   |- Pick two numbers (24, 15) (numbers left: [2]). Try possible operations.\n    |- Try 24 + 15 = 39. Add 39 to the number set. Current number set: [39, 2], target: 21, just two numbers left.\n     |- Try 39 + 2 = 41. Evaluate 41 != 21, drop this branch.\n     |- Try 39 - 2 = 37. Evaluate 37 != 21, drop this branch.\n     |- Try 39 * 2 = 78. Evaluate 78 != 21, drop this branch.\n     |- Try 39 \/ 2 = 19.5. 19.5 is a decimal, drop this branch.\n    |- Try 24 - 15 = 9. Add 9 to the number set. Current number set: [9, 2], target: 21, just two numbers left.\n     |- Try 9 + 2 = 11. Evaluate 11 != 21, drop this branch.\n     |- Try 9 - 2 = 7. Evaluate 7 != 21, drop this branch.\n     |- Try 9 * 2 = 18. Evaluate 18 != 21, drop this branch.\n     |- Try 9 \/ 2 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 24 * 15 = 360. Add 360 to the number set. Current number set: [360, 2], target: 21, just two numbers left.\n     |- Try 360 + 2 = 362. Evaluate 362 != 21, drop this branch.\n     |- Try 360 - 2 = 358. Evaluate 358 != 21, drop this branch.\n     |- Try 360 * 2 = 720. Evaluate 720 != 21, drop this branch.\n     |- Try 360 \/ 2 = 180. Evaluate 180 != 21, drop this branch.\n    |- Try 24 \/ 15 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (24, 2) (numbers left: [15]). Try possible operations.\n    |- Try 24 + 2 = 26. Add 26 to the number set. Current number set: [26, 15], target: 21, just two numbers left.\n     |- Try 26 + 15 = 41. Evaluate 41 != 21, drop this branch.\n     |- Try 26 - 15 = 11. Evaluate 11 != 21, drop this branch.\n     |- Try 26 * 15 = 390. Evaluate 390 != 21, drop this branch.\n     |- Try 26 \/ 15 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 24 - 2 = 22. Add 22 to the number set. Current number set: [22, 15], target: 21, just two numbers left.\n     |- Try 22 + 15 = 37. Evaluate 37 != 21, drop this branch.\n     |- Try 22 - 15 = 7. Evaluate 7 != 21, drop this branch.\n     |- Try 22 * 15 = 330. Evaluate 330 != 21, drop this branch.\n     |- Try 22 \/ 15 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 24 * 2 = 48. Add 48 to the number set. Current number set: [48, 15], target: 21, just two numbers left.\n     |- Try 48 + 15 = 63. Evaluate 63 != 21, drop this branch.\n     |- Try 48 - 15 = 33. Evaluate 33 != 21, drop this branch.\n     |- Try 48 * 15 = 720. Evaluate 720 != 21, drop this branch.\n     |- Try 48 \/ 15 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 24 \/ 2 = 12. Add 12 to the number set. Current number set: [12, 15], target: 21, just two numbers left.\n     |- Try 15 + 12 = 27. Evaluate 27 != 21, drop this branch.\n     |- Try 15 - 12 = 3. Evaluate 3 != 21, drop this branch.\n     |- Try 15 * 12 = 180. Evaluate 180 != 21, drop this branch.\n     |- Try 15 \/ 12 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (15, 2) (numbers left: [24]). Try possible operations.\n    |- Try 15 + 2 = 17. Add 17 to the number set. Current number set: [17, 24], target: 21, just two numbers left.\n     |- Try 24 + 17 = 41. Evaluate 41 != 21, drop this branch.\n     |- Try 24 - 17 = 7. Evaluate 7 != 21, drop this branch.\n     |- Try 24 * 17 = 408. Evaluate 408 != 21, drop this branch.\n     |- Try 24 \/ 17 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 15 - 2 = 13. Add 13 to the number set. Current number set: [13, 24], target: 21, just two numbers left.\n     |- Try 24 + 13 = 37. Evaluate 37 != 21, drop this branch.\n     |- Try 24 - 13 = 11. Evaluate 11 != 21, drop this branch.\n     |- Try 24 * 13 = 312. Evaluate 312 != 21, drop this branch.\n     |- Try 24 \/ 13 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 15 * 2 = 30. Add 30 to the number set. Current number set: [30, 24], target: 21, just two numbers left.\n     |- Try 30 + 24 = 54. Evaluate 54 != 21, drop this branch.\n     |- Try 30 - 24 = 6. Evaluate 6 != 21, drop this branch.\n     |- Try 30 * 24 = 720. Evaluate 720 != 21, drop this branch.\n     |- Try 30 \/ 24 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 15 \/ 2 = 7.5. 7.5 is a decimal, drop this branch.\n  |- Try 39 * 15 = 585. Add 585 to the number set. Current number set: [585, 15, 2], target: 21. Options for choosing two numbers: [(585, 15), (585, 2), (15, 2)].\n   |- Pick two numbers (585, 15) (numbers left: [2]). Try possible operations.\n    |- Try 585 + 15 = 600. Add 600 to the number set. Current number set: [600, 2], target: 21, just two numbers left.\n     |- Try 600 + 2 = 602. Evaluate 602 != 21, drop this branch.\n     |- Try 600 - 2 = 598. Evaluate 598 != 21, drop this branch.\n     |- Try 600 * 2 = 1200. Evaluate 1200 != 21, drop this branch.\n     |- Try 600 \/ 2 = 300. Evaluate 300 != 21, drop this branch.\n    |- Try 585 - 15 = 570. Add 570 to the number set. Current number set: [570, 2], target: 21, just two numbers left.\n     |- Try 570 + 2 = 572. Evaluate 572 != 21, drop this branch.\n     |- Try 570 - 2 = 568. Evaluate 568 != 21, drop this branch.\n     |- Try 570 * 2 = 1140. Evaluate 1140 != 21, drop this branch.\n     |- Try 570 \/ 2 = 285. Evaluate 285 != 21, drop this branch.\n    |- Try 585 * 15 = 8775. 8775 exceeds the maximum intermediate result, drop this branch.\n    |- Try 585 \/ 15 = 39. Add 39 to the number set. Current number set: [39, 2], target: 21, just two numbers left.\n     |- Try 39 + 2 = 41. Evaluate 41 != 21, drop this branch.\n     |- Try 39 - 2 = 37. Evaluate 37 != 21, drop this branch.\n     |- Try 39 * 2 = 78. Evaluate 78 != 21, drop this branch.\n     |- Try 39 \/ 2 = 19.5. 19.5 is a decimal, drop this branch.\n   |- Pick two numbers (585, 2) (numbers left: [15]). Try possible operations.\n    |- Try 585 + 2 = 587. Add 587 to the number set. Current number set: [587, 15], target: 21, just two numbers left.\n     |- Try 587 + 15 = 602. Evaluate 602 != 21, drop this branch.\n     |- Try 587 - 15 = 572. Evaluate 572 != 21, drop this branch.\n     |- Try 587 * 15 = 8805. 8805 exceeds the maximum intermediate result, drop this branch.\n     |- Try 587 \/ 15 = 39.1. 39.1 is a decimal, drop this branch.\n    |- Try 585 - 2 = 583. Add 583 to the number set. Current number set: [583, 15], target: 21, just two numbers left.\n     |- Try 583 + 15 = 598. Evaluate 598 != 21, drop this branch.\n     |- Try 583 - 15 = 568. Evaluate 568 != 21, drop this branch.\n     |- Try 583 * 15 = 8745. 8745 exceeds the maximum intermediate result, drop this branch.\n     |- Try 583 \/ 15 = 38.9. 38.9 is a decimal, drop this branch.\n    |- Try 585 * 2 = 1170. Add 1170 to the number set. Current number set: [1170, 15], target: 21, just two numbers left.\n     |- Try 1170 + 15 = 1185. Evaluate 1185 != 21, drop this branch.\n     |- Try 1170 - 15 = 1155. Evaluate 1155 != 21, drop this branch.\n     |- Try 1170 * 15 = 17550. 17550 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1170 \/ 15 = 78. Evaluate 78 != 21, drop this branch.\n    |- Try 585 \/ 2 = 292.5. 292.5 is a decimal, drop this branch.\n   |- Pick two numbers (15, 2) (numbers left: [585]). Try possible operations.\n    |- Try 15 + 2 = 17. Add 17 to the number set. Current number set: [17, 585], target: 21, just two numbers left.\n     |- Try 585 + 17 = 602. Evaluate 602 != 21, drop this branch.\n     |- Try 585 - 17 = 568. Evaluate 568 != 21, drop this branch.\n     |- Try 585 * 17 = 9945. 9945 exceeds the maximum intermediate result, drop this branch.\n     |- Try 585 \/ 17 = 34.4. 34.4 is a decimal, drop this branch.\n    |- Try 15 - 2 = 13. Add 13 to the number set. Current number set: [13, 585], target: 21, just two numbers left.\n     |- Try 585 + 13 = 598. Evaluate 598 != 21, drop this branch.\n     |- Try 585 - 13 = 572. Evaluate 572 != 21, drop this branch.\n     |- Try 585 * 13 = 7605. 7605 exceeds the maximum intermediate result, drop this branch.\n     |- Try 585 \/ 13 = 45. Evaluate 45 != 21, drop this branch.\n    |- Try 15 * 2 = 30. Add 30 to the number set. Current number set: [30, 585], target: 21, just two numbers left.\n     |- Try 585 + 30 = 615. Evaluate 615 != 21, drop this branch.\n     |- Try 585 - 30 = 555. Evaluate 555 != 21, drop this branch.\n     |- Try 585 * 30 = 17550. 17550 exceeds the maximum intermediate result, drop this branch.\n     |- Try 585 \/ 30 = 19.5. 19.5 is a decimal, drop this branch.\n    |- Try 15 \/ 2 = 7.5. 7.5 is a decimal, drop this branch.\n  |- Try 39 \/ 15 = 2.6. 2.6 is a decimal, drop this branch.\n |- Pick two numbers (15, 15) (numbers left: [39, 2]). Try possible operations.\n  |- Try 15 + 15 = 30. Add 30 to the number set. Current number set: [30, 39, 2], target: 21. Options for choosing two numbers: [(30, 39), (30, 2), (39, 2)].\n   |- Pick two numbers (30, 39) (numbers left: [2]). Try possible operations.\n    |- Try 39 + 30 = 69. Add 69 to the number set. Current number set: [69, 2], target: 21, just two numbers left.\n     |- Try 69 + 2 = 71. Evaluate 71 != 21, drop this branch.\n     |- Try 69 - 2 = 67. Evaluate 67 != 21, drop this branch.\n     |- Try 69 * 2 = 138. Evaluate 138 != 21, drop this branch.\n     |- Try 69 \/ 2 = 34.5. 34.5 is a decimal, drop this branch.\n    |- Try 39 - 30 = 9. Add 9 to the number set. Current number set: [9, 2], target: 21, just two numbers left.\n     |- Try 9 + 2 = 11. Evaluate 11 != 21, drop this branch.\n     |- Try 9 - 2 = 7. Evaluate 7 != 21, drop this branch.\n     |- Try 9 * 2 = 18. Evaluate 18 != 21, drop this branch.\n     |- Try 9 \/ 2 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 39 * 30 = 1170. Add 1170 to the number set. Current number set: [1170, 2], target: 21, just two numbers left.\n     |- Try 1170 + 2 = 1172. Evaluate 1172 != 21, drop this branch.\n     |- Try 1170 - 2 = 1168. Evaluate 1168 != 21, drop this branch.\n     |- Try 1170 * 2 = 2340. 2340 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1170 \/ 2 = 585. Evaluate 585 != 21, drop this branch.\n    |- Try 39 \/ 30 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (30, 2) (numbers left: [39]). Try possible operations.\n    |- Try 30 + 2 = 32. Add 32 to the number set. Current number set: [32, 39], target: 21, just two numbers left.\n     |- Try 39 + 32 = 71. Evaluate 71 != 21, drop this branch.\n     |- Try 39 - 32 = 7. Evaluate 7 != 21, drop this branch.\n     |- Try 39 * 32 = 1248. Evaluate 1248 != 21, drop this branch.\n     |- Try 39 \/ 32 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 30 - 2 = 28. Add 28 to the number set. Current number set: [28, 39], target: 21, just two numbers left.\n     |- Try 39 + 28 = 67. Evaluate 67 != 21, drop this branch.\n     |- Try 39 - 28 = 11. Evaluate 11 != 21, drop this branch.\n     |- Try 39 * 28 = 1092. Evaluate 1092 != 21, drop this branch.\n     |- Try 39 \/ 28 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 30 * 2 = 60. Add 60 to the number set. Current number set: [60, 39], target: 21, just two numbers left.\n     |- Try 60 + 39 = 99. Evaluate 99 != 21, drop this branch.\n     |- Try 60 - 39 = 21. Evaluate 21 == 21, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 60 - 39 = 21\nThe step before: 30 * 2 = 60\nThe first step: 15 + 15 = 30\n\nOutput the solution in the required format:\n<Solution>\n15 + 15 = 30\n30 * 2 = 60\n60 - 39 = 21\n<\/Solution>\n","item":{"nums":[15,39,15,2],"solution":["15 + 15 = 30","30 * 2 = 60","60 - 39 = 21"],"target":21}}
+{"instance_id":"countdown_8k_47","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [22, 48, 5, 16]\nTarget: 48","reference_output":"# Search Procedure\nInitial number set: [22, 48, 5, 16], target: 48. Options for choosing two numbers: [(22, 48), (22, 5), (22, 16), (48, 5), (48, 16), (5, 16)].\n |- Pick two numbers (22, 48) (numbers left: [5, 16]). Try possible operations.\n  |- Try 48 + 22 = 70. Add 70 to the number set. Current number set: [70, 5, 16], target: 48. Options for choosing two numbers: [(70, 5), (70, 16), (5, 16)].\n   |- Pick two numbers (70, 5) (numbers left: [16]). Try possible operations.\n    |- Try 70 + 5 = 75. Add 75 to the number set. Current number set: [75, 16], target: 48, just two numbers left.\n     |- Try 75 + 16 = 91. Evaluate 91 != 48, drop this branch.\n     |- Try 75 - 16 = 59. Evaluate 59 != 48, drop this branch.\n     |- Try 75 * 16 = 1200. Evaluate 1200 != 48, drop this branch.\n     |- Try 75 \/ 16 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 70 - 5 = 65. Add 65 to the number set. Current number set: [65, 16], target: 48, just two numbers left.\n     |- Try 65 + 16 = 81. Evaluate 81 != 48, drop this branch.\n     |- Try 65 - 16 = 49. Evaluate 49 != 48, drop this branch.\n     |- Try 65 * 16 = 1040. Evaluate 1040 != 48, drop this branch.\n     |- Try 65 \/ 16 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 70 * 5 = 350. Add 350 to the number set. Current number set: [350, 16], target: 48, just two numbers left.\n     |- Try 350 + 16 = 366. Evaluate 366 != 48, drop this branch.\n     |- Try 350 - 16 = 334. Evaluate 334 != 48, drop this branch.\n     |- Try 350 * 16 = 5600. 5600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 350 \/ 16 = 21.9. 21.9 is a decimal, drop this branch.\n    |- Try 70 \/ 5 = 14. Add 14 to the number set. Current number set: [14, 16], target: 48, just two numbers left.\n     |- Try 16 + 14 = 30. Evaluate 30 != 48, drop this branch.\n     |- Try 16 - 14 = 2. Evaluate 2 != 48, drop this branch.\n     |- Try 16 * 14 = 224. Evaluate 224 != 48, drop this branch.\n     |- Try 16 \/ 14 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (70, 16) (numbers left: [5]). Try possible operations.\n    |- Try 70 + 16 = 86. Add 86 to the number set. Current number set: [86, 5], target: 48, just two numbers left.\n     |- Try 86 + 5 = 91. Evaluate 91 != 48, drop this branch.\n     |- Try 86 - 5 = 81. Evaluate 81 != 48, drop this branch.\n     |- Try 86 * 5 = 430. Evaluate 430 != 48, drop this branch.\n     |- Try 86 \/ 5 = 17.2. 17.2 is a decimal, drop this branch.\n    |- Try 70 - 16 = 54. Add 54 to the number set. Current number set: [54, 5], target: 48, just two numbers left.\n     |- Try 54 + 5 = 59. Evaluate 59 != 48, drop this branch.\n     |- Try 54 - 5 = 49. Evaluate 49 != 48, drop this branch.\n     |- Try 54 * 5 = 270. Evaluate 270 != 48, drop this branch.\n     |- Try 54 \/ 5 = 10.8. 10.8 is a decimal, drop this branch.\n    |- Try 70 * 16 = 1120. Add 1120 to the number set. Current number set: [1120, 5], target: 48, just two numbers left.\n     |- Try 1120 + 5 = 1125. Evaluate 1125 != 48, drop this branch.\n     |- Try 1120 - 5 = 1115. Evaluate 1115 != 48, drop this branch.\n     |- Try 1120 * 5 = 5600. 5600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1120 \/ 5 = 224. Evaluate 224 != 48, drop this branch.\n    |- Try 70 \/ 16 = 4.4. 4.4 is a decimal, drop this branch.\n   |- Pick two numbers (5, 16) (numbers left: [70]). Try possible operations.\n    |- Try 16 + 5 = 21. Add 21 to the number set. Current number set: [21, 70], target: 48, just two numbers left.\n     |- Try 70 + 21 = 91. Evaluate 91 != 48, drop this branch.\n     |- Try 70 - 21 = 49. Evaluate 49 != 48, drop this branch.\n     |- Try 70 * 21 = 1470. Evaluate 1470 != 48, drop this branch.\n     |- Try 70 \/ 21 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 16 - 5 = 11. Add 11 to the number set. Current number set: [11, 70], target: 48, just two numbers left.\n     |- Try 70 + 11 = 81. Evaluate 81 != 48, drop this branch.\n     |- Try 70 - 11 = 59. Evaluate 59 != 48, drop this branch.\n     |- Try 70 * 11 = 770. Evaluate 770 != 48, drop this branch.\n     |- Try 70 \/ 11 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 16 * 5 = 80. Add 80 to the number set. Current number set: [80, 70], target: 48, just two numbers left.\n     |- Try 80 + 70 = 150. Evaluate 150 != 48, drop this branch.\n     |- Try 80 - 70 = 10. Evaluate 10 != 48, drop this branch.\n     |- Try 80 * 70 = 5600. 5600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 80 \/ 70 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 16 \/ 5 = 3.2. 3.2 is a decimal, drop this branch.\n  |- Try 48 - 22 = 26. Add 26 to the number set. Current number set: [26, 5, 16], target: 48. Options for choosing two numbers: [(26, 5), (26, 16), (5, 16)].\n   |- Pick two numbers (26, 5) (numbers left: [16]). Try possible operations.\n    |- Try 26 + 5 = 31. Add 31 to the number set. Current number set: [31, 16], target: 48, just two numbers left.\n     |- Try 31 + 16 = 47. Evaluate 47 != 48, drop this branch.\n     |- Try 31 - 16 = 15. Evaluate 15 != 48, drop this branch.\n     |- Try 31 * 16 = 496. Evaluate 496 != 48, drop this branch.\n     |- Try 31 \/ 16 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 26 - 5 = 21. Add 21 to the number set. Current number set: [21, 16], target: 48, just two numbers left.\n     |- Try 21 + 16 = 37. Evaluate 37 != 48, drop this branch.\n     |- Try 21 - 16 = 5. Evaluate 5 != 48, drop this branch.\n     |- Try 21 * 16 = 336. Evaluate 336 != 48, drop this branch.\n     |- Try 21 \/ 16 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 26 * 5 = 130. Add 130 to the number set. Current number set: [130, 16], target: 48, just two numbers left.\n     |- Try 130 + 16 = 146. Evaluate 146 != 48, drop this branch.\n     |- Try 130 - 16 = 114. Evaluate 114 != 48, drop this branch.\n     |- Try 130 * 16 = 2080. 2080 exceeds the maximum intermediate result, drop this branch.\n     |- Try 130 \/ 16 = 8.1. 8.1 is a decimal, drop this branch.\n    |- Try 26 \/ 5 = 5.2. 5.2 is a decimal, drop this branch.\n   |- Pick two numbers (26, 16) (numbers left: [5]). Try possible operations.\n    |- Try 26 + 16 = 42. Add 42 to the number set. Current number set: [42, 5], target: 48, just two numbers left.\n     |- Try 42 + 5 = 47. Evaluate 47 != 48, drop this branch.\n     |- Try 42 - 5 = 37. Evaluate 37 != 48, drop this branch.\n     |- Try 42 * 5 = 210. Evaluate 210 != 48, drop this branch.\n     |- Try 42 \/ 5 = 8.4. 8.4 is a decimal, drop this branch.\n    |- Try 26 - 16 = 10. Add 10 to the number set. Current number set: [10, 5], target: 48, just two numbers left.\n     |- Try 10 + 5 = 15. Evaluate 15 != 48, drop this branch.\n     |- Try 10 - 5 = 5. Evaluate 5 != 48, drop this branch.\n     |- Try 10 * 5 = 50. Evaluate 50 != 48, drop this branch.\n     |- Try 10 \/ 5 = 2. Evaluate 2 != 48, drop this branch.\n    |- Try 26 * 16 = 416. Add 416 to the number set. Current number set: [416, 5], target: 48, just two numbers left.\n     |- Try 416 + 5 = 421. Evaluate 421 != 48, drop this branch.\n     |- Try 416 - 5 = 411. Evaluate 411 != 48, drop this branch.\n     |- Try 416 * 5 = 2080. 2080 exceeds the maximum intermediate result, drop this branch.\n     |- Try 416 \/ 5 = 83.2. 83.2 is a decimal, drop this branch.\n    |- Try 26 \/ 16 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (5, 16) (numbers left: [26]). Try possible operations.\n    |- Try 16 + 5 = 21. Add 21 to the number set. Current number set: [21, 26], target: 48, just two numbers left.\n     |- Try 26 + 21 = 47. Evaluate 47 != 48, drop this branch.\n     |- Try 26 - 21 = 5. Evaluate 5 != 48, drop this branch.\n     |- Try 26 * 21 = 546. Evaluate 546 != 48, drop this branch.\n     |- Try 26 \/ 21 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 16 - 5 = 11. Add 11 to the number set. Current number set: [11, 26], target: 48, just two numbers left.\n     |- Try 26 + 11 = 37. Evaluate 37 != 48, drop this branch.\n     |- Try 26 - 11 = 15. Evaluate 15 != 48, drop this branch.\n     |- Try 26 * 11 = 286. Evaluate 286 != 48, drop this branch.\n     |- Try 26 \/ 11 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 16 * 5 = 80. Add 80 to the number set. Current number set: [80, 26], target: 48, just two numbers left.\n     |- Try 80 + 26 = 106. Evaluate 106 != 48, drop this branch.\n     |- Try 80 - 26 = 54. Evaluate 54 != 48, drop this branch.\n     |- Try 80 * 26 = 2080. 2080 exceeds the maximum intermediate result, drop this branch.\n     |- Try 80 \/ 26 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 16 \/ 5 = 3.2. 3.2 is a decimal, drop this branch.\n  |- Try 48 * 22 = 1056. Add 1056 to the number set. Current number set: [1056, 5, 16], target: 48. Options for choosing two numbers: [(1056, 5), (1056, 16), (5, 16)].\n   |- Pick two numbers (1056, 5) (numbers left: [16]). Try possible operations.\n    |- Try 1056 + 5 = 1061. Add 1061 to the number set. Current number set: [1061, 16], target: 48, just two numbers left.\n     |- Try 1061 + 16 = 1077. Evaluate 1077 != 48, drop this branch.\n     |- Try 1061 - 16 = 1045. Evaluate 1045 != 48, drop this branch.\n     |- Try 1061 * 16 = 16976. 16976 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1061 \/ 16 = 66.3. 66.3 is a decimal, drop this branch.\n    |- Try 1056 - 5 = 1051. Add 1051 to the number set. Current number set: [1051, 16], target: 48, just two numbers left.\n     |- Try 1051 + 16 = 1067. Evaluate 1067 != 48, drop this branch.\n     |- Try 1051 - 16 = 1035. Evaluate 1035 != 48, drop this branch.\n     |- Try 1051 * 16 = 16816. 16816 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1051 \/ 16 = 65.7. 65.7 is a decimal, drop this branch.\n    |- Try 1056 * 5 = 5280. 5280 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1056 \/ 5 = 211.2. 211.2 is a decimal, drop this branch.\n   |- Pick two numbers (1056, 16) (numbers left: [5]). Try possible operations.\n    |- Try 1056 + 16 = 1072. Add 1072 to the number set. Current number set: [1072, 5], target: 48, just two numbers left.\n     |- Try 1072 + 5 = 1077. Evaluate 1077 != 48, drop this branch.\n     |- Try 1072 - 5 = 1067. Evaluate 1067 != 48, drop this branch.\n     |- Try 1072 * 5 = 5360. 5360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1072 \/ 5 = 214.4. 214.4 is a decimal, drop this branch.\n    |- Try 1056 - 16 = 1040. Add 1040 to the number set. Current number set: [1040, 5], target: 48, just two numbers left.\n     |- Try 1040 + 5 = 1045. Evaluate 1045 != 48, drop this branch.\n     |- Try 1040 - 5 = 1035. Evaluate 1035 != 48, drop this branch.\n     |- Try 1040 * 5 = 5200. 5200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1040 \/ 5 = 208. Evaluate 208 != 48, drop this branch.\n    |- Try 1056 * 16 = 16896. 16896 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1056 \/ 16 = 66. Add 66 to the number set. Current number set: [66, 5], target: 48, just two numbers left.\n     |- Try 66 + 5 = 71. Evaluate 71 != 48, drop this branch.\n     |- Try 66 - 5 = 61. Evaluate 61 != 48, drop this branch.\n     |- Try 66 * 5 = 330. Evaluate 330 != 48, drop this branch.\n     |- Try 66 \/ 5 = 13.2. 13.2 is a decimal, drop this branch.\n   |- Pick two numbers (5, 16) (numbers left: [1056]). Try possible operations.\n    |- Try 16 + 5 = 21. Add 21 to the number set. Current number set: [21, 1056], target: 48, just two numbers left.\n     |- Try 1056 + 21 = 1077. Evaluate 1077 != 48, drop this branch.\n     |- Try 1056 - 21 = 1035. Evaluate 1035 != 48, drop this branch.\n     |- Try 1056 * 21 = 22176. 22176 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1056 \/ 21 = 50.3. 50.3 is a decimal, drop this branch.\n    |- Try 16 - 5 = 11. Add 11 to the number set. Current number set: [11, 1056], target: 48, just two numbers left.\n     |- Try 1056 + 11 = 1067. Evaluate 1067 != 48, drop this branch.\n     |- Try 1056 - 11 = 1045. Evaluate 1045 != 48, drop this branch.\n     |- Try 1056 * 11 = 11616. 11616 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1056 \/ 11 = 96. Evaluate 96 != 48, drop this branch.\n    |- Try 16 * 5 = 80. Add 80 to the number set. Current number set: [80, 1056], target: 48, just two numbers left.\n     |- Try 1056 + 80 = 1136. Evaluate 1136 != 48, drop this branch.\n     |- Try 1056 - 80 = 976. Evaluate 976 != 48, drop this branch.\n     |- Try 1056 * 80 = 84480. 84480 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1056 \/ 80 = 13.2. 13.2 is a decimal, drop this branch.\n    |- Try 16 \/ 5 = 3.2. 3.2 is a decimal, drop this branch.\n  |- Try 48 \/ 22 = 2.2. 2.2 is a decimal, drop this branch.\n |- Pick two numbers (22, 5) (numbers left: [48, 16]). Try possible operations.\n  |- Try 22 + 5 = 27. Add 27 to the number set. Current number set: [27, 48, 16], target: 48. Options for choosing two numbers: [(27, 48), (27, 16), (48, 16)].\n   |- Pick two numbers (27, 48) (numbers left: [16]). Try possible operations.\n    |- Try 48 + 27 = 75. Add 75 to the number set. Current number set: [75, 16], target: 48, just two numbers left.\n     |- Try 75 + 16 = 91. Evaluate 91 != 48, drop this branch.\n     |- Try 75 - 16 = 59. Evaluate 59 != 48, drop this branch.\n     |- Try 75 * 16 = 1200. Evaluate 1200 != 48, drop this branch.\n     |- Try 75 \/ 16 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 48 - 27 = 21. Add 21 to the number set. Current number set: [21, 16], target: 48, just two numbers left.\n     |- Try 21 + 16 = 37. Evaluate 37 != 48, drop this branch.\n     |- Try 21 - 16 = 5. Evaluate 5 != 48, drop this branch.\n     |- Try 21 * 16 = 336. Evaluate 336 != 48, drop this branch.\n     |- Try 21 \/ 16 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 48 * 27 = 1296. Add 1296 to the number set. Current number set: [1296, 16], target: 48, just two numbers left.\n     |- Try 1296 + 16 = 1312. Evaluate 1312 != 48, drop this branch.\n     |- Try 1296 - 16 = 1280. Evaluate 1280 != 48, drop this branch.\n     |- Try 1296 * 16 = 20736. 20736 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1296 \/ 16 = 81. Evaluate 81 != 48, drop this branch.\n    |- Try 48 \/ 27 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (27, 16) (numbers left: [48]). Try possible operations.\n    |- Try 27 + 16 = 43. Add 43 to the number set. Current number set: [43, 48], target: 48, just two numbers left.\n     |- Try 48 + 43 = 91. Evaluate 91 != 48, drop this branch.\n     |- Try 48 - 43 = 5. Evaluate 5 != 48, drop this branch.\n     |- Try 48 * 43 = 2064. 2064 exceeds the maximum intermediate result, drop this branch.\n     |- Try 48 \/ 43 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 27 - 16 = 11. Add 11 to the number set. Current number set: [11, 48], target: 48, just two numbers left.\n     |- Try 48 + 11 = 59. Evaluate 59 != 48, drop this branch.\n     |- Try 48 - 11 = 37. Evaluate 37 != 48, drop this branch.\n     |- Try 48 * 11 = 528. Evaluate 528 != 48, drop this branch.\n     |- Try 48 \/ 11 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 27 * 16 = 432. Add 432 to the number set. Current number set: [432, 48], target: 48, just two numbers left.\n     |- Try 432 + 48 = 480. Evaluate 480 != 48, drop this branch.\n     |- Try 432 - 48 = 384. Evaluate 384 != 48, drop this branch.\n     |- Try 432 * 48 = 20736. 20736 exceeds the maximum intermediate result, drop this branch.\n     |- Try 432 \/ 48 = 9. Evaluate 9 != 48, drop this branch.\n    |- Try 27 \/ 16 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (48, 16) (numbers left: [27]). Try possible operations.\n    |- Try 48 + 16 = 64. Add 64 to the number set. Current number set: [64, 27], target: 48, just two numbers left.\n     |- Try 64 + 27 = 91. Evaluate 91 != 48, drop this branch.\n     |- Try 64 - 27 = 37. Evaluate 37 != 48, drop this branch.\n     |- Try 64 * 27 = 1728. Evaluate 1728 != 48, drop this branch.\n     |- Try 64 \/ 27 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 48 - 16 = 32. Add 32 to the number set. Current number set: [32, 27], target: 48, just two numbers left.\n     |- Try 32 + 27 = 59. Evaluate 59 != 48, drop this branch.\n     |- Try 32 - 27 = 5. Evaluate 5 != 48, drop this branch.\n     |- Try 32 * 27 = 864. Evaluate 864 != 48, drop this branch.\n     |- Try 32 \/ 27 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 48 * 16 = 768. Add 768 to the number set. Current number set: [768, 27], target: 48, just two numbers left.\n     |- Try 768 + 27 = 795. Evaluate 795 != 48, drop this branch.\n     |- Try 768 - 27 = 741. Evaluate 741 != 48, drop this branch.\n     |- Try 768 * 27 = 20736. 20736 exceeds the maximum intermediate result, drop this branch.\n     |- Try 768 \/ 27 = 28.4. 28.4 is a decimal, drop this branch.\n    |- Try 48 \/ 16 = 3. Add 3 to the number set. Current number set: [3, 27], target: 48, just two numbers left.\n     |- Try 27 + 3 = 30. Evaluate 30 != 48, drop this branch.\n     |- Try 27 - 3 = 24. Evaluate 24 != 48, drop this branch.\n     |- Try 27 * 3 = 81. Evaluate 81 != 48, drop this branch.\n     |- Try 27 \/ 3 = 9. Evaluate 9 != 48, drop this branch.\n  |- Try 22 - 5 = 17. Add 17 to the number set. Current number set: [17, 48, 16], target: 48. Options for choosing two numbers: [(17, 48), (17, 16), (48, 16)].\n   |- Pick two numbers (17, 48) (numbers left: [16]). Try possible operations.\n    |- Try 48 + 17 = 65. Add 65 to the number set. Current number set: [65, 16], target: 48, just two numbers left.\n     |- Try 65 + 16 = 81. Evaluate 81 != 48, drop this branch.\n     |- Try 65 - 16 = 49. Evaluate 49 != 48, drop this branch.\n     |- Try 65 * 16 = 1040. Evaluate 1040 != 48, drop this branch.\n     |- Try 65 \/ 16 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 48 - 17 = 31. Add 31 to the number set. Current number set: [31, 16], target: 48, just two numbers left.\n     |- Try 31 + 16 = 47. Evaluate 47 != 48, drop this branch.\n     |- Try 31 - 16 = 15. Evaluate 15 != 48, drop this branch.\n     |- Try 31 * 16 = 496. Evaluate 496 != 48, drop this branch.\n     |- Try 31 \/ 16 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 48 * 17 = 816. Add 816 to the number set. Current number set: [816, 16], target: 48, just two numbers left.\n     |- Try 816 + 16 = 832. Evaluate 832 != 48, drop this branch.\n     |- Try 816 - 16 = 800. Evaluate 800 != 48, drop this branch.\n     |- Try 816 * 16 = 13056. 13056 exceeds the maximum intermediate result, drop this branch.\n     |- Try 816 \/ 16 = 51. Evaluate 51 != 48, drop this branch.\n    |- Try 48 \/ 17 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (17, 16) (numbers left: [48]). Try possible operations.\n    |- Try 17 + 16 = 33. Add 33 to the number set. Current number set: [33, 48], target: 48, just two numbers left.\n     |- Try 48 + 33 = 81. Evaluate 81 != 48, drop this branch.\n     |- Try 48 - 33 = 15. Evaluate 15 != 48, drop this branch.\n     |- Try 48 * 33 = 1584. Evaluate 1584 != 48, drop this branch.\n     |- Try 48 \/ 33 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 17 - 16 = 1. Add 1 to the number set. Current number set: [1, 48], target: 48, just two numbers left.\n     |- Try 48 + 1 = 49. Evaluate 49 != 48, drop this branch.\n     |- Try 48 - 1 = 47. Evaluate 47 != 48, drop this branch.\n     |- Try 48 * 1 = 48. Evaluate 48 == 48, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 48 * 1 = 48\nThe step before: 17 - 16 = 1\nThe first step: 22 - 5 = 17\n\nOutput the solution in the required format:\n<Solution>\n22 - 5 = 17\n17 - 16 = 1\n48 * 1 = 48\n<\/Solution>\n","item":{"nums":[22,48,5,16],"solution":["22 - 5 = 17","17 - 16 = 1","48 * 1 = 48"],"target":48}}
+{"instance_id":"countdown_8k_48","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [19, 43, 41, 39]\nTarget: 15","reference_output":"# Search Procedure\nInitial number set: [19, 43, 41, 39], target: 15. Options for choosing two numbers: [(19, 43), (19, 41), (19, 39), (43, 41), (43, 39), (41, 39)].\n |- Pick two numbers (19, 43) (numbers left: [41, 39]). Try possible operations.\n  |- Try 43 + 19 = 62. Add 62 to the number set. Current number set: [62, 41, 39], target: 15. Options for choosing two numbers: [(62, 41), (62, 39), (41, 39)].\n   |- Pick two numbers (62, 41) (numbers left: [39]). Try possible operations.\n    |- Try 62 + 41 = 103. Add 103 to the number set. Current number set: [103, 39], target: 15, just two numbers left.\n     |- Try 103 + 39 = 142. Evaluate 142 != 15, drop this branch.\n     |- Try 103 - 39 = 64. Evaluate 64 != 15, drop this branch.\n     |- Try 103 * 39 = 4017. 4017 exceeds the maximum intermediate result, drop this branch.\n     |- Try 103 \/ 39 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 62 - 41 = 21. Add 21 to the number set. Current number set: [21, 39], target: 15, just two numbers left.\n     |- Try 39 + 21 = 60. Evaluate 60 != 15, drop this branch.\n     |- Try 39 - 21 = 18. Evaluate 18 != 15, drop this branch.\n     |- Try 39 * 21 = 819. Evaluate 819 != 15, drop this branch.\n     |- Try 39 \/ 21 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 62 * 41 = 2542. 2542 exceeds the maximum intermediate result, drop this branch.\n    |- Try 62 \/ 41 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (62, 39) (numbers left: [41]). Try possible operations.\n    |- Try 62 + 39 = 101. Add 101 to the number set. Current number set: [101, 41], target: 15, just two numbers left.\n     |- Try 101 + 41 = 142. Evaluate 142 != 15, drop this branch.\n     |- Try 101 - 41 = 60. Evaluate 60 != 15, drop this branch.\n     |- Try 101 * 41 = 4141. 4141 exceeds the maximum intermediate result, drop this branch.\n     |- Try 101 \/ 41 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 62 - 39 = 23. Add 23 to the number set. Current number set: [23, 41], target: 15, just two numbers left.\n     |- Try 41 + 23 = 64. Evaluate 64 != 15, drop this branch.\n     |- Try 41 - 23 = 18. Evaluate 18 != 15, drop this branch.\n     |- Try 41 * 23 = 943. Evaluate 943 != 15, drop this branch.\n     |- Try 41 \/ 23 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 62 * 39 = 2418. 2418 exceeds the maximum intermediate result, drop this branch.\n    |- Try 62 \/ 39 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (41, 39) (numbers left: [62]). Try possible operations.\n    |- Try 41 + 39 = 80. Add 80 to the number set. Current number set: [80, 62], target: 15, just two numbers left.\n     |- Try 80 + 62 = 142. Evaluate 142 != 15, drop this branch.\n     |- Try 80 - 62 = 18. Evaluate 18 != 15, drop this branch.\n     |- Try 80 * 62 = 4960. 4960 exceeds the maximum intermediate result, drop this branch.\n     |- Try 80 \/ 62 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 41 - 39 = 2. Add 2 to the number set. Current number set: [2, 62], target: 15, just two numbers left.\n     |- Try 62 + 2 = 64. Evaluate 64 != 15, drop this branch.\n     |- Try 62 - 2 = 60. Evaluate 60 != 15, drop this branch.\n     |- Try 62 * 2 = 124. Evaluate 124 != 15, drop this branch.\n     |- Try 62 \/ 2 = 31. Evaluate 31 != 15, drop this branch.\n    |- Try 41 * 39 = 1599. Add 1599 to the number set. Current number set: [1599, 62], target: 15, just two numbers left.\n     |- Try 1599 + 62 = 1661. Evaluate 1661 != 15, drop this branch.\n     |- Try 1599 - 62 = 1537. Evaluate 1537 != 15, drop this branch.\n     |- Try 1599 * 62 = 99138. 99138 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1599 \/ 62 = 25.8. 25.8 is a decimal, drop this branch.\n    |- Try 41 \/ 39 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 43 - 19 = 24. Add 24 to the number set. Current number set: [24, 41, 39], target: 15. Options for choosing two numbers: [(24, 41), (24, 39), (41, 39)].\n   |- Pick two numbers (24, 41) (numbers left: [39]). Try possible operations.\n    |- Try 41 + 24 = 65. Add 65 to the number set. Current number set: [65, 39], target: 15, just two numbers left.\n     |- Try 65 + 39 = 104. Evaluate 104 != 15, drop this branch.\n     |- Try 65 - 39 = 26. Evaluate 26 != 15, drop this branch.\n     |- Try 65 * 39 = 2535. 2535 exceeds the maximum intermediate result, drop this branch.\n     |- Try 65 \/ 39 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 41 - 24 = 17. Add 17 to the number set. Current number set: [17, 39], target: 15, just two numbers left.\n     |- Try 39 + 17 = 56. Evaluate 56 != 15, drop this branch.\n     |- Try 39 - 17 = 22. Evaluate 22 != 15, drop this branch.\n     |- Try 39 * 17 = 663. Evaluate 663 != 15, drop this branch.\n     |- Try 39 \/ 17 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 41 * 24 = 984. Add 984 to the number set. Current number set: [984, 39], target: 15, just two numbers left.\n     |- Try 984 + 39 = 1023. Evaluate 1023 != 15, drop this branch.\n     |- Try 984 - 39 = 945. Evaluate 945 != 15, drop this branch.\n     |- Try 984 * 39 = 38376. 38376 exceeds the maximum intermediate result, drop this branch.\n     |- Try 984 \/ 39 = 25.2. 25.2 is a decimal, drop this branch.\n    |- Try 41 \/ 24 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (24, 39) (numbers left: [41]). Try possible operations.\n    |- Try 39 + 24 = 63. Add 63 to the number set. Current number set: [63, 41], target: 15, just two numbers left.\n     |- Try 63 + 41 = 104. Evaluate 104 != 15, drop this branch.\n     |- Try 63 - 41 = 22. Evaluate 22 != 15, drop this branch.\n     |- Try 63 * 41 = 2583. 2583 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 41 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 39 - 24 = 15. Add 15 to the number set. Current number set: [15, 41], target: 15, just two numbers left.\n     |- Try 41 + 15 = 56. Evaluate 56 != 15, drop this branch.\n     |- Try 41 - 15 = 26. Evaluate 26 != 15, drop this branch.\n     |- Try 41 * 15 = 615. Evaluate 615 != 15, drop this branch.\n     |- Try 41 \/ 15 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 39 * 24 = 936. Add 936 to the number set. Current number set: [936, 41], target: 15, just two numbers left.\n     |- Try 936 + 41 = 977. Evaluate 977 != 15, drop this branch.\n     |- Try 936 - 41 = 895. Evaluate 895 != 15, drop this branch.\n     |- Try 936 * 41 = 38376. 38376 exceeds the maximum intermediate result, drop this branch.\n     |- Try 936 \/ 41 = 22.8. 22.8 is a decimal, drop this branch.\n    |- Try 39 \/ 24 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (41, 39) (numbers left: [24]). Try possible operations.\n    |- Try 41 + 39 = 80. Add 80 to the number set. Current number set: [80, 24], target: 15, just two numbers left.\n     |- Try 80 + 24 = 104. Evaluate 104 != 15, drop this branch.\n     |- Try 80 - 24 = 56. Evaluate 56 != 15, drop this branch.\n     |- Try 80 * 24 = 1920. Evaluate 1920 != 15, drop this branch.\n     |- Try 80 \/ 24 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 41 - 39 = 2. Add 2 to the number set. Current number set: [2, 24], target: 15, just two numbers left.\n     |- Try 24 + 2 = 26. Evaluate 26 != 15, drop this branch.\n     |- Try 24 - 2 = 22. Evaluate 22 != 15, drop this branch.\n     |- Try 24 * 2 = 48. Evaluate 48 != 15, drop this branch.\n     |- Try 24 \/ 2 = 12. Evaluate 12 != 15, drop this branch.\n    |- Try 41 * 39 = 1599. Add 1599 to the number set. Current number set: [1599, 24], target: 15, just two numbers left.\n     |- Try 1599 + 24 = 1623. Evaluate 1623 != 15, drop this branch.\n     |- Try 1599 - 24 = 1575. Evaluate 1575 != 15, drop this branch.\n     |- Try 1599 * 24 = 38376. 38376 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1599 \/ 24 = 66.6. 66.6 is a decimal, drop this branch.\n    |- Try 41 \/ 39 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 43 * 19 = 817. Add 817 to the number set. Current number set: [817, 41, 39], target: 15. Options for choosing two numbers: [(817, 41), (817, 39), (41, 39)].\n   |- Pick two numbers (817, 41) (numbers left: [39]). Try possible operations.\n    |- Try 817 + 41 = 858. Add 858 to the number set. Current number set: [858, 39], target: 15, just two numbers left.\n     |- Try 858 + 39 = 897. Evaluate 897 != 15, drop this branch.\n     |- Try 858 - 39 = 819. Evaluate 819 != 15, drop this branch.\n     |- Try 858 * 39 = 33462. 33462 exceeds the maximum intermediate result, drop this branch.\n     |- Try 858 \/ 39 = 22. Evaluate 22 != 15, drop this branch.\n    |- Try 817 - 41 = 776. Add 776 to the number set. Current number set: [776, 39], target: 15, just two numbers left.\n     |- Try 776 + 39 = 815. Evaluate 815 != 15, drop this branch.\n     |- Try 776 - 39 = 737. Evaluate 737 != 15, drop this branch.\n     |- Try 776 * 39 = 30264. 30264 exceeds the maximum intermediate result, drop this branch.\n     |- Try 776 \/ 39 = 19.9. 19.9 is a decimal, drop this branch.\n    |- Try 817 * 41 = 33497. 33497 exceeds the maximum intermediate result, drop this branch.\n    |- Try 817 \/ 41 = 19.9. 19.9 is a decimal, drop this branch.\n   |- Pick two numbers (817, 39) (numbers left: [41]). Try possible operations.\n    |- Try 817 + 39 = 856. Add 856 to the number set. Current number set: [856, 41], target: 15, just two numbers left.\n     |- Try 856 + 41 = 897. Evaluate 897 != 15, drop this branch.\n     |- Try 856 - 41 = 815. Evaluate 815 != 15, drop this branch.\n     |- Try 856 * 41 = 35096. 35096 exceeds the maximum intermediate result, drop this branch.\n     |- Try 856 \/ 41 = 20.9. 20.9 is a decimal, drop this branch.\n    |- Try 817 - 39 = 778. Add 778 to the number set. Current number set: [778, 41], target: 15, just two numbers left.\n     |- Try 778 + 41 = 819. Evaluate 819 != 15, drop this branch.\n     |- Try 778 - 41 = 737. Evaluate 737 != 15, drop this branch.\n     |- Try 778 * 41 = 31898. 31898 exceeds the maximum intermediate result, drop this branch.\n     |- Try 778 \/ 41 = 19.0. 19.0 is a decimal, drop this branch.\n    |- Try 817 * 39 = 31863. 31863 exceeds the maximum intermediate result, drop this branch.\n    |- Try 817 \/ 39 = 20.9. 20.9 is a decimal, drop this branch.\n   |- Pick two numbers (41, 39) (numbers left: [817]). Try possible operations.\n    |- Try 41 + 39 = 80. Add 80 to the number set. Current number set: [80, 817], target: 15, just two numbers left.\n     |- Try 817 + 80 = 897. Evaluate 897 != 15, drop this branch.\n     |- Try 817 - 80 = 737. Evaluate 737 != 15, drop this branch.\n     |- Try 817 * 80 = 65360. 65360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 817 \/ 80 = 10.2. 10.2 is a decimal, drop this branch.\n    |- Try 41 - 39 = 2. Add 2 to the number set. Current number set: [2, 817], target: 15, just two numbers left.\n     |- Try 817 + 2 = 819. Evaluate 819 != 15, drop this branch.\n     |- Try 817 - 2 = 815. Evaluate 815 != 15, drop this branch.\n     |- Try 817 * 2 = 1634. Evaluate 1634 != 15, drop this branch.\n     |- Try 817 \/ 2 = 408.5. 408.5 is a decimal, drop this branch.\n    |- Try 41 * 39 = 1599. Add 1599 to the number set. Current number set: [1599, 817], target: 15, just two numbers left.\n     |- Try 1599 + 817 = 2416. 2416 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1599 - 817 = 782. Evaluate 782 != 15, drop this branch.\n     |- Try 1599 * 817 = 1306383. 1306383 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1599 \/ 817 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 41 \/ 39 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 43 \/ 19 = 2.3. 2.3 is a decimal, drop this branch.\n |- Pick two numbers (19, 41) (numbers left: [43, 39]). Try possible operations.\n  |- Try 41 + 19 = 60. Add 60 to the number set. Current number set: [60, 43, 39], target: 15. Options for choosing two numbers: [(60, 43), (60, 39), (43, 39)].\n   |- Pick two numbers (60, 43) (numbers left: [39]). Try possible operations.\n    |- Try 60 + 43 = 103. Add 103 to the number set. Current number set: [103, 39], target: 15, just two numbers left.\n     |- Try 103 + 39 = 142. Evaluate 142 != 15, drop this branch.\n     |- Try 103 - 39 = 64. Evaluate 64 != 15, drop this branch.\n     |- Try 103 * 39 = 4017. 4017 exceeds the maximum intermediate result, drop this branch.\n     |- Try 103 \/ 39 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 60 - 43 = 17. Add 17 to the number set. Current number set: [17, 39], target: 15, just two numbers left.\n     |- Try 39 + 17 = 56. Evaluate 56 != 15, drop this branch.\n     |- Try 39 - 17 = 22. Evaluate 22 != 15, drop this branch.\n     |- Try 39 * 17 = 663. Evaluate 663 != 15, drop this branch.\n     |- Try 39 \/ 17 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 60 * 43 = 2580. 2580 exceeds the maximum intermediate result, drop this branch.\n    |- Try 60 \/ 43 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (60, 39) (numbers left: [43]). Try possible operations.\n    |- Try 60 + 39 = 99. Add 99 to the number set. Current number set: [99, 43], target: 15, just two numbers left.\n     |- Try 99 + 43 = 142. Evaluate 142 != 15, drop this branch.\n     |- Try 99 - 43 = 56. Evaluate 56 != 15, drop this branch.\n     |- Try 99 * 43 = 4257. 4257 exceeds the maximum intermediate result, drop this branch.\n     |- Try 99 \/ 43 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 60 - 39 = 21. Add 21 to the number set. Current number set: [21, 43], target: 15, just two numbers left.\n     |- Try 43 + 21 = 64. Evaluate 64 != 15, drop this branch.\n     |- Try 43 - 21 = 22. Evaluate 22 != 15, drop this branch.\n     |- Try 43 * 21 = 903. Evaluate 903 != 15, drop this branch.\n     |- Try 43 \/ 21 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 60 * 39 = 2340. 2340 exceeds the maximum intermediate result, drop this branch.\n    |- Try 60 \/ 39 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (43, 39) (numbers left: [60]). Try possible operations.\n    |- Try 43 + 39 = 82. Add 82 to the number set. Current number set: [82, 60], target: 15, just two numbers left.\n     |- Try 82 + 60 = 142. Evaluate 142 != 15, drop this branch.\n     |- Try 82 - 60 = 22. Evaluate 22 != 15, drop this branch.\n     |- Try 82 * 60 = 4920. 4920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 82 \/ 60 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 43 - 39 = 4. Add 4 to the number set. Current number set: [4, 60], target: 15, just two numbers left.\n     |- Try 60 + 4 = 64. Evaluate 64 != 15, drop this branch.\n     |- Try 60 - 4 = 56. Evaluate 56 != 15, drop this branch.\n     |- Try 60 * 4 = 240. Evaluate 240 != 15, drop this branch.\n     |- Try 60 \/ 4 = 15. Evaluate 15 == 15, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 60 \/ 4 = 15\nThe step before: 43 - 39 = 4\nThe first step: 41 + 19 = 60\n\nOutput the solution in the required format:\n<Solution>\n41 + 19 = 60\n43 - 39 = 4\n60 \/ 4 = 15\n<\/Solution>\n","item":{"nums":[19,43,41,39],"solution":["41 + 19 = 60","43 - 39 = 4","60 \/ 4 = 15"],"target":15}}
+{"instance_id":"countdown_8k_49","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [18, 26, 10, 40]\nTarget: 21","reference_output":"# Search Procedure\nInitial number set: [18, 26, 10, 40], target: 21. Options for choosing two numbers: [(18, 26), (18, 10), (18, 40), (26, 10), (26, 40), (10, 40)].\n |- Pick two numbers (18, 26) (numbers left: [10, 40]). Try possible operations.\n  |- Try 26 + 18 = 44. Add 44 to the number set. Current number set: [44, 10, 40], target: 21. Options for choosing two numbers: [(44, 10), (44, 40), (10, 40)].\n   |- Pick two numbers (44, 10) (numbers left: [40]). Try possible operations.\n    |- Try 44 + 10 = 54. Add 54 to the number set. Current number set: [54, 40], target: 21, just two numbers left.\n     |- Try 54 + 40 = 94. Evaluate 94 != 21, drop this branch.\n     |- Try 54 - 40 = 14. Evaluate 14 != 21, drop this branch.\n     |- Try 54 * 40 = 2160. 2160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 54 \/ 40 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 44 - 10 = 34. Add 34 to the number set. Current number set: [34, 40], target: 21, just two numbers left.\n     |- Try 40 + 34 = 74. Evaluate 74 != 21, drop this branch.\n     |- Try 40 - 34 = 6. Evaluate 6 != 21, drop this branch.\n     |- Try 40 * 34 = 1360. Evaluate 1360 != 21, drop this branch.\n     |- Try 40 \/ 34 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 44 * 10 = 440. Add 440 to the number set. Current number set: [440, 40], target: 21, just two numbers left.\n     |- Try 440 + 40 = 480. Evaluate 480 != 21, drop this branch.\n     |- Try 440 - 40 = 400. Evaluate 400 != 21, drop this branch.\n     |- Try 440 * 40 = 17600. 17600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 440 \/ 40 = 11. Evaluate 11 != 21, drop this branch.\n    |- Try 44 \/ 10 = 4.4. 4.4 is a decimal, drop this branch.\n   |- Pick two numbers (44, 40) (numbers left: [10]). Try possible operations.\n    |- Try 44 + 40 = 84. Add 84 to the number set. Current number set: [84, 10], target: 21, just two numbers left.\n     |- Try 84 + 10 = 94. Evaluate 94 != 21, drop this branch.\n     |- Try 84 - 10 = 74. Evaluate 74 != 21, drop this branch.\n     |- Try 84 * 10 = 840. Evaluate 840 != 21, drop this branch.\n     |- Try 84 \/ 10 = 8.4. 8.4 is a decimal, drop this branch.\n    |- Try 44 - 40 = 4. Add 4 to the number set. Current number set: [4, 10], target: 21, just two numbers left.\n     |- Try 10 + 4 = 14. Evaluate 14 != 21, drop this branch.\n     |- Try 10 - 4 = 6. Evaluate 6 != 21, drop this branch.\n     |- Try 10 * 4 = 40. Evaluate 40 != 21, drop this branch.\n     |- Try 10 \/ 4 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 44 * 40 = 1760. Add 1760 to the number set. Current number set: [1760, 10], target: 21, just two numbers left.\n     |- Try 1760 + 10 = 1770. Evaluate 1770 != 21, drop this branch.\n     |- Try 1760 - 10 = 1750. Evaluate 1750 != 21, drop this branch.\n     |- Try 1760 * 10 = 17600. 17600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1760 \/ 10 = 176. Evaluate 176 != 21, drop this branch.\n    |- Try 44 \/ 40 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (10, 40) (numbers left: [44]). Try possible operations.\n    |- Try 40 + 10 = 50. Add 50 to the number set. Current number set: [50, 44], target: 21, just two numbers left.\n     |- Try 50 + 44 = 94. Evaluate 94 != 21, drop this branch.\n     |- Try 50 - 44 = 6. Evaluate 6 != 21, drop this branch.\n     |- Try 50 * 44 = 2200. 2200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 50 \/ 44 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 40 - 10 = 30. Add 30 to the number set. Current number set: [30, 44], target: 21, just two numbers left.\n     |- Try 44 + 30 = 74. Evaluate 74 != 21, drop this branch.\n     |- Try 44 - 30 = 14. Evaluate 14 != 21, drop this branch.\n     |- Try 44 * 30 = 1320. Evaluate 1320 != 21, drop this branch.\n     |- Try 44 \/ 30 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 40 * 10 = 400. Add 400 to the number set. Current number set: [400, 44], target: 21, just two numbers left.\n     |- Try 400 + 44 = 444. Evaluate 444 != 21, drop this branch.\n     |- Try 400 - 44 = 356. Evaluate 356 != 21, drop this branch.\n     |- Try 400 * 44 = 17600. 17600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 400 \/ 44 = 9.1. 9.1 is a decimal, drop this branch.\n    |- Try 40 \/ 10 = 4. Add 4 to the number set. Current number set: [4, 44], target: 21, just two numbers left.\n     |- Try 44 + 4 = 48. Evaluate 48 != 21, drop this branch.\n     |- Try 44 - 4 = 40. Evaluate 40 != 21, drop this branch.\n     |- Try 44 * 4 = 176. Evaluate 176 != 21, drop this branch.\n     |- Try 44 \/ 4 = 11. Evaluate 11 != 21, drop this branch.\n  |- Try 26 - 18 = 8. Add 8 to the number set. Current number set: [8, 10, 40], target: 21. Options for choosing two numbers: [(8, 10), (8, 40), (10, 40)].\n   |- Pick two numbers (8, 10) (numbers left: [40]). Try possible operations.\n    |- Try 10 + 8 = 18. Add 18 to the number set. Current number set: [18, 40], target: 21, just two numbers left.\n     |- Try 40 + 18 = 58. Evaluate 58 != 21, drop this branch.\n     |- Try 40 - 18 = 22. Evaluate 22 != 21, drop this branch.\n     |- Try 40 * 18 = 720. Evaluate 720 != 21, drop this branch.\n     |- Try 40 \/ 18 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 10 - 8 = 2. Add 2 to the number set. Current number set: [2, 40], target: 21, just two numbers left.\n     |- Try 40 + 2 = 42. Evaluate 42 != 21, drop this branch.\n     |- Try 40 - 2 = 38. Evaluate 38 != 21, drop this branch.\n     |- Try 40 * 2 = 80. Evaluate 80 != 21, drop this branch.\n     |- Try 40 \/ 2 = 20. Evaluate 20 != 21, drop this branch.\n    |- Try 10 * 8 = 80. Add 80 to the number set. Current number set: [80, 40], target: 21, just two numbers left.\n     |- Try 80 + 40 = 120. Evaluate 120 != 21, drop this branch.\n     |- Try 80 - 40 = 40. Evaluate 40 != 21, drop this branch.\n     |- Try 80 * 40 = 3200. 3200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 80 \/ 40 = 2. Evaluate 2 != 21, drop this branch.\n    |- Try 10 \/ 8 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (8, 40) (numbers left: [10]). Try possible operations.\n    |- Try 40 + 8 = 48. Add 48 to the number set. Current number set: [48, 10], target: 21, just two numbers left.\n     |- Try 48 + 10 = 58. Evaluate 58 != 21, drop this branch.\n     |- Try 48 - 10 = 38. Evaluate 38 != 21, drop this branch.\n     |- Try 48 * 10 = 480. Evaluate 480 != 21, drop this branch.\n     |- Try 48 \/ 10 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 40 - 8 = 32. Add 32 to the number set. Current number set: [32, 10], target: 21, just two numbers left.\n     |- Try 32 + 10 = 42. Evaluate 42 != 21, drop this branch.\n     |- Try 32 - 10 = 22. Evaluate 22 != 21, drop this branch.\n     |- Try 32 * 10 = 320. Evaluate 320 != 21, drop this branch.\n     |- Try 32 \/ 10 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 40 * 8 = 320. Add 320 to the number set. Current number set: [320, 10], target: 21, just two numbers left.\n     |- Try 320 + 10 = 330. Evaluate 330 != 21, drop this branch.\n     |- Try 320 - 10 = 310. Evaluate 310 != 21, drop this branch.\n     |- Try 320 * 10 = 3200. 3200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 320 \/ 10 = 32. Evaluate 32 != 21, drop this branch.\n    |- Try 40 \/ 8 = 5. Add 5 to the number set. Current number set: [5, 10], target: 21, just two numbers left.\n     |- Try 10 + 5 = 15. Evaluate 15 != 21, drop this branch.\n     |- Try 10 - 5 = 5. Evaluate 5 != 21, drop this branch.\n     |- Try 10 * 5 = 50. Evaluate 50 != 21, drop this branch.\n     |- Try 10 \/ 5 = 2. Evaluate 2 != 21, drop this branch.\n   |- Pick two numbers (10, 40) (numbers left: [8]). Try possible operations.\n    |- Try 40 + 10 = 50. Add 50 to the number set. Current number set: [50, 8], target: 21, just two numbers left.\n     |- Try 50 + 8 = 58. Evaluate 58 != 21, drop this branch.\n     |- Try 50 - 8 = 42. Evaluate 42 != 21, drop this branch.\n     |- Try 50 * 8 = 400. Evaluate 400 != 21, drop this branch.\n     |- Try 50 \/ 8 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 40 - 10 = 30. Add 30 to the number set. Current number set: [30, 8], target: 21, just two numbers left.\n     |- Try 30 + 8 = 38. Evaluate 38 != 21, drop this branch.\n     |- Try 30 - 8 = 22. Evaluate 22 != 21, drop this branch.\n     |- Try 30 * 8 = 240. Evaluate 240 != 21, drop this branch.\n     |- Try 30 \/ 8 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 40 * 10 = 400. Add 400 to the number set. Current number set: [400, 8], target: 21, just two numbers left.\n     |- Try 400 + 8 = 408. Evaluate 408 != 21, drop this branch.\n     |- Try 400 - 8 = 392. Evaluate 392 != 21, drop this branch.\n     |- Try 400 * 8 = 3200. 3200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 400 \/ 8 = 50. Evaluate 50 != 21, drop this branch.\n    |- Try 40 \/ 10 = 4. Add 4 to the number set. Current number set: [4, 8], target: 21, just two numbers left.\n     |- Try 8 + 4 = 12. Evaluate 12 != 21, drop this branch.\n     |- Try 8 - 4 = 4. Evaluate 4 != 21, drop this branch.\n     |- Try 8 * 4 = 32. Evaluate 32 != 21, drop this branch.\n     |- Try 8 \/ 4 = 2. Evaluate 2 != 21, drop this branch.\n  |- Try 26 * 18 = 468. Add 468 to the number set. Current number set: [468, 10, 40], target: 21. Options for choosing two numbers: [(468, 10), (468, 40), (10, 40)].\n   |- Pick two numbers (468, 10) (numbers left: [40]). Try possible operations.\n    |- Try 468 + 10 = 478. Add 478 to the number set. Current number set: [478, 40], target: 21, just two numbers left.\n     |- Try 478 + 40 = 518. Evaluate 518 != 21, drop this branch.\n     |- Try 478 - 40 = 438. Evaluate 438 != 21, drop this branch.\n     |- Try 478 * 40 = 19120. 19120 exceeds the maximum intermediate result, drop this branch.\n     |- Try 478 \/ 40 = 11.9. 11.9 is a decimal, drop this branch.\n    |- Try 468 - 10 = 458. Add 458 to the number set. Current number set: [458, 40], target: 21, just two numbers left.\n     |- Try 458 + 40 = 498. Evaluate 498 != 21, drop this branch.\n     |- Try 458 - 40 = 418. Evaluate 418 != 21, drop this branch.\n     |- Try 458 * 40 = 18320. 18320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 458 \/ 40 = 11.4. 11.4 is a decimal, drop this branch.\n    |- Try 468 * 10 = 4680. 4680 exceeds the maximum intermediate result, drop this branch.\n    |- Try 468 \/ 10 = 46.8. 46.8 is a decimal, drop this branch.\n   |- Pick two numbers (468, 40) (numbers left: [10]). Try possible operations.\n    |- Try 468 + 40 = 508. Add 508 to the number set. Current number set: [508, 10], target: 21, just two numbers left.\n     |- Try 508 + 10 = 518. Evaluate 518 != 21, drop this branch.\n     |- Try 508 - 10 = 498. Evaluate 498 != 21, drop this branch.\n     |- Try 508 * 10 = 5080. 5080 exceeds the maximum intermediate result, drop this branch.\n     |- Try 508 \/ 10 = 50.8. 50.8 is a decimal, drop this branch.\n    |- Try 468 - 40 = 428. Add 428 to the number set. Current number set: [428, 10], target: 21, just two numbers left.\n     |- Try 428 + 10 = 438. Evaluate 438 != 21, drop this branch.\n     |- Try 428 - 10 = 418. Evaluate 418 != 21, drop this branch.\n     |- Try 428 * 10 = 4280. 4280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 428 \/ 10 = 42.8. 42.8 is a decimal, drop this branch.\n    |- Try 468 * 40 = 18720. 18720 exceeds the maximum intermediate result, drop this branch.\n    |- Try 468 \/ 40 = 11.7. 11.7 is a decimal, drop this branch.\n   |- Pick two numbers (10, 40) (numbers left: [468]). Try possible operations.\n    |- Try 40 + 10 = 50. Add 50 to the number set. Current number set: [50, 468], target: 21, just two numbers left.\n     |- Try 468 + 50 = 518. Evaluate 518 != 21, drop this branch.\n     |- Try 468 - 50 = 418. Evaluate 418 != 21, drop this branch.\n     |- Try 468 * 50 = 23400. 23400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 468 \/ 50 = 9.4. 9.4 is a decimal, drop this branch.\n    |- Try 40 - 10 = 30. Add 30 to the number set. Current number set: [30, 468], target: 21, just two numbers left.\n     |- Try 468 + 30 = 498. Evaluate 498 != 21, drop this branch.\n     |- Try 468 - 30 = 438. Evaluate 438 != 21, drop this branch.\n     |- Try 468 * 30 = 14040. 14040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 468 \/ 30 = 15.6. 15.6 is a decimal, drop this branch.\n    |- Try 40 * 10 = 400. Add 400 to the number set. Current number set: [400, 468], target: 21, just two numbers left.\n     |- Try 468 + 400 = 868. Evaluate 868 != 21, drop this branch.\n     |- Try 468 - 400 = 68. Evaluate 68 != 21, drop this branch.\n     |- Try 468 * 400 = 187200. 187200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 468 \/ 400 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 40 \/ 10 = 4. Add 4 to the number set. Current number set: [4, 468], target: 21, just two numbers left.\n     |- Try 468 + 4 = 472. Evaluate 472 != 21, drop this branch.\n     |- Try 468 - 4 = 464. Evaluate 464 != 21, drop this branch.\n     |- Try 468 * 4 = 1872. Evaluate 1872 != 21, drop this branch.\n     |- Try 468 \/ 4 = 117. Evaluate 117 != 21, drop this branch.\n  |- Try 26 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n |- Pick two numbers (18, 10) (numbers left: [26, 40]). Try possible operations.\n  |- Try 18 + 10 = 28. Add 28 to the number set. Current number set: [28, 26, 40], target: 21. Options for choosing two numbers: [(28, 26), (28, 40), (26, 40)].\n   |- Pick two numbers (28, 26) (numbers left: [40]). Try possible operations.\n    |- Try 28 + 26 = 54. Add 54 to the number set. Current number set: [54, 40], target: 21, just two numbers left.\n     |- Try 54 + 40 = 94. Evaluate 94 != 21, drop this branch.\n     |- Try 54 - 40 = 14. Evaluate 14 != 21, drop this branch.\n     |- Try 54 * 40 = 2160. 2160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 54 \/ 40 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 28 - 26 = 2. Add 2 to the number set. Current number set: [2, 40], target: 21, just two numbers left.\n     |- Try 40 + 2 = 42. Evaluate 42 != 21, drop this branch.\n     |- Try 40 - 2 = 38. Evaluate 38 != 21, drop this branch.\n     |- Try 40 * 2 = 80. Evaluate 80 != 21, drop this branch.\n     |- Try 40 \/ 2 = 20. Evaluate 20 != 21, drop this branch.\n    |- Try 28 * 26 = 728. Add 728 to the number set. Current number set: [728, 40], target: 21, just two numbers left.\n     |- Try 728 + 40 = 768. Evaluate 768 != 21, drop this branch.\n     |- Try 728 - 40 = 688. Evaluate 688 != 21, drop this branch.\n     |- Try 728 * 40 = 29120. 29120 exceeds the maximum intermediate result, drop this branch.\n     |- Try 728 \/ 40 = 18.2. 18.2 is a decimal, drop this branch.\n    |- Try 28 \/ 26 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (28, 40) (numbers left: [26]). Try possible operations.\n    |- Try 40 + 28 = 68. Add 68 to the number set. Current number set: [68, 26], target: 21, just two numbers left.\n     |- Try 68 + 26 = 94. Evaluate 94 != 21, drop this branch.\n     |- Try 68 - 26 = 42. Evaluate 42 != 21, drop this branch.\n     |- Try 68 * 26 = 1768. Evaluate 1768 != 21, drop this branch.\n     |- Try 68 \/ 26 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 40 - 28 = 12. Add 12 to the number set. Current number set: [12, 26], target: 21, just two numbers left.\n     |- Try 26 + 12 = 38. Evaluate 38 != 21, drop this branch.\n     |- Try 26 - 12 = 14. Evaluate 14 != 21, drop this branch.\n     |- Try 26 * 12 = 312. Evaluate 312 != 21, drop this branch.\n     |- Try 26 \/ 12 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 40 * 28 = 1120. Add 1120 to the number set. Current number set: [1120, 26], target: 21, just two numbers left.\n     |- Try 1120 + 26 = 1146. Evaluate 1146 != 21, drop this branch.\n     |- Try 1120 - 26 = 1094. Evaluate 1094 != 21, drop this branch.\n     |- Try 1120 * 26 = 29120. 29120 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1120 \/ 26 = 43.1. 43.1 is a decimal, drop this branch.\n    |- Try 40 \/ 28 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (26, 40) (numbers left: [28]). Try possible operations.\n    |- Try 40 + 26 = 66. Add 66 to the number set. Current number set: [66, 28], target: 21, just two numbers left.\n     |- Try 66 + 28 = 94. Evaluate 94 != 21, drop this branch.\n     |- Try 66 - 28 = 38. Evaluate 38 != 21, drop this branch.\n     |- Try 66 * 28 = 1848. Evaluate 1848 != 21, drop this branch.\n     |- Try 66 \/ 28 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 40 - 26 = 14. Add 14 to the number set. Current number set: [14, 28], target: 21, just two numbers left.\n     |- Try 28 + 14 = 42. Evaluate 42 != 21, drop this branch.\n     |- Try 28 - 14 = 14. Evaluate 14 != 21, drop this branch.\n     |- Try 28 * 14 = 392. Evaluate 392 != 21, drop this branch.\n     |- Try 28 \/ 14 = 2. Evaluate 2 != 21, drop this branch.\n    |- Try 40 * 26 = 1040. Add 1040 to the number set. Current number set: [1040, 28], target: 21, just two numbers left.\n     |- Try 1040 + 28 = 1068. Evaluate 1068 != 21, drop this branch.\n     |- Try 1040 - 28 = 1012. Evaluate 1012 != 21, drop this branch.\n     |- Try 1040 * 28 = 29120. 29120 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1040 \/ 28 = 37.1. 37.1 is a decimal, drop this branch.\n    |- Try 40 \/ 26 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 18 - 10 = 8. Add 8 to the number set. Current number set: [8, 26, 40], target: 21. Options for choosing two numbers: [(8, 26), (8, 40), (26, 40)].\n   |- Pick two numbers (8, 26) (numbers left: [40]). Try possible operations.\n    |- Try 26 + 8 = 34. Add 34 to the number set. Current number set: [34, 40], target: 21, just two numbers left.\n     |- Try 40 + 34 = 74. Evaluate 74 != 21, drop this branch.\n     |- Try 40 - 34 = 6. Evaluate 6 != 21, drop this branch.\n     |- Try 40 * 34 = 1360. Evaluate 1360 != 21, drop this branch.\n     |- Try 40 \/ 34 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 26 - 8 = 18. Add 18 to the number set. Current number set: [18, 40], target: 21, just two numbers left.\n     |- Try 40 + 18 = 58. Evaluate 58 != 21, drop this branch.\n     |- Try 40 - 18 = 22. Evaluate 22 != 21, drop this branch.\n     |- Try 40 * 18 = 720. Evaluate 720 != 21, drop this branch.\n     |- Try 40 \/ 18 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 26 * 8 = 208. Add 208 to the number set. Current number set: [208, 40], target: 21, just two numbers left.\n     |- Try 208 + 40 = 248. Evaluate 248 != 21, drop this branch.\n     |- Try 208 - 40 = 168. Evaluate 168 != 21, drop this branch.\n     |- Try 208 * 40 = 8320. 8320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 208 \/ 40 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 26 \/ 8 = 3.2. 3.2 is a decimal, drop this branch.\n   |- Pick two numbers (8, 40) (numbers left: [26]). Try possible operations.\n    |- Try 40 + 8 = 48. Add 48 to the number set. Current number set: [48, 26], target: 21, just two numbers left.\n     |- Try 48 + 26 = 74. Evaluate 74 != 21, drop this branch.\n     |- Try 48 - 26 = 22. Evaluate 22 != 21, drop this branch.\n     |- Try 48 * 26 = 1248. Evaluate 1248 != 21, drop this branch.\n     |- Try 48 \/ 26 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 40 - 8 = 32. Add 32 to the number set. Current number set: [32, 26], target: 21, just two numbers left.\n     |- Try 32 + 26 = 58. Evaluate 58 != 21, drop this branch.\n     |- Try 32 - 26 = 6. Evaluate 6 != 21, drop this branch.\n     |- Try 32 * 26 = 832. Evaluate 832 != 21, drop this branch.\n     |- Try 32 \/ 26 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 40 * 8 = 320. Add 320 to the number set. Current number set: [320, 26], target: 21, just two numbers left.\n     |- Try 320 + 26 = 346. Evaluate 346 != 21, drop this branch.\n     |- Try 320 - 26 = 294. Evaluate 294 != 21, drop this branch.\n     |- Try 320 * 26 = 8320. 8320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 320 \/ 26 = 12.3. 12.3 is a decimal, drop this branch.\n    |- Try 40 \/ 8 = 5. Add 5 to the number set. Current number set: [5, 26], target: 21, just two numbers left.\n     |- Try 26 + 5 = 31. Evaluate 31 != 21, drop this branch.\n     |- Try 26 - 5 = 21. Evaluate 21 == 21, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 26 - 5 = 21\nThe step before: 40 \/ 8 = 5\nThe first step: 18 - 10 = 8\n\nOutput the solution in the required format:\n<Solution>\n18 - 10 = 8\n40 \/ 8 = 5\n26 - 5 = 21\n<\/Solution>\n","item":{"nums":[18,26,10,40],"solution":["18 - 10 = 8","40 \/ 8 = 5","26 - 5 = 21"],"target":21}}
+{"instance_id":"countdown_8k_50","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [13, 13, 4, 16]\nTarget: 21","reference_output":"# Search Procedure\nInitial number set: [13, 13, 4, 16], target: 21. Options for choosing two numbers: [(13, 13), (13, 4), (13, 16), (13, 4), (13, 16), (4, 16)].\n |- Pick two numbers (13, 13) (numbers left: [4, 16]). Try possible operations.\n  |- Try 13 + 13 = 26. Add 26 to the number set. Current number set: [26, 4, 16], target: 21. Options for choosing two numbers: [(26, 4), (26, 16), (4, 16)].\n   |- Pick two numbers (26, 4) (numbers left: [16]). Try possible operations.\n    |- Try 26 + 4 = 30. Add 30 to the number set. Current number set: [30, 16], target: 21, just two numbers left.\n     |- Try 30 + 16 = 46. Evaluate 46 != 21, drop this branch.\n     |- Try 30 - 16 = 14. Evaluate 14 != 21, drop this branch.\n     |- Try 30 * 16 = 480. Evaluate 480 != 21, drop this branch.\n     |- Try 30 \/ 16 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 26 - 4 = 22. Add 22 to the number set. Current number set: [22, 16], target: 21, just two numbers left.\n     |- Try 22 + 16 = 38. Evaluate 38 != 21, drop this branch.\n     |- Try 22 - 16 = 6. Evaluate 6 != 21, drop this branch.\n     |- Try 22 * 16 = 352. Evaluate 352 != 21, drop this branch.\n     |- Try 22 \/ 16 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 26 * 4 = 104. Add 104 to the number set. Current number set: [104, 16], target: 21, just two numbers left.\n     |- Try 104 + 16 = 120. Evaluate 120 != 21, drop this branch.\n     |- Try 104 - 16 = 88. Evaluate 88 != 21, drop this branch.\n     |- Try 104 * 16 = 1664. Evaluate 1664 != 21, drop this branch.\n     |- Try 104 \/ 16 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 26 \/ 4 = 6.5. 6.5 is a decimal, drop this branch.\n   |- Pick two numbers (26, 16) (numbers left: [4]). Try possible operations.\n    |- Try 26 + 16 = 42. Add 42 to the number set. Current number set: [42, 4], target: 21, just two numbers left.\n     |- Try 42 + 4 = 46. Evaluate 46 != 21, drop this branch.\n     |- Try 42 - 4 = 38. Evaluate 38 != 21, drop this branch.\n     |- Try 42 * 4 = 168. Evaluate 168 != 21, drop this branch.\n     |- Try 42 \/ 4 = 10.5. 10.5 is a decimal, drop this branch.\n    |- Try 26 - 16 = 10. Add 10 to the number set. Current number set: [10, 4], target: 21, just two numbers left.\n     |- Try 10 + 4 = 14. Evaluate 14 != 21, drop this branch.\n     |- Try 10 - 4 = 6. Evaluate 6 != 21, drop this branch.\n     |- Try 10 * 4 = 40. Evaluate 40 != 21, drop this branch.\n     |- Try 10 \/ 4 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 26 * 16 = 416. Add 416 to the number set. Current number set: [416, 4], target: 21, just two numbers left.\n     |- Try 416 + 4 = 420. Evaluate 420 != 21, drop this branch.\n     |- Try 416 - 4 = 412. Evaluate 412 != 21, drop this branch.\n     |- Try 416 * 4 = 1664. Evaluate 1664 != 21, drop this branch.\n     |- Try 416 \/ 4 = 104. Evaluate 104 != 21, drop this branch.\n    |- Try 26 \/ 16 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (4, 16) (numbers left: [26]). Try possible operations.\n    |- Try 16 + 4 = 20. Add 20 to the number set. Current number set: [20, 26], target: 21, just two numbers left.\n     |- Try 26 + 20 = 46. Evaluate 46 != 21, drop this branch.\n     |- Try 26 - 20 = 6. Evaluate 6 != 21, drop this branch.\n     |- Try 26 * 20 = 520. Evaluate 520 != 21, drop this branch.\n     |- Try 26 \/ 20 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 16 - 4 = 12. Add 12 to the number set. Current number set: [12, 26], target: 21, just two numbers left.\n     |- Try 26 + 12 = 38. Evaluate 38 != 21, drop this branch.\n     |- Try 26 - 12 = 14. Evaluate 14 != 21, drop this branch.\n     |- Try 26 * 12 = 312. Evaluate 312 != 21, drop this branch.\n     |- Try 26 \/ 12 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 16 * 4 = 64. Add 64 to the number set. Current number set: [64, 26], target: 21, just two numbers left.\n     |- Try 64 + 26 = 90. Evaluate 90 != 21, drop this branch.\n     |- Try 64 - 26 = 38. Evaluate 38 != 21, drop this branch.\n     |- Try 64 * 26 = 1664. Evaluate 1664 != 21, drop this branch.\n     |- Try 64 \/ 26 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 16 \/ 4 = 4. Add 4 to the number set. Current number set: [4, 26], target: 21, just two numbers left.\n     |- Try 26 + 4 = 30. Evaluate 30 != 21, drop this branch.\n     |- Try 26 - 4 = 22. Evaluate 22 != 21, drop this branch.\n     |- Try 26 * 4 = 104. Evaluate 104 != 21, drop this branch.\n     |- Try 26 \/ 4 = 6.5. 6.5 is a decimal, drop this branch.\n  |- Try 13 - 13 = 0. Add 0 to the number set. Current number set: [0, 4, 16], target: 21. Options for choosing two numbers: [(0, 4), (0, 16), (4, 16)].\n   |- Pick two numbers (0, 4) (numbers left: [16]). Try possible operations.\n    |- Try 4 + 0 = 4. Add 4 to the number set. Current number set: [4, 16], target: 21, just two numbers left.\n     |- Try 16 + 4 = 20. Evaluate 20 != 21, drop this branch.\n     |- Try 16 - 4 = 12. Evaluate 12 != 21, drop this branch.\n     |- Try 16 * 4 = 64. Evaluate 64 != 21, drop this branch.\n     |- Try 16 \/ 4 = 4. Evaluate 4 != 21, drop this branch.\n    |- Try 4 - 0 = 4. Add 4 to the number set. Current number set: [4, 16], target: 21, just two numbers left.\n     |- Try 16 + 4 = 20. Evaluate 20 != 21, drop this branch.\n     |- Try 16 - 4 = 12. Evaluate 12 != 21, drop this branch.\n     |- Try 16 * 4 = 64. Evaluate 64 != 21, drop this branch.\n     |- Try 16 \/ 4 = 4. Evaluate 4 != 21, drop this branch.\n    |- Try 4 * 0 = 0. Add 0 to the number set. Current number set: [0, 16], target: 21, just two numbers left.\n     |- Try 16 + 0 = 16. Evaluate 16 != 21, drop this branch.\n     |- Try 16 - 0 = 16. Evaluate 16 != 21, drop this branch.\n     |- Try 16 * 0 = 0. Evaluate 0 != 21, drop this branch.\n     |- Try 16 \/ 0 (invalid operation). drop this branch.\n    |- Try 4 \/ 0 (invalid operation). drop this branch.\n   |- Pick two numbers (0, 16) (numbers left: [4]). Try possible operations.\n    |- Try 16 + 0 = 16. Add 16 to the number set. Current number set: [16, 4], target: 21, just two numbers left.\n     |- Try 16 + 4 = 20. Evaluate 20 != 21, drop this branch.\n     |- Try 16 - 4 = 12. Evaluate 12 != 21, drop this branch.\n     |- Try 16 * 4 = 64. Evaluate 64 != 21, drop this branch.\n     |- Try 16 \/ 4 = 4. Evaluate 4 != 21, drop this branch.\n    |- Try 16 - 0 = 16. Add 16 to the number set. Current number set: [16, 4], target: 21, just two numbers left.\n     |- Try 16 + 4 = 20. Evaluate 20 != 21, drop this branch.\n     |- Try 16 - 4 = 12. Evaluate 12 != 21, drop this branch.\n     |- Try 16 * 4 = 64. Evaluate 64 != 21, drop this branch.\n     |- Try 16 \/ 4 = 4. Evaluate 4 != 21, drop this branch.\n    |- Try 16 * 0 = 0. Add 0 to the number set. Current number set: [0, 4], target: 21, just two numbers left.\n     |- Try 4 + 0 = 4. Evaluate 4 != 21, drop this branch.\n     |- Try 4 - 0 = 4. Evaluate 4 != 21, drop this branch.\n     |- Try 4 * 0 = 0. Evaluate 0 != 21, drop this branch.\n     |- Try 4 \/ 0 (invalid operation). drop this branch.\n    |- Try 16 \/ 0 (invalid operation). drop this branch.\n   |- Pick two numbers (4, 16) (numbers left: [0]). Try possible operations.\n    |- Try 16 + 4 = 20. Add 20 to the number set. Current number set: [20, 0], target: 21, just two numbers left.\n     |- Try 20 + 0 = 20. Evaluate 20 != 21, drop this branch.\n     |- Try 20 - 0 = 20. Evaluate 20 != 21, drop this branch.\n     |- Try 20 * 0 = 0. Evaluate 0 != 21, drop this branch.\n     |- Try 20 \/ 0 (invalid operation). drop this branch.\n    |- Try 16 - 4 = 12. Add 12 to the number set. Current number set: [12, 0], target: 21, just two numbers left.\n     |- Try 12 + 0 = 12. Evaluate 12 != 21, drop this branch.\n     |- Try 12 - 0 = 12. Evaluate 12 != 21, drop this branch.\n     |- Try 12 * 0 = 0. Evaluate 0 != 21, drop this branch.\n     |- Try 12 \/ 0 (invalid operation). drop this branch.\n    |- Try 16 * 4 = 64. Add 64 to the number set. Current number set: [64, 0], target: 21, just two numbers left.\n     |- Try 64 + 0 = 64. Evaluate 64 != 21, drop this branch.\n     |- Try 64 - 0 = 64. Evaluate 64 != 21, drop this branch.\n     |- Try 64 * 0 = 0. Evaluate 0 != 21, drop this branch.\n     |- Try 64 \/ 0 (invalid operation). drop this branch.\n    |- Try 16 \/ 4 = 4. Add 4 to the number set. Current number set: [4, 0], target: 21, just two numbers left.\n     |- Try 4 + 0 = 4. Evaluate 4 != 21, drop this branch.\n     |- Try 4 - 0 = 4. Evaluate 4 != 21, drop this branch.\n     |- Try 4 * 0 = 0. Evaluate 0 != 21, drop this branch.\n     |- Try 4 \/ 0 (invalid operation). drop this branch.\n  |- Try 13 * 13 = 169. Add 169 to the number set. Current number set: [169, 4, 16], target: 21. Options for choosing two numbers: [(169, 4), (169, 16), (4, 16)].\n   |- Pick two numbers (169, 4) (numbers left: [16]). Try possible operations.\n    |- Try 169 + 4 = 173. Add 173 to the number set. Current number set: [173, 16], target: 21, just two numbers left.\n     |- Try 173 + 16 = 189. Evaluate 189 != 21, drop this branch.\n     |- Try 173 - 16 = 157. Evaluate 157 != 21, drop this branch.\n     |- Try 173 * 16 = 2768. 2768 exceeds the maximum intermediate result, drop this branch.\n     |- Try 173 \/ 16 = 10.8. 10.8 is a decimal, drop this branch.\n    |- Try 169 - 4 = 165. Add 165 to the number set. Current number set: [165, 16], target: 21, just two numbers left.\n     |- Try 165 + 16 = 181. Evaluate 181 != 21, drop this branch.\n     |- Try 165 - 16 = 149. Evaluate 149 != 21, drop this branch.\n     |- Try 165 * 16 = 2640. 2640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 165 \/ 16 = 10.3. 10.3 is a decimal, drop this branch.\n    |- Try 169 * 4 = 676. Add 676 to the number set. Current number set: [676, 16], target: 21, just two numbers left.\n     |- Try 676 + 16 = 692. Evaluate 692 != 21, drop this branch.\n     |- Try 676 - 16 = 660. Evaluate 660 != 21, drop this branch.\n     |- Try 676 * 16 = 10816. 10816 exceeds the maximum intermediate result, drop this branch.\n     |- Try 676 \/ 16 = 42.2. 42.2 is a decimal, drop this branch.\n    |- Try 169 \/ 4 = 42.2. 42.2 is a decimal, drop this branch.\n   |- Pick two numbers (169, 16) (numbers left: [4]). Try possible operations.\n    |- Try 169 + 16 = 185. Add 185 to the number set. Current number set: [185, 4], target: 21, just two numbers left.\n     |- Try 185 + 4 = 189. Evaluate 189 != 21, drop this branch.\n     |- Try 185 - 4 = 181. Evaluate 181 != 21, drop this branch.\n     |- Try 185 * 4 = 740. Evaluate 740 != 21, drop this branch.\n     |- Try 185 \/ 4 = 46.2. 46.2 is a decimal, drop this branch.\n    |- Try 169 - 16 = 153. Add 153 to the number set. Current number set: [153, 4], target: 21, just two numbers left.\n     |- Try 153 + 4 = 157. Evaluate 157 != 21, drop this branch.\n     |- Try 153 - 4 = 149. Evaluate 149 != 21, drop this branch.\n     |- Try 153 * 4 = 612. Evaluate 612 != 21, drop this branch.\n     |- Try 153 \/ 4 = 38.2. 38.2 is a decimal, drop this branch.\n    |- Try 169 * 16 = 2704. 2704 exceeds the maximum intermediate result, drop this branch.\n    |- Try 169 \/ 16 = 10.6. 10.6 is a decimal, drop this branch.\n   |- Pick two numbers (4, 16) (numbers left: [169]). Try possible operations.\n    |- Try 16 + 4 = 20. Add 20 to the number set. Current number set: [20, 169], target: 21, just two numbers left.\n     |- Try 169 + 20 = 189. Evaluate 189 != 21, drop this branch.\n     |- Try 169 - 20 = 149. Evaluate 149 != 21, drop this branch.\n     |- Try 169 * 20 = 3380. 3380 exceeds the maximum intermediate result, drop this branch.\n     |- Try 169 \/ 20 = 8.4. 8.4 is a decimal, drop this branch.\n    |- Try 16 - 4 = 12. Add 12 to the number set. Current number set: [12, 169], target: 21, just two numbers left.\n     |- Try 169 + 12 = 181. Evaluate 181 != 21, drop this branch.\n     |- Try 169 - 12 = 157. Evaluate 157 != 21, drop this branch.\n     |- Try 169 * 12 = 2028. 2028 exceeds the maximum intermediate result, drop this branch.\n     |- Try 169 \/ 12 = 14.1. 14.1 is a decimal, drop this branch.\n    |- Try 16 * 4 = 64. Add 64 to the number set. Current number set: [64, 169], target: 21, just two numbers left.\n     |- Try 169 + 64 = 233. Evaluate 233 != 21, drop this branch.\n     |- Try 169 - 64 = 105. Evaluate 105 != 21, drop this branch.\n     |- Try 169 * 64 = 10816. 10816 exceeds the maximum intermediate result, drop this branch.\n     |- Try 169 \/ 64 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 16 \/ 4 = 4. Add 4 to the number set. Current number set: [4, 169], target: 21, just two numbers left.\n     |- Try 169 + 4 = 173. Evaluate 173 != 21, drop this branch.\n     |- Try 169 - 4 = 165. Evaluate 165 != 21, drop this branch.\n     |- Try 169 * 4 = 676. Evaluate 676 != 21, drop this branch.\n     |- Try 169 \/ 4 = 42.2. 42.2 is a decimal, drop this branch.\n  |- Try 13 \/ 13 = 1. Add 1 to the number set. Current number set: [1, 4, 16], target: 21. Options for choosing two numbers: [(1, 4), (1, 16), (4, 16)].\n   |- Pick two numbers (1, 4) (numbers left: [16]). Try possible operations.\n    |- Try 4 + 1 = 5. Add 5 to the number set. Current number set: [5, 16], target: 21, just two numbers left.\n     |- Try 16 + 5 = 21. Evaluate 21 == 21, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 16 + 5 = 21\nThe step before: 4 + 1 = 5\nThe first step: 13 \/ 13 = 1\n\nOutput the solution in the required format:\n<Solution>\n13 \/ 13 = 1\n4 + 1 = 5\n16 + 5 = 21\n<\/Solution>\n","item":{"nums":[13,13,4,16],"solution":["13 \/ 13 = 1","4 + 1 = 5","16 + 5 = 21"],"target":21}}
+{"instance_id":"countdown_8k_51","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [44, 35, 41, 31]\nTarget: 12","reference_output":"# Search Procedure\nInitial number set: [44, 35, 41, 31], target: 12. Options for choosing two numbers: [(44, 35), (44, 41), (44, 31), (35, 41), (35, 31), (41, 31)].\n |- Pick two numbers (44, 35) (numbers left: [41, 31]). Try possible operations.\n  |- Try 44 + 35 = 79. Add 79 to the number set. Current number set: [79, 41, 31], target: 12. Options for choosing two numbers: [(79, 41), (79, 31), (41, 31)].\n   |- Pick two numbers (79, 41) (numbers left: [31]). Try possible operations.\n    |- Try 79 + 41 = 120. Add 120 to the number set. Current number set: [120, 31], target: 12, just two numbers left.\n     |- Try 120 + 31 = 151. Evaluate 151 != 12, drop this branch.\n     |- Try 120 - 31 = 89. Evaluate 89 != 12, drop this branch.\n     |- Try 120 * 31 = 3720. 3720 exceeds the maximum intermediate result, drop this branch.\n     |- Try 120 \/ 31 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 79 - 41 = 38. Add 38 to the number set. Current number set: [38, 31], target: 12, just two numbers left.\n     |- Try 38 + 31 = 69. Evaluate 69 != 12, drop this branch.\n     |- Try 38 - 31 = 7. Evaluate 7 != 12, drop this branch.\n     |- Try 38 * 31 = 1178. Evaluate 1178 != 12, drop this branch.\n     |- Try 38 \/ 31 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 79 * 41 = 3239. 3239 exceeds the maximum intermediate result, drop this branch.\n    |- Try 79 \/ 41 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (79, 31) (numbers left: [41]). Try possible operations.\n    |- Try 79 + 31 = 110. Add 110 to the number set. Current number set: [110, 41], target: 12, just two numbers left.\n     |- Try 110 + 41 = 151. Evaluate 151 != 12, drop this branch.\n     |- Try 110 - 41 = 69. Evaluate 69 != 12, drop this branch.\n     |- Try 110 * 41 = 4510. 4510 exceeds the maximum intermediate result, drop this branch.\n     |- Try 110 \/ 41 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 79 - 31 = 48. Add 48 to the number set. Current number set: [48, 41], target: 12, just two numbers left.\n     |- Try 48 + 41 = 89. Evaluate 89 != 12, drop this branch.\n     |- Try 48 - 41 = 7. Evaluate 7 != 12, drop this branch.\n     |- Try 48 * 41 = 1968. Evaluate 1968 != 12, drop this branch.\n     |- Try 48 \/ 41 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 79 * 31 = 2449. 2449 exceeds the maximum intermediate result, drop this branch.\n    |- Try 79 \/ 31 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (41, 31) (numbers left: [79]). Try possible operations.\n    |- Try 41 + 31 = 72. Add 72 to the number set. Current number set: [72, 79], target: 12, just two numbers left.\n     |- Try 79 + 72 = 151. Evaluate 151 != 12, drop this branch.\n     |- Try 79 - 72 = 7. Evaluate 7 != 12, drop this branch.\n     |- Try 79 * 72 = 5688. 5688 exceeds the maximum intermediate result, drop this branch.\n     |- Try 79 \/ 72 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 41 - 31 = 10. Add 10 to the number set. Current number set: [10, 79], target: 12, just two numbers left.\n     |- Try 79 + 10 = 89. Evaluate 89 != 12, drop this branch.\n     |- Try 79 - 10 = 69. Evaluate 69 != 12, drop this branch.\n     |- Try 79 * 10 = 790. Evaluate 790 != 12, drop this branch.\n     |- Try 79 \/ 10 = 7.9. 7.9 is a decimal, drop this branch.\n    |- Try 41 * 31 = 1271. Add 1271 to the number set. Current number set: [1271, 79], target: 12, just two numbers left.\n     |- Try 1271 + 79 = 1350. Evaluate 1350 != 12, drop this branch.\n     |- Try 1271 - 79 = 1192. Evaluate 1192 != 12, drop this branch.\n     |- Try 1271 * 79 = 100409. 100409 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1271 \/ 79 = 16.1. 16.1 is a decimal, drop this branch.\n    |- Try 41 \/ 31 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 44 - 35 = 9. Add 9 to the number set. Current number set: [9, 41, 31], target: 12. Options for choosing two numbers: [(9, 41), (9, 31), (41, 31)].\n   |- Pick two numbers (9, 41) (numbers left: [31]). Try possible operations.\n    |- Try 41 + 9 = 50. Add 50 to the number set. Current number set: [50, 31], target: 12, just two numbers left.\n     |- Try 50 + 31 = 81. Evaluate 81 != 12, drop this branch.\n     |- Try 50 - 31 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 50 * 31 = 1550. Evaluate 1550 != 12, drop this branch.\n     |- Try 50 \/ 31 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 41 - 9 = 32. Add 32 to the number set. Current number set: [32, 31], target: 12, just two numbers left.\n     |- Try 32 + 31 = 63. Evaluate 63 != 12, drop this branch.\n     |- Try 32 - 31 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 32 * 31 = 992. Evaluate 992 != 12, drop this branch.\n     |- Try 32 \/ 31 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 41 * 9 = 369. Add 369 to the number set. Current number set: [369, 31], target: 12, just two numbers left.\n     |- Try 369 + 31 = 400. Evaluate 400 != 12, drop this branch.\n     |- Try 369 - 31 = 338. Evaluate 338 != 12, drop this branch.\n     |- Try 369 * 31 = 11439. 11439 exceeds the maximum intermediate result, drop this branch.\n     |- Try 369 \/ 31 = 11.9. 11.9 is a decimal, drop this branch.\n    |- Try 41 \/ 9 = 4.6. 4.6 is a decimal, drop this branch.\n   |- Pick two numbers (9, 31) (numbers left: [41]). Try possible operations.\n    |- Try 31 + 9 = 40. Add 40 to the number set. Current number set: [40, 41], target: 12, just two numbers left.\n     |- Try 41 + 40 = 81. Evaluate 81 != 12, drop this branch.\n     |- Try 41 - 40 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 41 * 40 = 1640. Evaluate 1640 != 12, drop this branch.\n     |- Try 41 \/ 40 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 31 - 9 = 22. Add 22 to the number set. Current number set: [22, 41], target: 12, just two numbers left.\n     |- Try 41 + 22 = 63. Evaluate 63 != 12, drop this branch.\n     |- Try 41 - 22 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 41 * 22 = 902. Evaluate 902 != 12, drop this branch.\n     |- Try 41 \/ 22 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 31 * 9 = 279. Add 279 to the number set. Current number set: [279, 41], target: 12, just two numbers left.\n     |- Try 279 + 41 = 320. Evaluate 320 != 12, drop this branch.\n     |- Try 279 - 41 = 238. Evaluate 238 != 12, drop this branch.\n     |- Try 279 * 41 = 11439. 11439 exceeds the maximum intermediate result, drop this branch.\n     |- Try 279 \/ 41 = 6.8. 6.8 is a decimal, drop this branch.\n    |- Try 31 \/ 9 = 3.4. 3.4 is a decimal, drop this branch.\n   |- Pick two numbers (41, 31) (numbers left: [9]). Try possible operations.\n    |- Try 41 + 31 = 72. Add 72 to the number set. Current number set: [72, 9], target: 12, just two numbers left.\n     |- Try 72 + 9 = 81. Evaluate 81 != 12, drop this branch.\n     |- Try 72 - 9 = 63. Evaluate 63 != 12, drop this branch.\n     |- Try 72 * 9 = 648. Evaluate 648 != 12, drop this branch.\n     |- Try 72 \/ 9 = 8. Evaluate 8 != 12, drop this branch.\n    |- Try 41 - 31 = 10. Add 10 to the number set. Current number set: [10, 9], target: 12, just two numbers left.\n     |- Try 10 + 9 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 10 - 9 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 10 * 9 = 90. Evaluate 90 != 12, drop this branch.\n     |- Try 10 \/ 9 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 41 * 31 = 1271. Add 1271 to the number set. Current number set: [1271, 9], target: 12, just two numbers left.\n     |- Try 1271 + 9 = 1280. Evaluate 1280 != 12, drop this branch.\n     |- Try 1271 - 9 = 1262. Evaluate 1262 != 12, drop this branch.\n     |- Try 1271 * 9 = 11439. 11439 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1271 \/ 9 = 141.2. 141.2 is a decimal, drop this branch.\n    |- Try 41 \/ 31 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 44 * 35 = 1540. Add 1540 to the number set. Current number set: [1540, 41, 31], target: 12. Options for choosing two numbers: [(1540, 41), (1540, 31), (41, 31)].\n   |- Pick two numbers (1540, 41) (numbers left: [31]). Try possible operations.\n    |- Try 1540 + 41 = 1581. Add 1581 to the number set. Current number set: [1581, 31], target: 12, just two numbers left.\n     |- Try 1581 + 31 = 1612. Evaluate 1612 != 12, drop this branch.\n     |- Try 1581 - 31 = 1550. Evaluate 1550 != 12, drop this branch.\n     |- Try 1581 * 31 = 49011. 49011 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1581 \/ 31 = 51. Evaluate 51 != 12, drop this branch.\n    |- Try 1540 - 41 = 1499. Add 1499 to the number set. Current number set: [1499, 31], target: 12, just two numbers left.\n     |- Try 1499 + 31 = 1530. Evaluate 1530 != 12, drop this branch.\n     |- Try 1499 - 31 = 1468. Evaluate 1468 != 12, drop this branch.\n     |- Try 1499 * 31 = 46469. 46469 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1499 \/ 31 = 48.4. 48.4 is a decimal, drop this branch.\n    |- Try 1540 * 41 = 63140. 63140 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1540 \/ 41 = 37.6. 37.6 is a decimal, drop this branch.\n   |- Pick two numbers (1540, 31) (numbers left: [41]). Try possible operations.\n    |- Try 1540 + 31 = 1571. Add 1571 to the number set. Current number set: [1571, 41], target: 12, just two numbers left.\n     |- Try 1571 + 41 = 1612. Evaluate 1612 != 12, drop this branch.\n     |- Try 1571 - 41 = 1530. Evaluate 1530 != 12, drop this branch.\n     |- Try 1571 * 41 = 64411. 64411 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1571 \/ 41 = 38.3. 38.3 is a decimal, drop this branch.\n    |- Try 1540 - 31 = 1509. Add 1509 to the number set. Current number set: [1509, 41], target: 12, just two numbers left.\n     |- Try 1509 + 41 = 1550. Evaluate 1550 != 12, drop this branch.\n     |- Try 1509 - 41 = 1468. Evaluate 1468 != 12, drop this branch.\n     |- Try 1509 * 41 = 61869. 61869 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1509 \/ 41 = 36.8. 36.8 is a decimal, drop this branch.\n    |- Try 1540 * 31 = 47740. 47740 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1540 \/ 31 = 49.7. 49.7 is a decimal, drop this branch.\n   |- Pick two numbers (41, 31) (numbers left: [1540]). Try possible operations.\n    |- Try 41 + 31 = 72. Add 72 to the number set. Current number set: [72, 1540], target: 12, just two numbers left.\n     |- Try 1540 + 72 = 1612. Evaluate 1612 != 12, drop this branch.\n     |- Try 1540 - 72 = 1468. Evaluate 1468 != 12, drop this branch.\n     |- Try 1540 * 72 = 110880. 110880 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1540 \/ 72 = 21.4. 21.4 is a decimal, drop this branch.\n    |- Try 41 - 31 = 10. Add 10 to the number set. Current number set: [10, 1540], target: 12, just two numbers left.\n     |- Try 1540 + 10 = 1550. Evaluate 1550 != 12, drop this branch.\n     |- Try 1540 - 10 = 1530. Evaluate 1530 != 12, drop this branch.\n     |- Try 1540 * 10 = 15400. 15400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1540 \/ 10 = 154. Evaluate 154 != 12, drop this branch.\n    |- Try 41 * 31 = 1271. Add 1271 to the number set. Current number set: [1271, 1540], target: 12, just two numbers left.\n     |- Try 1540 + 1271 = 2811. 2811 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1540 - 1271 = 269. Evaluate 269 != 12, drop this branch.\n     |- Try 1540 * 1271 = 1957340. 1957340 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1540 \/ 1271 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 41 \/ 31 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 44 \/ 35 = 1.3. 1.3 is a decimal, drop this branch.\n |- Pick two numbers (44, 41) (numbers left: [35, 31]). Try possible operations.\n  |- Try 44 + 41 = 85. Add 85 to the number set. Current number set: [85, 35, 31], target: 12. Options for choosing two numbers: [(85, 35), (85, 31), (35, 31)].\n   |- Pick two numbers (85, 35) (numbers left: [31]). Try possible operations.\n    |- Try 85 + 35 = 120. Add 120 to the number set. Current number set: [120, 31], target: 12, just two numbers left.\n     |- Try 120 + 31 = 151. Evaluate 151 != 12, drop this branch.\n     |- Try 120 - 31 = 89. Evaluate 89 != 12, drop this branch.\n     |- Try 120 * 31 = 3720. 3720 exceeds the maximum intermediate result, drop this branch.\n     |- Try 120 \/ 31 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 85 - 35 = 50. Add 50 to the number set. Current number set: [50, 31], target: 12, just two numbers left.\n     |- Try 50 + 31 = 81. Evaluate 81 != 12, drop this branch.\n     |- Try 50 - 31 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 50 * 31 = 1550. Evaluate 1550 != 12, drop this branch.\n     |- Try 50 \/ 31 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 85 * 35 = 2975. 2975 exceeds the maximum intermediate result, drop this branch.\n    |- Try 85 \/ 35 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (85, 31) (numbers left: [35]). Try possible operations.\n    |- Try 85 + 31 = 116. Add 116 to the number set. Current number set: [116, 35], target: 12, just two numbers left.\n     |- Try 116 + 35 = 151. Evaluate 151 != 12, drop this branch.\n     |- Try 116 - 35 = 81. Evaluate 81 != 12, drop this branch.\n     |- Try 116 * 35 = 4060. 4060 exceeds the maximum intermediate result, drop this branch.\n     |- Try 116 \/ 35 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 85 - 31 = 54. Add 54 to the number set. Current number set: [54, 35], target: 12, just two numbers left.\n     |- Try 54 + 35 = 89. Evaluate 89 != 12, drop this branch.\n     |- Try 54 - 35 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 54 * 35 = 1890. Evaluate 1890 != 12, drop this branch.\n     |- Try 54 \/ 35 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 85 * 31 = 2635. 2635 exceeds the maximum intermediate result, drop this branch.\n    |- Try 85 \/ 31 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (35, 31) (numbers left: [85]). Try possible operations.\n    |- Try 35 + 31 = 66. Add 66 to the number set. Current number set: [66, 85], target: 12, just two numbers left.\n     |- Try 85 + 66 = 151. Evaluate 151 != 12, drop this branch.\n     |- Try 85 - 66 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 85 * 66 = 5610. 5610 exceeds the maximum intermediate result, drop this branch.\n     |- Try 85 \/ 66 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 35 - 31 = 4. Add 4 to the number set. Current number set: [4, 85], target: 12, just two numbers left.\n     |- Try 85 + 4 = 89. Evaluate 89 != 12, drop this branch.\n     |- Try 85 - 4 = 81. Evaluate 81 != 12, drop this branch.\n     |- Try 85 * 4 = 340. Evaluate 340 != 12, drop this branch.\n     |- Try 85 \/ 4 = 21.2. 21.2 is a decimal, drop this branch.\n    |- Try 35 * 31 = 1085. Add 1085 to the number set. Current number set: [1085, 85], target: 12, just two numbers left.\n     |- Try 1085 + 85 = 1170. Evaluate 1170 != 12, drop this branch.\n     |- Try 1085 - 85 = 1000. Evaluate 1000 != 12, drop this branch.\n     |- Try 1085 * 85 = 92225. 92225 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1085 \/ 85 = 12.8. 12.8 is a decimal, drop this branch.\n    |- Try 35 \/ 31 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 44 - 41 = 3. Add 3 to the number set. Current number set: [3, 35, 31], target: 12. Options for choosing two numbers: [(3, 35), (3, 31), (35, 31)].\n   |- Pick two numbers (3, 35) (numbers left: [31]). Try possible operations.\n    |- Try 35 + 3 = 38. Add 38 to the number set. Current number set: [38, 31], target: 12, just two numbers left.\n     |- Try 38 + 31 = 69. Evaluate 69 != 12, drop this branch.\n     |- Try 38 - 31 = 7. Evaluate 7 != 12, drop this branch.\n     |- Try 38 * 31 = 1178. Evaluate 1178 != 12, drop this branch.\n     |- Try 38 \/ 31 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 35 - 3 = 32. Add 32 to the number set. Current number set: [32, 31], target: 12, just two numbers left.\n     |- Try 32 + 31 = 63. Evaluate 63 != 12, drop this branch.\n     |- Try 32 - 31 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 32 * 31 = 992. Evaluate 992 != 12, drop this branch.\n     |- Try 32 \/ 31 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 35 * 3 = 105. Add 105 to the number set. Current number set: [105, 31], target: 12, just two numbers left.\n     |- Try 105 + 31 = 136. Evaluate 136 != 12, drop this branch.\n     |- Try 105 - 31 = 74. Evaluate 74 != 12, drop this branch.\n     |- Try 105 * 31 = 3255. 3255 exceeds the maximum intermediate result, drop this branch.\n     |- Try 105 \/ 31 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 35 \/ 3 = 11.7. 11.7 is a decimal, drop this branch.\n   |- Pick two numbers (3, 31) (numbers left: [35]). Try possible operations.\n    |- Try 31 + 3 = 34. Add 34 to the number set. Current number set: [34, 35], target: 12, just two numbers left.\n     |- Try 35 + 34 = 69. Evaluate 69 != 12, drop this branch.\n     |- Try 35 - 34 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 35 * 34 = 1190. Evaluate 1190 != 12, drop this branch.\n     |- Try 35 \/ 34 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 31 - 3 = 28. Add 28 to the number set. Current number set: [28, 35], target: 12, just two numbers left.\n     |- Try 35 + 28 = 63. Evaluate 63 != 12, drop this branch.\n     |- Try 35 - 28 = 7. Evaluate 7 != 12, drop this branch.\n     |- Try 35 * 28 = 980. Evaluate 980 != 12, drop this branch.\n     |- Try 35 \/ 28 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 31 * 3 = 93. Add 93 to the number set. Current number set: [93, 35], target: 12, just two numbers left.\n     |- Try 93 + 35 = 128. Evaluate 128 != 12, drop this branch.\n     |- Try 93 - 35 = 58. Evaluate 58 != 12, drop this branch.\n     |- Try 93 * 35 = 3255. 3255 exceeds the maximum intermediate result, drop this branch.\n     |- Try 93 \/ 35 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 31 \/ 3 = 10.3. 10.3 is a decimal, drop this branch.\n   |- Pick two numbers (35, 31) (numbers left: [3]). Try possible operations.\n    |- Try 35 + 31 = 66. Add 66 to the number set. Current number set: [66, 3], target: 12, just two numbers left.\n     |- Try 66 + 3 = 69. Evaluate 69 != 12, drop this branch.\n     |- Try 66 - 3 = 63. Evaluate 63 != 12, drop this branch.\n     |- Try 66 * 3 = 198. Evaluate 198 != 12, drop this branch.\n     |- Try 66 \/ 3 = 22. Evaluate 22 != 12, drop this branch.\n    |- Try 35 - 31 = 4. Add 4 to the number set. Current number set: [4, 3], target: 12, just two numbers left.\n     |- Try 4 + 3 = 7. Evaluate 7 != 12, drop this branch.\n     |- Try 4 - 3 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 4 * 3 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 4 * 3 = 12\nThe step before: 35 - 31 = 4\nThe first step: 44 - 41 = 3\n\nOutput the solution in the required format:\n<Solution>\n44 - 41 = 3\n35 - 31 = 4\n4 * 3 = 12\n<\/Solution>\n","item":{"nums":[44,35,41,31],"solution":["44 - 41 = 3","35 - 31 = 4","4 * 3 = 12"],"target":12}}
+{"instance_id":"countdown_8k_52","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [47, 36, 49, 12]\nTarget: 32","reference_output":"# Search Procedure\nInitial number set: [47, 36, 49, 12], target: 32. Options for choosing two numbers: [(47, 36), (47, 49), (47, 12), (36, 49), (36, 12), (49, 12)].\n |- Pick two numbers (47, 36) (numbers left: [49, 12]). Try possible operations.\n  |- Try 47 + 36 = 83. Add 83 to the number set. Current number set: [83, 49, 12], target: 32. Options for choosing two numbers: [(83, 49), (83, 12), (49, 12)].\n   |- Pick two numbers (83, 49) (numbers left: [12]). Try possible operations.\n    |- Try 83 + 49 = 132. Add 132 to the number set. Current number set: [132, 12], target: 32, just two numbers left.\n     |- Try 132 + 12 = 144. Evaluate 144 != 32, drop this branch.\n     |- Try 132 - 12 = 120. Evaluate 120 != 32, drop this branch.\n     |- Try 132 * 12 = 1584. Evaluate 1584 != 32, drop this branch.\n     |- Try 132 \/ 12 = 11. Evaluate 11 != 32, drop this branch.\n    |- Try 83 - 49 = 34. Add 34 to the number set. Current number set: [34, 12], target: 32, just two numbers left.\n     |- Try 34 + 12 = 46. Evaluate 46 != 32, drop this branch.\n     |- Try 34 - 12 = 22. Evaluate 22 != 32, drop this branch.\n     |- Try 34 * 12 = 408. Evaluate 408 != 32, drop this branch.\n     |- Try 34 \/ 12 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 83 * 49 = 4067. 4067 exceeds the maximum intermediate result, drop this branch.\n    |- Try 83 \/ 49 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (83, 12) (numbers left: [49]). Try possible operations.\n    |- Try 83 + 12 = 95. Add 95 to the number set. Current number set: [95, 49], target: 32, just two numbers left.\n     |- Try 95 + 49 = 144. Evaluate 144 != 32, drop this branch.\n     |- Try 95 - 49 = 46. Evaluate 46 != 32, drop this branch.\n     |- Try 95 * 49 = 4655. 4655 exceeds the maximum intermediate result, drop this branch.\n     |- Try 95 \/ 49 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 83 - 12 = 71. Add 71 to the number set. Current number set: [71, 49], target: 32, just two numbers left.\n     |- Try 71 + 49 = 120. Evaluate 120 != 32, drop this branch.\n     |- Try 71 - 49 = 22. Evaluate 22 != 32, drop this branch.\n     |- Try 71 * 49 = 3479. 3479 exceeds the maximum intermediate result, drop this branch.\n     |- Try 71 \/ 49 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 83 * 12 = 996. Add 996 to the number set. Current number set: [996, 49], target: 32, just two numbers left.\n     |- Try 996 + 49 = 1045. Evaluate 1045 != 32, drop this branch.\n     |- Try 996 - 49 = 947. Evaluate 947 != 32, drop this branch.\n     |- Try 996 * 49 = 48804. 48804 exceeds the maximum intermediate result, drop this branch.\n     |- Try 996 \/ 49 = 20.3. 20.3 is a decimal, drop this branch.\n    |- Try 83 \/ 12 = 6.9. 6.9 is a decimal, drop this branch.\n   |- Pick two numbers (49, 12) (numbers left: [83]). Try possible operations.\n    |- Try 49 + 12 = 61. Add 61 to the number set. Current number set: [61, 83], target: 32, just two numbers left.\n     |- Try 83 + 61 = 144. Evaluate 144 != 32, drop this branch.\n     |- Try 83 - 61 = 22. Evaluate 22 != 32, drop this branch.\n     |- Try 83 * 61 = 5063. 5063 exceeds the maximum intermediate result, drop this branch.\n     |- Try 83 \/ 61 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 49 - 12 = 37. Add 37 to the number set. Current number set: [37, 83], target: 32, just two numbers left.\n     |- Try 83 + 37 = 120. Evaluate 120 != 32, drop this branch.\n     |- Try 83 - 37 = 46. Evaluate 46 != 32, drop this branch.\n     |- Try 83 * 37 = 3071. 3071 exceeds the maximum intermediate result, drop this branch.\n     |- Try 83 \/ 37 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 49 * 12 = 588. Add 588 to the number set. Current number set: [588, 83], target: 32, just two numbers left.\n     |- Try 588 + 83 = 671. Evaluate 671 != 32, drop this branch.\n     |- Try 588 - 83 = 505. Evaluate 505 != 32, drop this branch.\n     |- Try 588 * 83 = 48804. 48804 exceeds the maximum intermediate result, drop this branch.\n     |- Try 588 \/ 83 = 7.1. 7.1 is a decimal, drop this branch.\n    |- Try 49 \/ 12 = 4.1. 4.1 is a decimal, drop this branch.\n  |- Try 47 - 36 = 11. Add 11 to the number set. Current number set: [11, 49, 12], target: 32. Options for choosing two numbers: [(11, 49), (11, 12), (49, 12)].\n   |- Pick two numbers (11, 49) (numbers left: [12]). Try possible operations.\n    |- Try 49 + 11 = 60. Add 60 to the number set. Current number set: [60, 12], target: 32, just two numbers left.\n     |- Try 60 + 12 = 72. Evaluate 72 != 32, drop this branch.\n     |- Try 60 - 12 = 48. Evaluate 48 != 32, drop this branch.\n     |- Try 60 * 12 = 720. Evaluate 720 != 32, drop this branch.\n     |- Try 60 \/ 12 = 5. Evaluate 5 != 32, drop this branch.\n    |- Try 49 - 11 = 38. Add 38 to the number set. Current number set: [38, 12], target: 32, just two numbers left.\n     |- Try 38 + 12 = 50. Evaluate 50 != 32, drop this branch.\n     |- Try 38 - 12 = 26. Evaluate 26 != 32, drop this branch.\n     |- Try 38 * 12 = 456. Evaluate 456 != 32, drop this branch.\n     |- Try 38 \/ 12 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 49 * 11 = 539. Add 539 to the number set. Current number set: [539, 12], target: 32, just two numbers left.\n     |- Try 539 + 12 = 551. Evaluate 551 != 32, drop this branch.\n     |- Try 539 - 12 = 527. Evaluate 527 != 32, drop this branch.\n     |- Try 539 * 12 = 6468. 6468 exceeds the maximum intermediate result, drop this branch.\n     |- Try 539 \/ 12 = 44.9. 44.9 is a decimal, drop this branch.\n    |- Try 49 \/ 11 = 4.5. 4.5 is a decimal, drop this branch.\n   |- Pick two numbers (11, 12) (numbers left: [49]). Try possible operations.\n    |- Try 12 + 11 = 23. Add 23 to the number set. Current number set: [23, 49], target: 32, just two numbers left.\n     |- Try 49 + 23 = 72. Evaluate 72 != 32, drop this branch.\n     |- Try 49 - 23 = 26. Evaluate 26 != 32, drop this branch.\n     |- Try 49 * 23 = 1127. Evaluate 1127 != 32, drop this branch.\n     |- Try 49 \/ 23 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 12 - 11 = 1. Add 1 to the number set. Current number set: [1, 49], target: 32, just two numbers left.\n     |- Try 49 + 1 = 50. Evaluate 50 != 32, drop this branch.\n     |- Try 49 - 1 = 48. Evaluate 48 != 32, drop this branch.\n     |- Try 49 * 1 = 49. Evaluate 49 != 32, drop this branch.\n     |- Try 49 \/ 1 = 49. Evaluate 49 != 32, drop this branch.\n    |- Try 12 * 11 = 132. Add 132 to the number set. Current number set: [132, 49], target: 32, just two numbers left.\n     |- Try 132 + 49 = 181. Evaluate 181 != 32, drop this branch.\n     |- Try 132 - 49 = 83. Evaluate 83 != 32, drop this branch.\n     |- Try 132 * 49 = 6468. 6468 exceeds the maximum intermediate result, drop this branch.\n     |- Try 132 \/ 49 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 12 \/ 11 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (49, 12) (numbers left: [11]). Try possible operations.\n    |- Try 49 + 12 = 61. Add 61 to the number set. Current number set: [61, 11], target: 32, just two numbers left.\n     |- Try 61 + 11 = 72. Evaluate 72 != 32, drop this branch.\n     |- Try 61 - 11 = 50. Evaluate 50 != 32, drop this branch.\n     |- Try 61 * 11 = 671. Evaluate 671 != 32, drop this branch.\n     |- Try 61 \/ 11 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 49 - 12 = 37. Add 37 to the number set. Current number set: [37, 11], target: 32, just two numbers left.\n     |- Try 37 + 11 = 48. Evaluate 48 != 32, drop this branch.\n     |- Try 37 - 11 = 26. Evaluate 26 != 32, drop this branch.\n     |- Try 37 * 11 = 407. Evaluate 407 != 32, drop this branch.\n     |- Try 37 \/ 11 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 49 * 12 = 588. Add 588 to the number set. Current number set: [588, 11], target: 32, just two numbers left.\n     |- Try 588 + 11 = 599. Evaluate 599 != 32, drop this branch.\n     |- Try 588 - 11 = 577. Evaluate 577 != 32, drop this branch.\n     |- Try 588 * 11 = 6468. 6468 exceeds the maximum intermediate result, drop this branch.\n     |- Try 588 \/ 11 = 53.5. 53.5 is a decimal, drop this branch.\n    |- Try 49 \/ 12 = 4.1. 4.1 is a decimal, drop this branch.\n  |- Try 47 * 36 = 1692. Add 1692 to the number set. Current number set: [1692, 49, 12], target: 32. Options for choosing two numbers: [(1692, 49), (1692, 12), (49, 12)].\n   |- Pick two numbers (1692, 49) (numbers left: [12]). Try possible operations.\n    |- Try 1692 + 49 = 1741. Add 1741 to the number set. Current number set: [1741, 12], target: 32, just two numbers left.\n     |- Try 1741 + 12 = 1753. Evaluate 1753 != 32, drop this branch.\n     |- Try 1741 - 12 = 1729. Evaluate 1729 != 32, drop this branch.\n     |- Try 1741 * 12 = 20892. 20892 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1741 \/ 12 = 145.1. 145.1 is a decimal, drop this branch.\n    |- Try 1692 - 49 = 1643. Add 1643 to the number set. Current number set: [1643, 12], target: 32, just two numbers left.\n     |- Try 1643 + 12 = 1655. Evaluate 1655 != 32, drop this branch.\n     |- Try 1643 - 12 = 1631. Evaluate 1631 != 32, drop this branch.\n     |- Try 1643 * 12 = 19716. 19716 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1643 \/ 12 = 136.9. 136.9 is a decimal, drop this branch.\n    |- Try 1692 * 49 = 82908. 82908 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1692 \/ 49 = 34.5. 34.5 is a decimal, drop this branch.\n   |- Pick two numbers (1692, 12) (numbers left: [49]). Try possible operations.\n    |- Try 1692 + 12 = 1704. Add 1704 to the number set. Current number set: [1704, 49], target: 32, just two numbers left.\n     |- Try 1704 + 49 = 1753. Evaluate 1753 != 32, drop this branch.\n     |- Try 1704 - 49 = 1655. Evaluate 1655 != 32, drop this branch.\n     |- Try 1704 * 49 = 83496. 83496 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1704 \/ 49 = 34.8. 34.8 is a decimal, drop this branch.\n    |- Try 1692 - 12 = 1680. Add 1680 to the number set. Current number set: [1680, 49], target: 32, just two numbers left.\n     |- Try 1680 + 49 = 1729. Evaluate 1729 != 32, drop this branch.\n     |- Try 1680 - 49 = 1631. Evaluate 1631 != 32, drop this branch.\n     |- Try 1680 * 49 = 82320. 82320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1680 \/ 49 = 34.3. 34.3 is a decimal, drop this branch.\n    |- Try 1692 * 12 = 20304. 20304 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1692 \/ 12 = 141. Add 141 to the number set. Current number set: [141, 49], target: 32, just two numbers left.\n     |- Try 141 + 49 = 190. Evaluate 190 != 32, drop this branch.\n     |- Try 141 - 49 = 92. Evaluate 92 != 32, drop this branch.\n     |- Try 141 * 49 = 6909. 6909 exceeds the maximum intermediate result, drop this branch.\n     |- Try 141 \/ 49 = 2.9. 2.9 is a decimal, drop this branch.\n   |- Pick two numbers (49, 12) (numbers left: [1692]). Try possible operations.\n    |- Try 49 + 12 = 61. Add 61 to the number set. Current number set: [61, 1692], target: 32, just two numbers left.\n     |- Try 1692 + 61 = 1753. Evaluate 1753 != 32, drop this branch.\n     |- Try 1692 - 61 = 1631. Evaluate 1631 != 32, drop this branch.\n     |- Try 1692 * 61 = 103212. 103212 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1692 \/ 61 = 27.7. 27.7 is a decimal, drop this branch.\n    |- Try 49 - 12 = 37. Add 37 to the number set. Current number set: [37, 1692], target: 32, just two numbers left.\n     |- Try 1692 + 37 = 1729. Evaluate 1729 != 32, drop this branch.\n     |- Try 1692 - 37 = 1655. Evaluate 1655 != 32, drop this branch.\n     |- Try 1692 * 37 = 62604. 62604 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1692 \/ 37 = 45.7. 45.7 is a decimal, drop this branch.\n    |- Try 49 * 12 = 588. Add 588 to the number set. Current number set: [588, 1692], target: 32, just two numbers left.\n     |- Try 1692 + 588 = 2280. 2280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1692 - 588 = 1104. Evaluate 1104 != 32, drop this branch.\n     |- Try 1692 * 588 = 994896. 994896 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1692 \/ 588 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 49 \/ 12 = 4.1. 4.1 is a decimal, drop this branch.\n  |- Try 47 \/ 36 = 1.3. 1.3 is a decimal, drop this branch.\n |- Pick two numbers (47, 49) (numbers left: [36, 12]). Try possible operations.\n  |- Try 49 + 47 = 96. Add 96 to the number set. Current number set: [96, 36, 12], target: 32. Options for choosing two numbers: [(96, 36), (96, 12), (36, 12)].\n   |- Pick two numbers (96, 36) (numbers left: [12]). Try possible operations.\n    |- Try 96 + 36 = 132. Add 132 to the number set. Current number set: [132, 12], target: 32, just two numbers left.\n     |- Try 132 + 12 = 144. Evaluate 144 != 32, drop this branch.\n     |- Try 132 - 12 = 120. Evaluate 120 != 32, drop this branch.\n     |- Try 132 * 12 = 1584. Evaluate 1584 != 32, drop this branch.\n     |- Try 132 \/ 12 = 11. Evaluate 11 != 32, drop this branch.\n    |- Try 96 - 36 = 60. Add 60 to the number set. Current number set: [60, 12], target: 32, just two numbers left.\n     |- Try 60 + 12 = 72. Evaluate 72 != 32, drop this branch.\n     |- Try 60 - 12 = 48. Evaluate 48 != 32, drop this branch.\n     |- Try 60 * 12 = 720. Evaluate 720 != 32, drop this branch.\n     |- Try 60 \/ 12 = 5. Evaluate 5 != 32, drop this branch.\n    |- Try 96 * 36 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n    |- Try 96 \/ 36 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (96, 12) (numbers left: [36]). Try possible operations.\n    |- Try 96 + 12 = 108. Add 108 to the number set. Current number set: [108, 36], target: 32, just two numbers left.\n     |- Try 108 + 36 = 144. Evaluate 144 != 32, drop this branch.\n     |- Try 108 - 36 = 72. Evaluate 72 != 32, drop this branch.\n     |- Try 108 * 36 = 3888. 3888 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 36 = 3. Evaluate 3 != 32, drop this branch.\n    |- Try 96 - 12 = 84. Add 84 to the number set. Current number set: [84, 36], target: 32, just two numbers left.\n     |- Try 84 + 36 = 120. Evaluate 120 != 32, drop this branch.\n     |- Try 84 - 36 = 48. Evaluate 48 != 32, drop this branch.\n     |- Try 84 * 36 = 3024. 3024 exceeds the maximum intermediate result, drop this branch.\n     |- Try 84 \/ 36 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 96 * 12 = 1152. Add 1152 to the number set. Current number set: [1152, 36], target: 32, just two numbers left.\n     |- Try 1152 + 36 = 1188. Evaluate 1188 != 32, drop this branch.\n     |- Try 1152 - 36 = 1116. Evaluate 1116 != 32, drop this branch.\n     |- Try 1152 * 36 = 41472. 41472 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1152 \/ 36 = 32. Evaluate 32 == 32, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 1152 \/ 36 = 32\nThe step before: 96 * 12 = 1152\nThe first step: 49 + 47 = 96\n\nOutput the solution in the required format:\n<Solution>\n49 + 47 = 96\n96 * 12 = 1152\n1152 \/ 36 = 32\n<\/Solution>\n","item":{"nums":[47,36,49,12],"solution":["49 + 47 = 96","96 * 12 = 1152","1152 \/ 36 = 32"],"target":32}}
+{"instance_id":"countdown_8k_53","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [42, 6, 15, 23]\nTarget: 31","reference_output":"# Search Procedure\nInitial number set: [42, 6, 15, 23], target: 31. Options for choosing two numbers: [(42, 6), (42, 15), (42, 23), (6, 15), (6, 23), (15, 23)].\n |- Pick two numbers (42, 6) (numbers left: [15, 23]). Try possible operations.\n  |- Try 42 + 6 = 48. Add 48 to the number set. Current number set: [48, 15, 23], target: 31. Options for choosing two numbers: [(48, 15), (48, 23), (15, 23)].\n   |- Pick two numbers (48, 15) (numbers left: [23]). Try possible operations.\n    |- Try 48 + 15 = 63. Add 63 to the number set. Current number set: [63, 23], target: 31, just two numbers left.\n     |- Try 63 + 23 = 86. Evaluate 86 != 31, drop this branch.\n     |- Try 63 - 23 = 40. Evaluate 40 != 31, drop this branch.\n     |- Try 63 * 23 = 1449. Evaluate 1449 != 31, drop this branch.\n     |- Try 63 \/ 23 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 48 - 15 = 33. Add 33 to the number set. Current number set: [33, 23], target: 31, just two numbers left.\n     |- Try 33 + 23 = 56. Evaluate 56 != 31, drop this branch.\n     |- Try 33 - 23 = 10. Evaluate 10 != 31, drop this branch.\n     |- Try 33 * 23 = 759. Evaluate 759 != 31, drop this branch.\n     |- Try 33 \/ 23 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 48 * 15 = 720. Add 720 to the number set. Current number set: [720, 23], target: 31, just two numbers left.\n     |- Try 720 + 23 = 743. Evaluate 743 != 31, drop this branch.\n     |- Try 720 - 23 = 697. Evaluate 697 != 31, drop this branch.\n     |- Try 720 * 23 = 16560. 16560 exceeds the maximum intermediate result, drop this branch.\n     |- Try 720 \/ 23 = 31.3. 31.3 is a decimal, drop this branch.\n    |- Try 48 \/ 15 = 3.2. 3.2 is a decimal, drop this branch.\n   |- Pick two numbers (48, 23) (numbers left: [15]). Try possible operations.\n    |- Try 48 + 23 = 71. Add 71 to the number set. Current number set: [71, 15], target: 31, just two numbers left.\n     |- Try 71 + 15 = 86. Evaluate 86 != 31, drop this branch.\n     |- Try 71 - 15 = 56. Evaluate 56 != 31, drop this branch.\n     |- Try 71 * 15 = 1065. Evaluate 1065 != 31, drop this branch.\n     |- Try 71 \/ 15 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 48 - 23 = 25. Add 25 to the number set. Current number set: [25, 15], target: 31, just two numbers left.\n     |- Try 25 + 15 = 40. Evaluate 40 != 31, drop this branch.\n     |- Try 25 - 15 = 10. Evaluate 10 != 31, drop this branch.\n     |- Try 25 * 15 = 375. Evaluate 375 != 31, drop this branch.\n     |- Try 25 \/ 15 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 48 * 23 = 1104. Add 1104 to the number set. Current number set: [1104, 15], target: 31, just two numbers left.\n     |- Try 1104 + 15 = 1119. Evaluate 1119 != 31, drop this branch.\n     |- Try 1104 - 15 = 1089. Evaluate 1089 != 31, drop this branch.\n     |- Try 1104 * 15 = 16560. 16560 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1104 \/ 15 = 73.6. 73.6 is a decimal, drop this branch.\n    |- Try 48 \/ 23 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (15, 23) (numbers left: [48]). Try possible operations.\n    |- Try 23 + 15 = 38. Add 38 to the number set. Current number set: [38, 48], target: 31, just two numbers left.\n     |- Try 48 + 38 = 86. Evaluate 86 != 31, drop this branch.\n     |- Try 48 - 38 = 10. Evaluate 10 != 31, drop this branch.\n     |- Try 48 * 38 = 1824. Evaluate 1824 != 31, drop this branch.\n     |- Try 48 \/ 38 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 23 - 15 = 8. Add 8 to the number set. Current number set: [8, 48], target: 31, just two numbers left.\n     |- Try 48 + 8 = 56. Evaluate 56 != 31, drop this branch.\n     |- Try 48 - 8 = 40. Evaluate 40 != 31, drop this branch.\n     |- Try 48 * 8 = 384. Evaluate 384 != 31, drop this branch.\n     |- Try 48 \/ 8 = 6. Evaluate 6 != 31, drop this branch.\n    |- Try 23 * 15 = 345. Add 345 to the number set. Current number set: [345, 48], target: 31, just two numbers left.\n     |- Try 345 + 48 = 393. Evaluate 393 != 31, drop this branch.\n     |- Try 345 - 48 = 297. Evaluate 297 != 31, drop this branch.\n     |- Try 345 * 48 = 16560. 16560 exceeds the maximum intermediate result, drop this branch.\n     |- Try 345 \/ 48 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 23 \/ 15 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 42 - 6 = 36. Add 36 to the number set. Current number set: [36, 15, 23], target: 31. Options for choosing two numbers: [(36, 15), (36, 23), (15, 23)].\n   |- Pick two numbers (36, 15) (numbers left: [23]). Try possible operations.\n    |- Try 36 + 15 = 51. Add 51 to the number set. Current number set: [51, 23], target: 31, just two numbers left.\n     |- Try 51 + 23 = 74. Evaluate 74 != 31, drop this branch.\n     |- Try 51 - 23 = 28. Evaluate 28 != 31, drop this branch.\n     |- Try 51 * 23 = 1173. Evaluate 1173 != 31, drop this branch.\n     |- Try 51 \/ 23 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 36 - 15 = 21. Add 21 to the number set. Current number set: [21, 23], target: 31, just two numbers left.\n     |- Try 23 + 21 = 44. Evaluate 44 != 31, drop this branch.\n     |- Try 23 - 21 = 2. Evaluate 2 != 31, drop this branch.\n     |- Try 23 * 21 = 483. Evaluate 483 != 31, drop this branch.\n     |- Try 23 \/ 21 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 36 * 15 = 540. Add 540 to the number set. Current number set: [540, 23], target: 31, just two numbers left.\n     |- Try 540 + 23 = 563. Evaluate 563 != 31, drop this branch.\n     |- Try 540 - 23 = 517. Evaluate 517 != 31, drop this branch.\n     |- Try 540 * 23 = 12420. 12420 exceeds the maximum intermediate result, drop this branch.\n     |- Try 540 \/ 23 = 23.5. 23.5 is a decimal, drop this branch.\n    |- Try 36 \/ 15 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (36, 23) (numbers left: [15]). Try possible operations.\n    |- Try 36 + 23 = 59. Add 59 to the number set. Current number set: [59, 15], target: 31, just two numbers left.\n     |- Try 59 + 15 = 74. Evaluate 74 != 31, drop this branch.\n     |- Try 59 - 15 = 44. Evaluate 44 != 31, drop this branch.\n     |- Try 59 * 15 = 885. Evaluate 885 != 31, drop this branch.\n     |- Try 59 \/ 15 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 36 - 23 = 13. Add 13 to the number set. Current number set: [13, 15], target: 31, just two numbers left.\n     |- Try 15 + 13 = 28. Evaluate 28 != 31, drop this branch.\n     |- Try 15 - 13 = 2. Evaluate 2 != 31, drop this branch.\n     |- Try 15 * 13 = 195. Evaluate 195 != 31, drop this branch.\n     |- Try 15 \/ 13 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 36 * 23 = 828. Add 828 to the number set. Current number set: [828, 15], target: 31, just two numbers left.\n     |- Try 828 + 15 = 843. Evaluate 843 != 31, drop this branch.\n     |- Try 828 - 15 = 813. Evaluate 813 != 31, drop this branch.\n     |- Try 828 * 15 = 12420. 12420 exceeds the maximum intermediate result, drop this branch.\n     |- Try 828 \/ 15 = 55.2. 55.2 is a decimal, drop this branch.\n    |- Try 36 \/ 23 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (15, 23) (numbers left: [36]). Try possible operations.\n    |- Try 23 + 15 = 38. Add 38 to the number set. Current number set: [38, 36], target: 31, just two numbers left.\n     |- Try 38 + 36 = 74. Evaluate 74 != 31, drop this branch.\n     |- Try 38 - 36 = 2. Evaluate 2 != 31, drop this branch.\n     |- Try 38 * 36 = 1368. Evaluate 1368 != 31, drop this branch.\n     |- Try 38 \/ 36 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 23 - 15 = 8. Add 8 to the number set. Current number set: [8, 36], target: 31, just two numbers left.\n     |- Try 36 + 8 = 44. Evaluate 44 != 31, drop this branch.\n     |- Try 36 - 8 = 28. Evaluate 28 != 31, drop this branch.\n     |- Try 36 * 8 = 288. Evaluate 288 != 31, drop this branch.\n     |- Try 36 \/ 8 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 23 * 15 = 345. Add 345 to the number set. Current number set: [345, 36], target: 31, just two numbers left.\n     |- Try 345 + 36 = 381. Evaluate 381 != 31, drop this branch.\n     |- Try 345 - 36 = 309. Evaluate 309 != 31, drop this branch.\n     |- Try 345 * 36 = 12420. 12420 exceeds the maximum intermediate result, drop this branch.\n     |- Try 345 \/ 36 = 9.6. 9.6 is a decimal, drop this branch.\n    |- Try 23 \/ 15 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 42 * 6 = 252. Add 252 to the number set. Current number set: [252, 15, 23], target: 31. Options for choosing two numbers: [(252, 15), (252, 23), (15, 23)].\n   |- Pick two numbers (252, 15) (numbers left: [23]). Try possible operations.\n    |- Try 252 + 15 = 267. Add 267 to the number set. Current number set: [267, 23], target: 31, just two numbers left.\n     |- Try 267 + 23 = 290. Evaluate 290 != 31, drop this branch.\n     |- Try 267 - 23 = 244. Evaluate 244 != 31, drop this branch.\n     |- Try 267 * 23 = 6141. 6141 exceeds the maximum intermediate result, drop this branch.\n     |- Try 267 \/ 23 = 11.6. 11.6 is a decimal, drop this branch.\n    |- Try 252 - 15 = 237. Add 237 to the number set. Current number set: [237, 23], target: 31, just two numbers left.\n     |- Try 237 + 23 = 260. Evaluate 260 != 31, drop this branch.\n     |- Try 237 - 23 = 214. Evaluate 214 != 31, drop this branch.\n     |- Try 237 * 23 = 5451. 5451 exceeds the maximum intermediate result, drop this branch.\n     |- Try 237 \/ 23 = 10.3. 10.3 is a decimal, drop this branch.\n    |- Try 252 * 15 = 3780. 3780 exceeds the maximum intermediate result, drop this branch.\n    |- Try 252 \/ 15 = 16.8. 16.8 is a decimal, drop this branch.\n   |- Pick two numbers (252, 23) (numbers left: [15]). Try possible operations.\n    |- Try 252 + 23 = 275. Add 275 to the number set. Current number set: [275, 15], target: 31, just two numbers left.\n     |- Try 275 + 15 = 290. Evaluate 290 != 31, drop this branch.\n     |- Try 275 - 15 = 260. Evaluate 260 != 31, drop this branch.\n     |- Try 275 * 15 = 4125. 4125 exceeds the maximum intermediate result, drop this branch.\n     |- Try 275 \/ 15 = 18.3. 18.3 is a decimal, drop this branch.\n    |- Try 252 - 23 = 229. Add 229 to the number set. Current number set: [229, 15], target: 31, just two numbers left.\n     |- Try 229 + 15 = 244. Evaluate 244 != 31, drop this branch.\n     |- Try 229 - 15 = 214. Evaluate 214 != 31, drop this branch.\n     |- Try 229 * 15 = 3435. 3435 exceeds the maximum intermediate result, drop this branch.\n     |- Try 229 \/ 15 = 15.3. 15.3 is a decimal, drop this branch.\n    |- Try 252 * 23 = 5796. 5796 exceeds the maximum intermediate result, drop this branch.\n    |- Try 252 \/ 23 = 11.0. 11.0 is a decimal, drop this branch.\n   |- Pick two numbers (15, 23) (numbers left: [252]). Try possible operations.\n    |- Try 23 + 15 = 38. Add 38 to the number set. Current number set: [38, 252], target: 31, just two numbers left.\n     |- Try 252 + 38 = 290. Evaluate 290 != 31, drop this branch.\n     |- Try 252 - 38 = 214. Evaluate 214 != 31, drop this branch.\n     |- Try 252 * 38 = 9576. 9576 exceeds the maximum intermediate result, drop this branch.\n     |- Try 252 \/ 38 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 23 - 15 = 8. Add 8 to the number set. Current number set: [8, 252], target: 31, just two numbers left.\n     |- Try 252 + 8 = 260. Evaluate 260 != 31, drop this branch.\n     |- Try 252 - 8 = 244. Evaluate 244 != 31, drop this branch.\n     |- Try 252 * 8 = 2016. 2016 exceeds the maximum intermediate result, drop this branch.\n     |- Try 252 \/ 8 = 31.5. 31.5 is a decimal, drop this branch.\n    |- Try 23 * 15 = 345. Add 345 to the number set. Current number set: [345, 252], target: 31, just two numbers left.\n     |- Try 345 + 252 = 597. Evaluate 597 != 31, drop this branch.\n     |- Try 345 - 252 = 93. Evaluate 93 != 31, drop this branch.\n     |- Try 345 * 252 = 86940. 86940 exceeds the maximum intermediate result, drop this branch.\n     |- Try 345 \/ 252 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 23 \/ 15 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 42 \/ 6 = 7. Add 7 to the number set. Current number set: [7, 15, 23], target: 31. Options for choosing two numbers: [(7, 15), (7, 23), (15, 23)].\n   |- Pick two numbers (7, 15) (numbers left: [23]). Try possible operations.\n    |- Try 15 + 7 = 22. Add 22 to the number set. Current number set: [22, 23], target: 31, just two numbers left.\n     |- Try 23 + 22 = 45. Evaluate 45 != 31, drop this branch.\n     |- Try 23 - 22 = 1. Evaluate 1 != 31, drop this branch.\n     |- Try 23 * 22 = 506. Evaluate 506 != 31, drop this branch.\n     |- Try 23 \/ 22 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 15 - 7 = 8. Add 8 to the number set. Current number set: [8, 23], target: 31, just two numbers left.\n     |- Try 23 + 8 = 31. Evaluate 31 == 31, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 23 + 8 = 31\nThe step before: 15 - 7 = 8\nThe first step: 42 \/ 6 = 7\n\nOutput the solution in the required format:\n<Solution>\n42 \/ 6 = 7\n15 - 7 = 8\n23 + 8 = 31\n<\/Solution>\n","item":{"nums":[42,6,15,23],"solution":["42 \/ 6 = 7","15 - 7 = 8","23 + 8 = 31"],"target":31}}
+{"instance_id":"countdown_8k_54","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [30, 8, 31, 4]\nTarget: 24","reference_output":"# Search Procedure\nInitial number set: [30, 8, 31, 4], target: 24. Options for choosing two numbers: [(30, 8), (30, 31), (30, 4), (8, 31), (8, 4), (31, 4)].\n |- Pick two numbers (30, 8) (numbers left: [31, 4]). Try possible operations.\n  |- Try 30 + 8 = 38. Add 38 to the number set. Current number set: [38, 31, 4], target: 24. Options for choosing two numbers: [(38, 31), (38, 4), (31, 4)].\n   |- Pick two numbers (38, 31) (numbers left: [4]). Try possible operations.\n    |- Try 38 + 31 = 69. Add 69 to the number set. Current number set: [69, 4], target: 24, just two numbers left.\n     |- Try 69 + 4 = 73. Evaluate 73 != 24, drop this branch.\n     |- Try 69 - 4 = 65. Evaluate 65 != 24, drop this branch.\n     |- Try 69 * 4 = 276. Evaluate 276 != 24, drop this branch.\n     |- Try 69 \/ 4 = 17.2. 17.2 is a decimal, drop this branch.\n    |- Try 38 - 31 = 7. Add 7 to the number set. Current number set: [7, 4], target: 24, just two numbers left.\n     |- Try 7 + 4 = 11. Evaluate 11 != 24, drop this branch.\n     |- Try 7 - 4 = 3. Evaluate 3 != 24, drop this branch.\n     |- Try 7 * 4 = 28. Evaluate 28 != 24, drop this branch.\n     |- Try 7 \/ 4 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 38 * 31 = 1178. Add 1178 to the number set. Current number set: [1178, 4], target: 24, just two numbers left.\n     |- Try 1178 + 4 = 1182. Evaluate 1182 != 24, drop this branch.\n     |- Try 1178 - 4 = 1174. Evaluate 1174 != 24, drop this branch.\n     |- Try 1178 * 4 = 4712. 4712 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1178 \/ 4 = 294.5. 294.5 is a decimal, drop this branch.\n    |- Try 38 \/ 31 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (38, 4) (numbers left: [31]). Try possible operations.\n    |- Try 38 + 4 = 42. Add 42 to the number set. Current number set: [42, 31], target: 24, just two numbers left.\n     |- Try 42 + 31 = 73. Evaluate 73 != 24, drop this branch.\n     |- Try 42 - 31 = 11. Evaluate 11 != 24, drop this branch.\n     |- Try 42 * 31 = 1302. Evaluate 1302 != 24, drop this branch.\n     |- Try 42 \/ 31 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 38 - 4 = 34. Add 34 to the number set. Current number set: [34, 31], target: 24, just two numbers left.\n     |- Try 34 + 31 = 65. Evaluate 65 != 24, drop this branch.\n     |- Try 34 - 31 = 3. Evaluate 3 != 24, drop this branch.\n     |- Try 34 * 31 = 1054. Evaluate 1054 != 24, drop this branch.\n     |- Try 34 \/ 31 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 38 * 4 = 152. Add 152 to the number set. Current number set: [152, 31], target: 24, just two numbers left.\n     |- Try 152 + 31 = 183. Evaluate 183 != 24, drop this branch.\n     |- Try 152 - 31 = 121. Evaluate 121 != 24, drop this branch.\n     |- Try 152 * 31 = 4712. 4712 exceeds the maximum intermediate result, drop this branch.\n     |- Try 152 \/ 31 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 38 \/ 4 = 9.5. 9.5 is a decimal, drop this branch.\n   |- Pick two numbers (31, 4) (numbers left: [38]). Try possible operations.\n    |- Try 31 + 4 = 35. Add 35 to the number set. Current number set: [35, 38], target: 24, just two numbers left.\n     |- Try 38 + 35 = 73. Evaluate 73 != 24, drop this branch.\n     |- Try 38 - 35 = 3. Evaluate 3 != 24, drop this branch.\n     |- Try 38 * 35 = 1330. Evaluate 1330 != 24, drop this branch.\n     |- Try 38 \/ 35 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 31 - 4 = 27. Add 27 to the number set. Current number set: [27, 38], target: 24, just two numbers left.\n     |- Try 38 + 27 = 65. Evaluate 65 != 24, drop this branch.\n     |- Try 38 - 27 = 11. Evaluate 11 != 24, drop this branch.\n     |- Try 38 * 27 = 1026. Evaluate 1026 != 24, drop this branch.\n     |- Try 38 \/ 27 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 31 * 4 = 124. Add 124 to the number set. Current number set: [124, 38], target: 24, just two numbers left.\n     |- Try 124 + 38 = 162. Evaluate 162 != 24, drop this branch.\n     |- Try 124 - 38 = 86. Evaluate 86 != 24, drop this branch.\n     |- Try 124 * 38 = 4712. 4712 exceeds the maximum intermediate result, drop this branch.\n     |- Try 124 \/ 38 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 31 \/ 4 = 7.8. 7.8 is a decimal, drop this branch.\n  |- Try 30 - 8 = 22. Add 22 to the number set. Current number set: [22, 31, 4], target: 24. Options for choosing two numbers: [(22, 31), (22, 4), (31, 4)].\n   |- Pick two numbers (22, 31) (numbers left: [4]). Try possible operations.\n    |- Try 31 + 22 = 53. Add 53 to the number set. Current number set: [53, 4], target: 24, just two numbers left.\n     |- Try 53 + 4 = 57. Evaluate 57 != 24, drop this branch.\n     |- Try 53 - 4 = 49. Evaluate 49 != 24, drop this branch.\n     |- Try 53 * 4 = 212. Evaluate 212 != 24, drop this branch.\n     |- Try 53 \/ 4 = 13.2. 13.2 is a decimal, drop this branch.\n    |- Try 31 - 22 = 9. Add 9 to the number set. Current number set: [9, 4], target: 24, just two numbers left.\n     |- Try 9 + 4 = 13. Evaluate 13 != 24, drop this branch.\n     |- Try 9 - 4 = 5. Evaluate 5 != 24, drop this branch.\n     |- Try 9 * 4 = 36. Evaluate 36 != 24, drop this branch.\n     |- Try 9 \/ 4 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 31 * 22 = 682. Add 682 to the number set. Current number set: [682, 4], target: 24, just two numbers left.\n     |- Try 682 + 4 = 686. Evaluate 686 != 24, drop this branch.\n     |- Try 682 - 4 = 678. Evaluate 678 != 24, drop this branch.\n     |- Try 682 * 4 = 2728. 2728 exceeds the maximum intermediate result, drop this branch.\n     |- Try 682 \/ 4 = 170.5. 170.5 is a decimal, drop this branch.\n    |- Try 31 \/ 22 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (22, 4) (numbers left: [31]). Try possible operations.\n    |- Try 22 + 4 = 26. Add 26 to the number set. Current number set: [26, 31], target: 24, just two numbers left.\n     |- Try 31 + 26 = 57. Evaluate 57 != 24, drop this branch.\n     |- Try 31 - 26 = 5. Evaluate 5 != 24, drop this branch.\n     |- Try 31 * 26 = 806. Evaluate 806 != 24, drop this branch.\n     |- Try 31 \/ 26 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 22 - 4 = 18. Add 18 to the number set. Current number set: [18, 31], target: 24, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 24, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 24, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 24, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 22 * 4 = 88. Add 88 to the number set. Current number set: [88, 31], target: 24, just two numbers left.\n     |- Try 88 + 31 = 119. Evaluate 119 != 24, drop this branch.\n     |- Try 88 - 31 = 57. Evaluate 57 != 24, drop this branch.\n     |- Try 88 * 31 = 2728. 2728 exceeds the maximum intermediate result, drop this branch.\n     |- Try 88 \/ 31 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 22 \/ 4 = 5.5. 5.5 is a decimal, drop this branch.\n   |- Pick two numbers (31, 4) (numbers left: [22]). Try possible operations.\n    |- Try 31 + 4 = 35. Add 35 to the number set. Current number set: [35, 22], target: 24, just two numbers left.\n     |- Try 35 + 22 = 57. Evaluate 57 != 24, drop this branch.\n     |- Try 35 - 22 = 13. Evaluate 13 != 24, drop this branch.\n     |- Try 35 * 22 = 770. Evaluate 770 != 24, drop this branch.\n     |- Try 35 \/ 22 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 31 - 4 = 27. Add 27 to the number set. Current number set: [27, 22], target: 24, just two numbers left.\n     |- Try 27 + 22 = 49. Evaluate 49 != 24, drop this branch.\n     |- Try 27 - 22 = 5. Evaluate 5 != 24, drop this branch.\n     |- Try 27 * 22 = 594. Evaluate 594 != 24, drop this branch.\n     |- Try 27 \/ 22 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 31 * 4 = 124. Add 124 to the number set. Current number set: [124, 22], target: 24, just two numbers left.\n     |- Try 124 + 22 = 146. Evaluate 146 != 24, drop this branch.\n     |- Try 124 - 22 = 102. Evaluate 102 != 24, drop this branch.\n     |- Try 124 * 22 = 2728. 2728 exceeds the maximum intermediate result, drop this branch.\n     |- Try 124 \/ 22 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 31 \/ 4 = 7.8. 7.8 is a decimal, drop this branch.\n  |- Try 30 * 8 = 240. Add 240 to the number set. Current number set: [240, 31, 4], target: 24. Options for choosing two numbers: [(240, 31), (240, 4), (31, 4)].\n   |- Pick two numbers (240, 31) (numbers left: [4]). Try possible operations.\n    |- Try 240 + 31 = 271. Add 271 to the number set. Current number set: [271, 4], target: 24, just two numbers left.\n     |- Try 271 + 4 = 275. Evaluate 275 != 24, drop this branch.\n     |- Try 271 - 4 = 267. Evaluate 267 != 24, drop this branch.\n     |- Try 271 * 4 = 1084. Evaluate 1084 != 24, drop this branch.\n     |- Try 271 \/ 4 = 67.8. 67.8 is a decimal, drop this branch.\n    |- Try 240 - 31 = 209. Add 209 to the number set. Current number set: [209, 4], target: 24, just two numbers left.\n     |- Try 209 + 4 = 213. Evaluate 213 != 24, drop this branch.\n     |- Try 209 - 4 = 205. Evaluate 205 != 24, drop this branch.\n     |- Try 209 * 4 = 836. Evaluate 836 != 24, drop this branch.\n     |- Try 209 \/ 4 = 52.2. 52.2 is a decimal, drop this branch.\n    |- Try 240 * 31 = 7440. 7440 exceeds the maximum intermediate result, drop this branch.\n    |- Try 240 \/ 31 = 7.7. 7.7 is a decimal, drop this branch.\n   |- Pick two numbers (240, 4) (numbers left: [31]). Try possible operations.\n    |- Try 240 + 4 = 244. Add 244 to the number set. Current number set: [244, 31], target: 24, just two numbers left.\n     |- Try 244 + 31 = 275. Evaluate 275 != 24, drop this branch.\n     |- Try 244 - 31 = 213. Evaluate 213 != 24, drop this branch.\n     |- Try 244 * 31 = 7564. 7564 exceeds the maximum intermediate result, drop this branch.\n     |- Try 244 \/ 31 = 7.9. 7.9 is a decimal, drop this branch.\n    |- Try 240 - 4 = 236. Add 236 to the number set. Current number set: [236, 31], target: 24, just two numbers left.\n     |- Try 236 + 31 = 267. Evaluate 267 != 24, drop this branch.\n     |- Try 236 - 31 = 205. Evaluate 205 != 24, drop this branch.\n     |- Try 236 * 31 = 7316. 7316 exceeds the maximum intermediate result, drop this branch.\n     |- Try 236 \/ 31 = 7.6. 7.6 is a decimal, drop this branch.\n    |- Try 240 * 4 = 960. Add 960 to the number set. Current number set: [960, 31], target: 24, just two numbers left.\n     |- Try 960 + 31 = 991. Evaluate 991 != 24, drop this branch.\n     |- Try 960 - 31 = 929. Evaluate 929 != 24, drop this branch.\n     |- Try 960 * 31 = 29760. 29760 exceeds the maximum intermediate result, drop this branch.\n     |- Try 960 \/ 31 = 31.0. 31.0 is a decimal, drop this branch.\n    |- Try 240 \/ 4 = 60. Add 60 to the number set. Current number set: [60, 31], target: 24, just two numbers left.\n     |- Try 60 + 31 = 91. Evaluate 91 != 24, drop this branch.\n     |- Try 60 - 31 = 29. Evaluate 29 != 24, drop this branch.\n     |- Try 60 * 31 = 1860. Evaluate 1860 != 24, drop this branch.\n     |- Try 60 \/ 31 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (31, 4) (numbers left: [240]). Try possible operations.\n    |- Try 31 + 4 = 35. Add 35 to the number set. Current number set: [35, 240], target: 24, just two numbers left.\n     |- Try 240 + 35 = 275. Evaluate 275 != 24, drop this branch.\n     |- Try 240 - 35 = 205. Evaluate 205 != 24, drop this branch.\n     |- Try 240 * 35 = 8400. 8400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 240 \/ 35 = 6.9. 6.9 is a decimal, drop this branch.\n    |- Try 31 - 4 = 27. Add 27 to the number set. Current number set: [27, 240], target: 24, just two numbers left.\n     |- Try 240 + 27 = 267. Evaluate 267 != 24, drop this branch.\n     |- Try 240 - 27 = 213. Evaluate 213 != 24, drop this branch.\n     |- Try 240 * 27 = 6480. 6480 exceeds the maximum intermediate result, drop this branch.\n     |- Try 240 \/ 27 = 8.9. 8.9 is a decimal, drop this branch.\n    |- Try 31 * 4 = 124. Add 124 to the number set. Current number set: [124, 240], target: 24, just two numbers left.\n     |- Try 240 + 124 = 364. Evaluate 364 != 24, drop this branch.\n     |- Try 240 - 124 = 116. Evaluate 116 != 24, drop this branch.\n     |- Try 240 * 124 = 29760. 29760 exceeds the maximum intermediate result, drop this branch.\n     |- Try 240 \/ 124 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 31 \/ 4 = 7.8. 7.8 is a decimal, drop this branch.\n  |- Try 30 \/ 8 = 3.8. 3.8 is a decimal, drop this branch.\n |- Pick two numbers (30, 31) (numbers left: [8, 4]). Try possible operations.\n  |- Try 31 + 30 = 61. Add 61 to the number set. Current number set: [61, 8, 4], target: 24. Options for choosing two numbers: [(61, 8), (61, 4), (8, 4)].\n   |- Pick two numbers (61, 8) (numbers left: [4]). Try possible operations.\n    |- Try 61 + 8 = 69. Add 69 to the number set. Current number set: [69, 4], target: 24, just two numbers left.\n     |- Try 69 + 4 = 73. Evaluate 73 != 24, drop this branch.\n     |- Try 69 - 4 = 65. Evaluate 65 != 24, drop this branch.\n     |- Try 69 * 4 = 276. Evaluate 276 != 24, drop this branch.\n     |- Try 69 \/ 4 = 17.2. 17.2 is a decimal, drop this branch.\n    |- Try 61 - 8 = 53. Add 53 to the number set. Current number set: [53, 4], target: 24, just two numbers left.\n     |- Try 53 + 4 = 57. Evaluate 57 != 24, drop this branch.\n     |- Try 53 - 4 = 49. Evaluate 49 != 24, drop this branch.\n     |- Try 53 * 4 = 212. Evaluate 212 != 24, drop this branch.\n     |- Try 53 \/ 4 = 13.2. 13.2 is a decimal, drop this branch.\n    |- Try 61 * 8 = 488. Add 488 to the number set. Current number set: [488, 4], target: 24, just two numbers left.\n     |- Try 488 + 4 = 492. Evaluate 492 != 24, drop this branch.\n     |- Try 488 - 4 = 484. Evaluate 484 != 24, drop this branch.\n     |- Try 488 * 4 = 1952. Evaluate 1952 != 24, drop this branch.\n     |- Try 488 \/ 4 = 122. Evaluate 122 != 24, drop this branch.\n    |- Try 61 \/ 8 = 7.6. 7.6 is a decimal, drop this branch.\n   |- Pick two numbers (61, 4) (numbers left: [8]). Try possible operations.\n    |- Try 61 + 4 = 65. Add 65 to the number set. Current number set: [65, 8], target: 24, just two numbers left.\n     |- Try 65 + 8 = 73. Evaluate 73 != 24, drop this branch.\n     |- Try 65 - 8 = 57. Evaluate 57 != 24, drop this branch.\n     |- Try 65 * 8 = 520. Evaluate 520 != 24, drop this branch.\n     |- Try 65 \/ 8 = 8.1. 8.1 is a decimal, drop this branch.\n    |- Try 61 - 4 = 57. Add 57 to the number set. Current number set: [57, 8], target: 24, just two numbers left.\n     |- Try 57 + 8 = 65. Evaluate 65 != 24, drop this branch.\n     |- Try 57 - 8 = 49. Evaluate 49 != 24, drop this branch.\n     |- Try 57 * 8 = 456. Evaluate 456 != 24, drop this branch.\n     |- Try 57 \/ 8 = 7.1. 7.1 is a decimal, drop this branch.\n    |- Try 61 * 4 = 244. Add 244 to the number set. Current number set: [244, 8], target: 24, just two numbers left.\n     |- Try 244 + 8 = 252. Evaluate 252 != 24, drop this branch.\n     |- Try 244 - 8 = 236. Evaluate 236 != 24, drop this branch.\n     |- Try 244 * 8 = 1952. Evaluate 1952 != 24, drop this branch.\n     |- Try 244 \/ 8 = 30.5. 30.5 is a decimal, drop this branch.\n    |- Try 61 \/ 4 = 15.2. 15.2 is a decimal, drop this branch.\n   |- Pick two numbers (8, 4) (numbers left: [61]). Try possible operations.\n    |- Try 8 + 4 = 12. Add 12 to the number set. Current number set: [12, 61], target: 24, just two numbers left.\n     |- Try 61 + 12 = 73. Evaluate 73 != 24, drop this branch.\n     |- Try 61 - 12 = 49. Evaluate 49 != 24, drop this branch.\n     |- Try 61 * 12 = 732. Evaluate 732 != 24, drop this branch.\n     |- Try 61 \/ 12 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 8 - 4 = 4. Add 4 to the number set. Current number set: [4, 61], target: 24, just two numbers left.\n     |- Try 61 + 4 = 65. Evaluate 65 != 24, drop this branch.\n     |- Try 61 - 4 = 57. Evaluate 57 != 24, drop this branch.\n     |- Try 61 * 4 = 244. Evaluate 244 != 24, drop this branch.\n     |- Try 61 \/ 4 = 15.2. 15.2 is a decimal, drop this branch.\n    |- Try 8 * 4 = 32. Add 32 to the number set. Current number set: [32, 61], target: 24, just two numbers left.\n     |- Try 61 + 32 = 93. Evaluate 93 != 24, drop this branch.\n     |- Try 61 - 32 = 29. Evaluate 29 != 24, drop this branch.\n     |- Try 61 * 32 = 1952. Evaluate 1952 != 24, drop this branch.\n     |- Try 61 \/ 32 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 8 \/ 4 = 2. Add 2 to the number set. Current number set: [2, 61], target: 24, just two numbers left.\n     |- Try 61 + 2 = 63. Evaluate 63 != 24, drop this branch.\n     |- Try 61 - 2 = 59. Evaluate 59 != 24, drop this branch.\n     |- Try 61 * 2 = 122. Evaluate 122 != 24, drop this branch.\n     |- Try 61 \/ 2 = 30.5. 30.5 is a decimal, drop this branch.\n  |- Try 31 - 30 = 1. Add 1 to the number set. Current number set: [1, 8, 4], target: 24. Options for choosing two numbers: [(1, 8), (1, 4), (8, 4)].\n   |- Pick two numbers (1, 8) (numbers left: [4]). Try possible operations.\n    |- Try 8 + 1 = 9. Add 9 to the number set. Current number set: [9, 4], target: 24, just two numbers left.\n     |- Try 9 + 4 = 13. Evaluate 13 != 24, drop this branch.\n     |- Try 9 - 4 = 5. Evaluate 5 != 24, drop this branch.\n     |- Try 9 * 4 = 36. Evaluate 36 != 24, drop this branch.\n     |- Try 9 \/ 4 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 8 - 1 = 7. Add 7 to the number set. Current number set: [7, 4], target: 24, just two numbers left.\n     |- Try 7 + 4 = 11. Evaluate 11 != 24, drop this branch.\n     |- Try 7 - 4 = 3. Evaluate 3 != 24, drop this branch.\n     |- Try 7 * 4 = 28. Evaluate 28 != 24, drop this branch.\n     |- Try 7 \/ 4 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 8 * 1 = 8. Add 8 to the number set. Current number set: [8, 4], target: 24, just two numbers left.\n     |- Try 8 + 4 = 12. Evaluate 12 != 24, drop this branch.\n     |- Try 8 - 4 = 4. Evaluate 4 != 24, drop this branch.\n     |- Try 8 * 4 = 32. Evaluate 32 != 24, drop this branch.\n     |- Try 8 \/ 4 = 2. Evaluate 2 != 24, drop this branch.\n    |- Try 8 \/ 1 = 8. Add 8 to the number set. Current number set: [8, 4], target: 24, just two numbers left.\n     |- Try 8 + 4 = 12. Evaluate 12 != 24, drop this branch.\n     |- Try 8 - 4 = 4. Evaluate 4 != 24, drop this branch.\n     |- Try 8 * 4 = 32. Evaluate 32 != 24, drop this branch.\n     |- Try 8 \/ 4 = 2. Evaluate 2 != 24, drop this branch.\n   |- Pick two numbers (1, 4) (numbers left: [8]). Try possible operations.\n    |- Try 4 + 1 = 5. Add 5 to the number set. Current number set: [5, 8], target: 24, just two numbers left.\n     |- Try 8 + 5 = 13. Evaluate 13 != 24, drop this branch.\n     |- Try 8 - 5 = 3. Evaluate 3 != 24, drop this branch.\n     |- Try 8 * 5 = 40. Evaluate 40 != 24, drop this branch.\n     |- Try 8 \/ 5 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 4 - 1 = 3. Add 3 to the number set. Current number set: [3, 8], target: 24, just two numbers left.\n     |- Try 8 + 3 = 11. Evaluate 11 != 24, drop this branch.\n     |- Try 8 - 3 = 5. Evaluate 5 != 24, drop this branch.\n     |- Try 8 * 3 = 24. Evaluate 24 == 24, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 8 * 3 = 24\nThe step before: 4 - 1 = 3\nThe first step: 31 - 30 = 1\n\nOutput the solution in the required format:\n<Solution>\n31 - 30 = 1\n4 - 1 = 3\n8 * 3 = 24\n<\/Solution>\n","item":{"nums":[30,8,31,4],"solution":["31 - 30 = 1","4 - 1 = 3","8 * 3 = 24"],"target":24}}
+{"instance_id":"countdown_8k_55","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [44, 25, 34, 20]\nTarget: 50","reference_output":"# Search Procedure\nInitial number set: [44, 25, 34, 20], target: 50. Options for choosing two numbers: [(44, 25), (44, 34), (44, 20), (25, 34), (25, 20), (34, 20)].\n |- Pick two numbers (44, 25) (numbers left: [34, 20]). Try possible operations.\n  |- Try 44 + 25 = 69. Add 69 to the number set. Current number set: [69, 34, 20], target: 50. Options for choosing two numbers: [(69, 34), (69, 20), (34, 20)].\n   |- Pick two numbers (69, 34) (numbers left: [20]). Try possible operations.\n    |- Try 69 + 34 = 103. Add 103 to the number set. Current number set: [103, 20], target: 50, just two numbers left.\n     |- Try 103 + 20 = 123. Evaluate 123 != 50, drop this branch.\n     |- Try 103 - 20 = 83. Evaluate 83 != 50, drop this branch.\n     |- Try 103 * 20 = 2060. 2060 exceeds the maximum intermediate result, drop this branch.\n     |- Try 103 \/ 20 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 69 - 34 = 35. Add 35 to the number set. Current number set: [35, 20], target: 50, just two numbers left.\n     |- Try 35 + 20 = 55. Evaluate 55 != 50, drop this branch.\n     |- Try 35 - 20 = 15. Evaluate 15 != 50, drop this branch.\n     |- Try 35 * 20 = 700. Evaluate 700 != 50, drop this branch.\n     |- Try 35 \/ 20 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 69 * 34 = 2346. 2346 exceeds the maximum intermediate result, drop this branch.\n    |- Try 69 \/ 34 = 2.0. 2.0 is a decimal, drop this branch.\n   |- Pick two numbers (69, 20) (numbers left: [34]). Try possible operations.\n    |- Try 69 + 20 = 89. Add 89 to the number set. Current number set: [89, 34], target: 50, just two numbers left.\n     |- Try 89 + 34 = 123. Evaluate 123 != 50, drop this branch.\n     |- Try 89 - 34 = 55. Evaluate 55 != 50, drop this branch.\n     |- Try 89 * 34 = 3026. 3026 exceeds the maximum intermediate result, drop this branch.\n     |- Try 89 \/ 34 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 69 - 20 = 49. Add 49 to the number set. Current number set: [49, 34], target: 50, just two numbers left.\n     |- Try 49 + 34 = 83. Evaluate 83 != 50, drop this branch.\n     |- Try 49 - 34 = 15. Evaluate 15 != 50, drop this branch.\n     |- Try 49 * 34 = 1666. Evaluate 1666 != 50, drop this branch.\n     |- Try 49 \/ 34 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 69 * 20 = 1380. Add 1380 to the number set. Current number set: [1380, 34], target: 50, just two numbers left.\n     |- Try 1380 + 34 = 1414. Evaluate 1414 != 50, drop this branch.\n     |- Try 1380 - 34 = 1346. Evaluate 1346 != 50, drop this branch.\n     |- Try 1380 * 34 = 46920. 46920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1380 \/ 34 = 40.6. 40.6 is a decimal, drop this branch.\n    |- Try 69 \/ 20 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (34, 20) (numbers left: [69]). Try possible operations.\n    |- Try 34 + 20 = 54. Add 54 to the number set. Current number set: [54, 69], target: 50, just two numbers left.\n     |- Try 69 + 54 = 123. Evaluate 123 != 50, drop this branch.\n     |- Try 69 - 54 = 15. Evaluate 15 != 50, drop this branch.\n     |- Try 69 * 54 = 3726. 3726 exceeds the maximum intermediate result, drop this branch.\n     |- Try 69 \/ 54 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 34 - 20 = 14. Add 14 to the number set. Current number set: [14, 69], target: 50, just two numbers left.\n     |- Try 69 + 14 = 83. Evaluate 83 != 50, drop this branch.\n     |- Try 69 - 14 = 55. Evaluate 55 != 50, drop this branch.\n     |- Try 69 * 14 = 966. Evaluate 966 != 50, drop this branch.\n     |- Try 69 \/ 14 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 34 * 20 = 680. Add 680 to the number set. Current number set: [680, 69], target: 50, just two numbers left.\n     |- Try 680 + 69 = 749. Evaluate 749 != 50, drop this branch.\n     |- Try 680 - 69 = 611. Evaluate 611 != 50, drop this branch.\n     |- Try 680 * 69 = 46920. 46920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 680 \/ 69 = 9.9. 9.9 is a decimal, drop this branch.\n    |- Try 34 \/ 20 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 44 - 25 = 19. Add 19 to the number set. Current number set: [19, 34, 20], target: 50. Options for choosing two numbers: [(19, 34), (19, 20), (34, 20)].\n   |- Pick two numbers (19, 34) (numbers left: [20]). Try possible operations.\n    |- Try 34 + 19 = 53. Add 53 to the number set. Current number set: [53, 20], target: 50, just two numbers left.\n     |- Try 53 + 20 = 73. Evaluate 73 != 50, drop this branch.\n     |- Try 53 - 20 = 33. Evaluate 33 != 50, drop this branch.\n     |- Try 53 * 20 = 1060. Evaluate 1060 != 50, drop this branch.\n     |- Try 53 \/ 20 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 34 - 19 = 15. Add 15 to the number set. Current number set: [15, 20], target: 50, just two numbers left.\n     |- Try 20 + 15 = 35. Evaluate 35 != 50, drop this branch.\n     |- Try 20 - 15 = 5. Evaluate 5 != 50, drop this branch.\n     |- Try 20 * 15 = 300. Evaluate 300 != 50, drop this branch.\n     |- Try 20 \/ 15 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 34 * 19 = 646. Add 646 to the number set. Current number set: [646, 20], target: 50, just two numbers left.\n     |- Try 646 + 20 = 666. Evaluate 666 != 50, drop this branch.\n     |- Try 646 - 20 = 626. Evaluate 626 != 50, drop this branch.\n     |- Try 646 * 20 = 12920. 12920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 646 \/ 20 = 32.3. 32.3 is a decimal, drop this branch.\n    |- Try 34 \/ 19 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (19, 20) (numbers left: [34]). Try possible operations.\n    |- Try 20 + 19 = 39. Add 39 to the number set. Current number set: [39, 34], target: 50, just two numbers left.\n     |- Try 39 + 34 = 73. Evaluate 73 != 50, drop this branch.\n     |- Try 39 - 34 = 5. Evaluate 5 != 50, drop this branch.\n     |- Try 39 * 34 = 1326. Evaluate 1326 != 50, drop this branch.\n     |- Try 39 \/ 34 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 20 - 19 = 1. Add 1 to the number set. Current number set: [1, 34], target: 50, just two numbers left.\n     |- Try 34 + 1 = 35. Evaluate 35 != 50, drop this branch.\n     |- Try 34 - 1 = 33. Evaluate 33 != 50, drop this branch.\n     |- Try 34 * 1 = 34. Evaluate 34 != 50, drop this branch.\n     |- Try 34 \/ 1 = 34. Evaluate 34 != 50, drop this branch.\n    |- Try 20 * 19 = 380. Add 380 to the number set. Current number set: [380, 34], target: 50, just two numbers left.\n     |- Try 380 + 34 = 414. Evaluate 414 != 50, drop this branch.\n     |- Try 380 - 34 = 346. Evaluate 346 != 50, drop this branch.\n     |- Try 380 * 34 = 12920. 12920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 380 \/ 34 = 11.2. 11.2 is a decimal, drop this branch.\n    |- Try 20 \/ 19 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (34, 20) (numbers left: [19]). Try possible operations.\n    |- Try 34 + 20 = 54. Add 54 to the number set. Current number set: [54, 19], target: 50, just two numbers left.\n     |- Try 54 + 19 = 73. Evaluate 73 != 50, drop this branch.\n     |- Try 54 - 19 = 35. Evaluate 35 != 50, drop this branch.\n     |- Try 54 * 19 = 1026. Evaluate 1026 != 50, drop this branch.\n     |- Try 54 \/ 19 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 34 - 20 = 14. Add 14 to the number set. Current number set: [14, 19], target: 50, just two numbers left.\n     |- Try 19 + 14 = 33. Evaluate 33 != 50, drop this branch.\n     |- Try 19 - 14 = 5. Evaluate 5 != 50, drop this branch.\n     |- Try 19 * 14 = 266. Evaluate 266 != 50, drop this branch.\n     |- Try 19 \/ 14 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 34 * 20 = 680. Add 680 to the number set. Current number set: [680, 19], target: 50, just two numbers left.\n     |- Try 680 + 19 = 699. Evaluate 699 != 50, drop this branch.\n     |- Try 680 - 19 = 661. Evaluate 661 != 50, drop this branch.\n     |- Try 680 * 19 = 12920. 12920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 680 \/ 19 = 35.8. 35.8 is a decimal, drop this branch.\n    |- Try 34 \/ 20 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 44 * 25 = 1100. Add 1100 to the number set. Current number set: [1100, 34, 20], target: 50. Options for choosing two numbers: [(1100, 34), (1100, 20), (34, 20)].\n   |- Pick two numbers (1100, 34) (numbers left: [20]). Try possible operations.\n    |- Try 1100 + 34 = 1134. Add 1134 to the number set. Current number set: [1134, 20], target: 50, just two numbers left.\n     |- Try 1134 + 20 = 1154. Evaluate 1154 != 50, drop this branch.\n     |- Try 1134 - 20 = 1114. Evaluate 1114 != 50, drop this branch.\n     |- Try 1134 * 20 = 22680. 22680 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1134 \/ 20 = 56.7. 56.7 is a decimal, drop this branch.\n    |- Try 1100 - 34 = 1066. Add 1066 to the number set. Current number set: [1066, 20], target: 50, just two numbers left.\n     |- Try 1066 + 20 = 1086. Evaluate 1086 != 50, drop this branch.\n     |- Try 1066 - 20 = 1046. Evaluate 1046 != 50, drop this branch.\n     |- Try 1066 * 20 = 21320. 21320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1066 \/ 20 = 53.3. 53.3 is a decimal, drop this branch.\n    |- Try 1100 * 34 = 37400. 37400 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1100 \/ 34 = 32.4. 32.4 is a decimal, drop this branch.\n   |- Pick two numbers (1100, 20) (numbers left: [34]). Try possible operations.\n    |- Try 1100 + 20 = 1120. Add 1120 to the number set. Current number set: [1120, 34], target: 50, just two numbers left.\n     |- Try 1120 + 34 = 1154. Evaluate 1154 != 50, drop this branch.\n     |- Try 1120 - 34 = 1086. Evaluate 1086 != 50, drop this branch.\n     |- Try 1120 * 34 = 38080. 38080 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1120 \/ 34 = 32.9. 32.9 is a decimal, drop this branch.\n    |- Try 1100 - 20 = 1080. Add 1080 to the number set. Current number set: [1080, 34], target: 50, just two numbers left.\n     |- Try 1080 + 34 = 1114. Evaluate 1114 != 50, drop this branch.\n     |- Try 1080 - 34 = 1046. Evaluate 1046 != 50, drop this branch.\n     |- Try 1080 * 34 = 36720. 36720 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1080 \/ 34 = 31.8. 31.8 is a decimal, drop this branch.\n    |- Try 1100 * 20 = 22000. 22000 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1100 \/ 20 = 55. Add 55 to the number set. Current number set: [55, 34], target: 50, just two numbers left.\n     |- Try 55 + 34 = 89. Evaluate 89 != 50, drop this branch.\n     |- Try 55 - 34 = 21. Evaluate 21 != 50, drop this branch.\n     |- Try 55 * 34 = 1870. Evaluate 1870 != 50, drop this branch.\n     |- Try 55 \/ 34 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (34, 20) (numbers left: [1100]). Try possible operations.\n    |- Try 34 + 20 = 54. Add 54 to the number set. Current number set: [54, 1100], target: 50, just two numbers left.\n     |- Try 1100 + 54 = 1154. Evaluate 1154 != 50, drop this branch.\n     |- Try 1100 - 54 = 1046. Evaluate 1046 != 50, drop this branch.\n     |- Try 1100 * 54 = 59400. 59400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1100 \/ 54 = 20.4. 20.4 is a decimal, drop this branch.\n    |- Try 34 - 20 = 14. Add 14 to the number set. Current number set: [14, 1100], target: 50, just two numbers left.\n     |- Try 1100 + 14 = 1114. Evaluate 1114 != 50, drop this branch.\n     |- Try 1100 - 14 = 1086. Evaluate 1086 != 50, drop this branch.\n     |- Try 1100 * 14 = 15400. 15400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1100 \/ 14 = 78.6. 78.6 is a decimal, drop this branch.\n    |- Try 34 * 20 = 680. Add 680 to the number set. Current number set: [680, 1100], target: 50, just two numbers left.\n     |- Try 1100 + 680 = 1780. Evaluate 1780 != 50, drop this branch.\n     |- Try 1100 - 680 = 420. Evaluate 420 != 50, drop this branch.\n     |- Try 1100 * 680 = 748000. 748000 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1100 \/ 680 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 34 \/ 20 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 44 \/ 25 = 1.8. 1.8 is a decimal, drop this branch.\n |- Pick two numbers (44, 34) (numbers left: [25, 20]). Try possible operations.\n  |- Try 44 + 34 = 78. Add 78 to the number set. Current number set: [78, 25, 20], target: 50. Options for choosing two numbers: [(78, 25), (78, 20), (25, 20)].\n   |- Pick two numbers (78, 25) (numbers left: [20]). Try possible operations.\n    |- Try 78 + 25 = 103. Add 103 to the number set. Current number set: [103, 20], target: 50, just two numbers left.\n     |- Try 103 + 20 = 123. Evaluate 123 != 50, drop this branch.\n     |- Try 103 - 20 = 83. Evaluate 83 != 50, drop this branch.\n     |- Try 103 * 20 = 2060. 2060 exceeds the maximum intermediate result, drop this branch.\n     |- Try 103 \/ 20 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 78 - 25 = 53. Add 53 to the number set. Current number set: [53, 20], target: 50, just two numbers left.\n     |- Try 53 + 20 = 73. Evaluate 73 != 50, drop this branch.\n     |- Try 53 - 20 = 33. Evaluate 33 != 50, drop this branch.\n     |- Try 53 * 20 = 1060. Evaluate 1060 != 50, drop this branch.\n     |- Try 53 \/ 20 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 78 * 25 = 1950. Add 1950 to the number set. Current number set: [1950, 20], target: 50, just two numbers left.\n     |- Try 1950 + 20 = 1970. Evaluate 1970 != 50, drop this branch.\n     |- Try 1950 - 20 = 1930. Evaluate 1930 != 50, drop this branch.\n     |- Try 1950 * 20 = 39000. 39000 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1950 \/ 20 = 97.5. 97.5 is a decimal, drop this branch.\n    |- Try 78 \/ 25 = 3.1. 3.1 is a decimal, drop this branch.\n   |- Pick two numbers (78, 20) (numbers left: [25]). Try possible operations.\n    |- Try 78 + 20 = 98. Add 98 to the number set. Current number set: [98, 25], target: 50, just two numbers left.\n     |- Try 98 + 25 = 123. Evaluate 123 != 50, drop this branch.\n     |- Try 98 - 25 = 73. Evaluate 73 != 50, drop this branch.\n     |- Try 98 * 25 = 2450. 2450 exceeds the maximum intermediate result, drop this branch.\n     |- Try 98 \/ 25 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 78 - 20 = 58. Add 58 to the number set. Current number set: [58, 25], target: 50, just two numbers left.\n     |- Try 58 + 25 = 83. Evaluate 83 != 50, drop this branch.\n     |- Try 58 - 25 = 33. Evaluate 33 != 50, drop this branch.\n     |- Try 58 * 25 = 1450. Evaluate 1450 != 50, drop this branch.\n     |- Try 58 \/ 25 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 78 * 20 = 1560. Add 1560 to the number set. Current number set: [1560, 25], target: 50, just two numbers left.\n     |- Try 1560 + 25 = 1585. Evaluate 1585 != 50, drop this branch.\n     |- Try 1560 - 25 = 1535. Evaluate 1535 != 50, drop this branch.\n     |- Try 1560 * 25 = 39000. 39000 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1560 \/ 25 = 62.4. 62.4 is a decimal, drop this branch.\n    |- Try 78 \/ 20 = 3.9. 3.9 is a decimal, drop this branch.\n   |- Pick two numbers (25, 20) (numbers left: [78]). Try possible operations.\n    |- Try 25 + 20 = 45. Add 45 to the number set. Current number set: [45, 78], target: 50, just two numbers left.\n     |- Try 78 + 45 = 123. Evaluate 123 != 50, drop this branch.\n     |- Try 78 - 45 = 33. Evaluate 33 != 50, drop this branch.\n     |- Try 78 * 45 = 3510. 3510 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 45 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 20 = 5. Add 5 to the number set. Current number set: [5, 78], target: 50, just two numbers left.\n     |- Try 78 + 5 = 83. Evaluate 83 != 50, drop this branch.\n     |- Try 78 - 5 = 73. Evaluate 73 != 50, drop this branch.\n     |- Try 78 * 5 = 390. Evaluate 390 != 50, drop this branch.\n     |- Try 78 \/ 5 = 15.6. 15.6 is a decimal, drop this branch.\n    |- Try 25 * 20 = 500. Add 500 to the number set. Current number set: [500, 78], target: 50, just two numbers left.\n     |- Try 500 + 78 = 578. Evaluate 578 != 50, drop this branch.\n     |- Try 500 - 78 = 422. Evaluate 422 != 50, drop this branch.\n     |- Try 500 * 78 = 39000. 39000 exceeds the maximum intermediate result, drop this branch.\n     |- Try 500 \/ 78 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 25 \/ 20 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 44 - 34 = 10. Add 10 to the number set. Current number set: [10, 25, 20], target: 50. Options for choosing two numbers: [(10, 25), (10, 20), (25, 20)].\n   |- Pick two numbers (10, 25) (numbers left: [20]). Try possible operations.\n    |- Try 25 + 10 = 35. Add 35 to the number set. Current number set: [35, 20], target: 50, just two numbers left.\n     |- Try 35 + 20 = 55. Evaluate 55 != 50, drop this branch.\n     |- Try 35 - 20 = 15. Evaluate 15 != 50, drop this branch.\n     |- Try 35 * 20 = 700. Evaluate 700 != 50, drop this branch.\n     |- Try 35 \/ 20 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 25 - 10 = 15. Add 15 to the number set. Current number set: [15, 20], target: 50, just two numbers left.\n     |- Try 20 + 15 = 35. Evaluate 35 != 50, drop this branch.\n     |- Try 20 - 15 = 5. Evaluate 5 != 50, drop this branch.\n     |- Try 20 * 15 = 300. Evaluate 300 != 50, drop this branch.\n     |- Try 20 \/ 15 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 25 * 10 = 250. Add 250 to the number set. Current number set: [250, 20], target: 50, just two numbers left.\n     |- Try 250 + 20 = 270. Evaluate 270 != 50, drop this branch.\n     |- Try 250 - 20 = 230. Evaluate 230 != 50, drop this branch.\n     |- Try 250 * 20 = 5000. 5000 exceeds the maximum intermediate result, drop this branch.\n     |- Try 250 \/ 20 = 12.5. 12.5 is a decimal, drop this branch.\n    |- Try 25 \/ 10 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (10, 20) (numbers left: [25]). Try possible operations.\n    |- Try 20 + 10 = 30. Add 30 to the number set. Current number set: [30, 25], target: 50, just two numbers left.\n     |- Try 30 + 25 = 55. Evaluate 55 != 50, drop this branch.\n     |- Try 30 - 25 = 5. Evaluate 5 != 50, drop this branch.\n     |- Try 30 * 25 = 750. Evaluate 750 != 50, drop this branch.\n     |- Try 30 \/ 25 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 20 - 10 = 10. Add 10 to the number set. Current number set: [10, 25], target: 50, just two numbers left.\n     |- Try 25 + 10 = 35. Evaluate 35 != 50, drop this branch.\n     |- Try 25 - 10 = 15. Evaluate 15 != 50, drop this branch.\n     |- Try 25 * 10 = 250. Evaluate 250 != 50, drop this branch.\n     |- Try 25 \/ 10 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 20 * 10 = 200. Add 200 to the number set. Current number set: [200, 25], target: 50, just two numbers left.\n     |- Try 200 + 25 = 225. Evaluate 225 != 50, drop this branch.\n     |- Try 200 - 25 = 175. Evaluate 175 != 50, drop this branch.\n     |- Try 200 * 25 = 5000. 5000 exceeds the maximum intermediate result, drop this branch.\n     |- Try 200 \/ 25 = 8. Evaluate 8 != 50, drop this branch.\n    |- Try 20 \/ 10 = 2. Add 2 to the number set. Current number set: [2, 25], target: 50, just two numbers left.\n     |- Try 25 + 2 = 27. Evaluate 27 != 50, drop this branch.\n     |- Try 25 - 2 = 23. Evaluate 23 != 50, drop this branch.\n     |- Try 25 * 2 = 50. Evaluate 50 == 50, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 25 * 2 = 50\nThe step before: 20 \/ 10 = 2\nThe first step: 44 - 34 = 10\n\nOutput the solution in the required format:\n<Solution>\n44 - 34 = 10\n20 \/ 10 = 2\n25 * 2 = 50\n<\/Solution>\n","item":{"nums":[44,25,34,20],"solution":["44 - 34 = 10","20 \/ 10 = 2","25 * 2 = 50"],"target":50}}
+{"instance_id":"countdown_8k_56","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [39, 13, 17, 34]\nTarget: 17","reference_output":"# Search Procedure\nInitial number set: [39, 13, 17, 34], target: 17. Options for choosing two numbers: [(39, 13), (39, 17), (39, 34), (13, 17), (13, 34), (17, 34)].\n |- Pick two numbers (39, 13) (numbers left: [17, 34]). Try possible operations.\n  |- Try 39 + 13 = 52. Add 52 to the number set. Current number set: [52, 17, 34], target: 17. Options for choosing two numbers: [(52, 17), (52, 34), (17, 34)].\n   |- Pick two numbers (52, 17) (numbers left: [34]). Try possible operations.\n    |- Try 52 + 17 = 69. Add 69 to the number set. Current number set: [69, 34], target: 17, just two numbers left.\n     |- Try 69 + 34 = 103. Evaluate 103 != 17, drop this branch.\n     |- Try 69 - 34 = 35. Evaluate 35 != 17, drop this branch.\n     |- Try 69 * 34 = 2346. 2346 exceeds the maximum intermediate result, drop this branch.\n     |- Try 69 \/ 34 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 52 - 17 = 35. Add 35 to the number set. Current number set: [35, 34], target: 17, just two numbers left.\n     |- Try 35 + 34 = 69. Evaluate 69 != 17, drop this branch.\n     |- Try 35 - 34 = 1. Evaluate 1 != 17, drop this branch.\n     |- Try 35 * 34 = 1190. Evaluate 1190 != 17, drop this branch.\n     |- Try 35 \/ 34 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 52 * 17 = 884. Add 884 to the number set. Current number set: [884, 34], target: 17, just two numbers left.\n     |- Try 884 + 34 = 918. Evaluate 918 != 17, drop this branch.\n     |- Try 884 - 34 = 850. Evaluate 850 != 17, drop this branch.\n     |- Try 884 * 34 = 30056. 30056 exceeds the maximum intermediate result, drop this branch.\n     |- Try 884 \/ 34 = 26. Evaluate 26 != 17, drop this branch.\n    |- Try 52 \/ 17 = 3.1. 3.1 is a decimal, drop this branch.\n   |- Pick two numbers (52, 34) (numbers left: [17]). Try possible operations.\n    |- Try 52 + 34 = 86. Add 86 to the number set. Current number set: [86, 17], target: 17, just two numbers left.\n     |- Try 86 + 17 = 103. Evaluate 103 != 17, drop this branch.\n     |- Try 86 - 17 = 69. Evaluate 69 != 17, drop this branch.\n     |- Try 86 * 17 = 1462. Evaluate 1462 != 17, drop this branch.\n     |- Try 86 \/ 17 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 52 - 34 = 18. Add 18 to the number set. Current number set: [18, 17], target: 17, just two numbers left.\n     |- Try 18 + 17 = 35. Evaluate 35 != 17, drop this branch.\n     |- Try 18 - 17 = 1. Evaluate 1 != 17, drop this branch.\n     |- Try 18 * 17 = 306. Evaluate 306 != 17, drop this branch.\n     |- Try 18 \/ 17 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 52 * 34 = 1768. Add 1768 to the number set. Current number set: [1768, 17], target: 17, just two numbers left.\n     |- Try 1768 + 17 = 1785. Evaluate 1785 != 17, drop this branch.\n     |- Try 1768 - 17 = 1751. Evaluate 1751 != 17, drop this branch.\n     |- Try 1768 * 17 = 30056. 30056 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1768 \/ 17 = 104. Evaluate 104 != 17, drop this branch.\n    |- Try 52 \/ 34 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (17, 34) (numbers left: [52]). Try possible operations.\n    |- Try 34 + 17 = 51. Add 51 to the number set. Current number set: [51, 52], target: 17, just two numbers left.\n     |- Try 52 + 51 = 103. Evaluate 103 != 17, drop this branch.\n     |- Try 52 - 51 = 1. Evaluate 1 != 17, drop this branch.\n     |- Try 52 * 51 = 2652. 2652 exceeds the maximum intermediate result, drop this branch.\n     |- Try 52 \/ 51 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 34 - 17 = 17. Add 17 to the number set. Current number set: [17, 52], target: 17, just two numbers left.\n     |- Try 52 + 17 = 69. Evaluate 69 != 17, drop this branch.\n     |- Try 52 - 17 = 35. Evaluate 35 != 17, drop this branch.\n     |- Try 52 * 17 = 884. Evaluate 884 != 17, drop this branch.\n     |- Try 52 \/ 17 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 34 * 17 = 578. Add 578 to the number set. Current number set: [578, 52], target: 17, just two numbers left.\n     |- Try 578 + 52 = 630. Evaluate 630 != 17, drop this branch.\n     |- Try 578 - 52 = 526. Evaluate 526 != 17, drop this branch.\n     |- Try 578 * 52 = 30056. 30056 exceeds the maximum intermediate result, drop this branch.\n     |- Try 578 \/ 52 = 11.1. 11.1 is a decimal, drop this branch.\n    |- Try 34 \/ 17 = 2. Add 2 to the number set. Current number set: [2, 52], target: 17, just two numbers left.\n     |- Try 52 + 2 = 54. Evaluate 54 != 17, drop this branch.\n     |- Try 52 - 2 = 50. Evaluate 50 != 17, drop this branch.\n     |- Try 52 * 2 = 104. Evaluate 104 != 17, drop this branch.\n     |- Try 52 \/ 2 = 26. Evaluate 26 != 17, drop this branch.\n  |- Try 39 - 13 = 26. Add 26 to the number set. Current number set: [26, 17, 34], target: 17. Options for choosing two numbers: [(26, 17), (26, 34), (17, 34)].\n   |- Pick two numbers (26, 17) (numbers left: [34]). Try possible operations.\n    |- Try 26 + 17 = 43. Add 43 to the number set. Current number set: [43, 34], target: 17, just two numbers left.\n     |- Try 43 + 34 = 77. Evaluate 77 != 17, drop this branch.\n     |- Try 43 - 34 = 9. Evaluate 9 != 17, drop this branch.\n     |- Try 43 * 34 = 1462. Evaluate 1462 != 17, drop this branch.\n     |- Try 43 \/ 34 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 26 - 17 = 9. Add 9 to the number set. Current number set: [9, 34], target: 17, just two numbers left.\n     |- Try 34 + 9 = 43. Evaluate 43 != 17, drop this branch.\n     |- Try 34 - 9 = 25. Evaluate 25 != 17, drop this branch.\n     |- Try 34 * 9 = 306. Evaluate 306 != 17, drop this branch.\n     |- Try 34 \/ 9 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 26 * 17 = 442. Add 442 to the number set. Current number set: [442, 34], target: 17, just two numbers left.\n     |- Try 442 + 34 = 476. Evaluate 476 != 17, drop this branch.\n     |- Try 442 - 34 = 408. Evaluate 408 != 17, drop this branch.\n     |- Try 442 * 34 = 15028. 15028 exceeds the maximum intermediate result, drop this branch.\n     |- Try 442 \/ 34 = 13. Evaluate 13 != 17, drop this branch.\n    |- Try 26 \/ 17 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (26, 34) (numbers left: [17]). Try possible operations.\n    |- Try 34 + 26 = 60. Add 60 to the number set. Current number set: [60, 17], target: 17, just two numbers left.\n     |- Try 60 + 17 = 77. Evaluate 77 != 17, drop this branch.\n     |- Try 60 - 17 = 43. Evaluate 43 != 17, drop this branch.\n     |- Try 60 * 17 = 1020. Evaluate 1020 != 17, drop this branch.\n     |- Try 60 \/ 17 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 34 - 26 = 8. Add 8 to the number set. Current number set: [8, 17], target: 17, just two numbers left.\n     |- Try 17 + 8 = 25. Evaluate 25 != 17, drop this branch.\n     |- Try 17 - 8 = 9. Evaluate 9 != 17, drop this branch.\n     |- Try 17 * 8 = 136. Evaluate 136 != 17, drop this branch.\n     |- Try 17 \/ 8 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 34 * 26 = 884. Add 884 to the number set. Current number set: [884, 17], target: 17, just two numbers left.\n     |- Try 884 + 17 = 901. Evaluate 901 != 17, drop this branch.\n     |- Try 884 - 17 = 867. Evaluate 867 != 17, drop this branch.\n     |- Try 884 * 17 = 15028. 15028 exceeds the maximum intermediate result, drop this branch.\n     |- Try 884 \/ 17 = 52. Evaluate 52 != 17, drop this branch.\n    |- Try 34 \/ 26 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (17, 34) (numbers left: [26]). Try possible operations.\n    |- Try 34 + 17 = 51. Add 51 to the number set. Current number set: [51, 26], target: 17, just two numbers left.\n     |- Try 51 + 26 = 77. Evaluate 77 != 17, drop this branch.\n     |- Try 51 - 26 = 25. Evaluate 25 != 17, drop this branch.\n     |- Try 51 * 26 = 1326. Evaluate 1326 != 17, drop this branch.\n     |- Try 51 \/ 26 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 34 - 17 = 17. Add 17 to the number set. Current number set: [17, 26], target: 17, just two numbers left.\n     |- Try 26 + 17 = 43. Evaluate 43 != 17, drop this branch.\n     |- Try 26 - 17 = 9. Evaluate 9 != 17, drop this branch.\n     |- Try 26 * 17 = 442. Evaluate 442 != 17, drop this branch.\n     |- Try 26 \/ 17 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 34 * 17 = 578. Add 578 to the number set. Current number set: [578, 26], target: 17, just two numbers left.\n     |- Try 578 + 26 = 604. Evaluate 604 != 17, drop this branch.\n     |- Try 578 - 26 = 552. Evaluate 552 != 17, drop this branch.\n     |- Try 578 * 26 = 15028. 15028 exceeds the maximum intermediate result, drop this branch.\n     |- Try 578 \/ 26 = 22.2. 22.2 is a decimal, drop this branch.\n    |- Try 34 \/ 17 = 2. Add 2 to the number set. Current number set: [2, 26], target: 17, just two numbers left.\n     |- Try 26 + 2 = 28. Evaluate 28 != 17, drop this branch.\n     |- Try 26 - 2 = 24. Evaluate 24 != 17, drop this branch.\n     |- Try 26 * 2 = 52. Evaluate 52 != 17, drop this branch.\n     |- Try 26 \/ 2 = 13. Evaluate 13 != 17, drop this branch.\n  |- Try 39 * 13 = 507. Add 507 to the number set. Current number set: [507, 17, 34], target: 17. Options for choosing two numbers: [(507, 17), (507, 34), (17, 34)].\n   |- Pick two numbers (507, 17) (numbers left: [34]). Try possible operations.\n    |- Try 507 + 17 = 524. Add 524 to the number set. Current number set: [524, 34], target: 17, just two numbers left.\n     |- Try 524 + 34 = 558. Evaluate 558 != 17, drop this branch.\n     |- Try 524 - 34 = 490. Evaluate 490 != 17, drop this branch.\n     |- Try 524 * 34 = 17816. 17816 exceeds the maximum intermediate result, drop this branch.\n     |- Try 524 \/ 34 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 507 - 17 = 490. Add 490 to the number set. Current number set: [490, 34], target: 17, just two numbers left.\n     |- Try 490 + 34 = 524. Evaluate 524 != 17, drop this branch.\n     |- Try 490 - 34 = 456. Evaluate 456 != 17, drop this branch.\n     |- Try 490 * 34 = 16660. 16660 exceeds the maximum intermediate result, drop this branch.\n     |- Try 490 \/ 34 = 14.4. 14.4 is a decimal, drop this branch.\n    |- Try 507 * 17 = 8619. 8619 exceeds the maximum intermediate result, drop this branch.\n    |- Try 507 \/ 17 = 29.8. 29.8 is a decimal, drop this branch.\n   |- Pick two numbers (507, 34) (numbers left: [17]). Try possible operations.\n    |- Try 507 + 34 = 541. Add 541 to the number set. Current number set: [541, 17], target: 17, just two numbers left.\n     |- Try 541 + 17 = 558. Evaluate 558 != 17, drop this branch.\n     |- Try 541 - 17 = 524. Evaluate 524 != 17, drop this branch.\n     |- Try 541 * 17 = 9197. 9197 exceeds the maximum intermediate result, drop this branch.\n     |- Try 541 \/ 17 = 31.8. 31.8 is a decimal, drop this branch.\n    |- Try 507 - 34 = 473. Add 473 to the number set. Current number set: [473, 17], target: 17, just two numbers left.\n     |- Try 473 + 17 = 490. Evaluate 490 != 17, drop this branch.\n     |- Try 473 - 17 = 456. Evaluate 456 != 17, drop this branch.\n     |- Try 473 * 17 = 8041. 8041 exceeds the maximum intermediate result, drop this branch.\n     |- Try 473 \/ 17 = 27.8. 27.8 is a decimal, drop this branch.\n    |- Try 507 * 34 = 17238. 17238 exceeds the maximum intermediate result, drop this branch.\n    |- Try 507 \/ 34 = 14.9. 14.9 is a decimal, drop this branch.\n   |- Pick two numbers (17, 34) (numbers left: [507]). Try possible operations.\n    |- Try 34 + 17 = 51. Add 51 to the number set. Current number set: [51, 507], target: 17, just two numbers left.\n     |- Try 507 + 51 = 558. Evaluate 558 != 17, drop this branch.\n     |- Try 507 - 51 = 456. Evaluate 456 != 17, drop this branch.\n     |- Try 507 * 51 = 25857. 25857 exceeds the maximum intermediate result, drop this branch.\n     |- Try 507 \/ 51 = 9.9. 9.9 is a decimal, drop this branch.\n    |- Try 34 - 17 = 17. Add 17 to the number set. Current number set: [17, 507], target: 17, just two numbers left.\n     |- Try 507 + 17 = 524. Evaluate 524 != 17, drop this branch.\n     |- Try 507 - 17 = 490. Evaluate 490 != 17, drop this branch.\n     |- Try 507 * 17 = 8619. 8619 exceeds the maximum intermediate result, drop this branch.\n     |- Try 507 \/ 17 = 29.8. 29.8 is a decimal, drop this branch.\n    |- Try 34 * 17 = 578. Add 578 to the number set. Current number set: [578, 507], target: 17, just two numbers left.\n     |- Try 578 + 507 = 1085. Evaluate 1085 != 17, drop this branch.\n     |- Try 578 - 507 = 71. Evaluate 71 != 17, drop this branch.\n     |- Try 578 * 507 = 293046. 293046 exceeds the maximum intermediate result, drop this branch.\n     |- Try 578 \/ 507 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 34 \/ 17 = 2. Add 2 to the number set. Current number set: [2, 507], target: 17, just two numbers left.\n     |- Try 507 + 2 = 509. Evaluate 509 != 17, drop this branch.\n     |- Try 507 - 2 = 505. Evaluate 505 != 17, drop this branch.\n     |- Try 507 * 2 = 1014. Evaluate 1014 != 17, drop this branch.\n     |- Try 507 \/ 2 = 253.5. 253.5 is a decimal, drop this branch.\n  |- Try 39 \/ 13 = 3. Add 3 to the number set. Current number set: [3, 17, 34], target: 17. Options for choosing two numbers: [(3, 17), (3, 34), (17, 34)].\n   |- Pick two numbers (3, 17) (numbers left: [34]). Try possible operations.\n    |- Try 17 + 3 = 20. Add 20 to the number set. Current number set: [20, 34], target: 17, just two numbers left.\n     |- Try 34 + 20 = 54. Evaluate 54 != 17, drop this branch.\n     |- Try 34 - 20 = 14. Evaluate 14 != 17, drop this branch.\n     |- Try 34 * 20 = 680. Evaluate 680 != 17, drop this branch.\n     |- Try 34 \/ 20 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 17 - 3 = 14. Add 14 to the number set. Current number set: [14, 34], target: 17, just two numbers left.\n     |- Try 34 + 14 = 48. Evaluate 48 != 17, drop this branch.\n     |- Try 34 - 14 = 20. Evaluate 20 != 17, drop this branch.\n     |- Try 34 * 14 = 476. Evaluate 476 != 17, drop this branch.\n     |- Try 34 \/ 14 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 17 * 3 = 51. Add 51 to the number set. Current number set: [51, 34], target: 17, just two numbers left.\n     |- Try 51 + 34 = 85. Evaluate 85 != 17, drop this branch.\n     |- Try 51 - 34 = 17. Evaluate 17 == 17, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 51 - 34 = 17\nThe step before: 17 * 3 = 51\nThe first step: 39 \/ 13 = 3\n\nOutput the solution in the required format:\n<Solution>\n39 \/ 13 = 3\n17 * 3 = 51\n51 - 34 = 17\n<\/Solution>\n","item":{"nums":[39,13,17,34],"solution":["39 \/ 13 = 3","17 * 3 = 51","51 - 34 = 17"],"target":17}}
+{"instance_id":"countdown_8k_57","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [7, 12, 3, 19]\nTarget: 16","reference_output":"# Search Procedure\nInitial number set: [7, 12, 3, 19], target: 16. Options for choosing two numbers: [(7, 12), (7, 3), (7, 19), (12, 3), (12, 19), (3, 19)].\n |- Pick two numbers (7, 12) (numbers left: [3, 19]). Try possible operations.\n  |- Try 12 + 7 = 19. Add 19 to the number set. Current number set: [19, 3, 19], target: 16. Options for choosing two numbers: [(19, 3), (19, 19), (3, 19)].\n   |- Pick two numbers (19, 3) (numbers left: [19]). Try possible operations.\n    |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 19], target: 16, just two numbers left.\n     |- Try 22 + 19 = 41. Evaluate 41 != 16, drop this branch.\n     |- Try 22 - 19 = 3. Evaluate 3 != 16, drop this branch.\n     |- Try 22 * 19 = 418. Evaluate 418 != 16, drop this branch.\n     |- Try 22 \/ 19 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 19], target: 16, just two numbers left.\n     |- Try 19 + 16 = 35. Evaluate 35 != 16, drop this branch.\n     |- Try 19 - 16 = 3. Evaluate 3 != 16, drop this branch.\n     |- Try 19 * 16 = 304. Evaluate 304 != 16, drop this branch.\n     |- Try 19 \/ 16 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 19 * 3 = 57. Add 57 to the number set. Current number set: [57, 19], target: 16, just two numbers left.\n     |- Try 57 + 19 = 76. Evaluate 76 != 16, drop this branch.\n     |- Try 57 - 19 = 38. Evaluate 38 != 16, drop this branch.\n     |- Try 57 * 19 = 1083. Evaluate 1083 != 16, drop this branch.\n     |- Try 57 \/ 19 = 3. Evaluate 3 != 16, drop this branch.\n    |- Try 19 \/ 3 = 6.3. 6.3 is a decimal, drop this branch.\n   |- Pick two numbers (19, 19) (numbers left: [3]). Try possible operations.\n    |- Try 19 + 19 = 38. Add 38 to the number set. Current number set: [38, 3], target: 16, just two numbers left.\n     |- Try 38 + 3 = 41. Evaluate 41 != 16, drop this branch.\n     |- Try 38 - 3 = 35. Evaluate 35 != 16, drop this branch.\n     |- Try 38 * 3 = 114. Evaluate 114 != 16, drop this branch.\n     |- Try 38 \/ 3 = 12.7. 12.7 is a decimal, drop this branch.\n    |- Try 19 - 19 = 0. Add 0 to the number set. Current number set: [0, 3], target: 16, just two numbers left.\n     |- Try 3 + 0 = 3. Evaluate 3 != 16, drop this branch.\n     |- Try 3 - 0 = 3. Evaluate 3 != 16, drop this branch.\n     |- Try 3 * 0 = 0. Evaluate 0 != 16, drop this branch.\n     |- Try 3 \/ 0 (invalid operation). drop this branch.\n    |- Try 19 * 19 = 361. Add 361 to the number set. Current number set: [361, 3], target: 16, just two numbers left.\n     |- Try 361 + 3 = 364. Evaluate 364 != 16, drop this branch.\n     |- Try 361 - 3 = 358. Evaluate 358 != 16, drop this branch.\n     |- Try 361 * 3 = 1083. Evaluate 1083 != 16, drop this branch.\n     |- Try 361 \/ 3 = 120.3. 120.3 is a decimal, drop this branch.\n    |- Try 19 \/ 19 = 1. Add 1 to the number set. Current number set: [1, 3], target: 16, just two numbers left.\n     |- Try 3 + 1 = 4. Evaluate 4 != 16, drop this branch.\n     |- Try 3 - 1 = 2. Evaluate 2 != 16, drop this branch.\n     |- Try 3 * 1 = 3. Evaluate 3 != 16, drop this branch.\n     |- Try 3 \/ 1 = 3. Evaluate 3 != 16, drop this branch.\n   |- Pick two numbers (3, 19) (numbers left: [19]). Try possible operations.\n    |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 19], target: 16, just two numbers left.\n     |- Try 22 + 19 = 41. Evaluate 41 != 16, drop this branch.\n     |- Try 22 - 19 = 3. Evaluate 3 != 16, drop this branch.\n     |- Try 22 * 19 = 418. Evaluate 418 != 16, drop this branch.\n     |- Try 22 \/ 19 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 19], target: 16, just two numbers left.\n     |- Try 19 + 16 = 35. Evaluate 35 != 16, drop this branch.\n     |- Try 19 - 16 = 3. Evaluate 3 != 16, drop this branch.\n     |- Try 19 * 16 = 304. Evaluate 304 != 16, drop this branch.\n     |- Try 19 \/ 16 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 19 * 3 = 57. Add 57 to the number set. Current number set: [57, 19], target: 16, just two numbers left.\n     |- Try 57 + 19 = 76. Evaluate 76 != 16, drop this branch.\n     |- Try 57 - 19 = 38. Evaluate 38 != 16, drop this branch.\n     |- Try 57 * 19 = 1083. Evaluate 1083 != 16, drop this branch.\n     |- Try 57 \/ 19 = 3. Evaluate 3 != 16, drop this branch.\n    |- Try 19 \/ 3 = 6.3. 6.3 is a decimal, drop this branch.\n  |- Try 12 - 7 = 5. Add 5 to the number set. Current number set: [5, 3, 19], target: 16. Options for choosing two numbers: [(5, 3), (5, 19), (3, 19)].\n   |- Pick two numbers (5, 3) (numbers left: [19]). Try possible operations.\n    |- Try 5 + 3 = 8. Add 8 to the number set. Current number set: [8, 19], target: 16, just two numbers left.\n     |- Try 19 + 8 = 27. Evaluate 27 != 16, drop this branch.\n     |- Try 19 - 8 = 11. Evaluate 11 != 16, drop this branch.\n     |- Try 19 * 8 = 152. Evaluate 152 != 16, drop this branch.\n     |- Try 19 \/ 8 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 5 - 3 = 2. Add 2 to the number set. Current number set: [2, 19], target: 16, just two numbers left.\n     |- Try 19 + 2 = 21. Evaluate 21 != 16, drop this branch.\n     |- Try 19 - 2 = 17. Evaluate 17 != 16, drop this branch.\n     |- Try 19 * 2 = 38. Evaluate 38 != 16, drop this branch.\n     |- Try 19 \/ 2 = 9.5. 9.5 is a decimal, drop this branch.\n    |- Try 5 * 3 = 15. Add 15 to the number set. Current number set: [15, 19], target: 16, just two numbers left.\n     |- Try 19 + 15 = 34. Evaluate 34 != 16, drop this branch.\n     |- Try 19 - 15 = 4. Evaluate 4 != 16, drop this branch.\n     |- Try 19 * 15 = 285. Evaluate 285 != 16, drop this branch.\n     |- Try 19 \/ 15 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 5 \/ 3 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (5, 19) (numbers left: [3]). Try possible operations.\n    |- Try 19 + 5 = 24. Add 24 to the number set. Current number set: [24, 3], target: 16, just two numbers left.\n     |- Try 24 + 3 = 27. Evaluate 27 != 16, drop this branch.\n     |- Try 24 - 3 = 21. Evaluate 21 != 16, drop this branch.\n     |- Try 24 * 3 = 72. Evaluate 72 != 16, drop this branch.\n     |- Try 24 \/ 3 = 8. Evaluate 8 != 16, drop this branch.\n    |- Try 19 - 5 = 14. Add 14 to the number set. Current number set: [14, 3], target: 16, just two numbers left.\n     |- Try 14 + 3 = 17. Evaluate 17 != 16, drop this branch.\n     |- Try 14 - 3 = 11. Evaluate 11 != 16, drop this branch.\n     |- Try 14 * 3 = 42. Evaluate 42 != 16, drop this branch.\n     |- Try 14 \/ 3 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 19 * 5 = 95. Add 95 to the number set. Current number set: [95, 3], target: 16, just two numbers left.\n     |- Try 95 + 3 = 98. Evaluate 98 != 16, drop this branch.\n     |- Try 95 - 3 = 92. Evaluate 92 != 16, drop this branch.\n     |- Try 95 * 3 = 285. Evaluate 285 != 16, drop this branch.\n     |- Try 95 \/ 3 = 31.7. 31.7 is a decimal, drop this branch.\n    |- Try 19 \/ 5 = 3.8. 3.8 is a decimal, drop this branch.\n   |- Pick two numbers (3, 19) (numbers left: [5]). Try possible operations.\n    |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 5], target: 16, just two numbers left.\n     |- Try 22 + 5 = 27. Evaluate 27 != 16, drop this branch.\n     |- Try 22 - 5 = 17. Evaluate 17 != 16, drop this branch.\n     |- Try 22 * 5 = 110. Evaluate 110 != 16, drop this branch.\n     |- Try 22 \/ 5 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 5], target: 16, just two numbers left.\n     |- Try 16 + 5 = 21. Evaluate 21 != 16, drop this branch.\n     |- Try 16 - 5 = 11. Evaluate 11 != 16, drop this branch.\n     |- Try 16 * 5 = 80. Evaluate 80 != 16, drop this branch.\n     |- Try 16 \/ 5 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 19 * 3 = 57. Add 57 to the number set. Current number set: [57, 5], target: 16, just two numbers left.\n     |- Try 57 + 5 = 62. Evaluate 62 != 16, drop this branch.\n     |- Try 57 - 5 = 52. Evaluate 52 != 16, drop this branch.\n     |- Try 57 * 5 = 285. Evaluate 285 != 16, drop this branch.\n     |- Try 57 \/ 5 = 11.4. 11.4 is a decimal, drop this branch.\n    |- Try 19 \/ 3 = 6.3. 6.3 is a decimal, drop this branch.\n  |- Try 12 * 7 = 84. Add 84 to the number set. Current number set: [84, 3, 19], target: 16. Options for choosing two numbers: [(84, 3), (84, 19), (3, 19)].\n   |- Pick two numbers (84, 3) (numbers left: [19]). Try possible operations.\n    |- Try 84 + 3 = 87. Add 87 to the number set. Current number set: [87, 19], target: 16, just two numbers left.\n     |- Try 87 + 19 = 106. Evaluate 106 != 16, drop this branch.\n     |- Try 87 - 19 = 68. Evaluate 68 != 16, drop this branch.\n     |- Try 87 * 19 = 1653. Evaluate 1653 != 16, drop this branch.\n     |- Try 87 \/ 19 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 84 - 3 = 81. Add 81 to the number set. Current number set: [81, 19], target: 16, just two numbers left.\n     |- Try 81 + 19 = 100. Evaluate 100 != 16, drop this branch.\n     |- Try 81 - 19 = 62. Evaluate 62 != 16, drop this branch.\n     |- Try 81 * 19 = 1539. Evaluate 1539 != 16, drop this branch.\n     |- Try 81 \/ 19 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 84 * 3 = 252. Add 252 to the number set. Current number set: [252, 19], target: 16, just two numbers left.\n     |- Try 252 + 19 = 271. Evaluate 271 != 16, drop this branch.\n     |- Try 252 - 19 = 233. Evaluate 233 != 16, drop this branch.\n     |- Try 252 * 19 = 4788. 4788 exceeds the maximum intermediate result, drop this branch.\n     |- Try 252 \/ 19 = 13.3. 13.3 is a decimal, drop this branch.\n    |- Try 84 \/ 3 = 28. Add 28 to the number set. Current number set: [28, 19], target: 16, just two numbers left.\n     |- Try 28 + 19 = 47. Evaluate 47 != 16, drop this branch.\n     |- Try 28 - 19 = 9. Evaluate 9 != 16, drop this branch.\n     |- Try 28 * 19 = 532. Evaluate 532 != 16, drop this branch.\n     |- Try 28 \/ 19 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (84, 19) (numbers left: [3]). Try possible operations.\n    |- Try 84 + 19 = 103. Add 103 to the number set. Current number set: [103, 3], target: 16, just two numbers left.\n     |- Try 103 + 3 = 106. Evaluate 106 != 16, drop this branch.\n     |- Try 103 - 3 = 100. Evaluate 100 != 16, drop this branch.\n     |- Try 103 * 3 = 309. Evaluate 309 != 16, drop this branch.\n     |- Try 103 \/ 3 = 34.3. 34.3 is a decimal, drop this branch.\n    |- Try 84 - 19 = 65. Add 65 to the number set. Current number set: [65, 3], target: 16, just two numbers left.\n     |- Try 65 + 3 = 68. Evaluate 68 != 16, drop this branch.\n     |- Try 65 - 3 = 62. Evaluate 62 != 16, drop this branch.\n     |- Try 65 * 3 = 195. Evaluate 195 != 16, drop this branch.\n     |- Try 65 \/ 3 = 21.7. 21.7 is a decimal, drop this branch.\n    |- Try 84 * 19 = 1596. Add 1596 to the number set. Current number set: [1596, 3], target: 16, just two numbers left.\n     |- Try 1596 + 3 = 1599. Evaluate 1599 != 16, drop this branch.\n     |- Try 1596 - 3 = 1593. Evaluate 1593 != 16, drop this branch.\n     |- Try 1596 * 3 = 4788. 4788 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1596 \/ 3 = 532. Evaluate 532 != 16, drop this branch.\n    |- Try 84 \/ 19 = 4.4. 4.4 is a decimal, drop this branch.\n   |- Pick two numbers (3, 19) (numbers left: [84]). Try possible operations.\n    |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 84], target: 16, just two numbers left.\n     |- Try 84 + 22 = 106. Evaluate 106 != 16, drop this branch.\n     |- Try 84 - 22 = 62. Evaluate 62 != 16, drop this branch.\n     |- Try 84 * 22 = 1848. Evaluate 1848 != 16, drop this branch.\n     |- Try 84 \/ 22 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 84], target: 16, just two numbers left.\n     |- Try 84 + 16 = 100. Evaluate 100 != 16, drop this branch.\n     |- Try 84 - 16 = 68. Evaluate 68 != 16, drop this branch.\n     |- Try 84 * 16 = 1344. Evaluate 1344 != 16, drop this branch.\n     |- Try 84 \/ 16 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 19 * 3 = 57. Add 57 to the number set. Current number set: [57, 84], target: 16, just two numbers left.\n     |- Try 84 + 57 = 141. Evaluate 141 != 16, drop this branch.\n     |- Try 84 - 57 = 27. Evaluate 27 != 16, drop this branch.\n     |- Try 84 * 57 = 4788. 4788 exceeds the maximum intermediate result, drop this branch.\n     |- Try 84 \/ 57 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 19 \/ 3 = 6.3. 6.3 is a decimal, drop this branch.\n  |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n |- Pick two numbers (7, 3) (numbers left: [12, 19]). Try possible operations.\n  |- Try 7 + 3 = 10. Add 10 to the number set. Current number set: [10, 12, 19], target: 16. Options for choosing two numbers: [(10, 12), (10, 19), (12, 19)].\n   |- Pick two numbers (10, 12) (numbers left: [19]). Try possible operations.\n    |- Try 12 + 10 = 22. Add 22 to the number set. Current number set: [22, 19], target: 16, just two numbers left.\n     |- Try 22 + 19 = 41. Evaluate 41 != 16, drop this branch.\n     |- Try 22 - 19 = 3. Evaluate 3 != 16, drop this branch.\n     |- Try 22 * 19 = 418. Evaluate 418 != 16, drop this branch.\n     |- Try 22 \/ 19 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 12 - 10 = 2. Add 2 to the number set. Current number set: [2, 19], target: 16, just two numbers left.\n     |- Try 19 + 2 = 21. Evaluate 21 != 16, drop this branch.\n     |- Try 19 - 2 = 17. Evaluate 17 != 16, drop this branch.\n     |- Try 19 * 2 = 38. Evaluate 38 != 16, drop this branch.\n     |- Try 19 \/ 2 = 9.5. 9.5 is a decimal, drop this branch.\n    |- Try 12 * 10 = 120. Add 120 to the number set. Current number set: [120, 19], target: 16, just two numbers left.\n     |- Try 120 + 19 = 139. Evaluate 139 != 16, drop this branch.\n     |- Try 120 - 19 = 101. Evaluate 101 != 16, drop this branch.\n     |- Try 120 * 19 = 2280. 2280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 120 \/ 19 = 6.3. 6.3 is a decimal, drop this branch.\n    |- Try 12 \/ 10 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (10, 19) (numbers left: [12]). Try possible operations.\n    |- Try 19 + 10 = 29. Add 29 to the number set. Current number set: [29, 12], target: 16, just two numbers left.\n     |- Try 29 + 12 = 41. Evaluate 41 != 16, drop this branch.\n     |- Try 29 - 12 = 17. Evaluate 17 != 16, drop this branch.\n     |- Try 29 * 12 = 348. Evaluate 348 != 16, drop this branch.\n     |- Try 29 \/ 12 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 19 - 10 = 9. Add 9 to the number set. Current number set: [9, 12], target: 16, just two numbers left.\n     |- Try 12 + 9 = 21. Evaluate 21 != 16, drop this branch.\n     |- Try 12 - 9 = 3. Evaluate 3 != 16, drop this branch.\n     |- Try 12 * 9 = 108. Evaluate 108 != 16, drop this branch.\n     |- Try 12 \/ 9 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 19 * 10 = 190. Add 190 to the number set. Current number set: [190, 12], target: 16, just two numbers left.\n     |- Try 190 + 12 = 202. Evaluate 202 != 16, drop this branch.\n     |- Try 190 - 12 = 178. Evaluate 178 != 16, drop this branch.\n     |- Try 190 * 12 = 2280. 2280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 190 \/ 12 = 15.8. 15.8 is a decimal, drop this branch.\n    |- Try 19 \/ 10 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (12, 19) (numbers left: [10]). Try possible operations.\n    |- Try 19 + 12 = 31. Add 31 to the number set. Current number set: [31, 10], target: 16, just two numbers left.\n     |- Try 31 + 10 = 41. Evaluate 41 != 16, drop this branch.\n     |- Try 31 - 10 = 21. Evaluate 21 != 16, drop this branch.\n     |- Try 31 * 10 = 310. Evaluate 310 != 16, drop this branch.\n     |- Try 31 \/ 10 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 19 - 12 = 7. Add 7 to the number set. Current number set: [7, 10], target: 16, just two numbers left.\n     |- Try 10 + 7 = 17. Evaluate 17 != 16, drop this branch.\n     |- Try 10 - 7 = 3. Evaluate 3 != 16, drop this branch.\n     |- Try 10 * 7 = 70. Evaluate 70 != 16, drop this branch.\n     |- Try 10 \/ 7 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 19 * 12 = 228. Add 228 to the number set. Current number set: [228, 10], target: 16, just two numbers left.\n     |- Try 228 + 10 = 238. Evaluate 238 != 16, drop this branch.\n     |- Try 228 - 10 = 218. Evaluate 218 != 16, drop this branch.\n     |- Try 228 * 10 = 2280. 2280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 228 \/ 10 = 22.8. 22.8 is a decimal, drop this branch.\n    |- Try 19 \/ 12 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 7 - 3 = 4. Add 4 to the number set. Current number set: [4, 12, 19], target: 16. Options for choosing two numbers: [(4, 12), (4, 19), (12, 19)].\n   |- Pick two numbers (4, 12) (numbers left: [19]). Try possible operations.\n    |- Try 12 + 4 = 16. Add 16 to the number set. Current number set: [16, 19], target: 16, just two numbers left.\n     |- Try 19 + 16 = 35. Evaluate 35 != 16, drop this branch.\n     |- Try 19 - 16 = 3. Evaluate 3 != 16, drop this branch.\n     |- Try 19 * 16 = 304. Evaluate 304 != 16, drop this branch.\n     |- Try 19 \/ 16 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 12 - 4 = 8. Add 8 to the number set. Current number set: [8, 19], target: 16, just two numbers left.\n     |- Try 19 + 8 = 27. Evaluate 27 != 16, drop this branch.\n     |- Try 19 - 8 = 11. Evaluate 11 != 16, drop this branch.\n     |- Try 19 * 8 = 152. Evaluate 152 != 16, drop this branch.\n     |- Try 19 \/ 8 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 12 * 4 = 48. Add 48 to the number set. Current number set: [48, 19], target: 16, just two numbers left.\n     |- Try 48 + 19 = 67. Evaluate 67 != 16, drop this branch.\n     |- Try 48 - 19 = 29. Evaluate 29 != 16, drop this branch.\n     |- Try 48 * 19 = 912. Evaluate 912 != 16, drop this branch.\n     |- Try 48 \/ 19 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 12 \/ 4 = 3. Add 3 to the number set. Current number set: [3, 19], target: 16, just two numbers left.\n     |- Try 19 + 3 = 22. Evaluate 22 != 16, drop this branch.\n     |- Try 19 - 3 = 16. Evaluate 16 == 16, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 19 - 3 = 16\nThe step before: 12 \/ 4 = 3\nThe first step: 7 - 3 = 4\n\nOutput the solution in the required format:\n<Solution>\n7 - 3 = 4\n12 \/ 4 = 3\n19 - 3 = 16\n<\/Solution>\n","item":{"nums":[7,12,3,19],"solution":["7 - 3 = 4","12 \/ 4 = 3","19 - 3 = 16"],"target":16}}
+{"instance_id":"countdown_8k_58","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [24, 22, 12, 8]\nTarget: 33","reference_output":"# Search Procedure\nInitial number set: [24, 22, 12, 8], target: 33. Options for choosing two numbers: [(24, 22), (24, 12), (24, 8), (22, 12), (22, 8), (12, 8)].\n |- Pick two numbers (24, 22) (numbers left: [12, 8]). Try possible operations.\n  |- Try 24 + 22 = 46. Add 46 to the number set. Current number set: [46, 12, 8], target: 33. Options for choosing two numbers: [(46, 12), (46, 8), (12, 8)].\n   |- Pick two numbers (46, 12) (numbers left: [8]). Try possible operations.\n    |- Try 46 + 12 = 58. Add 58 to the number set. Current number set: [58, 8], target: 33, just two numbers left.\n     |- Try 58 + 8 = 66. Evaluate 66 != 33, drop this branch.\n     |- Try 58 - 8 = 50. Evaluate 50 != 33, drop this branch.\n     |- Try 58 * 8 = 464. Evaluate 464 != 33, drop this branch.\n     |- Try 58 \/ 8 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 46 - 12 = 34. Add 34 to the number set. Current number set: [34, 8], target: 33, just two numbers left.\n     |- Try 34 + 8 = 42. Evaluate 42 != 33, drop this branch.\n     |- Try 34 - 8 = 26. Evaluate 26 != 33, drop this branch.\n     |- Try 34 * 8 = 272. Evaluate 272 != 33, drop this branch.\n     |- Try 34 \/ 8 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 46 * 12 = 552. Add 552 to the number set. Current number set: [552, 8], target: 33, just two numbers left.\n     |- Try 552 + 8 = 560. Evaluate 560 != 33, drop this branch.\n     |- Try 552 - 8 = 544. Evaluate 544 != 33, drop this branch.\n     |- Try 552 * 8 = 4416. 4416 exceeds the maximum intermediate result, drop this branch.\n     |- Try 552 \/ 8 = 69. Evaluate 69 != 33, drop this branch.\n    |- Try 46 \/ 12 = 3.8. 3.8 is a decimal, drop this branch.\n   |- Pick two numbers (46, 8) (numbers left: [12]). Try possible operations.\n    |- Try 46 + 8 = 54. Add 54 to the number set. Current number set: [54, 12], target: 33, just two numbers left.\n     |- Try 54 + 12 = 66. Evaluate 66 != 33, drop this branch.\n     |- Try 54 - 12 = 42. Evaluate 42 != 33, drop this branch.\n     |- Try 54 * 12 = 648. Evaluate 648 != 33, drop this branch.\n     |- Try 54 \/ 12 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 46 - 8 = 38. Add 38 to the number set. Current number set: [38, 12], target: 33, just two numbers left.\n     |- Try 38 + 12 = 50. Evaluate 50 != 33, drop this branch.\n     |- Try 38 - 12 = 26. Evaluate 26 != 33, drop this branch.\n     |- Try 38 * 12 = 456. Evaluate 456 != 33, drop this branch.\n     |- Try 38 \/ 12 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 46 * 8 = 368. Add 368 to the number set. Current number set: [368, 12], target: 33, just two numbers left.\n     |- Try 368 + 12 = 380. Evaluate 380 != 33, drop this branch.\n     |- Try 368 - 12 = 356. Evaluate 356 != 33, drop this branch.\n     |- Try 368 * 12 = 4416. 4416 exceeds the maximum intermediate result, drop this branch.\n     |- Try 368 \/ 12 = 30.7. 30.7 is a decimal, drop this branch.\n    |- Try 46 \/ 8 = 5.8. 5.8 is a decimal, drop this branch.\n   |- Pick two numbers (12, 8) (numbers left: [46]). Try possible operations.\n    |- Try 12 + 8 = 20. Add 20 to the number set. Current number set: [20, 46], target: 33, just two numbers left.\n     |- Try 46 + 20 = 66. Evaluate 66 != 33, drop this branch.\n     |- Try 46 - 20 = 26. Evaluate 26 != 33, drop this branch.\n     |- Try 46 * 20 = 920. Evaluate 920 != 33, drop this branch.\n     |- Try 46 \/ 20 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 12 - 8 = 4. Add 4 to the number set. Current number set: [4, 46], target: 33, just two numbers left.\n     |- Try 46 + 4 = 50. Evaluate 50 != 33, drop this branch.\n     |- Try 46 - 4 = 42. Evaluate 42 != 33, drop this branch.\n     |- Try 46 * 4 = 184. Evaluate 184 != 33, drop this branch.\n     |- Try 46 \/ 4 = 11.5. 11.5 is a decimal, drop this branch.\n    |- Try 12 * 8 = 96. Add 96 to the number set. Current number set: [96, 46], target: 33, just two numbers left.\n     |- Try 96 + 46 = 142. Evaluate 142 != 33, drop this branch.\n     |- Try 96 - 46 = 50. Evaluate 50 != 33, drop this branch.\n     |- Try 96 * 46 = 4416. 4416 exceeds the maximum intermediate result, drop this branch.\n     |- Try 96 \/ 46 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 12 \/ 8 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 24 - 22 = 2. Add 2 to the number set. Current number set: [2, 12, 8], target: 33. Options for choosing two numbers: [(2, 12), (2, 8), (12, 8)].\n   |- Pick two numbers (2, 12) (numbers left: [8]). Try possible operations.\n    |- Try 12 + 2 = 14. Add 14 to the number set. Current number set: [14, 8], target: 33, just two numbers left.\n     |- Try 14 + 8 = 22. Evaluate 22 != 33, drop this branch.\n     |- Try 14 - 8 = 6. Evaluate 6 != 33, drop this branch.\n     |- Try 14 * 8 = 112. Evaluate 112 != 33, drop this branch.\n     |- Try 14 \/ 8 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 12 - 2 = 10. Add 10 to the number set. Current number set: [10, 8], target: 33, just two numbers left.\n     |- Try 10 + 8 = 18. Evaluate 18 != 33, drop this branch.\n     |- Try 10 - 8 = 2. Evaluate 2 != 33, drop this branch.\n     |- Try 10 * 8 = 80. Evaluate 80 != 33, drop this branch.\n     |- Try 10 \/ 8 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 12 * 2 = 24. Add 24 to the number set. Current number set: [24, 8], target: 33, just two numbers left.\n     |- Try 24 + 8 = 32. Evaluate 32 != 33, drop this branch.\n     |- Try 24 - 8 = 16. Evaluate 16 != 33, drop this branch.\n     |- Try 24 * 8 = 192. Evaluate 192 != 33, drop this branch.\n     |- Try 24 \/ 8 = 3. Evaluate 3 != 33, drop this branch.\n    |- Try 12 \/ 2 = 6. Add 6 to the number set. Current number set: [6, 8], target: 33, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 33, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 33, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 33, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (2, 8) (numbers left: [12]). Try possible operations.\n    |- Try 8 + 2 = 10. Add 10 to the number set. Current number set: [10, 12], target: 33, just two numbers left.\n     |- Try 12 + 10 = 22. Evaluate 22 != 33, drop this branch.\n     |- Try 12 - 10 = 2. Evaluate 2 != 33, drop this branch.\n     |- Try 12 * 10 = 120. Evaluate 120 != 33, drop this branch.\n     |- Try 12 \/ 10 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 8 - 2 = 6. Add 6 to the number set. Current number set: [6, 12], target: 33, just two numbers left.\n     |- Try 12 + 6 = 18. Evaluate 18 != 33, drop this branch.\n     |- Try 12 - 6 = 6. Evaluate 6 != 33, drop this branch.\n     |- Try 12 * 6 = 72. Evaluate 72 != 33, drop this branch.\n     |- Try 12 \/ 6 = 2. Evaluate 2 != 33, drop this branch.\n    |- Try 8 * 2 = 16. Add 16 to the number set. Current number set: [16, 12], target: 33, just two numbers left.\n     |- Try 16 + 12 = 28. Evaluate 28 != 33, drop this branch.\n     |- Try 16 - 12 = 4. Evaluate 4 != 33, drop this branch.\n     |- Try 16 * 12 = 192. Evaluate 192 != 33, drop this branch.\n     |- Try 16 \/ 12 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 8 \/ 2 = 4. Add 4 to the number set. Current number set: [4, 12], target: 33, just two numbers left.\n     |- Try 12 + 4 = 16. Evaluate 16 != 33, drop this branch.\n     |- Try 12 - 4 = 8. Evaluate 8 != 33, drop this branch.\n     |- Try 12 * 4 = 48. Evaluate 48 != 33, drop this branch.\n     |- Try 12 \/ 4 = 3. Evaluate 3 != 33, drop this branch.\n   |- Pick two numbers (12, 8) (numbers left: [2]). Try possible operations.\n    |- Try 12 + 8 = 20. Add 20 to the number set. Current number set: [20, 2], target: 33, just two numbers left.\n     |- Try 20 + 2 = 22. Evaluate 22 != 33, drop this branch.\n     |- Try 20 - 2 = 18. Evaluate 18 != 33, drop this branch.\n     |- Try 20 * 2 = 40. Evaluate 40 != 33, drop this branch.\n     |- Try 20 \/ 2 = 10. Evaluate 10 != 33, drop this branch.\n    |- Try 12 - 8 = 4. Add 4 to the number set. Current number set: [4, 2], target: 33, just two numbers left.\n     |- Try 4 + 2 = 6. Evaluate 6 != 33, drop this branch.\n     |- Try 4 - 2 = 2. Evaluate 2 != 33, drop this branch.\n     |- Try 4 * 2 = 8. Evaluate 8 != 33, drop this branch.\n     |- Try 4 \/ 2 = 2. Evaluate 2 != 33, drop this branch.\n    |- Try 12 * 8 = 96. Add 96 to the number set. Current number set: [96, 2], target: 33, just two numbers left.\n     |- Try 96 + 2 = 98. Evaluate 98 != 33, drop this branch.\n     |- Try 96 - 2 = 94. Evaluate 94 != 33, drop this branch.\n     |- Try 96 * 2 = 192. Evaluate 192 != 33, drop this branch.\n     |- Try 96 \/ 2 = 48. Evaluate 48 != 33, drop this branch.\n    |- Try 12 \/ 8 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 24 * 22 = 528. Add 528 to the number set. Current number set: [528, 12, 8], target: 33. Options for choosing two numbers: [(528, 12), (528, 8), (12, 8)].\n   |- Pick two numbers (528, 12) (numbers left: [8]). Try possible operations.\n    |- Try 528 + 12 = 540. Add 540 to the number set. Current number set: [540, 8], target: 33, just two numbers left.\n     |- Try 540 + 8 = 548. Evaluate 548 != 33, drop this branch.\n     |- Try 540 - 8 = 532. Evaluate 532 != 33, drop this branch.\n     |- Try 540 * 8 = 4320. 4320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 540 \/ 8 = 67.5. 67.5 is a decimal, drop this branch.\n    |- Try 528 - 12 = 516. Add 516 to the number set. Current number set: [516, 8], target: 33, just two numbers left.\n     |- Try 516 + 8 = 524. Evaluate 524 != 33, drop this branch.\n     |- Try 516 - 8 = 508. Evaluate 508 != 33, drop this branch.\n     |- Try 516 * 8 = 4128. 4128 exceeds the maximum intermediate result, drop this branch.\n     |- Try 516 \/ 8 = 64.5. 64.5 is a decimal, drop this branch.\n    |- Try 528 * 12 = 6336. 6336 exceeds the maximum intermediate result, drop this branch.\n    |- Try 528 \/ 12 = 44. Add 44 to the number set. Current number set: [44, 8], target: 33, just two numbers left.\n     |- Try 44 + 8 = 52. Evaluate 52 != 33, drop this branch.\n     |- Try 44 - 8 = 36. Evaluate 36 != 33, drop this branch.\n     |- Try 44 * 8 = 352. Evaluate 352 != 33, drop this branch.\n     |- Try 44 \/ 8 = 5.5. 5.5 is a decimal, drop this branch.\n   |- Pick two numbers (528, 8) (numbers left: [12]). Try possible operations.\n    |- Try 528 + 8 = 536. Add 536 to the number set. Current number set: [536, 12], target: 33, just two numbers left.\n     |- Try 536 + 12 = 548. Evaluate 548 != 33, drop this branch.\n     |- Try 536 - 12 = 524. Evaluate 524 != 33, drop this branch.\n     |- Try 536 * 12 = 6432. 6432 exceeds the maximum intermediate result, drop this branch.\n     |- Try 536 \/ 12 = 44.7. 44.7 is a decimal, drop this branch.\n    |- Try 528 - 8 = 520. Add 520 to the number set. Current number set: [520, 12], target: 33, just two numbers left.\n     |- Try 520 + 12 = 532. Evaluate 532 != 33, drop this branch.\n     |- Try 520 - 12 = 508. Evaluate 508 != 33, drop this branch.\n     |- Try 520 * 12 = 6240. 6240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 520 \/ 12 = 43.3. 43.3 is a decimal, drop this branch.\n    |- Try 528 * 8 = 4224. 4224 exceeds the maximum intermediate result, drop this branch.\n    |- Try 528 \/ 8 = 66. Add 66 to the number set. Current number set: [66, 12], target: 33, just two numbers left.\n     |- Try 66 + 12 = 78. Evaluate 78 != 33, drop this branch.\n     |- Try 66 - 12 = 54. Evaluate 54 != 33, drop this branch.\n     |- Try 66 * 12 = 792. Evaluate 792 != 33, drop this branch.\n     |- Try 66 \/ 12 = 5.5. 5.5 is a decimal, drop this branch.\n   |- Pick two numbers (12, 8) (numbers left: [528]). Try possible operations.\n    |- Try 12 + 8 = 20. Add 20 to the number set. Current number set: [20, 528], target: 33, just two numbers left.\n     |- Try 528 + 20 = 548. Evaluate 548 != 33, drop this branch.\n     |- Try 528 - 20 = 508. Evaluate 508 != 33, drop this branch.\n     |- Try 528 * 20 = 10560. 10560 exceeds the maximum intermediate result, drop this branch.\n     |- Try 528 \/ 20 = 26.4. 26.4 is a decimal, drop this branch.\n    |- Try 12 - 8 = 4. Add 4 to the number set. Current number set: [4, 528], target: 33, just two numbers left.\n     |- Try 528 + 4 = 532. Evaluate 532 != 33, drop this branch.\n     |- Try 528 - 4 = 524. Evaluate 524 != 33, drop this branch.\n     |- Try 528 * 4 = 2112. 2112 exceeds the maximum intermediate result, drop this branch.\n     |- Try 528 \/ 4 = 132. Evaluate 132 != 33, drop this branch.\n    |- Try 12 * 8 = 96. Add 96 to the number set. Current number set: [96, 528], target: 33, just two numbers left.\n     |- Try 528 + 96 = 624. Evaluate 624 != 33, drop this branch.\n     |- Try 528 - 96 = 432. Evaluate 432 != 33, drop this branch.\n     |- Try 528 * 96 = 50688. 50688 exceeds the maximum intermediate result, drop this branch.\n     |- Try 528 \/ 96 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 12 \/ 8 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 24 \/ 22 = 1.1. 1.1 is a decimal, drop this branch.\n |- Pick two numbers (24, 12) (numbers left: [22, 8]). Try possible operations.\n  |- Try 24 + 12 = 36. Add 36 to the number set. Current number set: [36, 22, 8], target: 33. Options for choosing two numbers: [(36, 22), (36, 8), (22, 8)].\n   |- Pick two numbers (36, 22) (numbers left: [8]). Try possible operations.\n    |- Try 36 + 22 = 58. Add 58 to the number set. Current number set: [58, 8], target: 33, just two numbers left.\n     |- Try 58 + 8 = 66. Evaluate 66 != 33, drop this branch.\n     |- Try 58 - 8 = 50. Evaluate 50 != 33, drop this branch.\n     |- Try 58 * 8 = 464. Evaluate 464 != 33, drop this branch.\n     |- Try 58 \/ 8 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 36 - 22 = 14. Add 14 to the number set. Current number set: [14, 8], target: 33, just two numbers left.\n     |- Try 14 + 8 = 22. Evaluate 22 != 33, drop this branch.\n     |- Try 14 - 8 = 6. Evaluate 6 != 33, drop this branch.\n     |- Try 14 * 8 = 112. Evaluate 112 != 33, drop this branch.\n     |- Try 14 \/ 8 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 36 * 22 = 792. Add 792 to the number set. Current number set: [792, 8], target: 33, just two numbers left.\n     |- Try 792 + 8 = 800. Evaluate 800 != 33, drop this branch.\n     |- Try 792 - 8 = 784. Evaluate 784 != 33, drop this branch.\n     |- Try 792 * 8 = 6336. 6336 exceeds the maximum intermediate result, drop this branch.\n     |- Try 792 \/ 8 = 99. Evaluate 99 != 33, drop this branch.\n    |- Try 36 \/ 22 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (36, 8) (numbers left: [22]). Try possible operations.\n    |- Try 36 + 8 = 44. Add 44 to the number set. Current number set: [44, 22], target: 33, just two numbers left.\n     |- Try 44 + 22 = 66. Evaluate 66 != 33, drop this branch.\n     |- Try 44 - 22 = 22. Evaluate 22 != 33, drop this branch.\n     |- Try 44 * 22 = 968. Evaluate 968 != 33, drop this branch.\n     |- Try 44 \/ 22 = 2. Evaluate 2 != 33, drop this branch.\n    |- Try 36 - 8 = 28. Add 28 to the number set. Current number set: [28, 22], target: 33, just two numbers left.\n     |- Try 28 + 22 = 50. Evaluate 50 != 33, drop this branch.\n     |- Try 28 - 22 = 6. Evaluate 6 != 33, drop this branch.\n     |- Try 28 * 22 = 616. Evaluate 616 != 33, drop this branch.\n     |- Try 28 \/ 22 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 36 * 8 = 288. Add 288 to the number set. Current number set: [288, 22], target: 33, just two numbers left.\n     |- Try 288 + 22 = 310. Evaluate 310 != 33, drop this branch.\n     |- Try 288 - 22 = 266. Evaluate 266 != 33, drop this branch.\n     |- Try 288 * 22 = 6336. 6336 exceeds the maximum intermediate result, drop this branch.\n     |- Try 288 \/ 22 = 13.1. 13.1 is a decimal, drop this branch.\n    |- Try 36 \/ 8 = 4.5. 4.5 is a decimal, drop this branch.\n   |- Pick two numbers (22, 8) (numbers left: [36]). Try possible operations.\n    |- Try 22 + 8 = 30. Add 30 to the number set. Current number set: [30, 36], target: 33, just two numbers left.\n     |- Try 36 + 30 = 66. Evaluate 66 != 33, drop this branch.\n     |- Try 36 - 30 = 6. Evaluate 6 != 33, drop this branch.\n     |- Try 36 * 30 = 1080. Evaluate 1080 != 33, drop this branch.\n     |- Try 36 \/ 30 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 22 - 8 = 14. Add 14 to the number set. Current number set: [14, 36], target: 33, just two numbers left.\n     |- Try 36 + 14 = 50. Evaluate 50 != 33, drop this branch.\n     |- Try 36 - 14 = 22. Evaluate 22 != 33, drop this branch.\n     |- Try 36 * 14 = 504. Evaluate 504 != 33, drop this branch.\n     |- Try 36 \/ 14 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 22 * 8 = 176. Add 176 to the number set. Current number set: [176, 36], target: 33, just two numbers left.\n     |- Try 176 + 36 = 212. Evaluate 212 != 33, drop this branch.\n     |- Try 176 - 36 = 140. Evaluate 140 != 33, drop this branch.\n     |- Try 176 * 36 = 6336. 6336 exceeds the maximum intermediate result, drop this branch.\n     |- Try 176 \/ 36 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 22 \/ 8 = 2.8. 2.8 is a decimal, drop this branch.\n  |- Try 24 - 12 = 12. Add 12 to the number set. Current number set: [12, 22, 8], target: 33. Options for choosing two numbers: [(12, 22), (12, 8), (22, 8)].\n   |- Pick two numbers (12, 22) (numbers left: [8]). Try possible operations.\n    |- Try 22 + 12 = 34. Add 34 to the number set. Current number set: [34, 8], target: 33, just two numbers left.\n     |- Try 34 + 8 = 42. Evaluate 42 != 33, drop this branch.\n     |- Try 34 - 8 = 26. Evaluate 26 != 33, drop this branch.\n     |- Try 34 * 8 = 272. Evaluate 272 != 33, drop this branch.\n     |- Try 34 \/ 8 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 22 - 12 = 10. Add 10 to the number set. Current number set: [10, 8], target: 33, just two numbers left.\n     |- Try 10 + 8 = 18. Evaluate 18 != 33, drop this branch.\n     |- Try 10 - 8 = 2. Evaluate 2 != 33, drop this branch.\n     |- Try 10 * 8 = 80. Evaluate 80 != 33, drop this branch.\n     |- Try 10 \/ 8 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 22 * 12 = 264. Add 264 to the number set. Current number set: [264, 8], target: 33, just two numbers left.\n     |- Try 264 + 8 = 272. Evaluate 272 != 33, drop this branch.\n     |- Try 264 - 8 = 256. Evaluate 256 != 33, drop this branch.\n     |- Try 264 * 8 = 2112. 2112 exceeds the maximum intermediate result, drop this branch.\n     |- Try 264 \/ 8 = 33. Evaluate 33 == 33, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 264 \/ 8 = 33\nThe step before: 22 * 12 = 264\nThe first step: 24 - 12 = 12\n\nOutput the solution in the required format:\n<Solution>\n24 - 12 = 12\n22 * 12 = 264\n264 \/ 8 = 33\n<\/Solution>\n","item":{"nums":[24,22,12,8],"solution":["24 - 12 = 12","22 * 12 = 264","264 \/ 8 = 33"],"target":33}}
+{"instance_id":"countdown_8k_59","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [12, 12, 48, 33]\nTarget: 14","reference_output":"# Search Procedure\nInitial number set: [12, 12, 48, 33], target: 14. Options for choosing two numbers: [(12, 12), (12, 48), (12, 33), (12, 48), (12, 33), (48, 33)].\n |- Pick two numbers (12, 12) (numbers left: [48, 33]). Try possible operations.\n  |- Try 12 + 12 = 24. Add 24 to the number set. Current number set: [24, 48, 33], target: 14. Options for choosing two numbers: [(24, 48), (24, 33), (48, 33)].\n   |- Pick two numbers (24, 48) (numbers left: [33]). Try possible operations.\n    |- Try 48 + 24 = 72. Add 72 to the number set. Current number set: [72, 33], target: 14, just two numbers left.\n     |- Try 72 + 33 = 105. Evaluate 105 != 14, drop this branch.\n     |- Try 72 - 33 = 39. Evaluate 39 != 14, drop this branch.\n     |- Try 72 * 33 = 2376. 2376 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 33 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 48 - 24 = 24. Add 24 to the number set. Current number set: [24, 33], target: 14, just two numbers left.\n     |- Try 33 + 24 = 57. Evaluate 57 != 14, drop this branch.\n     |- Try 33 - 24 = 9. Evaluate 9 != 14, drop this branch.\n     |- Try 33 * 24 = 792. Evaluate 792 != 14, drop this branch.\n     |- Try 33 \/ 24 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 48 * 24 = 1152. Add 1152 to the number set. Current number set: [1152, 33], target: 14, just two numbers left.\n     |- Try 1152 + 33 = 1185. Evaluate 1185 != 14, drop this branch.\n     |- Try 1152 - 33 = 1119. Evaluate 1119 != 14, drop this branch.\n     |- Try 1152 * 33 = 38016. 38016 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1152 \/ 33 = 34.9. 34.9 is a decimal, drop this branch.\n    |- Try 48 \/ 24 = 2. Add 2 to the number set. Current number set: [2, 33], target: 14, just two numbers left.\n     |- Try 33 + 2 = 35. Evaluate 35 != 14, drop this branch.\n     |- Try 33 - 2 = 31. Evaluate 31 != 14, drop this branch.\n     |- Try 33 * 2 = 66. Evaluate 66 != 14, drop this branch.\n     |- Try 33 \/ 2 = 16.5. 16.5 is a decimal, drop this branch.\n   |- Pick two numbers (24, 33) (numbers left: [48]). Try possible operations.\n    |- Try 33 + 24 = 57. Add 57 to the number set. Current number set: [57, 48], target: 14, just two numbers left.\n     |- Try 57 + 48 = 105. Evaluate 105 != 14, drop this branch.\n     |- Try 57 - 48 = 9. Evaluate 9 != 14, drop this branch.\n     |- Try 57 * 48 = 2736. 2736 exceeds the maximum intermediate result, drop this branch.\n     |- Try 57 \/ 48 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 33 - 24 = 9. Add 9 to the number set. Current number set: [9, 48], target: 14, just two numbers left.\n     |- Try 48 + 9 = 57. Evaluate 57 != 14, drop this branch.\n     |- Try 48 - 9 = 39. Evaluate 39 != 14, drop this branch.\n     |- Try 48 * 9 = 432. Evaluate 432 != 14, drop this branch.\n     |- Try 48 \/ 9 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 33 * 24 = 792. Add 792 to the number set. Current number set: [792, 48], target: 14, just two numbers left.\n     |- Try 792 + 48 = 840. Evaluate 840 != 14, drop this branch.\n     |- Try 792 - 48 = 744. Evaluate 744 != 14, drop this branch.\n     |- Try 792 * 48 = 38016. 38016 exceeds the maximum intermediate result, drop this branch.\n     |- Try 792 \/ 48 = 16.5. 16.5 is a decimal, drop this branch.\n    |- Try 33 \/ 24 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (48, 33) (numbers left: [24]). Try possible operations.\n    |- Try 48 + 33 = 81. Add 81 to the number set. Current number set: [81, 24], target: 14, just two numbers left.\n     |- Try 81 + 24 = 105. Evaluate 105 != 14, drop this branch.\n     |- Try 81 - 24 = 57. Evaluate 57 != 14, drop this branch.\n     |- Try 81 * 24 = 1944. Evaluate 1944 != 14, drop this branch.\n     |- Try 81 \/ 24 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 48 - 33 = 15. Add 15 to the number set. Current number set: [15, 24], target: 14, just two numbers left.\n     |- Try 24 + 15 = 39. Evaluate 39 != 14, drop this branch.\n     |- Try 24 - 15 = 9. Evaluate 9 != 14, drop this branch.\n     |- Try 24 * 15 = 360. Evaluate 360 != 14, drop this branch.\n     |- Try 24 \/ 15 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 48 * 33 = 1584. Add 1584 to the number set. Current number set: [1584, 24], target: 14, just two numbers left.\n     |- Try 1584 + 24 = 1608. Evaluate 1608 != 14, drop this branch.\n     |- Try 1584 - 24 = 1560. Evaluate 1560 != 14, drop this branch.\n     |- Try 1584 * 24 = 38016. 38016 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1584 \/ 24 = 66. Evaluate 66 != 14, drop this branch.\n    |- Try 48 \/ 33 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 12 - 12 = 0. Add 0 to the number set. Current number set: [0, 48, 33], target: 14. Options for choosing two numbers: [(0, 48), (0, 33), (48, 33)].\n   |- Pick two numbers (0, 48) (numbers left: [33]). Try possible operations.\n    |- Try 48 + 0 = 48. Add 48 to the number set. Current number set: [48, 33], target: 14, just two numbers left.\n     |- Try 48 + 33 = 81. Evaluate 81 != 14, drop this branch.\n     |- Try 48 - 33 = 15. Evaluate 15 != 14, drop this branch.\n     |- Try 48 * 33 = 1584. Evaluate 1584 != 14, drop this branch.\n     |- Try 48 \/ 33 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 48 - 0 = 48. Add 48 to the number set. Current number set: [48, 33], target: 14, just two numbers left.\n     |- Try 48 + 33 = 81. Evaluate 81 != 14, drop this branch.\n     |- Try 48 - 33 = 15. Evaluate 15 != 14, drop this branch.\n     |- Try 48 * 33 = 1584. Evaluate 1584 != 14, drop this branch.\n     |- Try 48 \/ 33 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 48 * 0 = 0. Add 0 to the number set. Current number set: [0, 33], target: 14, just two numbers left.\n     |- Try 33 + 0 = 33. Evaluate 33 != 14, drop this branch.\n     |- Try 33 - 0 = 33. Evaluate 33 != 14, drop this branch.\n     |- Try 33 * 0 = 0. Evaluate 0 != 14, drop this branch.\n     |- Try 33 \/ 0 (invalid operation). drop this branch.\n    |- Try 48 \/ 0 (invalid operation). drop this branch.\n   |- Pick two numbers (0, 33) (numbers left: [48]). Try possible operations.\n    |- Try 33 + 0 = 33. Add 33 to the number set. Current number set: [33, 48], target: 14, just two numbers left.\n     |- Try 48 + 33 = 81. Evaluate 81 != 14, drop this branch.\n     |- Try 48 - 33 = 15. Evaluate 15 != 14, drop this branch.\n     |- Try 48 * 33 = 1584. Evaluate 1584 != 14, drop this branch.\n     |- Try 48 \/ 33 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 33 - 0 = 33. Add 33 to the number set. Current number set: [33, 48], target: 14, just two numbers left.\n     |- Try 48 + 33 = 81. Evaluate 81 != 14, drop this branch.\n     |- Try 48 - 33 = 15. Evaluate 15 != 14, drop this branch.\n     |- Try 48 * 33 = 1584. Evaluate 1584 != 14, drop this branch.\n     |- Try 48 \/ 33 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 33 * 0 = 0. Add 0 to the number set. Current number set: [0, 48], target: 14, just two numbers left.\n     |- Try 48 + 0 = 48. Evaluate 48 != 14, drop this branch.\n     |- Try 48 - 0 = 48. Evaluate 48 != 14, drop this branch.\n     |- Try 48 * 0 = 0. Evaluate 0 != 14, drop this branch.\n     |- Try 48 \/ 0 (invalid operation). drop this branch.\n    |- Try 33 \/ 0 (invalid operation). drop this branch.\n   |- Pick two numbers (48, 33) (numbers left: [0]). Try possible operations.\n    |- Try 48 + 33 = 81. Add 81 to the number set. Current number set: [81, 0], target: 14, just two numbers left.\n     |- Try 81 + 0 = 81. Evaluate 81 != 14, drop this branch.\n     |- Try 81 - 0 = 81. Evaluate 81 != 14, drop this branch.\n     |- Try 81 * 0 = 0. Evaluate 0 != 14, drop this branch.\n     |- Try 81 \/ 0 (invalid operation). drop this branch.\n    |- Try 48 - 33 = 15. Add 15 to the number set. Current number set: [15, 0], target: 14, just two numbers left.\n     |- Try 15 + 0 = 15. Evaluate 15 != 14, drop this branch.\n     |- Try 15 - 0 = 15. Evaluate 15 != 14, drop this branch.\n     |- Try 15 * 0 = 0. Evaluate 0 != 14, drop this branch.\n     |- Try 15 \/ 0 (invalid operation). drop this branch.\n    |- Try 48 * 33 = 1584. Add 1584 to the number set. Current number set: [1584, 0], target: 14, just two numbers left.\n     |- Try 1584 + 0 = 1584. Evaluate 1584 != 14, drop this branch.\n     |- Try 1584 - 0 = 1584. Evaluate 1584 != 14, drop this branch.\n     |- Try 1584 * 0 = 0. Evaluate 0 != 14, drop this branch.\n     |- Try 1584 \/ 0 (invalid operation). drop this branch.\n    |- Try 48 \/ 33 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 12 * 12 = 144. Add 144 to the number set. Current number set: [144, 48, 33], target: 14. Options for choosing two numbers: [(144, 48), (144, 33), (48, 33)].\n   |- Pick two numbers (144, 48) (numbers left: [33]). Try possible operations.\n    |- Try 144 + 48 = 192. Add 192 to the number set. Current number set: [192, 33], target: 14, just two numbers left.\n     |- Try 192 + 33 = 225. Evaluate 225 != 14, drop this branch.\n     |- Try 192 - 33 = 159. Evaluate 159 != 14, drop this branch.\n     |- Try 192 * 33 = 6336. 6336 exceeds the maximum intermediate result, drop this branch.\n     |- Try 192 \/ 33 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 144 - 48 = 96. Add 96 to the number set. Current number set: [96, 33], target: 14, just two numbers left.\n     |- Try 96 + 33 = 129. Evaluate 129 != 14, drop this branch.\n     |- Try 96 - 33 = 63. Evaluate 63 != 14, drop this branch.\n     |- Try 96 * 33 = 3168. 3168 exceeds the maximum intermediate result, drop this branch.\n     |- Try 96 \/ 33 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 144 * 48 = 6912. 6912 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 48 = 3. Add 3 to the number set. Current number set: [3, 33], target: 14, just two numbers left.\n     |- Try 33 + 3 = 36. Evaluate 36 != 14, drop this branch.\n     |- Try 33 - 3 = 30. Evaluate 30 != 14, drop this branch.\n     |- Try 33 * 3 = 99. Evaluate 99 != 14, drop this branch.\n     |- Try 33 \/ 3 = 11. Evaluate 11 != 14, drop this branch.\n   |- Pick two numbers (144, 33) (numbers left: [48]). Try possible operations.\n    |- Try 144 + 33 = 177. Add 177 to the number set. Current number set: [177, 48], target: 14, just two numbers left.\n     |- Try 177 + 48 = 225. Evaluate 225 != 14, drop this branch.\n     |- Try 177 - 48 = 129. Evaluate 129 != 14, drop this branch.\n     |- Try 177 * 48 = 8496. 8496 exceeds the maximum intermediate result, drop this branch.\n     |- Try 177 \/ 48 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 144 - 33 = 111. Add 111 to the number set. Current number set: [111, 48], target: 14, just two numbers left.\n     |- Try 111 + 48 = 159. Evaluate 159 != 14, drop this branch.\n     |- Try 111 - 48 = 63. Evaluate 63 != 14, drop this branch.\n     |- Try 111 * 48 = 5328. 5328 exceeds the maximum intermediate result, drop this branch.\n     |- Try 111 \/ 48 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 144 * 33 = 4752. 4752 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 33 = 4.4. 4.4 is a decimal, drop this branch.\n   |- Pick two numbers (48, 33) (numbers left: [144]). Try possible operations.\n    |- Try 48 + 33 = 81. Add 81 to the number set. Current number set: [81, 144], target: 14, just two numbers left.\n     |- Try 144 + 81 = 225. Evaluate 225 != 14, drop this branch.\n     |- Try 144 - 81 = 63. Evaluate 63 != 14, drop this branch.\n     |- Try 144 * 81 = 11664. 11664 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 81 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 48 - 33 = 15. Add 15 to the number set. Current number set: [15, 144], target: 14, just two numbers left.\n     |- Try 144 + 15 = 159. Evaluate 159 != 14, drop this branch.\n     |- Try 144 - 15 = 129. Evaluate 129 != 14, drop this branch.\n     |- Try 144 * 15 = 2160. 2160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 15 = 9.6. 9.6 is a decimal, drop this branch.\n    |- Try 48 * 33 = 1584. Add 1584 to the number set. Current number set: [1584, 144], target: 14, just two numbers left.\n     |- Try 1584 + 144 = 1728. Evaluate 1728 != 14, drop this branch.\n     |- Try 1584 - 144 = 1440. Evaluate 1440 != 14, drop this branch.\n     |- Try 1584 * 144 = 228096. 228096 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1584 \/ 144 = 11. Evaluate 11 != 14, drop this branch.\n    |- Try 48 \/ 33 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 12 \/ 12 = 1. Add 1 to the number set. Current number set: [1, 48, 33], target: 14. Options for choosing two numbers: [(1, 48), (1, 33), (48, 33)].\n   |- Pick two numbers (1, 48) (numbers left: [33]). Try possible operations.\n    |- Try 48 + 1 = 49. Add 49 to the number set. Current number set: [49, 33], target: 14, just two numbers left.\n     |- Try 49 + 33 = 82. Evaluate 82 != 14, drop this branch.\n     |- Try 49 - 33 = 16. Evaluate 16 != 14, drop this branch.\n     |- Try 49 * 33 = 1617. Evaluate 1617 != 14, drop this branch.\n     |- Try 49 \/ 33 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 48 - 1 = 47. Add 47 to the number set. Current number set: [47, 33], target: 14, just two numbers left.\n     |- Try 47 + 33 = 80. Evaluate 80 != 14, drop this branch.\n     |- Try 47 - 33 = 14. Evaluate 14 == 14, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 47 - 33 = 14\nThe step before: 48 - 1 = 47\nThe first step: 12 \/ 12 = 1\n\nOutput the solution in the required format:\n<Solution>\n12 \/ 12 = 1\n48 - 1 = 47\n47 - 33 = 14\n<\/Solution>\n","item":{"nums":[12,12,48,33],"solution":["12 \/ 12 = 1","48 - 1 = 47","47 - 33 = 14"],"target":14}}
+{"instance_id":"countdown_8k_60","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [22, 22, 24, 19]\nTarget: 30","reference_output":"# Search Procedure\nInitial number set: [22, 22, 24, 19], target: 30. Options for choosing two numbers: [(22, 22), (22, 24), (22, 19), (22, 24), (22, 19), (24, 19)].\n |- Pick two numbers (22, 22) (numbers left: [24, 19]). Try possible operations.\n  |- Try 22 + 22 = 44. Add 44 to the number set. Current number set: [44, 24, 19], target: 30. Options for choosing two numbers: [(44, 24), (44, 19), (24, 19)].\n   |- Pick two numbers (44, 24) (numbers left: [19]). Try possible operations.\n    |- Try 44 + 24 = 68. Add 68 to the number set. Current number set: [68, 19], target: 30, just two numbers left.\n     |- Try 68 + 19 = 87. Evaluate 87 != 30, drop this branch.\n     |- Try 68 - 19 = 49. Evaluate 49 != 30, drop this branch.\n     |- Try 68 * 19 = 1292. Evaluate 1292 != 30, drop this branch.\n     |- Try 68 \/ 19 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 44 - 24 = 20. Add 20 to the number set. Current number set: [20, 19], target: 30, just two numbers left.\n     |- Try 20 + 19 = 39. Evaluate 39 != 30, drop this branch.\n     |- Try 20 - 19 = 1. Evaluate 1 != 30, drop this branch.\n     |- Try 20 * 19 = 380. Evaluate 380 != 30, drop this branch.\n     |- Try 20 \/ 19 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 44 * 24 = 1056. Add 1056 to the number set. Current number set: [1056, 19], target: 30, just two numbers left.\n     |- Try 1056 + 19 = 1075. Evaluate 1075 != 30, drop this branch.\n     |- Try 1056 - 19 = 1037. Evaluate 1037 != 30, drop this branch.\n     |- Try 1056 * 19 = 20064. 20064 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1056 \/ 19 = 55.6. 55.6 is a decimal, drop this branch.\n    |- Try 44 \/ 24 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (44, 19) (numbers left: [24]). Try possible operations.\n    |- Try 44 + 19 = 63. Add 63 to the number set. Current number set: [63, 24], target: 30, just two numbers left.\n     |- Try 63 + 24 = 87. Evaluate 87 != 30, drop this branch.\n     |- Try 63 - 24 = 39. Evaluate 39 != 30, drop this branch.\n     |- Try 63 * 24 = 1512. Evaluate 1512 != 30, drop this branch.\n     |- Try 63 \/ 24 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 44 - 19 = 25. Add 25 to the number set. Current number set: [25, 24], target: 30, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 30, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 30, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 30, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 44 * 19 = 836. Add 836 to the number set. Current number set: [836, 24], target: 30, just two numbers left.\n     |- Try 836 + 24 = 860. Evaluate 860 != 30, drop this branch.\n     |- Try 836 - 24 = 812. Evaluate 812 != 30, drop this branch.\n     |- Try 836 * 24 = 20064. 20064 exceeds the maximum intermediate result, drop this branch.\n     |- Try 836 \/ 24 = 34.8. 34.8 is a decimal, drop this branch.\n    |- Try 44 \/ 19 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (24, 19) (numbers left: [44]). Try possible operations.\n    |- Try 24 + 19 = 43. Add 43 to the number set. Current number set: [43, 44], target: 30, just two numbers left.\n     |- Try 44 + 43 = 87. Evaluate 87 != 30, drop this branch.\n     |- Try 44 - 43 = 1. Evaluate 1 != 30, drop this branch.\n     |- Try 44 * 43 = 1892. Evaluate 1892 != 30, drop this branch.\n     |- Try 44 \/ 43 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 24 - 19 = 5. Add 5 to the number set. Current number set: [5, 44], target: 30, just two numbers left.\n     |- Try 44 + 5 = 49. Evaluate 49 != 30, drop this branch.\n     |- Try 44 - 5 = 39. Evaluate 39 != 30, drop this branch.\n     |- Try 44 * 5 = 220. Evaluate 220 != 30, drop this branch.\n     |- Try 44 \/ 5 = 8.8. 8.8 is a decimal, drop this branch.\n    |- Try 24 * 19 = 456. Add 456 to the number set. Current number set: [456, 44], target: 30, just two numbers left.\n     |- Try 456 + 44 = 500. Evaluate 500 != 30, drop this branch.\n     |- Try 456 - 44 = 412. Evaluate 412 != 30, drop this branch.\n     |- Try 456 * 44 = 20064. 20064 exceeds the maximum intermediate result, drop this branch.\n     |- Try 456 \/ 44 = 10.4. 10.4 is a decimal, drop this branch.\n    |- Try 24 \/ 19 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 22 - 22 = 0. Add 0 to the number set. Current number set: [0, 24, 19], target: 30. Options for choosing two numbers: [(0, 24), (0, 19), (24, 19)].\n   |- Pick two numbers (0, 24) (numbers left: [19]). Try possible operations.\n    |- Try 24 + 0 = 24. Add 24 to the number set. Current number set: [24, 19], target: 30, just two numbers left.\n     |- Try 24 + 19 = 43. Evaluate 43 != 30, drop this branch.\n     |- Try 24 - 19 = 5. Evaluate 5 != 30, drop this branch.\n     |- Try 24 * 19 = 456. Evaluate 456 != 30, drop this branch.\n     |- Try 24 \/ 19 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 24 - 0 = 24. Add 24 to the number set. Current number set: [24, 19], target: 30, just two numbers left.\n     |- Try 24 + 19 = 43. Evaluate 43 != 30, drop this branch.\n     |- Try 24 - 19 = 5. Evaluate 5 != 30, drop this branch.\n     |- Try 24 * 19 = 456. Evaluate 456 != 30, drop this branch.\n     |- Try 24 \/ 19 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 24 * 0 = 0. Add 0 to the number set. Current number set: [0, 19], target: 30, just two numbers left.\n     |- Try 19 + 0 = 19. Evaluate 19 != 30, drop this branch.\n     |- Try 19 - 0 = 19. Evaluate 19 != 30, drop this branch.\n     |- Try 19 * 0 = 0. Evaluate 0 != 30, drop this branch.\n     |- Try 19 \/ 0 (invalid operation). drop this branch.\n    |- Try 24 \/ 0 (invalid operation). drop this branch.\n   |- Pick two numbers (0, 19) (numbers left: [24]). Try possible operations.\n    |- Try 19 + 0 = 19. Add 19 to the number set. Current number set: [19, 24], target: 30, just two numbers left.\n     |- Try 24 + 19 = 43. Evaluate 43 != 30, drop this branch.\n     |- Try 24 - 19 = 5. Evaluate 5 != 30, drop this branch.\n     |- Try 24 * 19 = 456. Evaluate 456 != 30, drop this branch.\n     |- Try 24 \/ 19 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 19 - 0 = 19. Add 19 to the number set. Current number set: [19, 24], target: 30, just two numbers left.\n     |- Try 24 + 19 = 43. Evaluate 43 != 30, drop this branch.\n     |- Try 24 - 19 = 5. Evaluate 5 != 30, drop this branch.\n     |- Try 24 * 19 = 456. Evaluate 456 != 30, drop this branch.\n     |- Try 24 \/ 19 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 19 * 0 = 0. Add 0 to the number set. Current number set: [0, 24], target: 30, just two numbers left.\n     |- Try 24 + 0 = 24. Evaluate 24 != 30, drop this branch.\n     |- Try 24 - 0 = 24. Evaluate 24 != 30, drop this branch.\n     |- Try 24 * 0 = 0. Evaluate 0 != 30, drop this branch.\n     |- Try 24 \/ 0 (invalid operation). drop this branch.\n    |- Try 19 \/ 0 (invalid operation). drop this branch.\n   |- Pick two numbers (24, 19) (numbers left: [0]). Try possible operations.\n    |- Try 24 + 19 = 43. Add 43 to the number set. Current number set: [43, 0], target: 30, just two numbers left.\n     |- Try 43 + 0 = 43. Evaluate 43 != 30, drop this branch.\n     |- Try 43 - 0 = 43. Evaluate 43 != 30, drop this branch.\n     |- Try 43 * 0 = 0. Evaluate 0 != 30, drop this branch.\n     |- Try 43 \/ 0 (invalid operation). drop this branch.\n    |- Try 24 - 19 = 5. Add 5 to the number set. Current number set: [5, 0], target: 30, just two numbers left.\n     |- Try 5 + 0 = 5. Evaluate 5 != 30, drop this branch.\n     |- Try 5 - 0 = 5. Evaluate 5 != 30, drop this branch.\n     |- Try 5 * 0 = 0. Evaluate 0 != 30, drop this branch.\n     |- Try 5 \/ 0 (invalid operation). drop this branch.\n    |- Try 24 * 19 = 456. Add 456 to the number set. Current number set: [456, 0], target: 30, just two numbers left.\n     |- Try 456 + 0 = 456. Evaluate 456 != 30, drop this branch.\n     |- Try 456 - 0 = 456. Evaluate 456 != 30, drop this branch.\n     |- Try 456 * 0 = 0. Evaluate 0 != 30, drop this branch.\n     |- Try 456 \/ 0 (invalid operation). drop this branch.\n    |- Try 24 \/ 19 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 22 * 22 = 484. Add 484 to the number set. Current number set: [484, 24, 19], target: 30. Options for choosing two numbers: [(484, 24), (484, 19), (24, 19)].\n   |- Pick two numbers (484, 24) (numbers left: [19]). Try possible operations.\n    |- Try 484 + 24 = 508. Add 508 to the number set. Current number set: [508, 19], target: 30, just two numbers left.\n     |- Try 508 + 19 = 527. Evaluate 527 != 30, drop this branch.\n     |- Try 508 - 19 = 489. Evaluate 489 != 30, drop this branch.\n     |- Try 508 * 19 = 9652. 9652 exceeds the maximum intermediate result, drop this branch.\n     |- Try 508 \/ 19 = 26.7. 26.7 is a decimal, drop this branch.\n    |- Try 484 - 24 = 460. Add 460 to the number set. Current number set: [460, 19], target: 30, just two numbers left.\n     |- Try 460 + 19 = 479. Evaluate 479 != 30, drop this branch.\n     |- Try 460 - 19 = 441. Evaluate 441 != 30, drop this branch.\n     |- Try 460 * 19 = 8740. 8740 exceeds the maximum intermediate result, drop this branch.\n     |- Try 460 \/ 19 = 24.2. 24.2 is a decimal, drop this branch.\n    |- Try 484 * 24 = 11616. 11616 exceeds the maximum intermediate result, drop this branch.\n    |- Try 484 \/ 24 = 20.2. 20.2 is a decimal, drop this branch.\n   |- Pick two numbers (484, 19) (numbers left: [24]). Try possible operations.\n    |- Try 484 + 19 = 503. Add 503 to the number set. Current number set: [503, 24], target: 30, just two numbers left.\n     |- Try 503 + 24 = 527. Evaluate 527 != 30, drop this branch.\n     |- Try 503 - 24 = 479. Evaluate 479 != 30, drop this branch.\n     |- Try 503 * 24 = 12072. 12072 exceeds the maximum intermediate result, drop this branch.\n     |- Try 503 \/ 24 = 21.0. 21.0 is a decimal, drop this branch.\n    |- Try 484 - 19 = 465. Add 465 to the number set. Current number set: [465, 24], target: 30, just two numbers left.\n     |- Try 465 + 24 = 489. Evaluate 489 != 30, drop this branch.\n     |- Try 465 - 24 = 441. Evaluate 441 != 30, drop this branch.\n     |- Try 465 * 24 = 11160. 11160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 465 \/ 24 = 19.4. 19.4 is a decimal, drop this branch.\n    |- Try 484 * 19 = 9196. 9196 exceeds the maximum intermediate result, drop this branch.\n    |- Try 484 \/ 19 = 25.5. 25.5 is a decimal, drop this branch.\n   |- Pick two numbers (24, 19) (numbers left: [484]). Try possible operations.\n    |- Try 24 + 19 = 43. Add 43 to the number set. Current number set: [43, 484], target: 30, just two numbers left.\n     |- Try 484 + 43 = 527. Evaluate 527 != 30, drop this branch.\n     |- Try 484 - 43 = 441. Evaluate 441 != 30, drop this branch.\n     |- Try 484 * 43 = 20812. 20812 exceeds the maximum intermediate result, drop this branch.\n     |- Try 484 \/ 43 = 11.3. 11.3 is a decimal, drop this branch.\n    |- Try 24 - 19 = 5. Add 5 to the number set. Current number set: [5, 484], target: 30, just two numbers left.\n     |- Try 484 + 5 = 489. Evaluate 489 != 30, drop this branch.\n     |- Try 484 - 5 = 479. Evaluate 479 != 30, drop this branch.\n     |- Try 484 * 5 = 2420. 2420 exceeds the maximum intermediate result, drop this branch.\n     |- Try 484 \/ 5 = 96.8. 96.8 is a decimal, drop this branch.\n    |- Try 24 * 19 = 456. Add 456 to the number set. Current number set: [456, 484], target: 30, just two numbers left.\n     |- Try 484 + 456 = 940. Evaluate 940 != 30, drop this branch.\n     |- Try 484 - 456 = 28. Evaluate 28 != 30, drop this branch.\n     |- Try 484 * 456 = 220704. 220704 exceeds the maximum intermediate result, drop this branch.\n     |- Try 484 \/ 456 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 24 \/ 19 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 22 \/ 22 = 1. Add 1 to the number set. Current number set: [1, 24, 19], target: 30. Options for choosing two numbers: [(1, 24), (1, 19), (24, 19)].\n   |- Pick two numbers (1, 24) (numbers left: [19]). Try possible operations.\n    |- Try 24 + 1 = 25. Add 25 to the number set. Current number set: [25, 19], target: 30, just two numbers left.\n     |- Try 25 + 19 = 44. Evaluate 44 != 30, drop this branch.\n     |- Try 25 - 19 = 6. Evaluate 6 != 30, drop this branch.\n     |- Try 25 * 19 = 475. Evaluate 475 != 30, drop this branch.\n     |- Try 25 \/ 19 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 24 - 1 = 23. Add 23 to the number set. Current number set: [23, 19], target: 30, just two numbers left.\n     |- Try 23 + 19 = 42. Evaluate 42 != 30, drop this branch.\n     |- Try 23 - 19 = 4. Evaluate 4 != 30, drop this branch.\n     |- Try 23 * 19 = 437. Evaluate 437 != 30, drop this branch.\n     |- Try 23 \/ 19 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 24 * 1 = 24. Add 24 to the number set. Current number set: [24, 19], target: 30, just two numbers left.\n     |- Try 24 + 19 = 43. Evaluate 43 != 30, drop this branch.\n     |- Try 24 - 19 = 5. Evaluate 5 != 30, drop this branch.\n     |- Try 24 * 19 = 456. Evaluate 456 != 30, drop this branch.\n     |- Try 24 \/ 19 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 24 \/ 1 = 24. Add 24 to the number set. Current number set: [24, 19], target: 30, just two numbers left.\n     |- Try 24 + 19 = 43. Evaluate 43 != 30, drop this branch.\n     |- Try 24 - 19 = 5. Evaluate 5 != 30, drop this branch.\n     |- Try 24 * 19 = 456. Evaluate 456 != 30, drop this branch.\n     |- Try 24 \/ 19 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (1, 19) (numbers left: [24]). Try possible operations.\n    |- Try 19 + 1 = 20. Add 20 to the number set. Current number set: [20, 24], target: 30, just two numbers left.\n     |- Try 24 + 20 = 44. Evaluate 44 != 30, drop this branch.\n     |- Try 24 - 20 = 4. Evaluate 4 != 30, drop this branch.\n     |- Try 24 * 20 = 480. Evaluate 480 != 30, drop this branch.\n     |- Try 24 \/ 20 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 19 - 1 = 18. Add 18 to the number set. Current number set: [18, 24], target: 30, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 30, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 30, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 30, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 19 * 1 = 19. Add 19 to the number set. Current number set: [19, 24], target: 30, just two numbers left.\n     |- Try 24 + 19 = 43. Evaluate 43 != 30, drop this branch.\n     |- Try 24 - 19 = 5. Evaluate 5 != 30, drop this branch.\n     |- Try 24 * 19 = 456. Evaluate 456 != 30, drop this branch.\n     |- Try 24 \/ 19 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 19 \/ 1 = 19. Add 19 to the number set. Current number set: [19, 24], target: 30, just two numbers left.\n     |- Try 24 + 19 = 43. Evaluate 43 != 30, drop this branch.\n     |- Try 24 - 19 = 5. Evaluate 5 != 30, drop this branch.\n     |- Try 24 * 19 = 456. Evaluate 456 != 30, drop this branch.\n     |- Try 24 \/ 19 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (24, 19) (numbers left: [1]). Try possible operations.\n    |- Try 24 + 19 = 43. Add 43 to the number set. Current number set: [43, 1], target: 30, just two numbers left.\n     |- Try 43 + 1 = 44. Evaluate 44 != 30, drop this branch.\n     |- Try 43 - 1 = 42. Evaluate 42 != 30, drop this branch.\n     |- Try 43 * 1 = 43. Evaluate 43 != 30, drop this branch.\n     |- Try 43 \/ 1 = 43. Evaluate 43 != 30, drop this branch.\n    |- Try 24 - 19 = 5. Add 5 to the number set. Current number set: [5, 1], target: 30, just two numbers left.\n     |- Try 5 + 1 = 6. Evaluate 6 != 30, drop this branch.\n     |- Try 5 - 1 = 4. Evaluate 4 != 30, drop this branch.\n     |- Try 5 * 1 = 5. Evaluate 5 != 30, drop this branch.\n     |- Try 5 \/ 1 = 5. Evaluate 5 != 30, drop this branch.\n    |- Try 24 * 19 = 456. Add 456 to the number set. Current number set: [456, 1], target: 30, just two numbers left.\n     |- Try 456 + 1 = 457. Evaluate 457 != 30, drop this branch.\n     |- Try 456 - 1 = 455. Evaluate 455 != 30, drop this branch.\n     |- Try 456 * 1 = 456. Evaluate 456 != 30, drop this branch.\n     |- Try 456 \/ 1 = 456. Evaluate 456 != 30, drop this branch.\n    |- Try 24 \/ 19 = 1.3. 1.3 is a decimal, drop this branch.\n |- Pick two numbers (22, 24) (numbers left: [22, 19]). Try possible operations.\n  |- Try 24 + 22 = 46. Add 46 to the number set. Current number set: [46, 22, 19], target: 30. Options for choosing two numbers: [(46, 22), (46, 19), (22, 19)].\n   |- Pick two numbers (46, 22) (numbers left: [19]). Try possible operations.\n    |- Try 46 + 22 = 68. Add 68 to the number set. Current number set: [68, 19], target: 30, just two numbers left.\n     |- Try 68 + 19 = 87. Evaluate 87 != 30, drop this branch.\n     |- Try 68 - 19 = 49. Evaluate 49 != 30, drop this branch.\n     |- Try 68 * 19 = 1292. Evaluate 1292 != 30, drop this branch.\n     |- Try 68 \/ 19 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 46 - 22 = 24. Add 24 to the number set. Current number set: [24, 19], target: 30, just two numbers left.\n     |- Try 24 + 19 = 43. Evaluate 43 != 30, drop this branch.\n     |- Try 24 - 19 = 5. Evaluate 5 != 30, drop this branch.\n     |- Try 24 * 19 = 456. Evaluate 456 != 30, drop this branch.\n     |- Try 24 \/ 19 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 46 * 22 = 1012. Add 1012 to the number set. Current number set: [1012, 19], target: 30, just two numbers left.\n     |- Try 1012 + 19 = 1031. Evaluate 1031 != 30, drop this branch.\n     |- Try 1012 - 19 = 993. Evaluate 993 != 30, drop this branch.\n     |- Try 1012 * 19 = 19228. 19228 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1012 \/ 19 = 53.3. 53.3 is a decimal, drop this branch.\n    |- Try 46 \/ 22 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (46, 19) (numbers left: [22]). Try possible operations.\n    |- Try 46 + 19 = 65. Add 65 to the number set. Current number set: [65, 22], target: 30, just two numbers left.\n     |- Try 65 + 22 = 87. Evaluate 87 != 30, drop this branch.\n     |- Try 65 - 22 = 43. Evaluate 43 != 30, drop this branch.\n     |- Try 65 * 22 = 1430. Evaluate 1430 != 30, drop this branch.\n     |- Try 65 \/ 22 = 3.0. 3.0 is a decimal, drop this branch.\n    |- Try 46 - 19 = 27. Add 27 to the number set. Current number set: [27, 22], target: 30, just two numbers left.\n     |- Try 27 + 22 = 49. Evaluate 49 != 30, drop this branch.\n     |- Try 27 - 22 = 5. Evaluate 5 != 30, drop this branch.\n     |- Try 27 * 22 = 594. Evaluate 594 != 30, drop this branch.\n     |- Try 27 \/ 22 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 46 * 19 = 874. Add 874 to the number set. Current number set: [874, 22], target: 30, just two numbers left.\n     |- Try 874 + 22 = 896. Evaluate 896 != 30, drop this branch.\n     |- Try 874 - 22 = 852. Evaluate 852 != 30, drop this branch.\n     |- Try 874 * 22 = 19228. 19228 exceeds the maximum intermediate result, drop this branch.\n     |- Try 874 \/ 22 = 39.7. 39.7 is a decimal, drop this branch.\n    |- Try 46 \/ 19 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (22, 19) (numbers left: [46]). Try possible operations.\n    |- Try 22 + 19 = 41. Add 41 to the number set. Current number set: [41, 46], target: 30, just two numbers left.\n     |- Try 46 + 41 = 87. Evaluate 87 != 30, drop this branch.\n     |- Try 46 - 41 = 5. Evaluate 5 != 30, drop this branch.\n     |- Try 46 * 41 = 1886. Evaluate 1886 != 30, drop this branch.\n     |- Try 46 \/ 41 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 22 - 19 = 3. Add 3 to the number set. Current number set: [3, 46], target: 30, just two numbers left.\n     |- Try 46 + 3 = 49. Evaluate 49 != 30, drop this branch.\n     |- Try 46 - 3 = 43. Evaluate 43 != 30, drop this branch.\n     |- Try 46 * 3 = 138. Evaluate 138 != 30, drop this branch.\n     |- Try 46 \/ 3 = 15.3. 15.3 is a decimal, drop this branch.\n    |- Try 22 * 19 = 418. Add 418 to the number set. Current number set: [418, 46], target: 30, just two numbers left.\n     |- Try 418 + 46 = 464. Evaluate 464 != 30, drop this branch.\n     |- Try 418 - 46 = 372. Evaluate 372 != 30, drop this branch.\n     |- Try 418 * 46 = 19228. 19228 exceeds the maximum intermediate result, drop this branch.\n     |- Try 418 \/ 46 = 9.1. 9.1 is a decimal, drop this branch.\n    |- Try 22 \/ 19 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 24 - 22 = 2. Add 2 to the number set. Current number set: [2, 22, 19], target: 30. Options for choosing two numbers: [(2, 22), (2, 19), (22, 19)].\n   |- Pick two numbers (2, 22) (numbers left: [19]). Try possible operations.\n    |- Try 22 + 2 = 24. Add 24 to the number set. Current number set: [24, 19], target: 30, just two numbers left.\n     |- Try 24 + 19 = 43. Evaluate 43 != 30, drop this branch.\n     |- Try 24 - 19 = 5. Evaluate 5 != 30, drop this branch.\n     |- Try 24 * 19 = 456. Evaluate 456 != 30, drop this branch.\n     |- Try 24 \/ 19 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 22 - 2 = 20. Add 20 to the number set. Current number set: [20, 19], target: 30, just two numbers left.\n     |- Try 20 + 19 = 39. Evaluate 39 != 30, drop this branch.\n     |- Try 20 - 19 = 1. Evaluate 1 != 30, drop this branch.\n     |- Try 20 * 19 = 380. Evaluate 380 != 30, drop this branch.\n     |- Try 20 \/ 19 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 22 * 2 = 44. Add 44 to the number set. Current number set: [44, 19], target: 30, just two numbers left.\n     |- Try 44 + 19 = 63. Evaluate 63 != 30, drop this branch.\n     |- Try 44 - 19 = 25. Evaluate 25 != 30, drop this branch.\n     |- Try 44 * 19 = 836. Evaluate 836 != 30, drop this branch.\n     |- Try 44 \/ 19 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 22 \/ 2 = 11. Add 11 to the number set. Current number set: [11, 19], target: 30, just two numbers left.\n     |- Try 19 + 11 = 30. Evaluate 30 == 30, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 19 + 11 = 30\nThe step before: 22 \/ 2 = 11\nThe first step: 24 - 22 = 2\n\nOutput the solution in the required format:\n<Solution>\n24 - 22 = 2\n22 \/ 2 = 11\n19 + 11 = 30\n<\/Solution>\n","item":{"nums":[22,22,24,19],"solution":["24 - 22 = 2","22 \/ 2 = 11","19 + 11 = 30"],"target":30}}
+{"instance_id":"countdown_8k_61","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [14, 44, 28, 7]\nTarget: 50","reference_output":"# Search Procedure\nInitial number set: [14, 44, 28, 7], target: 50. Options for choosing two numbers: [(14, 44), (14, 28), (14, 7), (44, 28), (44, 7), (28, 7)].\n |- Pick two numbers (14, 44) (numbers left: [28, 7]). Try possible operations.\n  |- Try 44 + 14 = 58. Add 58 to the number set. Current number set: [58, 28, 7], target: 50. Options for choosing two numbers: [(58, 28), (58, 7), (28, 7)].\n   |- Pick two numbers (58, 28) (numbers left: [7]). Try possible operations.\n    |- Try 58 + 28 = 86. Add 86 to the number set. Current number set: [86, 7], target: 50, just two numbers left.\n     |- Try 86 + 7 = 93. Evaluate 93 != 50, drop this branch.\n     |- Try 86 - 7 = 79. Evaluate 79 != 50, drop this branch.\n     |- Try 86 * 7 = 602. Evaluate 602 != 50, drop this branch.\n     |- Try 86 \/ 7 = 12.3. 12.3 is a decimal, drop this branch.\n    |- Try 58 - 28 = 30. Add 30 to the number set. Current number set: [30, 7], target: 50, just two numbers left.\n     |- Try 30 + 7 = 37. Evaluate 37 != 50, drop this branch.\n     |- Try 30 - 7 = 23. Evaluate 23 != 50, drop this branch.\n     |- Try 30 * 7 = 210. Evaluate 210 != 50, drop this branch.\n     |- Try 30 \/ 7 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 58 * 28 = 1624. Add 1624 to the number set. Current number set: [1624, 7], target: 50, just two numbers left.\n     |- Try 1624 + 7 = 1631. Evaluate 1631 != 50, drop this branch.\n     |- Try 1624 - 7 = 1617. Evaluate 1617 != 50, drop this branch.\n     |- Try 1624 * 7 = 11368. 11368 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1624 \/ 7 = 232. Evaluate 232 != 50, drop this branch.\n    |- Try 58 \/ 28 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (58, 7) (numbers left: [28]). Try possible operations.\n    |- Try 58 + 7 = 65. Add 65 to the number set. Current number set: [65, 28], target: 50, just two numbers left.\n     |- Try 65 + 28 = 93. Evaluate 93 != 50, drop this branch.\n     |- Try 65 - 28 = 37. Evaluate 37 != 50, drop this branch.\n     |- Try 65 * 28 = 1820. Evaluate 1820 != 50, drop this branch.\n     |- Try 65 \/ 28 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 58 - 7 = 51. Add 51 to the number set. Current number set: [51, 28], target: 50, just two numbers left.\n     |- Try 51 + 28 = 79. Evaluate 79 != 50, drop this branch.\n     |- Try 51 - 28 = 23. Evaluate 23 != 50, drop this branch.\n     |- Try 51 * 28 = 1428. Evaluate 1428 != 50, drop this branch.\n     |- Try 51 \/ 28 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 58 * 7 = 406. Add 406 to the number set. Current number set: [406, 28], target: 50, just two numbers left.\n     |- Try 406 + 28 = 434. Evaluate 434 != 50, drop this branch.\n     |- Try 406 - 28 = 378. Evaluate 378 != 50, drop this branch.\n     |- Try 406 * 28 = 11368. 11368 exceeds the maximum intermediate result, drop this branch.\n     |- Try 406 \/ 28 = 14.5. 14.5 is a decimal, drop this branch.\n    |- Try 58 \/ 7 = 8.3. 8.3 is a decimal, drop this branch.\n   |- Pick two numbers (28, 7) (numbers left: [58]). Try possible operations.\n    |- Try 28 + 7 = 35. Add 35 to the number set. Current number set: [35, 58], target: 50, just two numbers left.\n     |- Try 58 + 35 = 93. Evaluate 93 != 50, drop this branch.\n     |- Try 58 - 35 = 23. Evaluate 23 != 50, drop this branch.\n     |- Try 58 * 35 = 2030. 2030 exceeds the maximum intermediate result, drop this branch.\n     |- Try 58 \/ 35 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 28 - 7 = 21. Add 21 to the number set. Current number set: [21, 58], target: 50, just two numbers left.\n     |- Try 58 + 21 = 79. Evaluate 79 != 50, drop this branch.\n     |- Try 58 - 21 = 37. Evaluate 37 != 50, drop this branch.\n     |- Try 58 * 21 = 1218. Evaluate 1218 != 50, drop this branch.\n     |- Try 58 \/ 21 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 28 * 7 = 196. Add 196 to the number set. Current number set: [196, 58], target: 50, just two numbers left.\n     |- Try 196 + 58 = 254. Evaluate 254 != 50, drop this branch.\n     |- Try 196 - 58 = 138. Evaluate 138 != 50, drop this branch.\n     |- Try 196 * 58 = 11368. 11368 exceeds the maximum intermediate result, drop this branch.\n     |- Try 196 \/ 58 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 28 \/ 7 = 4. Add 4 to the number set. Current number set: [4, 58], target: 50, just two numbers left.\n     |- Try 58 + 4 = 62. Evaluate 62 != 50, drop this branch.\n     |- Try 58 - 4 = 54. Evaluate 54 != 50, drop this branch.\n     |- Try 58 * 4 = 232. Evaluate 232 != 50, drop this branch.\n     |- Try 58 \/ 4 = 14.5. 14.5 is a decimal, drop this branch.\n  |- Try 44 - 14 = 30. Add 30 to the number set. Current number set: [30, 28, 7], target: 50. Options for choosing two numbers: [(30, 28), (30, 7), (28, 7)].\n   |- Pick two numbers (30, 28) (numbers left: [7]). Try possible operations.\n    |- Try 30 + 28 = 58. Add 58 to the number set. Current number set: [58, 7], target: 50, just two numbers left.\n     |- Try 58 + 7 = 65. Evaluate 65 != 50, drop this branch.\n     |- Try 58 - 7 = 51. Evaluate 51 != 50, drop this branch.\n     |- Try 58 * 7 = 406. Evaluate 406 != 50, drop this branch.\n     |- Try 58 \/ 7 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 30 - 28 = 2. Add 2 to the number set. Current number set: [2, 7], target: 50, just two numbers left.\n     |- Try 7 + 2 = 9. Evaluate 9 != 50, drop this branch.\n     |- Try 7 - 2 = 5. Evaluate 5 != 50, drop this branch.\n     |- Try 7 * 2 = 14. Evaluate 14 != 50, drop this branch.\n     |- Try 7 \/ 2 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 30 * 28 = 840. Add 840 to the number set. Current number set: [840, 7], target: 50, just two numbers left.\n     |- Try 840 + 7 = 847. Evaluate 847 != 50, drop this branch.\n     |- Try 840 - 7 = 833. Evaluate 833 != 50, drop this branch.\n     |- Try 840 * 7 = 5880. 5880 exceeds the maximum intermediate result, drop this branch.\n     |- Try 840 \/ 7 = 120. Evaluate 120 != 50, drop this branch.\n    |- Try 30 \/ 28 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (30, 7) (numbers left: [28]). Try possible operations.\n    |- Try 30 + 7 = 37. Add 37 to the number set. Current number set: [37, 28], target: 50, just two numbers left.\n     |- Try 37 + 28 = 65. Evaluate 65 != 50, drop this branch.\n     |- Try 37 - 28 = 9. Evaluate 9 != 50, drop this branch.\n     |- Try 37 * 28 = 1036. Evaluate 1036 != 50, drop this branch.\n     |- Try 37 \/ 28 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 30 - 7 = 23. Add 23 to the number set. Current number set: [23, 28], target: 50, just two numbers left.\n     |- Try 28 + 23 = 51. Evaluate 51 != 50, drop this branch.\n     |- Try 28 - 23 = 5. Evaluate 5 != 50, drop this branch.\n     |- Try 28 * 23 = 644. Evaluate 644 != 50, drop this branch.\n     |- Try 28 \/ 23 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 30 * 7 = 210. Add 210 to the number set. Current number set: [210, 28], target: 50, just two numbers left.\n     |- Try 210 + 28 = 238. Evaluate 238 != 50, drop this branch.\n     |- Try 210 - 28 = 182. Evaluate 182 != 50, drop this branch.\n     |- Try 210 * 28 = 5880. 5880 exceeds the maximum intermediate result, drop this branch.\n     |- Try 210 \/ 28 = 7.5. 7.5 is a decimal, drop this branch.\n    |- Try 30 \/ 7 = 4.3. 4.3 is a decimal, drop this branch.\n   |- Pick two numbers (28, 7) (numbers left: [30]). Try possible operations.\n    |- Try 28 + 7 = 35. Add 35 to the number set. Current number set: [35, 30], target: 50, just two numbers left.\n     |- Try 35 + 30 = 65. Evaluate 65 != 50, drop this branch.\n     |- Try 35 - 30 = 5. Evaluate 5 != 50, drop this branch.\n     |- Try 35 * 30 = 1050. Evaluate 1050 != 50, drop this branch.\n     |- Try 35 \/ 30 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 28 - 7 = 21. Add 21 to the number set. Current number set: [21, 30], target: 50, just two numbers left.\n     |- Try 30 + 21 = 51. Evaluate 51 != 50, drop this branch.\n     |- Try 30 - 21 = 9. Evaluate 9 != 50, drop this branch.\n     |- Try 30 * 21 = 630. Evaluate 630 != 50, drop this branch.\n     |- Try 30 \/ 21 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 28 * 7 = 196. Add 196 to the number set. Current number set: [196, 30], target: 50, just two numbers left.\n     |- Try 196 + 30 = 226. Evaluate 226 != 50, drop this branch.\n     |- Try 196 - 30 = 166. Evaluate 166 != 50, drop this branch.\n     |- Try 196 * 30 = 5880. 5880 exceeds the maximum intermediate result, drop this branch.\n     |- Try 196 \/ 30 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 28 \/ 7 = 4. Add 4 to the number set. Current number set: [4, 30], target: 50, just two numbers left.\n     |- Try 30 + 4 = 34. Evaluate 34 != 50, drop this branch.\n     |- Try 30 - 4 = 26. Evaluate 26 != 50, drop this branch.\n     |- Try 30 * 4 = 120. Evaluate 120 != 50, drop this branch.\n     |- Try 30 \/ 4 = 7.5. 7.5 is a decimal, drop this branch.\n  |- Try 44 * 14 = 616. Add 616 to the number set. Current number set: [616, 28, 7], target: 50. Options for choosing two numbers: [(616, 28), (616, 7), (28, 7)].\n   |- Pick two numbers (616, 28) (numbers left: [7]). Try possible operations.\n    |- Try 616 + 28 = 644. Add 644 to the number set. Current number set: [644, 7], target: 50, just two numbers left.\n     |- Try 644 + 7 = 651. Evaluate 651 != 50, drop this branch.\n     |- Try 644 - 7 = 637. Evaluate 637 != 50, drop this branch.\n     |- Try 644 * 7 = 4508. 4508 exceeds the maximum intermediate result, drop this branch.\n     |- Try 644 \/ 7 = 92. Evaluate 92 != 50, drop this branch.\n    |- Try 616 - 28 = 588. Add 588 to the number set. Current number set: [588, 7], target: 50, just two numbers left.\n     |- Try 588 + 7 = 595. Evaluate 595 != 50, drop this branch.\n     |- Try 588 - 7 = 581. Evaluate 581 != 50, drop this branch.\n     |- Try 588 * 7 = 4116. 4116 exceeds the maximum intermediate result, drop this branch.\n     |- Try 588 \/ 7 = 84. Evaluate 84 != 50, drop this branch.\n    |- Try 616 * 28 = 17248. 17248 exceeds the maximum intermediate result, drop this branch.\n    |- Try 616 \/ 28 = 22. Add 22 to the number set. Current number set: [22, 7], target: 50, just two numbers left.\n     |- Try 22 + 7 = 29. Evaluate 29 != 50, drop this branch.\n     |- Try 22 - 7 = 15. Evaluate 15 != 50, drop this branch.\n     |- Try 22 * 7 = 154. Evaluate 154 != 50, drop this branch.\n     |- Try 22 \/ 7 = 3.1. 3.1 is a decimal, drop this branch.\n   |- Pick two numbers (616, 7) (numbers left: [28]). Try possible operations.\n    |- Try 616 + 7 = 623. Add 623 to the number set. Current number set: [623, 28], target: 50, just two numbers left.\n     |- Try 623 + 28 = 651. Evaluate 651 != 50, drop this branch.\n     |- Try 623 - 28 = 595. Evaluate 595 != 50, drop this branch.\n     |- Try 623 * 28 = 17444. 17444 exceeds the maximum intermediate result, drop this branch.\n     |- Try 623 \/ 28 = 22.2. 22.2 is a decimal, drop this branch.\n    |- Try 616 - 7 = 609. Add 609 to the number set. Current number set: [609, 28], target: 50, just two numbers left.\n     |- Try 609 + 28 = 637. Evaluate 637 != 50, drop this branch.\n     |- Try 609 - 28 = 581. Evaluate 581 != 50, drop this branch.\n     |- Try 609 * 28 = 17052. 17052 exceeds the maximum intermediate result, drop this branch.\n     |- Try 609 \/ 28 = 21.8. 21.8 is a decimal, drop this branch.\n    |- Try 616 * 7 = 4312. 4312 exceeds the maximum intermediate result, drop this branch.\n    |- Try 616 \/ 7 = 88. Add 88 to the number set. Current number set: [88, 28], target: 50, just two numbers left.\n     |- Try 88 + 28 = 116. Evaluate 116 != 50, drop this branch.\n     |- Try 88 - 28 = 60. Evaluate 60 != 50, drop this branch.\n     |- Try 88 * 28 = 2464. 2464 exceeds the maximum intermediate result, drop this branch.\n     |- Try 88 \/ 28 = 3.1. 3.1 is a decimal, drop this branch.\n   |- Pick two numbers (28, 7) (numbers left: [616]). Try possible operations.\n    |- Try 28 + 7 = 35. Add 35 to the number set. Current number set: [35, 616], target: 50, just two numbers left.\n     |- Try 616 + 35 = 651. Evaluate 651 != 50, drop this branch.\n     |- Try 616 - 35 = 581. Evaluate 581 != 50, drop this branch.\n     |- Try 616 * 35 = 21560. 21560 exceeds the maximum intermediate result, drop this branch.\n     |- Try 616 \/ 35 = 17.6. 17.6 is a decimal, drop this branch.\n    |- Try 28 - 7 = 21. Add 21 to the number set. Current number set: [21, 616], target: 50, just two numbers left.\n     |- Try 616 + 21 = 637. Evaluate 637 != 50, drop this branch.\n     |- Try 616 - 21 = 595. Evaluate 595 != 50, drop this branch.\n     |- Try 616 * 21 = 12936. 12936 exceeds the maximum intermediate result, drop this branch.\n     |- Try 616 \/ 21 = 29.3. 29.3 is a decimal, drop this branch.\n    |- Try 28 * 7 = 196. Add 196 to the number set. Current number set: [196, 616], target: 50, just two numbers left.\n     |- Try 616 + 196 = 812. Evaluate 812 != 50, drop this branch.\n     |- Try 616 - 196 = 420. Evaluate 420 != 50, drop this branch.\n     |- Try 616 * 196 = 120736. 120736 exceeds the maximum intermediate result, drop this branch.\n     |- Try 616 \/ 196 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 28 \/ 7 = 4. Add 4 to the number set. Current number set: [4, 616], target: 50, just two numbers left.\n     |- Try 616 + 4 = 620. Evaluate 620 != 50, drop this branch.\n     |- Try 616 - 4 = 612. Evaluate 612 != 50, drop this branch.\n     |- Try 616 * 4 = 2464. 2464 exceeds the maximum intermediate result, drop this branch.\n     |- Try 616 \/ 4 = 154. Evaluate 154 != 50, drop this branch.\n  |- Try 44 \/ 14 = 3.1. 3.1 is a decimal, drop this branch.\n |- Pick two numbers (14, 28) (numbers left: [44, 7]). Try possible operations.\n  |- Try 28 + 14 = 42. Add 42 to the number set. Current number set: [42, 44, 7], target: 50. Options for choosing two numbers: [(42, 44), (42, 7), (44, 7)].\n   |- Pick two numbers (42, 44) (numbers left: [7]). Try possible operations.\n    |- Try 44 + 42 = 86. Add 86 to the number set. Current number set: [86, 7], target: 50, just two numbers left.\n     |- Try 86 + 7 = 93. Evaluate 93 != 50, drop this branch.\n     |- Try 86 - 7 = 79. Evaluate 79 != 50, drop this branch.\n     |- Try 86 * 7 = 602. Evaluate 602 != 50, drop this branch.\n     |- Try 86 \/ 7 = 12.3. 12.3 is a decimal, drop this branch.\n    |- Try 44 - 42 = 2. Add 2 to the number set. Current number set: [2, 7], target: 50, just two numbers left.\n     |- Try 7 + 2 = 9. Evaluate 9 != 50, drop this branch.\n     |- Try 7 - 2 = 5. Evaluate 5 != 50, drop this branch.\n     |- Try 7 * 2 = 14. Evaluate 14 != 50, drop this branch.\n     |- Try 7 \/ 2 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 44 * 42 = 1848. Add 1848 to the number set. Current number set: [1848, 7], target: 50, just two numbers left.\n     |- Try 1848 + 7 = 1855. Evaluate 1855 != 50, drop this branch.\n     |- Try 1848 - 7 = 1841. Evaluate 1841 != 50, drop this branch.\n     |- Try 1848 * 7 = 12936. 12936 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1848 \/ 7 = 264. Evaluate 264 != 50, drop this branch.\n    |- Try 44 \/ 42 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (42, 7) (numbers left: [44]). Try possible operations.\n    |- Try 42 + 7 = 49. Add 49 to the number set. Current number set: [49, 44], target: 50, just two numbers left.\n     |- Try 49 + 44 = 93. Evaluate 93 != 50, drop this branch.\n     |- Try 49 - 44 = 5. Evaluate 5 != 50, drop this branch.\n     |- Try 49 * 44 = 2156. 2156 exceeds the maximum intermediate result, drop this branch.\n     |- Try 49 \/ 44 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 42 - 7 = 35. Add 35 to the number set. Current number set: [35, 44], target: 50, just two numbers left.\n     |- Try 44 + 35 = 79. Evaluate 79 != 50, drop this branch.\n     |- Try 44 - 35 = 9. Evaluate 9 != 50, drop this branch.\n     |- Try 44 * 35 = 1540. Evaluate 1540 != 50, drop this branch.\n     |- Try 44 \/ 35 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 42 * 7 = 294. Add 294 to the number set. Current number set: [294, 44], target: 50, just two numbers left.\n     |- Try 294 + 44 = 338. Evaluate 338 != 50, drop this branch.\n     |- Try 294 - 44 = 250. Evaluate 250 != 50, drop this branch.\n     |- Try 294 * 44 = 12936. 12936 exceeds the maximum intermediate result, drop this branch.\n     |- Try 294 \/ 44 = 6.7. 6.7 is a decimal, drop this branch.\n    |- Try 42 \/ 7 = 6. Add 6 to the number set. Current number set: [6, 44], target: 50, just two numbers left.\n     |- Try 44 + 6 = 50. Evaluate 50 == 50, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 44 + 6 = 50\nThe step before: 42 \/ 7 = 6\nThe first step: 28 + 14 = 42\n\nOutput the solution in the required format:\n<Solution>\n28 + 14 = 42\n42 \/ 7 = 6\n44 + 6 = 50\n<\/Solution>\n","item":{"nums":[14,44,28,7],"solution":["28 + 14 = 42","42 \/ 7 = 6","44 + 6 = 50"],"target":50}}
+{"instance_id":"countdown_8k_62","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [43, 2, 31, 11]\nTarget: 35","reference_output":"# Search Procedure\nInitial number set: [43, 2, 31, 11], target: 35. Options for choosing two numbers: [(43, 2), (43, 31), (43, 11), (2, 31), (2, 11), (31, 11)].\n |- Pick two numbers (43, 2) (numbers left: [31, 11]). Try possible operations.\n  |- Try 43 + 2 = 45. Add 45 to the number set. Current number set: [45, 31, 11], target: 35. Options for choosing two numbers: [(45, 31), (45, 11), (31, 11)].\n   |- Pick two numbers (45, 31) (numbers left: [11]). Try possible operations.\n    |- Try 45 + 31 = 76. Add 76 to the number set. Current number set: [76, 11], target: 35, just two numbers left.\n     |- Try 76 + 11 = 87. Evaluate 87 != 35, drop this branch.\n     |- Try 76 - 11 = 65. Evaluate 65 != 35, drop this branch.\n     |- Try 76 * 11 = 836. Evaluate 836 != 35, drop this branch.\n     |- Try 76 \/ 11 = 6.9. 6.9 is a decimal, drop this branch.\n    |- Try 45 - 31 = 14. Add 14 to the number set. Current number set: [14, 11], target: 35, just two numbers left.\n     |- Try 14 + 11 = 25. Evaluate 25 != 35, drop this branch.\n     |- Try 14 - 11 = 3. Evaluate 3 != 35, drop this branch.\n     |- Try 14 * 11 = 154. Evaluate 154 != 35, drop this branch.\n     |- Try 14 \/ 11 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 45 * 31 = 1395. Add 1395 to the number set. Current number set: [1395, 11], target: 35, just two numbers left.\n     |- Try 1395 + 11 = 1406. Evaluate 1406 != 35, drop this branch.\n     |- Try 1395 - 11 = 1384. Evaluate 1384 != 35, drop this branch.\n     |- Try 1395 * 11 = 15345. 15345 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1395 \/ 11 = 126.8. 126.8 is a decimal, drop this branch.\n    |- Try 45 \/ 31 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (45, 11) (numbers left: [31]). Try possible operations.\n    |- Try 45 + 11 = 56. Add 56 to the number set. Current number set: [56, 31], target: 35, just two numbers left.\n     |- Try 56 + 31 = 87. Evaluate 87 != 35, drop this branch.\n     |- Try 56 - 31 = 25. Evaluate 25 != 35, drop this branch.\n     |- Try 56 * 31 = 1736. Evaluate 1736 != 35, drop this branch.\n     |- Try 56 \/ 31 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 45 - 11 = 34. Add 34 to the number set. Current number set: [34, 31], target: 35, just two numbers left.\n     |- Try 34 + 31 = 65. Evaluate 65 != 35, drop this branch.\n     |- Try 34 - 31 = 3. Evaluate 3 != 35, drop this branch.\n     |- Try 34 * 31 = 1054. Evaluate 1054 != 35, drop this branch.\n     |- Try 34 \/ 31 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 45 * 11 = 495. Add 495 to the number set. Current number set: [495, 31], target: 35, just two numbers left.\n     |- Try 495 + 31 = 526. Evaluate 526 != 35, drop this branch.\n     |- Try 495 - 31 = 464. Evaluate 464 != 35, drop this branch.\n     |- Try 495 * 31 = 15345. 15345 exceeds the maximum intermediate result, drop this branch.\n     |- Try 495 \/ 31 = 16.0. 16.0 is a decimal, drop this branch.\n    |- Try 45 \/ 11 = 4.1. 4.1 is a decimal, drop this branch.\n   |- Pick two numbers (31, 11) (numbers left: [45]). Try possible operations.\n    |- Try 31 + 11 = 42. Add 42 to the number set. Current number set: [42, 45], target: 35, just two numbers left.\n     |- Try 45 + 42 = 87. Evaluate 87 != 35, drop this branch.\n     |- Try 45 - 42 = 3. Evaluate 3 != 35, drop this branch.\n     |- Try 45 * 42 = 1890. Evaluate 1890 != 35, drop this branch.\n     |- Try 45 \/ 42 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 31 - 11 = 20. Add 20 to the number set. Current number set: [20, 45], target: 35, just two numbers left.\n     |- Try 45 + 20 = 65. Evaluate 65 != 35, drop this branch.\n     |- Try 45 - 20 = 25. Evaluate 25 != 35, drop this branch.\n     |- Try 45 * 20 = 900. Evaluate 900 != 35, drop this branch.\n     |- Try 45 \/ 20 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 31 * 11 = 341. Add 341 to the number set. Current number set: [341, 45], target: 35, just two numbers left.\n     |- Try 341 + 45 = 386. Evaluate 386 != 35, drop this branch.\n     |- Try 341 - 45 = 296. Evaluate 296 != 35, drop this branch.\n     |- Try 341 * 45 = 15345. 15345 exceeds the maximum intermediate result, drop this branch.\n     |- Try 341 \/ 45 = 7.6. 7.6 is a decimal, drop this branch.\n    |- Try 31 \/ 11 = 2.8. 2.8 is a decimal, drop this branch.\n  |- Try 43 - 2 = 41. Add 41 to the number set. Current number set: [41, 31, 11], target: 35. Options for choosing two numbers: [(41, 31), (41, 11), (31, 11)].\n   |- Pick two numbers (41, 31) (numbers left: [11]). Try possible operations.\n    |- Try 41 + 31 = 72. Add 72 to the number set. Current number set: [72, 11], target: 35, just two numbers left.\n     |- Try 72 + 11 = 83. Evaluate 83 != 35, drop this branch.\n     |- Try 72 - 11 = 61. Evaluate 61 != 35, drop this branch.\n     |- Try 72 * 11 = 792. Evaluate 792 != 35, drop this branch.\n     |- Try 72 \/ 11 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 41 - 31 = 10. Add 10 to the number set. Current number set: [10, 11], target: 35, just two numbers left.\n     |- Try 11 + 10 = 21. Evaluate 21 != 35, drop this branch.\n     |- Try 11 - 10 = 1. Evaluate 1 != 35, drop this branch.\n     |- Try 11 * 10 = 110. Evaluate 110 != 35, drop this branch.\n     |- Try 11 \/ 10 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 41 * 31 = 1271. Add 1271 to the number set. Current number set: [1271, 11], target: 35, just two numbers left.\n     |- Try 1271 + 11 = 1282. Evaluate 1282 != 35, drop this branch.\n     |- Try 1271 - 11 = 1260. Evaluate 1260 != 35, drop this branch.\n     |- Try 1271 * 11 = 13981. 13981 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1271 \/ 11 = 115.5. 115.5 is a decimal, drop this branch.\n    |- Try 41 \/ 31 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (41, 11) (numbers left: [31]). Try possible operations.\n    |- Try 41 + 11 = 52. Add 52 to the number set. Current number set: [52, 31], target: 35, just two numbers left.\n     |- Try 52 + 31 = 83. Evaluate 83 != 35, drop this branch.\n     |- Try 52 - 31 = 21. Evaluate 21 != 35, drop this branch.\n     |- Try 52 * 31 = 1612. Evaluate 1612 != 35, drop this branch.\n     |- Try 52 \/ 31 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 41 - 11 = 30. Add 30 to the number set. Current number set: [30, 31], target: 35, just two numbers left.\n     |- Try 31 + 30 = 61. Evaluate 61 != 35, drop this branch.\n     |- Try 31 - 30 = 1. Evaluate 1 != 35, drop this branch.\n     |- Try 31 * 30 = 930. Evaluate 930 != 35, drop this branch.\n     |- Try 31 \/ 30 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 41 * 11 = 451. Add 451 to the number set. Current number set: [451, 31], target: 35, just two numbers left.\n     |- Try 451 + 31 = 482. Evaluate 482 != 35, drop this branch.\n     |- Try 451 - 31 = 420. Evaluate 420 != 35, drop this branch.\n     |- Try 451 * 31 = 13981. 13981 exceeds the maximum intermediate result, drop this branch.\n     |- Try 451 \/ 31 = 14.5. 14.5 is a decimal, drop this branch.\n    |- Try 41 \/ 11 = 3.7. 3.7 is a decimal, drop this branch.\n   |- Pick two numbers (31, 11) (numbers left: [41]). Try possible operations.\n    |- Try 31 + 11 = 42. Add 42 to the number set. Current number set: [42, 41], target: 35, just two numbers left.\n     |- Try 42 + 41 = 83. Evaluate 83 != 35, drop this branch.\n     |- Try 42 - 41 = 1. Evaluate 1 != 35, drop this branch.\n     |- Try 42 * 41 = 1722. Evaluate 1722 != 35, drop this branch.\n     |- Try 42 \/ 41 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 31 - 11 = 20. Add 20 to the number set. Current number set: [20, 41], target: 35, just two numbers left.\n     |- Try 41 + 20 = 61. Evaluate 61 != 35, drop this branch.\n     |- Try 41 - 20 = 21. Evaluate 21 != 35, drop this branch.\n     |- Try 41 * 20 = 820. Evaluate 820 != 35, drop this branch.\n     |- Try 41 \/ 20 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 31 * 11 = 341. Add 341 to the number set. Current number set: [341, 41], target: 35, just two numbers left.\n     |- Try 341 + 41 = 382. Evaluate 382 != 35, drop this branch.\n     |- Try 341 - 41 = 300. Evaluate 300 != 35, drop this branch.\n     |- Try 341 * 41 = 13981. 13981 exceeds the maximum intermediate result, drop this branch.\n     |- Try 341 \/ 41 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 31 \/ 11 = 2.8. 2.8 is a decimal, drop this branch.\n  |- Try 43 * 2 = 86. Add 86 to the number set. Current number set: [86, 31, 11], target: 35. Options for choosing two numbers: [(86, 31), (86, 11), (31, 11)].\n   |- Pick two numbers (86, 31) (numbers left: [11]). Try possible operations.\n    |- Try 86 + 31 = 117. Add 117 to the number set. Current number set: [117, 11], target: 35, just two numbers left.\n     |- Try 117 + 11 = 128. Evaluate 128 != 35, drop this branch.\n     |- Try 117 - 11 = 106. Evaluate 106 != 35, drop this branch.\n     |- Try 117 * 11 = 1287. Evaluate 1287 != 35, drop this branch.\n     |- Try 117 \/ 11 = 10.6. 10.6 is a decimal, drop this branch.\n    |- Try 86 - 31 = 55. Add 55 to the number set. Current number set: [55, 11], target: 35, just two numbers left.\n     |- Try 55 + 11 = 66. Evaluate 66 != 35, drop this branch.\n     |- Try 55 - 11 = 44. Evaluate 44 != 35, drop this branch.\n     |- Try 55 * 11 = 605. Evaluate 605 != 35, drop this branch.\n     |- Try 55 \/ 11 = 5. Evaluate 5 != 35, drop this branch.\n    |- Try 86 * 31 = 2666. 2666 exceeds the maximum intermediate result, drop this branch.\n    |- Try 86 \/ 31 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (86, 11) (numbers left: [31]). Try possible operations.\n    |- Try 86 + 11 = 97. Add 97 to the number set. Current number set: [97, 31], target: 35, just two numbers left.\n     |- Try 97 + 31 = 128. Evaluate 128 != 35, drop this branch.\n     |- Try 97 - 31 = 66. Evaluate 66 != 35, drop this branch.\n     |- Try 97 * 31 = 3007. 3007 exceeds the maximum intermediate result, drop this branch.\n     |- Try 97 \/ 31 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 86 - 11 = 75. Add 75 to the number set. Current number set: [75, 31], target: 35, just two numbers left.\n     |- Try 75 + 31 = 106. Evaluate 106 != 35, drop this branch.\n     |- Try 75 - 31 = 44. Evaluate 44 != 35, drop this branch.\n     |- Try 75 * 31 = 2325. 2325 exceeds the maximum intermediate result, drop this branch.\n     |- Try 75 \/ 31 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 86 * 11 = 946. Add 946 to the number set. Current number set: [946, 31], target: 35, just two numbers left.\n     |- Try 946 + 31 = 977. Evaluate 977 != 35, drop this branch.\n     |- Try 946 - 31 = 915. Evaluate 915 != 35, drop this branch.\n     |- Try 946 * 31 = 29326. 29326 exceeds the maximum intermediate result, drop this branch.\n     |- Try 946 \/ 31 = 30.5. 30.5 is a decimal, drop this branch.\n    |- Try 86 \/ 11 = 7.8. 7.8 is a decimal, drop this branch.\n   |- Pick two numbers (31, 11) (numbers left: [86]). Try possible operations.\n    |- Try 31 + 11 = 42. Add 42 to the number set. Current number set: [42, 86], target: 35, just two numbers left.\n     |- Try 86 + 42 = 128. Evaluate 128 != 35, drop this branch.\n     |- Try 86 - 42 = 44. Evaluate 44 != 35, drop this branch.\n     |- Try 86 * 42 = 3612. 3612 exceeds the maximum intermediate result, drop this branch.\n     |- Try 86 \/ 42 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 31 - 11 = 20. Add 20 to the number set. Current number set: [20, 86], target: 35, just two numbers left.\n     |- Try 86 + 20 = 106. Evaluate 106 != 35, drop this branch.\n     |- Try 86 - 20 = 66. Evaluate 66 != 35, drop this branch.\n     |- Try 86 * 20 = 1720. Evaluate 1720 != 35, drop this branch.\n     |- Try 86 \/ 20 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 31 * 11 = 341. Add 341 to the number set. Current number set: [341, 86], target: 35, just two numbers left.\n     |- Try 341 + 86 = 427. Evaluate 427 != 35, drop this branch.\n     |- Try 341 - 86 = 255. Evaluate 255 != 35, drop this branch.\n     |- Try 341 * 86 = 29326. 29326 exceeds the maximum intermediate result, drop this branch.\n     |- Try 341 \/ 86 = 4.0. 4.0 is a decimal, drop this branch.\n    |- Try 31 \/ 11 = 2.8. 2.8 is a decimal, drop this branch.\n  |- Try 43 \/ 2 = 21.5. 21.5 is a decimal, drop this branch.\n |- Pick two numbers (43, 31) (numbers left: [2, 11]). Try possible operations.\n  |- Try 43 + 31 = 74. Add 74 to the number set. Current number set: [74, 2, 11], target: 35. Options for choosing two numbers: [(74, 2), (74, 11), (2, 11)].\n   |- Pick two numbers (74, 2) (numbers left: [11]). Try possible operations.\n    |- Try 74 + 2 = 76. Add 76 to the number set. Current number set: [76, 11], target: 35, just two numbers left.\n     |- Try 76 + 11 = 87. Evaluate 87 != 35, drop this branch.\n     |- Try 76 - 11 = 65. Evaluate 65 != 35, drop this branch.\n     |- Try 76 * 11 = 836. Evaluate 836 != 35, drop this branch.\n     |- Try 76 \/ 11 = 6.9. 6.9 is a decimal, drop this branch.\n    |- Try 74 - 2 = 72. Add 72 to the number set. Current number set: [72, 11], target: 35, just two numbers left.\n     |- Try 72 + 11 = 83. Evaluate 83 != 35, drop this branch.\n     |- Try 72 - 11 = 61. Evaluate 61 != 35, drop this branch.\n     |- Try 72 * 11 = 792. Evaluate 792 != 35, drop this branch.\n     |- Try 72 \/ 11 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 74 * 2 = 148. Add 148 to the number set. Current number set: [148, 11], target: 35, just two numbers left.\n     |- Try 148 + 11 = 159. Evaluate 159 != 35, drop this branch.\n     |- Try 148 - 11 = 137. Evaluate 137 != 35, drop this branch.\n     |- Try 148 * 11 = 1628. Evaluate 1628 != 35, drop this branch.\n     |- Try 148 \/ 11 = 13.5. 13.5 is a decimal, drop this branch.\n    |- Try 74 \/ 2 = 37. Add 37 to the number set. Current number set: [37, 11], target: 35, just two numbers left.\n     |- Try 37 + 11 = 48. Evaluate 48 != 35, drop this branch.\n     |- Try 37 - 11 = 26. Evaluate 26 != 35, drop this branch.\n     |- Try 37 * 11 = 407. Evaluate 407 != 35, drop this branch.\n     |- Try 37 \/ 11 = 3.4. 3.4 is a decimal, drop this branch.\n   |- Pick two numbers (74, 11) (numbers left: [2]). Try possible operations.\n    |- Try 74 + 11 = 85. Add 85 to the number set. Current number set: [85, 2], target: 35, just two numbers left.\n     |- Try 85 + 2 = 87. Evaluate 87 != 35, drop this branch.\n     |- Try 85 - 2 = 83. Evaluate 83 != 35, drop this branch.\n     |- Try 85 * 2 = 170. Evaluate 170 != 35, drop this branch.\n     |- Try 85 \/ 2 = 42.5. 42.5 is a decimal, drop this branch.\n    |- Try 74 - 11 = 63. Add 63 to the number set. Current number set: [63, 2], target: 35, just two numbers left.\n     |- Try 63 + 2 = 65. Evaluate 65 != 35, drop this branch.\n     |- Try 63 - 2 = 61. Evaluate 61 != 35, drop this branch.\n     |- Try 63 * 2 = 126. Evaluate 126 != 35, drop this branch.\n     |- Try 63 \/ 2 = 31.5. 31.5 is a decimal, drop this branch.\n    |- Try 74 * 11 = 814. Add 814 to the number set. Current number set: [814, 2], target: 35, just two numbers left.\n     |- Try 814 + 2 = 816. Evaluate 816 != 35, drop this branch.\n     |- Try 814 - 2 = 812. Evaluate 812 != 35, drop this branch.\n     |- Try 814 * 2 = 1628. Evaluate 1628 != 35, drop this branch.\n     |- Try 814 \/ 2 = 407. Evaluate 407 != 35, drop this branch.\n    |- Try 74 \/ 11 = 6.7. 6.7 is a decimal, drop this branch.\n   |- Pick two numbers (2, 11) (numbers left: [74]). Try possible operations.\n    |- Try 11 + 2 = 13. Add 13 to the number set. Current number set: [13, 74], target: 35, just two numbers left.\n     |- Try 74 + 13 = 87. Evaluate 87 != 35, drop this branch.\n     |- Try 74 - 13 = 61. Evaluate 61 != 35, drop this branch.\n     |- Try 74 * 13 = 962. Evaluate 962 != 35, drop this branch.\n     |- Try 74 \/ 13 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 11 - 2 = 9. Add 9 to the number set. Current number set: [9, 74], target: 35, just two numbers left.\n     |- Try 74 + 9 = 83. Evaluate 83 != 35, drop this branch.\n     |- Try 74 - 9 = 65. Evaluate 65 != 35, drop this branch.\n     |- Try 74 * 9 = 666. Evaluate 666 != 35, drop this branch.\n     |- Try 74 \/ 9 = 8.2. 8.2 is a decimal, drop this branch.\n    |- Try 11 * 2 = 22. Add 22 to the number set. Current number set: [22, 74], target: 35, just two numbers left.\n     |- Try 74 + 22 = 96. Evaluate 96 != 35, drop this branch.\n     |- Try 74 - 22 = 52. Evaluate 52 != 35, drop this branch.\n     |- Try 74 * 22 = 1628. Evaluate 1628 != 35, drop this branch.\n     |- Try 74 \/ 22 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 11 \/ 2 = 5.5. 5.5 is a decimal, drop this branch.\n  |- Try 43 - 31 = 12. Add 12 to the number set. Current number set: [12, 2, 11], target: 35. Options for choosing two numbers: [(12, 2), (12, 11), (2, 11)].\n   |- Pick two numbers (12, 2) (numbers left: [11]). Try possible operations.\n    |- Try 12 + 2 = 14. Add 14 to the number set. Current number set: [14, 11], target: 35, just two numbers left.\n     |- Try 14 + 11 = 25. Evaluate 25 != 35, drop this branch.\n     |- Try 14 - 11 = 3. Evaluate 3 != 35, drop this branch.\n     |- Try 14 * 11 = 154. Evaluate 154 != 35, drop this branch.\n     |- Try 14 \/ 11 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 12 - 2 = 10. Add 10 to the number set. Current number set: [10, 11], target: 35, just two numbers left.\n     |- Try 11 + 10 = 21. Evaluate 21 != 35, drop this branch.\n     |- Try 11 - 10 = 1. Evaluate 1 != 35, drop this branch.\n     |- Try 11 * 10 = 110. Evaluate 110 != 35, drop this branch.\n     |- Try 11 \/ 10 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 12 * 2 = 24. Add 24 to the number set. Current number set: [24, 11], target: 35, just two numbers left.\n     |- Try 24 + 11 = 35. Evaluate 35 == 35, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 24 + 11 = 35\nThe step before: 12 * 2 = 24\nThe first step: 43 - 31 = 12\n\nOutput the solution in the required format:\n<Solution>\n43 - 31 = 12\n12 * 2 = 24\n24 + 11 = 35\n<\/Solution>\n","item":{"nums":[43,2,31,11],"solution":["43 - 31 = 12","12 * 2 = 24","24 + 11 = 35"],"target":35}}
+{"instance_id":"countdown_8k_63","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [25, 24, 38, 42]\nTarget: 16","reference_output":"# Search Procedure\nInitial number set: [25, 24, 38, 42], target: 16. Options for choosing two numbers: [(25, 24), (25, 38), (25, 42), (24, 38), (24, 42), (38, 42)].\n |- Pick two numbers (25, 24) (numbers left: [38, 42]). Try possible operations.\n  |- Try 25 + 24 = 49. Add 49 to the number set. Current number set: [49, 38, 42], target: 16. Options for choosing two numbers: [(49, 38), (49, 42), (38, 42)].\n   |- Pick two numbers (49, 38) (numbers left: [42]). Try possible operations.\n    |- Try 49 + 38 = 87. Add 87 to the number set. Current number set: [87, 42], target: 16, just two numbers left.\n     |- Try 87 + 42 = 129. Evaluate 129 != 16, drop this branch.\n     |- Try 87 - 42 = 45. Evaluate 45 != 16, drop this branch.\n     |- Try 87 * 42 = 3654. 3654 exceeds the maximum intermediate result, drop this branch.\n     |- Try 87 \/ 42 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 49 - 38 = 11. Add 11 to the number set. Current number set: [11, 42], target: 16, just two numbers left.\n     |- Try 42 + 11 = 53. Evaluate 53 != 16, drop this branch.\n     |- Try 42 - 11 = 31. Evaluate 31 != 16, drop this branch.\n     |- Try 42 * 11 = 462. Evaluate 462 != 16, drop this branch.\n     |- Try 42 \/ 11 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 49 * 38 = 1862. Add 1862 to the number set. Current number set: [1862, 42], target: 16, just two numbers left.\n     |- Try 1862 + 42 = 1904. Evaluate 1904 != 16, drop this branch.\n     |- Try 1862 - 42 = 1820. Evaluate 1820 != 16, drop this branch.\n     |- Try 1862 * 42 = 78204. 78204 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1862 \/ 42 = 44.3. 44.3 is a decimal, drop this branch.\n    |- Try 49 \/ 38 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (49, 42) (numbers left: [38]). Try possible operations.\n    |- Try 49 + 42 = 91. Add 91 to the number set. Current number set: [91, 38], target: 16, just two numbers left.\n     |- Try 91 + 38 = 129. Evaluate 129 != 16, drop this branch.\n     |- Try 91 - 38 = 53. Evaluate 53 != 16, drop this branch.\n     |- Try 91 * 38 = 3458. 3458 exceeds the maximum intermediate result, drop this branch.\n     |- Try 91 \/ 38 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 49 - 42 = 7. Add 7 to the number set. Current number set: [7, 38], target: 16, just two numbers left.\n     |- Try 38 + 7 = 45. Evaluate 45 != 16, drop this branch.\n     |- Try 38 - 7 = 31. Evaluate 31 != 16, drop this branch.\n     |- Try 38 * 7 = 266. Evaluate 266 != 16, drop this branch.\n     |- Try 38 \/ 7 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 49 * 42 = 2058. 2058 exceeds the maximum intermediate result, drop this branch.\n    |- Try 49 \/ 42 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (38, 42) (numbers left: [49]). Try possible operations.\n    |- Try 42 + 38 = 80. Add 80 to the number set. Current number set: [80, 49], target: 16, just two numbers left.\n     |- Try 80 + 49 = 129. Evaluate 129 != 16, drop this branch.\n     |- Try 80 - 49 = 31. Evaluate 31 != 16, drop this branch.\n     |- Try 80 * 49 = 3920. 3920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 80 \/ 49 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 42 - 38 = 4. Add 4 to the number set. Current number set: [4, 49], target: 16, just two numbers left.\n     |- Try 49 + 4 = 53. Evaluate 53 != 16, drop this branch.\n     |- Try 49 - 4 = 45. Evaluate 45 != 16, drop this branch.\n     |- Try 49 * 4 = 196. Evaluate 196 != 16, drop this branch.\n     |- Try 49 \/ 4 = 12.2. 12.2 is a decimal, drop this branch.\n    |- Try 42 * 38 = 1596. Add 1596 to the number set. Current number set: [1596, 49], target: 16, just two numbers left.\n     |- Try 1596 + 49 = 1645. Evaluate 1645 != 16, drop this branch.\n     |- Try 1596 - 49 = 1547. Evaluate 1547 != 16, drop this branch.\n     |- Try 1596 * 49 = 78204. 78204 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1596 \/ 49 = 32.6. 32.6 is a decimal, drop this branch.\n    |- Try 42 \/ 38 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 25 - 24 = 1. Add 1 to the number set. Current number set: [1, 38, 42], target: 16. Options for choosing two numbers: [(1, 38), (1, 42), (38, 42)].\n   |- Pick two numbers (1, 38) (numbers left: [42]). Try possible operations.\n    |- Try 38 + 1 = 39. Add 39 to the number set. Current number set: [39, 42], target: 16, just two numbers left.\n     |- Try 42 + 39 = 81. Evaluate 81 != 16, drop this branch.\n     |- Try 42 - 39 = 3. Evaluate 3 != 16, drop this branch.\n     |- Try 42 * 39 = 1638. Evaluate 1638 != 16, drop this branch.\n     |- Try 42 \/ 39 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 38 - 1 = 37. Add 37 to the number set. Current number set: [37, 42], target: 16, just two numbers left.\n     |- Try 42 + 37 = 79. Evaluate 79 != 16, drop this branch.\n     |- Try 42 - 37 = 5. Evaluate 5 != 16, drop this branch.\n     |- Try 42 * 37 = 1554. Evaluate 1554 != 16, drop this branch.\n     |- Try 42 \/ 37 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 38 * 1 = 38. Add 38 to the number set. Current number set: [38, 42], target: 16, just two numbers left.\n     |- Try 42 + 38 = 80. Evaluate 80 != 16, drop this branch.\n     |- Try 42 - 38 = 4. Evaluate 4 != 16, drop this branch.\n     |- Try 42 * 38 = 1596. Evaluate 1596 != 16, drop this branch.\n     |- Try 42 \/ 38 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 38 \/ 1 = 38. Add 38 to the number set. Current number set: [38, 42], target: 16, just two numbers left.\n     |- Try 42 + 38 = 80. Evaluate 80 != 16, drop this branch.\n     |- Try 42 - 38 = 4. Evaluate 4 != 16, drop this branch.\n     |- Try 42 * 38 = 1596. Evaluate 1596 != 16, drop this branch.\n     |- Try 42 \/ 38 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (1, 42) (numbers left: [38]). Try possible operations.\n    |- Try 42 + 1 = 43. Add 43 to the number set. Current number set: [43, 38], target: 16, just two numbers left.\n     |- Try 43 + 38 = 81. Evaluate 81 != 16, drop this branch.\n     |- Try 43 - 38 = 5. Evaluate 5 != 16, drop this branch.\n     |- Try 43 * 38 = 1634. Evaluate 1634 != 16, drop this branch.\n     |- Try 43 \/ 38 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 42 - 1 = 41. Add 41 to the number set. Current number set: [41, 38], target: 16, just two numbers left.\n     |- Try 41 + 38 = 79. Evaluate 79 != 16, drop this branch.\n     |- Try 41 - 38 = 3. Evaluate 3 != 16, drop this branch.\n     |- Try 41 * 38 = 1558. Evaluate 1558 != 16, drop this branch.\n     |- Try 41 \/ 38 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 42 * 1 = 42. Add 42 to the number set. Current number set: [42, 38], target: 16, just two numbers left.\n     |- Try 42 + 38 = 80. Evaluate 80 != 16, drop this branch.\n     |- Try 42 - 38 = 4. Evaluate 4 != 16, drop this branch.\n     |- Try 42 * 38 = 1596. Evaluate 1596 != 16, drop this branch.\n     |- Try 42 \/ 38 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 42 \/ 1 = 42. Add 42 to the number set. Current number set: [42, 38], target: 16, just two numbers left.\n     |- Try 42 + 38 = 80. Evaluate 80 != 16, drop this branch.\n     |- Try 42 - 38 = 4. Evaluate 4 != 16, drop this branch.\n     |- Try 42 * 38 = 1596. Evaluate 1596 != 16, drop this branch.\n     |- Try 42 \/ 38 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (38, 42) (numbers left: [1]). Try possible operations.\n    |- Try 42 + 38 = 80. Add 80 to the number set. Current number set: [80, 1], target: 16, just two numbers left.\n     |- Try 80 + 1 = 81. Evaluate 81 != 16, drop this branch.\n     |- Try 80 - 1 = 79. Evaluate 79 != 16, drop this branch.\n     |- Try 80 * 1 = 80. Evaluate 80 != 16, drop this branch.\n     |- Try 80 \/ 1 = 80. Evaluate 80 != 16, drop this branch.\n    |- Try 42 - 38 = 4. Add 4 to the number set. Current number set: [4, 1], target: 16, just two numbers left.\n     |- Try 4 + 1 = 5. Evaluate 5 != 16, drop this branch.\n     |- Try 4 - 1 = 3. Evaluate 3 != 16, drop this branch.\n     |- Try 4 * 1 = 4. Evaluate 4 != 16, drop this branch.\n     |- Try 4 \/ 1 = 4. Evaluate 4 != 16, drop this branch.\n    |- Try 42 * 38 = 1596. Add 1596 to the number set. Current number set: [1596, 1], target: 16, just two numbers left.\n     |- Try 1596 + 1 = 1597. Evaluate 1597 != 16, drop this branch.\n     |- Try 1596 - 1 = 1595. Evaluate 1595 != 16, drop this branch.\n     |- Try 1596 * 1 = 1596. Evaluate 1596 != 16, drop this branch.\n     |- Try 1596 \/ 1 = 1596. Evaluate 1596 != 16, drop this branch.\n    |- Try 42 \/ 38 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 25 * 24 = 600. Add 600 to the number set. Current number set: [600, 38, 42], target: 16. Options for choosing two numbers: [(600, 38), (600, 42), (38, 42)].\n   |- Pick two numbers (600, 38) (numbers left: [42]). Try possible operations.\n    |- Try 600 + 38 = 638. Add 638 to the number set. Current number set: [638, 42], target: 16, just two numbers left.\n     |- Try 638 + 42 = 680. Evaluate 680 != 16, drop this branch.\n     |- Try 638 - 42 = 596. Evaluate 596 != 16, drop this branch.\n     |- Try 638 * 42 = 26796. 26796 exceeds the maximum intermediate result, drop this branch.\n     |- Try 638 \/ 42 = 15.2. 15.2 is a decimal, drop this branch.\n    |- Try 600 - 38 = 562. Add 562 to the number set. Current number set: [562, 42], target: 16, just two numbers left.\n     |- Try 562 + 42 = 604. Evaluate 604 != 16, drop this branch.\n     |- Try 562 - 42 = 520. Evaluate 520 != 16, drop this branch.\n     |- Try 562 * 42 = 23604. 23604 exceeds the maximum intermediate result, drop this branch.\n     |- Try 562 \/ 42 = 13.4. 13.4 is a decimal, drop this branch.\n    |- Try 600 * 38 = 22800. 22800 exceeds the maximum intermediate result, drop this branch.\n    |- Try 600 \/ 38 = 15.8. 15.8 is a decimal, drop this branch.\n   |- Pick two numbers (600, 42) (numbers left: [38]). Try possible operations.\n    |- Try 600 + 42 = 642. Add 642 to the number set. Current number set: [642, 38], target: 16, just two numbers left.\n     |- Try 642 + 38 = 680. Evaluate 680 != 16, drop this branch.\n     |- Try 642 - 38 = 604. Evaluate 604 != 16, drop this branch.\n     |- Try 642 * 38 = 24396. 24396 exceeds the maximum intermediate result, drop this branch.\n     |- Try 642 \/ 38 = 16.9. 16.9 is a decimal, drop this branch.\n    |- Try 600 - 42 = 558. Add 558 to the number set. Current number set: [558, 38], target: 16, just two numbers left.\n     |- Try 558 + 38 = 596. Evaluate 596 != 16, drop this branch.\n     |- Try 558 - 38 = 520. Evaluate 520 != 16, drop this branch.\n     |- Try 558 * 38 = 21204. 21204 exceeds the maximum intermediate result, drop this branch.\n     |- Try 558 \/ 38 = 14.7. 14.7 is a decimal, drop this branch.\n    |- Try 600 * 42 = 25200. 25200 exceeds the maximum intermediate result, drop this branch.\n    |- Try 600 \/ 42 = 14.3. 14.3 is a decimal, drop this branch.\n   |- Pick two numbers (38, 42) (numbers left: [600]). Try possible operations.\n    |- Try 42 + 38 = 80. Add 80 to the number set. Current number set: [80, 600], target: 16, just two numbers left.\n     |- Try 600 + 80 = 680. Evaluate 680 != 16, drop this branch.\n     |- Try 600 - 80 = 520. Evaluate 520 != 16, drop this branch.\n     |- Try 600 * 80 = 48000. 48000 exceeds the maximum intermediate result, drop this branch.\n     |- Try 600 \/ 80 = 7.5. 7.5 is a decimal, drop this branch.\n    |- Try 42 - 38 = 4. Add 4 to the number set. Current number set: [4, 600], target: 16, just two numbers left.\n     |- Try 600 + 4 = 604. Evaluate 604 != 16, drop this branch.\n     |- Try 600 - 4 = 596. Evaluate 596 != 16, drop this branch.\n     |- Try 600 * 4 = 2400. 2400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 600 \/ 4 = 150. Evaluate 150 != 16, drop this branch.\n    |- Try 42 * 38 = 1596. Add 1596 to the number set. Current number set: [1596, 600], target: 16, just two numbers left.\n     |- Try 1596 + 600 = 2196. 2196 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1596 - 600 = 996. Evaluate 996 != 16, drop this branch.\n     |- Try 1596 * 600 = 957600. 957600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1596 \/ 600 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 42 \/ 38 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n |- Pick two numbers (25, 38) (numbers left: [24, 42]). Try possible operations.\n  |- Try 38 + 25 = 63. Add 63 to the number set. Current number set: [63, 24, 42], target: 16. Options for choosing two numbers: [(63, 24), (63, 42), (24, 42)].\n   |- Pick two numbers (63, 24) (numbers left: [42]). Try possible operations.\n    |- Try 63 + 24 = 87. Add 87 to the number set. Current number set: [87, 42], target: 16, just two numbers left.\n     |- Try 87 + 42 = 129. Evaluate 129 != 16, drop this branch.\n     |- Try 87 - 42 = 45. Evaluate 45 != 16, drop this branch.\n     |- Try 87 * 42 = 3654. 3654 exceeds the maximum intermediate result, drop this branch.\n     |- Try 87 \/ 42 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 63 - 24 = 39. Add 39 to the number set. Current number set: [39, 42], target: 16, just two numbers left.\n     |- Try 42 + 39 = 81. Evaluate 81 != 16, drop this branch.\n     |- Try 42 - 39 = 3. Evaluate 3 != 16, drop this branch.\n     |- Try 42 * 39 = 1638. Evaluate 1638 != 16, drop this branch.\n     |- Try 42 \/ 39 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 63 * 24 = 1512. Add 1512 to the number set. Current number set: [1512, 42], target: 16, just two numbers left.\n     |- Try 1512 + 42 = 1554. Evaluate 1554 != 16, drop this branch.\n     |- Try 1512 - 42 = 1470. Evaluate 1470 != 16, drop this branch.\n     |- Try 1512 * 42 = 63504. 63504 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1512 \/ 42 = 36. Evaluate 36 != 16, drop this branch.\n    |- Try 63 \/ 24 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (63, 42) (numbers left: [24]). Try possible operations.\n    |- Try 63 + 42 = 105. Add 105 to the number set. Current number set: [105, 24], target: 16, just two numbers left.\n     |- Try 105 + 24 = 129. Evaluate 129 != 16, drop this branch.\n     |- Try 105 - 24 = 81. Evaluate 81 != 16, drop this branch.\n     |- Try 105 * 24 = 2520. 2520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 105 \/ 24 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 63 - 42 = 21. Add 21 to the number set. Current number set: [21, 24], target: 16, just two numbers left.\n     |- Try 24 + 21 = 45. Evaluate 45 != 16, drop this branch.\n     |- Try 24 - 21 = 3. Evaluate 3 != 16, drop this branch.\n     |- Try 24 * 21 = 504. Evaluate 504 != 16, drop this branch.\n     |- Try 24 \/ 21 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 63 * 42 = 2646. 2646 exceeds the maximum intermediate result, drop this branch.\n    |- Try 63 \/ 42 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (24, 42) (numbers left: [63]). Try possible operations.\n    |- Try 42 + 24 = 66. Add 66 to the number set. Current number set: [66, 63], target: 16, just two numbers left.\n     |- Try 66 + 63 = 129. Evaluate 129 != 16, drop this branch.\n     |- Try 66 - 63 = 3. Evaluate 3 != 16, drop this branch.\n     |- Try 66 * 63 = 4158. 4158 exceeds the maximum intermediate result, drop this branch.\n     |- Try 66 \/ 63 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 42 - 24 = 18. Add 18 to the number set. Current number set: [18, 63], target: 16, just two numbers left.\n     |- Try 63 + 18 = 81. Evaluate 81 != 16, drop this branch.\n     |- Try 63 - 18 = 45. Evaluate 45 != 16, drop this branch.\n     |- Try 63 * 18 = 1134. Evaluate 1134 != 16, drop this branch.\n     |- Try 63 \/ 18 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 42 * 24 = 1008. Add 1008 to the number set. Current number set: [1008, 63], target: 16, just two numbers left.\n     |- Try 1008 + 63 = 1071. Evaluate 1071 != 16, drop this branch.\n     |- Try 1008 - 63 = 945. Evaluate 945 != 16, drop this branch.\n     |- Try 1008 * 63 = 63504. 63504 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1008 \/ 63 = 16. Evaluate 16 == 16, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 1008 \/ 63 = 16\nThe step before: 42 * 24 = 1008\nThe first step: 38 + 25 = 63\n\nOutput the solution in the required format:\n<Solution>\n38 + 25 = 63\n42 * 24 = 1008\n1008 \/ 63 = 16\n<\/Solution>\n","item":{"nums":[25,24,38,42],"solution":["38 + 25 = 63","42 * 24 = 1008","1008 \/ 63 = 16"],"target":16}}
+{"instance_id":"countdown_8k_64","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [33, 42, 18, 14]\nTarget: 18","reference_output":"# Search Procedure\nInitial number set: [33, 42, 18, 14], target: 18. Options for choosing two numbers: [(33, 42), (33, 18), (33, 14), (42, 18), (42, 14), (18, 14)].\n |- Pick two numbers (33, 42) (numbers left: [18, 14]). Try possible operations.\n  |- Try 42 + 33 = 75. Add 75 to the number set. Current number set: [75, 18, 14], target: 18. Options for choosing two numbers: [(75, 18), (75, 14), (18, 14)].\n   |- Pick two numbers (75, 18) (numbers left: [14]). Try possible operations.\n    |- Try 75 + 18 = 93. Add 93 to the number set. Current number set: [93, 14], target: 18, just two numbers left.\n     |- Try 93 + 14 = 107. Evaluate 107 != 18, drop this branch.\n     |- Try 93 - 14 = 79. Evaluate 79 != 18, drop this branch.\n     |- Try 93 * 14 = 1302. Evaluate 1302 != 18, drop this branch.\n     |- Try 93 \/ 14 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 75 - 18 = 57. Add 57 to the number set. Current number set: [57, 14], target: 18, just two numbers left.\n     |- Try 57 + 14 = 71. Evaluate 71 != 18, drop this branch.\n     |- Try 57 - 14 = 43. Evaluate 43 != 18, drop this branch.\n     |- Try 57 * 14 = 798. Evaluate 798 != 18, drop this branch.\n     |- Try 57 \/ 14 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 75 * 18 = 1350. Add 1350 to the number set. Current number set: [1350, 14], target: 18, just two numbers left.\n     |- Try 1350 + 14 = 1364. Evaluate 1364 != 18, drop this branch.\n     |- Try 1350 - 14 = 1336. Evaluate 1336 != 18, drop this branch.\n     |- Try 1350 * 14 = 18900. 18900 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1350 \/ 14 = 96.4. 96.4 is a decimal, drop this branch.\n    |- Try 75 \/ 18 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (75, 14) (numbers left: [18]). Try possible operations.\n    |- Try 75 + 14 = 89. Add 89 to the number set. Current number set: [89, 18], target: 18, just two numbers left.\n     |- Try 89 + 18 = 107. Evaluate 107 != 18, drop this branch.\n     |- Try 89 - 18 = 71. Evaluate 71 != 18, drop this branch.\n     |- Try 89 * 18 = 1602. Evaluate 1602 != 18, drop this branch.\n     |- Try 89 \/ 18 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 75 - 14 = 61. Add 61 to the number set. Current number set: [61, 18], target: 18, just two numbers left.\n     |- Try 61 + 18 = 79. Evaluate 79 != 18, drop this branch.\n     |- Try 61 - 18 = 43. Evaluate 43 != 18, drop this branch.\n     |- Try 61 * 18 = 1098. Evaluate 1098 != 18, drop this branch.\n     |- Try 61 \/ 18 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 75 * 14 = 1050. Add 1050 to the number set. Current number set: [1050, 18], target: 18, just two numbers left.\n     |- Try 1050 + 18 = 1068. Evaluate 1068 != 18, drop this branch.\n     |- Try 1050 - 18 = 1032. Evaluate 1032 != 18, drop this branch.\n     |- Try 1050 * 18 = 18900. 18900 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1050 \/ 18 = 58.3. 58.3 is a decimal, drop this branch.\n    |- Try 75 \/ 14 = 5.4. 5.4 is a decimal, drop this branch.\n   |- Pick two numbers (18, 14) (numbers left: [75]). Try possible operations.\n    |- Try 18 + 14 = 32. Add 32 to the number set. Current number set: [32, 75], target: 18, just two numbers left.\n     |- Try 75 + 32 = 107. Evaluate 107 != 18, drop this branch.\n     |- Try 75 - 32 = 43. Evaluate 43 != 18, drop this branch.\n     |- Try 75 * 32 = 2400. 2400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 75 \/ 32 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 18 - 14 = 4. Add 4 to the number set. Current number set: [4, 75], target: 18, just two numbers left.\n     |- Try 75 + 4 = 79. Evaluate 79 != 18, drop this branch.\n     |- Try 75 - 4 = 71. Evaluate 71 != 18, drop this branch.\n     |- Try 75 * 4 = 300. Evaluate 300 != 18, drop this branch.\n     |- Try 75 \/ 4 = 18.8. 18.8 is a decimal, drop this branch.\n    |- Try 18 * 14 = 252. Add 252 to the number set. Current number set: [252, 75], target: 18, just two numbers left.\n     |- Try 252 + 75 = 327. Evaluate 327 != 18, drop this branch.\n     |- Try 252 - 75 = 177. Evaluate 177 != 18, drop this branch.\n     |- Try 252 * 75 = 18900. 18900 exceeds the maximum intermediate result, drop this branch.\n     |- Try 252 \/ 75 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 \/ 14 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 42 - 33 = 9. Add 9 to the number set. Current number set: [9, 18, 14], target: 18. Options for choosing two numbers: [(9, 18), (9, 14), (18, 14)].\n   |- Pick two numbers (9, 18) (numbers left: [14]). Try possible operations.\n    |- Try 18 + 9 = 27. Add 27 to the number set. Current number set: [27, 14], target: 18, just two numbers left.\n     |- Try 27 + 14 = 41. Evaluate 41 != 18, drop this branch.\n     |- Try 27 - 14 = 13. Evaluate 13 != 18, drop this branch.\n     |- Try 27 * 14 = 378. Evaluate 378 != 18, drop this branch.\n     |- Try 27 \/ 14 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 18 - 9 = 9. Add 9 to the number set. Current number set: [9, 14], target: 18, just two numbers left.\n     |- Try 14 + 9 = 23. Evaluate 23 != 18, drop this branch.\n     |- Try 14 - 9 = 5. Evaluate 5 != 18, drop this branch.\n     |- Try 14 * 9 = 126. Evaluate 126 != 18, drop this branch.\n     |- Try 14 \/ 9 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 18 * 9 = 162. Add 162 to the number set. Current number set: [162, 14], target: 18, just two numbers left.\n     |- Try 162 + 14 = 176. Evaluate 176 != 18, drop this branch.\n     |- Try 162 - 14 = 148. Evaluate 148 != 18, drop this branch.\n     |- Try 162 * 14 = 2268. 2268 exceeds the maximum intermediate result, drop this branch.\n     |- Try 162 \/ 14 = 11.6. 11.6 is a decimal, drop this branch.\n    |- Try 18 \/ 9 = 2. Add 2 to the number set. Current number set: [2, 14], target: 18, just two numbers left.\n     |- Try 14 + 2 = 16. Evaluate 16 != 18, drop this branch.\n     |- Try 14 - 2 = 12. Evaluate 12 != 18, drop this branch.\n     |- Try 14 * 2 = 28. Evaluate 28 != 18, drop this branch.\n     |- Try 14 \/ 2 = 7. Evaluate 7 != 18, drop this branch.\n   |- Pick two numbers (9, 14) (numbers left: [18]). Try possible operations.\n    |- Try 14 + 9 = 23. Add 23 to the number set. Current number set: [23, 18], target: 18, just two numbers left.\n     |- Try 23 + 18 = 41. Evaluate 41 != 18, drop this branch.\n     |- Try 23 - 18 = 5. Evaluate 5 != 18, drop this branch.\n     |- Try 23 * 18 = 414. Evaluate 414 != 18, drop this branch.\n     |- Try 23 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 14 - 9 = 5. Add 5 to the number set. Current number set: [5, 18], target: 18, just two numbers left.\n     |- Try 18 + 5 = 23. Evaluate 23 != 18, drop this branch.\n     |- Try 18 - 5 = 13. Evaluate 13 != 18, drop this branch.\n     |- Try 18 * 5 = 90. Evaluate 90 != 18, drop this branch.\n     |- Try 18 \/ 5 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 14 * 9 = 126. Add 126 to the number set. Current number set: [126, 18], target: 18, just two numbers left.\n     |- Try 126 + 18 = 144. Evaluate 144 != 18, drop this branch.\n     |- Try 126 - 18 = 108. Evaluate 108 != 18, drop this branch.\n     |- Try 126 * 18 = 2268. 2268 exceeds the maximum intermediate result, drop this branch.\n     |- Try 126 \/ 18 = 7. Evaluate 7 != 18, drop this branch.\n    |- Try 14 \/ 9 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (18, 14) (numbers left: [9]). Try possible operations.\n    |- Try 18 + 14 = 32. Add 32 to the number set. Current number set: [32, 9], target: 18, just two numbers left.\n     |- Try 32 + 9 = 41. Evaluate 41 != 18, drop this branch.\n     |- Try 32 - 9 = 23. Evaluate 23 != 18, drop this branch.\n     |- Try 32 * 9 = 288. Evaluate 288 != 18, drop this branch.\n     |- Try 32 \/ 9 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 18 - 14 = 4. Add 4 to the number set. Current number set: [4, 9], target: 18, just two numbers left.\n     |- Try 9 + 4 = 13. Evaluate 13 != 18, drop this branch.\n     |- Try 9 - 4 = 5. Evaluate 5 != 18, drop this branch.\n     |- Try 9 * 4 = 36. Evaluate 36 != 18, drop this branch.\n     |- Try 9 \/ 4 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 18 * 14 = 252. Add 252 to the number set. Current number set: [252, 9], target: 18, just two numbers left.\n     |- Try 252 + 9 = 261. Evaluate 261 != 18, drop this branch.\n     |- Try 252 - 9 = 243. Evaluate 243 != 18, drop this branch.\n     |- Try 252 * 9 = 2268. 2268 exceeds the maximum intermediate result, drop this branch.\n     |- Try 252 \/ 9 = 28. Evaluate 28 != 18, drop this branch.\n    |- Try 18 \/ 14 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 42 * 33 = 1386. Add 1386 to the number set. Current number set: [1386, 18, 14], target: 18. Options for choosing two numbers: [(1386, 18), (1386, 14), (18, 14)].\n   |- Pick two numbers (1386, 18) (numbers left: [14]). Try possible operations.\n    |- Try 1386 + 18 = 1404. Add 1404 to the number set. Current number set: [1404, 14], target: 18, just two numbers left.\n     |- Try 1404 + 14 = 1418. Evaluate 1418 != 18, drop this branch.\n     |- Try 1404 - 14 = 1390. Evaluate 1390 != 18, drop this branch.\n     |- Try 1404 * 14 = 19656. 19656 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1404 \/ 14 = 100.3. 100.3 is a decimal, drop this branch.\n    |- Try 1386 - 18 = 1368. Add 1368 to the number set. Current number set: [1368, 14], target: 18, just two numbers left.\n     |- Try 1368 + 14 = 1382. Evaluate 1382 != 18, drop this branch.\n     |- Try 1368 - 14 = 1354. Evaluate 1354 != 18, drop this branch.\n     |- Try 1368 * 14 = 19152. 19152 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1368 \/ 14 = 97.7. 97.7 is a decimal, drop this branch.\n    |- Try 1386 * 18 = 24948. 24948 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1386 \/ 18 = 77. Add 77 to the number set. Current number set: [77, 14], target: 18, just two numbers left.\n     |- Try 77 + 14 = 91. Evaluate 91 != 18, drop this branch.\n     |- Try 77 - 14 = 63. Evaluate 63 != 18, drop this branch.\n     |- Try 77 * 14 = 1078. Evaluate 1078 != 18, drop this branch.\n     |- Try 77 \/ 14 = 5.5. 5.5 is a decimal, drop this branch.\n   |- Pick two numbers (1386, 14) (numbers left: [18]). Try possible operations.\n    |- Try 1386 + 14 = 1400. Add 1400 to the number set. Current number set: [1400, 18], target: 18, just two numbers left.\n     |- Try 1400 + 18 = 1418. Evaluate 1418 != 18, drop this branch.\n     |- Try 1400 - 18 = 1382. Evaluate 1382 != 18, drop this branch.\n     |- Try 1400 * 18 = 25200. 25200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1400 \/ 18 = 77.8. 77.8 is a decimal, drop this branch.\n    |- Try 1386 - 14 = 1372. Add 1372 to the number set. Current number set: [1372, 18], target: 18, just two numbers left.\n     |- Try 1372 + 18 = 1390. Evaluate 1390 != 18, drop this branch.\n     |- Try 1372 - 18 = 1354. Evaluate 1354 != 18, drop this branch.\n     |- Try 1372 * 18 = 24696. 24696 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1372 \/ 18 = 76.2. 76.2 is a decimal, drop this branch.\n    |- Try 1386 * 14 = 19404. 19404 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1386 \/ 14 = 99. Add 99 to the number set. Current number set: [99, 18], target: 18, just two numbers left.\n     |- Try 99 + 18 = 117. Evaluate 117 != 18, drop this branch.\n     |- Try 99 - 18 = 81. Evaluate 81 != 18, drop this branch.\n     |- Try 99 * 18 = 1782. Evaluate 1782 != 18, drop this branch.\n     |- Try 99 \/ 18 = 5.5. 5.5 is a decimal, drop this branch.\n   |- Pick two numbers (18, 14) (numbers left: [1386]). Try possible operations.\n    |- Try 18 + 14 = 32. Add 32 to the number set. Current number set: [32, 1386], target: 18, just two numbers left.\n     |- Try 1386 + 32 = 1418. Evaluate 1418 != 18, drop this branch.\n     |- Try 1386 - 32 = 1354. Evaluate 1354 != 18, drop this branch.\n     |- Try 1386 * 32 = 44352. 44352 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1386 \/ 32 = 43.3. 43.3 is a decimal, drop this branch.\n    |- Try 18 - 14 = 4. Add 4 to the number set. Current number set: [4, 1386], target: 18, just two numbers left.\n     |- Try 1386 + 4 = 1390. Evaluate 1390 != 18, drop this branch.\n     |- Try 1386 - 4 = 1382. Evaluate 1382 != 18, drop this branch.\n     |- Try 1386 * 4 = 5544. 5544 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1386 \/ 4 = 346.5. 346.5 is a decimal, drop this branch.\n    |- Try 18 * 14 = 252. Add 252 to the number set. Current number set: [252, 1386], target: 18, just two numbers left.\n     |- Try 1386 + 252 = 1638. Evaluate 1638 != 18, drop this branch.\n     |- Try 1386 - 252 = 1134. Evaluate 1134 != 18, drop this branch.\n     |- Try 1386 * 252 = 349272. 349272 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1386 \/ 252 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 18 \/ 14 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 42 \/ 33 = 1.3. 1.3 is a decimal, drop this branch.\n |- Pick two numbers (33, 18) (numbers left: [42, 14]). Try possible operations.\n  |- Try 33 + 18 = 51. Add 51 to the number set. Current number set: [51, 42, 14], target: 18. Options for choosing two numbers: [(51, 42), (51, 14), (42, 14)].\n   |- Pick two numbers (51, 42) (numbers left: [14]). Try possible operations.\n    |- Try 51 + 42 = 93. Add 93 to the number set. Current number set: [93, 14], target: 18, just two numbers left.\n     |- Try 93 + 14 = 107. Evaluate 107 != 18, drop this branch.\n     |- Try 93 - 14 = 79. Evaluate 79 != 18, drop this branch.\n     |- Try 93 * 14 = 1302. Evaluate 1302 != 18, drop this branch.\n     |- Try 93 \/ 14 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 51 - 42 = 9. Add 9 to the number set. Current number set: [9, 14], target: 18, just two numbers left.\n     |- Try 14 + 9 = 23. Evaluate 23 != 18, drop this branch.\n     |- Try 14 - 9 = 5. Evaluate 5 != 18, drop this branch.\n     |- Try 14 * 9 = 126. Evaluate 126 != 18, drop this branch.\n     |- Try 14 \/ 9 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 51 * 42 = 2142. 2142 exceeds the maximum intermediate result, drop this branch.\n    |- Try 51 \/ 42 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (51, 14) (numbers left: [42]). Try possible operations.\n    |- Try 51 + 14 = 65. Add 65 to the number set. Current number set: [65, 42], target: 18, just two numbers left.\n     |- Try 65 + 42 = 107. Evaluate 107 != 18, drop this branch.\n     |- Try 65 - 42 = 23. Evaluate 23 != 18, drop this branch.\n     |- Try 65 * 42 = 2730. 2730 exceeds the maximum intermediate result, drop this branch.\n     |- Try 65 \/ 42 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 51 - 14 = 37. Add 37 to the number set. Current number set: [37, 42], target: 18, just two numbers left.\n     |- Try 42 + 37 = 79. Evaluate 79 != 18, drop this branch.\n     |- Try 42 - 37 = 5. Evaluate 5 != 18, drop this branch.\n     |- Try 42 * 37 = 1554. Evaluate 1554 != 18, drop this branch.\n     |- Try 42 \/ 37 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 51 * 14 = 714. Add 714 to the number set. Current number set: [714, 42], target: 18, just two numbers left.\n     |- Try 714 + 42 = 756. Evaluate 756 != 18, drop this branch.\n     |- Try 714 - 42 = 672. Evaluate 672 != 18, drop this branch.\n     |- Try 714 * 42 = 29988. 29988 exceeds the maximum intermediate result, drop this branch.\n     |- Try 714 \/ 42 = 17. Evaluate 17 != 18, drop this branch.\n    |- Try 51 \/ 14 = 3.6. 3.6 is a decimal, drop this branch.\n   |- Pick two numbers (42, 14) (numbers left: [51]). Try possible operations.\n    |- Try 42 + 14 = 56. Add 56 to the number set. Current number set: [56, 51], target: 18, just two numbers left.\n     |- Try 56 + 51 = 107. Evaluate 107 != 18, drop this branch.\n     |- Try 56 - 51 = 5. Evaluate 5 != 18, drop this branch.\n     |- Try 56 * 51 = 2856. 2856 exceeds the maximum intermediate result, drop this branch.\n     |- Try 56 \/ 51 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 42 - 14 = 28. Add 28 to the number set. Current number set: [28, 51], target: 18, just two numbers left.\n     |- Try 51 + 28 = 79. Evaluate 79 != 18, drop this branch.\n     |- Try 51 - 28 = 23. Evaluate 23 != 18, drop this branch.\n     |- Try 51 * 28 = 1428. Evaluate 1428 != 18, drop this branch.\n     |- Try 51 \/ 28 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 42 * 14 = 588. Add 588 to the number set. Current number set: [588, 51], target: 18, just two numbers left.\n     |- Try 588 + 51 = 639. Evaluate 639 != 18, drop this branch.\n     |- Try 588 - 51 = 537. Evaluate 537 != 18, drop this branch.\n     |- Try 588 * 51 = 29988. 29988 exceeds the maximum intermediate result, drop this branch.\n     |- Try 588 \/ 51 = 11.5. 11.5 is a decimal, drop this branch.\n    |- Try 42 \/ 14 = 3. Add 3 to the number set. Current number set: [3, 51], target: 18, just two numbers left.\n     |- Try 51 + 3 = 54. Evaluate 54 != 18, drop this branch.\n     |- Try 51 - 3 = 48. Evaluate 48 != 18, drop this branch.\n     |- Try 51 * 3 = 153. Evaluate 153 != 18, drop this branch.\n     |- Try 51 \/ 3 = 17. Evaluate 17 != 18, drop this branch.\n  |- Try 33 - 18 = 15. Add 15 to the number set. Current number set: [15, 42, 14], target: 18. Options for choosing two numbers: [(15, 42), (15, 14), (42, 14)].\n   |- Pick two numbers (15, 42) (numbers left: [14]). Try possible operations.\n    |- Try 42 + 15 = 57. Add 57 to the number set. Current number set: [57, 14], target: 18, just two numbers left.\n     |- Try 57 + 14 = 71. Evaluate 71 != 18, drop this branch.\n     |- Try 57 - 14 = 43. Evaluate 43 != 18, drop this branch.\n     |- Try 57 * 14 = 798. Evaluate 798 != 18, drop this branch.\n     |- Try 57 \/ 14 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 42 - 15 = 27. Add 27 to the number set. Current number set: [27, 14], target: 18, just two numbers left.\n     |- Try 27 + 14 = 41. Evaluate 41 != 18, drop this branch.\n     |- Try 27 - 14 = 13. Evaluate 13 != 18, drop this branch.\n     |- Try 27 * 14 = 378. Evaluate 378 != 18, drop this branch.\n     |- Try 27 \/ 14 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 42 * 15 = 630. Add 630 to the number set. Current number set: [630, 14], target: 18, just two numbers left.\n     |- Try 630 + 14 = 644. Evaluate 644 != 18, drop this branch.\n     |- Try 630 - 14 = 616. Evaluate 616 != 18, drop this branch.\n     |- Try 630 * 14 = 8820. 8820 exceeds the maximum intermediate result, drop this branch.\n     |- Try 630 \/ 14 = 45. Evaluate 45 != 18, drop this branch.\n    |- Try 42 \/ 15 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (15, 14) (numbers left: [42]). Try possible operations.\n    |- Try 15 + 14 = 29. Add 29 to the number set. Current number set: [29, 42], target: 18, just two numbers left.\n     |- Try 42 + 29 = 71. Evaluate 71 != 18, drop this branch.\n     |- Try 42 - 29 = 13. Evaluate 13 != 18, drop this branch.\n     |- Try 42 * 29 = 1218. Evaluate 1218 != 18, drop this branch.\n     |- Try 42 \/ 29 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 15 - 14 = 1. Add 1 to the number set. Current number set: [1, 42], target: 18, just two numbers left.\n     |- Try 42 + 1 = 43. Evaluate 43 != 18, drop this branch.\n     |- Try 42 - 1 = 41. Evaluate 41 != 18, drop this branch.\n     |- Try 42 * 1 = 42. Evaluate 42 != 18, drop this branch.\n     |- Try 42 \/ 1 = 42. Evaluate 42 != 18, drop this branch.\n    |- Try 15 * 14 = 210. Add 210 to the number set. Current number set: [210, 42], target: 18, just two numbers left.\n     |- Try 210 + 42 = 252. Evaluate 252 != 18, drop this branch.\n     |- Try 210 - 42 = 168. Evaluate 168 != 18, drop this branch.\n     |- Try 210 * 42 = 8820. 8820 exceeds the maximum intermediate result, drop this branch.\n     |- Try 210 \/ 42 = 5. Evaluate 5 != 18, drop this branch.\n    |- Try 15 \/ 14 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (42, 14) (numbers left: [15]). Try possible operations.\n    |- Try 42 + 14 = 56. Add 56 to the number set. Current number set: [56, 15], target: 18, just two numbers left.\n     |- Try 56 + 15 = 71. Evaluate 71 != 18, drop this branch.\n     |- Try 56 - 15 = 41. Evaluate 41 != 18, drop this branch.\n     |- Try 56 * 15 = 840. Evaluate 840 != 18, drop this branch.\n     |- Try 56 \/ 15 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 42 - 14 = 28. Add 28 to the number set. Current number set: [28, 15], target: 18, just two numbers left.\n     |- Try 28 + 15 = 43. Evaluate 43 != 18, drop this branch.\n     |- Try 28 - 15 = 13. Evaluate 13 != 18, drop this branch.\n     |- Try 28 * 15 = 420. Evaluate 420 != 18, drop this branch.\n     |- Try 28 \/ 15 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 42 * 14 = 588. Add 588 to the number set. Current number set: [588, 15], target: 18, just two numbers left.\n     |- Try 588 + 15 = 603. Evaluate 603 != 18, drop this branch.\n     |- Try 588 - 15 = 573. Evaluate 573 != 18, drop this branch.\n     |- Try 588 * 15 = 8820. 8820 exceeds the maximum intermediate result, drop this branch.\n     |- Try 588 \/ 15 = 39.2. 39.2 is a decimal, drop this branch.\n    |- Try 42 \/ 14 = 3. Add 3 to the number set. Current number set: [3, 15], target: 18, just two numbers left.\n     |- Try 15 + 3 = 18. Evaluate 18 == 18, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 15 + 3 = 18\nThe step before: 42 \/ 14 = 3\nThe first step: 33 - 18 = 15\n\nOutput the solution in the required format:\n<Solution>\n33 - 18 = 15\n42 \/ 14 = 3\n15 + 3 = 18\n<\/Solution>\n","item":{"nums":[33,42,18,14],"solution":["33 - 18 = 15","42 \/ 14 = 3","15 + 3 = 18"],"target":18}}
+{"instance_id":"countdown_8k_65","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [35, 28, 37, 24]\nTarget: 26","reference_output":"# Search Procedure\nInitial number set: [35, 28, 37, 24], target: 26. Options for choosing two numbers: [(35, 28), (35, 37), (35, 24), (28, 37), (28, 24), (37, 24)].\n |- Pick two numbers (35, 28) (numbers left: [37, 24]). Try possible operations.\n  |- Try 35 + 28 = 63. Add 63 to the number set. Current number set: [63, 37, 24], target: 26. Options for choosing two numbers: [(63, 37), (63, 24), (37, 24)].\n   |- Pick two numbers (63, 37) (numbers left: [24]). Try possible operations.\n    |- Try 63 + 37 = 100. Add 100 to the number set. Current number set: [100, 24], target: 26, just two numbers left.\n     |- Try 100 + 24 = 124. Evaluate 124 != 26, drop this branch.\n     |- Try 100 - 24 = 76. Evaluate 76 != 26, drop this branch.\n     |- Try 100 * 24 = 2400. 2400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 100 \/ 24 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 63 - 37 = 26. Add 26 to the number set. Current number set: [26, 24], target: 26, just two numbers left.\n     |- Try 26 + 24 = 50. Evaluate 50 != 26, drop this branch.\n     |- Try 26 - 24 = 2. Evaluate 2 != 26, drop this branch.\n     |- Try 26 * 24 = 624. Evaluate 624 != 26, drop this branch.\n     |- Try 26 \/ 24 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 63 * 37 = 2331. 2331 exceeds the maximum intermediate result, drop this branch.\n    |- Try 63 \/ 37 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (63, 24) (numbers left: [37]). Try possible operations.\n    |- Try 63 + 24 = 87. Add 87 to the number set. Current number set: [87, 37], target: 26, just two numbers left.\n     |- Try 87 + 37 = 124. Evaluate 124 != 26, drop this branch.\n     |- Try 87 - 37 = 50. Evaluate 50 != 26, drop this branch.\n     |- Try 87 * 37 = 3219. 3219 exceeds the maximum intermediate result, drop this branch.\n     |- Try 87 \/ 37 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 63 - 24 = 39. Add 39 to the number set. Current number set: [39, 37], target: 26, just two numbers left.\n     |- Try 39 + 37 = 76. Evaluate 76 != 26, drop this branch.\n     |- Try 39 - 37 = 2. Evaluate 2 != 26, drop this branch.\n     |- Try 39 * 37 = 1443. Evaluate 1443 != 26, drop this branch.\n     |- Try 39 \/ 37 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 63 * 24 = 1512. Add 1512 to the number set. Current number set: [1512, 37], target: 26, just two numbers left.\n     |- Try 1512 + 37 = 1549. Evaluate 1549 != 26, drop this branch.\n     |- Try 1512 - 37 = 1475. Evaluate 1475 != 26, drop this branch.\n     |- Try 1512 * 37 = 55944. 55944 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1512 \/ 37 = 40.9. 40.9 is a decimal, drop this branch.\n    |- Try 63 \/ 24 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (37, 24) (numbers left: [63]). Try possible operations.\n    |- Try 37 + 24 = 61. Add 61 to the number set. Current number set: [61, 63], target: 26, just two numbers left.\n     |- Try 63 + 61 = 124. Evaluate 124 != 26, drop this branch.\n     |- Try 63 - 61 = 2. Evaluate 2 != 26, drop this branch.\n     |- Try 63 * 61 = 3843. 3843 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 61 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 37 - 24 = 13. Add 13 to the number set. Current number set: [13, 63], target: 26, just two numbers left.\n     |- Try 63 + 13 = 76. Evaluate 76 != 26, drop this branch.\n     |- Try 63 - 13 = 50. Evaluate 50 != 26, drop this branch.\n     |- Try 63 * 13 = 819. Evaluate 819 != 26, drop this branch.\n     |- Try 63 \/ 13 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 37 * 24 = 888. Add 888 to the number set. Current number set: [888, 63], target: 26, just two numbers left.\n     |- Try 888 + 63 = 951. Evaluate 951 != 26, drop this branch.\n     |- Try 888 - 63 = 825. Evaluate 825 != 26, drop this branch.\n     |- Try 888 * 63 = 55944. 55944 exceeds the maximum intermediate result, drop this branch.\n     |- Try 888 \/ 63 = 14.1. 14.1 is a decimal, drop this branch.\n    |- Try 37 \/ 24 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 35 - 28 = 7. Add 7 to the number set. Current number set: [7, 37, 24], target: 26. Options for choosing two numbers: [(7, 37), (7, 24), (37, 24)].\n   |- Pick two numbers (7, 37) (numbers left: [24]). Try possible operations.\n    |- Try 37 + 7 = 44. Add 44 to the number set. Current number set: [44, 24], target: 26, just two numbers left.\n     |- Try 44 + 24 = 68. Evaluate 68 != 26, drop this branch.\n     |- Try 44 - 24 = 20. Evaluate 20 != 26, drop this branch.\n     |- Try 44 * 24 = 1056. Evaluate 1056 != 26, drop this branch.\n     |- Try 44 \/ 24 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 37 - 7 = 30. Add 30 to the number set. Current number set: [30, 24], target: 26, just two numbers left.\n     |- Try 30 + 24 = 54. Evaluate 54 != 26, drop this branch.\n     |- Try 30 - 24 = 6. Evaluate 6 != 26, drop this branch.\n     |- Try 30 * 24 = 720. Evaluate 720 != 26, drop this branch.\n     |- Try 30 \/ 24 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 37 * 7 = 259. Add 259 to the number set. Current number set: [259, 24], target: 26, just two numbers left.\n     |- Try 259 + 24 = 283. Evaluate 283 != 26, drop this branch.\n     |- Try 259 - 24 = 235. Evaluate 235 != 26, drop this branch.\n     |- Try 259 * 24 = 6216. 6216 exceeds the maximum intermediate result, drop this branch.\n     |- Try 259 \/ 24 = 10.8. 10.8 is a decimal, drop this branch.\n    |- Try 37 \/ 7 = 5.3. 5.3 is a decimal, drop this branch.\n   |- Pick two numbers (7, 24) (numbers left: [37]). Try possible operations.\n    |- Try 24 + 7 = 31. Add 31 to the number set. Current number set: [31, 37], target: 26, just two numbers left.\n     |- Try 37 + 31 = 68. Evaluate 68 != 26, drop this branch.\n     |- Try 37 - 31 = 6. Evaluate 6 != 26, drop this branch.\n     |- Try 37 * 31 = 1147. Evaluate 1147 != 26, drop this branch.\n     |- Try 37 \/ 31 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 24 - 7 = 17. Add 17 to the number set. Current number set: [17, 37], target: 26, just two numbers left.\n     |- Try 37 + 17 = 54. Evaluate 54 != 26, drop this branch.\n     |- Try 37 - 17 = 20. Evaluate 20 != 26, drop this branch.\n     |- Try 37 * 17 = 629. Evaluate 629 != 26, drop this branch.\n     |- Try 37 \/ 17 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 24 * 7 = 168. Add 168 to the number set. Current number set: [168, 37], target: 26, just two numbers left.\n     |- Try 168 + 37 = 205. Evaluate 205 != 26, drop this branch.\n     |- Try 168 - 37 = 131. Evaluate 131 != 26, drop this branch.\n     |- Try 168 * 37 = 6216. 6216 exceeds the maximum intermediate result, drop this branch.\n     |- Try 168 \/ 37 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n   |- Pick two numbers (37, 24) (numbers left: [7]). Try possible operations.\n    |- Try 37 + 24 = 61. Add 61 to the number set. Current number set: [61, 7], target: 26, just two numbers left.\n     |- Try 61 + 7 = 68. Evaluate 68 != 26, drop this branch.\n     |- Try 61 - 7 = 54. Evaluate 54 != 26, drop this branch.\n     |- Try 61 * 7 = 427. Evaluate 427 != 26, drop this branch.\n     |- Try 61 \/ 7 = 8.7. 8.7 is a decimal, drop this branch.\n    |- Try 37 - 24 = 13. Add 13 to the number set. Current number set: [13, 7], target: 26, just two numbers left.\n     |- Try 13 + 7 = 20. Evaluate 20 != 26, drop this branch.\n     |- Try 13 - 7 = 6. Evaluate 6 != 26, drop this branch.\n     |- Try 13 * 7 = 91. Evaluate 91 != 26, drop this branch.\n     |- Try 13 \/ 7 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 37 * 24 = 888. Add 888 to the number set. Current number set: [888, 7], target: 26, just two numbers left.\n     |- Try 888 + 7 = 895. Evaluate 895 != 26, drop this branch.\n     |- Try 888 - 7 = 881. Evaluate 881 != 26, drop this branch.\n     |- Try 888 * 7 = 6216. 6216 exceeds the maximum intermediate result, drop this branch.\n     |- Try 888 \/ 7 = 126.9. 126.9 is a decimal, drop this branch.\n    |- Try 37 \/ 24 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 35 * 28 = 980. Add 980 to the number set. Current number set: [980, 37, 24], target: 26. Options for choosing two numbers: [(980, 37), (980, 24), (37, 24)].\n   |- Pick two numbers (980, 37) (numbers left: [24]). Try possible operations.\n    |- Try 980 + 37 = 1017. Add 1017 to the number set. Current number set: [1017, 24], target: 26, just two numbers left.\n     |- Try 1017 + 24 = 1041. Evaluate 1041 != 26, drop this branch.\n     |- Try 1017 - 24 = 993. Evaluate 993 != 26, drop this branch.\n     |- Try 1017 * 24 = 24408. 24408 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1017 \/ 24 = 42.4. 42.4 is a decimal, drop this branch.\n    |- Try 980 - 37 = 943. Add 943 to the number set. Current number set: [943, 24], target: 26, just two numbers left.\n     |- Try 943 + 24 = 967. Evaluate 967 != 26, drop this branch.\n     |- Try 943 - 24 = 919. Evaluate 919 != 26, drop this branch.\n     |- Try 943 * 24 = 22632. 22632 exceeds the maximum intermediate result, drop this branch.\n     |- Try 943 \/ 24 = 39.3. 39.3 is a decimal, drop this branch.\n    |- Try 980 * 37 = 36260. 36260 exceeds the maximum intermediate result, drop this branch.\n    |- Try 980 \/ 37 = 26.5. 26.5 is a decimal, drop this branch.\n   |- Pick two numbers (980, 24) (numbers left: [37]). Try possible operations.\n    |- Try 980 + 24 = 1004. Add 1004 to the number set. Current number set: [1004, 37], target: 26, just two numbers left.\n     |- Try 1004 + 37 = 1041. Evaluate 1041 != 26, drop this branch.\n     |- Try 1004 - 37 = 967. Evaluate 967 != 26, drop this branch.\n     |- Try 1004 * 37 = 37148. 37148 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1004 \/ 37 = 27.1. 27.1 is a decimal, drop this branch.\n    |- Try 980 - 24 = 956. Add 956 to the number set. Current number set: [956, 37], target: 26, just two numbers left.\n     |- Try 956 + 37 = 993. Evaluate 993 != 26, drop this branch.\n     |- Try 956 - 37 = 919. Evaluate 919 != 26, drop this branch.\n     |- Try 956 * 37 = 35372. 35372 exceeds the maximum intermediate result, drop this branch.\n     |- Try 956 \/ 37 = 25.8. 25.8 is a decimal, drop this branch.\n    |- Try 980 * 24 = 23520. 23520 exceeds the maximum intermediate result, drop this branch.\n    |- Try 980 \/ 24 = 40.8. 40.8 is a decimal, drop this branch.\n   |- Pick two numbers (37, 24) (numbers left: [980]). Try possible operations.\n    |- Try 37 + 24 = 61. Add 61 to the number set. Current number set: [61, 980], target: 26, just two numbers left.\n     |- Try 980 + 61 = 1041. Evaluate 1041 != 26, drop this branch.\n     |- Try 980 - 61 = 919. Evaluate 919 != 26, drop this branch.\n     |- Try 980 * 61 = 59780. 59780 exceeds the maximum intermediate result, drop this branch.\n     |- Try 980 \/ 61 = 16.1. 16.1 is a decimal, drop this branch.\n    |- Try 37 - 24 = 13. Add 13 to the number set. Current number set: [13, 980], target: 26, just two numbers left.\n     |- Try 980 + 13 = 993. Evaluate 993 != 26, drop this branch.\n     |- Try 980 - 13 = 967. Evaluate 967 != 26, drop this branch.\n     |- Try 980 * 13 = 12740. 12740 exceeds the maximum intermediate result, drop this branch.\n     |- Try 980 \/ 13 = 75.4. 75.4 is a decimal, drop this branch.\n    |- Try 37 * 24 = 888. Add 888 to the number set. Current number set: [888, 980], target: 26, just two numbers left.\n     |- Try 980 + 888 = 1868. Evaluate 1868 != 26, drop this branch.\n     |- Try 980 - 888 = 92. Evaluate 92 != 26, drop this branch.\n     |- Try 980 * 888 = 870240. 870240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 980 \/ 888 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 37 \/ 24 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 35 \/ 28 = 1.2. 1.2 is a decimal, drop this branch.\n |- Pick two numbers (35, 37) (numbers left: [28, 24]). Try possible operations.\n  |- Try 37 + 35 = 72. Add 72 to the number set. Current number set: [72, 28, 24], target: 26. Options for choosing two numbers: [(72, 28), (72, 24), (28, 24)].\n   |- Pick two numbers (72, 28) (numbers left: [24]). Try possible operations.\n    |- Try 72 + 28 = 100. Add 100 to the number set. Current number set: [100, 24], target: 26, just two numbers left.\n     |- Try 100 + 24 = 124. Evaluate 124 != 26, drop this branch.\n     |- Try 100 - 24 = 76. Evaluate 76 != 26, drop this branch.\n     |- Try 100 * 24 = 2400. 2400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 100 \/ 24 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 72 - 28 = 44. Add 44 to the number set. Current number set: [44, 24], target: 26, just two numbers left.\n     |- Try 44 + 24 = 68. Evaluate 68 != 26, drop this branch.\n     |- Try 44 - 24 = 20. Evaluate 20 != 26, drop this branch.\n     |- Try 44 * 24 = 1056. Evaluate 1056 != 26, drop this branch.\n     |- Try 44 \/ 24 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 72 * 28 = 2016. 2016 exceeds the maximum intermediate result, drop this branch.\n    |- Try 72 \/ 28 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (72, 24) (numbers left: [28]). Try possible operations.\n    |- Try 72 + 24 = 96. Add 96 to the number set. Current number set: [96, 28], target: 26, just two numbers left.\n     |- Try 96 + 28 = 124. Evaluate 124 != 26, drop this branch.\n     |- Try 96 - 28 = 68. Evaluate 68 != 26, drop this branch.\n     |- Try 96 * 28 = 2688. 2688 exceeds the maximum intermediate result, drop this branch.\n     |- Try 96 \/ 28 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 72 - 24 = 48. Add 48 to the number set. Current number set: [48, 28], target: 26, just two numbers left.\n     |- Try 48 + 28 = 76. Evaluate 76 != 26, drop this branch.\n     |- Try 48 - 28 = 20. Evaluate 20 != 26, drop this branch.\n     |- Try 48 * 28 = 1344. Evaluate 1344 != 26, drop this branch.\n     |- Try 48 \/ 28 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 72 * 24 = 1728. Add 1728 to the number set. Current number set: [1728, 28], target: 26, just two numbers left.\n     |- Try 1728 + 28 = 1756. Evaluate 1756 != 26, drop this branch.\n     |- Try 1728 - 28 = 1700. Evaluate 1700 != 26, drop this branch.\n     |- Try 1728 * 28 = 48384. 48384 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1728 \/ 28 = 61.7. 61.7 is a decimal, drop this branch.\n    |- Try 72 \/ 24 = 3. Add 3 to the number set. Current number set: [3, 28], target: 26, just two numbers left.\n     |- Try 28 + 3 = 31. Evaluate 31 != 26, drop this branch.\n     |- Try 28 - 3 = 25. Evaluate 25 != 26, drop this branch.\n     |- Try 28 * 3 = 84. Evaluate 84 != 26, drop this branch.\n     |- Try 28 \/ 3 = 9.3. 9.3 is a decimal, drop this branch.\n   |- Pick two numbers (28, 24) (numbers left: [72]). Try possible operations.\n    |- Try 28 + 24 = 52. Add 52 to the number set. Current number set: [52, 72], target: 26, just two numbers left.\n     |- Try 72 + 52 = 124. Evaluate 124 != 26, drop this branch.\n     |- Try 72 - 52 = 20. Evaluate 20 != 26, drop this branch.\n     |- Try 72 * 52 = 3744. 3744 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 52 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 28 - 24 = 4. Add 4 to the number set. Current number set: [4, 72], target: 26, just two numbers left.\n     |- Try 72 + 4 = 76. Evaluate 76 != 26, drop this branch.\n     |- Try 72 - 4 = 68. Evaluate 68 != 26, drop this branch.\n     |- Try 72 * 4 = 288. Evaluate 288 != 26, drop this branch.\n     |- Try 72 \/ 4 = 18. Evaluate 18 != 26, drop this branch.\n    |- Try 28 * 24 = 672. Add 672 to the number set. Current number set: [672, 72], target: 26, just two numbers left.\n     |- Try 672 + 72 = 744. Evaluate 744 != 26, drop this branch.\n     |- Try 672 - 72 = 600. Evaluate 600 != 26, drop this branch.\n     |- Try 672 * 72 = 48384. 48384 exceeds the maximum intermediate result, drop this branch.\n     |- Try 672 \/ 72 = 9.3. 9.3 is a decimal, drop this branch.\n    |- Try 28 \/ 24 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 37 - 35 = 2. Add 2 to the number set. Current number set: [2, 28, 24], target: 26. Options for choosing two numbers: [(2, 28), (2, 24), (28, 24)].\n   |- Pick two numbers (2, 28) (numbers left: [24]). Try possible operations.\n    |- Try 28 + 2 = 30. Add 30 to the number set. Current number set: [30, 24], target: 26, just two numbers left.\n     |- Try 30 + 24 = 54. Evaluate 54 != 26, drop this branch.\n     |- Try 30 - 24 = 6. Evaluate 6 != 26, drop this branch.\n     |- Try 30 * 24 = 720. Evaluate 720 != 26, drop this branch.\n     |- Try 30 \/ 24 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 28 - 2 = 26. Add 26 to the number set. Current number set: [26, 24], target: 26, just two numbers left.\n     |- Try 26 + 24 = 50. Evaluate 50 != 26, drop this branch.\n     |- Try 26 - 24 = 2. Evaluate 2 != 26, drop this branch.\n     |- Try 26 * 24 = 624. Evaluate 624 != 26, drop this branch.\n     |- Try 26 \/ 24 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 28 * 2 = 56. Add 56 to the number set. Current number set: [56, 24], target: 26, just two numbers left.\n     |- Try 56 + 24 = 80. Evaluate 80 != 26, drop this branch.\n     |- Try 56 - 24 = 32. Evaluate 32 != 26, drop this branch.\n     |- Try 56 * 24 = 1344. Evaluate 1344 != 26, drop this branch.\n     |- Try 56 \/ 24 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 28 \/ 2 = 14. Add 14 to the number set. Current number set: [14, 24], target: 26, just two numbers left.\n     |- Try 24 + 14 = 38. Evaluate 38 != 26, drop this branch.\n     |- Try 24 - 14 = 10. Evaluate 10 != 26, drop this branch.\n     |- Try 24 * 14 = 336. Evaluate 336 != 26, drop this branch.\n     |- Try 24 \/ 14 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (2, 24) (numbers left: [28]). Try possible operations.\n    |- Try 24 + 2 = 26. Add 26 to the number set. Current number set: [26, 28], target: 26, just two numbers left.\n     |- Try 28 + 26 = 54. Evaluate 54 != 26, drop this branch.\n     |- Try 28 - 26 = 2. Evaluate 2 != 26, drop this branch.\n     |- Try 28 * 26 = 728. Evaluate 728 != 26, drop this branch.\n     |- Try 28 \/ 26 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 24 - 2 = 22. Add 22 to the number set. Current number set: [22, 28], target: 26, just two numbers left.\n     |- Try 28 + 22 = 50. Evaluate 50 != 26, drop this branch.\n     |- Try 28 - 22 = 6. Evaluate 6 != 26, drop this branch.\n     |- Try 28 * 22 = 616. Evaluate 616 != 26, drop this branch.\n     |- Try 28 \/ 22 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 24 * 2 = 48. Add 48 to the number set. Current number set: [48, 28], target: 26, just two numbers left.\n     |- Try 48 + 28 = 76. Evaluate 76 != 26, drop this branch.\n     |- Try 48 - 28 = 20. Evaluate 20 != 26, drop this branch.\n     |- Try 48 * 28 = 1344. Evaluate 1344 != 26, drop this branch.\n     |- Try 48 \/ 28 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 24 \/ 2 = 12. Add 12 to the number set. Current number set: [12, 28], target: 26, just two numbers left.\n     |- Try 28 + 12 = 40. Evaluate 40 != 26, drop this branch.\n     |- Try 28 - 12 = 16. Evaluate 16 != 26, drop this branch.\n     |- Try 28 * 12 = 336. Evaluate 336 != 26, drop this branch.\n     |- Try 28 \/ 12 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (28, 24) (numbers left: [2]). Try possible operations.\n    |- Try 28 + 24 = 52. Add 52 to the number set. Current number set: [52, 2], target: 26, just two numbers left.\n     |- Try 52 + 2 = 54. Evaluate 54 != 26, drop this branch.\n     |- Try 52 - 2 = 50. Evaluate 50 != 26, drop this branch.\n     |- Try 52 * 2 = 104. Evaluate 104 != 26, drop this branch.\n     |- Try 52 \/ 2 = 26. Evaluate 26 == 26, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 52 \/ 2 = 26\nThe step before: 28 + 24 = 52\nThe first step: 37 - 35 = 2\n\nOutput the solution in the required format:\n<Solution>\n37 - 35 = 2\n28 + 24 = 52\n52 \/ 2 = 26\n<\/Solution>\n","item":{"nums":[35,28,37,24],"solution":["37 - 35 = 2","28 + 24 = 52","52 \/ 2 = 26"],"target":26}}
+{"instance_id":"countdown_8k_66","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [31, 39, 28, 6]\nTarget: 19","reference_output":"# Search Procedure\nInitial number set: [31, 39, 28, 6], target: 19. Options for choosing two numbers: [(31, 39), (31, 28), (31, 6), (39, 28), (39, 6), (28, 6)].\n |- Pick two numbers (31, 39) (numbers left: [28, 6]). Try possible operations.\n  |- Try 39 + 31 = 70. Add 70 to the number set. Current number set: [70, 28, 6], target: 19. Options for choosing two numbers: [(70, 28), (70, 6), (28, 6)].\n   |- Pick two numbers (70, 28) (numbers left: [6]). Try possible operations.\n    |- Try 70 + 28 = 98. Add 98 to the number set. Current number set: [98, 6], target: 19, just two numbers left.\n     |- Try 98 + 6 = 104. Evaluate 104 != 19, drop this branch.\n     |- Try 98 - 6 = 92. Evaluate 92 != 19, drop this branch.\n     |- Try 98 * 6 = 588. Evaluate 588 != 19, drop this branch.\n     |- Try 98 \/ 6 = 16.3. 16.3 is a decimal, drop this branch.\n    |- Try 70 - 28 = 42. Add 42 to the number set. Current number set: [42, 6], target: 19, just two numbers left.\n     |- Try 42 + 6 = 48. Evaluate 48 != 19, drop this branch.\n     |- Try 42 - 6 = 36. Evaluate 36 != 19, drop this branch.\n     |- Try 42 * 6 = 252. Evaluate 252 != 19, drop this branch.\n     |- Try 42 \/ 6 = 7. Evaluate 7 != 19, drop this branch.\n    |- Try 70 * 28 = 1960. Add 1960 to the number set. Current number set: [1960, 6], target: 19, just two numbers left.\n     |- Try 1960 + 6 = 1966. Evaluate 1966 != 19, drop this branch.\n     |- Try 1960 - 6 = 1954. Evaluate 1954 != 19, drop this branch.\n     |- Try 1960 * 6 = 11760. 11760 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1960 \/ 6 = 326.7. 326.7 is a decimal, drop this branch.\n    |- Try 70 \/ 28 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (70, 6) (numbers left: [28]). Try possible operations.\n    |- Try 70 + 6 = 76. Add 76 to the number set. Current number set: [76, 28], target: 19, just two numbers left.\n     |- Try 76 + 28 = 104. Evaluate 104 != 19, drop this branch.\n     |- Try 76 - 28 = 48. Evaluate 48 != 19, drop this branch.\n     |- Try 76 * 28 = 2128. 2128 exceeds the maximum intermediate result, drop this branch.\n     |- Try 76 \/ 28 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 70 - 6 = 64. Add 64 to the number set. Current number set: [64, 28], target: 19, just two numbers left.\n     |- Try 64 + 28 = 92. Evaluate 92 != 19, drop this branch.\n     |- Try 64 - 28 = 36. Evaluate 36 != 19, drop this branch.\n     |- Try 64 * 28 = 1792. Evaluate 1792 != 19, drop this branch.\n     |- Try 64 \/ 28 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 70 * 6 = 420. Add 420 to the number set. Current number set: [420, 28], target: 19, just two numbers left.\n     |- Try 420 + 28 = 448. Evaluate 448 != 19, drop this branch.\n     |- Try 420 - 28 = 392. Evaluate 392 != 19, drop this branch.\n     |- Try 420 * 28 = 11760. 11760 exceeds the maximum intermediate result, drop this branch.\n     |- Try 420 \/ 28 = 15. Evaluate 15 != 19, drop this branch.\n    |- Try 70 \/ 6 = 11.7. 11.7 is a decimal, drop this branch.\n   |- Pick two numbers (28, 6) (numbers left: [70]). Try possible operations.\n    |- Try 28 + 6 = 34. Add 34 to the number set. Current number set: [34, 70], target: 19, just two numbers left.\n     |- Try 70 + 34 = 104. Evaluate 104 != 19, drop this branch.\n     |- Try 70 - 34 = 36. Evaluate 36 != 19, drop this branch.\n     |- Try 70 * 34 = 2380. 2380 exceeds the maximum intermediate result, drop this branch.\n     |- Try 70 \/ 34 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 28 - 6 = 22. Add 22 to the number set. Current number set: [22, 70], target: 19, just two numbers left.\n     |- Try 70 + 22 = 92. Evaluate 92 != 19, drop this branch.\n     |- Try 70 - 22 = 48. Evaluate 48 != 19, drop this branch.\n     |- Try 70 * 22 = 1540. Evaluate 1540 != 19, drop this branch.\n     |- Try 70 \/ 22 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 28 * 6 = 168. Add 168 to the number set. Current number set: [168, 70], target: 19, just two numbers left.\n     |- Try 168 + 70 = 238. Evaluate 238 != 19, drop this branch.\n     |- Try 168 - 70 = 98. Evaluate 98 != 19, drop this branch.\n     |- Try 168 * 70 = 11760. 11760 exceeds the maximum intermediate result, drop this branch.\n     |- Try 168 \/ 70 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 28 \/ 6 = 4.7. 4.7 is a decimal, drop this branch.\n  |- Try 39 - 31 = 8. Add 8 to the number set. Current number set: [8, 28, 6], target: 19. Options for choosing two numbers: [(8, 28), (8, 6), (28, 6)].\n   |- Pick two numbers (8, 28) (numbers left: [6]). Try possible operations.\n    |- Try 28 + 8 = 36. Add 36 to the number set. Current number set: [36, 6], target: 19, just two numbers left.\n     |- Try 36 + 6 = 42. Evaluate 42 != 19, drop this branch.\n     |- Try 36 - 6 = 30. Evaluate 30 != 19, drop this branch.\n     |- Try 36 * 6 = 216. Evaluate 216 != 19, drop this branch.\n     |- Try 36 \/ 6 = 6. Evaluate 6 != 19, drop this branch.\n    |- Try 28 - 8 = 20. Add 20 to the number set. Current number set: [20, 6], target: 19, just two numbers left.\n     |- Try 20 + 6 = 26. Evaluate 26 != 19, drop this branch.\n     |- Try 20 - 6 = 14. Evaluate 14 != 19, drop this branch.\n     |- Try 20 * 6 = 120. Evaluate 120 != 19, drop this branch.\n     |- Try 20 \/ 6 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 28 * 8 = 224. Add 224 to the number set. Current number set: [224, 6], target: 19, just two numbers left.\n     |- Try 224 + 6 = 230. Evaluate 230 != 19, drop this branch.\n     |- Try 224 - 6 = 218. Evaluate 218 != 19, drop this branch.\n     |- Try 224 * 6 = 1344. Evaluate 1344 != 19, drop this branch.\n     |- Try 224 \/ 6 = 37.3. 37.3 is a decimal, drop this branch.\n    |- Try 28 \/ 8 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (8, 6) (numbers left: [28]). Try possible operations.\n    |- Try 8 + 6 = 14. Add 14 to the number set. Current number set: [14, 28], target: 19, just two numbers left.\n     |- Try 28 + 14 = 42. Evaluate 42 != 19, drop this branch.\n     |- Try 28 - 14 = 14. Evaluate 14 != 19, drop this branch.\n     |- Try 28 * 14 = 392. Evaluate 392 != 19, drop this branch.\n     |- Try 28 \/ 14 = 2. Evaluate 2 != 19, drop this branch.\n    |- Try 8 - 6 = 2. Add 2 to the number set. Current number set: [2, 28], target: 19, just two numbers left.\n     |- Try 28 + 2 = 30. Evaluate 30 != 19, drop this branch.\n     |- Try 28 - 2 = 26. Evaluate 26 != 19, drop this branch.\n     |- Try 28 * 2 = 56. Evaluate 56 != 19, drop this branch.\n     |- Try 28 \/ 2 = 14. Evaluate 14 != 19, drop this branch.\n    |- Try 8 * 6 = 48. Add 48 to the number set. Current number set: [48, 28], target: 19, just two numbers left.\n     |- Try 48 + 28 = 76. Evaluate 76 != 19, drop this branch.\n     |- Try 48 - 28 = 20. Evaluate 20 != 19, drop this branch.\n     |- Try 48 * 28 = 1344. Evaluate 1344 != 19, drop this branch.\n     |- Try 48 \/ 28 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (28, 6) (numbers left: [8]). Try possible operations.\n    |- Try 28 + 6 = 34. Add 34 to the number set. Current number set: [34, 8], target: 19, just two numbers left.\n     |- Try 34 + 8 = 42. Evaluate 42 != 19, drop this branch.\n     |- Try 34 - 8 = 26. Evaluate 26 != 19, drop this branch.\n     |- Try 34 * 8 = 272. Evaluate 272 != 19, drop this branch.\n     |- Try 34 \/ 8 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 28 - 6 = 22. Add 22 to the number set. Current number set: [22, 8], target: 19, just two numbers left.\n     |- Try 22 + 8 = 30. Evaluate 30 != 19, drop this branch.\n     |- Try 22 - 8 = 14. Evaluate 14 != 19, drop this branch.\n     |- Try 22 * 8 = 176. Evaluate 176 != 19, drop this branch.\n     |- Try 22 \/ 8 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 28 * 6 = 168. Add 168 to the number set. Current number set: [168, 8], target: 19, just two numbers left.\n     |- Try 168 + 8 = 176. Evaluate 176 != 19, drop this branch.\n     |- Try 168 - 8 = 160. Evaluate 160 != 19, drop this branch.\n     |- Try 168 * 8 = 1344. Evaluate 1344 != 19, drop this branch.\n     |- Try 168 \/ 8 = 21. Evaluate 21 != 19, drop this branch.\n    |- Try 28 \/ 6 = 4.7. 4.7 is a decimal, drop this branch.\n  |- Try 39 * 31 = 1209. Add 1209 to the number set. Current number set: [1209, 28, 6], target: 19. Options for choosing two numbers: [(1209, 28), (1209, 6), (28, 6)].\n   |- Pick two numbers (1209, 28) (numbers left: [6]). Try possible operations.\n    |- Try 1209 + 28 = 1237. Add 1237 to the number set. Current number set: [1237, 6], target: 19, just two numbers left.\n     |- Try 1237 + 6 = 1243. Evaluate 1243 != 19, drop this branch.\n     |- Try 1237 - 6 = 1231. Evaluate 1231 != 19, drop this branch.\n     |- Try 1237 * 6 = 7422. 7422 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1237 \/ 6 = 206.2. 206.2 is a decimal, drop this branch.\n    |- Try 1209 - 28 = 1181. Add 1181 to the number set. Current number set: [1181, 6], target: 19, just two numbers left.\n     |- Try 1181 + 6 = 1187. Evaluate 1187 != 19, drop this branch.\n     |- Try 1181 - 6 = 1175. Evaluate 1175 != 19, drop this branch.\n     |- Try 1181 * 6 = 7086. 7086 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1181 \/ 6 = 196.8. 196.8 is a decimal, drop this branch.\n    |- Try 1209 * 28 = 33852. 33852 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1209 \/ 28 = 43.2. 43.2 is a decimal, drop this branch.\n   |- Pick two numbers (1209, 6) (numbers left: [28]). Try possible operations.\n    |- Try 1209 + 6 = 1215. Add 1215 to the number set. Current number set: [1215, 28], target: 19, just two numbers left.\n     |- Try 1215 + 28 = 1243. Evaluate 1243 != 19, drop this branch.\n     |- Try 1215 - 28 = 1187. Evaluate 1187 != 19, drop this branch.\n     |- Try 1215 * 28 = 34020. 34020 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1215 \/ 28 = 43.4. 43.4 is a decimal, drop this branch.\n    |- Try 1209 - 6 = 1203. Add 1203 to the number set. Current number set: [1203, 28], target: 19, just two numbers left.\n     |- Try 1203 + 28 = 1231. Evaluate 1231 != 19, drop this branch.\n     |- Try 1203 - 28 = 1175. Evaluate 1175 != 19, drop this branch.\n     |- Try 1203 * 28 = 33684. 33684 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1203 \/ 28 = 43.0. 43.0 is a decimal, drop this branch.\n    |- Try 1209 * 6 = 7254. 7254 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1209 \/ 6 = 201.5. 201.5 is a decimal, drop this branch.\n   |- Pick two numbers (28, 6) (numbers left: [1209]). Try possible operations.\n    |- Try 28 + 6 = 34. Add 34 to the number set. Current number set: [34, 1209], target: 19, just two numbers left.\n     |- Try 1209 + 34 = 1243. Evaluate 1243 != 19, drop this branch.\n     |- Try 1209 - 34 = 1175. Evaluate 1175 != 19, drop this branch.\n     |- Try 1209 * 34 = 41106. 41106 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1209 \/ 34 = 35.6. 35.6 is a decimal, drop this branch.\n    |- Try 28 - 6 = 22. Add 22 to the number set. Current number set: [22, 1209], target: 19, just two numbers left.\n     |- Try 1209 + 22 = 1231. Evaluate 1231 != 19, drop this branch.\n     |- Try 1209 - 22 = 1187. Evaluate 1187 != 19, drop this branch.\n     |- Try 1209 * 22 = 26598. 26598 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1209 \/ 22 = 55.0. 55.0 is a decimal, drop this branch.\n    |- Try 28 * 6 = 168. Add 168 to the number set. Current number set: [168, 1209], target: 19, just two numbers left.\n     |- Try 1209 + 168 = 1377. Evaluate 1377 != 19, drop this branch.\n     |- Try 1209 - 168 = 1041. Evaluate 1041 != 19, drop this branch.\n     |- Try 1209 * 168 = 203112. 203112 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1209 \/ 168 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 28 \/ 6 = 4.7. 4.7 is a decimal, drop this branch.\n  |- Try 39 \/ 31 = 1.3. 1.3 is a decimal, drop this branch.\n |- Pick two numbers (31, 28) (numbers left: [39, 6]). Try possible operations.\n  |- Try 31 + 28 = 59. Add 59 to the number set. Current number set: [59, 39, 6], target: 19. Options for choosing two numbers: [(59, 39), (59, 6), (39, 6)].\n   |- Pick two numbers (59, 39) (numbers left: [6]). Try possible operations.\n    |- Try 59 + 39 = 98. Add 98 to the number set. Current number set: [98, 6], target: 19, just two numbers left.\n     |- Try 98 + 6 = 104. Evaluate 104 != 19, drop this branch.\n     |- Try 98 - 6 = 92. Evaluate 92 != 19, drop this branch.\n     |- Try 98 * 6 = 588. Evaluate 588 != 19, drop this branch.\n     |- Try 98 \/ 6 = 16.3. 16.3 is a decimal, drop this branch.\n    |- Try 59 - 39 = 20. Add 20 to the number set. Current number set: [20, 6], target: 19, just two numbers left.\n     |- Try 20 + 6 = 26. Evaluate 26 != 19, drop this branch.\n     |- Try 20 - 6 = 14. Evaluate 14 != 19, drop this branch.\n     |- Try 20 * 6 = 120. Evaluate 120 != 19, drop this branch.\n     |- Try 20 \/ 6 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 59 * 39 = 2301. 2301 exceeds the maximum intermediate result, drop this branch.\n    |- Try 59 \/ 39 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (59, 6) (numbers left: [39]). Try possible operations.\n    |- Try 59 + 6 = 65. Add 65 to the number set. Current number set: [65, 39], target: 19, just two numbers left.\n     |- Try 65 + 39 = 104. Evaluate 104 != 19, drop this branch.\n     |- Try 65 - 39 = 26. Evaluate 26 != 19, drop this branch.\n     |- Try 65 * 39 = 2535. 2535 exceeds the maximum intermediate result, drop this branch.\n     |- Try 65 \/ 39 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 59 - 6 = 53. Add 53 to the number set. Current number set: [53, 39], target: 19, just two numbers left.\n     |- Try 53 + 39 = 92. Evaluate 92 != 19, drop this branch.\n     |- Try 53 - 39 = 14. Evaluate 14 != 19, drop this branch.\n     |- Try 53 * 39 = 2067. 2067 exceeds the maximum intermediate result, drop this branch.\n     |- Try 53 \/ 39 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 59 * 6 = 354. Add 354 to the number set. Current number set: [354, 39], target: 19, just two numbers left.\n     |- Try 354 + 39 = 393. Evaluate 393 != 19, drop this branch.\n     |- Try 354 - 39 = 315. Evaluate 315 != 19, drop this branch.\n     |- Try 354 * 39 = 13806. 13806 exceeds the maximum intermediate result, drop this branch.\n     |- Try 354 \/ 39 = 9.1. 9.1 is a decimal, drop this branch.\n    |- Try 59 \/ 6 = 9.8. 9.8 is a decimal, drop this branch.\n   |- Pick two numbers (39, 6) (numbers left: [59]). Try possible operations.\n    |- Try 39 + 6 = 45. Add 45 to the number set. Current number set: [45, 59], target: 19, just two numbers left.\n     |- Try 59 + 45 = 104. Evaluate 104 != 19, drop this branch.\n     |- Try 59 - 45 = 14. Evaluate 14 != 19, drop this branch.\n     |- Try 59 * 45 = 2655. 2655 exceeds the maximum intermediate result, drop this branch.\n     |- Try 59 \/ 45 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 39 - 6 = 33. Add 33 to the number set. Current number set: [33, 59], target: 19, just two numbers left.\n     |- Try 59 + 33 = 92. Evaluate 92 != 19, drop this branch.\n     |- Try 59 - 33 = 26. Evaluate 26 != 19, drop this branch.\n     |- Try 59 * 33 = 1947. Evaluate 1947 != 19, drop this branch.\n     |- Try 59 \/ 33 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 39 * 6 = 234. Add 234 to the number set. Current number set: [234, 59], target: 19, just two numbers left.\n     |- Try 234 + 59 = 293. Evaluate 293 != 19, drop this branch.\n     |- Try 234 - 59 = 175. Evaluate 175 != 19, drop this branch.\n     |- Try 234 * 59 = 13806. 13806 exceeds the maximum intermediate result, drop this branch.\n     |- Try 234 \/ 59 = 4.0. 4.0 is a decimal, drop this branch.\n    |- Try 39 \/ 6 = 6.5. 6.5 is a decimal, drop this branch.\n  |- Try 31 - 28 = 3. Add 3 to the number set. Current number set: [3, 39, 6], target: 19. Options for choosing two numbers: [(3, 39), (3, 6), (39, 6)].\n   |- Pick two numbers (3, 39) (numbers left: [6]). Try possible operations.\n    |- Try 39 + 3 = 42. Add 42 to the number set. Current number set: [42, 6], target: 19, just two numbers left.\n     |- Try 42 + 6 = 48. Evaluate 48 != 19, drop this branch.\n     |- Try 42 - 6 = 36. Evaluate 36 != 19, drop this branch.\n     |- Try 42 * 6 = 252. Evaluate 252 != 19, drop this branch.\n     |- Try 42 \/ 6 = 7. Evaluate 7 != 19, drop this branch.\n    |- Try 39 - 3 = 36. Add 36 to the number set. Current number set: [36, 6], target: 19, just two numbers left.\n     |- Try 36 + 6 = 42. Evaluate 42 != 19, drop this branch.\n     |- Try 36 - 6 = 30. Evaluate 30 != 19, drop this branch.\n     |- Try 36 * 6 = 216. Evaluate 216 != 19, drop this branch.\n     |- Try 36 \/ 6 = 6. Evaluate 6 != 19, drop this branch.\n    |- Try 39 * 3 = 117. Add 117 to the number set. Current number set: [117, 6], target: 19, just two numbers left.\n     |- Try 117 + 6 = 123. Evaluate 123 != 19, drop this branch.\n     |- Try 117 - 6 = 111. Evaluate 111 != 19, drop this branch.\n     |- Try 117 * 6 = 702. Evaluate 702 != 19, drop this branch.\n     |- Try 117 \/ 6 = 19.5. 19.5 is a decimal, drop this branch.\n    |- Try 39 \/ 3 = 13. Add 13 to the number set. Current number set: [13, 6], target: 19, just two numbers left.\n     |- Try 13 + 6 = 19. Evaluate 19 == 19, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 13 + 6 = 19\nThe step before: 39 \/ 3 = 13\nThe first step: 31 - 28 = 3\n\nOutput the solution in the required format:\n<Solution>\n31 - 28 = 3\n39 \/ 3 = 13\n13 + 6 = 19\n<\/Solution>\n","item":{"nums":[31,39,28,6],"solution":["31 - 28 = 3","39 \/ 3 = 13","13 + 6 = 19"],"target":19}}
+{"instance_id":"countdown_8k_67","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [37, 4, 26, 7]\nTarget: 21","reference_output":"# Search Procedure\nInitial number set: [37, 4, 26, 7], target: 21. Options for choosing two numbers: [(37, 4), (37, 26), (37, 7), (4, 26), (4, 7), (26, 7)].\n |- Pick two numbers (37, 4) (numbers left: [26, 7]). Try possible operations.\n  |- Try 37 + 4 = 41. Add 41 to the number set. Current number set: [41, 26, 7], target: 21. Options for choosing two numbers: [(41, 26), (41, 7), (26, 7)].\n   |- Pick two numbers (41, 26) (numbers left: [7]). Try possible operations.\n    |- Try 41 + 26 = 67. Add 67 to the number set. Current number set: [67, 7], target: 21, just two numbers left.\n     |- Try 67 + 7 = 74. Evaluate 74 != 21, drop this branch.\n     |- Try 67 - 7 = 60. Evaluate 60 != 21, drop this branch.\n     |- Try 67 * 7 = 469. Evaluate 469 != 21, drop this branch.\n     |- Try 67 \/ 7 = 9.6. 9.6 is a decimal, drop this branch.\n    |- Try 41 - 26 = 15. Add 15 to the number set. Current number set: [15, 7], target: 21, just two numbers left.\n     |- Try 15 + 7 = 22. Evaluate 22 != 21, drop this branch.\n     |- Try 15 - 7 = 8. Evaluate 8 != 21, drop this branch.\n     |- Try 15 * 7 = 105. Evaluate 105 != 21, drop this branch.\n     |- Try 15 \/ 7 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 41 * 26 = 1066. Add 1066 to the number set. Current number set: [1066, 7], target: 21, just two numbers left.\n     |- Try 1066 + 7 = 1073. Evaluate 1073 != 21, drop this branch.\n     |- Try 1066 - 7 = 1059. Evaluate 1059 != 21, drop this branch.\n     |- Try 1066 * 7 = 7462. 7462 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1066 \/ 7 = 152.3. 152.3 is a decimal, drop this branch.\n    |- Try 41 \/ 26 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (41, 7) (numbers left: [26]). Try possible operations.\n    |- Try 41 + 7 = 48. Add 48 to the number set. Current number set: [48, 26], target: 21, just two numbers left.\n     |- Try 48 + 26 = 74. Evaluate 74 != 21, drop this branch.\n     |- Try 48 - 26 = 22. Evaluate 22 != 21, drop this branch.\n     |- Try 48 * 26 = 1248. Evaluate 1248 != 21, drop this branch.\n     |- Try 48 \/ 26 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 41 - 7 = 34. Add 34 to the number set. Current number set: [34, 26], target: 21, just two numbers left.\n     |- Try 34 + 26 = 60. Evaluate 60 != 21, drop this branch.\n     |- Try 34 - 26 = 8. Evaluate 8 != 21, drop this branch.\n     |- Try 34 * 26 = 884. Evaluate 884 != 21, drop this branch.\n     |- Try 34 \/ 26 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 41 * 7 = 287. Add 287 to the number set. Current number set: [287, 26], target: 21, just two numbers left.\n     |- Try 287 + 26 = 313. Evaluate 313 != 21, drop this branch.\n     |- Try 287 - 26 = 261. Evaluate 261 != 21, drop this branch.\n     |- Try 287 * 26 = 7462. 7462 exceeds the maximum intermediate result, drop this branch.\n     |- Try 287 \/ 26 = 11.0. 11.0 is a decimal, drop this branch.\n    |- Try 41 \/ 7 = 5.9. 5.9 is a decimal, drop this branch.\n   |- Pick two numbers (26, 7) (numbers left: [41]). Try possible operations.\n    |- Try 26 + 7 = 33. Add 33 to the number set. Current number set: [33, 41], target: 21, just two numbers left.\n     |- Try 41 + 33 = 74. Evaluate 74 != 21, drop this branch.\n     |- Try 41 - 33 = 8. Evaluate 8 != 21, drop this branch.\n     |- Try 41 * 33 = 1353. Evaluate 1353 != 21, drop this branch.\n     |- Try 41 \/ 33 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 26 - 7 = 19. Add 19 to the number set. Current number set: [19, 41], target: 21, just two numbers left.\n     |- Try 41 + 19 = 60. Evaluate 60 != 21, drop this branch.\n     |- Try 41 - 19 = 22. Evaluate 22 != 21, drop this branch.\n     |- Try 41 * 19 = 779. Evaluate 779 != 21, drop this branch.\n     |- Try 41 \/ 19 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 26 * 7 = 182. Add 182 to the number set. Current number set: [182, 41], target: 21, just two numbers left.\n     |- Try 182 + 41 = 223. Evaluate 223 != 21, drop this branch.\n     |- Try 182 - 41 = 141. Evaluate 141 != 21, drop this branch.\n     |- Try 182 * 41 = 7462. 7462 exceeds the maximum intermediate result, drop this branch.\n     |- Try 182 \/ 41 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 26 \/ 7 = 3.7. 3.7 is a decimal, drop this branch.\n  |- Try 37 - 4 = 33. Add 33 to the number set. Current number set: [33, 26, 7], target: 21. Options for choosing two numbers: [(33, 26), (33, 7), (26, 7)].\n   |- Pick two numbers (33, 26) (numbers left: [7]). Try possible operations.\n    |- Try 33 + 26 = 59. Add 59 to the number set. Current number set: [59, 7], target: 21, just two numbers left.\n     |- Try 59 + 7 = 66. Evaluate 66 != 21, drop this branch.\n     |- Try 59 - 7 = 52. Evaluate 52 != 21, drop this branch.\n     |- Try 59 * 7 = 413. Evaluate 413 != 21, drop this branch.\n     |- Try 59 \/ 7 = 8.4. 8.4 is a decimal, drop this branch.\n    |- Try 33 - 26 = 7. Add 7 to the number set. Current number set: [7, 7], target: 21, just two numbers left.\n     |- Try 7 + 7 = 14. Evaluate 14 != 21, drop this branch.\n     |- Try 7 - 7 = 0. Evaluate 0 != 21, drop this branch.\n     |- Try 7 * 7 = 49. Evaluate 49 != 21, drop this branch.\n     |- Try 7 \/ 7 = 1. Evaluate 1 != 21, drop this branch.\n    |- Try 33 * 26 = 858. Add 858 to the number set. Current number set: [858, 7], target: 21, just two numbers left.\n     |- Try 858 + 7 = 865. Evaluate 865 != 21, drop this branch.\n     |- Try 858 - 7 = 851. Evaluate 851 != 21, drop this branch.\n     |- Try 858 * 7 = 6006. 6006 exceeds the maximum intermediate result, drop this branch.\n     |- Try 858 \/ 7 = 122.6. 122.6 is a decimal, drop this branch.\n    |- Try 33 \/ 26 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (33, 7) (numbers left: [26]). Try possible operations.\n    |- Try 33 + 7 = 40. Add 40 to the number set. Current number set: [40, 26], target: 21, just two numbers left.\n     |- Try 40 + 26 = 66. Evaluate 66 != 21, drop this branch.\n     |- Try 40 - 26 = 14. Evaluate 14 != 21, drop this branch.\n     |- Try 40 * 26 = 1040. Evaluate 1040 != 21, drop this branch.\n     |- Try 40 \/ 26 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 33 - 7 = 26. Add 26 to the number set. Current number set: [26, 26], target: 21, just two numbers left.\n     |- Try 26 + 26 = 52. Evaluate 52 != 21, drop this branch.\n     |- Try 26 - 26 = 0. Evaluate 0 != 21, drop this branch.\n     |- Try 26 * 26 = 676. Evaluate 676 != 21, drop this branch.\n     |- Try 26 \/ 26 = 1. Evaluate 1 != 21, drop this branch.\n    |- Try 33 * 7 = 231. Add 231 to the number set. Current number set: [231, 26], target: 21, just two numbers left.\n     |- Try 231 + 26 = 257. Evaluate 257 != 21, drop this branch.\n     |- Try 231 - 26 = 205. Evaluate 205 != 21, drop this branch.\n     |- Try 231 * 26 = 6006. 6006 exceeds the maximum intermediate result, drop this branch.\n     |- Try 231 \/ 26 = 8.9. 8.9 is a decimal, drop this branch.\n    |- Try 33 \/ 7 = 4.7. 4.7 is a decimal, drop this branch.\n   |- Pick two numbers (26, 7) (numbers left: [33]). Try possible operations.\n    |- Try 26 + 7 = 33. Add 33 to the number set. Current number set: [33, 33], target: 21, just two numbers left.\n     |- Try 33 + 33 = 66. Evaluate 66 != 21, drop this branch.\n     |- Try 33 - 33 = 0. Evaluate 0 != 21, drop this branch.\n     |- Try 33 * 33 = 1089. Evaluate 1089 != 21, drop this branch.\n     |- Try 33 \/ 33 = 1. Evaluate 1 != 21, drop this branch.\n    |- Try 26 - 7 = 19. Add 19 to the number set. Current number set: [19, 33], target: 21, just two numbers left.\n     |- Try 33 + 19 = 52. Evaluate 52 != 21, drop this branch.\n     |- Try 33 - 19 = 14. Evaluate 14 != 21, drop this branch.\n     |- Try 33 * 19 = 627. Evaluate 627 != 21, drop this branch.\n     |- Try 33 \/ 19 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 26 * 7 = 182. Add 182 to the number set. Current number set: [182, 33], target: 21, just two numbers left.\n     |- Try 182 + 33 = 215. Evaluate 215 != 21, drop this branch.\n     |- Try 182 - 33 = 149. Evaluate 149 != 21, drop this branch.\n     |- Try 182 * 33 = 6006. 6006 exceeds the maximum intermediate result, drop this branch.\n     |- Try 182 \/ 33 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 26 \/ 7 = 3.7. 3.7 is a decimal, drop this branch.\n  |- Try 37 * 4 = 148. Add 148 to the number set. Current number set: [148, 26, 7], target: 21. Options for choosing two numbers: [(148, 26), (148, 7), (26, 7)].\n   |- Pick two numbers (148, 26) (numbers left: [7]). Try possible operations.\n    |- Try 148 + 26 = 174. Add 174 to the number set. Current number set: [174, 7], target: 21, just two numbers left.\n     |- Try 174 + 7 = 181. Evaluate 181 != 21, drop this branch.\n     |- Try 174 - 7 = 167. Evaluate 167 != 21, drop this branch.\n     |- Try 174 * 7 = 1218. Evaluate 1218 != 21, drop this branch.\n     |- Try 174 \/ 7 = 24.9. 24.9 is a decimal, drop this branch.\n    |- Try 148 - 26 = 122. Add 122 to the number set. Current number set: [122, 7], target: 21, just two numbers left.\n     |- Try 122 + 7 = 129. Evaluate 129 != 21, drop this branch.\n     |- Try 122 - 7 = 115. Evaluate 115 != 21, drop this branch.\n     |- Try 122 * 7 = 854. Evaluate 854 != 21, drop this branch.\n     |- Try 122 \/ 7 = 17.4. 17.4 is a decimal, drop this branch.\n    |- Try 148 * 26 = 3848. 3848 exceeds the maximum intermediate result, drop this branch.\n    |- Try 148 \/ 26 = 5.7. 5.7 is a decimal, drop this branch.\n   |- Pick two numbers (148, 7) (numbers left: [26]). Try possible operations.\n    |- Try 148 + 7 = 155. Add 155 to the number set. Current number set: [155, 26], target: 21, just two numbers left.\n     |- Try 155 + 26 = 181. Evaluate 181 != 21, drop this branch.\n     |- Try 155 - 26 = 129. Evaluate 129 != 21, drop this branch.\n     |- Try 155 * 26 = 4030. 4030 exceeds the maximum intermediate result, drop this branch.\n     |- Try 155 \/ 26 = 6.0. 6.0 is a decimal, drop this branch.\n    |- Try 148 - 7 = 141. Add 141 to the number set. Current number set: [141, 26], target: 21, just two numbers left.\n     |- Try 141 + 26 = 167. Evaluate 167 != 21, drop this branch.\n     |- Try 141 - 26 = 115. Evaluate 115 != 21, drop this branch.\n     |- Try 141 * 26 = 3666. 3666 exceeds the maximum intermediate result, drop this branch.\n     |- Try 141 \/ 26 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 148 * 7 = 1036. Add 1036 to the number set. Current number set: [1036, 26], target: 21, just two numbers left.\n     |- Try 1036 + 26 = 1062. Evaluate 1062 != 21, drop this branch.\n     |- Try 1036 - 26 = 1010. Evaluate 1010 != 21, drop this branch.\n     |- Try 1036 * 26 = 26936. 26936 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1036 \/ 26 = 39.8. 39.8 is a decimal, drop this branch.\n    |- Try 148 \/ 7 = 21.1. 21.1 is a decimal, drop this branch.\n   |- Pick two numbers (26, 7) (numbers left: [148]). Try possible operations.\n    |- Try 26 + 7 = 33. Add 33 to the number set. Current number set: [33, 148], target: 21, just two numbers left.\n     |- Try 148 + 33 = 181. Evaluate 181 != 21, drop this branch.\n     |- Try 148 - 33 = 115. Evaluate 115 != 21, drop this branch.\n     |- Try 148 * 33 = 4884. 4884 exceeds the maximum intermediate result, drop this branch.\n     |- Try 148 \/ 33 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 26 - 7 = 19. Add 19 to the number set. Current number set: [19, 148], target: 21, just two numbers left.\n     |- Try 148 + 19 = 167. Evaluate 167 != 21, drop this branch.\n     |- Try 148 - 19 = 129. Evaluate 129 != 21, drop this branch.\n     |- Try 148 * 19 = 2812. 2812 exceeds the maximum intermediate result, drop this branch.\n     |- Try 148 \/ 19 = 7.8. 7.8 is a decimal, drop this branch.\n    |- Try 26 * 7 = 182. Add 182 to the number set. Current number set: [182, 148], target: 21, just two numbers left.\n     |- Try 182 + 148 = 330. Evaluate 330 != 21, drop this branch.\n     |- Try 182 - 148 = 34. Evaluate 34 != 21, drop this branch.\n     |- Try 182 * 148 = 26936. 26936 exceeds the maximum intermediate result, drop this branch.\n     |- Try 182 \/ 148 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 26 \/ 7 = 3.7. 3.7 is a decimal, drop this branch.\n  |- Try 37 \/ 4 = 9.2. 9.2 is a decimal, drop this branch.\n |- Pick two numbers (37, 26) (numbers left: [4, 7]). Try possible operations.\n  |- Try 37 + 26 = 63. Add 63 to the number set. Current number set: [63, 4, 7], target: 21. Options for choosing two numbers: [(63, 4), (63, 7), (4, 7)].\n   |- Pick two numbers (63, 4) (numbers left: [7]). Try possible operations.\n    |- Try 63 + 4 = 67. Add 67 to the number set. Current number set: [67, 7], target: 21, just two numbers left.\n     |- Try 67 + 7 = 74. Evaluate 74 != 21, drop this branch.\n     |- Try 67 - 7 = 60. Evaluate 60 != 21, drop this branch.\n     |- Try 67 * 7 = 469. Evaluate 469 != 21, drop this branch.\n     |- Try 67 \/ 7 = 9.6. 9.6 is a decimal, drop this branch.\n    |- Try 63 - 4 = 59. Add 59 to the number set. Current number set: [59, 7], target: 21, just two numbers left.\n     |- Try 59 + 7 = 66. Evaluate 66 != 21, drop this branch.\n     |- Try 59 - 7 = 52. Evaluate 52 != 21, drop this branch.\n     |- Try 59 * 7 = 413. Evaluate 413 != 21, drop this branch.\n     |- Try 59 \/ 7 = 8.4. 8.4 is a decimal, drop this branch.\n    |- Try 63 * 4 = 252. Add 252 to the number set. Current number set: [252, 7], target: 21, just two numbers left.\n     |- Try 252 + 7 = 259. Evaluate 259 != 21, drop this branch.\n     |- Try 252 - 7 = 245. Evaluate 245 != 21, drop this branch.\n     |- Try 252 * 7 = 1764. Evaluate 1764 != 21, drop this branch.\n     |- Try 252 \/ 7 = 36. Evaluate 36 != 21, drop this branch.\n    |- Try 63 \/ 4 = 15.8. 15.8 is a decimal, drop this branch.\n   |- Pick two numbers (63, 7) (numbers left: [4]). Try possible operations.\n    |- Try 63 + 7 = 70. Add 70 to the number set. Current number set: [70, 4], target: 21, just two numbers left.\n     |- Try 70 + 4 = 74. Evaluate 74 != 21, drop this branch.\n     |- Try 70 - 4 = 66. Evaluate 66 != 21, drop this branch.\n     |- Try 70 * 4 = 280. Evaluate 280 != 21, drop this branch.\n     |- Try 70 \/ 4 = 17.5. 17.5 is a decimal, drop this branch.\n    |- Try 63 - 7 = 56. Add 56 to the number set. Current number set: [56, 4], target: 21, just two numbers left.\n     |- Try 56 + 4 = 60. Evaluate 60 != 21, drop this branch.\n     |- Try 56 - 4 = 52. Evaluate 52 != 21, drop this branch.\n     |- Try 56 * 4 = 224. Evaluate 224 != 21, drop this branch.\n     |- Try 56 \/ 4 = 14. Evaluate 14 != 21, drop this branch.\n    |- Try 63 * 7 = 441. Add 441 to the number set. Current number set: [441, 4], target: 21, just two numbers left.\n     |- Try 441 + 4 = 445. Evaluate 445 != 21, drop this branch.\n     |- Try 441 - 4 = 437. Evaluate 437 != 21, drop this branch.\n     |- Try 441 * 4 = 1764. Evaluate 1764 != 21, drop this branch.\n     |- Try 441 \/ 4 = 110.2. 110.2 is a decimal, drop this branch.\n    |- Try 63 \/ 7 = 9. Add 9 to the number set. Current number set: [9, 4], target: 21, just two numbers left.\n     |- Try 9 + 4 = 13. Evaluate 13 != 21, drop this branch.\n     |- Try 9 - 4 = 5. Evaluate 5 != 21, drop this branch.\n     |- Try 9 * 4 = 36. Evaluate 36 != 21, drop this branch.\n     |- Try 9 \/ 4 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (4, 7) (numbers left: [63]). Try possible operations.\n    |- Try 7 + 4 = 11. Add 11 to the number set. Current number set: [11, 63], target: 21, just two numbers left.\n     |- Try 63 + 11 = 74. Evaluate 74 != 21, drop this branch.\n     |- Try 63 - 11 = 52. Evaluate 52 != 21, drop this branch.\n     |- Try 63 * 11 = 693. Evaluate 693 != 21, drop this branch.\n     |- Try 63 \/ 11 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 7 - 4 = 3. Add 3 to the number set. Current number set: [3, 63], target: 21, just two numbers left.\n     |- Try 63 + 3 = 66. Evaluate 66 != 21, drop this branch.\n     |- Try 63 - 3 = 60. Evaluate 60 != 21, drop this branch.\n     |- Try 63 * 3 = 189. Evaluate 189 != 21, drop this branch.\n     |- Try 63 \/ 3 = 21. Evaluate 21 == 21, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 63 \/ 3 = 21\nThe step before: 7 - 4 = 3\nThe first step: 37 + 26 = 63\n\nOutput the solution in the required format:\n<Solution>\n37 + 26 = 63\n7 - 4 = 3\n63 \/ 3 = 21\n<\/Solution>\n","item":{"nums":[37,4,26,7],"solution":["37 + 26 = 63","7 - 4 = 3","63 \/ 3 = 21"],"target":21}}
+{"instance_id":"countdown_8k_68","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [30, 41, 10, 11]\nTarget: 31","reference_output":"# Search Procedure\nInitial number set: [30, 41, 10, 11], target: 31. Options for choosing two numbers: [(30, 41), (30, 10), (30, 11), (41, 10), (41, 11), (10, 11)].\n |- Pick two numbers (30, 41) (numbers left: [10, 11]). Try possible operations.\n  |- Try 41 + 30 = 71. Add 71 to the number set. Current number set: [71, 10, 11], target: 31. Options for choosing two numbers: [(71, 10), (71, 11), (10, 11)].\n   |- Pick two numbers (71, 10) (numbers left: [11]). Try possible operations.\n    |- Try 71 + 10 = 81. Add 81 to the number set. Current number set: [81, 11], target: 31, just two numbers left.\n     |- Try 81 + 11 = 92. Evaluate 92 != 31, drop this branch.\n     |- Try 81 - 11 = 70. Evaluate 70 != 31, drop this branch.\n     |- Try 81 * 11 = 891. Evaluate 891 != 31, drop this branch.\n     |- Try 81 \/ 11 = 7.4. 7.4 is a decimal, drop this branch.\n    |- Try 71 - 10 = 61. Add 61 to the number set. Current number set: [61, 11], target: 31, just two numbers left.\n     |- Try 61 + 11 = 72. Evaluate 72 != 31, drop this branch.\n     |- Try 61 - 11 = 50. Evaluate 50 != 31, drop this branch.\n     |- Try 61 * 11 = 671. Evaluate 671 != 31, drop this branch.\n     |- Try 61 \/ 11 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 71 * 10 = 710. Add 710 to the number set. Current number set: [710, 11], target: 31, just two numbers left.\n     |- Try 710 + 11 = 721. Evaluate 721 != 31, drop this branch.\n     |- Try 710 - 11 = 699. Evaluate 699 != 31, drop this branch.\n     |- Try 710 * 11 = 7810. 7810 exceeds the maximum intermediate result, drop this branch.\n     |- Try 710 \/ 11 = 64.5. 64.5 is a decimal, drop this branch.\n    |- Try 71 \/ 10 = 7.1. 7.1 is a decimal, drop this branch.\n   |- Pick two numbers (71, 11) (numbers left: [10]). Try possible operations.\n    |- Try 71 + 11 = 82. Add 82 to the number set. Current number set: [82, 10], target: 31, just two numbers left.\n     |- Try 82 + 10 = 92. Evaluate 92 != 31, drop this branch.\n     |- Try 82 - 10 = 72. Evaluate 72 != 31, drop this branch.\n     |- Try 82 * 10 = 820. Evaluate 820 != 31, drop this branch.\n     |- Try 82 \/ 10 = 8.2. 8.2 is a decimal, drop this branch.\n    |- Try 71 - 11 = 60. Add 60 to the number set. Current number set: [60, 10], target: 31, just two numbers left.\n     |- Try 60 + 10 = 70. Evaluate 70 != 31, drop this branch.\n     |- Try 60 - 10 = 50. Evaluate 50 != 31, drop this branch.\n     |- Try 60 * 10 = 600. Evaluate 600 != 31, drop this branch.\n     |- Try 60 \/ 10 = 6. Evaluate 6 != 31, drop this branch.\n    |- Try 71 * 11 = 781. Add 781 to the number set. Current number set: [781, 10], target: 31, just two numbers left.\n     |- Try 781 + 10 = 791. Evaluate 791 != 31, drop this branch.\n     |- Try 781 - 10 = 771. Evaluate 771 != 31, drop this branch.\n     |- Try 781 * 10 = 7810. 7810 exceeds the maximum intermediate result, drop this branch.\n     |- Try 781 \/ 10 = 78.1. 78.1 is a decimal, drop this branch.\n    |- Try 71 \/ 11 = 6.5. 6.5 is a decimal, drop this branch.\n   |- Pick two numbers (10, 11) (numbers left: [71]). Try possible operations.\n    |- Try 11 + 10 = 21. Add 21 to the number set. Current number set: [21, 71], target: 31, just two numbers left.\n     |- Try 71 + 21 = 92. Evaluate 92 != 31, drop this branch.\n     |- Try 71 - 21 = 50. Evaluate 50 != 31, drop this branch.\n     |- Try 71 * 21 = 1491. Evaluate 1491 != 31, drop this branch.\n     |- Try 71 \/ 21 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 11 - 10 = 1. Add 1 to the number set. Current number set: [1, 71], target: 31, just two numbers left.\n     |- Try 71 + 1 = 72. Evaluate 72 != 31, drop this branch.\n     |- Try 71 - 1 = 70. Evaluate 70 != 31, drop this branch.\n     |- Try 71 * 1 = 71. Evaluate 71 != 31, drop this branch.\n     |- Try 71 \/ 1 = 71. Evaluate 71 != 31, drop this branch.\n    |- Try 11 * 10 = 110. Add 110 to the number set. Current number set: [110, 71], target: 31, just two numbers left.\n     |- Try 110 + 71 = 181. Evaluate 181 != 31, drop this branch.\n     |- Try 110 - 71 = 39. Evaluate 39 != 31, drop this branch.\n     |- Try 110 * 71 = 7810. 7810 exceeds the maximum intermediate result, drop this branch.\n     |- Try 110 \/ 71 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 11 \/ 10 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 41 - 30 = 11. Add 11 to the number set. Current number set: [11, 10, 11], target: 31. Options for choosing two numbers: [(11, 10), (11, 11), (10, 11)].\n   |- Pick two numbers (11, 10) (numbers left: [11]). Try possible operations.\n    |- Try 11 + 10 = 21. Add 21 to the number set. Current number set: [21, 11], target: 31, just two numbers left.\n     |- Try 21 + 11 = 32. Evaluate 32 != 31, drop this branch.\n     |- Try 21 - 11 = 10. Evaluate 10 != 31, drop this branch.\n     |- Try 21 * 11 = 231. Evaluate 231 != 31, drop this branch.\n     |- Try 21 \/ 11 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 11 - 10 = 1. Add 1 to the number set. Current number set: [1, 11], target: 31, just two numbers left.\n     |- Try 11 + 1 = 12. Evaluate 12 != 31, drop this branch.\n     |- Try 11 - 1 = 10. Evaluate 10 != 31, drop this branch.\n     |- Try 11 * 1 = 11. Evaluate 11 != 31, drop this branch.\n     |- Try 11 \/ 1 = 11. Evaluate 11 != 31, drop this branch.\n    |- Try 11 * 10 = 110. Add 110 to the number set. Current number set: [110, 11], target: 31, just two numbers left.\n     |- Try 110 + 11 = 121. Evaluate 121 != 31, drop this branch.\n     |- Try 110 - 11 = 99. Evaluate 99 != 31, drop this branch.\n     |- Try 110 * 11 = 1210. Evaluate 1210 != 31, drop this branch.\n     |- Try 110 \/ 11 = 10. Evaluate 10 != 31, drop this branch.\n    |- Try 11 \/ 10 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (11, 11) (numbers left: [10]). Try possible operations.\n    |- Try 11 + 11 = 22. Add 22 to the number set. Current number set: [22, 10], target: 31, just two numbers left.\n     |- Try 22 + 10 = 32. Evaluate 32 != 31, drop this branch.\n     |- Try 22 - 10 = 12. Evaluate 12 != 31, drop this branch.\n     |- Try 22 * 10 = 220. Evaluate 220 != 31, drop this branch.\n     |- Try 22 \/ 10 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 11 - 11 = 0. Add 0 to the number set. Current number set: [0, 10], target: 31, just two numbers left.\n     |- Try 10 + 0 = 10. Evaluate 10 != 31, drop this branch.\n     |- Try 10 - 0 = 10. Evaluate 10 != 31, drop this branch.\n     |- Try 10 * 0 = 0. Evaluate 0 != 31, drop this branch.\n     |- Try 10 \/ 0 (invalid operation). drop this branch.\n    |- Try 11 * 11 = 121. Add 121 to the number set. Current number set: [121, 10], target: 31, just two numbers left.\n     |- Try 121 + 10 = 131. Evaluate 131 != 31, drop this branch.\n     |- Try 121 - 10 = 111. Evaluate 111 != 31, drop this branch.\n     |- Try 121 * 10 = 1210. Evaluate 1210 != 31, drop this branch.\n     |- Try 121 \/ 10 = 12.1. 12.1 is a decimal, drop this branch.\n    |- Try 11 \/ 11 = 1. Add 1 to the number set. Current number set: [1, 10], target: 31, just two numbers left.\n     |- Try 10 + 1 = 11. Evaluate 11 != 31, drop this branch.\n     |- Try 10 - 1 = 9. Evaluate 9 != 31, drop this branch.\n     |- Try 10 * 1 = 10. Evaluate 10 != 31, drop this branch.\n     |- Try 10 \/ 1 = 10. Evaluate 10 != 31, drop this branch.\n   |- Pick two numbers (10, 11) (numbers left: [11]). Try possible operations.\n    |- Try 11 + 10 = 21. Add 21 to the number set. Current number set: [21, 11], target: 31, just two numbers left.\n     |- Try 21 + 11 = 32. Evaluate 32 != 31, drop this branch.\n     |- Try 21 - 11 = 10. Evaluate 10 != 31, drop this branch.\n     |- Try 21 * 11 = 231. Evaluate 231 != 31, drop this branch.\n     |- Try 21 \/ 11 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 11 - 10 = 1. Add 1 to the number set. Current number set: [1, 11], target: 31, just two numbers left.\n     |- Try 11 + 1 = 12. Evaluate 12 != 31, drop this branch.\n     |- Try 11 - 1 = 10. Evaluate 10 != 31, drop this branch.\n     |- Try 11 * 1 = 11. Evaluate 11 != 31, drop this branch.\n     |- Try 11 \/ 1 = 11. Evaluate 11 != 31, drop this branch.\n    |- Try 11 * 10 = 110. Add 110 to the number set. Current number set: [110, 11], target: 31, just two numbers left.\n     |- Try 110 + 11 = 121. Evaluate 121 != 31, drop this branch.\n     |- Try 110 - 11 = 99. Evaluate 99 != 31, drop this branch.\n     |- Try 110 * 11 = 1210. Evaluate 1210 != 31, drop this branch.\n     |- Try 110 \/ 11 = 10. Evaluate 10 != 31, drop this branch.\n    |- Try 11 \/ 10 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 41 * 30 = 1230. Add 1230 to the number set. Current number set: [1230, 10, 11], target: 31. Options for choosing two numbers: [(1230, 10), (1230, 11), (10, 11)].\n   |- Pick two numbers (1230, 10) (numbers left: [11]). Try possible operations.\n    |- Try 1230 + 10 = 1240. Add 1240 to the number set. Current number set: [1240, 11], target: 31, just two numbers left.\n     |- Try 1240 + 11 = 1251. Evaluate 1251 != 31, drop this branch.\n     |- Try 1240 - 11 = 1229. Evaluate 1229 != 31, drop this branch.\n     |- Try 1240 * 11 = 13640. 13640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1240 \/ 11 = 112.7. 112.7 is a decimal, drop this branch.\n    |- Try 1230 - 10 = 1220. Add 1220 to the number set. Current number set: [1220, 11], target: 31, just two numbers left.\n     |- Try 1220 + 11 = 1231. Evaluate 1231 != 31, drop this branch.\n     |- Try 1220 - 11 = 1209. Evaluate 1209 != 31, drop this branch.\n     |- Try 1220 * 11 = 13420. 13420 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1220 \/ 11 = 110.9. 110.9 is a decimal, drop this branch.\n    |- Try 1230 * 10 = 12300. 12300 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1230 \/ 10 = 123. Add 123 to the number set. Current number set: [123, 11], target: 31, just two numbers left.\n     |- Try 123 + 11 = 134. Evaluate 134 != 31, drop this branch.\n     |- Try 123 - 11 = 112. Evaluate 112 != 31, drop this branch.\n     |- Try 123 * 11 = 1353. Evaluate 1353 != 31, drop this branch.\n     |- Try 123 \/ 11 = 11.2. 11.2 is a decimal, drop this branch.\n   |- Pick two numbers (1230, 11) (numbers left: [10]). Try possible operations.\n    |- Try 1230 + 11 = 1241. Add 1241 to the number set. Current number set: [1241, 10], target: 31, just two numbers left.\n     |- Try 1241 + 10 = 1251. Evaluate 1251 != 31, drop this branch.\n     |- Try 1241 - 10 = 1231. Evaluate 1231 != 31, drop this branch.\n     |- Try 1241 * 10 = 12410. 12410 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1241 \/ 10 = 124.1. 124.1 is a decimal, drop this branch.\n    |- Try 1230 - 11 = 1219. Add 1219 to the number set. Current number set: [1219, 10], target: 31, just two numbers left.\n     |- Try 1219 + 10 = 1229. Evaluate 1229 != 31, drop this branch.\n     |- Try 1219 - 10 = 1209. Evaluate 1209 != 31, drop this branch.\n     |- Try 1219 * 10 = 12190. 12190 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1219 \/ 10 = 121.9. 121.9 is a decimal, drop this branch.\n    |- Try 1230 * 11 = 13530. 13530 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1230 \/ 11 = 111.8. 111.8 is a decimal, drop this branch.\n   |- Pick two numbers (10, 11) (numbers left: [1230]). Try possible operations.\n    |- Try 11 + 10 = 21. Add 21 to the number set. Current number set: [21, 1230], target: 31, just two numbers left.\n     |- Try 1230 + 21 = 1251. Evaluate 1251 != 31, drop this branch.\n     |- Try 1230 - 21 = 1209. Evaluate 1209 != 31, drop this branch.\n     |- Try 1230 * 21 = 25830. 25830 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1230 \/ 21 = 58.6. 58.6 is a decimal, drop this branch.\n    |- Try 11 - 10 = 1. Add 1 to the number set. Current number set: [1, 1230], target: 31, just two numbers left.\n     |- Try 1230 + 1 = 1231. Evaluate 1231 != 31, drop this branch.\n     |- Try 1230 - 1 = 1229. Evaluate 1229 != 31, drop this branch.\n     |- Try 1230 * 1 = 1230. Evaluate 1230 != 31, drop this branch.\n     |- Try 1230 \/ 1 = 1230. Evaluate 1230 != 31, drop this branch.\n    |- Try 11 * 10 = 110. Add 110 to the number set. Current number set: [110, 1230], target: 31, just two numbers left.\n     |- Try 1230 + 110 = 1340. Evaluate 1340 != 31, drop this branch.\n     |- Try 1230 - 110 = 1120. Evaluate 1120 != 31, drop this branch.\n     |- Try 1230 * 110 = 135300. 135300 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1230 \/ 110 = 11.2. 11.2 is a decimal, drop this branch.\n    |- Try 11 \/ 10 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 41 \/ 30 = 1.4. 1.4 is a decimal, drop this branch.\n |- Pick two numbers (30, 10) (numbers left: [41, 11]). Try possible operations.\n  |- Try 30 + 10 = 40. Add 40 to the number set. Current number set: [40, 41, 11], target: 31. Options for choosing two numbers: [(40, 41), (40, 11), (41, 11)].\n   |- Pick two numbers (40, 41) (numbers left: [11]). Try possible operations.\n    |- Try 41 + 40 = 81. Add 81 to the number set. Current number set: [81, 11], target: 31, just two numbers left.\n     |- Try 81 + 11 = 92. Evaluate 92 != 31, drop this branch.\n     |- Try 81 - 11 = 70. Evaluate 70 != 31, drop this branch.\n     |- Try 81 * 11 = 891. Evaluate 891 != 31, drop this branch.\n     |- Try 81 \/ 11 = 7.4. 7.4 is a decimal, drop this branch.\n    |- Try 41 - 40 = 1. Add 1 to the number set. Current number set: [1, 11], target: 31, just two numbers left.\n     |- Try 11 + 1 = 12. Evaluate 12 != 31, drop this branch.\n     |- Try 11 - 1 = 10. Evaluate 10 != 31, drop this branch.\n     |- Try 11 * 1 = 11. Evaluate 11 != 31, drop this branch.\n     |- Try 11 \/ 1 = 11. Evaluate 11 != 31, drop this branch.\n    |- Try 41 * 40 = 1640. Add 1640 to the number set. Current number set: [1640, 11], target: 31, just two numbers left.\n     |- Try 1640 + 11 = 1651. Evaluate 1651 != 31, drop this branch.\n     |- Try 1640 - 11 = 1629. Evaluate 1629 != 31, drop this branch.\n     |- Try 1640 * 11 = 18040. 18040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1640 \/ 11 = 149.1. 149.1 is a decimal, drop this branch.\n    |- Try 41 \/ 40 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (40, 11) (numbers left: [41]). Try possible operations.\n    |- Try 40 + 11 = 51. Add 51 to the number set. Current number set: [51, 41], target: 31, just two numbers left.\n     |- Try 51 + 41 = 92. Evaluate 92 != 31, drop this branch.\n     |- Try 51 - 41 = 10. Evaluate 10 != 31, drop this branch.\n     |- Try 51 * 41 = 2091. 2091 exceeds the maximum intermediate result, drop this branch.\n     |- Try 51 \/ 41 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 40 - 11 = 29. Add 29 to the number set. Current number set: [29, 41], target: 31, just two numbers left.\n     |- Try 41 + 29 = 70. Evaluate 70 != 31, drop this branch.\n     |- Try 41 - 29 = 12. Evaluate 12 != 31, drop this branch.\n     |- Try 41 * 29 = 1189. Evaluate 1189 != 31, drop this branch.\n     |- Try 41 \/ 29 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 40 * 11 = 440. Add 440 to the number set. Current number set: [440, 41], target: 31, just two numbers left.\n     |- Try 440 + 41 = 481. Evaluate 481 != 31, drop this branch.\n     |- Try 440 - 41 = 399. Evaluate 399 != 31, drop this branch.\n     |- Try 440 * 41 = 18040. 18040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 440 \/ 41 = 10.7. 10.7 is a decimal, drop this branch.\n    |- Try 40 \/ 11 = 3.6. 3.6 is a decimal, drop this branch.\n   |- Pick two numbers (41, 11) (numbers left: [40]). Try possible operations.\n    |- Try 41 + 11 = 52. Add 52 to the number set. Current number set: [52, 40], target: 31, just two numbers left.\n     |- Try 52 + 40 = 92. Evaluate 92 != 31, drop this branch.\n     |- Try 52 - 40 = 12. Evaluate 12 != 31, drop this branch.\n     |- Try 52 * 40 = 2080. 2080 exceeds the maximum intermediate result, drop this branch.\n     |- Try 52 \/ 40 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 41 - 11 = 30. Add 30 to the number set. Current number set: [30, 40], target: 31, just two numbers left.\n     |- Try 40 + 30 = 70. Evaluate 70 != 31, drop this branch.\n     |- Try 40 - 30 = 10. Evaluate 10 != 31, drop this branch.\n     |- Try 40 * 30 = 1200. Evaluate 1200 != 31, drop this branch.\n     |- Try 40 \/ 30 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 41 * 11 = 451. Add 451 to the number set. Current number set: [451, 40], target: 31, just two numbers left.\n     |- Try 451 + 40 = 491. Evaluate 491 != 31, drop this branch.\n     |- Try 451 - 40 = 411. Evaluate 411 != 31, drop this branch.\n     |- Try 451 * 40 = 18040. 18040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 451 \/ 40 = 11.3. 11.3 is a decimal, drop this branch.\n    |- Try 41 \/ 11 = 3.7. 3.7 is a decimal, drop this branch.\n  |- Try 30 - 10 = 20. Add 20 to the number set. Current number set: [20, 41, 11], target: 31. Options for choosing two numbers: [(20, 41), (20, 11), (41, 11)].\n   |- Pick two numbers (20, 41) (numbers left: [11]). Try possible operations.\n    |- Try 41 + 20 = 61. Add 61 to the number set. Current number set: [61, 11], target: 31, just two numbers left.\n     |- Try 61 + 11 = 72. Evaluate 72 != 31, drop this branch.\n     |- Try 61 - 11 = 50. Evaluate 50 != 31, drop this branch.\n     |- Try 61 * 11 = 671. Evaluate 671 != 31, drop this branch.\n     |- Try 61 \/ 11 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 41 - 20 = 21. Add 21 to the number set. Current number set: [21, 11], target: 31, just two numbers left.\n     |- Try 21 + 11 = 32. Evaluate 32 != 31, drop this branch.\n     |- Try 21 - 11 = 10. Evaluate 10 != 31, drop this branch.\n     |- Try 21 * 11 = 231. Evaluate 231 != 31, drop this branch.\n     |- Try 21 \/ 11 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 41 * 20 = 820. Add 820 to the number set. Current number set: [820, 11], target: 31, just two numbers left.\n     |- Try 820 + 11 = 831. Evaluate 831 != 31, drop this branch.\n     |- Try 820 - 11 = 809. Evaluate 809 != 31, drop this branch.\n     |- Try 820 * 11 = 9020. 9020 exceeds the maximum intermediate result, drop this branch.\n     |- Try 820 \/ 11 = 74.5. 74.5 is a decimal, drop this branch.\n    |- Try 41 \/ 20 = 2.0. 2.0 is a decimal, drop this branch.\n   |- Pick two numbers (20, 11) (numbers left: [41]). Try possible operations.\n    |- Try 20 + 11 = 31. Add 31 to the number set. Current number set: [31, 41], target: 31, just two numbers left.\n     |- Try 41 + 31 = 72. Evaluate 72 != 31, drop this branch.\n     |- Try 41 - 31 = 10. Evaluate 10 != 31, drop this branch.\n     |- Try 41 * 31 = 1271. Evaluate 1271 != 31, drop this branch.\n     |- Try 41 \/ 31 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 20 - 11 = 9. Add 9 to the number set. Current number set: [9, 41], target: 31, just two numbers left.\n     |- Try 41 + 9 = 50. Evaluate 50 != 31, drop this branch.\n     |- Try 41 - 9 = 32. Evaluate 32 != 31, drop this branch.\n     |- Try 41 * 9 = 369. Evaluate 369 != 31, drop this branch.\n     |- Try 41 \/ 9 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 20 * 11 = 220. Add 220 to the number set. Current number set: [220, 41], target: 31, just two numbers left.\n     |- Try 220 + 41 = 261. Evaluate 261 != 31, drop this branch.\n     |- Try 220 - 41 = 179. Evaluate 179 != 31, drop this branch.\n     |- Try 220 * 41 = 9020. 9020 exceeds the maximum intermediate result, drop this branch.\n     |- Try 220 \/ 41 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 20 \/ 11 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (41, 11) (numbers left: [20]). Try possible operations.\n    |- Try 41 + 11 = 52. Add 52 to the number set. Current number set: [52, 20], target: 31, just two numbers left.\n     |- Try 52 + 20 = 72. Evaluate 72 != 31, drop this branch.\n     |- Try 52 - 20 = 32. Evaluate 32 != 31, drop this branch.\n     |- Try 52 * 20 = 1040. Evaluate 1040 != 31, drop this branch.\n     |- Try 52 \/ 20 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 41 - 11 = 30. Add 30 to the number set. Current number set: [30, 20], target: 31, just two numbers left.\n     |- Try 30 + 20 = 50. Evaluate 50 != 31, drop this branch.\n     |- Try 30 - 20 = 10. Evaluate 10 != 31, drop this branch.\n     |- Try 30 * 20 = 600. Evaluate 600 != 31, drop this branch.\n     |- Try 30 \/ 20 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 41 * 11 = 451. Add 451 to the number set. Current number set: [451, 20], target: 31, just two numbers left.\n     |- Try 451 + 20 = 471. Evaluate 471 != 31, drop this branch.\n     |- Try 451 - 20 = 431. Evaluate 431 != 31, drop this branch.\n     |- Try 451 * 20 = 9020. 9020 exceeds the maximum intermediate result, drop this branch.\n     |- Try 451 \/ 20 = 22.6. 22.6 is a decimal, drop this branch.\n    |- Try 41 \/ 11 = 3.7. 3.7 is a decimal, drop this branch.\n  |- Try 30 * 10 = 300. Add 300 to the number set. Current number set: [300, 41, 11], target: 31. Options for choosing two numbers: [(300, 41), (300, 11), (41, 11)].\n   |- Pick two numbers (300, 41) (numbers left: [11]). Try possible operations.\n    |- Try 300 + 41 = 341. Add 341 to the number set. Current number set: [341, 11], target: 31, just two numbers left.\n     |- Try 341 + 11 = 352. Evaluate 352 != 31, drop this branch.\n     |- Try 341 - 11 = 330. Evaluate 330 != 31, drop this branch.\n     |- Try 341 * 11 = 3751. 3751 exceeds the maximum intermediate result, drop this branch.\n     |- Try 341 \/ 11 = 31. Evaluate 31 == 31, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 341 \/ 11 = 31\nThe step before: 300 + 41 = 341\nThe first step: 30 * 10 = 300\n\nOutput the solution in the required format:\n<Solution>\n30 * 10 = 300\n300 + 41 = 341\n341 \/ 11 = 31\n<\/Solution>\n","item":{"nums":[30,41,10,11],"solution":["30 * 10 = 300","300 + 41 = 341","341 \/ 11 = 31"],"target":31}}
+{"instance_id":"countdown_8k_69","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [24, 30, 45, 3]\nTarget: 23","reference_output":"# Search Procedure\nInitial number set: [24, 30, 45, 3], target: 23. Options for choosing two numbers: [(24, 30), (24, 45), (24, 3), (30, 45), (30, 3), (45, 3)].\n |- Pick two numbers (24, 30) (numbers left: [45, 3]). Try possible operations.\n  |- Try 30 + 24 = 54. Add 54 to the number set. Current number set: [54, 45, 3], target: 23. Options for choosing two numbers: [(54, 45), (54, 3), (45, 3)].\n   |- Pick two numbers (54, 45) (numbers left: [3]). Try possible operations.\n    |- Try 54 + 45 = 99. Add 99 to the number set. Current number set: [99, 3], target: 23, just two numbers left.\n     |- Try 99 + 3 = 102. Evaluate 102 != 23, drop this branch.\n     |- Try 99 - 3 = 96. Evaluate 96 != 23, drop this branch.\n     |- Try 99 * 3 = 297. Evaluate 297 != 23, drop this branch.\n     |- Try 99 \/ 3 = 33. Evaluate 33 != 23, drop this branch.\n    |- Try 54 - 45 = 9. Add 9 to the number set. Current number set: [9, 3], target: 23, just two numbers left.\n     |- Try 9 + 3 = 12. Evaluate 12 != 23, drop this branch.\n     |- Try 9 - 3 = 6. Evaluate 6 != 23, drop this branch.\n     |- Try 9 * 3 = 27. Evaluate 27 != 23, drop this branch.\n     |- Try 9 \/ 3 = 3. Evaluate 3 != 23, drop this branch.\n    |- Try 54 * 45 = 2430. 2430 exceeds the maximum intermediate result, drop this branch.\n    |- Try 54 \/ 45 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (54, 3) (numbers left: [45]). Try possible operations.\n    |- Try 54 + 3 = 57. Add 57 to the number set. Current number set: [57, 45], target: 23, just two numbers left.\n     |- Try 57 + 45 = 102. Evaluate 102 != 23, drop this branch.\n     |- Try 57 - 45 = 12. Evaluate 12 != 23, drop this branch.\n     |- Try 57 * 45 = 2565. 2565 exceeds the maximum intermediate result, drop this branch.\n     |- Try 57 \/ 45 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 54 - 3 = 51. Add 51 to the number set. Current number set: [51, 45], target: 23, just two numbers left.\n     |- Try 51 + 45 = 96. Evaluate 96 != 23, drop this branch.\n     |- Try 51 - 45 = 6. Evaluate 6 != 23, drop this branch.\n     |- Try 51 * 45 = 2295. 2295 exceeds the maximum intermediate result, drop this branch.\n     |- Try 51 \/ 45 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 54 * 3 = 162. Add 162 to the number set. Current number set: [162, 45], target: 23, just two numbers left.\n     |- Try 162 + 45 = 207. Evaluate 207 != 23, drop this branch.\n     |- Try 162 - 45 = 117. Evaluate 117 != 23, drop this branch.\n     |- Try 162 * 45 = 7290. 7290 exceeds the maximum intermediate result, drop this branch.\n     |- Try 162 \/ 45 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 54 \/ 3 = 18. Add 18 to the number set. Current number set: [18, 45], target: 23, just two numbers left.\n     |- Try 45 + 18 = 63. Evaluate 63 != 23, drop this branch.\n     |- Try 45 - 18 = 27. Evaluate 27 != 23, drop this branch.\n     |- Try 45 * 18 = 810. Evaluate 810 != 23, drop this branch.\n     |- Try 45 \/ 18 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (45, 3) (numbers left: [54]). Try possible operations.\n    |- Try 45 + 3 = 48. Add 48 to the number set. Current number set: [48, 54], target: 23, just two numbers left.\n     |- Try 54 + 48 = 102. Evaluate 102 != 23, drop this branch.\n     |- Try 54 - 48 = 6. Evaluate 6 != 23, drop this branch.\n     |- Try 54 * 48 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n     |- Try 54 \/ 48 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 45 - 3 = 42. Add 42 to the number set. Current number set: [42, 54], target: 23, just two numbers left.\n     |- Try 54 + 42 = 96. Evaluate 96 != 23, drop this branch.\n     |- Try 54 - 42 = 12. Evaluate 12 != 23, drop this branch.\n     |- Try 54 * 42 = 2268. 2268 exceeds the maximum intermediate result, drop this branch.\n     |- Try 54 \/ 42 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 45 * 3 = 135. Add 135 to the number set. Current number set: [135, 54], target: 23, just two numbers left.\n     |- Try 135 + 54 = 189. Evaluate 189 != 23, drop this branch.\n     |- Try 135 - 54 = 81. Evaluate 81 != 23, drop this branch.\n     |- Try 135 * 54 = 7290. 7290 exceeds the maximum intermediate result, drop this branch.\n     |- Try 135 \/ 54 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 45 \/ 3 = 15. Add 15 to the number set. Current number set: [15, 54], target: 23, just two numbers left.\n     |- Try 54 + 15 = 69. Evaluate 69 != 23, drop this branch.\n     |- Try 54 - 15 = 39. Evaluate 39 != 23, drop this branch.\n     |- Try 54 * 15 = 810. Evaluate 810 != 23, drop this branch.\n     |- Try 54 \/ 15 = 3.6. 3.6 is a decimal, drop this branch.\n  |- Try 30 - 24 = 6. Add 6 to the number set. Current number set: [6, 45, 3], target: 23. Options for choosing two numbers: [(6, 45), (6, 3), (45, 3)].\n   |- Pick two numbers (6, 45) (numbers left: [3]). Try possible operations.\n    |- Try 45 + 6 = 51. Add 51 to the number set. Current number set: [51, 3], target: 23, just two numbers left.\n     |- Try 51 + 3 = 54. Evaluate 54 != 23, drop this branch.\n     |- Try 51 - 3 = 48. Evaluate 48 != 23, drop this branch.\n     |- Try 51 * 3 = 153. Evaluate 153 != 23, drop this branch.\n     |- Try 51 \/ 3 = 17. Evaluate 17 != 23, drop this branch.\n    |- Try 45 - 6 = 39. Add 39 to the number set. Current number set: [39, 3], target: 23, just two numbers left.\n     |- Try 39 + 3 = 42. Evaluate 42 != 23, drop this branch.\n     |- Try 39 - 3 = 36. Evaluate 36 != 23, drop this branch.\n     |- Try 39 * 3 = 117. Evaluate 117 != 23, drop this branch.\n     |- Try 39 \/ 3 = 13. Evaluate 13 != 23, drop this branch.\n    |- Try 45 * 6 = 270. Add 270 to the number set. Current number set: [270, 3], target: 23, just two numbers left.\n     |- Try 270 + 3 = 273. Evaluate 273 != 23, drop this branch.\n     |- Try 270 - 3 = 267. Evaluate 267 != 23, drop this branch.\n     |- Try 270 * 3 = 810. Evaluate 810 != 23, drop this branch.\n     |- Try 270 \/ 3 = 90. Evaluate 90 != 23, drop this branch.\n    |- Try 45 \/ 6 = 7.5. 7.5 is a decimal, drop this branch.\n   |- Pick two numbers (6, 3) (numbers left: [45]). Try possible operations.\n    |- Try 6 + 3 = 9. Add 9 to the number set. Current number set: [9, 45], target: 23, just two numbers left.\n     |- Try 45 + 9 = 54. Evaluate 54 != 23, drop this branch.\n     |- Try 45 - 9 = 36. Evaluate 36 != 23, drop this branch.\n     |- Try 45 * 9 = 405. Evaluate 405 != 23, drop this branch.\n     |- Try 45 \/ 9 = 5. Evaluate 5 != 23, drop this branch.\n    |- Try 6 - 3 = 3. Add 3 to the number set. Current number set: [3, 45], target: 23, just two numbers left.\n     |- Try 45 + 3 = 48. Evaluate 48 != 23, drop this branch.\n     |- Try 45 - 3 = 42. Evaluate 42 != 23, drop this branch.\n     |- Try 45 * 3 = 135. Evaluate 135 != 23, drop this branch.\n     |- Try 45 \/ 3 = 15. Evaluate 15 != 23, drop this branch.\n    |- Try 6 * 3 = 18. Add 18 to the number set. Current number set: [18, 45], target: 23, just two numbers left.\n     |- Try 45 + 18 = 63. Evaluate 63 != 23, drop this branch.\n     |- Try 45 - 18 = 27. Evaluate 27 != 23, drop this branch.\n     |- Try 45 * 18 = 810. Evaluate 810 != 23, drop this branch.\n     |- Try 45 \/ 18 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 6 \/ 3 = 2. Add 2 to the number set. Current number set: [2, 45], target: 23, just two numbers left.\n     |- Try 45 + 2 = 47. Evaluate 47 != 23, drop this branch.\n     |- Try 45 - 2 = 43. Evaluate 43 != 23, drop this branch.\n     |- Try 45 * 2 = 90. Evaluate 90 != 23, drop this branch.\n     |- Try 45 \/ 2 = 22.5. 22.5 is a decimal, drop this branch.\n   |- Pick two numbers (45, 3) (numbers left: [6]). Try possible operations.\n    |- Try 45 + 3 = 48. Add 48 to the number set. Current number set: [48, 6], target: 23, just two numbers left.\n     |- Try 48 + 6 = 54. Evaluate 54 != 23, drop this branch.\n     |- Try 48 - 6 = 42. Evaluate 42 != 23, drop this branch.\n     |- Try 48 * 6 = 288. Evaluate 288 != 23, drop this branch.\n     |- Try 48 \/ 6 = 8. Evaluate 8 != 23, drop this branch.\n    |- Try 45 - 3 = 42. Add 42 to the number set. Current number set: [42, 6], target: 23, just two numbers left.\n     |- Try 42 + 6 = 48. Evaluate 48 != 23, drop this branch.\n     |- Try 42 - 6 = 36. Evaluate 36 != 23, drop this branch.\n     |- Try 42 * 6 = 252. Evaluate 252 != 23, drop this branch.\n     |- Try 42 \/ 6 = 7. Evaluate 7 != 23, drop this branch.\n    |- Try 45 * 3 = 135. Add 135 to the number set. Current number set: [135, 6], target: 23, just two numbers left.\n     |- Try 135 + 6 = 141. Evaluate 141 != 23, drop this branch.\n     |- Try 135 - 6 = 129. Evaluate 129 != 23, drop this branch.\n     |- Try 135 * 6 = 810. Evaluate 810 != 23, drop this branch.\n     |- Try 135 \/ 6 = 22.5. 22.5 is a decimal, drop this branch.\n    |- Try 45 \/ 3 = 15. Add 15 to the number set. Current number set: [15, 6], target: 23, just two numbers left.\n     |- Try 15 + 6 = 21. Evaluate 21 != 23, drop this branch.\n     |- Try 15 - 6 = 9. Evaluate 9 != 23, drop this branch.\n     |- Try 15 * 6 = 90. Evaluate 90 != 23, drop this branch.\n     |- Try 15 \/ 6 = 2.5. 2.5 is a decimal, drop this branch.\n  |- Try 30 * 24 = 720. Add 720 to the number set. Current number set: [720, 45, 3], target: 23. Options for choosing two numbers: [(720, 45), (720, 3), (45, 3)].\n   |- Pick two numbers (720, 45) (numbers left: [3]). Try possible operations.\n    |- Try 720 + 45 = 765. Add 765 to the number set. Current number set: [765, 3], target: 23, just two numbers left.\n     |- Try 765 + 3 = 768. Evaluate 768 != 23, drop this branch.\n     |- Try 765 - 3 = 762. Evaluate 762 != 23, drop this branch.\n     |- Try 765 * 3 = 2295. 2295 exceeds the maximum intermediate result, drop this branch.\n     |- Try 765 \/ 3 = 255. Evaluate 255 != 23, drop this branch.\n    |- Try 720 - 45 = 675. Add 675 to the number set. Current number set: [675, 3], target: 23, just two numbers left.\n     |- Try 675 + 3 = 678. Evaluate 678 != 23, drop this branch.\n     |- Try 675 - 3 = 672. Evaluate 672 != 23, drop this branch.\n     |- Try 675 * 3 = 2025. 2025 exceeds the maximum intermediate result, drop this branch.\n     |- Try 675 \/ 3 = 225. Evaluate 225 != 23, drop this branch.\n    |- Try 720 * 45 = 32400. 32400 exceeds the maximum intermediate result, drop this branch.\n    |- Try 720 \/ 45 = 16. Add 16 to the number set. Current number set: [16, 3], target: 23, just two numbers left.\n     |- Try 16 + 3 = 19. Evaluate 19 != 23, drop this branch.\n     |- Try 16 - 3 = 13. Evaluate 13 != 23, drop this branch.\n     |- Try 16 * 3 = 48. Evaluate 48 != 23, drop this branch.\n     |- Try 16 \/ 3 = 5.3. 5.3 is a decimal, drop this branch.\n   |- Pick two numbers (720, 3) (numbers left: [45]). Try possible operations.\n    |- Try 720 + 3 = 723. Add 723 to the number set. Current number set: [723, 45], target: 23, just two numbers left.\n     |- Try 723 + 45 = 768. Evaluate 768 != 23, drop this branch.\n     |- Try 723 - 45 = 678. Evaluate 678 != 23, drop this branch.\n     |- Try 723 * 45 = 32535. 32535 exceeds the maximum intermediate result, drop this branch.\n     |- Try 723 \/ 45 = 16.1. 16.1 is a decimal, drop this branch.\n    |- Try 720 - 3 = 717. Add 717 to the number set. Current number set: [717, 45], target: 23, just two numbers left.\n     |- Try 717 + 45 = 762. Evaluate 762 != 23, drop this branch.\n     |- Try 717 - 45 = 672. Evaluate 672 != 23, drop this branch.\n     |- Try 717 * 45 = 32265. 32265 exceeds the maximum intermediate result, drop this branch.\n     |- Try 717 \/ 45 = 15.9. 15.9 is a decimal, drop this branch.\n    |- Try 720 * 3 = 2160. 2160 exceeds the maximum intermediate result, drop this branch.\n    |- Try 720 \/ 3 = 240. Add 240 to the number set. Current number set: [240, 45], target: 23, just two numbers left.\n     |- Try 240 + 45 = 285. Evaluate 285 != 23, drop this branch.\n     |- Try 240 - 45 = 195. Evaluate 195 != 23, drop this branch.\n     |- Try 240 * 45 = 10800. 10800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 240 \/ 45 = 5.3. 5.3 is a decimal, drop this branch.\n   |- Pick two numbers (45, 3) (numbers left: [720]). Try possible operations.\n    |- Try 45 + 3 = 48. Add 48 to the number set. Current number set: [48, 720], target: 23, just two numbers left.\n     |- Try 720 + 48 = 768. Evaluate 768 != 23, drop this branch.\n     |- Try 720 - 48 = 672. Evaluate 672 != 23, drop this branch.\n     |- Try 720 * 48 = 34560. 34560 exceeds the maximum intermediate result, drop this branch.\n     |- Try 720 \/ 48 = 15. Evaluate 15 != 23, drop this branch.\n    |- Try 45 - 3 = 42. Add 42 to the number set. Current number set: [42, 720], target: 23, just two numbers left.\n     |- Try 720 + 42 = 762. Evaluate 762 != 23, drop this branch.\n     |- Try 720 - 42 = 678. Evaluate 678 != 23, drop this branch.\n     |- Try 720 * 42 = 30240. 30240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 720 \/ 42 = 17.1. 17.1 is a decimal, drop this branch.\n    |- Try 45 * 3 = 135. Add 135 to the number set. Current number set: [135, 720], target: 23, just two numbers left.\n     |- Try 720 + 135 = 855. Evaluate 855 != 23, drop this branch.\n     |- Try 720 - 135 = 585. Evaluate 585 != 23, drop this branch.\n     |- Try 720 * 135 = 97200. 97200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 720 \/ 135 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 45 \/ 3 = 15. Add 15 to the number set. Current number set: [15, 720], target: 23, just two numbers left.\n     |- Try 720 + 15 = 735. Evaluate 735 != 23, drop this branch.\n     |- Try 720 - 15 = 705. Evaluate 705 != 23, drop this branch.\n     |- Try 720 * 15 = 10800. 10800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 720 \/ 15 = 48. Evaluate 48 != 23, drop this branch.\n  |- Try 30 \/ 24 = 1.2. 1.2 is a decimal, drop this branch.\n |- Pick two numbers (24, 45) (numbers left: [30, 3]). Try possible operations.\n  |- Try 45 + 24 = 69. Add 69 to the number set. Current number set: [69, 30, 3], target: 23. Options for choosing two numbers: [(69, 30), (69, 3), (30, 3)].\n   |- Pick two numbers (69, 30) (numbers left: [3]). Try possible operations.\n    |- Try 69 + 30 = 99. Add 99 to the number set. Current number set: [99, 3], target: 23, just two numbers left.\n     |- Try 99 + 3 = 102. Evaluate 102 != 23, drop this branch.\n     |- Try 99 - 3 = 96. Evaluate 96 != 23, drop this branch.\n     |- Try 99 * 3 = 297. Evaluate 297 != 23, drop this branch.\n     |- Try 99 \/ 3 = 33. Evaluate 33 != 23, drop this branch.\n    |- Try 69 - 30 = 39. Add 39 to the number set. Current number set: [39, 3], target: 23, just two numbers left.\n     |- Try 39 + 3 = 42. Evaluate 42 != 23, drop this branch.\n     |- Try 39 - 3 = 36. Evaluate 36 != 23, drop this branch.\n     |- Try 39 * 3 = 117. Evaluate 117 != 23, drop this branch.\n     |- Try 39 \/ 3 = 13. Evaluate 13 != 23, drop this branch.\n    |- Try 69 * 30 = 2070. 2070 exceeds the maximum intermediate result, drop this branch.\n    |- Try 69 \/ 30 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (69, 3) (numbers left: [30]). Try possible operations.\n    |- Try 69 + 3 = 72. Add 72 to the number set. Current number set: [72, 30], target: 23, just two numbers left.\n     |- Try 72 + 30 = 102. Evaluate 102 != 23, drop this branch.\n     |- Try 72 - 30 = 42. Evaluate 42 != 23, drop this branch.\n     |- Try 72 * 30 = 2160. 2160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 30 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 69 - 3 = 66. Add 66 to the number set. Current number set: [66, 30], target: 23, just two numbers left.\n     |- Try 66 + 30 = 96. Evaluate 96 != 23, drop this branch.\n     |- Try 66 - 30 = 36. Evaluate 36 != 23, drop this branch.\n     |- Try 66 * 30 = 1980. Evaluate 1980 != 23, drop this branch.\n     |- Try 66 \/ 30 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 69 * 3 = 207. Add 207 to the number set. Current number set: [207, 30], target: 23, just two numbers left.\n     |- Try 207 + 30 = 237. Evaluate 237 != 23, drop this branch.\n     |- Try 207 - 30 = 177. Evaluate 177 != 23, drop this branch.\n     |- Try 207 * 30 = 6210. 6210 exceeds the maximum intermediate result, drop this branch.\n     |- Try 207 \/ 30 = 6.9. 6.9 is a decimal, drop this branch.\n    |- Try 69 \/ 3 = 23. Add 23 to the number set. Current number set: [23, 30], target: 23, just two numbers left.\n     |- Try 30 + 23 = 53. Evaluate 53 != 23, drop this branch.\n     |- Try 30 - 23 = 7. Evaluate 7 != 23, drop this branch.\n     |- Try 30 * 23 = 690. Evaluate 690 != 23, drop this branch.\n     |- Try 30 \/ 23 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (30, 3) (numbers left: [69]). Try possible operations.\n    |- Try 30 + 3 = 33. Add 33 to the number set. Current number set: [33, 69], target: 23, just two numbers left.\n     |- Try 69 + 33 = 102. Evaluate 102 != 23, drop this branch.\n     |- Try 69 - 33 = 36. Evaluate 36 != 23, drop this branch.\n     |- Try 69 * 33 = 2277. 2277 exceeds the maximum intermediate result, drop this branch.\n     |- Try 69 \/ 33 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 30 - 3 = 27. Add 27 to the number set. Current number set: [27, 69], target: 23, just two numbers left.\n     |- Try 69 + 27 = 96. Evaluate 96 != 23, drop this branch.\n     |- Try 69 - 27 = 42. Evaluate 42 != 23, drop this branch.\n     |- Try 69 * 27 = 1863. Evaluate 1863 != 23, drop this branch.\n     |- Try 69 \/ 27 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 30 * 3 = 90. Add 90 to the number set. Current number set: [90, 69], target: 23, just two numbers left.\n     |- Try 90 + 69 = 159. Evaluate 159 != 23, drop this branch.\n     |- Try 90 - 69 = 21. Evaluate 21 != 23, drop this branch.\n     |- Try 90 * 69 = 6210. 6210 exceeds the maximum intermediate result, drop this branch.\n     |- Try 90 \/ 69 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 30 \/ 3 = 10. Add 10 to the number set. Current number set: [10, 69], target: 23, just two numbers left.\n     |- Try 69 + 10 = 79. Evaluate 79 != 23, drop this branch.\n     |- Try 69 - 10 = 59. Evaluate 59 != 23, drop this branch.\n     |- Try 69 * 10 = 690. Evaluate 690 != 23, drop this branch.\n     |- Try 69 \/ 10 = 6.9. 6.9 is a decimal, drop this branch.\n  |- Try 45 - 24 = 21. Add 21 to the number set. Current number set: [21, 30, 3], target: 23. Options for choosing two numbers: [(21, 30), (21, 3), (30, 3)].\n   |- Pick two numbers (21, 30) (numbers left: [3]). Try possible operations.\n    |- Try 30 + 21 = 51. Add 51 to the number set. Current number set: [51, 3], target: 23, just two numbers left.\n     |- Try 51 + 3 = 54. Evaluate 54 != 23, drop this branch.\n     |- Try 51 - 3 = 48. Evaluate 48 != 23, drop this branch.\n     |- Try 51 * 3 = 153. Evaluate 153 != 23, drop this branch.\n     |- Try 51 \/ 3 = 17. Evaluate 17 != 23, drop this branch.\n    |- Try 30 - 21 = 9. Add 9 to the number set. Current number set: [9, 3], target: 23, just two numbers left.\n     |- Try 9 + 3 = 12. Evaluate 12 != 23, drop this branch.\n     |- Try 9 - 3 = 6. Evaluate 6 != 23, drop this branch.\n     |- Try 9 * 3 = 27. Evaluate 27 != 23, drop this branch.\n     |- Try 9 \/ 3 = 3. Evaluate 3 != 23, drop this branch.\n    |- Try 30 * 21 = 630. Add 630 to the number set. Current number set: [630, 3], target: 23, just two numbers left.\n     |- Try 630 + 3 = 633. Evaluate 633 != 23, drop this branch.\n     |- Try 630 - 3 = 627. Evaluate 627 != 23, drop this branch.\n     |- Try 630 * 3 = 1890. Evaluate 1890 != 23, drop this branch.\n     |- Try 630 \/ 3 = 210. Evaluate 210 != 23, drop this branch.\n    |- Try 30 \/ 21 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (21, 3) (numbers left: [30]). Try possible operations.\n    |- Try 21 + 3 = 24. Add 24 to the number set. Current number set: [24, 30], target: 23, just two numbers left.\n     |- Try 30 + 24 = 54. Evaluate 54 != 23, drop this branch.\n     |- Try 30 - 24 = 6. Evaluate 6 != 23, drop this branch.\n     |- Try 30 * 24 = 720. Evaluate 720 != 23, drop this branch.\n     |- Try 30 \/ 24 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 21 - 3 = 18. Add 18 to the number set. Current number set: [18, 30], target: 23, just two numbers left.\n     |- Try 30 + 18 = 48. Evaluate 48 != 23, drop this branch.\n     |- Try 30 - 18 = 12. Evaluate 12 != 23, drop this branch.\n     |- Try 30 * 18 = 540. Evaluate 540 != 23, drop this branch.\n     |- Try 30 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 21 * 3 = 63. Add 63 to the number set. Current number set: [63, 30], target: 23, just two numbers left.\n     |- Try 63 + 30 = 93. Evaluate 93 != 23, drop this branch.\n     |- Try 63 - 30 = 33. Evaluate 33 != 23, drop this branch.\n     |- Try 63 * 30 = 1890. Evaluate 1890 != 23, drop this branch.\n     |- Try 63 \/ 30 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 21 \/ 3 = 7. Add 7 to the number set. Current number set: [7, 30], target: 23, just two numbers left.\n     |- Try 30 + 7 = 37. Evaluate 37 != 23, drop this branch.\n     |- Try 30 - 7 = 23. Evaluate 23 == 23, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 30 - 7 = 23\nThe step before: 21 \/ 3 = 7\nThe first step: 45 - 24 = 21\n\nOutput the solution in the required format:\n<Solution>\n45 - 24 = 21\n21 \/ 3 = 7\n30 - 7 = 23\n<\/Solution>\n","item":{"nums":[24,30,45,3],"solution":["45 - 24 = 21","21 \/ 3 = 7","30 - 7 = 23"],"target":23}}
+{"instance_id":"countdown_8k_70","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [26, 16, 1, 3]\nTarget: 25","reference_output":"# Search Procedure\nInitial number set: [26, 16, 1, 3], target: 25. Options for choosing two numbers: [(26, 16), (26, 1), (26, 3), (16, 1), (16, 3), (1, 3)].\n |- Pick two numbers (26, 16) (numbers left: [1, 3]). Try possible operations.\n  |- Try 26 + 16 = 42. Add 42 to the number set. Current number set: [42, 1, 3], target: 25. Options for choosing two numbers: [(42, 1), (42, 3), (1, 3)].\n   |- Pick two numbers (42, 1) (numbers left: [3]). Try possible operations.\n    |- Try 42 + 1 = 43. Add 43 to the number set. Current number set: [43, 3], target: 25, just two numbers left.\n     |- Try 43 + 3 = 46. Evaluate 46 != 25, drop this branch.\n     |- Try 43 - 3 = 40. Evaluate 40 != 25, drop this branch.\n     |- Try 43 * 3 = 129. Evaluate 129 != 25, drop this branch.\n     |- Try 43 \/ 3 = 14.3. 14.3 is a decimal, drop this branch.\n    |- Try 42 - 1 = 41. Add 41 to the number set. Current number set: [41, 3], target: 25, just two numbers left.\n     |- Try 41 + 3 = 44. Evaluate 44 != 25, drop this branch.\n     |- Try 41 - 3 = 38. Evaluate 38 != 25, drop this branch.\n     |- Try 41 * 3 = 123. Evaluate 123 != 25, drop this branch.\n     |- Try 41 \/ 3 = 13.7. 13.7 is a decimal, drop this branch.\n    |- Try 42 * 1 = 42. Add 42 to the number set. Current number set: [42, 3], target: 25, just two numbers left.\n     |- Try 42 + 3 = 45. Evaluate 45 != 25, drop this branch.\n     |- Try 42 - 3 = 39. Evaluate 39 != 25, drop this branch.\n     |- Try 42 * 3 = 126. Evaluate 126 != 25, drop this branch.\n     |- Try 42 \/ 3 = 14. Evaluate 14 != 25, drop this branch.\n    |- Try 42 \/ 1 = 42. Add 42 to the number set. Current number set: [42, 3], target: 25, just two numbers left.\n     |- Try 42 + 3 = 45. Evaluate 45 != 25, drop this branch.\n     |- Try 42 - 3 = 39. Evaluate 39 != 25, drop this branch.\n     |- Try 42 * 3 = 126. Evaluate 126 != 25, drop this branch.\n     |- Try 42 \/ 3 = 14. Evaluate 14 != 25, drop this branch.\n   |- Pick two numbers (42, 3) (numbers left: [1]). Try possible operations.\n    |- Try 42 + 3 = 45. Add 45 to the number set. Current number set: [45, 1], target: 25, just two numbers left.\n     |- Try 45 + 1 = 46. Evaluate 46 != 25, drop this branch.\n     |- Try 45 - 1 = 44. Evaluate 44 != 25, drop this branch.\n     |- Try 45 * 1 = 45. Evaluate 45 != 25, drop this branch.\n     |- Try 45 \/ 1 = 45. Evaluate 45 != 25, drop this branch.\n    |- Try 42 - 3 = 39. Add 39 to the number set. Current number set: [39, 1], target: 25, just two numbers left.\n     |- Try 39 + 1 = 40. Evaluate 40 != 25, drop this branch.\n     |- Try 39 - 1 = 38. Evaluate 38 != 25, drop this branch.\n     |- Try 39 * 1 = 39. Evaluate 39 != 25, drop this branch.\n     |- Try 39 \/ 1 = 39. Evaluate 39 != 25, drop this branch.\n    |- Try 42 * 3 = 126. Add 126 to the number set. Current number set: [126, 1], target: 25, just two numbers left.\n     |- Try 126 + 1 = 127. Evaluate 127 != 25, drop this branch.\n     |- Try 126 - 1 = 125. Evaluate 125 != 25, drop this branch.\n     |- Try 126 * 1 = 126. Evaluate 126 != 25, drop this branch.\n     |- Try 126 \/ 1 = 126. Evaluate 126 != 25, drop this branch.\n    |- Try 42 \/ 3 = 14. Add 14 to the number set. Current number set: [14, 1], target: 25, just two numbers left.\n     |- Try 14 + 1 = 15. Evaluate 15 != 25, drop this branch.\n     |- Try 14 - 1 = 13. Evaluate 13 != 25, drop this branch.\n     |- Try 14 * 1 = 14. Evaluate 14 != 25, drop this branch.\n     |- Try 14 \/ 1 = 14. Evaluate 14 != 25, drop this branch.\n   |- Pick two numbers (1, 3) (numbers left: [42]). Try possible operations.\n    |- Try 3 + 1 = 4. Add 4 to the number set. Current number set: [4, 42], target: 25, just two numbers left.\n     |- Try 42 + 4 = 46. Evaluate 46 != 25, drop this branch.\n     |- Try 42 - 4 = 38. Evaluate 38 != 25, drop this branch.\n     |- Try 42 * 4 = 168. Evaluate 168 != 25, drop this branch.\n     |- Try 42 \/ 4 = 10.5. 10.5 is a decimal, drop this branch.\n    |- Try 3 - 1 = 2. Add 2 to the number set. Current number set: [2, 42], target: 25, just two numbers left.\n     |- Try 42 + 2 = 44. Evaluate 44 != 25, drop this branch.\n     |- Try 42 - 2 = 40. Evaluate 40 != 25, drop this branch.\n     |- Try 42 * 2 = 84. Evaluate 84 != 25, drop this branch.\n     |- Try 42 \/ 2 = 21. Evaluate 21 != 25, drop this branch.\n    |- Try 3 * 1 = 3. Add 3 to the number set. Current number set: [3, 42], target: 25, just two numbers left.\n     |- Try 42 + 3 = 45. Evaluate 45 != 25, drop this branch.\n     |- Try 42 - 3 = 39. Evaluate 39 != 25, drop this branch.\n     |- Try 42 * 3 = 126. Evaluate 126 != 25, drop this branch.\n     |- Try 42 \/ 3 = 14. Evaluate 14 != 25, drop this branch.\n    |- Try 3 \/ 1 = 3. Add 3 to the number set. Current number set: [3, 42], target: 25, just two numbers left.\n     |- Try 42 + 3 = 45. Evaluate 45 != 25, drop this branch.\n     |- Try 42 - 3 = 39. Evaluate 39 != 25, drop this branch.\n     |- Try 42 * 3 = 126. Evaluate 126 != 25, drop this branch.\n     |- Try 42 \/ 3 = 14. Evaluate 14 != 25, drop this branch.\n  |- Try 26 - 16 = 10. Add 10 to the number set. Current number set: [10, 1, 3], target: 25. Options for choosing two numbers: [(10, 1), (10, 3), (1, 3)].\n   |- Pick two numbers (10, 1) (numbers left: [3]). Try possible operations.\n    |- Try 10 + 1 = 11. Add 11 to the number set. Current number set: [11, 3], target: 25, just two numbers left.\n     |- Try 11 + 3 = 14. Evaluate 14 != 25, drop this branch.\n     |- Try 11 - 3 = 8. Evaluate 8 != 25, drop this branch.\n     |- Try 11 * 3 = 33. Evaluate 33 != 25, drop this branch.\n     |- Try 11 \/ 3 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 10 - 1 = 9. Add 9 to the number set. Current number set: [9, 3], target: 25, just two numbers left.\n     |- Try 9 + 3 = 12. Evaluate 12 != 25, drop this branch.\n     |- Try 9 - 3 = 6. Evaluate 6 != 25, drop this branch.\n     |- Try 9 * 3 = 27. Evaluate 27 != 25, drop this branch.\n     |- Try 9 \/ 3 = 3. Evaluate 3 != 25, drop this branch.\n    |- Try 10 * 1 = 10. Add 10 to the number set. Current number set: [10, 3], target: 25, just two numbers left.\n     |- Try 10 + 3 = 13. Evaluate 13 != 25, drop this branch.\n     |- Try 10 - 3 = 7. Evaluate 7 != 25, drop this branch.\n     |- Try 10 * 3 = 30. Evaluate 30 != 25, drop this branch.\n     |- Try 10 \/ 3 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 10 \/ 1 = 10. Add 10 to the number set. Current number set: [10, 3], target: 25, just two numbers left.\n     |- Try 10 + 3 = 13. Evaluate 13 != 25, drop this branch.\n     |- Try 10 - 3 = 7. Evaluate 7 != 25, drop this branch.\n     |- Try 10 * 3 = 30. Evaluate 30 != 25, drop this branch.\n     |- Try 10 \/ 3 = 3.3. 3.3 is a decimal, drop this branch.\n   |- Pick two numbers (10, 3) (numbers left: [1]). Try possible operations.\n    |- Try 10 + 3 = 13. Add 13 to the number set. Current number set: [13, 1], target: 25, just two numbers left.\n     |- Try 13 + 1 = 14. Evaluate 14 != 25, drop this branch.\n     |- Try 13 - 1 = 12. Evaluate 12 != 25, drop this branch.\n     |- Try 13 * 1 = 13. Evaluate 13 != 25, drop this branch.\n     |- Try 13 \/ 1 = 13. Evaluate 13 != 25, drop this branch.\n    |- Try 10 - 3 = 7. Add 7 to the number set. Current number set: [7, 1], target: 25, just two numbers left.\n     |- Try 7 + 1 = 8. Evaluate 8 != 25, drop this branch.\n     |- Try 7 - 1 = 6. Evaluate 6 != 25, drop this branch.\n     |- Try 7 * 1 = 7. Evaluate 7 != 25, drop this branch.\n     |- Try 7 \/ 1 = 7. Evaluate 7 != 25, drop this branch.\n    |- Try 10 * 3 = 30. Add 30 to the number set. Current number set: [30, 1], target: 25, just two numbers left.\n     |- Try 30 + 1 = 31. Evaluate 31 != 25, drop this branch.\n     |- Try 30 - 1 = 29. Evaluate 29 != 25, drop this branch.\n     |- Try 30 * 1 = 30. Evaluate 30 != 25, drop this branch.\n     |- Try 30 \/ 1 = 30. Evaluate 30 != 25, drop this branch.\n    |- Try 10 \/ 3 = 3.3. 3.3 is a decimal, drop this branch.\n   |- Pick two numbers (1, 3) (numbers left: [10]). Try possible operations.\n    |- Try 3 + 1 = 4. Add 4 to the number set. Current number set: [4, 10], target: 25, just two numbers left.\n     |- Try 10 + 4 = 14. Evaluate 14 != 25, drop this branch.\n     |- Try 10 - 4 = 6. Evaluate 6 != 25, drop this branch.\n     |- Try 10 * 4 = 40. Evaluate 40 != 25, drop this branch.\n     |- Try 10 \/ 4 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 3 - 1 = 2. Add 2 to the number set. Current number set: [2, 10], target: 25, just two numbers left.\n     |- Try 10 + 2 = 12. Evaluate 12 != 25, drop this branch.\n     |- Try 10 - 2 = 8. Evaluate 8 != 25, drop this branch.\n     |- Try 10 * 2 = 20. Evaluate 20 != 25, drop this branch.\n     |- Try 10 \/ 2 = 5. Evaluate 5 != 25, drop this branch.\n    |- Try 3 * 1 = 3. Add 3 to the number set. Current number set: [3, 10], target: 25, just two numbers left.\n     |- Try 10 + 3 = 13. Evaluate 13 != 25, drop this branch.\n     |- Try 10 - 3 = 7. Evaluate 7 != 25, drop this branch.\n     |- Try 10 * 3 = 30. Evaluate 30 != 25, drop this branch.\n     |- Try 10 \/ 3 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 3 \/ 1 = 3. Add 3 to the number set. Current number set: [3, 10], target: 25, just two numbers left.\n     |- Try 10 + 3 = 13. Evaluate 13 != 25, drop this branch.\n     |- Try 10 - 3 = 7. Evaluate 7 != 25, drop this branch.\n     |- Try 10 * 3 = 30. Evaluate 30 != 25, drop this branch.\n     |- Try 10 \/ 3 = 3.3. 3.3 is a decimal, drop this branch.\n  |- Try 26 * 16 = 416. Add 416 to the number set. Current number set: [416, 1, 3], target: 25. Options for choosing two numbers: [(416, 1), (416, 3), (1, 3)].\n   |- Pick two numbers (416, 1) (numbers left: [3]). Try possible operations.\n    |- Try 416 + 1 = 417. Add 417 to the number set. Current number set: [417, 3], target: 25, just two numbers left.\n     |- Try 417 + 3 = 420. Evaluate 420 != 25, drop this branch.\n     |- Try 417 - 3 = 414. Evaluate 414 != 25, drop this branch.\n     |- Try 417 * 3 = 1251. Evaluate 1251 != 25, drop this branch.\n     |- Try 417 \/ 3 = 139. Evaluate 139 != 25, drop this branch.\n    |- Try 416 - 1 = 415. Add 415 to the number set. Current number set: [415, 3], target: 25, just two numbers left.\n     |- Try 415 + 3 = 418. Evaluate 418 != 25, drop this branch.\n     |- Try 415 - 3 = 412. Evaluate 412 != 25, drop this branch.\n     |- Try 415 * 3 = 1245. Evaluate 1245 != 25, drop this branch.\n     |- Try 415 \/ 3 = 138.3. 138.3 is a decimal, drop this branch.\n    |- Try 416 * 1 = 416. Add 416 to the number set. Current number set: [416, 3], target: 25, just two numbers left.\n     |- Try 416 + 3 = 419. Evaluate 419 != 25, drop this branch.\n     |- Try 416 - 3 = 413. Evaluate 413 != 25, drop this branch.\n     |- Try 416 * 3 = 1248. Evaluate 1248 != 25, drop this branch.\n     |- Try 416 \/ 3 = 138.7. 138.7 is a decimal, drop this branch.\n    |- Try 416 \/ 1 = 416. Add 416 to the number set. Current number set: [416, 3], target: 25, just two numbers left.\n     |- Try 416 + 3 = 419. Evaluate 419 != 25, drop this branch.\n     |- Try 416 - 3 = 413. Evaluate 413 != 25, drop this branch.\n     |- Try 416 * 3 = 1248. Evaluate 1248 != 25, drop this branch.\n     |- Try 416 \/ 3 = 138.7. 138.7 is a decimal, drop this branch.\n   |- Pick two numbers (416, 3) (numbers left: [1]). Try possible operations.\n    |- Try 416 + 3 = 419. Add 419 to the number set. Current number set: [419, 1], target: 25, just two numbers left.\n     |- Try 419 + 1 = 420. Evaluate 420 != 25, drop this branch.\n     |- Try 419 - 1 = 418. Evaluate 418 != 25, drop this branch.\n     |- Try 419 * 1 = 419. Evaluate 419 != 25, drop this branch.\n     |- Try 419 \/ 1 = 419. Evaluate 419 != 25, drop this branch.\n    |- Try 416 - 3 = 413. Add 413 to the number set. Current number set: [413, 1], target: 25, just two numbers left.\n     |- Try 413 + 1 = 414. Evaluate 414 != 25, drop this branch.\n     |- Try 413 - 1 = 412. Evaluate 412 != 25, drop this branch.\n     |- Try 413 * 1 = 413. Evaluate 413 != 25, drop this branch.\n     |- Try 413 \/ 1 = 413. Evaluate 413 != 25, drop this branch.\n    |- Try 416 * 3 = 1248. Add 1248 to the number set. Current number set: [1248, 1], target: 25, just two numbers left.\n     |- Try 1248 + 1 = 1249. Evaluate 1249 != 25, drop this branch.\n     |- Try 1248 - 1 = 1247. Evaluate 1247 != 25, drop this branch.\n     |- Try 1248 * 1 = 1248. Evaluate 1248 != 25, drop this branch.\n     |- Try 1248 \/ 1 = 1248. Evaluate 1248 != 25, drop this branch.\n    |- Try 416 \/ 3 = 138.7. 138.7 is a decimal, drop this branch.\n   |- Pick two numbers (1, 3) (numbers left: [416]). Try possible operations.\n    |- Try 3 + 1 = 4. Add 4 to the number set. Current number set: [4, 416], target: 25, just two numbers left.\n     |- Try 416 + 4 = 420. Evaluate 420 != 25, drop this branch.\n     |- Try 416 - 4 = 412. Evaluate 412 != 25, drop this branch.\n     |- Try 416 * 4 = 1664. Evaluate 1664 != 25, drop this branch.\n     |- Try 416 \/ 4 = 104. Evaluate 104 != 25, drop this branch.\n    |- Try 3 - 1 = 2. Add 2 to the number set. Current number set: [2, 416], target: 25, just two numbers left.\n     |- Try 416 + 2 = 418. Evaluate 418 != 25, drop this branch.\n     |- Try 416 - 2 = 414. Evaluate 414 != 25, drop this branch.\n     |- Try 416 * 2 = 832. Evaluate 832 != 25, drop this branch.\n     |- Try 416 \/ 2 = 208. Evaluate 208 != 25, drop this branch.\n    |- Try 3 * 1 = 3. Add 3 to the number set. Current number set: [3, 416], target: 25, just two numbers left.\n     |- Try 416 + 3 = 419. Evaluate 419 != 25, drop this branch.\n     |- Try 416 - 3 = 413. Evaluate 413 != 25, drop this branch.\n     |- Try 416 * 3 = 1248. Evaluate 1248 != 25, drop this branch.\n     |- Try 416 \/ 3 = 138.7. 138.7 is a decimal, drop this branch.\n    |- Try 3 \/ 1 = 3. Add 3 to the number set. Current number set: [3, 416], target: 25, just two numbers left.\n     |- Try 416 + 3 = 419. Evaluate 419 != 25, drop this branch.\n     |- Try 416 - 3 = 413. Evaluate 413 != 25, drop this branch.\n     |- Try 416 * 3 = 1248. Evaluate 1248 != 25, drop this branch.\n     |- Try 416 \/ 3 = 138.7. 138.7 is a decimal, drop this branch.\n  |- Try 26 \/ 16 = 1.6. 1.6 is a decimal, drop this branch.\n |- Pick two numbers (26, 1) (numbers left: [16, 3]). Try possible operations.\n  |- Try 26 + 1 = 27. Add 27 to the number set. Current number set: [27, 16, 3], target: 25. Options for choosing two numbers: [(27, 16), (27, 3), (16, 3)].\n   |- Pick two numbers (27, 16) (numbers left: [3]). Try possible operations.\n    |- Try 27 + 16 = 43. Add 43 to the number set. Current number set: [43, 3], target: 25, just two numbers left.\n     |- Try 43 + 3 = 46. Evaluate 46 != 25, drop this branch.\n     |- Try 43 - 3 = 40. Evaluate 40 != 25, drop this branch.\n     |- Try 43 * 3 = 129. Evaluate 129 != 25, drop this branch.\n     |- Try 43 \/ 3 = 14.3. 14.3 is a decimal, drop this branch.\n    |- Try 27 - 16 = 11. Add 11 to the number set. Current number set: [11, 3], target: 25, just two numbers left.\n     |- Try 11 + 3 = 14. Evaluate 14 != 25, drop this branch.\n     |- Try 11 - 3 = 8. Evaluate 8 != 25, drop this branch.\n     |- Try 11 * 3 = 33. Evaluate 33 != 25, drop this branch.\n     |- Try 11 \/ 3 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 27 * 16 = 432. Add 432 to the number set. Current number set: [432, 3], target: 25, just two numbers left.\n     |- Try 432 + 3 = 435. Evaluate 435 != 25, drop this branch.\n     |- Try 432 - 3 = 429. Evaluate 429 != 25, drop this branch.\n     |- Try 432 * 3 = 1296. Evaluate 1296 != 25, drop this branch.\n     |- Try 432 \/ 3 = 144. Evaluate 144 != 25, drop this branch.\n    |- Try 27 \/ 16 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (27, 3) (numbers left: [16]). Try possible operations.\n    |- Try 27 + 3 = 30. Add 30 to the number set. Current number set: [30, 16], target: 25, just two numbers left.\n     |- Try 30 + 16 = 46. Evaluate 46 != 25, drop this branch.\n     |- Try 30 - 16 = 14. Evaluate 14 != 25, drop this branch.\n     |- Try 30 * 16 = 480. Evaluate 480 != 25, drop this branch.\n     |- Try 30 \/ 16 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 27 - 3 = 24. Add 24 to the number set. Current number set: [24, 16], target: 25, just two numbers left.\n     |- Try 24 + 16 = 40. Evaluate 40 != 25, drop this branch.\n     |- Try 24 - 16 = 8. Evaluate 8 != 25, drop this branch.\n     |- Try 24 * 16 = 384. Evaluate 384 != 25, drop this branch.\n     |- Try 24 \/ 16 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 27 * 3 = 81. Add 81 to the number set. Current number set: [81, 16], target: 25, just two numbers left.\n     |- Try 81 + 16 = 97. Evaluate 97 != 25, drop this branch.\n     |- Try 81 - 16 = 65. Evaluate 65 != 25, drop this branch.\n     |- Try 81 * 16 = 1296. Evaluate 1296 != 25, drop this branch.\n     |- Try 81 \/ 16 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 27 \/ 3 = 9. Add 9 to the number set. Current number set: [9, 16], target: 25, just two numbers left.\n     |- Try 16 + 9 = 25. Evaluate 25 == 25, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 16 + 9 = 25\nThe step before: 27 \/ 3 = 9\nThe first step: 26 + 1 = 27\n\nOutput the solution in the required format:\n<Solution>\n26 + 1 = 27\n27 \/ 3 = 9\n16 + 9 = 25\n<\/Solution>\n","item":{"nums":[26,16,1,3],"solution":["26 + 1 = 27","27 \/ 3 = 9","16 + 9 = 25"],"target":25}}
+{"instance_id":"countdown_8k_71","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [3, 13, 7, 32]\nTarget: 21","reference_output":"# Search Procedure\nInitial number set: [3, 13, 7, 32], target: 21. Options for choosing two numbers: [(3, 13), (3, 7), (3, 32), (13, 7), (13, 32), (7, 32)].\n |- Pick two numbers (3, 13) (numbers left: [7, 32]). Try possible operations.\n  |- Try 13 + 3 = 16. Add 16 to the number set. Current number set: [16, 7, 32], target: 21. Options for choosing two numbers: [(16, 7), (16, 32), (7, 32)].\n   |- Pick two numbers (16, 7) (numbers left: [32]). Try possible operations.\n    |- Try 16 + 7 = 23. Add 23 to the number set. Current number set: [23, 32], target: 21, just two numbers left.\n     |- Try 32 + 23 = 55. Evaluate 55 != 21, drop this branch.\n     |- Try 32 - 23 = 9. Evaluate 9 != 21, drop this branch.\n     |- Try 32 * 23 = 736. Evaluate 736 != 21, drop this branch.\n     |- Try 32 \/ 23 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 16 - 7 = 9. Add 9 to the number set. Current number set: [9, 32], target: 21, just two numbers left.\n     |- Try 32 + 9 = 41. Evaluate 41 != 21, drop this branch.\n     |- Try 32 - 9 = 23. Evaluate 23 != 21, drop this branch.\n     |- Try 32 * 9 = 288. Evaluate 288 != 21, drop this branch.\n     |- Try 32 \/ 9 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 16 * 7 = 112. Add 112 to the number set. Current number set: [112, 32], target: 21, just two numbers left.\n     |- Try 112 + 32 = 144. Evaluate 144 != 21, drop this branch.\n     |- Try 112 - 32 = 80. Evaluate 80 != 21, drop this branch.\n     |- Try 112 * 32 = 3584. 3584 exceeds the maximum intermediate result, drop this branch.\n     |- Try 112 \/ 32 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 16 \/ 7 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (16, 32) (numbers left: [7]). Try possible operations.\n    |- Try 32 + 16 = 48. Add 48 to the number set. Current number set: [48, 7], target: 21, just two numbers left.\n     |- Try 48 + 7 = 55. Evaluate 55 != 21, drop this branch.\n     |- Try 48 - 7 = 41. Evaluate 41 != 21, drop this branch.\n     |- Try 48 * 7 = 336. Evaluate 336 != 21, drop this branch.\n     |- Try 48 \/ 7 = 6.9. 6.9 is a decimal, drop this branch.\n    |- Try 32 - 16 = 16. Add 16 to the number set. Current number set: [16, 7], target: 21, just two numbers left.\n     |- Try 16 + 7 = 23. Evaluate 23 != 21, drop this branch.\n     |- Try 16 - 7 = 9. Evaluate 9 != 21, drop this branch.\n     |- Try 16 * 7 = 112. Evaluate 112 != 21, drop this branch.\n     |- Try 16 \/ 7 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 32 * 16 = 512. Add 512 to the number set. Current number set: [512, 7], target: 21, just two numbers left.\n     |- Try 512 + 7 = 519. Evaluate 519 != 21, drop this branch.\n     |- Try 512 - 7 = 505. Evaluate 505 != 21, drop this branch.\n     |- Try 512 * 7 = 3584. 3584 exceeds the maximum intermediate result, drop this branch.\n     |- Try 512 \/ 7 = 73.1. 73.1 is a decimal, drop this branch.\n    |- Try 32 \/ 16 = 2. Add 2 to the number set. Current number set: [2, 7], target: 21, just two numbers left.\n     |- Try 7 + 2 = 9. Evaluate 9 != 21, drop this branch.\n     |- Try 7 - 2 = 5. Evaluate 5 != 21, drop this branch.\n     |- Try 7 * 2 = 14. Evaluate 14 != 21, drop this branch.\n     |- Try 7 \/ 2 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (7, 32) (numbers left: [16]). Try possible operations.\n    |- Try 32 + 7 = 39. Add 39 to the number set. Current number set: [39, 16], target: 21, just two numbers left.\n     |- Try 39 + 16 = 55. Evaluate 55 != 21, drop this branch.\n     |- Try 39 - 16 = 23. Evaluate 23 != 21, drop this branch.\n     |- Try 39 * 16 = 624. Evaluate 624 != 21, drop this branch.\n     |- Try 39 \/ 16 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 32 - 7 = 25. Add 25 to the number set. Current number set: [25, 16], target: 21, just two numbers left.\n     |- Try 25 + 16 = 41. Evaluate 41 != 21, drop this branch.\n     |- Try 25 - 16 = 9. Evaluate 9 != 21, drop this branch.\n     |- Try 25 * 16 = 400. Evaluate 400 != 21, drop this branch.\n     |- Try 25 \/ 16 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 32 * 7 = 224. Add 224 to the number set. Current number set: [224, 16], target: 21, just two numbers left.\n     |- Try 224 + 16 = 240. Evaluate 240 != 21, drop this branch.\n     |- Try 224 - 16 = 208. Evaluate 208 != 21, drop this branch.\n     |- Try 224 * 16 = 3584. 3584 exceeds the maximum intermediate result, drop this branch.\n     |- Try 224 \/ 16 = 14. Evaluate 14 != 21, drop this branch.\n    |- Try 32 \/ 7 = 4.6. 4.6 is a decimal, drop this branch.\n  |- Try 13 - 3 = 10. Add 10 to the number set. Current number set: [10, 7, 32], target: 21. Options for choosing two numbers: [(10, 7), (10, 32), (7, 32)].\n   |- Pick two numbers (10, 7) (numbers left: [32]). Try possible operations.\n    |- Try 10 + 7 = 17. Add 17 to the number set. Current number set: [17, 32], target: 21, just two numbers left.\n     |- Try 32 + 17 = 49. Evaluate 49 != 21, drop this branch.\n     |- Try 32 - 17 = 15. Evaluate 15 != 21, drop this branch.\n     |- Try 32 * 17 = 544. Evaluate 544 != 21, drop this branch.\n     |- Try 32 \/ 17 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 10 - 7 = 3. Add 3 to the number set. Current number set: [3, 32], target: 21, just two numbers left.\n     |- Try 32 + 3 = 35. Evaluate 35 != 21, drop this branch.\n     |- Try 32 - 3 = 29. Evaluate 29 != 21, drop this branch.\n     |- Try 32 * 3 = 96. Evaluate 96 != 21, drop this branch.\n     |- Try 32 \/ 3 = 10.7. 10.7 is a decimal, drop this branch.\n    |- Try 10 * 7 = 70. Add 70 to the number set. Current number set: [70, 32], target: 21, just two numbers left.\n     |- Try 70 + 32 = 102. Evaluate 102 != 21, drop this branch.\n     |- Try 70 - 32 = 38. Evaluate 38 != 21, drop this branch.\n     |- Try 70 * 32 = 2240. 2240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 70 \/ 32 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 10 \/ 7 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (10, 32) (numbers left: [7]). Try possible operations.\n    |- Try 32 + 10 = 42. Add 42 to the number set. Current number set: [42, 7], target: 21, just two numbers left.\n     |- Try 42 + 7 = 49. Evaluate 49 != 21, drop this branch.\n     |- Try 42 - 7 = 35. Evaluate 35 != 21, drop this branch.\n     |- Try 42 * 7 = 294. Evaluate 294 != 21, drop this branch.\n     |- Try 42 \/ 7 = 6. Evaluate 6 != 21, drop this branch.\n    |- Try 32 - 10 = 22. Add 22 to the number set. Current number set: [22, 7], target: 21, just two numbers left.\n     |- Try 22 + 7 = 29. Evaluate 29 != 21, drop this branch.\n     |- Try 22 - 7 = 15. Evaluate 15 != 21, drop this branch.\n     |- Try 22 * 7 = 154. Evaluate 154 != 21, drop this branch.\n     |- Try 22 \/ 7 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 32 * 10 = 320. Add 320 to the number set. Current number set: [320, 7], target: 21, just two numbers left.\n     |- Try 320 + 7 = 327. Evaluate 327 != 21, drop this branch.\n     |- Try 320 - 7 = 313. Evaluate 313 != 21, drop this branch.\n     |- Try 320 * 7 = 2240. 2240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 320 \/ 7 = 45.7. 45.7 is a decimal, drop this branch.\n    |- Try 32 \/ 10 = 3.2. 3.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 32) (numbers left: [10]). Try possible operations.\n    |- Try 32 + 7 = 39. Add 39 to the number set. Current number set: [39, 10], target: 21, just two numbers left.\n     |- Try 39 + 10 = 49. Evaluate 49 != 21, drop this branch.\n     |- Try 39 - 10 = 29. Evaluate 29 != 21, drop this branch.\n     |- Try 39 * 10 = 390. Evaluate 390 != 21, drop this branch.\n     |- Try 39 \/ 10 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 32 - 7 = 25. Add 25 to the number set. Current number set: [25, 10], target: 21, just two numbers left.\n     |- Try 25 + 10 = 35. Evaluate 35 != 21, drop this branch.\n     |- Try 25 - 10 = 15. Evaluate 15 != 21, drop this branch.\n     |- Try 25 * 10 = 250. Evaluate 250 != 21, drop this branch.\n     |- Try 25 \/ 10 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 32 * 7 = 224. Add 224 to the number set. Current number set: [224, 10], target: 21, just two numbers left.\n     |- Try 224 + 10 = 234. Evaluate 234 != 21, drop this branch.\n     |- Try 224 - 10 = 214. Evaluate 214 != 21, drop this branch.\n     |- Try 224 * 10 = 2240. 2240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 224 \/ 10 = 22.4. 22.4 is a decimal, drop this branch.\n    |- Try 32 \/ 7 = 4.6. 4.6 is a decimal, drop this branch.\n  |- Try 13 * 3 = 39. Add 39 to the number set. Current number set: [39, 7, 32], target: 21. Options for choosing two numbers: [(39, 7), (39, 32), (7, 32)].\n   |- Pick two numbers (39, 7) (numbers left: [32]). Try possible operations.\n    |- Try 39 + 7 = 46. Add 46 to the number set. Current number set: [46, 32], target: 21, just two numbers left.\n     |- Try 46 + 32 = 78. Evaluate 78 != 21, drop this branch.\n     |- Try 46 - 32 = 14. Evaluate 14 != 21, drop this branch.\n     |- Try 46 * 32 = 1472. Evaluate 1472 != 21, drop this branch.\n     |- Try 46 \/ 32 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 39 - 7 = 32. Add 32 to the number set. Current number set: [32, 32], target: 21, just two numbers left.\n     |- Try 32 + 32 = 64. Evaluate 64 != 21, drop this branch.\n     |- Try 32 - 32 = 0. Evaluate 0 != 21, drop this branch.\n     |- Try 32 * 32 = 1024. Evaluate 1024 != 21, drop this branch.\n     |- Try 32 \/ 32 = 1. Evaluate 1 != 21, drop this branch.\n    |- Try 39 * 7 = 273. Add 273 to the number set. Current number set: [273, 32], target: 21, just two numbers left.\n     |- Try 273 + 32 = 305. Evaluate 305 != 21, drop this branch.\n     |- Try 273 - 32 = 241. Evaluate 241 != 21, drop this branch.\n     |- Try 273 * 32 = 8736. 8736 exceeds the maximum intermediate result, drop this branch.\n     |- Try 273 \/ 32 = 8.5. 8.5 is a decimal, drop this branch.\n    |- Try 39 \/ 7 = 5.6. 5.6 is a decimal, drop this branch.\n   |- Pick two numbers (39, 32) (numbers left: [7]). Try possible operations.\n    |- Try 39 + 32 = 71. Add 71 to the number set. Current number set: [71, 7], target: 21, just two numbers left.\n     |- Try 71 + 7 = 78. Evaluate 78 != 21, drop this branch.\n     |- Try 71 - 7 = 64. Evaluate 64 != 21, drop this branch.\n     |- Try 71 * 7 = 497. Evaluate 497 != 21, drop this branch.\n     |- Try 71 \/ 7 = 10.1. 10.1 is a decimal, drop this branch.\n    |- Try 39 - 32 = 7. Add 7 to the number set. Current number set: [7, 7], target: 21, just two numbers left.\n     |- Try 7 + 7 = 14. Evaluate 14 != 21, drop this branch.\n     |- Try 7 - 7 = 0. Evaluate 0 != 21, drop this branch.\n     |- Try 7 * 7 = 49. Evaluate 49 != 21, drop this branch.\n     |- Try 7 \/ 7 = 1. Evaluate 1 != 21, drop this branch.\n    |- Try 39 * 32 = 1248. Add 1248 to the number set. Current number set: [1248, 7], target: 21, just two numbers left.\n     |- Try 1248 + 7 = 1255. Evaluate 1255 != 21, drop this branch.\n     |- Try 1248 - 7 = 1241. Evaluate 1241 != 21, drop this branch.\n     |- Try 1248 * 7 = 8736. 8736 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1248 \/ 7 = 178.3. 178.3 is a decimal, drop this branch.\n    |- Try 39 \/ 32 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 32) (numbers left: [39]). Try possible operations.\n    |- Try 32 + 7 = 39. Add 39 to the number set. Current number set: [39, 39], target: 21, just two numbers left.\n     |- Try 39 + 39 = 78. Evaluate 78 != 21, drop this branch.\n     |- Try 39 - 39 = 0. Evaluate 0 != 21, drop this branch.\n     |- Try 39 * 39 = 1521. Evaluate 1521 != 21, drop this branch.\n     |- Try 39 \/ 39 = 1. Evaluate 1 != 21, drop this branch.\n    |- Try 32 - 7 = 25. Add 25 to the number set. Current number set: [25, 39], target: 21, just two numbers left.\n     |- Try 39 + 25 = 64. Evaluate 64 != 21, drop this branch.\n     |- Try 39 - 25 = 14. Evaluate 14 != 21, drop this branch.\n     |- Try 39 * 25 = 975. Evaluate 975 != 21, drop this branch.\n     |- Try 39 \/ 25 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 32 * 7 = 224. Add 224 to the number set. Current number set: [224, 39], target: 21, just two numbers left.\n     |- Try 224 + 39 = 263. Evaluate 263 != 21, drop this branch.\n     |- Try 224 - 39 = 185. Evaluate 185 != 21, drop this branch.\n     |- Try 224 * 39 = 8736. 8736 exceeds the maximum intermediate result, drop this branch.\n     |- Try 224 \/ 39 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 32 \/ 7 = 4.6. 4.6 is a decimal, drop this branch.\n  |- Try 13 \/ 3 = 4.3. 4.3 is a decimal, drop this branch.\n |- Pick two numbers (3, 7) (numbers left: [13, 32]). Try possible operations.\n  |- Try 7 + 3 = 10. Add 10 to the number set. Current number set: [10, 13, 32], target: 21. Options for choosing two numbers: [(10, 13), (10, 32), (13, 32)].\n   |- Pick two numbers (10, 13) (numbers left: [32]). Try possible operations.\n    |- Try 13 + 10 = 23. Add 23 to the number set. Current number set: [23, 32], target: 21, just two numbers left.\n     |- Try 32 + 23 = 55. Evaluate 55 != 21, drop this branch.\n     |- Try 32 - 23 = 9. Evaluate 9 != 21, drop this branch.\n     |- Try 32 * 23 = 736. Evaluate 736 != 21, drop this branch.\n     |- Try 32 \/ 23 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 13 - 10 = 3. Add 3 to the number set. Current number set: [3, 32], target: 21, just two numbers left.\n     |- Try 32 + 3 = 35. Evaluate 35 != 21, drop this branch.\n     |- Try 32 - 3 = 29. Evaluate 29 != 21, drop this branch.\n     |- Try 32 * 3 = 96. Evaluate 96 != 21, drop this branch.\n     |- Try 32 \/ 3 = 10.7. 10.7 is a decimal, drop this branch.\n    |- Try 13 * 10 = 130. Add 130 to the number set. Current number set: [130, 32], target: 21, just two numbers left.\n     |- Try 130 + 32 = 162. Evaluate 162 != 21, drop this branch.\n     |- Try 130 - 32 = 98. Evaluate 98 != 21, drop this branch.\n     |- Try 130 * 32 = 4160. 4160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 130 \/ 32 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 13 \/ 10 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (10, 32) (numbers left: [13]). Try possible operations.\n    |- Try 32 + 10 = 42. Add 42 to the number set. Current number set: [42, 13], target: 21, just two numbers left.\n     |- Try 42 + 13 = 55. Evaluate 55 != 21, drop this branch.\n     |- Try 42 - 13 = 29. Evaluate 29 != 21, drop this branch.\n     |- Try 42 * 13 = 546. Evaluate 546 != 21, drop this branch.\n     |- Try 42 \/ 13 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 32 - 10 = 22. Add 22 to the number set. Current number set: [22, 13], target: 21, just two numbers left.\n     |- Try 22 + 13 = 35. Evaluate 35 != 21, drop this branch.\n     |- Try 22 - 13 = 9. Evaluate 9 != 21, drop this branch.\n     |- Try 22 * 13 = 286. Evaluate 286 != 21, drop this branch.\n     |- Try 22 \/ 13 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 32 * 10 = 320. Add 320 to the number set. Current number set: [320, 13], target: 21, just two numbers left.\n     |- Try 320 + 13 = 333. Evaluate 333 != 21, drop this branch.\n     |- Try 320 - 13 = 307. Evaluate 307 != 21, drop this branch.\n     |- Try 320 * 13 = 4160. 4160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 320 \/ 13 = 24.6. 24.6 is a decimal, drop this branch.\n    |- Try 32 \/ 10 = 3.2. 3.2 is a decimal, drop this branch.\n   |- Pick two numbers (13, 32) (numbers left: [10]). Try possible operations.\n    |- Try 32 + 13 = 45. Add 45 to the number set. Current number set: [45, 10], target: 21, just two numbers left.\n     |- Try 45 + 10 = 55. Evaluate 55 != 21, drop this branch.\n     |- Try 45 - 10 = 35. Evaluate 35 != 21, drop this branch.\n     |- Try 45 * 10 = 450. Evaluate 450 != 21, drop this branch.\n     |- Try 45 \/ 10 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 32 - 13 = 19. Add 19 to the number set. Current number set: [19, 10], target: 21, just two numbers left.\n     |- Try 19 + 10 = 29. Evaluate 29 != 21, drop this branch.\n     |- Try 19 - 10 = 9. Evaluate 9 != 21, drop this branch.\n     |- Try 19 * 10 = 190. Evaluate 190 != 21, drop this branch.\n     |- Try 19 \/ 10 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 32 * 13 = 416. Add 416 to the number set. Current number set: [416, 10], target: 21, just two numbers left.\n     |- Try 416 + 10 = 426. Evaluate 426 != 21, drop this branch.\n     |- Try 416 - 10 = 406. Evaluate 406 != 21, drop this branch.\n     |- Try 416 * 10 = 4160. 4160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 416 \/ 10 = 41.6. 41.6 is a decimal, drop this branch.\n    |- Try 32 \/ 13 = 2.5. 2.5 is a decimal, drop this branch.\n  |- Try 7 - 3 = 4. Add 4 to the number set. Current number set: [4, 13, 32], target: 21. Options for choosing two numbers: [(4, 13), (4, 32), (13, 32)].\n   |- Pick two numbers (4, 13) (numbers left: [32]). Try possible operations.\n    |- Try 13 + 4 = 17. Add 17 to the number set. Current number set: [17, 32], target: 21, just two numbers left.\n     |- Try 32 + 17 = 49. Evaluate 49 != 21, drop this branch.\n     |- Try 32 - 17 = 15. Evaluate 15 != 21, drop this branch.\n     |- Try 32 * 17 = 544. Evaluate 544 != 21, drop this branch.\n     |- Try 32 \/ 17 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 13 - 4 = 9. Add 9 to the number set. Current number set: [9, 32], target: 21, just two numbers left.\n     |- Try 32 + 9 = 41. Evaluate 41 != 21, drop this branch.\n     |- Try 32 - 9 = 23. Evaluate 23 != 21, drop this branch.\n     |- Try 32 * 9 = 288. Evaluate 288 != 21, drop this branch.\n     |- Try 32 \/ 9 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 13 * 4 = 52. Add 52 to the number set. Current number set: [52, 32], target: 21, just two numbers left.\n     |- Try 52 + 32 = 84. Evaluate 84 != 21, drop this branch.\n     |- Try 52 - 32 = 20. Evaluate 20 != 21, drop this branch.\n     |- Try 52 * 32 = 1664. Evaluate 1664 != 21, drop this branch.\n     |- Try 52 \/ 32 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 13 \/ 4 = 3.2. 3.2 is a decimal, drop this branch.\n   |- Pick two numbers (4, 32) (numbers left: [13]). Try possible operations.\n    |- Try 32 + 4 = 36. Add 36 to the number set. Current number set: [36, 13], target: 21, just two numbers left.\n     |- Try 36 + 13 = 49. Evaluate 49 != 21, drop this branch.\n     |- Try 36 - 13 = 23. Evaluate 23 != 21, drop this branch.\n     |- Try 36 * 13 = 468. Evaluate 468 != 21, drop this branch.\n     |- Try 36 \/ 13 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 32 - 4 = 28. Add 28 to the number set. Current number set: [28, 13], target: 21, just two numbers left.\n     |- Try 28 + 13 = 41. Evaluate 41 != 21, drop this branch.\n     |- Try 28 - 13 = 15. Evaluate 15 != 21, drop this branch.\n     |- Try 28 * 13 = 364. Evaluate 364 != 21, drop this branch.\n     |- Try 28 \/ 13 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 32 * 4 = 128. Add 128 to the number set. Current number set: [128, 13], target: 21, just two numbers left.\n     |- Try 128 + 13 = 141. Evaluate 141 != 21, drop this branch.\n     |- Try 128 - 13 = 115. Evaluate 115 != 21, drop this branch.\n     |- Try 128 * 13 = 1664. Evaluate 1664 != 21, drop this branch.\n     |- Try 128 \/ 13 = 9.8. 9.8 is a decimal, drop this branch.\n    |- Try 32 \/ 4 = 8. Add 8 to the number set. Current number set: [8, 13], target: 21, just two numbers left.\n     |- Try 13 + 8 = 21. Evaluate 21 == 21, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 13 + 8 = 21\nThe step before: 32 \/ 4 = 8\nThe first step: 7 - 3 = 4\n\nOutput the solution in the required format:\n<Solution>\n7 - 3 = 4\n32 \/ 4 = 8\n13 + 8 = 21\n<\/Solution>\n","item":{"nums":[3,13,7,32],"solution":["7 - 3 = 4","32 \/ 4 = 8","13 + 8 = 21"],"target":21}}
+{"instance_id":"countdown_8k_72","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [6, 30, 41, 4]\nTarget: 41","reference_output":"# Search Procedure\nInitial number set: [6, 30, 41, 4], target: 41. Options for choosing two numbers: [(6, 30), (6, 41), (6, 4), (30, 41), (30, 4), (41, 4)].\n |- Pick two numbers (6, 30) (numbers left: [41, 4]). Try possible operations.\n  |- Try 30 + 6 = 36. Add 36 to the number set. Current number set: [36, 41, 4], target: 41. Options for choosing two numbers: [(36, 41), (36, 4), (41, 4)].\n   |- Pick two numbers (36, 41) (numbers left: [4]). Try possible operations.\n    |- Try 41 + 36 = 77. Add 77 to the number set. Current number set: [77, 4], target: 41, just two numbers left.\n     |- Try 77 + 4 = 81. Evaluate 81 != 41, drop this branch.\n     |- Try 77 - 4 = 73. Evaluate 73 != 41, drop this branch.\n     |- Try 77 * 4 = 308. Evaluate 308 != 41, drop this branch.\n     |- Try 77 \/ 4 = 19.2. 19.2 is a decimal, drop this branch.\n    |- Try 41 - 36 = 5. Add 5 to the number set. Current number set: [5, 4], target: 41, just two numbers left.\n     |- Try 5 + 4 = 9. Evaluate 9 != 41, drop this branch.\n     |- Try 5 - 4 = 1. Evaluate 1 != 41, drop this branch.\n     |- Try 5 * 4 = 20. Evaluate 20 != 41, drop this branch.\n     |- Try 5 \/ 4 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 41 * 36 = 1476. Add 1476 to the number set. Current number set: [1476, 4], target: 41, just two numbers left.\n     |- Try 1476 + 4 = 1480. Evaluate 1480 != 41, drop this branch.\n     |- Try 1476 - 4 = 1472. Evaluate 1472 != 41, drop this branch.\n     |- Try 1476 * 4 = 5904. 5904 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1476 \/ 4 = 369. Evaluate 369 != 41, drop this branch.\n    |- Try 41 \/ 36 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (36, 4) (numbers left: [41]). Try possible operations.\n    |- Try 36 + 4 = 40. Add 40 to the number set. Current number set: [40, 41], target: 41, just two numbers left.\n     |- Try 41 + 40 = 81. Evaluate 81 != 41, drop this branch.\n     |- Try 41 - 40 = 1. Evaluate 1 != 41, drop this branch.\n     |- Try 41 * 40 = 1640. Evaluate 1640 != 41, drop this branch.\n     |- Try 41 \/ 40 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 36 - 4 = 32. Add 32 to the number set. Current number set: [32, 41], target: 41, just two numbers left.\n     |- Try 41 + 32 = 73. Evaluate 73 != 41, drop this branch.\n     |- Try 41 - 32 = 9. Evaluate 9 != 41, drop this branch.\n     |- Try 41 * 32 = 1312. Evaluate 1312 != 41, drop this branch.\n     |- Try 41 \/ 32 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 36 * 4 = 144. Add 144 to the number set. Current number set: [144, 41], target: 41, just two numbers left.\n     |- Try 144 + 41 = 185. Evaluate 185 != 41, drop this branch.\n     |- Try 144 - 41 = 103. Evaluate 103 != 41, drop this branch.\n     |- Try 144 * 41 = 5904. 5904 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 41 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 36 \/ 4 = 9. Add 9 to the number set. Current number set: [9, 41], target: 41, just two numbers left.\n     |- Try 41 + 9 = 50. Evaluate 50 != 41, drop this branch.\n     |- Try 41 - 9 = 32. Evaluate 32 != 41, drop this branch.\n     |- Try 41 * 9 = 369. Evaluate 369 != 41, drop this branch.\n     |- Try 41 \/ 9 = 4.6. 4.6 is a decimal, drop this branch.\n   |- Pick two numbers (41, 4) (numbers left: [36]). Try possible operations.\n    |- Try 41 + 4 = 45. Add 45 to the number set. Current number set: [45, 36], target: 41, just two numbers left.\n     |- Try 45 + 36 = 81. Evaluate 81 != 41, drop this branch.\n     |- Try 45 - 36 = 9. Evaluate 9 != 41, drop this branch.\n     |- Try 45 * 36 = 1620. Evaluate 1620 != 41, drop this branch.\n     |- Try 45 \/ 36 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 41 - 4 = 37. Add 37 to the number set. Current number set: [37, 36], target: 41, just two numbers left.\n     |- Try 37 + 36 = 73. Evaluate 73 != 41, drop this branch.\n     |- Try 37 - 36 = 1. Evaluate 1 != 41, drop this branch.\n     |- Try 37 * 36 = 1332. Evaluate 1332 != 41, drop this branch.\n     |- Try 37 \/ 36 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 41 * 4 = 164. Add 164 to the number set. Current number set: [164, 36], target: 41, just two numbers left.\n     |- Try 164 + 36 = 200. Evaluate 200 != 41, drop this branch.\n     |- Try 164 - 36 = 128. Evaluate 128 != 41, drop this branch.\n     |- Try 164 * 36 = 5904. 5904 exceeds the maximum intermediate result, drop this branch.\n     |- Try 164 \/ 36 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 41 \/ 4 = 10.2. 10.2 is a decimal, drop this branch.\n  |- Try 30 - 6 = 24. Add 24 to the number set. Current number set: [24, 41, 4], target: 41. Options for choosing two numbers: [(24, 41), (24, 4), (41, 4)].\n   |- Pick two numbers (24, 41) (numbers left: [4]). Try possible operations.\n    |- Try 41 + 24 = 65. Add 65 to the number set. Current number set: [65, 4], target: 41, just two numbers left.\n     |- Try 65 + 4 = 69. Evaluate 69 != 41, drop this branch.\n     |- Try 65 - 4 = 61. Evaluate 61 != 41, drop this branch.\n     |- Try 65 * 4 = 260. Evaluate 260 != 41, drop this branch.\n     |- Try 65 \/ 4 = 16.2. 16.2 is a decimal, drop this branch.\n    |- Try 41 - 24 = 17. Add 17 to the number set. Current number set: [17, 4], target: 41, just two numbers left.\n     |- Try 17 + 4 = 21. Evaluate 21 != 41, drop this branch.\n     |- Try 17 - 4 = 13. Evaluate 13 != 41, drop this branch.\n     |- Try 17 * 4 = 68. Evaluate 68 != 41, drop this branch.\n     |- Try 17 \/ 4 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 41 * 24 = 984. Add 984 to the number set. Current number set: [984, 4], target: 41, just two numbers left.\n     |- Try 984 + 4 = 988. Evaluate 988 != 41, drop this branch.\n     |- Try 984 - 4 = 980. Evaluate 980 != 41, drop this branch.\n     |- Try 984 * 4 = 3936. 3936 exceeds the maximum intermediate result, drop this branch.\n     |- Try 984 \/ 4 = 246. Evaluate 246 != 41, drop this branch.\n    |- Try 41 \/ 24 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (24, 4) (numbers left: [41]). Try possible operations.\n    |- Try 24 + 4 = 28. Add 28 to the number set. Current number set: [28, 41], target: 41, just two numbers left.\n     |- Try 41 + 28 = 69. Evaluate 69 != 41, drop this branch.\n     |- Try 41 - 28 = 13. Evaluate 13 != 41, drop this branch.\n     |- Try 41 * 28 = 1148. Evaluate 1148 != 41, drop this branch.\n     |- Try 41 \/ 28 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 24 - 4 = 20. Add 20 to the number set. Current number set: [20, 41], target: 41, just two numbers left.\n     |- Try 41 + 20 = 61. Evaluate 61 != 41, drop this branch.\n     |- Try 41 - 20 = 21. Evaluate 21 != 41, drop this branch.\n     |- Try 41 * 20 = 820. Evaluate 820 != 41, drop this branch.\n     |- Try 41 \/ 20 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 24 * 4 = 96. Add 96 to the number set. Current number set: [96, 41], target: 41, just two numbers left.\n     |- Try 96 + 41 = 137. Evaluate 137 != 41, drop this branch.\n     |- Try 96 - 41 = 55. Evaluate 55 != 41, drop this branch.\n     |- Try 96 * 41 = 3936. 3936 exceeds the maximum intermediate result, drop this branch.\n     |- Try 96 \/ 41 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 24 \/ 4 = 6. Add 6 to the number set. Current number set: [6, 41], target: 41, just two numbers left.\n     |- Try 41 + 6 = 47. Evaluate 47 != 41, drop this branch.\n     |- Try 41 - 6 = 35. Evaluate 35 != 41, drop this branch.\n     |- Try 41 * 6 = 246. Evaluate 246 != 41, drop this branch.\n     |- Try 41 \/ 6 = 6.8. 6.8 is a decimal, drop this branch.\n   |- Pick two numbers (41, 4) (numbers left: [24]). Try possible operations.\n    |- Try 41 + 4 = 45. Add 45 to the number set. Current number set: [45, 24], target: 41, just two numbers left.\n     |- Try 45 + 24 = 69. Evaluate 69 != 41, drop this branch.\n     |- Try 45 - 24 = 21. Evaluate 21 != 41, drop this branch.\n     |- Try 45 * 24 = 1080. Evaluate 1080 != 41, drop this branch.\n     |- Try 45 \/ 24 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 41 - 4 = 37. Add 37 to the number set. Current number set: [37, 24], target: 41, just two numbers left.\n     |- Try 37 + 24 = 61. Evaluate 61 != 41, drop this branch.\n     |- Try 37 - 24 = 13. Evaluate 13 != 41, drop this branch.\n     |- Try 37 * 24 = 888. Evaluate 888 != 41, drop this branch.\n     |- Try 37 \/ 24 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 41 * 4 = 164. Add 164 to the number set. Current number set: [164, 24], target: 41, just two numbers left.\n     |- Try 164 + 24 = 188. Evaluate 188 != 41, drop this branch.\n     |- Try 164 - 24 = 140. Evaluate 140 != 41, drop this branch.\n     |- Try 164 * 24 = 3936. 3936 exceeds the maximum intermediate result, drop this branch.\n     |- Try 164 \/ 24 = 6.8. 6.8 is a decimal, drop this branch.\n    |- Try 41 \/ 4 = 10.2. 10.2 is a decimal, drop this branch.\n  |- Try 30 * 6 = 180. Add 180 to the number set. Current number set: [180, 41, 4], target: 41. Options for choosing two numbers: [(180, 41), (180, 4), (41, 4)].\n   |- Pick two numbers (180, 41) (numbers left: [4]). Try possible operations.\n    |- Try 180 + 41 = 221. Add 221 to the number set. Current number set: [221, 4], target: 41, just two numbers left.\n     |- Try 221 + 4 = 225. Evaluate 225 != 41, drop this branch.\n     |- Try 221 - 4 = 217. Evaluate 217 != 41, drop this branch.\n     |- Try 221 * 4 = 884. Evaluate 884 != 41, drop this branch.\n     |- Try 221 \/ 4 = 55.2. 55.2 is a decimal, drop this branch.\n    |- Try 180 - 41 = 139. Add 139 to the number set. Current number set: [139, 4], target: 41, just two numbers left.\n     |- Try 139 + 4 = 143. Evaluate 143 != 41, drop this branch.\n     |- Try 139 - 4 = 135. Evaluate 135 != 41, drop this branch.\n     |- Try 139 * 4 = 556. Evaluate 556 != 41, drop this branch.\n     |- Try 139 \/ 4 = 34.8. 34.8 is a decimal, drop this branch.\n    |- Try 180 * 41 = 7380. 7380 exceeds the maximum intermediate result, drop this branch.\n    |- Try 180 \/ 41 = 4.4. 4.4 is a decimal, drop this branch.\n   |- Pick two numbers (180, 4) (numbers left: [41]). Try possible operations.\n    |- Try 180 + 4 = 184. Add 184 to the number set. Current number set: [184, 41], target: 41, just two numbers left.\n     |- Try 184 + 41 = 225. Evaluate 225 != 41, drop this branch.\n     |- Try 184 - 41 = 143. Evaluate 143 != 41, drop this branch.\n     |- Try 184 * 41 = 7544. 7544 exceeds the maximum intermediate result, drop this branch.\n     |- Try 184 \/ 41 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 180 - 4 = 176. Add 176 to the number set. Current number set: [176, 41], target: 41, just two numbers left.\n     |- Try 176 + 41 = 217. Evaluate 217 != 41, drop this branch.\n     |- Try 176 - 41 = 135. Evaluate 135 != 41, drop this branch.\n     |- Try 176 * 41 = 7216. 7216 exceeds the maximum intermediate result, drop this branch.\n     |- Try 176 \/ 41 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 180 * 4 = 720. Add 720 to the number set. Current number set: [720, 41], target: 41, just two numbers left.\n     |- Try 720 + 41 = 761. Evaluate 761 != 41, drop this branch.\n     |- Try 720 - 41 = 679. Evaluate 679 != 41, drop this branch.\n     |- Try 720 * 41 = 29520. 29520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 720 \/ 41 = 17.6. 17.6 is a decimal, drop this branch.\n    |- Try 180 \/ 4 = 45. Add 45 to the number set. Current number set: [45, 41], target: 41, just two numbers left.\n     |- Try 45 + 41 = 86. Evaluate 86 != 41, drop this branch.\n     |- Try 45 - 41 = 4. Evaluate 4 != 41, drop this branch.\n     |- Try 45 * 41 = 1845. Evaluate 1845 != 41, drop this branch.\n     |- Try 45 \/ 41 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (41, 4) (numbers left: [180]). Try possible operations.\n    |- Try 41 + 4 = 45. Add 45 to the number set. Current number set: [45, 180], target: 41, just two numbers left.\n     |- Try 180 + 45 = 225. Evaluate 225 != 41, drop this branch.\n     |- Try 180 - 45 = 135. Evaluate 135 != 41, drop this branch.\n     |- Try 180 * 45 = 8100. 8100 exceeds the maximum intermediate result, drop this branch.\n     |- Try 180 \/ 45 = 4. Evaluate 4 != 41, drop this branch.\n    |- Try 41 - 4 = 37. Add 37 to the number set. Current number set: [37, 180], target: 41, just two numbers left.\n     |- Try 180 + 37 = 217. Evaluate 217 != 41, drop this branch.\n     |- Try 180 - 37 = 143. Evaluate 143 != 41, drop this branch.\n     |- Try 180 * 37 = 6660. 6660 exceeds the maximum intermediate result, drop this branch.\n     |- Try 180 \/ 37 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 41 * 4 = 164. Add 164 to the number set. Current number set: [164, 180], target: 41, just two numbers left.\n     |- Try 180 + 164 = 344. Evaluate 344 != 41, drop this branch.\n     |- Try 180 - 164 = 16. Evaluate 16 != 41, drop this branch.\n     |- Try 180 * 164 = 29520. 29520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 180 \/ 164 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 41 \/ 4 = 10.2. 10.2 is a decimal, drop this branch.\n  |- Try 30 \/ 6 = 5. Add 5 to the number set. Current number set: [5, 41, 4], target: 41. Options for choosing two numbers: [(5, 41), (5, 4), (41, 4)].\n   |- Pick two numbers (5, 41) (numbers left: [4]). Try possible operations.\n    |- Try 41 + 5 = 46. Add 46 to the number set. Current number set: [46, 4], target: 41, just two numbers left.\n     |- Try 46 + 4 = 50. Evaluate 50 != 41, drop this branch.\n     |- Try 46 - 4 = 42. Evaluate 42 != 41, drop this branch.\n     |- Try 46 * 4 = 184. Evaluate 184 != 41, drop this branch.\n     |- Try 46 \/ 4 = 11.5. 11.5 is a decimal, drop this branch.\n    |- Try 41 - 5 = 36. Add 36 to the number set. Current number set: [36, 4], target: 41, just two numbers left.\n     |- Try 36 + 4 = 40. Evaluate 40 != 41, drop this branch.\n     |- Try 36 - 4 = 32. Evaluate 32 != 41, drop this branch.\n     |- Try 36 * 4 = 144. Evaluate 144 != 41, drop this branch.\n     |- Try 36 \/ 4 = 9. Evaluate 9 != 41, drop this branch.\n    |- Try 41 * 5 = 205. Add 205 to the number set. Current number set: [205, 4], target: 41, just two numbers left.\n     |- Try 205 + 4 = 209. Evaluate 209 != 41, drop this branch.\n     |- Try 205 - 4 = 201. Evaluate 201 != 41, drop this branch.\n     |- Try 205 * 4 = 820. Evaluate 820 != 41, drop this branch.\n     |- Try 205 \/ 4 = 51.2. 51.2 is a decimal, drop this branch.\n    |- Try 41 \/ 5 = 8.2. 8.2 is a decimal, drop this branch.\n   |- Pick two numbers (5, 4) (numbers left: [41]). Try possible operations.\n    |- Try 5 + 4 = 9. Add 9 to the number set. Current number set: [9, 41], target: 41, just two numbers left.\n     |- Try 41 + 9 = 50. Evaluate 50 != 41, drop this branch.\n     |- Try 41 - 9 = 32. Evaluate 32 != 41, drop this branch.\n     |- Try 41 * 9 = 369. Evaluate 369 != 41, drop this branch.\n     |- Try 41 \/ 9 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 5 - 4 = 1. Add 1 to the number set. Current number set: [1, 41], target: 41, just two numbers left.\n     |- Try 41 + 1 = 42. Evaluate 42 != 41, drop this branch.\n     |- Try 41 - 1 = 40. Evaluate 40 != 41, drop this branch.\n     |- Try 41 * 1 = 41. Evaluate 41 == 41, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 41 * 1 = 41\nThe step before: 5 - 4 = 1\nThe first step: 30 \/ 6 = 5\n\nOutput the solution in the required format:\n<Solution>\n30 \/ 6 = 5\n5 - 4 = 1\n41 * 1 = 41\n<\/Solution>\n","item":{"nums":[6,30,41,4],"solution":["30 \/ 6 = 5","5 - 4 = 1","41 * 1 = 41"],"target":41}}
+{"instance_id":"countdown_8k_73","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [19, 40, 4, 45]\nTarget: 43","reference_output":"# Search Procedure\nInitial number set: [19, 40, 4, 45], target: 43. Options for choosing two numbers: [(19, 40), (19, 4), (19, 45), (40, 4), (40, 45), (4, 45)].\n |- Pick two numbers (19, 40) (numbers left: [4, 45]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 4, 45], target: 43. Options for choosing two numbers: [(59, 4), (59, 45), (4, 45)].\n   |- Pick two numbers (59, 4) (numbers left: [45]). Try possible operations.\n    |- Try 59 + 4 = 63. Add 63 to the number set. Current number set: [63, 45], target: 43, just two numbers left.\n     |- Try 63 + 45 = 108. Evaluate 108 != 43, drop this branch.\n     |- Try 63 - 45 = 18. Evaluate 18 != 43, drop this branch.\n     |- Try 63 * 45 = 2835. 2835 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 45 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 59 - 4 = 55. Add 55 to the number set. Current number set: [55, 45], target: 43, just two numbers left.\n     |- Try 55 + 45 = 100. Evaluate 100 != 43, drop this branch.\n     |- Try 55 - 45 = 10. Evaluate 10 != 43, drop this branch.\n     |- Try 55 * 45 = 2475. 2475 exceeds the maximum intermediate result, drop this branch.\n     |- Try 55 \/ 45 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 59 * 4 = 236. Add 236 to the number set. Current number set: [236, 45], target: 43, just two numbers left.\n     |- Try 236 + 45 = 281. Evaluate 281 != 43, drop this branch.\n     |- Try 236 - 45 = 191. Evaluate 191 != 43, drop this branch.\n     |- Try 236 * 45 = 10620. 10620 exceeds the maximum intermediate result, drop this branch.\n     |- Try 236 \/ 45 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 59 \/ 4 = 14.8. 14.8 is a decimal, drop this branch.\n   |- Pick two numbers (59, 45) (numbers left: [4]). Try possible operations.\n    |- Try 59 + 45 = 104. Add 104 to the number set. Current number set: [104, 4], target: 43, just two numbers left.\n     |- Try 104 + 4 = 108. Evaluate 108 != 43, drop this branch.\n     |- Try 104 - 4 = 100. Evaluate 100 != 43, drop this branch.\n     |- Try 104 * 4 = 416. Evaluate 416 != 43, drop this branch.\n     |- Try 104 \/ 4 = 26. Evaluate 26 != 43, drop this branch.\n    |- Try 59 - 45 = 14. Add 14 to the number set. Current number set: [14, 4], target: 43, just two numbers left.\n     |- Try 14 + 4 = 18. Evaluate 18 != 43, drop this branch.\n     |- Try 14 - 4 = 10. Evaluate 10 != 43, drop this branch.\n     |- Try 14 * 4 = 56. Evaluate 56 != 43, drop this branch.\n     |- Try 14 \/ 4 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 59 * 45 = 2655. 2655 exceeds the maximum intermediate result, drop this branch.\n    |- Try 59 \/ 45 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (4, 45) (numbers left: [59]). Try possible operations.\n    |- Try 45 + 4 = 49. Add 49 to the number set. Current number set: [49, 59], target: 43, just two numbers left.\n     |- Try 59 + 49 = 108. Evaluate 108 != 43, drop this branch.\n     |- Try 59 - 49 = 10. Evaluate 10 != 43, drop this branch.\n     |- Try 59 * 49 = 2891. 2891 exceeds the maximum intermediate result, drop this branch.\n     |- Try 59 \/ 49 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 45 - 4 = 41. Add 41 to the number set. Current number set: [41, 59], target: 43, just two numbers left.\n     |- Try 59 + 41 = 100. Evaluate 100 != 43, drop this branch.\n     |- Try 59 - 41 = 18. Evaluate 18 != 43, drop this branch.\n     |- Try 59 * 41 = 2419. 2419 exceeds the maximum intermediate result, drop this branch.\n     |- Try 59 \/ 41 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 45 * 4 = 180. Add 180 to the number set. Current number set: [180, 59], target: 43, just two numbers left.\n     |- Try 180 + 59 = 239. Evaluate 239 != 43, drop this branch.\n     |- Try 180 - 59 = 121. Evaluate 121 != 43, drop this branch.\n     |- Try 180 * 59 = 10620. 10620 exceeds the maximum intermediate result, drop this branch.\n     |- Try 180 \/ 59 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 45 \/ 4 = 11.2. 11.2 is a decimal, drop this branch.\n  |- Try 40 - 19 = 21. Add 21 to the number set. Current number set: [21, 4, 45], target: 43. Options for choosing two numbers: [(21, 4), (21, 45), (4, 45)].\n   |- Pick two numbers (21, 4) (numbers left: [45]). Try possible operations.\n    |- Try 21 + 4 = 25. Add 25 to the number set. Current number set: [25, 45], target: 43, just two numbers left.\n     |- Try 45 + 25 = 70. Evaluate 70 != 43, drop this branch.\n     |- Try 45 - 25 = 20. Evaluate 20 != 43, drop this branch.\n     |- Try 45 * 25 = 1125. Evaluate 1125 != 43, drop this branch.\n     |- Try 45 \/ 25 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 21 - 4 = 17. Add 17 to the number set. Current number set: [17, 45], target: 43, just two numbers left.\n     |- Try 45 + 17 = 62. Evaluate 62 != 43, drop this branch.\n     |- Try 45 - 17 = 28. Evaluate 28 != 43, drop this branch.\n     |- Try 45 * 17 = 765. Evaluate 765 != 43, drop this branch.\n     |- Try 45 \/ 17 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 21 * 4 = 84. Add 84 to the number set. Current number set: [84, 45], target: 43, just two numbers left.\n     |- Try 84 + 45 = 129. Evaluate 129 != 43, drop this branch.\n     |- Try 84 - 45 = 39. Evaluate 39 != 43, drop this branch.\n     |- Try 84 * 45 = 3780. 3780 exceeds the maximum intermediate result, drop this branch.\n     |- Try 84 \/ 45 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 21 \/ 4 = 5.2. 5.2 is a decimal, drop this branch.\n   |- Pick two numbers (21, 45) (numbers left: [4]). Try possible operations.\n    |- Try 45 + 21 = 66. Add 66 to the number set. Current number set: [66, 4], target: 43, just two numbers left.\n     |- Try 66 + 4 = 70. Evaluate 70 != 43, drop this branch.\n     |- Try 66 - 4 = 62. Evaluate 62 != 43, drop this branch.\n     |- Try 66 * 4 = 264. Evaluate 264 != 43, drop this branch.\n     |- Try 66 \/ 4 = 16.5. 16.5 is a decimal, drop this branch.\n    |- Try 45 - 21 = 24. Add 24 to the number set. Current number set: [24, 4], target: 43, just two numbers left.\n     |- Try 24 + 4 = 28. Evaluate 28 != 43, drop this branch.\n     |- Try 24 - 4 = 20. Evaluate 20 != 43, drop this branch.\n     |- Try 24 * 4 = 96. Evaluate 96 != 43, drop this branch.\n     |- Try 24 \/ 4 = 6. Evaluate 6 != 43, drop this branch.\n    |- Try 45 * 21 = 945. Add 945 to the number set. Current number set: [945, 4], target: 43, just two numbers left.\n     |- Try 945 + 4 = 949. Evaluate 949 != 43, drop this branch.\n     |- Try 945 - 4 = 941. Evaluate 941 != 43, drop this branch.\n     |- Try 945 * 4 = 3780. 3780 exceeds the maximum intermediate result, drop this branch.\n     |- Try 945 \/ 4 = 236.2. 236.2 is a decimal, drop this branch.\n    |- Try 45 \/ 21 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (4, 45) (numbers left: [21]). Try possible operations.\n    |- Try 45 + 4 = 49. Add 49 to the number set. Current number set: [49, 21], target: 43, just two numbers left.\n     |- Try 49 + 21 = 70. Evaluate 70 != 43, drop this branch.\n     |- Try 49 - 21 = 28. Evaluate 28 != 43, drop this branch.\n     |- Try 49 * 21 = 1029. Evaluate 1029 != 43, drop this branch.\n     |- Try 49 \/ 21 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 45 - 4 = 41. Add 41 to the number set. Current number set: [41, 21], target: 43, just two numbers left.\n     |- Try 41 + 21 = 62. Evaluate 62 != 43, drop this branch.\n     |- Try 41 - 21 = 20. Evaluate 20 != 43, drop this branch.\n     |- Try 41 * 21 = 861. Evaluate 861 != 43, drop this branch.\n     |- Try 41 \/ 21 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 45 * 4 = 180. Add 180 to the number set. Current number set: [180, 21], target: 43, just two numbers left.\n     |- Try 180 + 21 = 201. Evaluate 201 != 43, drop this branch.\n     |- Try 180 - 21 = 159. Evaluate 159 != 43, drop this branch.\n     |- Try 180 * 21 = 3780. 3780 exceeds the maximum intermediate result, drop this branch.\n     |- Try 180 \/ 21 = 8.6. 8.6 is a decimal, drop this branch.\n    |- Try 45 \/ 4 = 11.2. 11.2 is a decimal, drop this branch.\n  |- Try 40 * 19 = 760. Add 760 to the number set. Current number set: [760, 4, 45], target: 43. Options for choosing two numbers: [(760, 4), (760, 45), (4, 45)].\n   |- Pick two numbers (760, 4) (numbers left: [45]). Try possible operations.\n    |- Try 760 + 4 = 764. Add 764 to the number set. Current number set: [764, 45], target: 43, just two numbers left.\n     |- Try 764 + 45 = 809. Evaluate 809 != 43, drop this branch.\n     |- Try 764 - 45 = 719. Evaluate 719 != 43, drop this branch.\n     |- Try 764 * 45 = 34380. 34380 exceeds the maximum intermediate result, drop this branch.\n     |- Try 764 \/ 45 = 17.0. 17.0 is a decimal, drop this branch.\n    |- Try 760 - 4 = 756. Add 756 to the number set. Current number set: [756, 45], target: 43, just two numbers left.\n     |- Try 756 + 45 = 801. Evaluate 801 != 43, drop this branch.\n     |- Try 756 - 45 = 711. Evaluate 711 != 43, drop this branch.\n     |- Try 756 * 45 = 34020. 34020 exceeds the maximum intermediate result, drop this branch.\n     |- Try 756 \/ 45 = 16.8. 16.8 is a decimal, drop this branch.\n    |- Try 760 * 4 = 3040. 3040 exceeds the maximum intermediate result, drop this branch.\n    |- Try 760 \/ 4 = 190. Add 190 to the number set. Current number set: [190, 45], target: 43, just two numbers left.\n     |- Try 190 + 45 = 235. Evaluate 235 != 43, drop this branch.\n     |- Try 190 - 45 = 145. Evaluate 145 != 43, drop this branch.\n     |- Try 190 * 45 = 8550. 8550 exceeds the maximum intermediate result, drop this branch.\n     |- Try 190 \/ 45 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (760, 45) (numbers left: [4]). Try possible operations.\n    |- Try 760 + 45 = 805. Add 805 to the number set. Current number set: [805, 4], target: 43, just two numbers left.\n     |- Try 805 + 4 = 809. Evaluate 809 != 43, drop this branch.\n     |- Try 805 - 4 = 801. Evaluate 801 != 43, drop this branch.\n     |- Try 805 * 4 = 3220. 3220 exceeds the maximum intermediate result, drop this branch.\n     |- Try 805 \/ 4 = 201.2. 201.2 is a decimal, drop this branch.\n    |- Try 760 - 45 = 715. Add 715 to the number set. Current number set: [715, 4], target: 43, just two numbers left.\n     |- Try 715 + 4 = 719. Evaluate 719 != 43, drop this branch.\n     |- Try 715 - 4 = 711. Evaluate 711 != 43, drop this branch.\n     |- Try 715 * 4 = 2860. 2860 exceeds the maximum intermediate result, drop this branch.\n     |- Try 715 \/ 4 = 178.8. 178.8 is a decimal, drop this branch.\n    |- Try 760 * 45 = 34200. 34200 exceeds the maximum intermediate result, drop this branch.\n    |- Try 760 \/ 45 = 16.9. 16.9 is a decimal, drop this branch.\n   |- Pick two numbers (4, 45) (numbers left: [760]). Try possible operations.\n    |- Try 45 + 4 = 49. Add 49 to the number set. Current number set: [49, 760], target: 43, just two numbers left.\n     |- Try 760 + 49 = 809. Evaluate 809 != 43, drop this branch.\n     |- Try 760 - 49 = 711. Evaluate 711 != 43, drop this branch.\n     |- Try 760 * 49 = 37240. 37240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 760 \/ 49 = 15.5. 15.5 is a decimal, drop this branch.\n    |- Try 45 - 4 = 41. Add 41 to the number set. Current number set: [41, 760], target: 43, just two numbers left.\n     |- Try 760 + 41 = 801. Evaluate 801 != 43, drop this branch.\n     |- Try 760 - 41 = 719. Evaluate 719 != 43, drop this branch.\n     |- Try 760 * 41 = 31160. 31160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 760 \/ 41 = 18.5. 18.5 is a decimal, drop this branch.\n    |- Try 45 * 4 = 180. Add 180 to the number set. Current number set: [180, 760], target: 43, just two numbers left.\n     |- Try 760 + 180 = 940. Evaluate 940 != 43, drop this branch.\n     |- Try 760 - 180 = 580. Evaluate 580 != 43, drop this branch.\n     |- Try 760 * 180 = 136800. 136800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 760 \/ 180 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 45 \/ 4 = 11.2. 11.2 is a decimal, drop this branch.\n  |- Try 40 \/ 19 = 2.1. 2.1 is a decimal, drop this branch.\n |- Pick two numbers (19, 4) (numbers left: [40, 45]). Try possible operations.\n  |- Try 19 + 4 = 23. Add 23 to the number set. Current number set: [23, 40, 45], target: 43. Options for choosing two numbers: [(23, 40), (23, 45), (40, 45)].\n   |- Pick two numbers (23, 40) (numbers left: [45]). Try possible operations.\n    |- Try 40 + 23 = 63. Add 63 to the number set. Current number set: [63, 45], target: 43, just two numbers left.\n     |- Try 63 + 45 = 108. Evaluate 108 != 43, drop this branch.\n     |- Try 63 - 45 = 18. Evaluate 18 != 43, drop this branch.\n     |- Try 63 * 45 = 2835. 2835 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 45 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 40 - 23 = 17. Add 17 to the number set. Current number set: [17, 45], target: 43, just two numbers left.\n     |- Try 45 + 17 = 62. Evaluate 62 != 43, drop this branch.\n     |- Try 45 - 17 = 28. Evaluate 28 != 43, drop this branch.\n     |- Try 45 * 17 = 765. Evaluate 765 != 43, drop this branch.\n     |- Try 45 \/ 17 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 40 * 23 = 920. Add 920 to the number set. Current number set: [920, 45], target: 43, just two numbers left.\n     |- Try 920 + 45 = 965. Evaluate 965 != 43, drop this branch.\n     |- Try 920 - 45 = 875. Evaluate 875 != 43, drop this branch.\n     |- Try 920 * 45 = 41400. 41400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 920 \/ 45 = 20.4. 20.4 is a decimal, drop this branch.\n    |- Try 40 \/ 23 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (23, 45) (numbers left: [40]). Try possible operations.\n    |- Try 45 + 23 = 68. Add 68 to the number set. Current number set: [68, 40], target: 43, just two numbers left.\n     |- Try 68 + 40 = 108. Evaluate 108 != 43, drop this branch.\n     |- Try 68 - 40 = 28. Evaluate 28 != 43, drop this branch.\n     |- Try 68 * 40 = 2720. 2720 exceeds the maximum intermediate result, drop this branch.\n     |- Try 68 \/ 40 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 45 - 23 = 22. Add 22 to the number set. Current number set: [22, 40], target: 43, just two numbers left.\n     |- Try 40 + 22 = 62. Evaluate 62 != 43, drop this branch.\n     |- Try 40 - 22 = 18. Evaluate 18 != 43, drop this branch.\n     |- Try 40 * 22 = 880. Evaluate 880 != 43, drop this branch.\n     |- Try 40 \/ 22 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 45 * 23 = 1035. Add 1035 to the number set. Current number set: [1035, 40], target: 43, just two numbers left.\n     |- Try 1035 + 40 = 1075. Evaluate 1075 != 43, drop this branch.\n     |- Try 1035 - 40 = 995. Evaluate 995 != 43, drop this branch.\n     |- Try 1035 * 40 = 41400. 41400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1035 \/ 40 = 25.9. 25.9 is a decimal, drop this branch.\n    |- Try 45 \/ 23 = 2.0. 2.0 is a decimal, drop this branch.\n   |- Pick two numbers (40, 45) (numbers left: [23]). Try possible operations.\n    |- Try 45 + 40 = 85. Add 85 to the number set. Current number set: [85, 23], target: 43, just two numbers left.\n     |- Try 85 + 23 = 108. Evaluate 108 != 43, drop this branch.\n     |- Try 85 - 23 = 62. Evaluate 62 != 43, drop this branch.\n     |- Try 85 * 23 = 1955. Evaluate 1955 != 43, drop this branch.\n     |- Try 85 \/ 23 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 45 - 40 = 5. Add 5 to the number set. Current number set: [5, 23], target: 43, just two numbers left.\n     |- Try 23 + 5 = 28. Evaluate 28 != 43, drop this branch.\n     |- Try 23 - 5 = 18. Evaluate 18 != 43, drop this branch.\n     |- Try 23 * 5 = 115. Evaluate 115 != 43, drop this branch.\n     |- Try 23 \/ 5 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 45 * 40 = 1800. Add 1800 to the number set. Current number set: [1800, 23], target: 43, just two numbers left.\n     |- Try 1800 + 23 = 1823. Evaluate 1823 != 43, drop this branch.\n     |- Try 1800 - 23 = 1777. Evaluate 1777 != 43, drop this branch.\n     |- Try 1800 * 23 = 41400. 41400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1800 \/ 23 = 78.3. 78.3 is a decimal, drop this branch.\n    |- Try 45 \/ 40 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 19 - 4 = 15. Add 15 to the number set. Current number set: [15, 40, 45], target: 43. Options for choosing two numbers: [(15, 40), (15, 45), (40, 45)].\n   |- Pick two numbers (15, 40) (numbers left: [45]). Try possible operations.\n    |- Try 40 + 15 = 55. Add 55 to the number set. Current number set: [55, 45], target: 43, just two numbers left.\n     |- Try 55 + 45 = 100. Evaluate 100 != 43, drop this branch.\n     |- Try 55 - 45 = 10. Evaluate 10 != 43, drop this branch.\n     |- Try 55 * 45 = 2475. 2475 exceeds the maximum intermediate result, drop this branch.\n     |- Try 55 \/ 45 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 40 - 15 = 25. Add 25 to the number set. Current number set: [25, 45], target: 43, just two numbers left.\n     |- Try 45 + 25 = 70. Evaluate 70 != 43, drop this branch.\n     |- Try 45 - 25 = 20. Evaluate 20 != 43, drop this branch.\n     |- Try 45 * 25 = 1125. Evaluate 1125 != 43, drop this branch.\n     |- Try 45 \/ 25 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 40 * 15 = 600. Add 600 to the number set. Current number set: [600, 45], target: 43, just two numbers left.\n     |- Try 600 + 45 = 645. Evaluate 645 != 43, drop this branch.\n     |- Try 600 - 45 = 555. Evaluate 555 != 43, drop this branch.\n     |- Try 600 * 45 = 27000. 27000 exceeds the maximum intermediate result, drop this branch.\n     |- Try 600 \/ 45 = 13.3. 13.3 is a decimal, drop this branch.\n    |- Try 40 \/ 15 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (15, 45) (numbers left: [40]). Try possible operations.\n    |- Try 45 + 15 = 60. Add 60 to the number set. Current number set: [60, 40], target: 43, just two numbers left.\n     |- Try 60 + 40 = 100. Evaluate 100 != 43, drop this branch.\n     |- Try 60 - 40 = 20. Evaluate 20 != 43, drop this branch.\n     |- Try 60 * 40 = 2400. 2400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 60 \/ 40 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 45 - 15 = 30. Add 30 to the number set. Current number set: [30, 40], target: 43, just two numbers left.\n     |- Try 40 + 30 = 70. Evaluate 70 != 43, drop this branch.\n     |- Try 40 - 30 = 10. Evaluate 10 != 43, drop this branch.\n     |- Try 40 * 30 = 1200. Evaluate 1200 != 43, drop this branch.\n     |- Try 40 \/ 30 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 45 * 15 = 675. Add 675 to the number set. Current number set: [675, 40], target: 43, just two numbers left.\n     |- Try 675 + 40 = 715. Evaluate 715 != 43, drop this branch.\n     |- Try 675 - 40 = 635. Evaluate 635 != 43, drop this branch.\n     |- Try 675 * 40 = 27000. 27000 exceeds the maximum intermediate result, drop this branch.\n     |- Try 675 \/ 40 = 16.9. 16.9 is a decimal, drop this branch.\n    |- Try 45 \/ 15 = 3. Add 3 to the number set. Current number set: [3, 40], target: 43, just two numbers left.\n     |- Try 40 + 3 = 43. Evaluate 43 == 43, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 40 + 3 = 43\nThe step before: 45 \/ 15 = 3\nThe first step: 19 - 4 = 15\n\nOutput the solution in the required format:\n<Solution>\n19 - 4 = 15\n45 \/ 15 = 3\n40 + 3 = 43\n<\/Solution>\n","item":{"nums":[19,40,4,45],"solution":["19 - 4 = 15","45 \/ 15 = 3","40 + 3 = 43"],"target":43}}
+{"instance_id":"countdown_8k_74","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [10, 30, 42, 29]\nTarget: 43","reference_output":"# Search Procedure\nInitial number set: [10, 30, 42, 29], target: 43. Options for choosing two numbers: [(10, 30), (10, 42), (10, 29), (30, 42), (30, 29), (42, 29)].\n |- Pick two numbers (10, 30) (numbers left: [42, 29]). Try possible operations.\n  |- Try 30 + 10 = 40. Add 40 to the number set. Current number set: [40, 42, 29], target: 43. Options for choosing two numbers: [(40, 42), (40, 29), (42, 29)].\n   |- Pick two numbers (40, 42) (numbers left: [29]). Try possible operations.\n    |- Try 42 + 40 = 82. Add 82 to the number set. Current number set: [82, 29], target: 43, just two numbers left.\n     |- Try 82 + 29 = 111. Evaluate 111 != 43, drop this branch.\n     |- Try 82 - 29 = 53. Evaluate 53 != 43, drop this branch.\n     |- Try 82 * 29 = 2378. 2378 exceeds the maximum intermediate result, drop this branch.\n     |- Try 82 \/ 29 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 42 - 40 = 2. Add 2 to the number set. Current number set: [2, 29], target: 43, just two numbers left.\n     |- Try 29 + 2 = 31. Evaluate 31 != 43, drop this branch.\n     |- Try 29 - 2 = 27. Evaluate 27 != 43, drop this branch.\n     |- Try 29 * 2 = 58. Evaluate 58 != 43, drop this branch.\n     |- Try 29 \/ 2 = 14.5. 14.5 is a decimal, drop this branch.\n    |- Try 42 * 40 = 1680. Add 1680 to the number set. Current number set: [1680, 29], target: 43, just two numbers left.\n     |- Try 1680 + 29 = 1709. Evaluate 1709 != 43, drop this branch.\n     |- Try 1680 - 29 = 1651. Evaluate 1651 != 43, drop this branch.\n     |- Try 1680 * 29 = 48720. 48720 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1680 \/ 29 = 57.9. 57.9 is a decimal, drop this branch.\n    |- Try 42 \/ 40 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (40, 29) (numbers left: [42]). Try possible operations.\n    |- Try 40 + 29 = 69. Add 69 to the number set. Current number set: [69, 42], target: 43, just two numbers left.\n     |- Try 69 + 42 = 111. Evaluate 111 != 43, drop this branch.\n     |- Try 69 - 42 = 27. Evaluate 27 != 43, drop this branch.\n     |- Try 69 * 42 = 2898. 2898 exceeds the maximum intermediate result, drop this branch.\n     |- Try 69 \/ 42 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 40 - 29 = 11. Add 11 to the number set. Current number set: [11, 42], target: 43, just two numbers left.\n     |- Try 42 + 11 = 53. Evaluate 53 != 43, drop this branch.\n     |- Try 42 - 11 = 31. Evaluate 31 != 43, drop this branch.\n     |- Try 42 * 11 = 462. Evaluate 462 != 43, drop this branch.\n     |- Try 42 \/ 11 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 40 * 29 = 1160. Add 1160 to the number set. Current number set: [1160, 42], target: 43, just two numbers left.\n     |- Try 1160 + 42 = 1202. Evaluate 1202 != 43, drop this branch.\n     |- Try 1160 - 42 = 1118. Evaluate 1118 != 43, drop this branch.\n     |- Try 1160 * 42 = 48720. 48720 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1160 \/ 42 = 27.6. 27.6 is a decimal, drop this branch.\n    |- Try 40 \/ 29 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (42, 29) (numbers left: [40]). Try possible operations.\n    |- Try 42 + 29 = 71. Add 71 to the number set. Current number set: [71, 40], target: 43, just two numbers left.\n     |- Try 71 + 40 = 111. Evaluate 111 != 43, drop this branch.\n     |- Try 71 - 40 = 31. Evaluate 31 != 43, drop this branch.\n     |- Try 71 * 40 = 2840. 2840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 71 \/ 40 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 42 - 29 = 13. Add 13 to the number set. Current number set: [13, 40], target: 43, just two numbers left.\n     |- Try 40 + 13 = 53. Evaluate 53 != 43, drop this branch.\n     |- Try 40 - 13 = 27. Evaluate 27 != 43, drop this branch.\n     |- Try 40 * 13 = 520. Evaluate 520 != 43, drop this branch.\n     |- Try 40 \/ 13 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 42 * 29 = 1218. Add 1218 to the number set. Current number set: [1218, 40], target: 43, just two numbers left.\n     |- Try 1218 + 40 = 1258. Evaluate 1258 != 43, drop this branch.\n     |- Try 1218 - 40 = 1178. Evaluate 1178 != 43, drop this branch.\n     |- Try 1218 * 40 = 48720. 48720 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1218 \/ 40 = 30.4. 30.4 is a decimal, drop this branch.\n    |- Try 42 \/ 29 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 30 - 10 = 20. Add 20 to the number set. Current number set: [20, 42, 29], target: 43. Options for choosing two numbers: [(20, 42), (20, 29), (42, 29)].\n   |- Pick two numbers (20, 42) (numbers left: [29]). Try possible operations.\n    |- Try 42 + 20 = 62. Add 62 to the number set. Current number set: [62, 29], target: 43, just two numbers left.\n     |- Try 62 + 29 = 91. Evaluate 91 != 43, drop this branch.\n     |- Try 62 - 29 = 33. Evaluate 33 != 43, drop this branch.\n     |- Try 62 * 29 = 1798. Evaluate 1798 != 43, drop this branch.\n     |- Try 62 \/ 29 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 42 - 20 = 22. Add 22 to the number set. Current number set: [22, 29], target: 43, just two numbers left.\n     |- Try 29 + 22 = 51. Evaluate 51 != 43, drop this branch.\n     |- Try 29 - 22 = 7. Evaluate 7 != 43, drop this branch.\n     |- Try 29 * 22 = 638. Evaluate 638 != 43, drop this branch.\n     |- Try 29 \/ 22 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 42 * 20 = 840. Add 840 to the number set. Current number set: [840, 29], target: 43, just two numbers left.\n     |- Try 840 + 29 = 869. Evaluate 869 != 43, drop this branch.\n     |- Try 840 - 29 = 811. Evaluate 811 != 43, drop this branch.\n     |- Try 840 * 29 = 24360. 24360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 840 \/ 29 = 29.0. 29.0 is a decimal, drop this branch.\n    |- Try 42 \/ 20 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (20, 29) (numbers left: [42]). Try possible operations.\n    |- Try 29 + 20 = 49. Add 49 to the number set. Current number set: [49, 42], target: 43, just two numbers left.\n     |- Try 49 + 42 = 91. Evaluate 91 != 43, drop this branch.\n     |- Try 49 - 42 = 7. Evaluate 7 != 43, drop this branch.\n     |- Try 49 * 42 = 2058. 2058 exceeds the maximum intermediate result, drop this branch.\n     |- Try 49 \/ 42 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 29 - 20 = 9. Add 9 to the number set. Current number set: [9, 42], target: 43, just two numbers left.\n     |- Try 42 + 9 = 51. Evaluate 51 != 43, drop this branch.\n     |- Try 42 - 9 = 33. Evaluate 33 != 43, drop this branch.\n     |- Try 42 * 9 = 378. Evaluate 378 != 43, drop this branch.\n     |- Try 42 \/ 9 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 29 * 20 = 580. Add 580 to the number set. Current number set: [580, 42], target: 43, just two numbers left.\n     |- Try 580 + 42 = 622. Evaluate 622 != 43, drop this branch.\n     |- Try 580 - 42 = 538. Evaluate 538 != 43, drop this branch.\n     |- Try 580 * 42 = 24360. 24360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 580 \/ 42 = 13.8. 13.8 is a decimal, drop this branch.\n    |- Try 29 \/ 20 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (42, 29) (numbers left: [20]). Try possible operations.\n    |- Try 42 + 29 = 71. Add 71 to the number set. Current number set: [71, 20], target: 43, just two numbers left.\n     |- Try 71 + 20 = 91. Evaluate 91 != 43, drop this branch.\n     |- Try 71 - 20 = 51. Evaluate 51 != 43, drop this branch.\n     |- Try 71 * 20 = 1420. Evaluate 1420 != 43, drop this branch.\n     |- Try 71 \/ 20 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 42 - 29 = 13. Add 13 to the number set. Current number set: [13, 20], target: 43, just two numbers left.\n     |- Try 20 + 13 = 33. Evaluate 33 != 43, drop this branch.\n     |- Try 20 - 13 = 7. Evaluate 7 != 43, drop this branch.\n     |- Try 20 * 13 = 260. Evaluate 260 != 43, drop this branch.\n     |- Try 20 \/ 13 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 42 * 29 = 1218. Add 1218 to the number set. Current number set: [1218, 20], target: 43, just two numbers left.\n     |- Try 1218 + 20 = 1238. Evaluate 1238 != 43, drop this branch.\n     |- Try 1218 - 20 = 1198. Evaluate 1198 != 43, drop this branch.\n     |- Try 1218 * 20 = 24360. 24360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1218 \/ 20 = 60.9. 60.9 is a decimal, drop this branch.\n    |- Try 42 \/ 29 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 30 * 10 = 300. Add 300 to the number set. Current number set: [300, 42, 29], target: 43. Options for choosing two numbers: [(300, 42), (300, 29), (42, 29)].\n   |- Pick two numbers (300, 42) (numbers left: [29]). Try possible operations.\n    |- Try 300 + 42 = 342. Add 342 to the number set. Current number set: [342, 29], target: 43, just two numbers left.\n     |- Try 342 + 29 = 371. Evaluate 371 != 43, drop this branch.\n     |- Try 342 - 29 = 313. Evaluate 313 != 43, drop this branch.\n     |- Try 342 * 29 = 9918. 9918 exceeds the maximum intermediate result, drop this branch.\n     |- Try 342 \/ 29 = 11.8. 11.8 is a decimal, drop this branch.\n    |- Try 300 - 42 = 258. Add 258 to the number set. Current number set: [258, 29], target: 43, just two numbers left.\n     |- Try 258 + 29 = 287. Evaluate 287 != 43, drop this branch.\n     |- Try 258 - 29 = 229. Evaluate 229 != 43, drop this branch.\n     |- Try 258 * 29 = 7482. 7482 exceeds the maximum intermediate result, drop this branch.\n     |- Try 258 \/ 29 = 8.9. 8.9 is a decimal, drop this branch.\n    |- Try 300 * 42 = 12600. 12600 exceeds the maximum intermediate result, drop this branch.\n    |- Try 300 \/ 42 = 7.1. 7.1 is a decimal, drop this branch.\n   |- Pick two numbers (300, 29) (numbers left: [42]). Try possible operations.\n    |- Try 300 + 29 = 329. Add 329 to the number set. Current number set: [329, 42], target: 43, just two numbers left.\n     |- Try 329 + 42 = 371. Evaluate 371 != 43, drop this branch.\n     |- Try 329 - 42 = 287. Evaluate 287 != 43, drop this branch.\n     |- Try 329 * 42 = 13818. 13818 exceeds the maximum intermediate result, drop this branch.\n     |- Try 329 \/ 42 = 7.8. 7.8 is a decimal, drop this branch.\n    |- Try 300 - 29 = 271. Add 271 to the number set. Current number set: [271, 42], target: 43, just two numbers left.\n     |- Try 271 + 42 = 313. Evaluate 313 != 43, drop this branch.\n     |- Try 271 - 42 = 229. Evaluate 229 != 43, drop this branch.\n     |- Try 271 * 42 = 11382. 11382 exceeds the maximum intermediate result, drop this branch.\n     |- Try 271 \/ 42 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 300 * 29 = 8700. 8700 exceeds the maximum intermediate result, drop this branch.\n    |- Try 300 \/ 29 = 10.3. 10.3 is a decimal, drop this branch.\n   |- Pick two numbers (42, 29) (numbers left: [300]). Try possible operations.\n    |- Try 42 + 29 = 71. Add 71 to the number set. Current number set: [71, 300], target: 43, just two numbers left.\n     |- Try 300 + 71 = 371. Evaluate 371 != 43, drop this branch.\n     |- Try 300 - 71 = 229. Evaluate 229 != 43, drop this branch.\n     |- Try 300 * 71 = 21300. 21300 exceeds the maximum intermediate result, drop this branch.\n     |- Try 300 \/ 71 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 42 - 29 = 13. Add 13 to the number set. Current number set: [13, 300], target: 43, just two numbers left.\n     |- Try 300 + 13 = 313. Evaluate 313 != 43, drop this branch.\n     |- Try 300 - 13 = 287. Evaluate 287 != 43, drop this branch.\n     |- Try 300 * 13 = 3900. 3900 exceeds the maximum intermediate result, drop this branch.\n     |- Try 300 \/ 13 = 23.1. 23.1 is a decimal, drop this branch.\n    |- Try 42 * 29 = 1218. Add 1218 to the number set. Current number set: [1218, 300], target: 43, just two numbers left.\n     |- Try 1218 + 300 = 1518. Evaluate 1518 != 43, drop this branch.\n     |- Try 1218 - 300 = 918. Evaluate 918 != 43, drop this branch.\n     |- Try 1218 * 300 = 365400. 365400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1218 \/ 300 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 42 \/ 29 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 30 \/ 10 = 3. Add 3 to the number set. Current number set: [3, 42, 29], target: 43. Options for choosing two numbers: [(3, 42), (3, 29), (42, 29)].\n   |- Pick two numbers (3, 42) (numbers left: [29]). Try possible operations.\n    |- Try 42 + 3 = 45. Add 45 to the number set. Current number set: [45, 29], target: 43, just two numbers left.\n     |- Try 45 + 29 = 74. Evaluate 74 != 43, drop this branch.\n     |- Try 45 - 29 = 16. Evaluate 16 != 43, drop this branch.\n     |- Try 45 * 29 = 1305. Evaluate 1305 != 43, drop this branch.\n     |- Try 45 \/ 29 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 42 - 3 = 39. Add 39 to the number set. Current number set: [39, 29], target: 43, just two numbers left.\n     |- Try 39 + 29 = 68. Evaluate 68 != 43, drop this branch.\n     |- Try 39 - 29 = 10. Evaluate 10 != 43, drop this branch.\n     |- Try 39 * 29 = 1131. Evaluate 1131 != 43, drop this branch.\n     |- Try 39 \/ 29 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 42 * 3 = 126. Add 126 to the number set. Current number set: [126, 29], target: 43, just two numbers left.\n     |- Try 126 + 29 = 155. Evaluate 155 != 43, drop this branch.\n     |- Try 126 - 29 = 97. Evaluate 97 != 43, drop this branch.\n     |- Try 126 * 29 = 3654. 3654 exceeds the maximum intermediate result, drop this branch.\n     |- Try 126 \/ 29 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 42 \/ 3 = 14. Add 14 to the number set. Current number set: [14, 29], target: 43, just two numbers left.\n     |- Try 29 + 14 = 43. Evaluate 43 == 43, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 29 + 14 = 43\nThe step before: 42 \/ 3 = 14\nThe first step: 30 \/ 10 = 3\n\nOutput the solution in the required format:\n<Solution>\n30 \/ 10 = 3\n42 \/ 3 = 14\n29 + 14 = 43\n<\/Solution>\n","item":{"nums":[10,30,42,29],"solution":["30 \/ 10 = 3","42 \/ 3 = 14","29 + 14 = 43"],"target":43}}
+{"instance_id":"countdown_8k_75","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [38, 45, 35, 9]\nTarget: 15","reference_output":"# Search Procedure\nInitial number set: [38, 45, 35, 9], target: 15. Options for choosing two numbers: [(38, 45), (38, 35), (38, 9), (45, 35), (45, 9), (35, 9)].\n |- Pick two numbers (38, 45) (numbers left: [35, 9]). Try possible operations.\n  |- Try 45 + 38 = 83. Add 83 to the number set. Current number set: [83, 35, 9], target: 15. Options for choosing two numbers: [(83, 35), (83, 9), (35, 9)].\n   |- Pick two numbers (83, 35) (numbers left: [9]). Try possible operations.\n    |- Try 83 + 35 = 118. Add 118 to the number set. Current number set: [118, 9], target: 15, just two numbers left.\n     |- Try 118 + 9 = 127. Evaluate 127 != 15, drop this branch.\n     |- Try 118 - 9 = 109. Evaluate 109 != 15, drop this branch.\n     |- Try 118 * 9 = 1062. Evaluate 1062 != 15, drop this branch.\n     |- Try 118 \/ 9 = 13.1. 13.1 is a decimal, drop this branch.\n    |- Try 83 - 35 = 48. Add 48 to the number set. Current number set: [48, 9], target: 15, just two numbers left.\n     |- Try 48 + 9 = 57. Evaluate 57 != 15, drop this branch.\n     |- Try 48 - 9 = 39. Evaluate 39 != 15, drop this branch.\n     |- Try 48 * 9 = 432. Evaluate 432 != 15, drop this branch.\n     |- Try 48 \/ 9 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 83 * 35 = 2905. 2905 exceeds the maximum intermediate result, drop this branch.\n    |- Try 83 \/ 35 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (83, 9) (numbers left: [35]). Try possible operations.\n    |- Try 83 + 9 = 92. Add 92 to the number set. Current number set: [92, 35], target: 15, just two numbers left.\n     |- Try 92 + 35 = 127. Evaluate 127 != 15, drop this branch.\n     |- Try 92 - 35 = 57. Evaluate 57 != 15, drop this branch.\n     |- Try 92 * 35 = 3220. 3220 exceeds the maximum intermediate result, drop this branch.\n     |- Try 92 \/ 35 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 83 - 9 = 74. Add 74 to the number set. Current number set: [74, 35], target: 15, just two numbers left.\n     |- Try 74 + 35 = 109. Evaluate 109 != 15, drop this branch.\n     |- Try 74 - 35 = 39. Evaluate 39 != 15, drop this branch.\n     |- Try 74 * 35 = 2590. 2590 exceeds the maximum intermediate result, drop this branch.\n     |- Try 74 \/ 35 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 83 * 9 = 747. Add 747 to the number set. Current number set: [747, 35], target: 15, just two numbers left.\n     |- Try 747 + 35 = 782. Evaluate 782 != 15, drop this branch.\n     |- Try 747 - 35 = 712. Evaluate 712 != 15, drop this branch.\n     |- Try 747 * 35 = 26145. 26145 exceeds the maximum intermediate result, drop this branch.\n     |- Try 747 \/ 35 = 21.3. 21.3 is a decimal, drop this branch.\n    |- Try 83 \/ 9 = 9.2. 9.2 is a decimal, drop this branch.\n   |- Pick two numbers (35, 9) (numbers left: [83]). Try possible operations.\n    |- Try 35 + 9 = 44. Add 44 to the number set. Current number set: [44, 83], target: 15, just two numbers left.\n     |- Try 83 + 44 = 127. Evaluate 127 != 15, drop this branch.\n     |- Try 83 - 44 = 39. Evaluate 39 != 15, drop this branch.\n     |- Try 83 * 44 = 3652. 3652 exceeds the maximum intermediate result, drop this branch.\n     |- Try 83 \/ 44 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 35 - 9 = 26. Add 26 to the number set. Current number set: [26, 83], target: 15, just two numbers left.\n     |- Try 83 + 26 = 109. Evaluate 109 != 15, drop this branch.\n     |- Try 83 - 26 = 57. Evaluate 57 != 15, drop this branch.\n     |- Try 83 * 26 = 2158. 2158 exceeds the maximum intermediate result, drop this branch.\n     |- Try 83 \/ 26 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 35 * 9 = 315. Add 315 to the number set. Current number set: [315, 83], target: 15, just two numbers left.\n     |- Try 315 + 83 = 398. Evaluate 398 != 15, drop this branch.\n     |- Try 315 - 83 = 232. Evaluate 232 != 15, drop this branch.\n     |- Try 315 * 83 = 26145. 26145 exceeds the maximum intermediate result, drop this branch.\n     |- Try 315 \/ 83 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 35 \/ 9 = 3.9. 3.9 is a decimal, drop this branch.\n  |- Try 45 - 38 = 7. Add 7 to the number set. Current number set: [7, 35, 9], target: 15. Options for choosing two numbers: [(7, 35), (7, 9), (35, 9)].\n   |- Pick two numbers (7, 35) (numbers left: [9]). Try possible operations.\n    |- Try 35 + 7 = 42. Add 42 to the number set. Current number set: [42, 9], target: 15, just two numbers left.\n     |- Try 42 + 9 = 51. Evaluate 51 != 15, drop this branch.\n     |- Try 42 - 9 = 33. Evaluate 33 != 15, drop this branch.\n     |- Try 42 * 9 = 378. Evaluate 378 != 15, drop this branch.\n     |- Try 42 \/ 9 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 35 - 7 = 28. Add 28 to the number set. Current number set: [28, 9], target: 15, just two numbers left.\n     |- Try 28 + 9 = 37. Evaluate 37 != 15, drop this branch.\n     |- Try 28 - 9 = 19. Evaluate 19 != 15, drop this branch.\n     |- Try 28 * 9 = 252. Evaluate 252 != 15, drop this branch.\n     |- Try 28 \/ 9 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 35 * 7 = 245. Add 245 to the number set. Current number set: [245, 9], target: 15, just two numbers left.\n     |- Try 245 + 9 = 254. Evaluate 254 != 15, drop this branch.\n     |- Try 245 - 9 = 236. Evaluate 236 != 15, drop this branch.\n     |- Try 245 * 9 = 2205. 2205 exceeds the maximum intermediate result, drop this branch.\n     |- Try 245 \/ 9 = 27.2. 27.2 is a decimal, drop this branch.\n    |- Try 35 \/ 7 = 5. Add 5 to the number set. Current number set: [5, 9], target: 15, just two numbers left.\n     |- Try 9 + 5 = 14. Evaluate 14 != 15, drop this branch.\n     |- Try 9 - 5 = 4. Evaluate 4 != 15, drop this branch.\n     |- Try 9 * 5 = 45. Evaluate 45 != 15, drop this branch.\n     |- Try 9 \/ 5 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (7, 9) (numbers left: [35]). Try possible operations.\n    |- Try 9 + 7 = 16. Add 16 to the number set. Current number set: [16, 35], target: 15, just two numbers left.\n     |- Try 35 + 16 = 51. Evaluate 51 != 15, drop this branch.\n     |- Try 35 - 16 = 19. Evaluate 19 != 15, drop this branch.\n     |- Try 35 * 16 = 560. Evaluate 560 != 15, drop this branch.\n     |- Try 35 \/ 16 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 9 - 7 = 2. Add 2 to the number set. Current number set: [2, 35], target: 15, just two numbers left.\n     |- Try 35 + 2 = 37. Evaluate 37 != 15, drop this branch.\n     |- Try 35 - 2 = 33. Evaluate 33 != 15, drop this branch.\n     |- Try 35 * 2 = 70. Evaluate 70 != 15, drop this branch.\n     |- Try 35 \/ 2 = 17.5. 17.5 is a decimal, drop this branch.\n    |- Try 9 * 7 = 63. Add 63 to the number set. Current number set: [63, 35], target: 15, just two numbers left.\n     |- Try 63 + 35 = 98. Evaluate 98 != 15, drop this branch.\n     |- Try 63 - 35 = 28. Evaluate 28 != 15, drop this branch.\n     |- Try 63 * 35 = 2205. 2205 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 35 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 9 \/ 7 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (35, 9) (numbers left: [7]). Try possible operations.\n    |- Try 35 + 9 = 44. Add 44 to the number set. Current number set: [44, 7], target: 15, just two numbers left.\n     |- Try 44 + 7 = 51. Evaluate 51 != 15, drop this branch.\n     |- Try 44 - 7 = 37. Evaluate 37 != 15, drop this branch.\n     |- Try 44 * 7 = 308. Evaluate 308 != 15, drop this branch.\n     |- Try 44 \/ 7 = 6.3. 6.3 is a decimal, drop this branch.\n    |- Try 35 - 9 = 26. Add 26 to the number set. Current number set: [26, 7], target: 15, just two numbers left.\n     |- Try 26 + 7 = 33. Evaluate 33 != 15, drop this branch.\n     |- Try 26 - 7 = 19. Evaluate 19 != 15, drop this branch.\n     |- Try 26 * 7 = 182. Evaluate 182 != 15, drop this branch.\n     |- Try 26 \/ 7 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 35 * 9 = 315. Add 315 to the number set. Current number set: [315, 7], target: 15, just two numbers left.\n     |- Try 315 + 7 = 322. Evaluate 322 != 15, drop this branch.\n     |- Try 315 - 7 = 308. Evaluate 308 != 15, drop this branch.\n     |- Try 315 * 7 = 2205. 2205 exceeds the maximum intermediate result, drop this branch.\n     |- Try 315 \/ 7 = 45. Evaluate 45 != 15, drop this branch.\n    |- Try 35 \/ 9 = 3.9. 3.9 is a decimal, drop this branch.\n  |- Try 45 * 38 = 1710. Add 1710 to the number set. Current number set: [1710, 35, 9], target: 15. Options for choosing two numbers: [(1710, 35), (1710, 9), (35, 9)].\n   |- Pick two numbers (1710, 35) (numbers left: [9]). Try possible operations.\n    |- Try 1710 + 35 = 1745. Add 1745 to the number set. Current number set: [1745, 9], target: 15, just two numbers left.\n     |- Try 1745 + 9 = 1754. Evaluate 1754 != 15, drop this branch.\n     |- Try 1745 - 9 = 1736. Evaluate 1736 != 15, drop this branch.\n     |- Try 1745 * 9 = 15705. 15705 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1745 \/ 9 = 193.9. 193.9 is a decimal, drop this branch.\n    |- Try 1710 - 35 = 1675. Add 1675 to the number set. Current number set: [1675, 9], target: 15, just two numbers left.\n     |- Try 1675 + 9 = 1684. Evaluate 1684 != 15, drop this branch.\n     |- Try 1675 - 9 = 1666. Evaluate 1666 != 15, drop this branch.\n     |- Try 1675 * 9 = 15075. 15075 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1675 \/ 9 = 186.1. 186.1 is a decimal, drop this branch.\n    |- Try 1710 * 35 = 59850. 59850 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1710 \/ 35 = 48.9. 48.9 is a decimal, drop this branch.\n   |- Pick two numbers (1710, 9) (numbers left: [35]). Try possible operations.\n    |- Try 1710 + 9 = 1719. Add 1719 to the number set. Current number set: [1719, 35], target: 15, just two numbers left.\n     |- Try 1719 + 35 = 1754. Evaluate 1754 != 15, drop this branch.\n     |- Try 1719 - 35 = 1684. Evaluate 1684 != 15, drop this branch.\n     |- Try 1719 * 35 = 60165. 60165 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1719 \/ 35 = 49.1. 49.1 is a decimal, drop this branch.\n    |- Try 1710 - 9 = 1701. Add 1701 to the number set. Current number set: [1701, 35], target: 15, just two numbers left.\n     |- Try 1701 + 35 = 1736. Evaluate 1736 != 15, drop this branch.\n     |- Try 1701 - 35 = 1666. Evaluate 1666 != 15, drop this branch.\n     |- Try 1701 * 35 = 59535. 59535 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1701 \/ 35 = 48.6. 48.6 is a decimal, drop this branch.\n    |- Try 1710 * 9 = 15390. 15390 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1710 \/ 9 = 190. Add 190 to the number set. Current number set: [190, 35], target: 15, just two numbers left.\n     |- Try 190 + 35 = 225. Evaluate 225 != 15, drop this branch.\n     |- Try 190 - 35 = 155. Evaluate 155 != 15, drop this branch.\n     |- Try 190 * 35 = 6650. 6650 exceeds the maximum intermediate result, drop this branch.\n     |- Try 190 \/ 35 = 5.4. 5.4 is a decimal, drop this branch.\n   |- Pick two numbers (35, 9) (numbers left: [1710]). Try possible operations.\n    |- Try 35 + 9 = 44. Add 44 to the number set. Current number set: [44, 1710], target: 15, just two numbers left.\n     |- Try 1710 + 44 = 1754. Evaluate 1754 != 15, drop this branch.\n     |- Try 1710 - 44 = 1666. Evaluate 1666 != 15, drop this branch.\n     |- Try 1710 * 44 = 75240. 75240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1710 \/ 44 = 38.9. 38.9 is a decimal, drop this branch.\n    |- Try 35 - 9 = 26. Add 26 to the number set. Current number set: [26, 1710], target: 15, just two numbers left.\n     |- Try 1710 + 26 = 1736. Evaluate 1736 != 15, drop this branch.\n     |- Try 1710 - 26 = 1684. Evaluate 1684 != 15, drop this branch.\n     |- Try 1710 * 26 = 44460. 44460 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1710 \/ 26 = 65.8. 65.8 is a decimal, drop this branch.\n    |- Try 35 * 9 = 315. Add 315 to the number set. Current number set: [315, 1710], target: 15, just two numbers left.\n     |- Try 1710 + 315 = 2025. 2025 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1710 - 315 = 1395. Evaluate 1395 != 15, drop this branch.\n     |- Try 1710 * 315 = 538650. 538650 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1710 \/ 315 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 35 \/ 9 = 3.9. 3.9 is a decimal, drop this branch.\n  |- Try 45 \/ 38 = 1.2. 1.2 is a decimal, drop this branch.\n |- Pick two numbers (38, 35) (numbers left: [45, 9]). Try possible operations.\n  |- Try 38 + 35 = 73. Add 73 to the number set. Current number set: [73, 45, 9], target: 15. Options for choosing two numbers: [(73, 45), (73, 9), (45, 9)].\n   |- Pick two numbers (73, 45) (numbers left: [9]). Try possible operations.\n    |- Try 73 + 45 = 118. Add 118 to the number set. Current number set: [118, 9], target: 15, just two numbers left.\n     |- Try 118 + 9 = 127. Evaluate 127 != 15, drop this branch.\n     |- Try 118 - 9 = 109. Evaluate 109 != 15, drop this branch.\n     |- Try 118 * 9 = 1062. Evaluate 1062 != 15, drop this branch.\n     |- Try 118 \/ 9 = 13.1. 13.1 is a decimal, drop this branch.\n    |- Try 73 - 45 = 28. Add 28 to the number set. Current number set: [28, 9], target: 15, just two numbers left.\n     |- Try 28 + 9 = 37. Evaluate 37 != 15, drop this branch.\n     |- Try 28 - 9 = 19. Evaluate 19 != 15, drop this branch.\n     |- Try 28 * 9 = 252. Evaluate 252 != 15, drop this branch.\n     |- Try 28 \/ 9 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 73 * 45 = 3285. 3285 exceeds the maximum intermediate result, drop this branch.\n    |- Try 73 \/ 45 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (73, 9) (numbers left: [45]). Try possible operations.\n    |- Try 73 + 9 = 82. Add 82 to the number set. Current number set: [82, 45], target: 15, just two numbers left.\n     |- Try 82 + 45 = 127. Evaluate 127 != 15, drop this branch.\n     |- Try 82 - 45 = 37. Evaluate 37 != 15, drop this branch.\n     |- Try 82 * 45 = 3690. 3690 exceeds the maximum intermediate result, drop this branch.\n     |- Try 82 \/ 45 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 73 - 9 = 64. Add 64 to the number set. Current number set: [64, 45], target: 15, just two numbers left.\n     |- Try 64 + 45 = 109. Evaluate 109 != 15, drop this branch.\n     |- Try 64 - 45 = 19. Evaluate 19 != 15, drop this branch.\n     |- Try 64 * 45 = 2880. 2880 exceeds the maximum intermediate result, drop this branch.\n     |- Try 64 \/ 45 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 73 * 9 = 657. Add 657 to the number set. Current number set: [657, 45], target: 15, just two numbers left.\n     |- Try 657 + 45 = 702. Evaluate 702 != 15, drop this branch.\n     |- Try 657 - 45 = 612. Evaluate 612 != 15, drop this branch.\n     |- Try 657 * 45 = 29565. 29565 exceeds the maximum intermediate result, drop this branch.\n     |- Try 657 \/ 45 = 14.6. 14.6 is a decimal, drop this branch.\n    |- Try 73 \/ 9 = 8.1. 8.1 is a decimal, drop this branch.\n   |- Pick two numbers (45, 9) (numbers left: [73]). Try possible operations.\n    |- Try 45 + 9 = 54. Add 54 to the number set. Current number set: [54, 73], target: 15, just two numbers left.\n     |- Try 73 + 54 = 127. Evaluate 127 != 15, drop this branch.\n     |- Try 73 - 54 = 19. Evaluate 19 != 15, drop this branch.\n     |- Try 73 * 54 = 3942. 3942 exceeds the maximum intermediate result, drop this branch.\n     |- Try 73 \/ 54 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 45 - 9 = 36. Add 36 to the number set. Current number set: [36, 73], target: 15, just two numbers left.\n     |- Try 73 + 36 = 109. Evaluate 109 != 15, drop this branch.\n     |- Try 73 - 36 = 37. Evaluate 37 != 15, drop this branch.\n     |- Try 73 * 36 = 2628. 2628 exceeds the maximum intermediate result, drop this branch.\n     |- Try 73 \/ 36 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 45 * 9 = 405. Add 405 to the number set. Current number set: [405, 73], target: 15, just two numbers left.\n     |- Try 405 + 73 = 478. Evaluate 478 != 15, drop this branch.\n     |- Try 405 - 73 = 332. Evaluate 332 != 15, drop this branch.\n     |- Try 405 * 73 = 29565. 29565 exceeds the maximum intermediate result, drop this branch.\n     |- Try 405 \/ 73 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 45 \/ 9 = 5. Add 5 to the number set. Current number set: [5, 73], target: 15, just two numbers left.\n     |- Try 73 + 5 = 78. Evaluate 78 != 15, drop this branch.\n     |- Try 73 - 5 = 68. Evaluate 68 != 15, drop this branch.\n     |- Try 73 * 5 = 365. Evaluate 365 != 15, drop this branch.\n     |- Try 73 \/ 5 = 14.6. 14.6 is a decimal, drop this branch.\n  |- Try 38 - 35 = 3. Add 3 to the number set. Current number set: [3, 45, 9], target: 15. Options for choosing two numbers: [(3, 45), (3, 9), (45, 9)].\n   |- Pick two numbers (3, 45) (numbers left: [9]). Try possible operations.\n    |- Try 45 + 3 = 48. Add 48 to the number set. Current number set: [48, 9], target: 15, just two numbers left.\n     |- Try 48 + 9 = 57. Evaluate 57 != 15, drop this branch.\n     |- Try 48 - 9 = 39. Evaluate 39 != 15, drop this branch.\n     |- Try 48 * 9 = 432. Evaluate 432 != 15, drop this branch.\n     |- Try 48 \/ 9 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 45 - 3 = 42. Add 42 to the number set. Current number set: [42, 9], target: 15, just two numbers left.\n     |- Try 42 + 9 = 51. Evaluate 51 != 15, drop this branch.\n     |- Try 42 - 9 = 33. Evaluate 33 != 15, drop this branch.\n     |- Try 42 * 9 = 378. Evaluate 378 != 15, drop this branch.\n     |- Try 42 \/ 9 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 45 * 3 = 135. Add 135 to the number set. Current number set: [135, 9], target: 15, just two numbers left.\n     |- Try 135 + 9 = 144. Evaluate 144 != 15, drop this branch.\n     |- Try 135 - 9 = 126. Evaluate 126 != 15, drop this branch.\n     |- Try 135 * 9 = 1215. Evaluate 1215 != 15, drop this branch.\n     |- Try 135 \/ 9 = 15. Evaluate 15 == 15, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 135 \/ 9 = 15\nThe step before: 45 * 3 = 135\nThe first step: 38 - 35 = 3\n\nOutput the solution in the required format:\n<Solution>\n38 - 35 = 3\n45 * 3 = 135\n135 \/ 9 = 15\n<\/Solution>\n","item":{"nums":[38,45,35,9],"solution":["38 - 35 = 3","45 * 3 = 135","135 \/ 9 = 15"],"target":15}}
+{"instance_id":"countdown_8k_76","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [43, 10, 11, 10]\nTarget: 46","reference_output":"# Search Procedure\nInitial number set: [43, 10, 11, 10], target: 46. Options for choosing two numbers: [(43, 10), (43, 11), (43, 10), (10, 11), (10, 10), (11, 10)].\n |- Pick two numbers (43, 10) (numbers left: [11, 10]). Try possible operations.\n  |- Try 43 + 10 = 53. Add 53 to the number set. Current number set: [53, 11, 10], target: 46. Options for choosing two numbers: [(53, 11), (53, 10), (11, 10)].\n   |- Pick two numbers (53, 11) (numbers left: [10]). Try possible operations.\n    |- Try 53 + 11 = 64. Add 64 to the number set. Current number set: [64, 10], target: 46, just two numbers left.\n     |- Try 64 + 10 = 74. Evaluate 74 != 46, drop this branch.\n     |- Try 64 - 10 = 54. Evaluate 54 != 46, drop this branch.\n     |- Try 64 * 10 = 640. Evaluate 640 != 46, drop this branch.\n     |- Try 64 \/ 10 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 53 - 11 = 42. Add 42 to the number set. Current number set: [42, 10], target: 46, just two numbers left.\n     |- Try 42 + 10 = 52. Evaluate 52 != 46, drop this branch.\n     |- Try 42 - 10 = 32. Evaluate 32 != 46, drop this branch.\n     |- Try 42 * 10 = 420. Evaluate 420 != 46, drop this branch.\n     |- Try 42 \/ 10 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 53 * 11 = 583. Add 583 to the number set. Current number set: [583, 10], target: 46, just two numbers left.\n     |- Try 583 + 10 = 593. Evaluate 593 != 46, drop this branch.\n     |- Try 583 - 10 = 573. Evaluate 573 != 46, drop this branch.\n     |- Try 583 * 10 = 5830. 5830 exceeds the maximum intermediate result, drop this branch.\n     |- Try 583 \/ 10 = 58.3. 58.3 is a decimal, drop this branch.\n    |- Try 53 \/ 11 = 4.8. 4.8 is a decimal, drop this branch.\n   |- Pick two numbers (53, 10) (numbers left: [11]). Try possible operations.\n    |- Try 53 + 10 = 63. Add 63 to the number set. Current number set: [63, 11], target: 46, just two numbers left.\n     |- Try 63 + 11 = 74. Evaluate 74 != 46, drop this branch.\n     |- Try 63 - 11 = 52. Evaluate 52 != 46, drop this branch.\n     |- Try 63 * 11 = 693. Evaluate 693 != 46, drop this branch.\n     |- Try 63 \/ 11 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 53 - 10 = 43. Add 43 to the number set. Current number set: [43, 11], target: 46, just two numbers left.\n     |- Try 43 + 11 = 54. Evaluate 54 != 46, drop this branch.\n     |- Try 43 - 11 = 32. Evaluate 32 != 46, drop this branch.\n     |- Try 43 * 11 = 473. Evaluate 473 != 46, drop this branch.\n     |- Try 43 \/ 11 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 53 * 10 = 530. Add 530 to the number set. Current number set: [530, 11], target: 46, just two numbers left.\n     |- Try 530 + 11 = 541. Evaluate 541 != 46, drop this branch.\n     |- Try 530 - 11 = 519. Evaluate 519 != 46, drop this branch.\n     |- Try 530 * 11 = 5830. 5830 exceeds the maximum intermediate result, drop this branch.\n     |- Try 530 \/ 11 = 48.2. 48.2 is a decimal, drop this branch.\n    |- Try 53 \/ 10 = 5.3. 5.3 is a decimal, drop this branch.\n   |- Pick two numbers (11, 10) (numbers left: [53]). Try possible operations.\n    |- Try 11 + 10 = 21. Add 21 to the number set. Current number set: [21, 53], target: 46, just two numbers left.\n     |- Try 53 + 21 = 74. Evaluate 74 != 46, drop this branch.\n     |- Try 53 - 21 = 32. Evaluate 32 != 46, drop this branch.\n     |- Try 53 * 21 = 1113. Evaluate 1113 != 46, drop this branch.\n     |- Try 53 \/ 21 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 11 - 10 = 1. Add 1 to the number set. Current number set: [1, 53], target: 46, just two numbers left.\n     |- Try 53 + 1 = 54. Evaluate 54 != 46, drop this branch.\n     |- Try 53 - 1 = 52. Evaluate 52 != 46, drop this branch.\n     |- Try 53 * 1 = 53. Evaluate 53 != 46, drop this branch.\n     |- Try 53 \/ 1 = 53. Evaluate 53 != 46, drop this branch.\n    |- Try 11 * 10 = 110. Add 110 to the number set. Current number set: [110, 53], target: 46, just two numbers left.\n     |- Try 110 + 53 = 163. Evaluate 163 != 46, drop this branch.\n     |- Try 110 - 53 = 57. Evaluate 57 != 46, drop this branch.\n     |- Try 110 * 53 = 5830. 5830 exceeds the maximum intermediate result, drop this branch.\n     |- Try 110 \/ 53 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 11 \/ 10 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 43 - 10 = 33. Add 33 to the number set. Current number set: [33, 11, 10], target: 46. Options for choosing two numbers: [(33, 11), (33, 10), (11, 10)].\n   |- Pick two numbers (33, 11) (numbers left: [10]). Try possible operations.\n    |- Try 33 + 11 = 44. Add 44 to the number set. Current number set: [44, 10], target: 46, just two numbers left.\n     |- Try 44 + 10 = 54. Evaluate 54 != 46, drop this branch.\n     |- Try 44 - 10 = 34. Evaluate 34 != 46, drop this branch.\n     |- Try 44 * 10 = 440. Evaluate 440 != 46, drop this branch.\n     |- Try 44 \/ 10 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 33 - 11 = 22. Add 22 to the number set. Current number set: [22, 10], target: 46, just two numbers left.\n     |- Try 22 + 10 = 32. Evaluate 32 != 46, drop this branch.\n     |- Try 22 - 10 = 12. Evaluate 12 != 46, drop this branch.\n     |- Try 22 * 10 = 220. Evaluate 220 != 46, drop this branch.\n     |- Try 22 \/ 10 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 33 * 11 = 363. Add 363 to the number set. Current number set: [363, 10], target: 46, just two numbers left.\n     |- Try 363 + 10 = 373. Evaluate 373 != 46, drop this branch.\n     |- Try 363 - 10 = 353. Evaluate 353 != 46, drop this branch.\n     |- Try 363 * 10 = 3630. 3630 exceeds the maximum intermediate result, drop this branch.\n     |- Try 363 \/ 10 = 36.3. 36.3 is a decimal, drop this branch.\n    |- Try 33 \/ 11 = 3. Add 3 to the number set. Current number set: [3, 10], target: 46, just two numbers left.\n     |- Try 10 + 3 = 13. Evaluate 13 != 46, drop this branch.\n     |- Try 10 - 3 = 7. Evaluate 7 != 46, drop this branch.\n     |- Try 10 * 3 = 30. Evaluate 30 != 46, drop this branch.\n     |- Try 10 \/ 3 = 3.3. 3.3 is a decimal, drop this branch.\n   |- Pick two numbers (33, 10) (numbers left: [11]). Try possible operations.\n    |- Try 33 + 10 = 43. Add 43 to the number set. Current number set: [43, 11], target: 46, just two numbers left.\n     |- Try 43 + 11 = 54. Evaluate 54 != 46, drop this branch.\n     |- Try 43 - 11 = 32. Evaluate 32 != 46, drop this branch.\n     |- Try 43 * 11 = 473. Evaluate 473 != 46, drop this branch.\n     |- Try 43 \/ 11 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 33 - 10 = 23. Add 23 to the number set. Current number set: [23, 11], target: 46, just two numbers left.\n     |- Try 23 + 11 = 34. Evaluate 34 != 46, drop this branch.\n     |- Try 23 - 11 = 12. Evaluate 12 != 46, drop this branch.\n     |- Try 23 * 11 = 253. Evaluate 253 != 46, drop this branch.\n     |- Try 23 \/ 11 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 33 * 10 = 330. Add 330 to the number set. Current number set: [330, 11], target: 46, just two numbers left.\n     |- Try 330 + 11 = 341. Evaluate 341 != 46, drop this branch.\n     |- Try 330 - 11 = 319. Evaluate 319 != 46, drop this branch.\n     |- Try 330 * 11 = 3630. 3630 exceeds the maximum intermediate result, drop this branch.\n     |- Try 330 \/ 11 = 30. Evaluate 30 != 46, drop this branch.\n    |- Try 33 \/ 10 = 3.3. 3.3 is a decimal, drop this branch.\n   |- Pick two numbers (11, 10) (numbers left: [33]). Try possible operations.\n    |- Try 11 + 10 = 21. Add 21 to the number set. Current number set: [21, 33], target: 46, just two numbers left.\n     |- Try 33 + 21 = 54. Evaluate 54 != 46, drop this branch.\n     |- Try 33 - 21 = 12. Evaluate 12 != 46, drop this branch.\n     |- Try 33 * 21 = 693. Evaluate 693 != 46, drop this branch.\n     |- Try 33 \/ 21 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 11 - 10 = 1. Add 1 to the number set. Current number set: [1, 33], target: 46, just two numbers left.\n     |- Try 33 + 1 = 34. Evaluate 34 != 46, drop this branch.\n     |- Try 33 - 1 = 32. Evaluate 32 != 46, drop this branch.\n     |- Try 33 * 1 = 33. Evaluate 33 != 46, drop this branch.\n     |- Try 33 \/ 1 = 33. Evaluate 33 != 46, drop this branch.\n    |- Try 11 * 10 = 110. Add 110 to the number set. Current number set: [110, 33], target: 46, just two numbers left.\n     |- Try 110 + 33 = 143. Evaluate 143 != 46, drop this branch.\n     |- Try 110 - 33 = 77. Evaluate 77 != 46, drop this branch.\n     |- Try 110 * 33 = 3630. 3630 exceeds the maximum intermediate result, drop this branch.\n     |- Try 110 \/ 33 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 11 \/ 10 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 43 * 10 = 430. Add 430 to the number set. Current number set: [430, 11, 10], target: 46. Options for choosing two numbers: [(430, 11), (430, 10), (11, 10)].\n   |- Pick two numbers (430, 11) (numbers left: [10]). Try possible operations.\n    |- Try 430 + 11 = 441. Add 441 to the number set. Current number set: [441, 10], target: 46, just two numbers left.\n     |- Try 441 + 10 = 451. Evaluate 451 != 46, drop this branch.\n     |- Try 441 - 10 = 431. Evaluate 431 != 46, drop this branch.\n     |- Try 441 * 10 = 4410. 4410 exceeds the maximum intermediate result, drop this branch.\n     |- Try 441 \/ 10 = 44.1. 44.1 is a decimal, drop this branch.\n    |- Try 430 - 11 = 419. Add 419 to the number set. Current number set: [419, 10], target: 46, just two numbers left.\n     |- Try 419 + 10 = 429. Evaluate 429 != 46, drop this branch.\n     |- Try 419 - 10 = 409. Evaluate 409 != 46, drop this branch.\n     |- Try 419 * 10 = 4190. 4190 exceeds the maximum intermediate result, drop this branch.\n     |- Try 419 \/ 10 = 41.9. 41.9 is a decimal, drop this branch.\n    |- Try 430 * 11 = 4730. 4730 exceeds the maximum intermediate result, drop this branch.\n    |- Try 430 \/ 11 = 39.1. 39.1 is a decimal, drop this branch.\n   |- Pick two numbers (430, 10) (numbers left: [11]). Try possible operations.\n    |- Try 430 + 10 = 440. Add 440 to the number set. Current number set: [440, 11], target: 46, just two numbers left.\n     |- Try 440 + 11 = 451. Evaluate 451 != 46, drop this branch.\n     |- Try 440 - 11 = 429. Evaluate 429 != 46, drop this branch.\n     |- Try 440 * 11 = 4840. 4840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 440 \/ 11 = 40. Evaluate 40 != 46, drop this branch.\n    |- Try 430 - 10 = 420. Add 420 to the number set. Current number set: [420, 11], target: 46, just two numbers left.\n     |- Try 420 + 11 = 431. Evaluate 431 != 46, drop this branch.\n     |- Try 420 - 11 = 409. Evaluate 409 != 46, drop this branch.\n     |- Try 420 * 11 = 4620. 4620 exceeds the maximum intermediate result, drop this branch.\n     |- Try 420 \/ 11 = 38.2. 38.2 is a decimal, drop this branch.\n    |- Try 430 * 10 = 4300. 4300 exceeds the maximum intermediate result, drop this branch.\n    |- Try 430 \/ 10 = 43. Add 43 to the number set. Current number set: [43, 11], target: 46, just two numbers left.\n     |- Try 43 + 11 = 54. Evaluate 54 != 46, drop this branch.\n     |- Try 43 - 11 = 32. Evaluate 32 != 46, drop this branch.\n     |- Try 43 * 11 = 473. Evaluate 473 != 46, drop this branch.\n     |- Try 43 \/ 11 = 3.9. 3.9 is a decimal, drop this branch.\n   |- Pick two numbers (11, 10) (numbers left: [430]). Try possible operations.\n    |- Try 11 + 10 = 21. Add 21 to the number set. Current number set: [21, 430], target: 46, just two numbers left.\n     |- Try 430 + 21 = 451. Evaluate 451 != 46, drop this branch.\n     |- Try 430 - 21 = 409. Evaluate 409 != 46, drop this branch.\n     |- Try 430 * 21 = 9030. 9030 exceeds the maximum intermediate result, drop this branch.\n     |- Try 430 \/ 21 = 20.5. 20.5 is a decimal, drop this branch.\n    |- Try 11 - 10 = 1. Add 1 to the number set. Current number set: [1, 430], target: 46, just two numbers left.\n     |- Try 430 + 1 = 431. Evaluate 431 != 46, drop this branch.\n     |- Try 430 - 1 = 429. Evaluate 429 != 46, drop this branch.\n     |- Try 430 * 1 = 430. Evaluate 430 != 46, drop this branch.\n     |- Try 430 \/ 1 = 430. Evaluate 430 != 46, drop this branch.\n    |- Try 11 * 10 = 110. Add 110 to the number set. Current number set: [110, 430], target: 46, just two numbers left.\n     |- Try 430 + 110 = 540. Evaluate 540 != 46, drop this branch.\n     |- Try 430 - 110 = 320. Evaluate 320 != 46, drop this branch.\n     |- Try 430 * 110 = 47300. 47300 exceeds the maximum intermediate result, drop this branch.\n     |- Try 430 \/ 110 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 11 \/ 10 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 43 \/ 10 = 4.3. 4.3 is a decimal, drop this branch.\n |- Pick two numbers (43, 11) (numbers left: [10, 10]). Try possible operations.\n  |- Try 43 + 11 = 54. Add 54 to the number set. Current number set: [54, 10, 10], target: 46. Options for choosing two numbers: [(54, 10), (54, 10), (10, 10)].\n   |- Pick two numbers (54, 10) (numbers left: [10]). Try possible operations.\n    |- Try 54 + 10 = 64. Add 64 to the number set. Current number set: [64, 10], target: 46, just two numbers left.\n     |- Try 64 + 10 = 74. Evaluate 74 != 46, drop this branch.\n     |- Try 64 - 10 = 54. Evaluate 54 != 46, drop this branch.\n     |- Try 64 * 10 = 640. Evaluate 640 != 46, drop this branch.\n     |- Try 64 \/ 10 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 54 - 10 = 44. Add 44 to the number set. Current number set: [44, 10], target: 46, just two numbers left.\n     |- Try 44 + 10 = 54. Evaluate 54 != 46, drop this branch.\n     |- Try 44 - 10 = 34. Evaluate 34 != 46, drop this branch.\n     |- Try 44 * 10 = 440. Evaluate 440 != 46, drop this branch.\n     |- Try 44 \/ 10 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 54 * 10 = 540. Add 540 to the number set. Current number set: [540, 10], target: 46, just two numbers left.\n     |- Try 540 + 10 = 550. Evaluate 550 != 46, drop this branch.\n     |- Try 540 - 10 = 530. Evaluate 530 != 46, drop this branch.\n     |- Try 540 * 10 = 5400. 5400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 540 \/ 10 = 54. Evaluate 54 != 46, drop this branch.\n    |- Try 54 \/ 10 = 5.4. 5.4 is a decimal, drop this branch.\n   |- Pick two numbers (54, 10) (numbers left: [10]). Try possible operations.\n    |- Try 54 + 10 = 64. Add 64 to the number set. Current number set: [64, 10], target: 46, just two numbers left.\n     |- Try 64 + 10 = 74. Evaluate 74 != 46, drop this branch.\n     |- Try 64 - 10 = 54. Evaluate 54 != 46, drop this branch.\n     |- Try 64 * 10 = 640. Evaluate 640 != 46, drop this branch.\n     |- Try 64 \/ 10 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 54 - 10 = 44. Add 44 to the number set. Current number set: [44, 10], target: 46, just two numbers left.\n     |- Try 44 + 10 = 54. Evaluate 54 != 46, drop this branch.\n     |- Try 44 - 10 = 34. Evaluate 34 != 46, drop this branch.\n     |- Try 44 * 10 = 440. Evaluate 440 != 46, drop this branch.\n     |- Try 44 \/ 10 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 54 * 10 = 540. Add 540 to the number set. Current number set: [540, 10], target: 46, just two numbers left.\n     |- Try 540 + 10 = 550. Evaluate 550 != 46, drop this branch.\n     |- Try 540 - 10 = 530. Evaluate 530 != 46, drop this branch.\n     |- Try 540 * 10 = 5400. 5400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 540 \/ 10 = 54. Evaluate 54 != 46, drop this branch.\n    |- Try 54 \/ 10 = 5.4. 5.4 is a decimal, drop this branch.\n   |- Pick two numbers (10, 10) (numbers left: [54]). Try possible operations.\n    |- Try 10 + 10 = 20. Add 20 to the number set. Current number set: [20, 54], target: 46, just two numbers left.\n     |- Try 54 + 20 = 74. Evaluate 74 != 46, drop this branch.\n     |- Try 54 - 20 = 34. Evaluate 34 != 46, drop this branch.\n     |- Try 54 * 20 = 1080. Evaluate 1080 != 46, drop this branch.\n     |- Try 54 \/ 20 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 10 - 10 = 0. Add 0 to the number set. Current number set: [0, 54], target: 46, just two numbers left.\n     |- Try 54 + 0 = 54. Evaluate 54 != 46, drop this branch.\n     |- Try 54 - 0 = 54. Evaluate 54 != 46, drop this branch.\n     |- Try 54 * 0 = 0. Evaluate 0 != 46, drop this branch.\n     |- Try 54 \/ 0 (invalid operation). drop this branch.\n    |- Try 10 * 10 = 100. Add 100 to the number set. Current number set: [100, 54], target: 46, just two numbers left.\n     |- Try 100 + 54 = 154. Evaluate 154 != 46, drop this branch.\n     |- Try 100 - 54 = 46. Evaluate 46 == 46, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 100 - 54 = 46\nThe step before: 10 * 10 = 100\nThe first step: 43 + 11 = 54\n\nOutput the solution in the required format:\n<Solution>\n43 + 11 = 54\n10 * 10 = 100\n100 - 54 = 46\n<\/Solution>\n","item":{"nums":[43,10,11,10],"solution":["43 + 11 = 54","10 * 10 = 100","100 - 54 = 46"],"target":46}}
+{"instance_id":"countdown_8k_77","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [10, 3, 43, 37]\nTarget: 12","reference_output":"# Search Procedure\nInitial number set: [10, 3, 43, 37], target: 12. Options for choosing two numbers: [(10, 3), (10, 43), (10, 37), (3, 43), (3, 37), (43, 37)].\n |- Pick two numbers (10, 3) (numbers left: [43, 37]). Try possible operations.\n  |- Try 10 + 3 = 13. Add 13 to the number set. Current number set: [13, 43, 37], target: 12. Options for choosing two numbers: [(13, 43), (13, 37), (43, 37)].\n   |- Pick two numbers (13, 43) (numbers left: [37]). Try possible operations.\n    |- Try 43 + 13 = 56. Add 56 to the number set. Current number set: [56, 37], target: 12, just two numbers left.\n     |- Try 56 + 37 = 93. Evaluate 93 != 12, drop this branch.\n     |- Try 56 - 37 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 56 * 37 = 2072. 2072 exceeds the maximum intermediate result, drop this branch.\n     |- Try 56 \/ 37 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 43 - 13 = 30. Add 30 to the number set. Current number set: [30, 37], target: 12, just two numbers left.\n     |- Try 37 + 30 = 67. Evaluate 67 != 12, drop this branch.\n     |- Try 37 - 30 = 7. Evaluate 7 != 12, drop this branch.\n     |- Try 37 * 30 = 1110. Evaluate 1110 != 12, drop this branch.\n     |- Try 37 \/ 30 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 43 * 13 = 559. Add 559 to the number set. Current number set: [559, 37], target: 12, just two numbers left.\n     |- Try 559 + 37 = 596. Evaluate 596 != 12, drop this branch.\n     |- Try 559 - 37 = 522. Evaluate 522 != 12, drop this branch.\n     |- Try 559 * 37 = 20683. 20683 exceeds the maximum intermediate result, drop this branch.\n     |- Try 559 \/ 37 = 15.1. 15.1 is a decimal, drop this branch.\n    |- Try 43 \/ 13 = 3.3. 3.3 is a decimal, drop this branch.\n   |- Pick two numbers (13, 37) (numbers left: [43]). Try possible operations.\n    |- Try 37 + 13 = 50. Add 50 to the number set. Current number set: [50, 43], target: 12, just two numbers left.\n     |- Try 50 + 43 = 93. Evaluate 93 != 12, drop this branch.\n     |- Try 50 - 43 = 7. Evaluate 7 != 12, drop this branch.\n     |- Try 50 * 43 = 2150. 2150 exceeds the maximum intermediate result, drop this branch.\n     |- Try 50 \/ 43 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 37 - 13 = 24. Add 24 to the number set. Current number set: [24, 43], target: 12, just two numbers left.\n     |- Try 43 + 24 = 67. Evaluate 67 != 12, drop this branch.\n     |- Try 43 - 24 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 43 * 24 = 1032. Evaluate 1032 != 12, drop this branch.\n     |- Try 43 \/ 24 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 37 * 13 = 481. Add 481 to the number set. Current number set: [481, 43], target: 12, just two numbers left.\n     |- Try 481 + 43 = 524. Evaluate 524 != 12, drop this branch.\n     |- Try 481 - 43 = 438. Evaluate 438 != 12, drop this branch.\n     |- Try 481 * 43 = 20683. 20683 exceeds the maximum intermediate result, drop this branch.\n     |- Try 481 \/ 43 = 11.2. 11.2 is a decimal, drop this branch.\n    |- Try 37 \/ 13 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (43, 37) (numbers left: [13]). Try possible operations.\n    |- Try 43 + 37 = 80. Add 80 to the number set. Current number set: [80, 13], target: 12, just two numbers left.\n     |- Try 80 + 13 = 93. Evaluate 93 != 12, drop this branch.\n     |- Try 80 - 13 = 67. Evaluate 67 != 12, drop this branch.\n     |- Try 80 * 13 = 1040. Evaluate 1040 != 12, drop this branch.\n     |- Try 80 \/ 13 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 43 - 37 = 6. Add 6 to the number set. Current number set: [6, 13], target: 12, just two numbers left.\n     |- Try 13 + 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 13 - 6 = 7. Evaluate 7 != 12, drop this branch.\n     |- Try 13 * 6 = 78. Evaluate 78 != 12, drop this branch.\n     |- Try 13 \/ 6 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 43 * 37 = 1591. Add 1591 to the number set. Current number set: [1591, 13], target: 12, just two numbers left.\n     |- Try 1591 + 13 = 1604. Evaluate 1604 != 12, drop this branch.\n     |- Try 1591 - 13 = 1578. Evaluate 1578 != 12, drop this branch.\n     |- Try 1591 * 13 = 20683. 20683 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1591 \/ 13 = 122.4. 122.4 is a decimal, drop this branch.\n    |- Try 43 \/ 37 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 10 - 3 = 7. Add 7 to the number set. Current number set: [7, 43, 37], target: 12. Options for choosing two numbers: [(7, 43), (7, 37), (43, 37)].\n   |- Pick two numbers (7, 43) (numbers left: [37]). Try possible operations.\n    |- Try 43 + 7 = 50. Add 50 to the number set. Current number set: [50, 37], target: 12, just two numbers left.\n     |- Try 50 + 37 = 87. Evaluate 87 != 12, drop this branch.\n     |- Try 50 - 37 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 50 * 37 = 1850. Evaluate 1850 != 12, drop this branch.\n     |- Try 50 \/ 37 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 43 - 7 = 36. Add 36 to the number set. Current number set: [36, 37], target: 12, just two numbers left.\n     |- Try 37 + 36 = 73. Evaluate 73 != 12, drop this branch.\n     |- Try 37 - 36 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 37 * 36 = 1332. Evaluate 1332 != 12, drop this branch.\n     |- Try 37 \/ 36 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 43 * 7 = 301. Add 301 to the number set. Current number set: [301, 37], target: 12, just two numbers left.\n     |- Try 301 + 37 = 338. Evaluate 338 != 12, drop this branch.\n     |- Try 301 - 37 = 264. Evaluate 264 != 12, drop this branch.\n     |- Try 301 * 37 = 11137. 11137 exceeds the maximum intermediate result, drop this branch.\n     |- Try 301 \/ 37 = 8.1. 8.1 is a decimal, drop this branch.\n    |- Try 43 \/ 7 = 6.1. 6.1 is a decimal, drop this branch.\n   |- Pick two numbers (7, 37) (numbers left: [43]). Try possible operations.\n    |- Try 37 + 7 = 44. Add 44 to the number set. Current number set: [44, 43], target: 12, just two numbers left.\n     |- Try 44 + 43 = 87. Evaluate 87 != 12, drop this branch.\n     |- Try 44 - 43 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 44 * 43 = 1892. Evaluate 1892 != 12, drop this branch.\n     |- Try 44 \/ 43 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 37 - 7 = 30. Add 30 to the number set. Current number set: [30, 43], target: 12, just two numbers left.\n     |- Try 43 + 30 = 73. Evaluate 73 != 12, drop this branch.\n     |- Try 43 - 30 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 43 * 30 = 1290. Evaluate 1290 != 12, drop this branch.\n     |- Try 43 \/ 30 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 37 * 7 = 259. Add 259 to the number set. Current number set: [259, 43], target: 12, just two numbers left.\n     |- Try 259 + 43 = 302. Evaluate 302 != 12, drop this branch.\n     |- Try 259 - 43 = 216. Evaluate 216 != 12, drop this branch.\n     |- Try 259 * 43 = 11137. 11137 exceeds the maximum intermediate result, drop this branch.\n     |- Try 259 \/ 43 = 6.0. 6.0 is a decimal, drop this branch.\n    |- Try 37 \/ 7 = 5.3. 5.3 is a decimal, drop this branch.\n   |- Pick two numbers (43, 37) (numbers left: [7]). Try possible operations.\n    |- Try 43 + 37 = 80. Add 80 to the number set. Current number set: [80, 7], target: 12, just two numbers left.\n     |- Try 80 + 7 = 87. Evaluate 87 != 12, drop this branch.\n     |- Try 80 - 7 = 73. Evaluate 73 != 12, drop this branch.\n     |- Try 80 * 7 = 560. Evaluate 560 != 12, drop this branch.\n     |- Try 80 \/ 7 = 11.4. 11.4 is a decimal, drop this branch.\n    |- Try 43 - 37 = 6. Add 6 to the number set. Current number set: [6, 7], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 43 * 37 = 1591. Add 1591 to the number set. Current number set: [1591, 7], target: 12, just two numbers left.\n     |- Try 1591 + 7 = 1598. Evaluate 1598 != 12, drop this branch.\n     |- Try 1591 - 7 = 1584. Evaluate 1584 != 12, drop this branch.\n     |- Try 1591 * 7 = 11137. 11137 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1591 \/ 7 = 227.3. 227.3 is a decimal, drop this branch.\n    |- Try 43 \/ 37 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 10 * 3 = 30. Add 30 to the number set. Current number set: [30, 43, 37], target: 12. Options for choosing two numbers: [(30, 43), (30, 37), (43, 37)].\n   |- Pick two numbers (30, 43) (numbers left: [37]). Try possible operations.\n    |- Try 43 + 30 = 73. Add 73 to the number set. Current number set: [73, 37], target: 12, just two numbers left.\n     |- Try 73 + 37 = 110. Evaluate 110 != 12, drop this branch.\n     |- Try 73 - 37 = 36. Evaluate 36 != 12, drop this branch.\n     |- Try 73 * 37 = 2701. 2701 exceeds the maximum intermediate result, drop this branch.\n     |- Try 73 \/ 37 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 43 - 30 = 13. Add 13 to the number set. Current number set: [13, 37], target: 12, just two numbers left.\n     |- Try 37 + 13 = 50. Evaluate 50 != 12, drop this branch.\n     |- Try 37 - 13 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 37 * 13 = 481. Evaluate 481 != 12, drop this branch.\n     |- Try 37 \/ 13 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 43 * 30 = 1290. Add 1290 to the number set. Current number set: [1290, 37], target: 12, just two numbers left.\n     |- Try 1290 + 37 = 1327. Evaluate 1327 != 12, drop this branch.\n     |- Try 1290 - 37 = 1253. Evaluate 1253 != 12, drop this branch.\n     |- Try 1290 * 37 = 47730. 47730 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1290 \/ 37 = 34.9. 34.9 is a decimal, drop this branch.\n    |- Try 43 \/ 30 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (30, 37) (numbers left: [43]). Try possible operations.\n    |- Try 37 + 30 = 67. Add 67 to the number set. Current number set: [67, 43], target: 12, just two numbers left.\n     |- Try 67 + 43 = 110. Evaluate 110 != 12, drop this branch.\n     |- Try 67 - 43 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 67 * 43 = 2881. 2881 exceeds the maximum intermediate result, drop this branch.\n     |- Try 67 \/ 43 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 37 - 30 = 7. Add 7 to the number set. Current number set: [7, 43], target: 12, just two numbers left.\n     |- Try 43 + 7 = 50. Evaluate 50 != 12, drop this branch.\n     |- Try 43 - 7 = 36. Evaluate 36 != 12, drop this branch.\n     |- Try 43 * 7 = 301. Evaluate 301 != 12, drop this branch.\n     |- Try 43 \/ 7 = 6.1. 6.1 is a decimal, drop this branch.\n    |- Try 37 * 30 = 1110. Add 1110 to the number set. Current number set: [1110, 43], target: 12, just two numbers left.\n     |- Try 1110 + 43 = 1153. Evaluate 1153 != 12, drop this branch.\n     |- Try 1110 - 43 = 1067. Evaluate 1067 != 12, drop this branch.\n     |- Try 1110 * 43 = 47730. 47730 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1110 \/ 43 = 25.8. 25.8 is a decimal, drop this branch.\n    |- Try 37 \/ 30 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (43, 37) (numbers left: [30]). Try possible operations.\n    |- Try 43 + 37 = 80. Add 80 to the number set. Current number set: [80, 30], target: 12, just two numbers left.\n     |- Try 80 + 30 = 110. Evaluate 110 != 12, drop this branch.\n     |- Try 80 - 30 = 50. Evaluate 50 != 12, drop this branch.\n     |- Try 80 * 30 = 2400. 2400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 80 \/ 30 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 43 - 37 = 6. Add 6 to the number set. Current number set: [6, 30], target: 12, just two numbers left.\n     |- Try 30 + 6 = 36. Evaluate 36 != 12, drop this branch.\n     |- Try 30 - 6 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 30 * 6 = 180. Evaluate 180 != 12, drop this branch.\n     |- Try 30 \/ 6 = 5. Evaluate 5 != 12, drop this branch.\n    |- Try 43 * 37 = 1591. Add 1591 to the number set. Current number set: [1591, 30], target: 12, just two numbers left.\n     |- Try 1591 + 30 = 1621. Evaluate 1621 != 12, drop this branch.\n     |- Try 1591 - 30 = 1561. Evaluate 1561 != 12, drop this branch.\n     |- Try 1591 * 30 = 47730. 47730 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1591 \/ 30 = 53.0. 53.0 is a decimal, drop this branch.\n    |- Try 43 \/ 37 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 10 \/ 3 = 3.3. 3.3 is a decimal, drop this branch.\n |- Pick two numbers (10, 43) (numbers left: [3, 37]). Try possible operations.\n  |- Try 43 + 10 = 53. Add 53 to the number set. Current number set: [53, 3, 37], target: 12. Options for choosing two numbers: [(53, 3), (53, 37), (3, 37)].\n   |- Pick two numbers (53, 3) (numbers left: [37]). Try possible operations.\n    |- Try 53 + 3 = 56. Add 56 to the number set. Current number set: [56, 37], target: 12, just two numbers left.\n     |- Try 56 + 37 = 93. Evaluate 93 != 12, drop this branch.\n     |- Try 56 - 37 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 56 * 37 = 2072. 2072 exceeds the maximum intermediate result, drop this branch.\n     |- Try 56 \/ 37 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 53 - 3 = 50. Add 50 to the number set. Current number set: [50, 37], target: 12, just two numbers left.\n     |- Try 50 + 37 = 87. Evaluate 87 != 12, drop this branch.\n     |- Try 50 - 37 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 50 * 37 = 1850. Evaluate 1850 != 12, drop this branch.\n     |- Try 50 \/ 37 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 53 * 3 = 159. Add 159 to the number set. Current number set: [159, 37], target: 12, just two numbers left.\n     |- Try 159 + 37 = 196. Evaluate 196 != 12, drop this branch.\n     |- Try 159 - 37 = 122. Evaluate 122 != 12, drop this branch.\n     |- Try 159 * 37 = 5883. 5883 exceeds the maximum intermediate result, drop this branch.\n     |- Try 159 \/ 37 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 53 \/ 3 = 17.7. 17.7 is a decimal, drop this branch.\n   |- Pick two numbers (53, 37) (numbers left: [3]). Try possible operations.\n    |- Try 53 + 37 = 90. Add 90 to the number set. Current number set: [90, 3], target: 12, just two numbers left.\n     |- Try 90 + 3 = 93. Evaluate 93 != 12, drop this branch.\n     |- Try 90 - 3 = 87. Evaluate 87 != 12, drop this branch.\n     |- Try 90 * 3 = 270. Evaluate 270 != 12, drop this branch.\n     |- Try 90 \/ 3 = 30. Evaluate 30 != 12, drop this branch.\n    |- Try 53 - 37 = 16. Add 16 to the number set. Current number set: [16, 3], target: 12, just two numbers left.\n     |- Try 16 + 3 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 16 - 3 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 16 * 3 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 16 \/ 3 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 53 * 37 = 1961. Add 1961 to the number set. Current number set: [1961, 3], target: 12, just two numbers left.\n     |- Try 1961 + 3 = 1964. Evaluate 1964 != 12, drop this branch.\n     |- Try 1961 - 3 = 1958. Evaluate 1958 != 12, drop this branch.\n     |- Try 1961 * 3 = 5883. 5883 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1961 \/ 3 = 653.7. 653.7 is a decimal, drop this branch.\n    |- Try 53 \/ 37 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (3, 37) (numbers left: [53]). Try possible operations.\n    |- Try 37 + 3 = 40. Add 40 to the number set. Current number set: [40, 53], target: 12, just two numbers left.\n     |- Try 53 + 40 = 93. Evaluate 93 != 12, drop this branch.\n     |- Try 53 - 40 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 53 * 40 = 2120. 2120 exceeds the maximum intermediate result, drop this branch.\n     |- Try 53 \/ 40 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 37 - 3 = 34. Add 34 to the number set. Current number set: [34, 53], target: 12, just two numbers left.\n     |- Try 53 + 34 = 87. Evaluate 87 != 12, drop this branch.\n     |- Try 53 - 34 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 53 * 34 = 1802. Evaluate 1802 != 12, drop this branch.\n     |- Try 53 \/ 34 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 37 * 3 = 111. Add 111 to the number set. Current number set: [111, 53], target: 12, just two numbers left.\n     |- Try 111 + 53 = 164. Evaluate 164 != 12, drop this branch.\n     |- Try 111 - 53 = 58. Evaluate 58 != 12, drop this branch.\n     |- Try 111 * 53 = 5883. 5883 exceeds the maximum intermediate result, drop this branch.\n     |- Try 111 \/ 53 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 37 \/ 3 = 12.3. 12.3 is a decimal, drop this branch.\n  |- Try 43 - 10 = 33. Add 33 to the number set. Current number set: [33, 3, 37], target: 12. Options for choosing two numbers: [(33, 3), (33, 37), (3, 37)].\n   |- Pick two numbers (33, 3) (numbers left: [37]). Try possible operations.\n    |- Try 33 + 3 = 36. Add 36 to the number set. Current number set: [36, 37], target: 12, just two numbers left.\n     |- Try 37 + 36 = 73. Evaluate 73 != 12, drop this branch.\n     |- Try 37 - 36 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 37 * 36 = 1332. Evaluate 1332 != 12, drop this branch.\n     |- Try 37 \/ 36 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 33 - 3 = 30. Add 30 to the number set. Current number set: [30, 37], target: 12, just two numbers left.\n     |- Try 37 + 30 = 67. Evaluate 67 != 12, drop this branch.\n     |- Try 37 - 30 = 7. Evaluate 7 != 12, drop this branch.\n     |- Try 37 * 30 = 1110. Evaluate 1110 != 12, drop this branch.\n     |- Try 37 \/ 30 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 33 * 3 = 99. Add 99 to the number set. Current number set: [99, 37], target: 12, just two numbers left.\n     |- Try 99 + 37 = 136. Evaluate 136 != 12, drop this branch.\n     |- Try 99 - 37 = 62. Evaluate 62 != 12, drop this branch.\n     |- Try 99 * 37 = 3663. 3663 exceeds the maximum intermediate result, drop this branch.\n     |- Try 99 \/ 37 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 33 \/ 3 = 11. Add 11 to the number set. Current number set: [11, 37], target: 12, just two numbers left.\n     |- Try 37 + 11 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 37 - 11 = 26. Evaluate 26 != 12, drop this branch.\n     |- Try 37 * 11 = 407. Evaluate 407 != 12, drop this branch.\n     |- Try 37 \/ 11 = 3.4. 3.4 is a decimal, drop this branch.\n   |- Pick two numbers (33, 37) (numbers left: [3]). Try possible operations.\n    |- Try 37 + 33 = 70. Add 70 to the number set. Current number set: [70, 3], target: 12, just two numbers left.\n     |- Try 70 + 3 = 73. Evaluate 73 != 12, drop this branch.\n     |- Try 70 - 3 = 67. Evaluate 67 != 12, drop this branch.\n     |- Try 70 * 3 = 210. Evaluate 210 != 12, drop this branch.\n     |- Try 70 \/ 3 = 23.3. 23.3 is a decimal, drop this branch.\n    |- Try 37 - 33 = 4. Add 4 to the number set. Current number set: [4, 3], target: 12, just two numbers left.\n     |- Try 4 + 3 = 7. Evaluate 7 != 12, drop this branch.\n     |- Try 4 - 3 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 4 * 3 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 4 * 3 = 12\nThe step before: 37 - 33 = 4\nThe first step: 43 - 10 = 33\n\nOutput the solution in the required format:\n<Solution>\n43 - 10 = 33\n37 - 33 = 4\n4 * 3 = 12\n<\/Solution>\n","item":{"nums":[10,3,43,37],"solution":["43 - 10 = 33","37 - 33 = 4","4 * 3 = 12"],"target":12}}
+{"instance_id":"countdown_8k_78","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [5, 10, 18, 2]\nTarget: 22","reference_output":"# Search Procedure\nInitial number set: [5, 10, 18, 2], target: 22. Options for choosing two numbers: [(5, 10), (5, 18), (5, 2), (10, 18), (10, 2), (18, 2)].\n |- Pick two numbers (5, 10) (numbers left: [18, 2]). Try possible operations.\n  |- Try 10 + 5 = 15. Add 15 to the number set. Current number set: [15, 18, 2], target: 22. Options for choosing two numbers: [(15, 18), (15, 2), (18, 2)].\n   |- Pick two numbers (15, 18) (numbers left: [2]). Try possible operations.\n    |- Try 18 + 15 = 33. Add 33 to the number set. Current number set: [33, 2], target: 22, just two numbers left.\n     |- Try 33 + 2 = 35. Evaluate 35 != 22, drop this branch.\n     |- Try 33 - 2 = 31. Evaluate 31 != 22, drop this branch.\n     |- Try 33 * 2 = 66. Evaluate 66 != 22, drop this branch.\n     |- Try 33 \/ 2 = 16.5. 16.5 is a decimal, drop this branch.\n    |- Try 18 - 15 = 3. Add 3 to the number set. Current number set: [3, 2], target: 22, just two numbers left.\n     |- Try 3 + 2 = 5. Evaluate 5 != 22, drop this branch.\n     |- Try 3 - 2 = 1. Evaluate 1 != 22, drop this branch.\n     |- Try 3 * 2 = 6. Evaluate 6 != 22, drop this branch.\n     |- Try 3 \/ 2 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 18 * 15 = 270. Add 270 to the number set. Current number set: [270, 2], target: 22, just two numbers left.\n     |- Try 270 + 2 = 272. Evaluate 272 != 22, drop this branch.\n     |- Try 270 - 2 = 268. Evaluate 268 != 22, drop this branch.\n     |- Try 270 * 2 = 540. Evaluate 540 != 22, drop this branch.\n     |- Try 270 \/ 2 = 135. Evaluate 135 != 22, drop this branch.\n    |- Try 18 \/ 15 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (15, 2) (numbers left: [18]). Try possible operations.\n    |- Try 15 + 2 = 17. Add 17 to the number set. Current number set: [17, 18], target: 22, just two numbers left.\n     |- Try 18 + 17 = 35. Evaluate 35 != 22, drop this branch.\n     |- Try 18 - 17 = 1. Evaluate 1 != 22, drop this branch.\n     |- Try 18 * 17 = 306. Evaluate 306 != 22, drop this branch.\n     |- Try 18 \/ 17 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 15 - 2 = 13. Add 13 to the number set. Current number set: [13, 18], target: 22, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 22, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 22, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 22, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 15 * 2 = 30. Add 30 to the number set. Current number set: [30, 18], target: 22, just two numbers left.\n     |- Try 30 + 18 = 48. Evaluate 48 != 22, drop this branch.\n     |- Try 30 - 18 = 12. Evaluate 12 != 22, drop this branch.\n     |- Try 30 * 18 = 540. Evaluate 540 != 22, drop this branch.\n     |- Try 30 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 15 \/ 2 = 7.5. 7.5 is a decimal, drop this branch.\n   |- Pick two numbers (18, 2) (numbers left: [15]). Try possible operations.\n    |- Try 18 + 2 = 20. Add 20 to the number set. Current number set: [20, 15], target: 22, just two numbers left.\n     |- Try 20 + 15 = 35. Evaluate 35 != 22, drop this branch.\n     |- Try 20 - 15 = 5. Evaluate 5 != 22, drop this branch.\n     |- Try 20 * 15 = 300. Evaluate 300 != 22, drop this branch.\n     |- Try 20 \/ 15 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 18 - 2 = 16. Add 16 to the number set. Current number set: [16, 15], target: 22, just two numbers left.\n     |- Try 16 + 15 = 31. Evaluate 31 != 22, drop this branch.\n     |- Try 16 - 15 = 1. Evaluate 1 != 22, drop this branch.\n     |- Try 16 * 15 = 240. Evaluate 240 != 22, drop this branch.\n     |- Try 16 \/ 15 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 18 * 2 = 36. Add 36 to the number set. Current number set: [36, 15], target: 22, just two numbers left.\n     |- Try 36 + 15 = 51. Evaluate 51 != 22, drop this branch.\n     |- Try 36 - 15 = 21. Evaluate 21 != 22, drop this branch.\n     |- Try 36 * 15 = 540. Evaluate 540 != 22, drop this branch.\n     |- Try 36 \/ 15 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 18 \/ 2 = 9. Add 9 to the number set. Current number set: [9, 15], target: 22, just two numbers left.\n     |- Try 15 + 9 = 24. Evaluate 24 != 22, drop this branch.\n     |- Try 15 - 9 = 6. Evaluate 6 != 22, drop this branch.\n     |- Try 15 * 9 = 135. Evaluate 135 != 22, drop this branch.\n     |- Try 15 \/ 9 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 10 - 5 = 5. Add 5 to the number set. Current number set: [5, 18, 2], target: 22. Options for choosing two numbers: [(5, 18), (5, 2), (18, 2)].\n   |- Pick two numbers (5, 18) (numbers left: [2]). Try possible operations.\n    |- Try 18 + 5 = 23. Add 23 to the number set. Current number set: [23, 2], target: 22, just two numbers left.\n     |- Try 23 + 2 = 25. Evaluate 25 != 22, drop this branch.\n     |- Try 23 - 2 = 21. Evaluate 21 != 22, drop this branch.\n     |- Try 23 * 2 = 46. Evaluate 46 != 22, drop this branch.\n     |- Try 23 \/ 2 = 11.5. 11.5 is a decimal, drop this branch.\n    |- Try 18 - 5 = 13. Add 13 to the number set. Current number set: [13, 2], target: 22, just two numbers left.\n     |- Try 13 + 2 = 15. Evaluate 15 != 22, drop this branch.\n     |- Try 13 - 2 = 11. Evaluate 11 != 22, drop this branch.\n     |- Try 13 * 2 = 26. Evaluate 26 != 22, drop this branch.\n     |- Try 13 \/ 2 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 18 * 5 = 90. Add 90 to the number set. Current number set: [90, 2], target: 22, just two numbers left.\n     |- Try 90 + 2 = 92. Evaluate 92 != 22, drop this branch.\n     |- Try 90 - 2 = 88. Evaluate 88 != 22, drop this branch.\n     |- Try 90 * 2 = 180. Evaluate 180 != 22, drop this branch.\n     |- Try 90 \/ 2 = 45. Evaluate 45 != 22, drop this branch.\n    |- Try 18 \/ 5 = 3.6. 3.6 is a decimal, drop this branch.\n   |- Pick two numbers (5, 2) (numbers left: [18]). Try possible operations.\n    |- Try 5 + 2 = 7. Add 7 to the number set. Current number set: [7, 18], target: 22, just two numbers left.\n     |- Try 18 + 7 = 25. Evaluate 25 != 22, drop this branch.\n     |- Try 18 - 7 = 11. Evaluate 11 != 22, drop this branch.\n     |- Try 18 * 7 = 126. Evaluate 126 != 22, drop this branch.\n     |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 5 - 2 = 3. Add 3 to the number set. Current number set: [3, 18], target: 22, just two numbers left.\n     |- Try 18 + 3 = 21. Evaluate 21 != 22, drop this branch.\n     |- Try 18 - 3 = 15. Evaluate 15 != 22, drop this branch.\n     |- Try 18 * 3 = 54. Evaluate 54 != 22, drop this branch.\n     |- Try 18 \/ 3 = 6. Evaluate 6 != 22, drop this branch.\n    |- Try 5 * 2 = 10. Add 10 to the number set. Current number set: [10, 18], target: 22, just two numbers left.\n     |- Try 18 + 10 = 28. Evaluate 28 != 22, drop this branch.\n     |- Try 18 - 10 = 8. Evaluate 8 != 22, drop this branch.\n     |- Try 18 * 10 = 180. Evaluate 180 != 22, drop this branch.\n     |- Try 18 \/ 10 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 5 \/ 2 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (18, 2) (numbers left: [5]). Try possible operations.\n    |- Try 18 + 2 = 20. Add 20 to the number set. Current number set: [20, 5], target: 22, just two numbers left.\n     |- Try 20 + 5 = 25. Evaluate 25 != 22, drop this branch.\n     |- Try 20 - 5 = 15. Evaluate 15 != 22, drop this branch.\n     |- Try 20 * 5 = 100. Evaluate 100 != 22, drop this branch.\n     |- Try 20 \/ 5 = 4. Evaluate 4 != 22, drop this branch.\n    |- Try 18 - 2 = 16. Add 16 to the number set. Current number set: [16, 5], target: 22, just two numbers left.\n     |- Try 16 + 5 = 21. Evaluate 21 != 22, drop this branch.\n     |- Try 16 - 5 = 11. Evaluate 11 != 22, drop this branch.\n     |- Try 16 * 5 = 80. Evaluate 80 != 22, drop this branch.\n     |- Try 16 \/ 5 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 18 * 2 = 36. Add 36 to the number set. Current number set: [36, 5], target: 22, just two numbers left.\n     |- Try 36 + 5 = 41. Evaluate 41 != 22, drop this branch.\n     |- Try 36 - 5 = 31. Evaluate 31 != 22, drop this branch.\n     |- Try 36 * 5 = 180. Evaluate 180 != 22, drop this branch.\n     |- Try 36 \/ 5 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 18 \/ 2 = 9. Add 9 to the number set. Current number set: [9, 5], target: 22, just two numbers left.\n     |- Try 9 + 5 = 14. Evaluate 14 != 22, drop this branch.\n     |- Try 9 - 5 = 4. Evaluate 4 != 22, drop this branch.\n     |- Try 9 * 5 = 45. Evaluate 45 != 22, drop this branch.\n     |- Try 9 \/ 5 = 1.8. 1.8 is a decimal, drop this branch.\n  |- Try 10 * 5 = 50. Add 50 to the number set. Current number set: [50, 18, 2], target: 22. Options for choosing two numbers: [(50, 18), (50, 2), (18, 2)].\n   |- Pick two numbers (50, 18) (numbers left: [2]). Try possible operations.\n    |- Try 50 + 18 = 68. Add 68 to the number set. Current number set: [68, 2], target: 22, just two numbers left.\n     |- Try 68 + 2 = 70. Evaluate 70 != 22, drop this branch.\n     |- Try 68 - 2 = 66. Evaluate 66 != 22, drop this branch.\n     |- Try 68 * 2 = 136. Evaluate 136 != 22, drop this branch.\n     |- Try 68 \/ 2 = 34. Evaluate 34 != 22, drop this branch.\n    |- Try 50 - 18 = 32. Add 32 to the number set. Current number set: [32, 2], target: 22, just two numbers left.\n     |- Try 32 + 2 = 34. Evaluate 34 != 22, drop this branch.\n     |- Try 32 - 2 = 30. Evaluate 30 != 22, drop this branch.\n     |- Try 32 * 2 = 64. Evaluate 64 != 22, drop this branch.\n     |- Try 32 \/ 2 = 16. Evaluate 16 != 22, drop this branch.\n    |- Try 50 * 18 = 900. Add 900 to the number set. Current number set: [900, 2], target: 22, just two numbers left.\n     |- Try 900 + 2 = 902. Evaluate 902 != 22, drop this branch.\n     |- Try 900 - 2 = 898. Evaluate 898 != 22, drop this branch.\n     |- Try 900 * 2 = 1800. Evaluate 1800 != 22, drop this branch.\n     |- Try 900 \/ 2 = 450. Evaluate 450 != 22, drop this branch.\n    |- Try 50 \/ 18 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (50, 2) (numbers left: [18]). Try possible operations.\n    |- Try 50 + 2 = 52. Add 52 to the number set. Current number set: [52, 18], target: 22, just two numbers left.\n     |- Try 52 + 18 = 70. Evaluate 70 != 22, drop this branch.\n     |- Try 52 - 18 = 34. Evaluate 34 != 22, drop this branch.\n     |- Try 52 * 18 = 936. Evaluate 936 != 22, drop this branch.\n     |- Try 52 \/ 18 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 50 - 2 = 48. Add 48 to the number set. Current number set: [48, 18], target: 22, just two numbers left.\n     |- Try 48 + 18 = 66. Evaluate 66 != 22, drop this branch.\n     |- Try 48 - 18 = 30. Evaluate 30 != 22, drop this branch.\n     |- Try 48 * 18 = 864. Evaluate 864 != 22, drop this branch.\n     |- Try 48 \/ 18 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 50 * 2 = 100. Add 100 to the number set. Current number set: [100, 18], target: 22, just two numbers left.\n     |- Try 100 + 18 = 118. Evaluate 118 != 22, drop this branch.\n     |- Try 100 - 18 = 82. Evaluate 82 != 22, drop this branch.\n     |- Try 100 * 18 = 1800. Evaluate 1800 != 22, drop this branch.\n     |- Try 100 \/ 18 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 50 \/ 2 = 25. Add 25 to the number set. Current number set: [25, 18], target: 22, just two numbers left.\n     |- Try 25 + 18 = 43. Evaluate 43 != 22, drop this branch.\n     |- Try 25 - 18 = 7. Evaluate 7 != 22, drop this branch.\n     |- Try 25 * 18 = 450. Evaluate 450 != 22, drop this branch.\n     |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (18, 2) (numbers left: [50]). Try possible operations.\n    |- Try 18 + 2 = 20. Add 20 to the number set. Current number set: [20, 50], target: 22, just two numbers left.\n     |- Try 50 + 20 = 70. Evaluate 70 != 22, drop this branch.\n     |- Try 50 - 20 = 30. Evaluate 30 != 22, drop this branch.\n     |- Try 50 * 20 = 1000. Evaluate 1000 != 22, drop this branch.\n     |- Try 50 \/ 20 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 18 - 2 = 16. Add 16 to the number set. Current number set: [16, 50], target: 22, just two numbers left.\n     |- Try 50 + 16 = 66. Evaluate 66 != 22, drop this branch.\n     |- Try 50 - 16 = 34. Evaluate 34 != 22, drop this branch.\n     |- Try 50 * 16 = 800. Evaluate 800 != 22, drop this branch.\n     |- Try 50 \/ 16 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 18 * 2 = 36. Add 36 to the number set. Current number set: [36, 50], target: 22, just two numbers left.\n     |- Try 50 + 36 = 86. Evaluate 86 != 22, drop this branch.\n     |- Try 50 - 36 = 14. Evaluate 14 != 22, drop this branch.\n     |- Try 50 * 36 = 1800. Evaluate 1800 != 22, drop this branch.\n     |- Try 50 \/ 36 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 18 \/ 2 = 9. Add 9 to the number set. Current number set: [9, 50], target: 22, just two numbers left.\n     |- Try 50 + 9 = 59. Evaluate 59 != 22, drop this branch.\n     |- Try 50 - 9 = 41. Evaluate 41 != 22, drop this branch.\n     |- Try 50 * 9 = 450. Evaluate 450 != 22, drop this branch.\n     |- Try 50 \/ 9 = 5.6. 5.6 is a decimal, drop this branch.\n  |- Try 10 \/ 5 = 2. Add 2 to the number set. Current number set: [2, 18, 2], target: 22. Options for choosing two numbers: [(2, 18), (2, 2), (18, 2)].\n   |- Pick two numbers (2, 18) (numbers left: [2]). Try possible operations.\n    |- Try 18 + 2 = 20. Add 20 to the number set. Current number set: [20, 2], target: 22, just two numbers left.\n     |- Try 20 + 2 = 22. Evaluate 22 == 22, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 20 + 2 = 22\nThe step before: 18 + 2 = 20\nThe first step: 10 \/ 5 = 2\n\nOutput the solution in the required format:\n<Solution>\n10 \/ 5 = 2\n18 + 2 = 20\n20 + 2 = 22\n<\/Solution>\n","item":{"nums":[5,10,18,2],"solution":["10 \/ 5 = 2","18 + 2 = 20","20 + 2 = 22"],"target":22}}
+{"instance_id":"countdown_8k_79","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [20, 12, 8, 24]\nTarget: 33","reference_output":"# Search Procedure\nInitial number set: [20, 12, 8, 24], target: 33. Options for choosing two numbers: [(20, 12), (20, 8), (20, 24), (12, 8), (12, 24), (8, 24)].\n |- Pick two numbers (20, 12) (numbers left: [8, 24]). Try possible operations.\n  |- Try 20 + 12 = 32. Add 32 to the number set. Current number set: [32, 8, 24], target: 33. Options for choosing two numbers: [(32, 8), (32, 24), (8, 24)].\n   |- Pick two numbers (32, 8) (numbers left: [24]). Try possible operations.\n    |- Try 32 + 8 = 40. Add 40 to the number set. Current number set: [40, 24], target: 33, just two numbers left.\n     |- Try 40 + 24 = 64. Evaluate 64 != 33, drop this branch.\n     |- Try 40 - 24 = 16. Evaluate 16 != 33, drop this branch.\n     |- Try 40 * 24 = 960. Evaluate 960 != 33, drop this branch.\n     |- Try 40 \/ 24 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 32 - 8 = 24. Add 24 to the number set. Current number set: [24, 24], target: 33, just two numbers left.\n     |- Try 24 + 24 = 48. Evaluate 48 != 33, drop this branch.\n     |- Try 24 - 24 = 0. Evaluate 0 != 33, drop this branch.\n     |- Try 24 * 24 = 576. Evaluate 576 != 33, drop this branch.\n     |- Try 24 \/ 24 = 1. Evaluate 1 != 33, drop this branch.\n    |- Try 32 * 8 = 256. Add 256 to the number set. Current number set: [256, 24], target: 33, just two numbers left.\n     |- Try 256 + 24 = 280. Evaluate 280 != 33, drop this branch.\n     |- Try 256 - 24 = 232. Evaluate 232 != 33, drop this branch.\n     |- Try 256 * 24 = 6144. 6144 exceeds the maximum intermediate result, drop this branch.\n     |- Try 256 \/ 24 = 10.7. 10.7 is a decimal, drop this branch.\n    |- Try 32 \/ 8 = 4. Add 4 to the number set. Current number set: [4, 24], target: 33, just two numbers left.\n     |- Try 24 + 4 = 28. Evaluate 28 != 33, drop this branch.\n     |- Try 24 - 4 = 20. Evaluate 20 != 33, drop this branch.\n     |- Try 24 * 4 = 96. Evaluate 96 != 33, drop this branch.\n     |- Try 24 \/ 4 = 6. Evaluate 6 != 33, drop this branch.\n   |- Pick two numbers (32, 24) (numbers left: [8]). Try possible operations.\n    |- Try 32 + 24 = 56. Add 56 to the number set. Current number set: [56, 8], target: 33, just two numbers left.\n     |- Try 56 + 8 = 64. Evaluate 64 != 33, drop this branch.\n     |- Try 56 - 8 = 48. Evaluate 48 != 33, drop this branch.\n     |- Try 56 * 8 = 448. Evaluate 448 != 33, drop this branch.\n     |- Try 56 \/ 8 = 7. Evaluate 7 != 33, drop this branch.\n    |- Try 32 - 24 = 8. Add 8 to the number set. Current number set: [8, 8], target: 33, just two numbers left.\n     |- Try 8 + 8 = 16. Evaluate 16 != 33, drop this branch.\n     |- Try 8 - 8 = 0. Evaluate 0 != 33, drop this branch.\n     |- Try 8 * 8 = 64. Evaluate 64 != 33, drop this branch.\n     |- Try 8 \/ 8 = 1. Evaluate 1 != 33, drop this branch.\n    |- Try 32 * 24 = 768. Add 768 to the number set. Current number set: [768, 8], target: 33, just two numbers left.\n     |- Try 768 + 8 = 776. Evaluate 776 != 33, drop this branch.\n     |- Try 768 - 8 = 760. Evaluate 760 != 33, drop this branch.\n     |- Try 768 * 8 = 6144. 6144 exceeds the maximum intermediate result, drop this branch.\n     |- Try 768 \/ 8 = 96. Evaluate 96 != 33, drop this branch.\n    |- Try 32 \/ 24 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (8, 24) (numbers left: [32]). Try possible operations.\n    |- Try 24 + 8 = 32. Add 32 to the number set. Current number set: [32, 32], target: 33, just two numbers left.\n     |- Try 32 + 32 = 64. Evaluate 64 != 33, drop this branch.\n     |- Try 32 - 32 = 0. Evaluate 0 != 33, drop this branch.\n     |- Try 32 * 32 = 1024. Evaluate 1024 != 33, drop this branch.\n     |- Try 32 \/ 32 = 1. Evaluate 1 != 33, drop this branch.\n    |- Try 24 - 8 = 16. Add 16 to the number set. Current number set: [16, 32], target: 33, just two numbers left.\n     |- Try 32 + 16 = 48. Evaluate 48 != 33, drop this branch.\n     |- Try 32 - 16 = 16. Evaluate 16 != 33, drop this branch.\n     |- Try 32 * 16 = 512. Evaluate 512 != 33, drop this branch.\n     |- Try 32 \/ 16 = 2. Evaluate 2 != 33, drop this branch.\n    |- Try 24 * 8 = 192. Add 192 to the number set. Current number set: [192, 32], target: 33, just two numbers left.\n     |- Try 192 + 32 = 224. Evaluate 224 != 33, drop this branch.\n     |- Try 192 - 32 = 160. Evaluate 160 != 33, drop this branch.\n     |- Try 192 * 32 = 6144. 6144 exceeds the maximum intermediate result, drop this branch.\n     |- Try 192 \/ 32 = 6. Evaluate 6 != 33, drop this branch.\n    |- Try 24 \/ 8 = 3. Add 3 to the number set. Current number set: [3, 32], target: 33, just two numbers left.\n     |- Try 32 + 3 = 35. Evaluate 35 != 33, drop this branch.\n     |- Try 32 - 3 = 29. Evaluate 29 != 33, drop this branch.\n     |- Try 32 * 3 = 96. Evaluate 96 != 33, drop this branch.\n     |- Try 32 \/ 3 = 10.7. 10.7 is a decimal, drop this branch.\n  |- Try 20 - 12 = 8. Add 8 to the number set. Current number set: [8, 8, 24], target: 33. Options for choosing two numbers: [(8, 8), (8, 24), (8, 24)].\n   |- Pick two numbers (8, 8) (numbers left: [24]). Try possible operations.\n    |- Try 8 + 8 = 16. Add 16 to the number set. Current number set: [16, 24], target: 33, just two numbers left.\n     |- Try 24 + 16 = 40. Evaluate 40 != 33, drop this branch.\n     |- Try 24 - 16 = 8. Evaluate 8 != 33, drop this branch.\n     |- Try 24 * 16 = 384. Evaluate 384 != 33, drop this branch.\n     |- Try 24 \/ 16 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 8 - 8 = 0. Add 0 to the number set. Current number set: [0, 24], target: 33, just two numbers left.\n     |- Try 24 + 0 = 24. Evaluate 24 != 33, drop this branch.\n     |- Try 24 - 0 = 24. Evaluate 24 != 33, drop this branch.\n     |- Try 24 * 0 = 0. Evaluate 0 != 33, drop this branch.\n     |- Try 24 \/ 0 (invalid operation). drop this branch.\n    |- Try 8 * 8 = 64. Add 64 to the number set. Current number set: [64, 24], target: 33, just two numbers left.\n     |- Try 64 + 24 = 88. Evaluate 88 != 33, drop this branch.\n     |- Try 64 - 24 = 40. Evaluate 40 != 33, drop this branch.\n     |- Try 64 * 24 = 1536. Evaluate 1536 != 33, drop this branch.\n     |- Try 64 \/ 24 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 8 \/ 8 = 1. Add 1 to the number set. Current number set: [1, 24], target: 33, just two numbers left.\n     |- Try 24 + 1 = 25. Evaluate 25 != 33, drop this branch.\n     |- Try 24 - 1 = 23. Evaluate 23 != 33, drop this branch.\n     |- Try 24 * 1 = 24. Evaluate 24 != 33, drop this branch.\n     |- Try 24 \/ 1 = 24. Evaluate 24 != 33, drop this branch.\n   |- Pick two numbers (8, 24) (numbers left: [8]). Try possible operations.\n    |- Try 24 + 8 = 32. Add 32 to the number set. Current number set: [32, 8], target: 33, just two numbers left.\n     |- Try 32 + 8 = 40. Evaluate 40 != 33, drop this branch.\n     |- Try 32 - 8 = 24. Evaluate 24 != 33, drop this branch.\n     |- Try 32 * 8 = 256. Evaluate 256 != 33, drop this branch.\n     |- Try 32 \/ 8 = 4. Evaluate 4 != 33, drop this branch.\n    |- Try 24 - 8 = 16. Add 16 to the number set. Current number set: [16, 8], target: 33, just two numbers left.\n     |- Try 16 + 8 = 24. Evaluate 24 != 33, drop this branch.\n     |- Try 16 - 8 = 8. Evaluate 8 != 33, drop this branch.\n     |- Try 16 * 8 = 128. Evaluate 128 != 33, drop this branch.\n     |- Try 16 \/ 8 = 2. Evaluate 2 != 33, drop this branch.\n    |- Try 24 * 8 = 192. Add 192 to the number set. Current number set: [192, 8], target: 33, just two numbers left.\n     |- Try 192 + 8 = 200. Evaluate 200 != 33, drop this branch.\n     |- Try 192 - 8 = 184. Evaluate 184 != 33, drop this branch.\n     |- Try 192 * 8 = 1536. Evaluate 1536 != 33, drop this branch.\n     |- Try 192 \/ 8 = 24. Evaluate 24 != 33, drop this branch.\n    |- Try 24 \/ 8 = 3. Add 3 to the number set. Current number set: [3, 8], target: 33, just two numbers left.\n     |- Try 8 + 3 = 11. Evaluate 11 != 33, drop this branch.\n     |- Try 8 - 3 = 5. Evaluate 5 != 33, drop this branch.\n     |- Try 8 * 3 = 24. Evaluate 24 != 33, drop this branch.\n     |- Try 8 \/ 3 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (8, 24) (numbers left: [8]). Try possible operations.\n    |- Try 24 + 8 = 32. Add 32 to the number set. Current number set: [32, 8], target: 33, just two numbers left.\n     |- Try 32 + 8 = 40. Evaluate 40 != 33, drop this branch.\n     |- Try 32 - 8 = 24. Evaluate 24 != 33, drop this branch.\n     |- Try 32 * 8 = 256. Evaluate 256 != 33, drop this branch.\n     |- Try 32 \/ 8 = 4. Evaluate 4 != 33, drop this branch.\n    |- Try 24 - 8 = 16. Add 16 to the number set. Current number set: [16, 8], target: 33, just two numbers left.\n     |- Try 16 + 8 = 24. Evaluate 24 != 33, drop this branch.\n     |- Try 16 - 8 = 8. Evaluate 8 != 33, drop this branch.\n     |- Try 16 * 8 = 128. Evaluate 128 != 33, drop this branch.\n     |- Try 16 \/ 8 = 2. Evaluate 2 != 33, drop this branch.\n    |- Try 24 * 8 = 192. Add 192 to the number set. Current number set: [192, 8], target: 33, just two numbers left.\n     |- Try 192 + 8 = 200. Evaluate 200 != 33, drop this branch.\n     |- Try 192 - 8 = 184. Evaluate 184 != 33, drop this branch.\n     |- Try 192 * 8 = 1536. Evaluate 1536 != 33, drop this branch.\n     |- Try 192 \/ 8 = 24. Evaluate 24 != 33, drop this branch.\n    |- Try 24 \/ 8 = 3. Add 3 to the number set. Current number set: [3, 8], target: 33, just two numbers left.\n     |- Try 8 + 3 = 11. Evaluate 11 != 33, drop this branch.\n     |- Try 8 - 3 = 5. Evaluate 5 != 33, drop this branch.\n     |- Try 8 * 3 = 24. Evaluate 24 != 33, drop this branch.\n     |- Try 8 \/ 3 = 2.7. 2.7 is a decimal, drop this branch.\n  |- Try 20 * 12 = 240. Add 240 to the number set. Current number set: [240, 8, 24], target: 33. Options for choosing two numbers: [(240, 8), (240, 24), (8, 24)].\n   |- Pick two numbers (240, 8) (numbers left: [24]). Try possible operations.\n    |- Try 240 + 8 = 248. Add 248 to the number set. Current number set: [248, 24], target: 33, just two numbers left.\n     |- Try 248 + 24 = 272. Evaluate 272 != 33, drop this branch.\n     |- Try 248 - 24 = 224. Evaluate 224 != 33, drop this branch.\n     |- Try 248 * 24 = 5952. 5952 exceeds the maximum intermediate result, drop this branch.\n     |- Try 248 \/ 24 = 10.3. 10.3 is a decimal, drop this branch.\n    |- Try 240 - 8 = 232. Add 232 to the number set. Current number set: [232, 24], target: 33, just two numbers left.\n     |- Try 232 + 24 = 256. Evaluate 256 != 33, drop this branch.\n     |- Try 232 - 24 = 208. Evaluate 208 != 33, drop this branch.\n     |- Try 232 * 24 = 5568. 5568 exceeds the maximum intermediate result, drop this branch.\n     |- Try 232 \/ 24 = 9.7. 9.7 is a decimal, drop this branch.\n    |- Try 240 * 8 = 1920. Add 1920 to the number set. Current number set: [1920, 24], target: 33, just two numbers left.\n     |- Try 1920 + 24 = 1944. Evaluate 1944 != 33, drop this branch.\n     |- Try 1920 - 24 = 1896. Evaluate 1896 != 33, drop this branch.\n     |- Try 1920 * 24 = 46080. 46080 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1920 \/ 24 = 80. Evaluate 80 != 33, drop this branch.\n    |- Try 240 \/ 8 = 30. Add 30 to the number set. Current number set: [30, 24], target: 33, just two numbers left.\n     |- Try 30 + 24 = 54. Evaluate 54 != 33, drop this branch.\n     |- Try 30 - 24 = 6. Evaluate 6 != 33, drop this branch.\n     |- Try 30 * 24 = 720. Evaluate 720 != 33, drop this branch.\n     |- Try 30 \/ 24 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (240, 24) (numbers left: [8]). Try possible operations.\n    |- Try 240 + 24 = 264. Add 264 to the number set. Current number set: [264, 8], target: 33, just two numbers left.\n     |- Try 264 + 8 = 272. Evaluate 272 != 33, drop this branch.\n     |- Try 264 - 8 = 256. Evaluate 256 != 33, drop this branch.\n     |- Try 264 * 8 = 2112. 2112 exceeds the maximum intermediate result, drop this branch.\n     |- Try 264 \/ 8 = 33. Evaluate 33 == 33, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 264 \/ 8 = 33\nThe step before: 240 + 24 = 264\nThe first step: 20 * 12 = 240\n\nOutput the solution in the required format:\n<Solution>\n20 * 12 = 240\n240 + 24 = 264\n264 \/ 8 = 33\n<\/Solution>\n","item":{"nums":[20,12,8,24],"solution":["20 * 12 = 240","240 + 24 = 264","264 \/ 8 = 33"],"target":33}}
+{"instance_id":"countdown_8k_80","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [29, 4, 9, 2]\nTarget: 28","reference_output":"# Search Procedure\nInitial number set: [29, 4, 9, 2], target: 28. Options for choosing two numbers: [(29, 4), (29, 9), (29, 2), (4, 9), (4, 2), (9, 2)].\n |- Pick two numbers (29, 4) (numbers left: [9, 2]). Try possible operations.\n  |- Try 29 + 4 = 33. Add 33 to the number set. Current number set: [33, 9, 2], target: 28. Options for choosing two numbers: [(33, 9), (33, 2), (9, 2)].\n   |- Pick two numbers (33, 9) (numbers left: [2]). Try possible operations.\n    |- Try 33 + 9 = 42. Add 42 to the number set. Current number set: [42, 2], target: 28, just two numbers left.\n     |- Try 42 + 2 = 44. Evaluate 44 != 28, drop this branch.\n     |- Try 42 - 2 = 40. Evaluate 40 != 28, drop this branch.\n     |- Try 42 * 2 = 84. Evaluate 84 != 28, drop this branch.\n     |- Try 42 \/ 2 = 21. Evaluate 21 != 28, drop this branch.\n    |- Try 33 - 9 = 24. Add 24 to the number set. Current number set: [24, 2], target: 28, just two numbers left.\n     |- Try 24 + 2 = 26. Evaluate 26 != 28, drop this branch.\n     |- Try 24 - 2 = 22. Evaluate 22 != 28, drop this branch.\n     |- Try 24 * 2 = 48. Evaluate 48 != 28, drop this branch.\n     |- Try 24 \/ 2 = 12. Evaluate 12 != 28, drop this branch.\n    |- Try 33 * 9 = 297. Add 297 to the number set. Current number set: [297, 2], target: 28, just two numbers left.\n     |- Try 297 + 2 = 299. Evaluate 299 != 28, drop this branch.\n     |- Try 297 - 2 = 295. Evaluate 295 != 28, drop this branch.\n     |- Try 297 * 2 = 594. Evaluate 594 != 28, drop this branch.\n     |- Try 297 \/ 2 = 148.5. 148.5 is a decimal, drop this branch.\n    |- Try 33 \/ 9 = 3.7. 3.7 is a decimal, drop this branch.\n   |- Pick two numbers (33, 2) (numbers left: [9]). Try possible operations.\n    |- Try 33 + 2 = 35. Add 35 to the number set. Current number set: [35, 9], target: 28, just two numbers left.\n     |- Try 35 + 9 = 44. Evaluate 44 != 28, drop this branch.\n     |- Try 35 - 9 = 26. Evaluate 26 != 28, drop this branch.\n     |- Try 35 * 9 = 315. Evaluate 315 != 28, drop this branch.\n     |- Try 35 \/ 9 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 33 - 2 = 31. Add 31 to the number set. Current number set: [31, 9], target: 28, just two numbers left.\n     |- Try 31 + 9 = 40. Evaluate 40 != 28, drop this branch.\n     |- Try 31 - 9 = 22. Evaluate 22 != 28, drop this branch.\n     |- Try 31 * 9 = 279. Evaluate 279 != 28, drop this branch.\n     |- Try 31 \/ 9 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 33 * 2 = 66. Add 66 to the number set. Current number set: [66, 9], target: 28, just two numbers left.\n     |- Try 66 + 9 = 75. Evaluate 75 != 28, drop this branch.\n     |- Try 66 - 9 = 57. Evaluate 57 != 28, drop this branch.\n     |- Try 66 * 9 = 594. Evaluate 594 != 28, drop this branch.\n     |- Try 66 \/ 9 = 7.3. 7.3 is a decimal, drop this branch.\n    |- Try 33 \/ 2 = 16.5. 16.5 is a decimal, drop this branch.\n   |- Pick two numbers (9, 2) (numbers left: [33]). Try possible operations.\n    |- Try 9 + 2 = 11. Add 11 to the number set. Current number set: [11, 33], target: 28, just two numbers left.\n     |- Try 33 + 11 = 44. Evaluate 44 != 28, drop this branch.\n     |- Try 33 - 11 = 22. Evaluate 22 != 28, drop this branch.\n     |- Try 33 * 11 = 363. Evaluate 363 != 28, drop this branch.\n     |- Try 33 \/ 11 = 3. Evaluate 3 != 28, drop this branch.\n    |- Try 9 - 2 = 7. Add 7 to the number set. Current number set: [7, 33], target: 28, just two numbers left.\n     |- Try 33 + 7 = 40. Evaluate 40 != 28, drop this branch.\n     |- Try 33 - 7 = 26. Evaluate 26 != 28, drop this branch.\n     |- Try 33 * 7 = 231. Evaluate 231 != 28, drop this branch.\n     |- Try 33 \/ 7 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 9 * 2 = 18. Add 18 to the number set. Current number set: [18, 33], target: 28, just two numbers left.\n     |- Try 33 + 18 = 51. Evaluate 51 != 28, drop this branch.\n     |- Try 33 - 18 = 15. Evaluate 15 != 28, drop this branch.\n     |- Try 33 * 18 = 594. Evaluate 594 != 28, drop this branch.\n     |- Try 33 \/ 18 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 9 \/ 2 = 4.5. 4.5 is a decimal, drop this branch.\n  |- Try 29 - 4 = 25. Add 25 to the number set. Current number set: [25, 9, 2], target: 28. Options for choosing two numbers: [(25, 9), (25, 2), (9, 2)].\n   |- Pick two numbers (25, 9) (numbers left: [2]). Try possible operations.\n    |- Try 25 + 9 = 34. Add 34 to the number set. Current number set: [34, 2], target: 28, just two numbers left.\n     |- Try 34 + 2 = 36. Evaluate 36 != 28, drop this branch.\n     |- Try 34 - 2 = 32. Evaluate 32 != 28, drop this branch.\n     |- Try 34 * 2 = 68. Evaluate 68 != 28, drop this branch.\n     |- Try 34 \/ 2 = 17. Evaluate 17 != 28, drop this branch.\n    |- Try 25 - 9 = 16. Add 16 to the number set. Current number set: [16, 2], target: 28, just two numbers left.\n     |- Try 16 + 2 = 18. Evaluate 18 != 28, drop this branch.\n     |- Try 16 - 2 = 14. Evaluate 14 != 28, drop this branch.\n     |- Try 16 * 2 = 32. Evaluate 32 != 28, drop this branch.\n     |- Try 16 \/ 2 = 8. Evaluate 8 != 28, drop this branch.\n    |- Try 25 * 9 = 225. Add 225 to the number set. Current number set: [225, 2], target: 28, just two numbers left.\n     |- Try 225 + 2 = 227. Evaluate 227 != 28, drop this branch.\n     |- Try 225 - 2 = 223. Evaluate 223 != 28, drop this branch.\n     |- Try 225 * 2 = 450. Evaluate 450 != 28, drop this branch.\n     |- Try 225 \/ 2 = 112.5. 112.5 is a decimal, drop this branch.\n    |- Try 25 \/ 9 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (25, 2) (numbers left: [9]). Try possible operations.\n    |- Try 25 + 2 = 27. Add 27 to the number set. Current number set: [27, 9], target: 28, just two numbers left.\n     |- Try 27 + 9 = 36. Evaluate 36 != 28, drop this branch.\n     |- Try 27 - 9 = 18. Evaluate 18 != 28, drop this branch.\n     |- Try 27 * 9 = 243. Evaluate 243 != 28, drop this branch.\n     |- Try 27 \/ 9 = 3. Evaluate 3 != 28, drop this branch.\n    |- Try 25 - 2 = 23. Add 23 to the number set. Current number set: [23, 9], target: 28, just two numbers left.\n     |- Try 23 + 9 = 32. Evaluate 32 != 28, drop this branch.\n     |- Try 23 - 9 = 14. Evaluate 14 != 28, drop this branch.\n     |- Try 23 * 9 = 207. Evaluate 207 != 28, drop this branch.\n     |- Try 23 \/ 9 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 25 * 2 = 50. Add 50 to the number set. Current number set: [50, 9], target: 28, just two numbers left.\n     |- Try 50 + 9 = 59. Evaluate 59 != 28, drop this branch.\n     |- Try 50 - 9 = 41. Evaluate 41 != 28, drop this branch.\n     |- Try 50 * 9 = 450. Evaluate 450 != 28, drop this branch.\n     |- Try 50 \/ 9 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 25 \/ 2 = 12.5. 12.5 is a decimal, drop this branch.\n   |- Pick two numbers (9, 2) (numbers left: [25]). Try possible operations.\n    |- Try 9 + 2 = 11. Add 11 to the number set. Current number set: [11, 25], target: 28, just two numbers left.\n     |- Try 25 + 11 = 36. Evaluate 36 != 28, drop this branch.\n     |- Try 25 - 11 = 14. Evaluate 14 != 28, drop this branch.\n     |- Try 25 * 11 = 275. Evaluate 275 != 28, drop this branch.\n     |- Try 25 \/ 11 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 9 - 2 = 7. Add 7 to the number set. Current number set: [7, 25], target: 28, just two numbers left.\n     |- Try 25 + 7 = 32. Evaluate 32 != 28, drop this branch.\n     |- Try 25 - 7 = 18. Evaluate 18 != 28, drop this branch.\n     |- Try 25 * 7 = 175. Evaluate 175 != 28, drop this branch.\n     |- Try 25 \/ 7 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 9 * 2 = 18. Add 18 to the number set. Current number set: [18, 25], target: 28, just two numbers left.\n     |- Try 25 + 18 = 43. Evaluate 43 != 28, drop this branch.\n     |- Try 25 - 18 = 7. Evaluate 7 != 28, drop this branch.\n     |- Try 25 * 18 = 450. Evaluate 450 != 28, drop this branch.\n     |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 9 \/ 2 = 4.5. 4.5 is a decimal, drop this branch.\n  |- Try 29 * 4 = 116. Add 116 to the number set. Current number set: [116, 9, 2], target: 28. Options for choosing two numbers: [(116, 9), (116, 2), (9, 2)].\n   |- Pick two numbers (116, 9) (numbers left: [2]). Try possible operations.\n    |- Try 116 + 9 = 125. Add 125 to the number set. Current number set: [125, 2], target: 28, just two numbers left.\n     |- Try 125 + 2 = 127. Evaluate 127 != 28, drop this branch.\n     |- Try 125 - 2 = 123. Evaluate 123 != 28, drop this branch.\n     |- Try 125 * 2 = 250. Evaluate 250 != 28, drop this branch.\n     |- Try 125 \/ 2 = 62.5. 62.5 is a decimal, drop this branch.\n    |- Try 116 - 9 = 107. Add 107 to the number set. Current number set: [107, 2], target: 28, just two numbers left.\n     |- Try 107 + 2 = 109. Evaluate 109 != 28, drop this branch.\n     |- Try 107 - 2 = 105. Evaluate 105 != 28, drop this branch.\n     |- Try 107 * 2 = 214. Evaluate 214 != 28, drop this branch.\n     |- Try 107 \/ 2 = 53.5. 53.5 is a decimal, drop this branch.\n    |- Try 116 * 9 = 1044. Add 1044 to the number set. Current number set: [1044, 2], target: 28, just two numbers left.\n     |- Try 1044 + 2 = 1046. Evaluate 1046 != 28, drop this branch.\n     |- Try 1044 - 2 = 1042. Evaluate 1042 != 28, drop this branch.\n     |- Try 1044 * 2 = 2088. 2088 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1044 \/ 2 = 522. Evaluate 522 != 28, drop this branch.\n    |- Try 116 \/ 9 = 12.9. 12.9 is a decimal, drop this branch.\n   |- Pick two numbers (116, 2) (numbers left: [9]). Try possible operations.\n    |- Try 116 + 2 = 118. Add 118 to the number set. Current number set: [118, 9], target: 28, just two numbers left.\n     |- Try 118 + 9 = 127. Evaluate 127 != 28, drop this branch.\n     |- Try 118 - 9 = 109. Evaluate 109 != 28, drop this branch.\n     |- Try 118 * 9 = 1062. Evaluate 1062 != 28, drop this branch.\n     |- Try 118 \/ 9 = 13.1. 13.1 is a decimal, drop this branch.\n    |- Try 116 - 2 = 114. Add 114 to the number set. Current number set: [114, 9], target: 28, just two numbers left.\n     |- Try 114 + 9 = 123. Evaluate 123 != 28, drop this branch.\n     |- Try 114 - 9 = 105. Evaluate 105 != 28, drop this branch.\n     |- Try 114 * 9 = 1026. Evaluate 1026 != 28, drop this branch.\n     |- Try 114 \/ 9 = 12.7. 12.7 is a decimal, drop this branch.\n    |- Try 116 * 2 = 232. Add 232 to the number set. Current number set: [232, 9], target: 28, just two numbers left.\n     |- Try 232 + 9 = 241. Evaluate 241 != 28, drop this branch.\n     |- Try 232 - 9 = 223. Evaluate 223 != 28, drop this branch.\n     |- Try 232 * 9 = 2088. 2088 exceeds the maximum intermediate result, drop this branch.\n     |- Try 232 \/ 9 = 25.8. 25.8 is a decimal, drop this branch.\n    |- Try 116 \/ 2 = 58. Add 58 to the number set. Current number set: [58, 9], target: 28, just two numbers left.\n     |- Try 58 + 9 = 67. Evaluate 67 != 28, drop this branch.\n     |- Try 58 - 9 = 49. Evaluate 49 != 28, drop this branch.\n     |- Try 58 * 9 = 522. Evaluate 522 != 28, drop this branch.\n     |- Try 58 \/ 9 = 6.4. 6.4 is a decimal, drop this branch.\n   |- Pick two numbers (9, 2) (numbers left: [116]). Try possible operations.\n    |- Try 9 + 2 = 11. Add 11 to the number set. Current number set: [11, 116], target: 28, just two numbers left.\n     |- Try 116 + 11 = 127. Evaluate 127 != 28, drop this branch.\n     |- Try 116 - 11 = 105. Evaluate 105 != 28, drop this branch.\n     |- Try 116 * 11 = 1276. Evaluate 1276 != 28, drop this branch.\n     |- Try 116 \/ 11 = 10.5. 10.5 is a decimal, drop this branch.\n    |- Try 9 - 2 = 7. Add 7 to the number set. Current number set: [7, 116], target: 28, just two numbers left.\n     |- Try 116 + 7 = 123. Evaluate 123 != 28, drop this branch.\n     |- Try 116 - 7 = 109. Evaluate 109 != 28, drop this branch.\n     |- Try 116 * 7 = 812. Evaluate 812 != 28, drop this branch.\n     |- Try 116 \/ 7 = 16.6. 16.6 is a decimal, drop this branch.\n    |- Try 9 * 2 = 18. Add 18 to the number set. Current number set: [18, 116], target: 28, just two numbers left.\n     |- Try 116 + 18 = 134. Evaluate 134 != 28, drop this branch.\n     |- Try 116 - 18 = 98. Evaluate 98 != 28, drop this branch.\n     |- Try 116 * 18 = 2088. 2088 exceeds the maximum intermediate result, drop this branch.\n     |- Try 116 \/ 18 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 9 \/ 2 = 4.5. 4.5 is a decimal, drop this branch.\n  |- Try 29 \/ 4 = 7.2. 7.2 is a decimal, drop this branch.\n |- Pick two numbers (29, 9) (numbers left: [4, 2]). Try possible operations.\n  |- Try 29 + 9 = 38. Add 38 to the number set. Current number set: [38, 4, 2], target: 28. Options for choosing two numbers: [(38, 4), (38, 2), (4, 2)].\n   |- Pick two numbers (38, 4) (numbers left: [2]). Try possible operations.\n    |- Try 38 + 4 = 42. Add 42 to the number set. Current number set: [42, 2], target: 28, just two numbers left.\n     |- Try 42 + 2 = 44. Evaluate 44 != 28, drop this branch.\n     |- Try 42 - 2 = 40. Evaluate 40 != 28, drop this branch.\n     |- Try 42 * 2 = 84. Evaluate 84 != 28, drop this branch.\n     |- Try 42 \/ 2 = 21. Evaluate 21 != 28, drop this branch.\n    |- Try 38 - 4 = 34. Add 34 to the number set. Current number set: [34, 2], target: 28, just two numbers left.\n     |- Try 34 + 2 = 36. Evaluate 36 != 28, drop this branch.\n     |- Try 34 - 2 = 32. Evaluate 32 != 28, drop this branch.\n     |- Try 34 * 2 = 68. Evaluate 68 != 28, drop this branch.\n     |- Try 34 \/ 2 = 17. Evaluate 17 != 28, drop this branch.\n    |- Try 38 * 4 = 152. Add 152 to the number set. Current number set: [152, 2], target: 28, just two numbers left.\n     |- Try 152 + 2 = 154. Evaluate 154 != 28, drop this branch.\n     |- Try 152 - 2 = 150. Evaluate 150 != 28, drop this branch.\n     |- Try 152 * 2 = 304. Evaluate 304 != 28, drop this branch.\n     |- Try 152 \/ 2 = 76. Evaluate 76 != 28, drop this branch.\n    |- Try 38 \/ 4 = 9.5. 9.5 is a decimal, drop this branch.\n   |- Pick two numbers (38, 2) (numbers left: [4]). Try possible operations.\n    |- Try 38 + 2 = 40. Add 40 to the number set. Current number set: [40, 4], target: 28, just two numbers left.\n     |- Try 40 + 4 = 44. Evaluate 44 != 28, drop this branch.\n     |- Try 40 - 4 = 36. Evaluate 36 != 28, drop this branch.\n     |- Try 40 * 4 = 160. Evaluate 160 != 28, drop this branch.\n     |- Try 40 \/ 4 = 10. Evaluate 10 != 28, drop this branch.\n    |- Try 38 - 2 = 36. Add 36 to the number set. Current number set: [36, 4], target: 28, just two numbers left.\n     |- Try 36 + 4 = 40. Evaluate 40 != 28, drop this branch.\n     |- Try 36 - 4 = 32. Evaluate 32 != 28, drop this branch.\n     |- Try 36 * 4 = 144. Evaluate 144 != 28, drop this branch.\n     |- Try 36 \/ 4 = 9. Evaluate 9 != 28, drop this branch.\n    |- Try 38 * 2 = 76. Add 76 to the number set. Current number set: [76, 4], target: 28, just two numbers left.\n     |- Try 76 + 4 = 80. Evaluate 80 != 28, drop this branch.\n     |- Try 76 - 4 = 72. Evaluate 72 != 28, drop this branch.\n     |- Try 76 * 4 = 304. Evaluate 304 != 28, drop this branch.\n     |- Try 76 \/ 4 = 19. Evaluate 19 != 28, drop this branch.\n    |- Try 38 \/ 2 = 19. Add 19 to the number set. Current number set: [19, 4], target: 28, just two numbers left.\n     |- Try 19 + 4 = 23. Evaluate 23 != 28, drop this branch.\n     |- Try 19 - 4 = 15. Evaluate 15 != 28, drop this branch.\n     |- Try 19 * 4 = 76. Evaluate 76 != 28, drop this branch.\n     |- Try 19 \/ 4 = 4.8. 4.8 is a decimal, drop this branch.\n   |- Pick two numbers (4, 2) (numbers left: [38]). Try possible operations.\n    |- Try 4 + 2 = 6. Add 6 to the number set. Current number set: [6, 38], target: 28, just two numbers left.\n     |- Try 38 + 6 = 44. Evaluate 44 != 28, drop this branch.\n     |- Try 38 - 6 = 32. Evaluate 32 != 28, drop this branch.\n     |- Try 38 * 6 = 228. Evaluate 228 != 28, drop this branch.\n     |- Try 38 \/ 6 = 6.3. 6.3 is a decimal, drop this branch.\n    |- Try 4 - 2 = 2. Add 2 to the number set. Current number set: [2, 38], target: 28, just two numbers left.\n     |- Try 38 + 2 = 40. Evaluate 40 != 28, drop this branch.\n     |- Try 38 - 2 = 36. Evaluate 36 != 28, drop this branch.\n     |- Try 38 * 2 = 76. Evaluate 76 != 28, drop this branch.\n     |- Try 38 \/ 2 = 19. Evaluate 19 != 28, drop this branch.\n    |- Try 4 * 2 = 8. Add 8 to the number set. Current number set: [8, 38], target: 28, just two numbers left.\n     |- Try 38 + 8 = 46. Evaluate 46 != 28, drop this branch.\n     |- Try 38 - 8 = 30. Evaluate 30 != 28, drop this branch.\n     |- Try 38 * 8 = 304. Evaluate 304 != 28, drop this branch.\n     |- Try 38 \/ 8 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 4 \/ 2 = 2. Add 2 to the number set. Current number set: [2, 38], target: 28, just two numbers left.\n     |- Try 38 + 2 = 40. Evaluate 40 != 28, drop this branch.\n     |- Try 38 - 2 = 36. Evaluate 36 != 28, drop this branch.\n     |- Try 38 * 2 = 76. Evaluate 76 != 28, drop this branch.\n     |- Try 38 \/ 2 = 19. Evaluate 19 != 28, drop this branch.\n  |- Try 29 - 9 = 20. Add 20 to the number set. Current number set: [20, 4, 2], target: 28. Options for choosing two numbers: [(20, 4), (20, 2), (4, 2)].\n   |- Pick two numbers (20, 4) (numbers left: [2]). Try possible operations.\n    |- Try 20 + 4 = 24. Add 24 to the number set. Current number set: [24, 2], target: 28, just two numbers left.\n     |- Try 24 + 2 = 26. Evaluate 26 != 28, drop this branch.\n     |- Try 24 - 2 = 22. Evaluate 22 != 28, drop this branch.\n     |- Try 24 * 2 = 48. Evaluate 48 != 28, drop this branch.\n     |- Try 24 \/ 2 = 12. Evaluate 12 != 28, drop this branch.\n    |- Try 20 - 4 = 16. Add 16 to the number set. Current number set: [16, 2], target: 28, just two numbers left.\n     |- Try 16 + 2 = 18. Evaluate 18 != 28, drop this branch.\n     |- Try 16 - 2 = 14. Evaluate 14 != 28, drop this branch.\n     |- Try 16 * 2 = 32. Evaluate 32 != 28, drop this branch.\n     |- Try 16 \/ 2 = 8. Evaluate 8 != 28, drop this branch.\n    |- Try 20 * 4 = 80. Add 80 to the number set. Current number set: [80, 2], target: 28, just two numbers left.\n     |- Try 80 + 2 = 82. Evaluate 82 != 28, drop this branch.\n     |- Try 80 - 2 = 78. Evaluate 78 != 28, drop this branch.\n     |- Try 80 * 2 = 160. Evaluate 160 != 28, drop this branch.\n     |- Try 80 \/ 2 = 40. Evaluate 40 != 28, drop this branch.\n    |- Try 20 \/ 4 = 5. Add 5 to the number set. Current number set: [5, 2], target: 28, just two numbers left.\n     |- Try 5 + 2 = 7. Evaluate 7 != 28, drop this branch.\n     |- Try 5 - 2 = 3. Evaluate 3 != 28, drop this branch.\n     |- Try 5 * 2 = 10. Evaluate 10 != 28, drop this branch.\n     |- Try 5 \/ 2 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (20, 2) (numbers left: [4]). Try possible operations.\n    |- Try 20 + 2 = 22. Add 22 to the number set. Current number set: [22, 4], target: 28, just two numbers left.\n     |- Try 22 + 4 = 26. Evaluate 26 != 28, drop this branch.\n     |- Try 22 - 4 = 18. Evaluate 18 != 28, drop this branch.\n     |- Try 22 * 4 = 88. Evaluate 88 != 28, drop this branch.\n     |- Try 22 \/ 4 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 20 - 2 = 18. Add 18 to the number set. Current number set: [18, 4], target: 28, just two numbers left.\n     |- Try 18 + 4 = 22. Evaluate 22 != 28, drop this branch.\n     |- Try 18 - 4 = 14. Evaluate 14 != 28, drop this branch.\n     |- Try 18 * 4 = 72. Evaluate 72 != 28, drop this branch.\n     |- Try 18 \/ 4 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 20 * 2 = 40. Add 40 to the number set. Current number set: [40, 4], target: 28, just two numbers left.\n     |- Try 40 + 4 = 44. Evaluate 44 != 28, drop this branch.\n     |- Try 40 - 4 = 36. Evaluate 36 != 28, drop this branch.\n     |- Try 40 * 4 = 160. Evaluate 160 != 28, drop this branch.\n     |- Try 40 \/ 4 = 10. Evaluate 10 != 28, drop this branch.\n    |- Try 20 \/ 2 = 10. Add 10 to the number set. Current number set: [10, 4], target: 28, just two numbers left.\n     |- Try 10 + 4 = 14. Evaluate 14 != 28, drop this branch.\n     |- Try 10 - 4 = 6. Evaluate 6 != 28, drop this branch.\n     |- Try 10 * 4 = 40. Evaluate 40 != 28, drop this branch.\n     |- Try 10 \/ 4 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (4, 2) (numbers left: [20]). Try possible operations.\n    |- Try 4 + 2 = 6. Add 6 to the number set. Current number set: [6, 20], target: 28, just two numbers left.\n     |- Try 20 + 6 = 26. Evaluate 26 != 28, drop this branch.\n     |- Try 20 - 6 = 14. Evaluate 14 != 28, drop this branch.\n     |- Try 20 * 6 = 120. Evaluate 120 != 28, drop this branch.\n     |- Try 20 \/ 6 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 4 - 2 = 2. Add 2 to the number set. Current number set: [2, 20], target: 28, just two numbers left.\n     |- Try 20 + 2 = 22. Evaluate 22 != 28, drop this branch.\n     |- Try 20 - 2 = 18. Evaluate 18 != 28, drop this branch.\n     |- Try 20 * 2 = 40. Evaluate 40 != 28, drop this branch.\n     |- Try 20 \/ 2 = 10. Evaluate 10 != 28, drop this branch.\n    |- Try 4 * 2 = 8. Add 8 to the number set. Current number set: [8, 20], target: 28, just two numbers left.\n     |- Try 20 + 8 = 28. Evaluate 28 == 28, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 20 + 8 = 28\nThe step before: 4 * 2 = 8\nThe first step: 29 - 9 = 20\n\nOutput the solution in the required format:\n<Solution>\n29 - 9 = 20\n4 * 2 = 8\n20 + 8 = 28\n<\/Solution>\n","item":{"nums":[29,4,9,2],"solution":["29 - 9 = 20","4 * 2 = 8","20 + 8 = 28"],"target":28}}
+{"instance_id":"countdown_8k_81","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [5, 31, 8, 23]\nTarget: 29","reference_output":"# Search Procedure\nInitial number set: [5, 31, 8, 23], target: 29. Options for choosing two numbers: [(5, 31), (5, 8), (5, 23), (31, 8), (31, 23), (8, 23)].\n |- Pick two numbers (5, 31) (numbers left: [8, 23]). Try possible operations.\n  |- Try 31 + 5 = 36. Add 36 to the number set. Current number set: [36, 8, 23], target: 29. Options for choosing two numbers: [(36, 8), (36, 23), (8, 23)].\n   |- Pick two numbers (36, 8) (numbers left: [23]). Try possible operations.\n    |- Try 36 + 8 = 44. Add 44 to the number set. Current number set: [44, 23], target: 29, just two numbers left.\n     |- Try 44 + 23 = 67. Evaluate 67 != 29, drop this branch.\n     |- Try 44 - 23 = 21. Evaluate 21 != 29, drop this branch.\n     |- Try 44 * 23 = 1012. Evaluate 1012 != 29, drop this branch.\n     |- Try 44 \/ 23 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 36 - 8 = 28. Add 28 to the number set. Current number set: [28, 23], target: 29, just two numbers left.\n     |- Try 28 + 23 = 51. Evaluate 51 != 29, drop this branch.\n     |- Try 28 - 23 = 5. Evaluate 5 != 29, drop this branch.\n     |- Try 28 * 23 = 644. Evaluate 644 != 29, drop this branch.\n     |- Try 28 \/ 23 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 36 * 8 = 288. Add 288 to the number set. Current number set: [288, 23], target: 29, just two numbers left.\n     |- Try 288 + 23 = 311. Evaluate 311 != 29, drop this branch.\n     |- Try 288 - 23 = 265. Evaluate 265 != 29, drop this branch.\n     |- Try 288 * 23 = 6624. 6624 exceeds the maximum intermediate result, drop this branch.\n     |- Try 288 \/ 23 = 12.5. 12.5 is a decimal, drop this branch.\n    |- Try 36 \/ 8 = 4.5. 4.5 is a decimal, drop this branch.\n   |- Pick two numbers (36, 23) (numbers left: [8]). Try possible operations.\n    |- Try 36 + 23 = 59. Add 59 to the number set. Current number set: [59, 8], target: 29, just two numbers left.\n     |- Try 59 + 8 = 67. Evaluate 67 != 29, drop this branch.\n     |- Try 59 - 8 = 51. Evaluate 51 != 29, drop this branch.\n     |- Try 59 * 8 = 472. Evaluate 472 != 29, drop this branch.\n     |- Try 59 \/ 8 = 7.4. 7.4 is a decimal, drop this branch.\n    |- Try 36 - 23 = 13. Add 13 to the number set. Current number set: [13, 8], target: 29, just two numbers left.\n     |- Try 13 + 8 = 21. Evaluate 21 != 29, drop this branch.\n     |- Try 13 - 8 = 5. Evaluate 5 != 29, drop this branch.\n     |- Try 13 * 8 = 104. Evaluate 104 != 29, drop this branch.\n     |- Try 13 \/ 8 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 36 * 23 = 828. Add 828 to the number set. Current number set: [828, 8], target: 29, just two numbers left.\n     |- Try 828 + 8 = 836. Evaluate 836 != 29, drop this branch.\n     |- Try 828 - 8 = 820. Evaluate 820 != 29, drop this branch.\n     |- Try 828 * 8 = 6624. 6624 exceeds the maximum intermediate result, drop this branch.\n     |- Try 828 \/ 8 = 103.5. 103.5 is a decimal, drop this branch.\n    |- Try 36 \/ 23 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (8, 23) (numbers left: [36]). Try possible operations.\n    |- Try 23 + 8 = 31. Add 31 to the number set. Current number set: [31, 36], target: 29, just two numbers left.\n     |- Try 36 + 31 = 67. Evaluate 67 != 29, drop this branch.\n     |- Try 36 - 31 = 5. Evaluate 5 != 29, drop this branch.\n     |- Try 36 * 31 = 1116. Evaluate 1116 != 29, drop this branch.\n     |- Try 36 \/ 31 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 23 - 8 = 15. Add 15 to the number set. Current number set: [15, 36], target: 29, just two numbers left.\n     |- Try 36 + 15 = 51. Evaluate 51 != 29, drop this branch.\n     |- Try 36 - 15 = 21. Evaluate 21 != 29, drop this branch.\n     |- Try 36 * 15 = 540. Evaluate 540 != 29, drop this branch.\n     |- Try 36 \/ 15 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 23 * 8 = 184. Add 184 to the number set. Current number set: [184, 36], target: 29, just two numbers left.\n     |- Try 184 + 36 = 220. Evaluate 220 != 29, drop this branch.\n     |- Try 184 - 36 = 148. Evaluate 148 != 29, drop this branch.\n     |- Try 184 * 36 = 6624. 6624 exceeds the maximum intermediate result, drop this branch.\n     |- Try 184 \/ 36 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 23 \/ 8 = 2.9. 2.9 is a decimal, drop this branch.\n  |- Try 31 - 5 = 26. Add 26 to the number set. Current number set: [26, 8, 23], target: 29. Options for choosing two numbers: [(26, 8), (26, 23), (8, 23)].\n   |- Pick two numbers (26, 8) (numbers left: [23]). Try possible operations.\n    |- Try 26 + 8 = 34. Add 34 to the number set. Current number set: [34, 23], target: 29, just two numbers left.\n     |- Try 34 + 23 = 57. Evaluate 57 != 29, drop this branch.\n     |- Try 34 - 23 = 11. Evaluate 11 != 29, drop this branch.\n     |- Try 34 * 23 = 782. Evaluate 782 != 29, drop this branch.\n     |- Try 34 \/ 23 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 26 - 8 = 18. Add 18 to the number set. Current number set: [18, 23], target: 29, just two numbers left.\n     |- Try 23 + 18 = 41. Evaluate 41 != 29, drop this branch.\n     |- Try 23 - 18 = 5. Evaluate 5 != 29, drop this branch.\n     |- Try 23 * 18 = 414. Evaluate 414 != 29, drop this branch.\n     |- Try 23 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 26 * 8 = 208. Add 208 to the number set. Current number set: [208, 23], target: 29, just two numbers left.\n     |- Try 208 + 23 = 231. Evaluate 231 != 29, drop this branch.\n     |- Try 208 - 23 = 185. Evaluate 185 != 29, drop this branch.\n     |- Try 208 * 23 = 4784. 4784 exceeds the maximum intermediate result, drop this branch.\n     |- Try 208 \/ 23 = 9.0. 9.0 is a decimal, drop this branch.\n    |- Try 26 \/ 8 = 3.2. 3.2 is a decimal, drop this branch.\n   |- Pick two numbers (26, 23) (numbers left: [8]). Try possible operations.\n    |- Try 26 + 23 = 49. Add 49 to the number set. Current number set: [49, 8], target: 29, just two numbers left.\n     |- Try 49 + 8 = 57. Evaluate 57 != 29, drop this branch.\n     |- Try 49 - 8 = 41. Evaluate 41 != 29, drop this branch.\n     |- Try 49 * 8 = 392. Evaluate 392 != 29, drop this branch.\n     |- Try 49 \/ 8 = 6.1. 6.1 is a decimal, drop this branch.\n    |- Try 26 - 23 = 3. Add 3 to the number set. Current number set: [3, 8], target: 29, just two numbers left.\n     |- Try 8 + 3 = 11. Evaluate 11 != 29, drop this branch.\n     |- Try 8 - 3 = 5. Evaluate 5 != 29, drop this branch.\n     |- Try 8 * 3 = 24. Evaluate 24 != 29, drop this branch.\n     |- Try 8 \/ 3 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 26 * 23 = 598. Add 598 to the number set. Current number set: [598, 8], target: 29, just two numbers left.\n     |- Try 598 + 8 = 606. Evaluate 606 != 29, drop this branch.\n     |- Try 598 - 8 = 590. Evaluate 590 != 29, drop this branch.\n     |- Try 598 * 8 = 4784. 4784 exceeds the maximum intermediate result, drop this branch.\n     |- Try 598 \/ 8 = 74.8. 74.8 is a decimal, drop this branch.\n    |- Try 26 \/ 23 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (8, 23) (numbers left: [26]). Try possible operations.\n    |- Try 23 + 8 = 31. Add 31 to the number set. Current number set: [31, 26], target: 29, just two numbers left.\n     |- Try 31 + 26 = 57. Evaluate 57 != 29, drop this branch.\n     |- Try 31 - 26 = 5. Evaluate 5 != 29, drop this branch.\n     |- Try 31 * 26 = 806. Evaluate 806 != 29, drop this branch.\n     |- Try 31 \/ 26 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 23 - 8 = 15. Add 15 to the number set. Current number set: [15, 26], target: 29, just two numbers left.\n     |- Try 26 + 15 = 41. Evaluate 41 != 29, drop this branch.\n     |- Try 26 - 15 = 11. Evaluate 11 != 29, drop this branch.\n     |- Try 26 * 15 = 390. Evaluate 390 != 29, drop this branch.\n     |- Try 26 \/ 15 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 23 * 8 = 184. Add 184 to the number set. Current number set: [184, 26], target: 29, just two numbers left.\n     |- Try 184 + 26 = 210. Evaluate 210 != 29, drop this branch.\n     |- Try 184 - 26 = 158. Evaluate 158 != 29, drop this branch.\n     |- Try 184 * 26 = 4784. 4784 exceeds the maximum intermediate result, drop this branch.\n     |- Try 184 \/ 26 = 7.1. 7.1 is a decimal, drop this branch.\n    |- Try 23 \/ 8 = 2.9. 2.9 is a decimal, drop this branch.\n  |- Try 31 * 5 = 155. Add 155 to the number set. Current number set: [155, 8, 23], target: 29. Options for choosing two numbers: [(155, 8), (155, 23), (8, 23)].\n   |- Pick two numbers (155, 8) (numbers left: [23]). Try possible operations.\n    |- Try 155 + 8 = 163. Add 163 to the number set. Current number set: [163, 23], target: 29, just two numbers left.\n     |- Try 163 + 23 = 186. Evaluate 186 != 29, drop this branch.\n     |- Try 163 - 23 = 140. Evaluate 140 != 29, drop this branch.\n     |- Try 163 * 23 = 3749. 3749 exceeds the maximum intermediate result, drop this branch.\n     |- Try 163 \/ 23 = 7.1. 7.1 is a decimal, drop this branch.\n    |- Try 155 - 8 = 147. Add 147 to the number set. Current number set: [147, 23], target: 29, just two numbers left.\n     |- Try 147 + 23 = 170. Evaluate 170 != 29, drop this branch.\n     |- Try 147 - 23 = 124. Evaluate 124 != 29, drop this branch.\n     |- Try 147 * 23 = 3381. 3381 exceeds the maximum intermediate result, drop this branch.\n     |- Try 147 \/ 23 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 155 * 8 = 1240. Add 1240 to the number set. Current number set: [1240, 23], target: 29, just two numbers left.\n     |- Try 1240 + 23 = 1263. Evaluate 1263 != 29, drop this branch.\n     |- Try 1240 - 23 = 1217. Evaluate 1217 != 29, drop this branch.\n     |- Try 1240 * 23 = 28520. 28520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1240 \/ 23 = 53.9. 53.9 is a decimal, drop this branch.\n    |- Try 155 \/ 8 = 19.4. 19.4 is a decimal, drop this branch.\n   |- Pick two numbers (155, 23) (numbers left: [8]). Try possible operations.\n    |- Try 155 + 23 = 178. Add 178 to the number set. Current number set: [178, 8], target: 29, just two numbers left.\n     |- Try 178 + 8 = 186. Evaluate 186 != 29, drop this branch.\n     |- Try 178 - 8 = 170. Evaluate 170 != 29, drop this branch.\n     |- Try 178 * 8 = 1424. Evaluate 1424 != 29, drop this branch.\n     |- Try 178 \/ 8 = 22.2. 22.2 is a decimal, drop this branch.\n    |- Try 155 - 23 = 132. Add 132 to the number set. Current number set: [132, 8], target: 29, just two numbers left.\n     |- Try 132 + 8 = 140. Evaluate 140 != 29, drop this branch.\n     |- Try 132 - 8 = 124. Evaluate 124 != 29, drop this branch.\n     |- Try 132 * 8 = 1056. Evaluate 1056 != 29, drop this branch.\n     |- Try 132 \/ 8 = 16.5. 16.5 is a decimal, drop this branch.\n    |- Try 155 * 23 = 3565. 3565 exceeds the maximum intermediate result, drop this branch.\n    |- Try 155 \/ 23 = 6.7. 6.7 is a decimal, drop this branch.\n   |- Pick two numbers (8, 23) (numbers left: [155]). Try possible operations.\n    |- Try 23 + 8 = 31. Add 31 to the number set. Current number set: [31, 155], target: 29, just two numbers left.\n     |- Try 155 + 31 = 186. Evaluate 186 != 29, drop this branch.\n     |- Try 155 - 31 = 124. Evaluate 124 != 29, drop this branch.\n     |- Try 155 * 31 = 4805. 4805 exceeds the maximum intermediate result, drop this branch.\n     |- Try 155 \/ 31 = 5. Evaluate 5 != 29, drop this branch.\n    |- Try 23 - 8 = 15. Add 15 to the number set. Current number set: [15, 155], target: 29, just two numbers left.\n     |- Try 155 + 15 = 170. Evaluate 170 != 29, drop this branch.\n     |- Try 155 - 15 = 140. Evaluate 140 != 29, drop this branch.\n     |- Try 155 * 15 = 2325. 2325 exceeds the maximum intermediate result, drop this branch.\n     |- Try 155 \/ 15 = 10.3. 10.3 is a decimal, drop this branch.\n    |- Try 23 * 8 = 184. Add 184 to the number set. Current number set: [184, 155], target: 29, just two numbers left.\n     |- Try 184 + 155 = 339. Evaluate 339 != 29, drop this branch.\n     |- Try 184 - 155 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 184 - 155 = 29\nThe step before: 23 * 8 = 184\nThe first step: 31 * 5 = 155\n\nOutput the solution in the required format:\n<Solution>\n31 * 5 = 155\n23 * 8 = 184\n184 - 155 = 29\n<\/Solution>\n","item":{"nums":[5,31,8,23],"solution":["31 * 5 = 155","23 * 8 = 184","184 - 155 = 29"],"target":29}}
+{"instance_id":"countdown_8k_82","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [19, 43, 9, 9]\nTarget: 47","reference_output":"# Search Procedure\nInitial number set: [19, 43, 9, 9], target: 47. Options for choosing two numbers: [(19, 43), (19, 9), (19, 9), (43, 9), (43, 9), (9, 9)].\n |- Pick two numbers (19, 43) (numbers left: [9, 9]). Try possible operations.\n  |- Try 43 + 19 = 62. Add 62 to the number set. Current number set: [62, 9, 9], target: 47. Options for choosing two numbers: [(62, 9), (62, 9), (9, 9)].\n   |- Pick two numbers (62, 9) (numbers left: [9]). Try possible operations.\n    |- Try 62 + 9 = 71. Add 71 to the number set. Current number set: [71, 9], target: 47, just two numbers left.\n     |- Try 71 + 9 = 80. Evaluate 80 != 47, drop this branch.\n     |- Try 71 - 9 = 62. Evaluate 62 != 47, drop this branch.\n     |- Try 71 * 9 = 639. Evaluate 639 != 47, drop this branch.\n     |- Try 71 \/ 9 = 7.9. 7.9 is a decimal, drop this branch.\n    |- Try 62 - 9 = 53. Add 53 to the number set. Current number set: [53, 9], target: 47, just two numbers left.\n     |- Try 53 + 9 = 62. Evaluate 62 != 47, drop this branch.\n     |- Try 53 - 9 = 44. Evaluate 44 != 47, drop this branch.\n     |- Try 53 * 9 = 477. Evaluate 477 != 47, drop this branch.\n     |- Try 53 \/ 9 = 5.9. 5.9 is a decimal, drop this branch.\n    |- Try 62 * 9 = 558. Add 558 to the number set. Current number set: [558, 9], target: 47, just two numbers left.\n     |- Try 558 + 9 = 567. Evaluate 567 != 47, drop this branch.\n     |- Try 558 - 9 = 549. Evaluate 549 != 47, drop this branch.\n     |- Try 558 * 9 = 5022. 5022 exceeds the maximum intermediate result, drop this branch.\n     |- Try 558 \/ 9 = 62. Evaluate 62 != 47, drop this branch.\n    |- Try 62 \/ 9 = 6.9. 6.9 is a decimal, drop this branch.\n   |- Pick two numbers (62, 9) (numbers left: [9]). Try possible operations.\n    |- Try 62 + 9 = 71. Add 71 to the number set. Current number set: [71, 9], target: 47, just two numbers left.\n     |- Try 71 + 9 = 80. Evaluate 80 != 47, drop this branch.\n     |- Try 71 - 9 = 62. Evaluate 62 != 47, drop this branch.\n     |- Try 71 * 9 = 639. Evaluate 639 != 47, drop this branch.\n     |- Try 71 \/ 9 = 7.9. 7.9 is a decimal, drop this branch.\n    |- Try 62 - 9 = 53. Add 53 to the number set. Current number set: [53, 9], target: 47, just two numbers left.\n     |- Try 53 + 9 = 62. Evaluate 62 != 47, drop this branch.\n     |- Try 53 - 9 = 44. Evaluate 44 != 47, drop this branch.\n     |- Try 53 * 9 = 477. Evaluate 477 != 47, drop this branch.\n     |- Try 53 \/ 9 = 5.9. 5.9 is a decimal, drop this branch.\n    |- Try 62 * 9 = 558. Add 558 to the number set. Current number set: [558, 9], target: 47, just two numbers left.\n     |- Try 558 + 9 = 567. Evaluate 567 != 47, drop this branch.\n     |- Try 558 - 9 = 549. Evaluate 549 != 47, drop this branch.\n     |- Try 558 * 9 = 5022. 5022 exceeds the maximum intermediate result, drop this branch.\n     |- Try 558 \/ 9 = 62. Evaluate 62 != 47, drop this branch.\n    |- Try 62 \/ 9 = 6.9. 6.9 is a decimal, drop this branch.\n   |- Pick two numbers (9, 9) (numbers left: [62]). Try possible operations.\n    |- Try 9 + 9 = 18. Add 18 to the number set. Current number set: [18, 62], target: 47, just two numbers left.\n     |- Try 62 + 18 = 80. Evaluate 80 != 47, drop this branch.\n     |- Try 62 - 18 = 44. Evaluate 44 != 47, drop this branch.\n     |- Try 62 * 18 = 1116. Evaluate 1116 != 47, drop this branch.\n     |- Try 62 \/ 18 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 9 - 9 = 0. Add 0 to the number set. Current number set: [0, 62], target: 47, just two numbers left.\n     |- Try 62 + 0 = 62. Evaluate 62 != 47, drop this branch.\n     |- Try 62 - 0 = 62. Evaluate 62 != 47, drop this branch.\n     |- Try 62 * 0 = 0. Evaluate 0 != 47, drop this branch.\n     |- Try 62 \/ 0 (invalid operation). drop this branch.\n    |- Try 9 * 9 = 81. Add 81 to the number set. Current number set: [81, 62], target: 47, just two numbers left.\n     |- Try 81 + 62 = 143. Evaluate 143 != 47, drop this branch.\n     |- Try 81 - 62 = 19. Evaluate 19 != 47, drop this branch.\n     |- Try 81 * 62 = 5022. 5022 exceeds the maximum intermediate result, drop this branch.\n     |- Try 81 \/ 62 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 9 \/ 9 = 1. Add 1 to the number set. Current number set: [1, 62], target: 47, just two numbers left.\n     |- Try 62 + 1 = 63. Evaluate 63 != 47, drop this branch.\n     |- Try 62 - 1 = 61. Evaluate 61 != 47, drop this branch.\n     |- Try 62 * 1 = 62. Evaluate 62 != 47, drop this branch.\n     |- Try 62 \/ 1 = 62. Evaluate 62 != 47, drop this branch.\n  |- Try 43 - 19 = 24. Add 24 to the number set. Current number set: [24, 9, 9], target: 47. Options for choosing two numbers: [(24, 9), (24, 9), (9, 9)].\n   |- Pick two numbers (24, 9) (numbers left: [9]). Try possible operations.\n    |- Try 24 + 9 = 33. Add 33 to the number set. Current number set: [33, 9], target: 47, just two numbers left.\n     |- Try 33 + 9 = 42. Evaluate 42 != 47, drop this branch.\n     |- Try 33 - 9 = 24. Evaluate 24 != 47, drop this branch.\n     |- Try 33 * 9 = 297. Evaluate 297 != 47, drop this branch.\n     |- Try 33 \/ 9 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 24 - 9 = 15. Add 15 to the number set. Current number set: [15, 9], target: 47, just two numbers left.\n     |- Try 15 + 9 = 24. Evaluate 24 != 47, drop this branch.\n     |- Try 15 - 9 = 6. Evaluate 6 != 47, drop this branch.\n     |- Try 15 * 9 = 135. Evaluate 135 != 47, drop this branch.\n     |- Try 15 \/ 9 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 24 * 9 = 216. Add 216 to the number set. Current number set: [216, 9], target: 47, just two numbers left.\n     |- Try 216 + 9 = 225. Evaluate 225 != 47, drop this branch.\n     |- Try 216 - 9 = 207. Evaluate 207 != 47, drop this branch.\n     |- Try 216 * 9 = 1944. Evaluate 1944 != 47, drop this branch.\n     |- Try 216 \/ 9 = 24. Evaluate 24 != 47, drop this branch.\n    |- Try 24 \/ 9 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (24, 9) (numbers left: [9]). Try possible operations.\n    |- Try 24 + 9 = 33. Add 33 to the number set. Current number set: [33, 9], target: 47, just two numbers left.\n     |- Try 33 + 9 = 42. Evaluate 42 != 47, drop this branch.\n     |- Try 33 - 9 = 24. Evaluate 24 != 47, drop this branch.\n     |- Try 33 * 9 = 297. Evaluate 297 != 47, drop this branch.\n     |- Try 33 \/ 9 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 24 - 9 = 15. Add 15 to the number set. Current number set: [15, 9], target: 47, just two numbers left.\n     |- Try 15 + 9 = 24. Evaluate 24 != 47, drop this branch.\n     |- Try 15 - 9 = 6. Evaluate 6 != 47, drop this branch.\n     |- Try 15 * 9 = 135. Evaluate 135 != 47, drop this branch.\n     |- Try 15 \/ 9 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 24 * 9 = 216. Add 216 to the number set. Current number set: [216, 9], target: 47, just two numbers left.\n     |- Try 216 + 9 = 225. Evaluate 225 != 47, drop this branch.\n     |- Try 216 - 9 = 207. Evaluate 207 != 47, drop this branch.\n     |- Try 216 * 9 = 1944. Evaluate 1944 != 47, drop this branch.\n     |- Try 216 \/ 9 = 24. Evaluate 24 != 47, drop this branch.\n    |- Try 24 \/ 9 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (9, 9) (numbers left: [24]). Try possible operations.\n    |- Try 9 + 9 = 18. Add 18 to the number set. Current number set: [18, 24], target: 47, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 47, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 47, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 47, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 9 - 9 = 0. Add 0 to the number set. Current number set: [0, 24], target: 47, just two numbers left.\n     |- Try 24 + 0 = 24. Evaluate 24 != 47, drop this branch.\n     |- Try 24 - 0 = 24. Evaluate 24 != 47, drop this branch.\n     |- Try 24 * 0 = 0. Evaluate 0 != 47, drop this branch.\n     |- Try 24 \/ 0 (invalid operation). drop this branch.\n    |- Try 9 * 9 = 81. Add 81 to the number set. Current number set: [81, 24], target: 47, just two numbers left.\n     |- Try 81 + 24 = 105. Evaluate 105 != 47, drop this branch.\n     |- Try 81 - 24 = 57. Evaluate 57 != 47, drop this branch.\n     |- Try 81 * 24 = 1944. Evaluate 1944 != 47, drop this branch.\n     |- Try 81 \/ 24 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 9 \/ 9 = 1. Add 1 to the number set. Current number set: [1, 24], target: 47, just two numbers left.\n     |- Try 24 + 1 = 25. Evaluate 25 != 47, drop this branch.\n     |- Try 24 - 1 = 23. Evaluate 23 != 47, drop this branch.\n     |- Try 24 * 1 = 24. Evaluate 24 != 47, drop this branch.\n     |- Try 24 \/ 1 = 24. Evaluate 24 != 47, drop this branch.\n  |- Try 43 * 19 = 817. Add 817 to the number set. Current number set: [817, 9, 9], target: 47. Options for choosing two numbers: [(817, 9), (817, 9), (9, 9)].\n   |- Pick two numbers (817, 9) (numbers left: [9]). Try possible operations.\n    |- Try 817 + 9 = 826. Add 826 to the number set. Current number set: [826, 9], target: 47, just two numbers left.\n     |- Try 826 + 9 = 835. Evaluate 835 != 47, drop this branch.\n     |- Try 826 - 9 = 817. Evaluate 817 != 47, drop this branch.\n     |- Try 826 * 9 = 7434. 7434 exceeds the maximum intermediate result, drop this branch.\n     |- Try 826 \/ 9 = 91.8. 91.8 is a decimal, drop this branch.\n    |- Try 817 - 9 = 808. Add 808 to the number set. Current number set: [808, 9], target: 47, just two numbers left.\n     |- Try 808 + 9 = 817. Evaluate 817 != 47, drop this branch.\n     |- Try 808 - 9 = 799. Evaluate 799 != 47, drop this branch.\n     |- Try 808 * 9 = 7272. 7272 exceeds the maximum intermediate result, drop this branch.\n     |- Try 808 \/ 9 = 89.8. 89.8 is a decimal, drop this branch.\n    |- Try 817 * 9 = 7353. 7353 exceeds the maximum intermediate result, drop this branch.\n    |- Try 817 \/ 9 = 90.8. 90.8 is a decimal, drop this branch.\n   |- Pick two numbers (817, 9) (numbers left: [9]). Try possible operations.\n    |- Try 817 + 9 = 826. Add 826 to the number set. Current number set: [826, 9], target: 47, just two numbers left.\n     |- Try 826 + 9 = 835. Evaluate 835 != 47, drop this branch.\n     |- Try 826 - 9 = 817. Evaluate 817 != 47, drop this branch.\n     |- Try 826 * 9 = 7434. 7434 exceeds the maximum intermediate result, drop this branch.\n     |- Try 826 \/ 9 = 91.8. 91.8 is a decimal, drop this branch.\n    |- Try 817 - 9 = 808. Add 808 to the number set. Current number set: [808, 9], target: 47, just two numbers left.\n     |- Try 808 + 9 = 817. Evaluate 817 != 47, drop this branch.\n     |- Try 808 - 9 = 799. Evaluate 799 != 47, drop this branch.\n     |- Try 808 * 9 = 7272. 7272 exceeds the maximum intermediate result, drop this branch.\n     |- Try 808 \/ 9 = 89.8. 89.8 is a decimal, drop this branch.\n    |- Try 817 * 9 = 7353. 7353 exceeds the maximum intermediate result, drop this branch.\n    |- Try 817 \/ 9 = 90.8. 90.8 is a decimal, drop this branch.\n   |- Pick two numbers (9, 9) (numbers left: [817]). Try possible operations.\n    |- Try 9 + 9 = 18. Add 18 to the number set. Current number set: [18, 817], target: 47, just two numbers left.\n     |- Try 817 + 18 = 835. Evaluate 835 != 47, drop this branch.\n     |- Try 817 - 18 = 799. Evaluate 799 != 47, drop this branch.\n     |- Try 817 * 18 = 14706. 14706 exceeds the maximum intermediate result, drop this branch.\n     |- Try 817 \/ 18 = 45.4. 45.4 is a decimal, drop this branch.\n    |- Try 9 - 9 = 0. Add 0 to the number set. Current number set: [0, 817], target: 47, just two numbers left.\n     |- Try 817 + 0 = 817. Evaluate 817 != 47, drop this branch.\n     |- Try 817 - 0 = 817. Evaluate 817 != 47, drop this branch.\n     |- Try 817 * 0 = 0. Evaluate 0 != 47, drop this branch.\n     |- Try 817 \/ 0 (invalid operation). drop this branch.\n    |- Try 9 * 9 = 81. Add 81 to the number set. Current number set: [81, 817], target: 47, just two numbers left.\n     |- Try 817 + 81 = 898. Evaluate 898 != 47, drop this branch.\n     |- Try 817 - 81 = 736. Evaluate 736 != 47, drop this branch.\n     |- Try 817 * 81 = 66177. 66177 exceeds the maximum intermediate result, drop this branch.\n     |- Try 817 \/ 81 = 10.1. 10.1 is a decimal, drop this branch.\n    |- Try 9 \/ 9 = 1. Add 1 to the number set. Current number set: [1, 817], target: 47, just two numbers left.\n     |- Try 817 + 1 = 818. Evaluate 818 != 47, drop this branch.\n     |- Try 817 - 1 = 816. Evaluate 816 != 47, drop this branch.\n     |- Try 817 * 1 = 817. Evaluate 817 != 47, drop this branch.\n     |- Try 817 \/ 1 = 817. Evaluate 817 != 47, drop this branch.\n  |- Try 43 \/ 19 = 2.3. 2.3 is a decimal, drop this branch.\n |- Pick two numbers (19, 9) (numbers left: [43, 9]). Try possible operations.\n  |- Try 19 + 9 = 28. Add 28 to the number set. Current number set: [28, 43, 9], target: 47. Options for choosing two numbers: [(28, 43), (28, 9), (43, 9)].\n   |- Pick two numbers (28, 43) (numbers left: [9]). Try possible operations.\n    |- Try 43 + 28 = 71. Add 71 to the number set. Current number set: [71, 9], target: 47, just two numbers left.\n     |- Try 71 + 9 = 80. Evaluate 80 != 47, drop this branch.\n     |- Try 71 - 9 = 62. Evaluate 62 != 47, drop this branch.\n     |- Try 71 * 9 = 639. Evaluate 639 != 47, drop this branch.\n     |- Try 71 \/ 9 = 7.9. 7.9 is a decimal, drop this branch.\n    |- Try 43 - 28 = 15. Add 15 to the number set. Current number set: [15, 9], target: 47, just two numbers left.\n     |- Try 15 + 9 = 24. Evaluate 24 != 47, drop this branch.\n     |- Try 15 - 9 = 6. Evaluate 6 != 47, drop this branch.\n     |- Try 15 * 9 = 135. Evaluate 135 != 47, drop this branch.\n     |- Try 15 \/ 9 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 43 * 28 = 1204. Add 1204 to the number set. Current number set: [1204, 9], target: 47, just two numbers left.\n     |- Try 1204 + 9 = 1213. Evaluate 1213 != 47, drop this branch.\n     |- Try 1204 - 9 = 1195. Evaluate 1195 != 47, drop this branch.\n     |- Try 1204 * 9 = 10836. 10836 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1204 \/ 9 = 133.8. 133.8 is a decimal, drop this branch.\n    |- Try 43 \/ 28 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (28, 9) (numbers left: [43]). Try possible operations.\n    |- Try 28 + 9 = 37. Add 37 to the number set. Current number set: [37, 43], target: 47, just two numbers left.\n     |- Try 43 + 37 = 80. Evaluate 80 != 47, drop this branch.\n     |- Try 43 - 37 = 6. Evaluate 6 != 47, drop this branch.\n     |- Try 43 * 37 = 1591. Evaluate 1591 != 47, drop this branch.\n     |- Try 43 \/ 37 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 28 - 9 = 19. Add 19 to the number set. Current number set: [19, 43], target: 47, just two numbers left.\n     |- Try 43 + 19 = 62. Evaluate 62 != 47, drop this branch.\n     |- Try 43 - 19 = 24. Evaluate 24 != 47, drop this branch.\n     |- Try 43 * 19 = 817. Evaluate 817 != 47, drop this branch.\n     |- Try 43 \/ 19 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 28 * 9 = 252. Add 252 to the number set. Current number set: [252, 43], target: 47, just two numbers left.\n     |- Try 252 + 43 = 295. Evaluate 295 != 47, drop this branch.\n     |- Try 252 - 43 = 209. Evaluate 209 != 47, drop this branch.\n     |- Try 252 * 43 = 10836. 10836 exceeds the maximum intermediate result, drop this branch.\n     |- Try 252 \/ 43 = 5.9. 5.9 is a decimal, drop this branch.\n    |- Try 28 \/ 9 = 3.1. 3.1 is a decimal, drop this branch.\n   |- Pick two numbers (43, 9) (numbers left: [28]). Try possible operations.\n    |- Try 43 + 9 = 52. Add 52 to the number set. Current number set: [52, 28], target: 47, just two numbers left.\n     |- Try 52 + 28 = 80. Evaluate 80 != 47, drop this branch.\n     |- Try 52 - 28 = 24. Evaluate 24 != 47, drop this branch.\n     |- Try 52 * 28 = 1456. Evaluate 1456 != 47, drop this branch.\n     |- Try 52 \/ 28 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 43 - 9 = 34. Add 34 to the number set. Current number set: [34, 28], target: 47, just two numbers left.\n     |- Try 34 + 28 = 62. Evaluate 62 != 47, drop this branch.\n     |- Try 34 - 28 = 6. Evaluate 6 != 47, drop this branch.\n     |- Try 34 * 28 = 952. Evaluate 952 != 47, drop this branch.\n     |- Try 34 \/ 28 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 43 * 9 = 387. Add 387 to the number set. Current number set: [387, 28], target: 47, just two numbers left.\n     |- Try 387 + 28 = 415. Evaluate 415 != 47, drop this branch.\n     |- Try 387 - 28 = 359. Evaluate 359 != 47, drop this branch.\n     |- Try 387 * 28 = 10836. 10836 exceeds the maximum intermediate result, drop this branch.\n     |- Try 387 \/ 28 = 13.8. 13.8 is a decimal, drop this branch.\n    |- Try 43 \/ 9 = 4.8. 4.8 is a decimal, drop this branch.\n  |- Try 19 - 9 = 10. Add 10 to the number set. Current number set: [10, 43, 9], target: 47. Options for choosing two numbers: [(10, 43), (10, 9), (43, 9)].\n   |- Pick two numbers (10, 43) (numbers left: [9]). Try possible operations.\n    |- Try 43 + 10 = 53. Add 53 to the number set. Current number set: [53, 9], target: 47, just two numbers left.\n     |- Try 53 + 9 = 62. Evaluate 62 != 47, drop this branch.\n     |- Try 53 - 9 = 44. Evaluate 44 != 47, drop this branch.\n     |- Try 53 * 9 = 477. Evaluate 477 != 47, drop this branch.\n     |- Try 53 \/ 9 = 5.9. 5.9 is a decimal, drop this branch.\n    |- Try 43 - 10 = 33. Add 33 to the number set. Current number set: [33, 9], target: 47, just two numbers left.\n     |- Try 33 + 9 = 42. Evaluate 42 != 47, drop this branch.\n     |- Try 33 - 9 = 24. Evaluate 24 != 47, drop this branch.\n     |- Try 33 * 9 = 297. Evaluate 297 != 47, drop this branch.\n     |- Try 33 \/ 9 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 43 * 10 = 430. Add 430 to the number set. Current number set: [430, 9], target: 47, just two numbers left.\n     |- Try 430 + 9 = 439. Evaluate 439 != 47, drop this branch.\n     |- Try 430 - 9 = 421. Evaluate 421 != 47, drop this branch.\n     |- Try 430 * 9 = 3870. 3870 exceeds the maximum intermediate result, drop this branch.\n     |- Try 430 \/ 9 = 47.8. 47.8 is a decimal, drop this branch.\n    |- Try 43 \/ 10 = 4.3. 4.3 is a decimal, drop this branch.\n   |- Pick two numbers (10, 9) (numbers left: [43]). Try possible operations.\n    |- Try 10 + 9 = 19. Add 19 to the number set. Current number set: [19, 43], target: 47, just two numbers left.\n     |- Try 43 + 19 = 62. Evaluate 62 != 47, drop this branch.\n     |- Try 43 - 19 = 24. Evaluate 24 != 47, drop this branch.\n     |- Try 43 * 19 = 817. Evaluate 817 != 47, drop this branch.\n     |- Try 43 \/ 19 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 10 - 9 = 1. Add 1 to the number set. Current number set: [1, 43], target: 47, just two numbers left.\n     |- Try 43 + 1 = 44. Evaluate 44 != 47, drop this branch.\n     |- Try 43 - 1 = 42. Evaluate 42 != 47, drop this branch.\n     |- Try 43 * 1 = 43. Evaluate 43 != 47, drop this branch.\n     |- Try 43 \/ 1 = 43. Evaluate 43 != 47, drop this branch.\n    |- Try 10 * 9 = 90. Add 90 to the number set. Current number set: [90, 43], target: 47, just two numbers left.\n     |- Try 90 + 43 = 133. Evaluate 133 != 47, drop this branch.\n     |- Try 90 - 43 = 47. Evaluate 47 == 47, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 90 - 43 = 47\nThe step before: 10 * 9 = 90\nThe first step: 19 - 9 = 10\n\nOutput the solution in the required format:\n<Solution>\n19 - 9 = 10\n10 * 9 = 90\n90 - 43 = 47\n<\/Solution>\n","item":{"nums":[19,43,9,9],"solution":["19 - 9 = 10","10 * 9 = 90","90 - 43 = 47"],"target":47}}
+{"instance_id":"countdown_8k_83","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [30, 33, 28, 36]\nTarget: 18","reference_output":"# Search Procedure\nInitial number set: [30, 33, 28, 36], target: 18. Options for choosing two numbers: [(30, 33), (30, 28), (30, 36), (33, 28), (33, 36), (28, 36)].\n |- Pick two numbers (30, 33) (numbers left: [28, 36]). Try possible operations.\n  |- Try 33 + 30 = 63. Add 63 to the number set. Current number set: [63, 28, 36], target: 18. Options for choosing two numbers: [(63, 28), (63, 36), (28, 36)].\n   |- Pick two numbers (63, 28) (numbers left: [36]). Try possible operations.\n    |- Try 63 + 28 = 91. Add 91 to the number set. Current number set: [91, 36], target: 18, just two numbers left.\n     |- Try 91 + 36 = 127. Evaluate 127 != 18, drop this branch.\n     |- Try 91 - 36 = 55. Evaluate 55 != 18, drop this branch.\n     |- Try 91 * 36 = 3276. 3276 exceeds the maximum intermediate result, drop this branch.\n     |- Try 91 \/ 36 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 63 - 28 = 35. Add 35 to the number set. Current number set: [35, 36], target: 18, just two numbers left.\n     |- Try 36 + 35 = 71. Evaluate 71 != 18, drop this branch.\n     |- Try 36 - 35 = 1. Evaluate 1 != 18, drop this branch.\n     |- Try 36 * 35 = 1260. Evaluate 1260 != 18, drop this branch.\n     |- Try 36 \/ 35 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 63 * 28 = 1764. Add 1764 to the number set. Current number set: [1764, 36], target: 18, just two numbers left.\n     |- Try 1764 + 36 = 1800. Evaluate 1800 != 18, drop this branch.\n     |- Try 1764 - 36 = 1728. Evaluate 1728 != 18, drop this branch.\n     |- Try 1764 * 36 = 63504. 63504 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1764 \/ 36 = 49. Evaluate 49 != 18, drop this branch.\n    |- Try 63 \/ 28 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (63, 36) (numbers left: [28]). Try possible operations.\n    |- Try 63 + 36 = 99. Add 99 to the number set. Current number set: [99, 28], target: 18, just two numbers left.\n     |- Try 99 + 28 = 127. Evaluate 127 != 18, drop this branch.\n     |- Try 99 - 28 = 71. Evaluate 71 != 18, drop this branch.\n     |- Try 99 * 28 = 2772. 2772 exceeds the maximum intermediate result, drop this branch.\n     |- Try 99 \/ 28 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 63 - 36 = 27. Add 27 to the number set. Current number set: [27, 28], target: 18, just two numbers left.\n     |- Try 28 + 27 = 55. Evaluate 55 != 18, drop this branch.\n     |- Try 28 - 27 = 1. Evaluate 1 != 18, drop this branch.\n     |- Try 28 * 27 = 756. Evaluate 756 != 18, drop this branch.\n     |- Try 28 \/ 27 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 63 * 36 = 2268. 2268 exceeds the maximum intermediate result, drop this branch.\n    |- Try 63 \/ 36 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (28, 36) (numbers left: [63]). Try possible operations.\n    |- Try 36 + 28 = 64. Add 64 to the number set. Current number set: [64, 63], target: 18, just two numbers left.\n     |- Try 64 + 63 = 127. Evaluate 127 != 18, drop this branch.\n     |- Try 64 - 63 = 1. Evaluate 1 != 18, drop this branch.\n     |- Try 64 * 63 = 4032. 4032 exceeds the maximum intermediate result, drop this branch.\n     |- Try 64 \/ 63 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 36 - 28 = 8. Add 8 to the number set. Current number set: [8, 63], target: 18, just two numbers left.\n     |- Try 63 + 8 = 71. Evaluate 71 != 18, drop this branch.\n     |- Try 63 - 8 = 55. Evaluate 55 != 18, drop this branch.\n     |- Try 63 * 8 = 504. Evaluate 504 != 18, drop this branch.\n     |- Try 63 \/ 8 = 7.9. 7.9 is a decimal, drop this branch.\n    |- Try 36 * 28 = 1008. Add 1008 to the number set. Current number set: [1008, 63], target: 18, just two numbers left.\n     |- Try 1008 + 63 = 1071. Evaluate 1071 != 18, drop this branch.\n     |- Try 1008 - 63 = 945. Evaluate 945 != 18, drop this branch.\n     |- Try 1008 * 63 = 63504. 63504 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1008 \/ 63 = 16. Evaluate 16 != 18, drop this branch.\n    |- Try 36 \/ 28 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 33 - 30 = 3. Add 3 to the number set. Current number set: [3, 28, 36], target: 18. Options for choosing two numbers: [(3, 28), (3, 36), (28, 36)].\n   |- Pick two numbers (3, 28) (numbers left: [36]). Try possible operations.\n    |- Try 28 + 3 = 31. Add 31 to the number set. Current number set: [31, 36], target: 18, just two numbers left.\n     |- Try 36 + 31 = 67. Evaluate 67 != 18, drop this branch.\n     |- Try 36 - 31 = 5. Evaluate 5 != 18, drop this branch.\n     |- Try 36 * 31 = 1116. Evaluate 1116 != 18, drop this branch.\n     |- Try 36 \/ 31 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 28 - 3 = 25. Add 25 to the number set. Current number set: [25, 36], target: 18, just two numbers left.\n     |- Try 36 + 25 = 61. Evaluate 61 != 18, drop this branch.\n     |- Try 36 - 25 = 11. Evaluate 11 != 18, drop this branch.\n     |- Try 36 * 25 = 900. Evaluate 900 != 18, drop this branch.\n     |- Try 36 \/ 25 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 28 * 3 = 84. Add 84 to the number set. Current number set: [84, 36], target: 18, just two numbers left.\n     |- Try 84 + 36 = 120. Evaluate 120 != 18, drop this branch.\n     |- Try 84 - 36 = 48. Evaluate 48 != 18, drop this branch.\n     |- Try 84 * 36 = 3024. 3024 exceeds the maximum intermediate result, drop this branch.\n     |- Try 84 \/ 36 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 28 \/ 3 = 9.3. 9.3 is a decimal, drop this branch.\n   |- Pick two numbers (3, 36) (numbers left: [28]). Try possible operations.\n    |- Try 36 + 3 = 39. Add 39 to the number set. Current number set: [39, 28], target: 18, just two numbers left.\n     |- Try 39 + 28 = 67. Evaluate 67 != 18, drop this branch.\n     |- Try 39 - 28 = 11. Evaluate 11 != 18, drop this branch.\n     |- Try 39 * 28 = 1092. Evaluate 1092 != 18, drop this branch.\n     |- Try 39 \/ 28 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 36 - 3 = 33. Add 33 to the number set. Current number set: [33, 28], target: 18, just two numbers left.\n     |- Try 33 + 28 = 61. Evaluate 61 != 18, drop this branch.\n     |- Try 33 - 28 = 5. Evaluate 5 != 18, drop this branch.\n     |- Try 33 * 28 = 924. Evaluate 924 != 18, drop this branch.\n     |- Try 33 \/ 28 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 36 * 3 = 108. Add 108 to the number set. Current number set: [108, 28], target: 18, just two numbers left.\n     |- Try 108 + 28 = 136. Evaluate 136 != 18, drop this branch.\n     |- Try 108 - 28 = 80. Evaluate 80 != 18, drop this branch.\n     |- Try 108 * 28 = 3024. 3024 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 28 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 36 \/ 3 = 12. Add 12 to the number set. Current number set: [12, 28], target: 18, just two numbers left.\n     |- Try 28 + 12 = 40. Evaluate 40 != 18, drop this branch.\n     |- Try 28 - 12 = 16. Evaluate 16 != 18, drop this branch.\n     |- Try 28 * 12 = 336. Evaluate 336 != 18, drop this branch.\n     |- Try 28 \/ 12 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (28, 36) (numbers left: [3]). Try possible operations.\n    |- Try 36 + 28 = 64. Add 64 to the number set. Current number set: [64, 3], target: 18, just two numbers left.\n     |- Try 64 + 3 = 67. Evaluate 67 != 18, drop this branch.\n     |- Try 64 - 3 = 61. Evaluate 61 != 18, drop this branch.\n     |- Try 64 * 3 = 192. Evaluate 192 != 18, drop this branch.\n     |- Try 64 \/ 3 = 21.3. 21.3 is a decimal, drop this branch.\n    |- Try 36 - 28 = 8. Add 8 to the number set. Current number set: [8, 3], target: 18, just two numbers left.\n     |- Try 8 + 3 = 11. Evaluate 11 != 18, drop this branch.\n     |- Try 8 - 3 = 5. Evaluate 5 != 18, drop this branch.\n     |- Try 8 * 3 = 24. Evaluate 24 != 18, drop this branch.\n     |- Try 8 \/ 3 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 36 * 28 = 1008. Add 1008 to the number set. Current number set: [1008, 3], target: 18, just two numbers left.\n     |- Try 1008 + 3 = 1011. Evaluate 1011 != 18, drop this branch.\n     |- Try 1008 - 3 = 1005. Evaluate 1005 != 18, drop this branch.\n     |- Try 1008 * 3 = 3024. 3024 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1008 \/ 3 = 336. Evaluate 336 != 18, drop this branch.\n    |- Try 36 \/ 28 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 33 * 30 = 990. Add 990 to the number set. Current number set: [990, 28, 36], target: 18. Options for choosing two numbers: [(990, 28), (990, 36), (28, 36)].\n   |- Pick two numbers (990, 28) (numbers left: [36]). Try possible operations.\n    |- Try 990 + 28 = 1018. Add 1018 to the number set. Current number set: [1018, 36], target: 18, just two numbers left.\n     |- Try 1018 + 36 = 1054. Evaluate 1054 != 18, drop this branch.\n     |- Try 1018 - 36 = 982. Evaluate 982 != 18, drop this branch.\n     |- Try 1018 * 36 = 36648. 36648 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1018 \/ 36 = 28.3. 28.3 is a decimal, drop this branch.\n    |- Try 990 - 28 = 962. Add 962 to the number set. Current number set: [962, 36], target: 18, just two numbers left.\n     |- Try 962 + 36 = 998. Evaluate 998 != 18, drop this branch.\n     |- Try 962 - 36 = 926. Evaluate 926 != 18, drop this branch.\n     |- Try 962 * 36 = 34632. 34632 exceeds the maximum intermediate result, drop this branch.\n     |- Try 962 \/ 36 = 26.7. 26.7 is a decimal, drop this branch.\n    |- Try 990 * 28 = 27720. 27720 exceeds the maximum intermediate result, drop this branch.\n    |- Try 990 \/ 28 = 35.4. 35.4 is a decimal, drop this branch.\n   |- Pick two numbers (990, 36) (numbers left: [28]). Try possible operations.\n    |- Try 990 + 36 = 1026. Add 1026 to the number set. Current number set: [1026, 28], target: 18, just two numbers left.\n     |- Try 1026 + 28 = 1054. Evaluate 1054 != 18, drop this branch.\n     |- Try 1026 - 28 = 998. Evaluate 998 != 18, drop this branch.\n     |- Try 1026 * 28 = 28728. 28728 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1026 \/ 28 = 36.6. 36.6 is a decimal, drop this branch.\n    |- Try 990 - 36 = 954. Add 954 to the number set. Current number set: [954, 28], target: 18, just two numbers left.\n     |- Try 954 + 28 = 982. Evaluate 982 != 18, drop this branch.\n     |- Try 954 - 28 = 926. Evaluate 926 != 18, drop this branch.\n     |- Try 954 * 28 = 26712. 26712 exceeds the maximum intermediate result, drop this branch.\n     |- Try 954 \/ 28 = 34.1. 34.1 is a decimal, drop this branch.\n    |- Try 990 * 36 = 35640. 35640 exceeds the maximum intermediate result, drop this branch.\n    |- Try 990 \/ 36 = 27.5. 27.5 is a decimal, drop this branch.\n   |- Pick two numbers (28, 36) (numbers left: [990]). Try possible operations.\n    |- Try 36 + 28 = 64. Add 64 to the number set. Current number set: [64, 990], target: 18, just two numbers left.\n     |- Try 990 + 64 = 1054. Evaluate 1054 != 18, drop this branch.\n     |- Try 990 - 64 = 926. Evaluate 926 != 18, drop this branch.\n     |- Try 990 * 64 = 63360. 63360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 990 \/ 64 = 15.5. 15.5 is a decimal, drop this branch.\n    |- Try 36 - 28 = 8. Add 8 to the number set. Current number set: [8, 990], target: 18, just two numbers left.\n     |- Try 990 + 8 = 998. Evaluate 998 != 18, drop this branch.\n     |- Try 990 - 8 = 982. Evaluate 982 != 18, drop this branch.\n     |- Try 990 * 8 = 7920. 7920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 990 \/ 8 = 123.8. 123.8 is a decimal, drop this branch.\n    |- Try 36 * 28 = 1008. Add 1008 to the number set. Current number set: [1008, 990], target: 18, just two numbers left.\n     |- Try 1008 + 990 = 1998. Evaluate 1998 != 18, drop this branch.\n     |- Try 1008 - 990 = 18. Evaluate 18 == 18, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 1008 - 990 = 18\nThe step before: 36 * 28 = 1008\nThe first step: 33 * 30 = 990\n\nOutput the solution in the required format:\n<Solution>\n33 * 30 = 990\n36 * 28 = 1008\n1008 - 990 = 18\n<\/Solution>\n","item":{"nums":[30,33,28,36],"solution":["33 * 30 = 990","36 * 28 = 1008","1008 - 990 = 18"],"target":18}}
+{"instance_id":"countdown_8k_84","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [33, 18, 27, 35]\nTarget: 38","reference_output":"# Search Procedure\nInitial number set: [33, 18, 27, 35], target: 38. Options for choosing two numbers: [(33, 18), (33, 27), (33, 35), (18, 27), (18, 35), (27, 35)].\n |- Pick two numbers (33, 18) (numbers left: [27, 35]). Try possible operations.\n  |- Try 33 + 18 = 51. Add 51 to the number set. Current number set: [51, 27, 35], target: 38. Options for choosing two numbers: [(51, 27), (51, 35), (27, 35)].\n   |- Pick two numbers (51, 27) (numbers left: [35]). Try possible operations.\n    |- Try 51 + 27 = 78. Add 78 to the number set. Current number set: [78, 35], target: 38, just two numbers left.\n     |- Try 78 + 35 = 113. Evaluate 113 != 38, drop this branch.\n     |- Try 78 - 35 = 43. Evaluate 43 != 38, drop this branch.\n     |- Try 78 * 35 = 2730. 2730 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 35 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 51 - 27 = 24. Add 24 to the number set. Current number set: [24, 35], target: 38, just two numbers left.\n     |- Try 35 + 24 = 59. Evaluate 59 != 38, drop this branch.\n     |- Try 35 - 24 = 11. Evaluate 11 != 38, drop this branch.\n     |- Try 35 * 24 = 840. Evaluate 840 != 38, drop this branch.\n     |- Try 35 \/ 24 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 51 * 27 = 1377. Add 1377 to the number set. Current number set: [1377, 35], target: 38, just two numbers left.\n     |- Try 1377 + 35 = 1412. Evaluate 1412 != 38, drop this branch.\n     |- Try 1377 - 35 = 1342. Evaluate 1342 != 38, drop this branch.\n     |- Try 1377 * 35 = 48195. 48195 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1377 \/ 35 = 39.3. 39.3 is a decimal, drop this branch.\n    |- Try 51 \/ 27 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (51, 35) (numbers left: [27]). Try possible operations.\n    |- Try 51 + 35 = 86. Add 86 to the number set. Current number set: [86, 27], target: 38, just two numbers left.\n     |- Try 86 + 27 = 113. Evaluate 113 != 38, drop this branch.\n     |- Try 86 - 27 = 59. Evaluate 59 != 38, drop this branch.\n     |- Try 86 * 27 = 2322. 2322 exceeds the maximum intermediate result, drop this branch.\n     |- Try 86 \/ 27 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 51 - 35 = 16. Add 16 to the number set. Current number set: [16, 27], target: 38, just two numbers left.\n     |- Try 27 + 16 = 43. Evaluate 43 != 38, drop this branch.\n     |- Try 27 - 16 = 11. Evaluate 11 != 38, drop this branch.\n     |- Try 27 * 16 = 432. Evaluate 432 != 38, drop this branch.\n     |- Try 27 \/ 16 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 51 * 35 = 1785. Add 1785 to the number set. Current number set: [1785, 27], target: 38, just two numbers left.\n     |- Try 1785 + 27 = 1812. Evaluate 1812 != 38, drop this branch.\n     |- Try 1785 - 27 = 1758. Evaluate 1758 != 38, drop this branch.\n     |- Try 1785 * 27 = 48195. 48195 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1785 \/ 27 = 66.1. 66.1 is a decimal, drop this branch.\n    |- Try 51 \/ 35 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (27, 35) (numbers left: [51]). Try possible operations.\n    |- Try 35 + 27 = 62. Add 62 to the number set. Current number set: [62, 51], target: 38, just two numbers left.\n     |- Try 62 + 51 = 113. Evaluate 113 != 38, drop this branch.\n     |- Try 62 - 51 = 11. Evaluate 11 != 38, drop this branch.\n     |- Try 62 * 51 = 3162. 3162 exceeds the maximum intermediate result, drop this branch.\n     |- Try 62 \/ 51 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 35 - 27 = 8. Add 8 to the number set. Current number set: [8, 51], target: 38, just two numbers left.\n     |- Try 51 + 8 = 59. Evaluate 59 != 38, drop this branch.\n     |- Try 51 - 8 = 43. Evaluate 43 != 38, drop this branch.\n     |- Try 51 * 8 = 408. Evaluate 408 != 38, drop this branch.\n     |- Try 51 \/ 8 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 35 * 27 = 945. Add 945 to the number set. Current number set: [945, 51], target: 38, just two numbers left.\n     |- Try 945 + 51 = 996. Evaluate 996 != 38, drop this branch.\n     |- Try 945 - 51 = 894. Evaluate 894 != 38, drop this branch.\n     |- Try 945 * 51 = 48195. 48195 exceeds the maximum intermediate result, drop this branch.\n     |- Try 945 \/ 51 = 18.5. 18.5 is a decimal, drop this branch.\n    |- Try 35 \/ 27 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 33 - 18 = 15. Add 15 to the number set. Current number set: [15, 27, 35], target: 38. Options for choosing two numbers: [(15, 27), (15, 35), (27, 35)].\n   |- Pick two numbers (15, 27) (numbers left: [35]). Try possible operations.\n    |- Try 27 + 15 = 42. Add 42 to the number set. Current number set: [42, 35], target: 38, just two numbers left.\n     |- Try 42 + 35 = 77. Evaluate 77 != 38, drop this branch.\n     |- Try 42 - 35 = 7. Evaluate 7 != 38, drop this branch.\n     |- Try 42 * 35 = 1470. Evaluate 1470 != 38, drop this branch.\n     |- Try 42 \/ 35 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 27 - 15 = 12. Add 12 to the number set. Current number set: [12, 35], target: 38, just two numbers left.\n     |- Try 35 + 12 = 47. Evaluate 47 != 38, drop this branch.\n     |- Try 35 - 12 = 23. Evaluate 23 != 38, drop this branch.\n     |- Try 35 * 12 = 420. Evaluate 420 != 38, drop this branch.\n     |- Try 35 \/ 12 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 27 * 15 = 405. Add 405 to the number set. Current number set: [405, 35], target: 38, just two numbers left.\n     |- Try 405 + 35 = 440. Evaluate 440 != 38, drop this branch.\n     |- Try 405 - 35 = 370. Evaluate 370 != 38, drop this branch.\n     |- Try 405 * 35 = 14175. 14175 exceeds the maximum intermediate result, drop this branch.\n     |- Try 405 \/ 35 = 11.6. 11.6 is a decimal, drop this branch.\n    |- Try 27 \/ 15 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (15, 35) (numbers left: [27]). Try possible operations.\n    |- Try 35 + 15 = 50. Add 50 to the number set. Current number set: [50, 27], target: 38, just two numbers left.\n     |- Try 50 + 27 = 77. Evaluate 77 != 38, drop this branch.\n     |- Try 50 - 27 = 23. Evaluate 23 != 38, drop this branch.\n     |- Try 50 * 27 = 1350. Evaluate 1350 != 38, drop this branch.\n     |- Try 50 \/ 27 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 35 - 15 = 20. Add 20 to the number set. Current number set: [20, 27], target: 38, just two numbers left.\n     |- Try 27 + 20 = 47. Evaluate 47 != 38, drop this branch.\n     |- Try 27 - 20 = 7. Evaluate 7 != 38, drop this branch.\n     |- Try 27 * 20 = 540. Evaluate 540 != 38, drop this branch.\n     |- Try 27 \/ 20 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 35 * 15 = 525. Add 525 to the number set. Current number set: [525, 27], target: 38, just two numbers left.\n     |- Try 525 + 27 = 552. Evaluate 552 != 38, drop this branch.\n     |- Try 525 - 27 = 498. Evaluate 498 != 38, drop this branch.\n     |- Try 525 * 27 = 14175. 14175 exceeds the maximum intermediate result, drop this branch.\n     |- Try 525 \/ 27 = 19.4. 19.4 is a decimal, drop this branch.\n    |- Try 35 \/ 15 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (27, 35) (numbers left: [15]). Try possible operations.\n    |- Try 35 + 27 = 62. Add 62 to the number set. Current number set: [62, 15], target: 38, just two numbers left.\n     |- Try 62 + 15 = 77. Evaluate 77 != 38, drop this branch.\n     |- Try 62 - 15 = 47. Evaluate 47 != 38, drop this branch.\n     |- Try 62 * 15 = 930. Evaluate 930 != 38, drop this branch.\n     |- Try 62 \/ 15 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 35 - 27 = 8. Add 8 to the number set. Current number set: [8, 15], target: 38, just two numbers left.\n     |- Try 15 + 8 = 23. Evaluate 23 != 38, drop this branch.\n     |- Try 15 - 8 = 7. Evaluate 7 != 38, drop this branch.\n     |- Try 15 * 8 = 120. Evaluate 120 != 38, drop this branch.\n     |- Try 15 \/ 8 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 35 * 27 = 945. Add 945 to the number set. Current number set: [945, 15], target: 38, just two numbers left.\n     |- Try 945 + 15 = 960. Evaluate 960 != 38, drop this branch.\n     |- Try 945 - 15 = 930. Evaluate 930 != 38, drop this branch.\n     |- Try 945 * 15 = 14175. 14175 exceeds the maximum intermediate result, drop this branch.\n     |- Try 945 \/ 15 = 63. Evaluate 63 != 38, drop this branch.\n    |- Try 35 \/ 27 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 33 * 18 = 594. Add 594 to the number set. Current number set: [594, 27, 35], target: 38. Options for choosing two numbers: [(594, 27), (594, 35), (27, 35)].\n   |- Pick two numbers (594, 27) (numbers left: [35]). Try possible operations.\n    |- Try 594 + 27 = 621. Add 621 to the number set. Current number set: [621, 35], target: 38, just two numbers left.\n     |- Try 621 + 35 = 656. Evaluate 656 != 38, drop this branch.\n     |- Try 621 - 35 = 586. Evaluate 586 != 38, drop this branch.\n     |- Try 621 * 35 = 21735. 21735 exceeds the maximum intermediate result, drop this branch.\n     |- Try 621 \/ 35 = 17.7. 17.7 is a decimal, drop this branch.\n    |- Try 594 - 27 = 567. Add 567 to the number set. Current number set: [567, 35], target: 38, just two numbers left.\n     |- Try 567 + 35 = 602. Evaluate 602 != 38, drop this branch.\n     |- Try 567 - 35 = 532. Evaluate 532 != 38, drop this branch.\n     |- Try 567 * 35 = 19845. 19845 exceeds the maximum intermediate result, drop this branch.\n     |- Try 567 \/ 35 = 16.2. 16.2 is a decimal, drop this branch.\n    |- Try 594 * 27 = 16038. 16038 exceeds the maximum intermediate result, drop this branch.\n    |- Try 594 \/ 27 = 22. Add 22 to the number set. Current number set: [22, 35], target: 38, just two numbers left.\n     |- Try 35 + 22 = 57. Evaluate 57 != 38, drop this branch.\n     |- Try 35 - 22 = 13. Evaluate 13 != 38, drop this branch.\n     |- Try 35 * 22 = 770. Evaluate 770 != 38, drop this branch.\n     |- Try 35 \/ 22 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (594, 35) (numbers left: [27]). Try possible operations.\n    |- Try 594 + 35 = 629. Add 629 to the number set. Current number set: [629, 27], target: 38, just two numbers left.\n     |- Try 629 + 27 = 656. Evaluate 656 != 38, drop this branch.\n     |- Try 629 - 27 = 602. Evaluate 602 != 38, drop this branch.\n     |- Try 629 * 27 = 16983. 16983 exceeds the maximum intermediate result, drop this branch.\n     |- Try 629 \/ 27 = 23.3. 23.3 is a decimal, drop this branch.\n    |- Try 594 - 35 = 559. Add 559 to the number set. Current number set: [559, 27], target: 38, just two numbers left.\n     |- Try 559 + 27 = 586. Evaluate 586 != 38, drop this branch.\n     |- Try 559 - 27 = 532. Evaluate 532 != 38, drop this branch.\n     |- Try 559 * 27 = 15093. 15093 exceeds the maximum intermediate result, drop this branch.\n     |- Try 559 \/ 27 = 20.7. 20.7 is a decimal, drop this branch.\n    |- Try 594 * 35 = 20790. 20790 exceeds the maximum intermediate result, drop this branch.\n    |- Try 594 \/ 35 = 17.0. 17.0 is a decimal, drop this branch.\n   |- Pick two numbers (27, 35) (numbers left: [594]). Try possible operations.\n    |- Try 35 + 27 = 62. Add 62 to the number set. Current number set: [62, 594], target: 38, just two numbers left.\n     |- Try 594 + 62 = 656. Evaluate 656 != 38, drop this branch.\n     |- Try 594 - 62 = 532. Evaluate 532 != 38, drop this branch.\n     |- Try 594 * 62 = 36828. 36828 exceeds the maximum intermediate result, drop this branch.\n     |- Try 594 \/ 62 = 9.6. 9.6 is a decimal, drop this branch.\n    |- Try 35 - 27 = 8. Add 8 to the number set. Current number set: [8, 594], target: 38, just two numbers left.\n     |- Try 594 + 8 = 602. Evaluate 602 != 38, drop this branch.\n     |- Try 594 - 8 = 586. Evaluate 586 != 38, drop this branch.\n     |- Try 594 * 8 = 4752. 4752 exceeds the maximum intermediate result, drop this branch.\n     |- Try 594 \/ 8 = 74.2. 74.2 is a decimal, drop this branch.\n    |- Try 35 * 27 = 945. Add 945 to the number set. Current number set: [945, 594], target: 38, just two numbers left.\n     |- Try 945 + 594 = 1539. Evaluate 1539 != 38, drop this branch.\n     |- Try 945 - 594 = 351. Evaluate 351 != 38, drop this branch.\n     |- Try 945 * 594 = 561330. 561330 exceeds the maximum intermediate result, drop this branch.\n     |- Try 945 \/ 594 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 35 \/ 27 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 33 \/ 18 = 1.8. 1.8 is a decimal, drop this branch.\n |- Pick two numbers (33, 27) (numbers left: [18, 35]). Try possible operations.\n  |- Try 33 + 27 = 60. Add 60 to the number set. Current number set: [60, 18, 35], target: 38. Options for choosing two numbers: [(60, 18), (60, 35), (18, 35)].\n   |- Pick two numbers (60, 18) (numbers left: [35]). Try possible operations.\n    |- Try 60 + 18 = 78. Add 78 to the number set. Current number set: [78, 35], target: 38, just two numbers left.\n     |- Try 78 + 35 = 113. Evaluate 113 != 38, drop this branch.\n     |- Try 78 - 35 = 43. Evaluate 43 != 38, drop this branch.\n     |- Try 78 * 35 = 2730. 2730 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 35 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 60 - 18 = 42. Add 42 to the number set. Current number set: [42, 35], target: 38, just two numbers left.\n     |- Try 42 + 35 = 77. Evaluate 77 != 38, drop this branch.\n     |- Try 42 - 35 = 7. Evaluate 7 != 38, drop this branch.\n     |- Try 42 * 35 = 1470. Evaluate 1470 != 38, drop this branch.\n     |- Try 42 \/ 35 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 60 * 18 = 1080. Add 1080 to the number set. Current number set: [1080, 35], target: 38, just two numbers left.\n     |- Try 1080 + 35 = 1115. Evaluate 1115 != 38, drop this branch.\n     |- Try 1080 - 35 = 1045. Evaluate 1045 != 38, drop this branch.\n     |- Try 1080 * 35 = 37800. 37800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1080 \/ 35 = 30.9. 30.9 is a decimal, drop this branch.\n    |- Try 60 \/ 18 = 3.3. 3.3 is a decimal, drop this branch.\n   |- Pick two numbers (60, 35) (numbers left: [18]). Try possible operations.\n    |- Try 60 + 35 = 95. Add 95 to the number set. Current number set: [95, 18], target: 38, just two numbers left.\n     |- Try 95 + 18 = 113. Evaluate 113 != 38, drop this branch.\n     |- Try 95 - 18 = 77. Evaluate 77 != 38, drop this branch.\n     |- Try 95 * 18 = 1710. Evaluate 1710 != 38, drop this branch.\n     |- Try 95 \/ 18 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 60 - 35 = 25. Add 25 to the number set. Current number set: [25, 18], target: 38, just two numbers left.\n     |- Try 25 + 18 = 43. Evaluate 43 != 38, drop this branch.\n     |- Try 25 - 18 = 7. Evaluate 7 != 38, drop this branch.\n     |- Try 25 * 18 = 450. Evaluate 450 != 38, drop this branch.\n     |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 60 * 35 = 2100. 2100 exceeds the maximum intermediate result, drop this branch.\n    |- Try 60 \/ 35 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (18, 35) (numbers left: [60]). Try possible operations.\n    |- Try 35 + 18 = 53. Add 53 to the number set. Current number set: [53, 60], target: 38, just two numbers left.\n     |- Try 60 + 53 = 113. Evaluate 113 != 38, drop this branch.\n     |- Try 60 - 53 = 7. Evaluate 7 != 38, drop this branch.\n     |- Try 60 * 53 = 3180. 3180 exceeds the maximum intermediate result, drop this branch.\n     |- Try 60 \/ 53 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 35 - 18 = 17. Add 17 to the number set. Current number set: [17, 60], target: 38, just two numbers left.\n     |- Try 60 + 17 = 77. Evaluate 77 != 38, drop this branch.\n     |- Try 60 - 17 = 43. Evaluate 43 != 38, drop this branch.\n     |- Try 60 * 17 = 1020. Evaluate 1020 != 38, drop this branch.\n     |- Try 60 \/ 17 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 35 * 18 = 630. Add 630 to the number set. Current number set: [630, 60], target: 38, just two numbers left.\n     |- Try 630 + 60 = 690. Evaluate 690 != 38, drop this branch.\n     |- Try 630 - 60 = 570. Evaluate 570 != 38, drop this branch.\n     |- Try 630 * 60 = 37800. 37800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 630 \/ 60 = 10.5. 10.5 is a decimal, drop this branch.\n    |- Try 35 \/ 18 = 1.9. 1.9 is a decimal, drop this branch.\n  |- Try 33 - 27 = 6. Add 6 to the number set. Current number set: [6, 18, 35], target: 38. Options for choosing two numbers: [(6, 18), (6, 35), (18, 35)].\n   |- Pick two numbers (6, 18) (numbers left: [35]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 35], target: 38, just two numbers left.\n     |- Try 35 + 24 = 59. Evaluate 59 != 38, drop this branch.\n     |- Try 35 - 24 = 11. Evaluate 11 != 38, drop this branch.\n     |- Try 35 * 24 = 840. Evaluate 840 != 38, drop this branch.\n     |- Try 35 \/ 24 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 35], target: 38, just two numbers left.\n     |- Try 35 + 12 = 47. Evaluate 47 != 38, drop this branch.\n     |- Try 35 - 12 = 23. Evaluate 23 != 38, drop this branch.\n     |- Try 35 * 12 = 420. Evaluate 420 != 38, drop this branch.\n     |- Try 35 \/ 12 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 35], target: 38, just two numbers left.\n     |- Try 108 + 35 = 143. Evaluate 143 != 38, drop this branch.\n     |- Try 108 - 35 = 73. Evaluate 73 != 38, drop this branch.\n     |- Try 108 * 35 = 3780. 3780 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 35 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 35], target: 38, just two numbers left.\n     |- Try 35 + 3 = 38. Evaluate 38 == 38, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 35 + 3 = 38\nThe step before: 18 \/ 6 = 3\nThe first step: 33 - 27 = 6\n\nOutput the solution in the required format:\n<Solution>\n33 - 27 = 6\n18 \/ 6 = 3\n35 + 3 = 38\n<\/Solution>\n","item":{"nums":[33,18,27,35],"solution":["33 - 27 = 6","18 \/ 6 = 3","35 + 3 = 38"],"target":38}}
+{"instance_id":"countdown_8k_85","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [11, 37, 4, 43]\nTarget: 36","reference_output":"# Search Procedure\nInitial number set: [11, 37, 4, 43], target: 36. Options for choosing two numbers: [(11, 37), (11, 4), (11, 43), (37, 4), (37, 43), (4, 43)].\n |- Pick two numbers (11, 37) (numbers left: [4, 43]). Try possible operations.\n  |- Try 37 + 11 = 48. Add 48 to the number set. Current number set: [48, 4, 43], target: 36. Options for choosing two numbers: [(48, 4), (48, 43), (4, 43)].\n   |- Pick two numbers (48, 4) (numbers left: [43]). Try possible operations.\n    |- Try 48 + 4 = 52. Add 52 to the number set. Current number set: [52, 43], target: 36, just two numbers left.\n     |- Try 52 + 43 = 95. Evaluate 95 != 36, drop this branch.\n     |- Try 52 - 43 = 9. Evaluate 9 != 36, drop this branch.\n     |- Try 52 * 43 = 2236. 2236 exceeds the maximum intermediate result, drop this branch.\n     |- Try 52 \/ 43 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 48 - 4 = 44. Add 44 to the number set. Current number set: [44, 43], target: 36, just two numbers left.\n     |- Try 44 + 43 = 87. Evaluate 87 != 36, drop this branch.\n     |- Try 44 - 43 = 1. Evaluate 1 != 36, drop this branch.\n     |- Try 44 * 43 = 1892. Evaluate 1892 != 36, drop this branch.\n     |- Try 44 \/ 43 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 48 * 4 = 192. Add 192 to the number set. Current number set: [192, 43], target: 36, just two numbers left.\n     |- Try 192 + 43 = 235. Evaluate 235 != 36, drop this branch.\n     |- Try 192 - 43 = 149. Evaluate 149 != 36, drop this branch.\n     |- Try 192 * 43 = 8256. 8256 exceeds the maximum intermediate result, drop this branch.\n     |- Try 192 \/ 43 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 48 \/ 4 = 12. Add 12 to the number set. Current number set: [12, 43], target: 36, just two numbers left.\n     |- Try 43 + 12 = 55. Evaluate 55 != 36, drop this branch.\n     |- Try 43 - 12 = 31. Evaluate 31 != 36, drop this branch.\n     |- Try 43 * 12 = 516. Evaluate 516 != 36, drop this branch.\n     |- Try 43 \/ 12 = 3.6. 3.6 is a decimal, drop this branch.\n   |- Pick two numbers (48, 43) (numbers left: [4]). Try possible operations.\n    |- Try 48 + 43 = 91. Add 91 to the number set. Current number set: [91, 4], target: 36, just two numbers left.\n     |- Try 91 + 4 = 95. Evaluate 95 != 36, drop this branch.\n     |- Try 91 - 4 = 87. Evaluate 87 != 36, drop this branch.\n     |- Try 91 * 4 = 364. Evaluate 364 != 36, drop this branch.\n     |- Try 91 \/ 4 = 22.8. 22.8 is a decimal, drop this branch.\n    |- Try 48 - 43 = 5. Add 5 to the number set. Current number set: [5, 4], target: 36, just two numbers left.\n     |- Try 5 + 4 = 9. Evaluate 9 != 36, drop this branch.\n     |- Try 5 - 4 = 1. Evaluate 1 != 36, drop this branch.\n     |- Try 5 * 4 = 20. Evaluate 20 != 36, drop this branch.\n     |- Try 5 \/ 4 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 48 * 43 = 2064. 2064 exceeds the maximum intermediate result, drop this branch.\n    |- Try 48 \/ 43 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (4, 43) (numbers left: [48]). Try possible operations.\n    |- Try 43 + 4 = 47. Add 47 to the number set. Current number set: [47, 48], target: 36, just two numbers left.\n     |- Try 48 + 47 = 95. Evaluate 95 != 36, drop this branch.\n     |- Try 48 - 47 = 1. Evaluate 1 != 36, drop this branch.\n     |- Try 48 * 47 = 2256. 2256 exceeds the maximum intermediate result, drop this branch.\n     |- Try 48 \/ 47 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 43 - 4 = 39. Add 39 to the number set. Current number set: [39, 48], target: 36, just two numbers left.\n     |- Try 48 + 39 = 87. Evaluate 87 != 36, drop this branch.\n     |- Try 48 - 39 = 9. Evaluate 9 != 36, drop this branch.\n     |- Try 48 * 39 = 1872. Evaluate 1872 != 36, drop this branch.\n     |- Try 48 \/ 39 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 43 * 4 = 172. Add 172 to the number set. Current number set: [172, 48], target: 36, just two numbers left.\n     |- Try 172 + 48 = 220. Evaluate 220 != 36, drop this branch.\n     |- Try 172 - 48 = 124. Evaluate 124 != 36, drop this branch.\n     |- Try 172 * 48 = 8256. 8256 exceeds the maximum intermediate result, drop this branch.\n     |- Try 172 \/ 48 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 43 \/ 4 = 10.8. 10.8 is a decimal, drop this branch.\n  |- Try 37 - 11 = 26. Add 26 to the number set. Current number set: [26, 4, 43], target: 36. Options for choosing two numbers: [(26, 4), (26, 43), (4, 43)].\n   |- Pick two numbers (26, 4) (numbers left: [43]). Try possible operations.\n    |- Try 26 + 4 = 30. Add 30 to the number set. Current number set: [30, 43], target: 36, just two numbers left.\n     |- Try 43 + 30 = 73. Evaluate 73 != 36, drop this branch.\n     |- Try 43 - 30 = 13. Evaluate 13 != 36, drop this branch.\n     |- Try 43 * 30 = 1290. Evaluate 1290 != 36, drop this branch.\n     |- Try 43 \/ 30 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 26 - 4 = 22. Add 22 to the number set. Current number set: [22, 43], target: 36, just two numbers left.\n     |- Try 43 + 22 = 65. Evaluate 65 != 36, drop this branch.\n     |- Try 43 - 22 = 21. Evaluate 21 != 36, drop this branch.\n     |- Try 43 * 22 = 946. Evaluate 946 != 36, drop this branch.\n     |- Try 43 \/ 22 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 26 * 4 = 104. Add 104 to the number set. Current number set: [104, 43], target: 36, just two numbers left.\n     |- Try 104 + 43 = 147. Evaluate 147 != 36, drop this branch.\n     |- Try 104 - 43 = 61. Evaluate 61 != 36, drop this branch.\n     |- Try 104 * 43 = 4472. 4472 exceeds the maximum intermediate result, drop this branch.\n     |- Try 104 \/ 43 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 26 \/ 4 = 6.5. 6.5 is a decimal, drop this branch.\n   |- Pick two numbers (26, 43) (numbers left: [4]). Try possible operations.\n    |- Try 43 + 26 = 69. Add 69 to the number set. Current number set: [69, 4], target: 36, just two numbers left.\n     |- Try 69 + 4 = 73. Evaluate 73 != 36, drop this branch.\n     |- Try 69 - 4 = 65. Evaluate 65 != 36, drop this branch.\n     |- Try 69 * 4 = 276. Evaluate 276 != 36, drop this branch.\n     |- Try 69 \/ 4 = 17.2. 17.2 is a decimal, drop this branch.\n    |- Try 43 - 26 = 17. Add 17 to the number set. Current number set: [17, 4], target: 36, just two numbers left.\n     |- Try 17 + 4 = 21. Evaluate 21 != 36, drop this branch.\n     |- Try 17 - 4 = 13. Evaluate 13 != 36, drop this branch.\n     |- Try 17 * 4 = 68. Evaluate 68 != 36, drop this branch.\n     |- Try 17 \/ 4 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 43 * 26 = 1118. Add 1118 to the number set. Current number set: [1118, 4], target: 36, just two numbers left.\n     |- Try 1118 + 4 = 1122. Evaluate 1122 != 36, drop this branch.\n     |- Try 1118 - 4 = 1114. Evaluate 1114 != 36, drop this branch.\n     |- Try 1118 * 4 = 4472. 4472 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1118 \/ 4 = 279.5. 279.5 is a decimal, drop this branch.\n    |- Try 43 \/ 26 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (4, 43) (numbers left: [26]). Try possible operations.\n    |- Try 43 + 4 = 47. Add 47 to the number set. Current number set: [47, 26], target: 36, just two numbers left.\n     |- Try 47 + 26 = 73. Evaluate 73 != 36, drop this branch.\n     |- Try 47 - 26 = 21. Evaluate 21 != 36, drop this branch.\n     |- Try 47 * 26 = 1222. Evaluate 1222 != 36, drop this branch.\n     |- Try 47 \/ 26 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 43 - 4 = 39. Add 39 to the number set. Current number set: [39, 26], target: 36, just two numbers left.\n     |- Try 39 + 26 = 65. Evaluate 65 != 36, drop this branch.\n     |- Try 39 - 26 = 13. Evaluate 13 != 36, drop this branch.\n     |- Try 39 * 26 = 1014. Evaluate 1014 != 36, drop this branch.\n     |- Try 39 \/ 26 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 43 * 4 = 172. Add 172 to the number set. Current number set: [172, 26], target: 36, just two numbers left.\n     |- Try 172 + 26 = 198. Evaluate 198 != 36, drop this branch.\n     |- Try 172 - 26 = 146. Evaluate 146 != 36, drop this branch.\n     |- Try 172 * 26 = 4472. 4472 exceeds the maximum intermediate result, drop this branch.\n     |- Try 172 \/ 26 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 43 \/ 4 = 10.8. 10.8 is a decimal, drop this branch.\n  |- Try 37 * 11 = 407. Add 407 to the number set. Current number set: [407, 4, 43], target: 36. Options for choosing two numbers: [(407, 4), (407, 43), (4, 43)].\n   |- Pick two numbers (407, 4) (numbers left: [43]). Try possible operations.\n    |- Try 407 + 4 = 411. Add 411 to the number set. Current number set: [411, 43], target: 36, just two numbers left.\n     |- Try 411 + 43 = 454. Evaluate 454 != 36, drop this branch.\n     |- Try 411 - 43 = 368. Evaluate 368 != 36, drop this branch.\n     |- Try 411 * 43 = 17673. 17673 exceeds the maximum intermediate result, drop this branch.\n     |- Try 411 \/ 43 = 9.6. 9.6 is a decimal, drop this branch.\n    |- Try 407 - 4 = 403. Add 403 to the number set. Current number set: [403, 43], target: 36, just two numbers left.\n     |- Try 403 + 43 = 446. Evaluate 446 != 36, drop this branch.\n     |- Try 403 - 43 = 360. Evaluate 360 != 36, drop this branch.\n     |- Try 403 * 43 = 17329. 17329 exceeds the maximum intermediate result, drop this branch.\n     |- Try 403 \/ 43 = 9.4. 9.4 is a decimal, drop this branch.\n    |- Try 407 * 4 = 1628. Add 1628 to the number set. Current number set: [1628, 43], target: 36, just two numbers left.\n     |- Try 1628 + 43 = 1671. Evaluate 1671 != 36, drop this branch.\n     |- Try 1628 - 43 = 1585. Evaluate 1585 != 36, drop this branch.\n     |- Try 1628 * 43 = 70004. 70004 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1628 \/ 43 = 37.9. 37.9 is a decimal, drop this branch.\n    |- Try 407 \/ 4 = 101.8. 101.8 is a decimal, drop this branch.\n   |- Pick two numbers (407, 43) (numbers left: [4]). Try possible operations.\n    |- Try 407 + 43 = 450. Add 450 to the number set. Current number set: [450, 4], target: 36, just two numbers left.\n     |- Try 450 + 4 = 454. Evaluate 454 != 36, drop this branch.\n     |- Try 450 - 4 = 446. Evaluate 446 != 36, drop this branch.\n     |- Try 450 * 4 = 1800. Evaluate 1800 != 36, drop this branch.\n     |- Try 450 \/ 4 = 112.5. 112.5 is a decimal, drop this branch.\n    |- Try 407 - 43 = 364. Add 364 to the number set. Current number set: [364, 4], target: 36, just two numbers left.\n     |- Try 364 + 4 = 368. Evaluate 368 != 36, drop this branch.\n     |- Try 364 - 4 = 360. Evaluate 360 != 36, drop this branch.\n     |- Try 364 * 4 = 1456. Evaluate 1456 != 36, drop this branch.\n     |- Try 364 \/ 4 = 91. Evaluate 91 != 36, drop this branch.\n    |- Try 407 * 43 = 17501. 17501 exceeds the maximum intermediate result, drop this branch.\n    |- Try 407 \/ 43 = 9.5. 9.5 is a decimal, drop this branch.\n   |- Pick two numbers (4, 43) (numbers left: [407]). Try possible operations.\n    |- Try 43 + 4 = 47. Add 47 to the number set. Current number set: [47, 407], target: 36, just two numbers left.\n     |- Try 407 + 47 = 454. Evaluate 454 != 36, drop this branch.\n     |- Try 407 - 47 = 360. Evaluate 360 != 36, drop this branch.\n     |- Try 407 * 47 = 19129. 19129 exceeds the maximum intermediate result, drop this branch.\n     |- Try 407 \/ 47 = 8.7. 8.7 is a decimal, drop this branch.\n    |- Try 43 - 4 = 39. Add 39 to the number set. Current number set: [39, 407], target: 36, just two numbers left.\n     |- Try 407 + 39 = 446. Evaluate 446 != 36, drop this branch.\n     |- Try 407 - 39 = 368. Evaluate 368 != 36, drop this branch.\n     |- Try 407 * 39 = 15873. 15873 exceeds the maximum intermediate result, drop this branch.\n     |- Try 407 \/ 39 = 10.4. 10.4 is a decimal, drop this branch.\n    |- Try 43 * 4 = 172. Add 172 to the number set. Current number set: [172, 407], target: 36, just two numbers left.\n     |- Try 407 + 172 = 579. Evaluate 579 != 36, drop this branch.\n     |- Try 407 - 172 = 235. Evaluate 235 != 36, drop this branch.\n     |- Try 407 * 172 = 70004. 70004 exceeds the maximum intermediate result, drop this branch.\n     |- Try 407 \/ 172 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 43 \/ 4 = 10.8. 10.8 is a decimal, drop this branch.\n  |- Try 37 \/ 11 = 3.4. 3.4 is a decimal, drop this branch.\n |- Pick two numbers (11, 4) (numbers left: [37, 43]). Try possible operations.\n  |- Try 11 + 4 = 15. Add 15 to the number set. Current number set: [15, 37, 43], target: 36. Options for choosing two numbers: [(15, 37), (15, 43), (37, 43)].\n   |- Pick two numbers (15, 37) (numbers left: [43]). Try possible operations.\n    |- Try 37 + 15 = 52. Add 52 to the number set. Current number set: [52, 43], target: 36, just two numbers left.\n     |- Try 52 + 43 = 95. Evaluate 95 != 36, drop this branch.\n     |- Try 52 - 43 = 9. Evaluate 9 != 36, drop this branch.\n     |- Try 52 * 43 = 2236. 2236 exceeds the maximum intermediate result, drop this branch.\n     |- Try 52 \/ 43 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 37 - 15 = 22. Add 22 to the number set. Current number set: [22, 43], target: 36, just two numbers left.\n     |- Try 43 + 22 = 65. Evaluate 65 != 36, drop this branch.\n     |- Try 43 - 22 = 21. Evaluate 21 != 36, drop this branch.\n     |- Try 43 * 22 = 946. Evaluate 946 != 36, drop this branch.\n     |- Try 43 \/ 22 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 37 * 15 = 555. Add 555 to the number set. Current number set: [555, 43], target: 36, just two numbers left.\n     |- Try 555 + 43 = 598. Evaluate 598 != 36, drop this branch.\n     |- Try 555 - 43 = 512. Evaluate 512 != 36, drop this branch.\n     |- Try 555 * 43 = 23865. 23865 exceeds the maximum intermediate result, drop this branch.\n     |- Try 555 \/ 43 = 12.9. 12.9 is a decimal, drop this branch.\n    |- Try 37 \/ 15 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (15, 43) (numbers left: [37]). Try possible operations.\n    |- Try 43 + 15 = 58. Add 58 to the number set. Current number set: [58, 37], target: 36, just two numbers left.\n     |- Try 58 + 37 = 95. Evaluate 95 != 36, drop this branch.\n     |- Try 58 - 37 = 21. Evaluate 21 != 36, drop this branch.\n     |- Try 58 * 37 = 2146. 2146 exceeds the maximum intermediate result, drop this branch.\n     |- Try 58 \/ 37 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 43 - 15 = 28. Add 28 to the number set. Current number set: [28, 37], target: 36, just two numbers left.\n     |- Try 37 + 28 = 65. Evaluate 65 != 36, drop this branch.\n     |- Try 37 - 28 = 9. Evaluate 9 != 36, drop this branch.\n     |- Try 37 * 28 = 1036. Evaluate 1036 != 36, drop this branch.\n     |- Try 37 \/ 28 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 43 * 15 = 645. Add 645 to the number set. Current number set: [645, 37], target: 36, just two numbers left.\n     |- Try 645 + 37 = 682. Evaluate 682 != 36, drop this branch.\n     |- Try 645 - 37 = 608. Evaluate 608 != 36, drop this branch.\n     |- Try 645 * 37 = 23865. 23865 exceeds the maximum intermediate result, drop this branch.\n     |- Try 645 \/ 37 = 17.4. 17.4 is a decimal, drop this branch.\n    |- Try 43 \/ 15 = 2.9. 2.9 is a decimal, drop this branch.\n   |- Pick two numbers (37, 43) (numbers left: [15]). Try possible operations.\n    |- Try 43 + 37 = 80. Add 80 to the number set. Current number set: [80, 15], target: 36, just two numbers left.\n     |- Try 80 + 15 = 95. Evaluate 95 != 36, drop this branch.\n     |- Try 80 - 15 = 65. Evaluate 65 != 36, drop this branch.\n     |- Try 80 * 15 = 1200. Evaluate 1200 != 36, drop this branch.\n     |- Try 80 \/ 15 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 43 - 37 = 6. Add 6 to the number set. Current number set: [6, 15], target: 36, just two numbers left.\n     |- Try 15 + 6 = 21. Evaluate 21 != 36, drop this branch.\n     |- Try 15 - 6 = 9. Evaluate 9 != 36, drop this branch.\n     |- Try 15 * 6 = 90. Evaluate 90 != 36, drop this branch.\n     |- Try 15 \/ 6 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 43 * 37 = 1591. Add 1591 to the number set. Current number set: [1591, 15], target: 36, just two numbers left.\n     |- Try 1591 + 15 = 1606. Evaluate 1606 != 36, drop this branch.\n     |- Try 1591 - 15 = 1576. Evaluate 1576 != 36, drop this branch.\n     |- Try 1591 * 15 = 23865. 23865 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1591 \/ 15 = 106.1. 106.1 is a decimal, drop this branch.\n    |- Try 43 \/ 37 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 11 - 4 = 7. Add 7 to the number set. Current number set: [7, 37, 43], target: 36. Options for choosing two numbers: [(7, 37), (7, 43), (37, 43)].\n   |- Pick two numbers (7, 37) (numbers left: [43]). Try possible operations.\n    |- Try 37 + 7 = 44. Add 44 to the number set. Current number set: [44, 43], target: 36, just two numbers left.\n     |- Try 44 + 43 = 87. Evaluate 87 != 36, drop this branch.\n     |- Try 44 - 43 = 1. Evaluate 1 != 36, drop this branch.\n     |- Try 44 * 43 = 1892. Evaluate 1892 != 36, drop this branch.\n     |- Try 44 \/ 43 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 37 - 7 = 30. Add 30 to the number set. Current number set: [30, 43], target: 36, just two numbers left.\n     |- Try 43 + 30 = 73. Evaluate 73 != 36, drop this branch.\n     |- Try 43 - 30 = 13. Evaluate 13 != 36, drop this branch.\n     |- Try 43 * 30 = 1290. Evaluate 1290 != 36, drop this branch.\n     |- Try 43 \/ 30 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 37 * 7 = 259. Add 259 to the number set. Current number set: [259, 43], target: 36, just two numbers left.\n     |- Try 259 + 43 = 302. Evaluate 302 != 36, drop this branch.\n     |- Try 259 - 43 = 216. Evaluate 216 != 36, drop this branch.\n     |- Try 259 * 43 = 11137. 11137 exceeds the maximum intermediate result, drop this branch.\n     |- Try 259 \/ 43 = 6.0. 6.0 is a decimal, drop this branch.\n    |- Try 37 \/ 7 = 5.3. 5.3 is a decimal, drop this branch.\n   |- Pick two numbers (7, 43) (numbers left: [37]). Try possible operations.\n    |- Try 43 + 7 = 50. Add 50 to the number set. Current number set: [50, 37], target: 36, just two numbers left.\n     |- Try 50 + 37 = 87. Evaluate 87 != 36, drop this branch.\n     |- Try 50 - 37 = 13. Evaluate 13 != 36, drop this branch.\n     |- Try 50 * 37 = 1850. Evaluate 1850 != 36, drop this branch.\n     |- Try 50 \/ 37 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 43 - 7 = 36. Add 36 to the number set. Current number set: [36, 37], target: 36, just two numbers left.\n     |- Try 37 + 36 = 73. Evaluate 73 != 36, drop this branch.\n     |- Try 37 - 36 = 1. Evaluate 1 != 36, drop this branch.\n     |- Try 37 * 36 = 1332. Evaluate 1332 != 36, drop this branch.\n     |- Try 37 \/ 36 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 43 * 7 = 301. Add 301 to the number set. Current number set: [301, 37], target: 36, just two numbers left.\n     |- Try 301 + 37 = 338. Evaluate 338 != 36, drop this branch.\n     |- Try 301 - 37 = 264. Evaluate 264 != 36, drop this branch.\n     |- Try 301 * 37 = 11137. 11137 exceeds the maximum intermediate result, drop this branch.\n     |- Try 301 \/ 37 = 8.1. 8.1 is a decimal, drop this branch.\n    |- Try 43 \/ 7 = 6.1. 6.1 is a decimal, drop this branch.\n   |- Pick two numbers (37, 43) (numbers left: [7]). Try possible operations.\n    |- Try 43 + 37 = 80. Add 80 to the number set. Current number set: [80, 7], target: 36, just two numbers left.\n     |- Try 80 + 7 = 87. Evaluate 87 != 36, drop this branch.\n     |- Try 80 - 7 = 73. Evaluate 73 != 36, drop this branch.\n     |- Try 80 * 7 = 560. Evaluate 560 != 36, drop this branch.\n     |- Try 80 \/ 7 = 11.4. 11.4 is a decimal, drop this branch.\n    |- Try 43 - 37 = 6. Add 6 to the number set. Current number set: [6, 7], target: 36, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 36, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 36, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 36, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 43 * 37 = 1591. Add 1591 to the number set. Current number set: [1591, 7], target: 36, just two numbers left.\n     |- Try 1591 + 7 = 1598. Evaluate 1598 != 36, drop this branch.\n     |- Try 1591 - 7 = 1584. Evaluate 1584 != 36, drop this branch.\n     |- Try 1591 * 7 = 11137. 11137 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1591 \/ 7 = 227.3. 227.3 is a decimal, drop this branch.\n    |- Try 43 \/ 37 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 11 * 4 = 44. Add 44 to the number set. Current number set: [44, 37, 43], target: 36. Options for choosing two numbers: [(44, 37), (44, 43), (37, 43)].\n   |- Pick two numbers (44, 37) (numbers left: [43]). Try possible operations.\n    |- Try 44 + 37 = 81. Add 81 to the number set. Current number set: [81, 43], target: 36, just two numbers left.\n     |- Try 81 + 43 = 124. Evaluate 124 != 36, drop this branch.\n     |- Try 81 - 43 = 38. Evaluate 38 != 36, drop this branch.\n     |- Try 81 * 43 = 3483. 3483 exceeds the maximum intermediate result, drop this branch.\n     |- Try 81 \/ 43 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 44 - 37 = 7. Add 7 to the number set. Current number set: [7, 43], target: 36, just two numbers left.\n     |- Try 43 + 7 = 50. Evaluate 50 != 36, drop this branch.\n     |- Try 43 - 7 = 36. Evaluate 36 == 36, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 43 - 7 = 36\nThe step before: 44 - 37 = 7\nThe first step: 11 * 4 = 44\n\nOutput the solution in the required format:\n<Solution>\n11 * 4 = 44\n44 - 37 = 7\n43 - 7 = 36\n<\/Solution>\n","item":{"nums":[11,37,4,43],"solution":["11 * 4 = 44","44 - 37 = 7","43 - 7 = 36"],"target":36}}
+{"instance_id":"countdown_8k_86","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [48, 10, 43, 29]\nTarget: 27","reference_output":"# Search Procedure\nInitial number set: [48, 10, 43, 29], target: 27. Options for choosing two numbers: [(48, 10), (48, 43), (48, 29), (10, 43), (10, 29), (43, 29)].\n |- Pick two numbers (48, 10) (numbers left: [43, 29]). Try possible operations.\n  |- Try 48 + 10 = 58. Add 58 to the number set. Current number set: [58, 43, 29], target: 27. Options for choosing two numbers: [(58, 43), (58, 29), (43, 29)].\n   |- Pick two numbers (58, 43) (numbers left: [29]). Try possible operations.\n    |- Try 58 + 43 = 101. Add 101 to the number set. Current number set: [101, 29], target: 27, just two numbers left.\n     |- Try 101 + 29 = 130. Evaluate 130 != 27, drop this branch.\n     |- Try 101 - 29 = 72. Evaluate 72 != 27, drop this branch.\n     |- Try 101 * 29 = 2929. 2929 exceeds the maximum intermediate result, drop this branch.\n     |- Try 101 \/ 29 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 58 - 43 = 15. Add 15 to the number set. Current number set: [15, 29], target: 27, just two numbers left.\n     |- Try 29 + 15 = 44. Evaluate 44 != 27, drop this branch.\n     |- Try 29 - 15 = 14. Evaluate 14 != 27, drop this branch.\n     |- Try 29 * 15 = 435. Evaluate 435 != 27, drop this branch.\n     |- Try 29 \/ 15 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 58 * 43 = 2494. 2494 exceeds the maximum intermediate result, drop this branch.\n    |- Try 58 \/ 43 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (58, 29) (numbers left: [43]). Try possible operations.\n    |- Try 58 + 29 = 87. Add 87 to the number set. Current number set: [87, 43], target: 27, just two numbers left.\n     |- Try 87 + 43 = 130. Evaluate 130 != 27, drop this branch.\n     |- Try 87 - 43 = 44. Evaluate 44 != 27, drop this branch.\n     |- Try 87 * 43 = 3741. 3741 exceeds the maximum intermediate result, drop this branch.\n     |- Try 87 \/ 43 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 58 - 29 = 29. Add 29 to the number set. Current number set: [29, 43], target: 27, just two numbers left.\n     |- Try 43 + 29 = 72. Evaluate 72 != 27, drop this branch.\n     |- Try 43 - 29 = 14. Evaluate 14 != 27, drop this branch.\n     |- Try 43 * 29 = 1247. Evaluate 1247 != 27, drop this branch.\n     |- Try 43 \/ 29 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 58 * 29 = 1682. Add 1682 to the number set. Current number set: [1682, 43], target: 27, just two numbers left.\n     |- Try 1682 + 43 = 1725. Evaluate 1725 != 27, drop this branch.\n     |- Try 1682 - 43 = 1639. Evaluate 1639 != 27, drop this branch.\n     |- Try 1682 * 43 = 72326. 72326 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1682 \/ 43 = 39.1. 39.1 is a decimal, drop this branch.\n    |- Try 58 \/ 29 = 2. Add 2 to the number set. Current number set: [2, 43], target: 27, just two numbers left.\n     |- Try 43 + 2 = 45. Evaluate 45 != 27, drop this branch.\n     |- Try 43 - 2 = 41. Evaluate 41 != 27, drop this branch.\n     |- Try 43 * 2 = 86. Evaluate 86 != 27, drop this branch.\n     |- Try 43 \/ 2 = 21.5. 21.5 is a decimal, drop this branch.\n   |- Pick two numbers (43, 29) (numbers left: [58]). Try possible operations.\n    |- Try 43 + 29 = 72. Add 72 to the number set. Current number set: [72, 58], target: 27, just two numbers left.\n     |- Try 72 + 58 = 130. Evaluate 130 != 27, drop this branch.\n     |- Try 72 - 58 = 14. Evaluate 14 != 27, drop this branch.\n     |- Try 72 * 58 = 4176. 4176 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 58 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 43 - 29 = 14. Add 14 to the number set. Current number set: [14, 58], target: 27, just two numbers left.\n     |- Try 58 + 14 = 72. Evaluate 72 != 27, drop this branch.\n     |- Try 58 - 14 = 44. Evaluate 44 != 27, drop this branch.\n     |- Try 58 * 14 = 812. Evaluate 812 != 27, drop this branch.\n     |- Try 58 \/ 14 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 43 * 29 = 1247. Add 1247 to the number set. Current number set: [1247, 58], target: 27, just two numbers left.\n     |- Try 1247 + 58 = 1305. Evaluate 1305 != 27, drop this branch.\n     |- Try 1247 - 58 = 1189. Evaluate 1189 != 27, drop this branch.\n     |- Try 1247 * 58 = 72326. 72326 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1247 \/ 58 = 21.5. 21.5 is a decimal, drop this branch.\n    |- Try 43 \/ 29 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 48 - 10 = 38. Add 38 to the number set. Current number set: [38, 43, 29], target: 27. Options for choosing two numbers: [(38, 43), (38, 29), (43, 29)].\n   |- Pick two numbers (38, 43) (numbers left: [29]). Try possible operations.\n    |- Try 43 + 38 = 81. Add 81 to the number set. Current number set: [81, 29], target: 27, just two numbers left.\n     |- Try 81 + 29 = 110. Evaluate 110 != 27, drop this branch.\n     |- Try 81 - 29 = 52. Evaluate 52 != 27, drop this branch.\n     |- Try 81 * 29 = 2349. 2349 exceeds the maximum intermediate result, drop this branch.\n     |- Try 81 \/ 29 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 43 - 38 = 5. Add 5 to the number set. Current number set: [5, 29], target: 27, just two numbers left.\n     |- Try 29 + 5 = 34. Evaluate 34 != 27, drop this branch.\n     |- Try 29 - 5 = 24. Evaluate 24 != 27, drop this branch.\n     |- Try 29 * 5 = 145. Evaluate 145 != 27, drop this branch.\n     |- Try 29 \/ 5 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 43 * 38 = 1634. Add 1634 to the number set. Current number set: [1634, 29], target: 27, just two numbers left.\n     |- Try 1634 + 29 = 1663. Evaluate 1663 != 27, drop this branch.\n     |- Try 1634 - 29 = 1605. Evaluate 1605 != 27, drop this branch.\n     |- Try 1634 * 29 = 47386. 47386 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1634 \/ 29 = 56.3. 56.3 is a decimal, drop this branch.\n    |- Try 43 \/ 38 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (38, 29) (numbers left: [43]). Try possible operations.\n    |- Try 38 + 29 = 67. Add 67 to the number set. Current number set: [67, 43], target: 27, just two numbers left.\n     |- Try 67 + 43 = 110. Evaluate 110 != 27, drop this branch.\n     |- Try 67 - 43 = 24. Evaluate 24 != 27, drop this branch.\n     |- Try 67 * 43 = 2881. 2881 exceeds the maximum intermediate result, drop this branch.\n     |- Try 67 \/ 43 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 38 - 29 = 9. Add 9 to the number set. Current number set: [9, 43], target: 27, just two numbers left.\n     |- Try 43 + 9 = 52. Evaluate 52 != 27, drop this branch.\n     |- Try 43 - 9 = 34. Evaluate 34 != 27, drop this branch.\n     |- Try 43 * 9 = 387. Evaluate 387 != 27, drop this branch.\n     |- Try 43 \/ 9 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 38 * 29 = 1102. Add 1102 to the number set. Current number set: [1102, 43], target: 27, just two numbers left.\n     |- Try 1102 + 43 = 1145. Evaluate 1145 != 27, drop this branch.\n     |- Try 1102 - 43 = 1059. Evaluate 1059 != 27, drop this branch.\n     |- Try 1102 * 43 = 47386. 47386 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1102 \/ 43 = 25.6. 25.6 is a decimal, drop this branch.\n    |- Try 38 \/ 29 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (43, 29) (numbers left: [38]). Try possible operations.\n    |- Try 43 + 29 = 72. Add 72 to the number set. Current number set: [72, 38], target: 27, just two numbers left.\n     |- Try 72 + 38 = 110. Evaluate 110 != 27, drop this branch.\n     |- Try 72 - 38 = 34. Evaluate 34 != 27, drop this branch.\n     |- Try 72 * 38 = 2736. 2736 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 38 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 43 - 29 = 14. Add 14 to the number set. Current number set: [14, 38], target: 27, just two numbers left.\n     |- Try 38 + 14 = 52. Evaluate 52 != 27, drop this branch.\n     |- Try 38 - 14 = 24. Evaluate 24 != 27, drop this branch.\n     |- Try 38 * 14 = 532. Evaluate 532 != 27, drop this branch.\n     |- Try 38 \/ 14 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 43 * 29 = 1247. Add 1247 to the number set. Current number set: [1247, 38], target: 27, just two numbers left.\n     |- Try 1247 + 38 = 1285. Evaluate 1285 != 27, drop this branch.\n     |- Try 1247 - 38 = 1209. Evaluate 1209 != 27, drop this branch.\n     |- Try 1247 * 38 = 47386. 47386 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1247 \/ 38 = 32.8. 32.8 is a decimal, drop this branch.\n    |- Try 43 \/ 29 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 48 * 10 = 480. Add 480 to the number set. Current number set: [480, 43, 29], target: 27. Options for choosing two numbers: [(480, 43), (480, 29), (43, 29)].\n   |- Pick two numbers (480, 43) (numbers left: [29]). Try possible operations.\n    |- Try 480 + 43 = 523. Add 523 to the number set. Current number set: [523, 29], target: 27, just two numbers left.\n     |- Try 523 + 29 = 552. Evaluate 552 != 27, drop this branch.\n     |- Try 523 - 29 = 494. Evaluate 494 != 27, drop this branch.\n     |- Try 523 * 29 = 15167. 15167 exceeds the maximum intermediate result, drop this branch.\n     |- Try 523 \/ 29 = 18.0. 18.0 is a decimal, drop this branch.\n    |- Try 480 - 43 = 437. Add 437 to the number set. Current number set: [437, 29], target: 27, just two numbers left.\n     |- Try 437 + 29 = 466. Evaluate 466 != 27, drop this branch.\n     |- Try 437 - 29 = 408. Evaluate 408 != 27, drop this branch.\n     |- Try 437 * 29 = 12673. 12673 exceeds the maximum intermediate result, drop this branch.\n     |- Try 437 \/ 29 = 15.1. 15.1 is a decimal, drop this branch.\n    |- Try 480 * 43 = 20640. 20640 exceeds the maximum intermediate result, drop this branch.\n    |- Try 480 \/ 43 = 11.2. 11.2 is a decimal, drop this branch.\n   |- Pick two numbers (480, 29) (numbers left: [43]). Try possible operations.\n    |- Try 480 + 29 = 509. Add 509 to the number set. Current number set: [509, 43], target: 27, just two numbers left.\n     |- Try 509 + 43 = 552. Evaluate 552 != 27, drop this branch.\n     |- Try 509 - 43 = 466. Evaluate 466 != 27, drop this branch.\n     |- Try 509 * 43 = 21887. 21887 exceeds the maximum intermediate result, drop this branch.\n     |- Try 509 \/ 43 = 11.8. 11.8 is a decimal, drop this branch.\n    |- Try 480 - 29 = 451. Add 451 to the number set. Current number set: [451, 43], target: 27, just two numbers left.\n     |- Try 451 + 43 = 494. Evaluate 494 != 27, drop this branch.\n     |- Try 451 - 43 = 408. Evaluate 408 != 27, drop this branch.\n     |- Try 451 * 43 = 19393. 19393 exceeds the maximum intermediate result, drop this branch.\n     |- Try 451 \/ 43 = 10.5. 10.5 is a decimal, drop this branch.\n    |- Try 480 * 29 = 13920. 13920 exceeds the maximum intermediate result, drop this branch.\n    |- Try 480 \/ 29 = 16.6. 16.6 is a decimal, drop this branch.\n   |- Pick two numbers (43, 29) (numbers left: [480]). Try possible operations.\n    |- Try 43 + 29 = 72. Add 72 to the number set. Current number set: [72, 480], target: 27, just two numbers left.\n     |- Try 480 + 72 = 552. Evaluate 552 != 27, drop this branch.\n     |- Try 480 - 72 = 408. Evaluate 408 != 27, drop this branch.\n     |- Try 480 * 72 = 34560. 34560 exceeds the maximum intermediate result, drop this branch.\n     |- Try 480 \/ 72 = 6.7. 6.7 is a decimal, drop this branch.\n    |- Try 43 - 29 = 14. Add 14 to the number set. Current number set: [14, 480], target: 27, just two numbers left.\n     |- Try 480 + 14 = 494. Evaluate 494 != 27, drop this branch.\n     |- Try 480 - 14 = 466. Evaluate 466 != 27, drop this branch.\n     |- Try 480 * 14 = 6720. 6720 exceeds the maximum intermediate result, drop this branch.\n     |- Try 480 \/ 14 = 34.3. 34.3 is a decimal, drop this branch.\n    |- Try 43 * 29 = 1247. Add 1247 to the number set. Current number set: [1247, 480], target: 27, just two numbers left.\n     |- Try 1247 + 480 = 1727. Evaluate 1727 != 27, drop this branch.\n     |- Try 1247 - 480 = 767. Evaluate 767 != 27, drop this branch.\n     |- Try 1247 * 480 = 598560. 598560 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1247 \/ 480 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 43 \/ 29 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 48 \/ 10 = 4.8. 4.8 is a decimal, drop this branch.\n |- Pick two numbers (48, 43) (numbers left: [10, 29]). Try possible operations.\n  |- Try 48 + 43 = 91. Add 91 to the number set. Current number set: [91, 10, 29], target: 27. Options for choosing two numbers: [(91, 10), (91, 29), (10, 29)].\n   |- Pick two numbers (91, 10) (numbers left: [29]). Try possible operations.\n    |- Try 91 + 10 = 101. Add 101 to the number set. Current number set: [101, 29], target: 27, just two numbers left.\n     |- Try 101 + 29 = 130. Evaluate 130 != 27, drop this branch.\n     |- Try 101 - 29 = 72. Evaluate 72 != 27, drop this branch.\n     |- Try 101 * 29 = 2929. 2929 exceeds the maximum intermediate result, drop this branch.\n     |- Try 101 \/ 29 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 91 - 10 = 81. Add 81 to the number set. Current number set: [81, 29], target: 27, just two numbers left.\n     |- Try 81 + 29 = 110. Evaluate 110 != 27, drop this branch.\n     |- Try 81 - 29 = 52. Evaluate 52 != 27, drop this branch.\n     |- Try 81 * 29 = 2349. 2349 exceeds the maximum intermediate result, drop this branch.\n     |- Try 81 \/ 29 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 91 * 10 = 910. Add 910 to the number set. Current number set: [910, 29], target: 27, just two numbers left.\n     |- Try 910 + 29 = 939. Evaluate 939 != 27, drop this branch.\n     |- Try 910 - 29 = 881. Evaluate 881 != 27, drop this branch.\n     |- Try 910 * 29 = 26390. 26390 exceeds the maximum intermediate result, drop this branch.\n     |- Try 910 \/ 29 = 31.4. 31.4 is a decimal, drop this branch.\n    |- Try 91 \/ 10 = 9.1. 9.1 is a decimal, drop this branch.\n   |- Pick two numbers (91, 29) (numbers left: [10]). Try possible operations.\n    |- Try 91 + 29 = 120. Add 120 to the number set. Current number set: [120, 10], target: 27, just two numbers left.\n     |- Try 120 + 10 = 130. Evaluate 130 != 27, drop this branch.\n     |- Try 120 - 10 = 110. Evaluate 110 != 27, drop this branch.\n     |- Try 120 * 10 = 1200. Evaluate 1200 != 27, drop this branch.\n     |- Try 120 \/ 10 = 12. Evaluate 12 != 27, drop this branch.\n    |- Try 91 - 29 = 62. Add 62 to the number set. Current number set: [62, 10], target: 27, just two numbers left.\n     |- Try 62 + 10 = 72. Evaluate 72 != 27, drop this branch.\n     |- Try 62 - 10 = 52. Evaluate 52 != 27, drop this branch.\n     |- Try 62 * 10 = 620. Evaluate 620 != 27, drop this branch.\n     |- Try 62 \/ 10 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 91 * 29 = 2639. 2639 exceeds the maximum intermediate result, drop this branch.\n    |- Try 91 \/ 29 = 3.1. 3.1 is a decimal, drop this branch.\n   |- Pick two numbers (10, 29) (numbers left: [91]). Try possible operations.\n    |- Try 29 + 10 = 39. Add 39 to the number set. Current number set: [39, 91], target: 27, just two numbers left.\n     |- Try 91 + 39 = 130. Evaluate 130 != 27, drop this branch.\n     |- Try 91 - 39 = 52. Evaluate 52 != 27, drop this branch.\n     |- Try 91 * 39 = 3549. 3549 exceeds the maximum intermediate result, drop this branch.\n     |- Try 91 \/ 39 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 29 - 10 = 19. Add 19 to the number set. Current number set: [19, 91], target: 27, just two numbers left.\n     |- Try 91 + 19 = 110. Evaluate 110 != 27, drop this branch.\n     |- Try 91 - 19 = 72. Evaluate 72 != 27, drop this branch.\n     |- Try 91 * 19 = 1729. Evaluate 1729 != 27, drop this branch.\n     |- Try 91 \/ 19 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 29 * 10 = 290. Add 290 to the number set. Current number set: [290, 91], target: 27, just two numbers left.\n     |- Try 290 + 91 = 381. Evaluate 381 != 27, drop this branch.\n     |- Try 290 - 91 = 199. Evaluate 199 != 27, drop this branch.\n     |- Try 290 * 91 = 26390. 26390 exceeds the maximum intermediate result, drop this branch.\n     |- Try 290 \/ 91 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 29 \/ 10 = 2.9. 2.9 is a decimal, drop this branch.\n  |- Try 48 - 43 = 5. Add 5 to the number set. Current number set: [5, 10, 29], target: 27. Options for choosing two numbers: [(5, 10), (5, 29), (10, 29)].\n   |- Pick two numbers (5, 10) (numbers left: [29]). Try possible operations.\n    |- Try 10 + 5 = 15. Add 15 to the number set. Current number set: [15, 29], target: 27, just two numbers left.\n     |- Try 29 + 15 = 44. Evaluate 44 != 27, drop this branch.\n     |- Try 29 - 15 = 14. Evaluate 14 != 27, drop this branch.\n     |- Try 29 * 15 = 435. Evaluate 435 != 27, drop this branch.\n     |- Try 29 \/ 15 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 10 - 5 = 5. Add 5 to the number set. Current number set: [5, 29], target: 27, just two numbers left.\n     |- Try 29 + 5 = 34. Evaluate 34 != 27, drop this branch.\n     |- Try 29 - 5 = 24. Evaluate 24 != 27, drop this branch.\n     |- Try 29 * 5 = 145. Evaluate 145 != 27, drop this branch.\n     |- Try 29 \/ 5 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 10 * 5 = 50. Add 50 to the number set. Current number set: [50, 29], target: 27, just two numbers left.\n     |- Try 50 + 29 = 79. Evaluate 79 != 27, drop this branch.\n     |- Try 50 - 29 = 21. Evaluate 21 != 27, drop this branch.\n     |- Try 50 * 29 = 1450. Evaluate 1450 != 27, drop this branch.\n     |- Try 50 \/ 29 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 10 \/ 5 = 2. Add 2 to the number set. Current number set: [2, 29], target: 27, just two numbers left.\n     |- Try 29 + 2 = 31. Evaluate 31 != 27, drop this branch.\n     |- Try 29 - 2 = 27. Evaluate 27 == 27, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 29 - 2 = 27\nThe step before: 10 \/ 5 = 2\nThe first step: 48 - 43 = 5\n\nOutput the solution in the required format:\n<Solution>\n48 - 43 = 5\n10 \/ 5 = 2\n29 - 2 = 27\n<\/Solution>\n","item":{"nums":[48,10,43,29],"solution":["48 - 43 = 5","10 \/ 5 = 2","29 - 2 = 27"],"target":27}}
+{"instance_id":"countdown_8k_87","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [12, 17, 45, 16]\nTarget: 33","reference_output":"# Search Procedure\nInitial number set: [12, 17, 45, 16], target: 33. Options for choosing two numbers: [(12, 17), (12, 45), (12, 16), (17, 45), (17, 16), (45, 16)].\n |- Pick two numbers (12, 17) (numbers left: [45, 16]). Try possible operations.\n  |- Try 17 + 12 = 29. Add 29 to the number set. Current number set: [29, 45, 16], target: 33. Options for choosing two numbers: [(29, 45), (29, 16), (45, 16)].\n   |- Pick two numbers (29, 45) (numbers left: [16]). Try possible operations.\n    |- Try 45 + 29 = 74. Add 74 to the number set. Current number set: [74, 16], target: 33, just two numbers left.\n     |- Try 74 + 16 = 90. Evaluate 90 != 33, drop this branch.\n     |- Try 74 - 16 = 58. Evaluate 58 != 33, drop this branch.\n     |- Try 74 * 16 = 1184. Evaluate 1184 != 33, drop this branch.\n     |- Try 74 \/ 16 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 45 - 29 = 16. Add 16 to the number set. Current number set: [16, 16], target: 33, just two numbers left.\n     |- Try 16 + 16 = 32. Evaluate 32 != 33, drop this branch.\n     |- Try 16 - 16 = 0. Evaluate 0 != 33, drop this branch.\n     |- Try 16 * 16 = 256. Evaluate 256 != 33, drop this branch.\n     |- Try 16 \/ 16 = 1. Evaluate 1 != 33, drop this branch.\n    |- Try 45 * 29 = 1305. Add 1305 to the number set. Current number set: [1305, 16], target: 33, just two numbers left.\n     |- Try 1305 + 16 = 1321. Evaluate 1321 != 33, drop this branch.\n     |- Try 1305 - 16 = 1289. Evaluate 1289 != 33, drop this branch.\n     |- Try 1305 * 16 = 20880. 20880 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1305 \/ 16 = 81.6. 81.6 is a decimal, drop this branch.\n    |- Try 45 \/ 29 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (29, 16) (numbers left: [45]). Try possible operations.\n    |- Try 29 + 16 = 45. Add 45 to the number set. Current number set: [45, 45], target: 33, just two numbers left.\n     |- Try 45 + 45 = 90. Evaluate 90 != 33, drop this branch.\n     |- Try 45 - 45 = 0. Evaluate 0 != 33, drop this branch.\n     |- Try 45 * 45 = 2025. 2025 exceeds the maximum intermediate result, drop this branch.\n     |- Try 45 \/ 45 = 1. Evaluate 1 != 33, drop this branch.\n    |- Try 29 - 16 = 13. Add 13 to the number set. Current number set: [13, 45], target: 33, just two numbers left.\n     |- Try 45 + 13 = 58. Evaluate 58 != 33, drop this branch.\n     |- Try 45 - 13 = 32. Evaluate 32 != 33, drop this branch.\n     |- Try 45 * 13 = 585. Evaluate 585 != 33, drop this branch.\n     |- Try 45 \/ 13 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 29 * 16 = 464. Add 464 to the number set. Current number set: [464, 45], target: 33, just two numbers left.\n     |- Try 464 + 45 = 509. Evaluate 509 != 33, drop this branch.\n     |- Try 464 - 45 = 419. Evaluate 419 != 33, drop this branch.\n     |- Try 464 * 45 = 20880. 20880 exceeds the maximum intermediate result, drop this branch.\n     |- Try 464 \/ 45 = 10.3. 10.3 is a decimal, drop this branch.\n    |- Try 29 \/ 16 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (45, 16) (numbers left: [29]). Try possible operations.\n    |- Try 45 + 16 = 61. Add 61 to the number set. Current number set: [61, 29], target: 33, just two numbers left.\n     |- Try 61 + 29 = 90. Evaluate 90 != 33, drop this branch.\n     |- Try 61 - 29 = 32. Evaluate 32 != 33, drop this branch.\n     |- Try 61 * 29 = 1769. Evaluate 1769 != 33, drop this branch.\n     |- Try 61 \/ 29 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 45 - 16 = 29. Add 29 to the number set. Current number set: [29, 29], target: 33, just two numbers left.\n     |- Try 29 + 29 = 58. Evaluate 58 != 33, drop this branch.\n     |- Try 29 - 29 = 0. Evaluate 0 != 33, drop this branch.\n     |- Try 29 * 29 = 841. Evaluate 841 != 33, drop this branch.\n     |- Try 29 \/ 29 = 1. Evaluate 1 != 33, drop this branch.\n    |- Try 45 * 16 = 720. Add 720 to the number set. Current number set: [720, 29], target: 33, just two numbers left.\n     |- Try 720 + 29 = 749. Evaluate 749 != 33, drop this branch.\n     |- Try 720 - 29 = 691. Evaluate 691 != 33, drop this branch.\n     |- Try 720 * 29 = 20880. 20880 exceeds the maximum intermediate result, drop this branch.\n     |- Try 720 \/ 29 = 24.8. 24.8 is a decimal, drop this branch.\n    |- Try 45 \/ 16 = 2.8. 2.8 is a decimal, drop this branch.\n  |- Try 17 - 12 = 5. Add 5 to the number set. Current number set: [5, 45, 16], target: 33. Options for choosing two numbers: [(5, 45), (5, 16), (45, 16)].\n   |- Pick two numbers (5, 45) (numbers left: [16]). Try possible operations.\n    |- Try 45 + 5 = 50. Add 50 to the number set. Current number set: [50, 16], target: 33, just two numbers left.\n     |- Try 50 + 16 = 66. Evaluate 66 != 33, drop this branch.\n     |- Try 50 - 16 = 34. Evaluate 34 != 33, drop this branch.\n     |- Try 50 * 16 = 800. Evaluate 800 != 33, drop this branch.\n     |- Try 50 \/ 16 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 45 - 5 = 40. Add 40 to the number set. Current number set: [40, 16], target: 33, just two numbers left.\n     |- Try 40 + 16 = 56. Evaluate 56 != 33, drop this branch.\n     |- Try 40 - 16 = 24. Evaluate 24 != 33, drop this branch.\n     |- Try 40 * 16 = 640. Evaluate 640 != 33, drop this branch.\n     |- Try 40 \/ 16 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 45 * 5 = 225. Add 225 to the number set. Current number set: [225, 16], target: 33, just two numbers left.\n     |- Try 225 + 16 = 241. Evaluate 241 != 33, drop this branch.\n     |- Try 225 - 16 = 209. Evaluate 209 != 33, drop this branch.\n     |- Try 225 * 16 = 3600. 3600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 225 \/ 16 = 14.1. 14.1 is a decimal, drop this branch.\n    |- Try 45 \/ 5 = 9. Add 9 to the number set. Current number set: [9, 16], target: 33, just two numbers left.\n     |- Try 16 + 9 = 25. Evaluate 25 != 33, drop this branch.\n     |- Try 16 - 9 = 7. Evaluate 7 != 33, drop this branch.\n     |- Try 16 * 9 = 144. Evaluate 144 != 33, drop this branch.\n     |- Try 16 \/ 9 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (5, 16) (numbers left: [45]). Try possible operations.\n    |- Try 16 + 5 = 21. Add 21 to the number set. Current number set: [21, 45], target: 33, just two numbers left.\n     |- Try 45 + 21 = 66. Evaluate 66 != 33, drop this branch.\n     |- Try 45 - 21 = 24. Evaluate 24 != 33, drop this branch.\n     |- Try 45 * 21 = 945. Evaluate 945 != 33, drop this branch.\n     |- Try 45 \/ 21 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 16 - 5 = 11. Add 11 to the number set. Current number set: [11, 45], target: 33, just two numbers left.\n     |- Try 45 + 11 = 56. Evaluate 56 != 33, drop this branch.\n     |- Try 45 - 11 = 34. Evaluate 34 != 33, drop this branch.\n     |- Try 45 * 11 = 495. Evaluate 495 != 33, drop this branch.\n     |- Try 45 \/ 11 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 16 * 5 = 80. Add 80 to the number set. Current number set: [80, 45], target: 33, just two numbers left.\n     |- Try 80 + 45 = 125. Evaluate 125 != 33, drop this branch.\n     |- Try 80 - 45 = 35. Evaluate 35 != 33, drop this branch.\n     |- Try 80 * 45 = 3600. 3600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 80 \/ 45 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 16 \/ 5 = 3.2. 3.2 is a decimal, drop this branch.\n   |- Pick two numbers (45, 16) (numbers left: [5]). Try possible operations.\n    |- Try 45 + 16 = 61. Add 61 to the number set. Current number set: [61, 5], target: 33, just two numbers left.\n     |- Try 61 + 5 = 66. Evaluate 66 != 33, drop this branch.\n     |- Try 61 - 5 = 56. Evaluate 56 != 33, drop this branch.\n     |- Try 61 * 5 = 305. Evaluate 305 != 33, drop this branch.\n     |- Try 61 \/ 5 = 12.2. 12.2 is a decimal, drop this branch.\n    |- Try 45 - 16 = 29. Add 29 to the number set. Current number set: [29, 5], target: 33, just two numbers left.\n     |- Try 29 + 5 = 34. Evaluate 34 != 33, drop this branch.\n     |- Try 29 - 5 = 24. Evaluate 24 != 33, drop this branch.\n     |- Try 29 * 5 = 145. Evaluate 145 != 33, drop this branch.\n     |- Try 29 \/ 5 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 45 * 16 = 720. Add 720 to the number set. Current number set: [720, 5], target: 33, just two numbers left.\n     |- Try 720 + 5 = 725. Evaluate 725 != 33, drop this branch.\n     |- Try 720 - 5 = 715. Evaluate 715 != 33, drop this branch.\n     |- Try 720 * 5 = 3600. 3600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 720 \/ 5 = 144. Evaluate 144 != 33, drop this branch.\n    |- Try 45 \/ 16 = 2.8. 2.8 is a decimal, drop this branch.\n  |- Try 17 * 12 = 204. Add 204 to the number set. Current number set: [204, 45, 16], target: 33. Options for choosing two numbers: [(204, 45), (204, 16), (45, 16)].\n   |- Pick two numbers (204, 45) (numbers left: [16]). Try possible operations.\n    |- Try 204 + 45 = 249. Add 249 to the number set. Current number set: [249, 16], target: 33, just two numbers left.\n     |- Try 249 + 16 = 265. Evaluate 265 != 33, drop this branch.\n     |- Try 249 - 16 = 233. Evaluate 233 != 33, drop this branch.\n     |- Try 249 * 16 = 3984. 3984 exceeds the maximum intermediate result, drop this branch.\n     |- Try 249 \/ 16 = 15.6. 15.6 is a decimal, drop this branch.\n    |- Try 204 - 45 = 159. Add 159 to the number set. Current number set: [159, 16], target: 33, just two numbers left.\n     |- Try 159 + 16 = 175. Evaluate 175 != 33, drop this branch.\n     |- Try 159 - 16 = 143. Evaluate 143 != 33, drop this branch.\n     |- Try 159 * 16 = 2544. 2544 exceeds the maximum intermediate result, drop this branch.\n     |- Try 159 \/ 16 = 9.9. 9.9 is a decimal, drop this branch.\n    |- Try 204 * 45 = 9180. 9180 exceeds the maximum intermediate result, drop this branch.\n    |- Try 204 \/ 45 = 4.5. 4.5 is a decimal, drop this branch.\n   |- Pick two numbers (204, 16) (numbers left: [45]). Try possible operations.\n    |- Try 204 + 16 = 220. Add 220 to the number set. Current number set: [220, 45], target: 33, just two numbers left.\n     |- Try 220 + 45 = 265. Evaluate 265 != 33, drop this branch.\n     |- Try 220 - 45 = 175. Evaluate 175 != 33, drop this branch.\n     |- Try 220 * 45 = 9900. 9900 exceeds the maximum intermediate result, drop this branch.\n     |- Try 220 \/ 45 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 204 - 16 = 188. Add 188 to the number set. Current number set: [188, 45], target: 33, just two numbers left.\n     |- Try 188 + 45 = 233. Evaluate 233 != 33, drop this branch.\n     |- Try 188 - 45 = 143. Evaluate 143 != 33, drop this branch.\n     |- Try 188 * 45 = 8460. 8460 exceeds the maximum intermediate result, drop this branch.\n     |- Try 188 \/ 45 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 204 * 16 = 3264. 3264 exceeds the maximum intermediate result, drop this branch.\n    |- Try 204 \/ 16 = 12.8. 12.8 is a decimal, drop this branch.\n   |- Pick two numbers (45, 16) (numbers left: [204]). Try possible operations.\n    |- Try 45 + 16 = 61. Add 61 to the number set. Current number set: [61, 204], target: 33, just two numbers left.\n     |- Try 204 + 61 = 265. Evaluate 265 != 33, drop this branch.\n     |- Try 204 - 61 = 143. Evaluate 143 != 33, drop this branch.\n     |- Try 204 * 61 = 12444. 12444 exceeds the maximum intermediate result, drop this branch.\n     |- Try 204 \/ 61 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 45 - 16 = 29. Add 29 to the number set. Current number set: [29, 204], target: 33, just two numbers left.\n     |- Try 204 + 29 = 233. Evaluate 233 != 33, drop this branch.\n     |- Try 204 - 29 = 175. Evaluate 175 != 33, drop this branch.\n     |- Try 204 * 29 = 5916. 5916 exceeds the maximum intermediate result, drop this branch.\n     |- Try 204 \/ 29 = 7.0. 7.0 is a decimal, drop this branch.\n    |- Try 45 * 16 = 720. Add 720 to the number set. Current number set: [720, 204], target: 33, just two numbers left.\n     |- Try 720 + 204 = 924. Evaluate 924 != 33, drop this branch.\n     |- Try 720 - 204 = 516. Evaluate 516 != 33, drop this branch.\n     |- Try 720 * 204 = 146880. 146880 exceeds the maximum intermediate result, drop this branch.\n     |- Try 720 \/ 204 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 45 \/ 16 = 2.8. 2.8 is a decimal, drop this branch.\n  |- Try 17 \/ 12 = 1.4. 1.4 is a decimal, drop this branch.\n |- Pick two numbers (12, 45) (numbers left: [17, 16]). Try possible operations.\n  |- Try 45 + 12 = 57. Add 57 to the number set. Current number set: [57, 17, 16], target: 33. Options for choosing two numbers: [(57, 17), (57, 16), (17, 16)].\n   |- Pick two numbers (57, 17) (numbers left: [16]). Try possible operations.\n    |- Try 57 + 17 = 74. Add 74 to the number set. Current number set: [74, 16], target: 33, just two numbers left.\n     |- Try 74 + 16 = 90. Evaluate 90 != 33, drop this branch.\n     |- Try 74 - 16 = 58. Evaluate 58 != 33, drop this branch.\n     |- Try 74 * 16 = 1184. Evaluate 1184 != 33, drop this branch.\n     |- Try 74 \/ 16 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 57 - 17 = 40. Add 40 to the number set. Current number set: [40, 16], target: 33, just two numbers left.\n     |- Try 40 + 16 = 56. Evaluate 56 != 33, drop this branch.\n     |- Try 40 - 16 = 24. Evaluate 24 != 33, drop this branch.\n     |- Try 40 * 16 = 640. Evaluate 640 != 33, drop this branch.\n     |- Try 40 \/ 16 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 57 * 17 = 969. Add 969 to the number set. Current number set: [969, 16], target: 33, just two numbers left.\n     |- Try 969 + 16 = 985. Evaluate 985 != 33, drop this branch.\n     |- Try 969 - 16 = 953. Evaluate 953 != 33, drop this branch.\n     |- Try 969 * 16 = 15504. 15504 exceeds the maximum intermediate result, drop this branch.\n     |- Try 969 \/ 16 = 60.6. 60.6 is a decimal, drop this branch.\n    |- Try 57 \/ 17 = 3.4. 3.4 is a decimal, drop this branch.\n   |- Pick two numbers (57, 16) (numbers left: [17]). Try possible operations.\n    |- Try 57 + 16 = 73. Add 73 to the number set. Current number set: [73, 17], target: 33, just two numbers left.\n     |- Try 73 + 17 = 90. Evaluate 90 != 33, drop this branch.\n     |- Try 73 - 17 = 56. Evaluate 56 != 33, drop this branch.\n     |- Try 73 * 17 = 1241. Evaluate 1241 != 33, drop this branch.\n     |- Try 73 \/ 17 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 57 - 16 = 41. Add 41 to the number set. Current number set: [41, 17], target: 33, just two numbers left.\n     |- Try 41 + 17 = 58. Evaluate 58 != 33, drop this branch.\n     |- Try 41 - 17 = 24. Evaluate 24 != 33, drop this branch.\n     |- Try 41 * 17 = 697. Evaluate 697 != 33, drop this branch.\n     |- Try 41 \/ 17 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 57 * 16 = 912. Add 912 to the number set. Current number set: [912, 17], target: 33, just two numbers left.\n     |- Try 912 + 17 = 929. Evaluate 929 != 33, drop this branch.\n     |- Try 912 - 17 = 895. Evaluate 895 != 33, drop this branch.\n     |- Try 912 * 17 = 15504. 15504 exceeds the maximum intermediate result, drop this branch.\n     |- Try 912 \/ 17 = 53.6. 53.6 is a decimal, drop this branch.\n    |- Try 57 \/ 16 = 3.6. 3.6 is a decimal, drop this branch.\n   |- Pick two numbers (17, 16) (numbers left: [57]). Try possible operations.\n    |- Try 17 + 16 = 33. Add 33 to the number set. Current number set: [33, 57], target: 33, just two numbers left.\n     |- Try 57 + 33 = 90. Evaluate 90 != 33, drop this branch.\n     |- Try 57 - 33 = 24. Evaluate 24 != 33, drop this branch.\n     |- Try 57 * 33 = 1881. Evaluate 1881 != 33, drop this branch.\n     |- Try 57 \/ 33 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 17 - 16 = 1. Add 1 to the number set. Current number set: [1, 57], target: 33, just two numbers left.\n     |- Try 57 + 1 = 58. Evaluate 58 != 33, drop this branch.\n     |- Try 57 - 1 = 56. Evaluate 56 != 33, drop this branch.\n     |- Try 57 * 1 = 57. Evaluate 57 != 33, drop this branch.\n     |- Try 57 \/ 1 = 57. Evaluate 57 != 33, drop this branch.\n    |- Try 17 * 16 = 272. Add 272 to the number set. Current number set: [272, 57], target: 33, just two numbers left.\n     |- Try 272 + 57 = 329. Evaluate 329 != 33, drop this branch.\n     |- Try 272 - 57 = 215. Evaluate 215 != 33, drop this branch.\n     |- Try 272 * 57 = 15504. 15504 exceeds the maximum intermediate result, drop this branch.\n     |- Try 272 \/ 57 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 17 \/ 16 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 45 - 12 = 33. Add 33 to the number set. Current number set: [33, 17, 16], target: 33. Options for choosing two numbers: [(33, 17), (33, 16), (17, 16)].\n   |- Pick two numbers (33, 17) (numbers left: [16]). Try possible operations.\n    |- Try 33 + 17 = 50. Add 50 to the number set. Current number set: [50, 16], target: 33, just two numbers left.\n     |- Try 50 + 16 = 66. Evaluate 66 != 33, drop this branch.\n     |- Try 50 - 16 = 34. Evaluate 34 != 33, drop this branch.\n     |- Try 50 * 16 = 800. Evaluate 800 != 33, drop this branch.\n     |- Try 50 \/ 16 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 33 - 17 = 16. Add 16 to the number set. Current number set: [16, 16], target: 33, just two numbers left.\n     |- Try 16 + 16 = 32. Evaluate 32 != 33, drop this branch.\n     |- Try 16 - 16 = 0. Evaluate 0 != 33, drop this branch.\n     |- Try 16 * 16 = 256. Evaluate 256 != 33, drop this branch.\n     |- Try 16 \/ 16 = 1. Evaluate 1 != 33, drop this branch.\n    |- Try 33 * 17 = 561. Add 561 to the number set. Current number set: [561, 16], target: 33, just two numbers left.\n     |- Try 561 + 16 = 577. Evaluate 577 != 33, drop this branch.\n     |- Try 561 - 16 = 545. Evaluate 545 != 33, drop this branch.\n     |- Try 561 * 16 = 8976. 8976 exceeds the maximum intermediate result, drop this branch.\n     |- Try 561 \/ 16 = 35.1. 35.1 is a decimal, drop this branch.\n    |- Try 33 \/ 17 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (33, 16) (numbers left: [17]). Try possible operations.\n    |- Try 33 + 16 = 49. Add 49 to the number set. Current number set: [49, 17], target: 33, just two numbers left.\n     |- Try 49 + 17 = 66. Evaluate 66 != 33, drop this branch.\n     |- Try 49 - 17 = 32. Evaluate 32 != 33, drop this branch.\n     |- Try 49 * 17 = 833. Evaluate 833 != 33, drop this branch.\n     |- Try 49 \/ 17 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 33 - 16 = 17. Add 17 to the number set. Current number set: [17, 17], target: 33, just two numbers left.\n     |- Try 17 + 17 = 34. Evaluate 34 != 33, drop this branch.\n     |- Try 17 - 17 = 0. Evaluate 0 != 33, drop this branch.\n     |- Try 17 * 17 = 289. Evaluate 289 != 33, drop this branch.\n     |- Try 17 \/ 17 = 1. Evaluate 1 != 33, drop this branch.\n    |- Try 33 * 16 = 528. Add 528 to the number set. Current number set: [528, 17], target: 33, just two numbers left.\n     |- Try 528 + 17 = 545. Evaluate 545 != 33, drop this branch.\n     |- Try 528 - 17 = 511. Evaluate 511 != 33, drop this branch.\n     |- Try 528 * 17 = 8976. 8976 exceeds the maximum intermediate result, drop this branch.\n     |- Try 528 \/ 17 = 31.1. 31.1 is a decimal, drop this branch.\n    |- Try 33 \/ 16 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (17, 16) (numbers left: [33]). Try possible operations.\n    |- Try 17 + 16 = 33. Add 33 to the number set. Current number set: [33, 33], target: 33, just two numbers left.\n     |- Try 33 + 33 = 66. Evaluate 66 != 33, drop this branch.\n     |- Try 33 - 33 = 0. Evaluate 0 != 33, drop this branch.\n     |- Try 33 * 33 = 1089. Evaluate 1089 != 33, drop this branch.\n     |- Try 33 \/ 33 = 1. Evaluate 1 != 33, drop this branch.\n    |- Try 17 - 16 = 1. Add 1 to the number set. Current number set: [1, 33], target: 33, just two numbers left.\n     |- Try 33 + 1 = 34. Evaluate 34 != 33, drop this branch.\n     |- Try 33 - 1 = 32. Evaluate 32 != 33, drop this branch.\n     |- Try 33 * 1 = 33. Evaluate 33 == 33, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 33 * 1 = 33\nThe step before: 17 - 16 = 1\nThe first step: 45 - 12 = 33\n\nOutput the solution in the required format:\n<Solution>\n45 - 12 = 33\n17 - 16 = 1\n33 * 1 = 33\n<\/Solution>\n","item":{"nums":[12,17,45,16],"solution":["45 - 12 = 33","17 - 16 = 1","33 * 1 = 33"],"target":33}}
+{"instance_id":"countdown_8k_88","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [1, 5, 1, 27]\nTarget: 37","reference_output":"# Search Procedure\nInitial number set: [1, 5, 1, 27], target: 37. Options for choosing two numbers: [(1, 5), (1, 1), (1, 27), (5, 1), (5, 27), (1, 27)].\n |- Pick two numbers (1, 5) (numbers left: [1, 27]). Try possible operations.\n  |- Try 5 + 1 = 6. Add 6 to the number set. Current number set: [6, 1, 27], target: 37. Options for choosing two numbers: [(6, 1), (6, 27), (1, 27)].\n   |- Pick two numbers (6, 1) (numbers left: [27]). Try possible operations.\n    |- Try 6 + 1 = 7. Add 7 to the number set. Current number set: [7, 27], target: 37, just two numbers left.\n     |- Try 27 + 7 = 34. Evaluate 34 != 37, drop this branch.\n     |- Try 27 - 7 = 20. Evaluate 20 != 37, drop this branch.\n     |- Try 27 * 7 = 189. Evaluate 189 != 37, drop this branch.\n     |- Try 27 \/ 7 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 6 - 1 = 5. Add 5 to the number set. Current number set: [5, 27], target: 37, just two numbers left.\n     |- Try 27 + 5 = 32. Evaluate 32 != 37, drop this branch.\n     |- Try 27 - 5 = 22. Evaluate 22 != 37, drop this branch.\n     |- Try 27 * 5 = 135. Evaluate 135 != 37, drop this branch.\n     |- Try 27 \/ 5 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 6 * 1 = 6. Add 6 to the number set. Current number set: [6, 27], target: 37, just two numbers left.\n     |- Try 27 + 6 = 33. Evaluate 33 != 37, drop this branch.\n     |- Try 27 - 6 = 21. Evaluate 21 != 37, drop this branch.\n     |- Try 27 * 6 = 162. Evaluate 162 != 37, drop this branch.\n     |- Try 27 \/ 6 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 6 \/ 1 = 6. Add 6 to the number set. Current number set: [6, 27], target: 37, just two numbers left.\n     |- Try 27 + 6 = 33. Evaluate 33 != 37, drop this branch.\n     |- Try 27 - 6 = 21. Evaluate 21 != 37, drop this branch.\n     |- Try 27 * 6 = 162. Evaluate 162 != 37, drop this branch.\n     |- Try 27 \/ 6 = 4.5. 4.5 is a decimal, drop this branch.\n   |- Pick two numbers (6, 27) (numbers left: [1]). Try possible operations.\n    |- Try 27 + 6 = 33. Add 33 to the number set. Current number set: [33, 1], target: 37, just two numbers left.\n     |- Try 33 + 1 = 34. Evaluate 34 != 37, drop this branch.\n     |- Try 33 - 1 = 32. Evaluate 32 != 37, drop this branch.\n     |- Try 33 * 1 = 33. Evaluate 33 != 37, drop this branch.\n     |- Try 33 \/ 1 = 33. Evaluate 33 != 37, drop this branch.\n    |- Try 27 - 6 = 21. Add 21 to the number set. Current number set: [21, 1], target: 37, just two numbers left.\n     |- Try 21 + 1 = 22. Evaluate 22 != 37, drop this branch.\n     |- Try 21 - 1 = 20. Evaluate 20 != 37, drop this branch.\n     |- Try 21 * 1 = 21. Evaluate 21 != 37, drop this branch.\n     |- Try 21 \/ 1 = 21. Evaluate 21 != 37, drop this branch.\n    |- Try 27 * 6 = 162. Add 162 to the number set. Current number set: [162, 1], target: 37, just two numbers left.\n     |- Try 162 + 1 = 163. Evaluate 163 != 37, drop this branch.\n     |- Try 162 - 1 = 161. Evaluate 161 != 37, drop this branch.\n     |- Try 162 * 1 = 162. Evaluate 162 != 37, drop this branch.\n     |- Try 162 \/ 1 = 162. Evaluate 162 != 37, drop this branch.\n    |- Try 27 \/ 6 = 4.5. 4.5 is a decimal, drop this branch.\n   |- Pick two numbers (1, 27) (numbers left: [6]). Try possible operations.\n    |- Try 27 + 1 = 28. Add 28 to the number set. Current number set: [28, 6], target: 37, just two numbers left.\n     |- Try 28 + 6 = 34. Evaluate 34 != 37, drop this branch.\n     |- Try 28 - 6 = 22. Evaluate 22 != 37, drop this branch.\n     |- Try 28 * 6 = 168. Evaluate 168 != 37, drop this branch.\n     |- Try 28 \/ 6 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 27 - 1 = 26. Add 26 to the number set. Current number set: [26, 6], target: 37, just two numbers left.\n     |- Try 26 + 6 = 32. Evaluate 32 != 37, drop this branch.\n     |- Try 26 - 6 = 20. Evaluate 20 != 37, drop this branch.\n     |- Try 26 * 6 = 156. Evaluate 156 != 37, drop this branch.\n     |- Try 26 \/ 6 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 27 * 1 = 27. Add 27 to the number set. Current number set: [27, 6], target: 37, just two numbers left.\n     |- Try 27 + 6 = 33. Evaluate 33 != 37, drop this branch.\n     |- Try 27 - 6 = 21. Evaluate 21 != 37, drop this branch.\n     |- Try 27 * 6 = 162. Evaluate 162 != 37, drop this branch.\n     |- Try 27 \/ 6 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 27 \/ 1 = 27. Add 27 to the number set. Current number set: [27, 6], target: 37, just two numbers left.\n     |- Try 27 + 6 = 33. Evaluate 33 != 37, drop this branch.\n     |- Try 27 - 6 = 21. Evaluate 21 != 37, drop this branch.\n     |- Try 27 * 6 = 162. Evaluate 162 != 37, drop this branch.\n     |- Try 27 \/ 6 = 4.5. 4.5 is a decimal, drop this branch.\n  |- Try 5 - 1 = 4. Add 4 to the number set. Current number set: [4, 1, 27], target: 37. Options for choosing two numbers: [(4, 1), (4, 27), (1, 27)].\n   |- Pick two numbers (4, 1) (numbers left: [27]). Try possible operations.\n    |- Try 4 + 1 = 5. Add 5 to the number set. Current number set: [5, 27], target: 37, just two numbers left.\n     |- Try 27 + 5 = 32. Evaluate 32 != 37, drop this branch.\n     |- Try 27 - 5 = 22. Evaluate 22 != 37, drop this branch.\n     |- Try 27 * 5 = 135. Evaluate 135 != 37, drop this branch.\n     |- Try 27 \/ 5 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 4 - 1 = 3. Add 3 to the number set. Current number set: [3, 27], target: 37, just two numbers left.\n     |- Try 27 + 3 = 30. Evaluate 30 != 37, drop this branch.\n     |- Try 27 - 3 = 24. Evaluate 24 != 37, drop this branch.\n     |- Try 27 * 3 = 81. Evaluate 81 != 37, drop this branch.\n     |- Try 27 \/ 3 = 9. Evaluate 9 != 37, drop this branch.\n    |- Try 4 * 1 = 4. Add 4 to the number set. Current number set: [4, 27], target: 37, just two numbers left.\n     |- Try 27 + 4 = 31. Evaluate 31 != 37, drop this branch.\n     |- Try 27 - 4 = 23. Evaluate 23 != 37, drop this branch.\n     |- Try 27 * 4 = 108. Evaluate 108 != 37, drop this branch.\n     |- Try 27 \/ 4 = 6.8. 6.8 is a decimal, drop this branch.\n    |- Try 4 \/ 1 = 4. Add 4 to the number set. Current number set: [4, 27], target: 37, just two numbers left.\n     |- Try 27 + 4 = 31. Evaluate 31 != 37, drop this branch.\n     |- Try 27 - 4 = 23. Evaluate 23 != 37, drop this branch.\n     |- Try 27 * 4 = 108. Evaluate 108 != 37, drop this branch.\n     |- Try 27 \/ 4 = 6.8. 6.8 is a decimal, drop this branch.\n   |- Pick two numbers (4, 27) (numbers left: [1]). Try possible operations.\n    |- Try 27 + 4 = 31. Add 31 to the number set. Current number set: [31, 1], target: 37, just two numbers left.\n     |- Try 31 + 1 = 32. Evaluate 32 != 37, drop this branch.\n     |- Try 31 - 1 = 30. Evaluate 30 != 37, drop this branch.\n     |- Try 31 * 1 = 31. Evaluate 31 != 37, drop this branch.\n     |- Try 31 \/ 1 = 31. Evaluate 31 != 37, drop this branch.\n    |- Try 27 - 4 = 23. Add 23 to the number set. Current number set: [23, 1], target: 37, just two numbers left.\n     |- Try 23 + 1 = 24. Evaluate 24 != 37, drop this branch.\n     |- Try 23 - 1 = 22. Evaluate 22 != 37, drop this branch.\n     |- Try 23 * 1 = 23. Evaluate 23 != 37, drop this branch.\n     |- Try 23 \/ 1 = 23. Evaluate 23 != 37, drop this branch.\n    |- Try 27 * 4 = 108. Add 108 to the number set. Current number set: [108, 1], target: 37, just two numbers left.\n     |- Try 108 + 1 = 109. Evaluate 109 != 37, drop this branch.\n     |- Try 108 - 1 = 107. Evaluate 107 != 37, drop this branch.\n     |- Try 108 * 1 = 108. Evaluate 108 != 37, drop this branch.\n     |- Try 108 \/ 1 = 108. Evaluate 108 != 37, drop this branch.\n    |- Try 27 \/ 4 = 6.8. 6.8 is a decimal, drop this branch.\n   |- Pick two numbers (1, 27) (numbers left: [4]). Try possible operations.\n    |- Try 27 + 1 = 28. Add 28 to the number set. Current number set: [28, 4], target: 37, just two numbers left.\n     |- Try 28 + 4 = 32. Evaluate 32 != 37, drop this branch.\n     |- Try 28 - 4 = 24. Evaluate 24 != 37, drop this branch.\n     |- Try 28 * 4 = 112. Evaluate 112 != 37, drop this branch.\n     |- Try 28 \/ 4 = 7. Evaluate 7 != 37, drop this branch.\n    |- Try 27 - 1 = 26. Add 26 to the number set. Current number set: [26, 4], target: 37, just two numbers left.\n     |- Try 26 + 4 = 30. Evaluate 30 != 37, drop this branch.\n     |- Try 26 - 4 = 22. Evaluate 22 != 37, drop this branch.\n     |- Try 26 * 4 = 104. Evaluate 104 != 37, drop this branch.\n     |- Try 26 \/ 4 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 27 * 1 = 27. Add 27 to the number set. Current number set: [27, 4], target: 37, just two numbers left.\n     |- Try 27 + 4 = 31. Evaluate 31 != 37, drop this branch.\n     |- Try 27 - 4 = 23. Evaluate 23 != 37, drop this branch.\n     |- Try 27 * 4 = 108. Evaluate 108 != 37, drop this branch.\n     |- Try 27 \/ 4 = 6.8. 6.8 is a decimal, drop this branch.\n    |- Try 27 \/ 1 = 27. Add 27 to the number set. Current number set: [27, 4], target: 37, just two numbers left.\n     |- Try 27 + 4 = 31. Evaluate 31 != 37, drop this branch.\n     |- Try 27 - 4 = 23. Evaluate 23 != 37, drop this branch.\n     |- Try 27 * 4 = 108. Evaluate 108 != 37, drop this branch.\n     |- Try 27 \/ 4 = 6.8. 6.8 is a decimal, drop this branch.\n  |- Try 5 * 1 = 5. Add 5 to the number set. Current number set: [5, 1, 27], target: 37. Options for choosing two numbers: [(5, 1), (5, 27), (1, 27)].\n   |- Pick two numbers (5, 1) (numbers left: [27]). Try possible operations.\n    |- Try 5 + 1 = 6. Add 6 to the number set. Current number set: [6, 27], target: 37, just two numbers left.\n     |- Try 27 + 6 = 33. Evaluate 33 != 37, drop this branch.\n     |- Try 27 - 6 = 21. Evaluate 21 != 37, drop this branch.\n     |- Try 27 * 6 = 162. Evaluate 162 != 37, drop this branch.\n     |- Try 27 \/ 6 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 5 - 1 = 4. Add 4 to the number set. Current number set: [4, 27], target: 37, just two numbers left.\n     |- Try 27 + 4 = 31. Evaluate 31 != 37, drop this branch.\n     |- Try 27 - 4 = 23. Evaluate 23 != 37, drop this branch.\n     |- Try 27 * 4 = 108. Evaluate 108 != 37, drop this branch.\n     |- Try 27 \/ 4 = 6.8. 6.8 is a decimal, drop this branch.\n    |- Try 5 * 1 = 5. Add 5 to the number set. Current number set: [5, 27], target: 37, just two numbers left.\n     |- Try 27 + 5 = 32. Evaluate 32 != 37, drop this branch.\n     |- Try 27 - 5 = 22. Evaluate 22 != 37, drop this branch.\n     |- Try 27 * 5 = 135. Evaluate 135 != 37, drop this branch.\n     |- Try 27 \/ 5 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 5 \/ 1 = 5. Add 5 to the number set. Current number set: [5, 27], target: 37, just two numbers left.\n     |- Try 27 + 5 = 32. Evaluate 32 != 37, drop this branch.\n     |- Try 27 - 5 = 22. Evaluate 22 != 37, drop this branch.\n     |- Try 27 * 5 = 135. Evaluate 135 != 37, drop this branch.\n     |- Try 27 \/ 5 = 5.4. 5.4 is a decimal, drop this branch.\n   |- Pick two numbers (5, 27) (numbers left: [1]). Try possible operations.\n    |- Try 27 + 5 = 32. Add 32 to the number set. Current number set: [32, 1], target: 37, just two numbers left.\n     |- Try 32 + 1 = 33. Evaluate 33 != 37, drop this branch.\n     |- Try 32 - 1 = 31. Evaluate 31 != 37, drop this branch.\n     |- Try 32 * 1 = 32. Evaluate 32 != 37, drop this branch.\n     |- Try 32 \/ 1 = 32. Evaluate 32 != 37, drop this branch.\n    |- Try 27 - 5 = 22. Add 22 to the number set. Current number set: [22, 1], target: 37, just two numbers left.\n     |- Try 22 + 1 = 23. Evaluate 23 != 37, drop this branch.\n     |- Try 22 - 1 = 21. Evaluate 21 != 37, drop this branch.\n     |- Try 22 * 1 = 22. Evaluate 22 != 37, drop this branch.\n     |- Try 22 \/ 1 = 22. Evaluate 22 != 37, drop this branch.\n    |- Try 27 * 5 = 135. Add 135 to the number set. Current number set: [135, 1], target: 37, just two numbers left.\n     |- Try 135 + 1 = 136. Evaluate 136 != 37, drop this branch.\n     |- Try 135 - 1 = 134. Evaluate 134 != 37, drop this branch.\n     |- Try 135 * 1 = 135. Evaluate 135 != 37, drop this branch.\n     |- Try 135 \/ 1 = 135. Evaluate 135 != 37, drop this branch.\n    |- Try 27 \/ 5 = 5.4. 5.4 is a decimal, drop this branch.\n   |- Pick two numbers (1, 27) (numbers left: [5]). Try possible operations.\n    |- Try 27 + 1 = 28. Add 28 to the number set. Current number set: [28, 5], target: 37, just two numbers left.\n     |- Try 28 + 5 = 33. Evaluate 33 != 37, drop this branch.\n     |- Try 28 - 5 = 23. Evaluate 23 != 37, drop this branch.\n     |- Try 28 * 5 = 140. Evaluate 140 != 37, drop this branch.\n     |- Try 28 \/ 5 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 27 - 1 = 26. Add 26 to the number set. Current number set: [26, 5], target: 37, just two numbers left.\n     |- Try 26 + 5 = 31. Evaluate 31 != 37, drop this branch.\n     |- Try 26 - 5 = 21. Evaluate 21 != 37, drop this branch.\n     |- Try 26 * 5 = 130. Evaluate 130 != 37, drop this branch.\n     |- Try 26 \/ 5 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 27 * 1 = 27. Add 27 to the number set. Current number set: [27, 5], target: 37, just two numbers left.\n     |- Try 27 + 5 = 32. Evaluate 32 != 37, drop this branch.\n     |- Try 27 - 5 = 22. Evaluate 22 != 37, drop this branch.\n     |- Try 27 * 5 = 135. Evaluate 135 != 37, drop this branch.\n     |- Try 27 \/ 5 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 27 \/ 1 = 27. Add 27 to the number set. Current number set: [27, 5], target: 37, just two numbers left.\n     |- Try 27 + 5 = 32. Evaluate 32 != 37, drop this branch.\n     |- Try 27 - 5 = 22. Evaluate 22 != 37, drop this branch.\n     |- Try 27 * 5 = 135. Evaluate 135 != 37, drop this branch.\n     |- Try 27 \/ 5 = 5.4. 5.4 is a decimal, drop this branch.\n  |- Try 5 \/ 1 = 5. Add 5 to the number set. Current number set: [5, 1, 27], target: 37. Options for choosing two numbers: [(5, 1), (5, 27), (1, 27)].\n   |- Pick two numbers (5, 1) (numbers left: [27]). Try possible operations.\n    |- Try 5 + 1 = 6. Add 6 to the number set. Current number set: [6, 27], target: 37, just two numbers left.\n     |- Try 27 + 6 = 33. Evaluate 33 != 37, drop this branch.\n     |- Try 27 - 6 = 21. Evaluate 21 != 37, drop this branch.\n     |- Try 27 * 6 = 162. Evaluate 162 != 37, drop this branch.\n     |- Try 27 \/ 6 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 5 - 1 = 4. Add 4 to the number set. Current number set: [4, 27], target: 37, just two numbers left.\n     |- Try 27 + 4 = 31. Evaluate 31 != 37, drop this branch.\n     |- Try 27 - 4 = 23. Evaluate 23 != 37, drop this branch.\n     |- Try 27 * 4 = 108. Evaluate 108 != 37, drop this branch.\n     |- Try 27 \/ 4 = 6.8. 6.8 is a decimal, drop this branch.\n    |- Try 5 * 1 = 5. Add 5 to the number set. Current number set: [5, 27], target: 37, just two numbers left.\n     |- Try 27 + 5 = 32. Evaluate 32 != 37, drop this branch.\n     |- Try 27 - 5 = 22. Evaluate 22 != 37, drop this branch.\n     |- Try 27 * 5 = 135. Evaluate 135 != 37, drop this branch.\n     |- Try 27 \/ 5 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 5 \/ 1 = 5. Add 5 to the number set. Current number set: [5, 27], target: 37, just two numbers left.\n     |- Try 27 + 5 = 32. Evaluate 32 != 37, drop this branch.\n     |- Try 27 - 5 = 22. Evaluate 22 != 37, drop this branch.\n     |- Try 27 * 5 = 135. Evaluate 135 != 37, drop this branch.\n     |- Try 27 \/ 5 = 5.4. 5.4 is a decimal, drop this branch.\n   |- Pick two numbers (5, 27) (numbers left: [1]). Try possible operations.\n    |- Try 27 + 5 = 32. Add 32 to the number set. Current number set: [32, 1], target: 37, just two numbers left.\n     |- Try 32 + 1 = 33. Evaluate 33 != 37, drop this branch.\n     |- Try 32 - 1 = 31. Evaluate 31 != 37, drop this branch.\n     |- Try 32 * 1 = 32. Evaluate 32 != 37, drop this branch.\n     |- Try 32 \/ 1 = 32. Evaluate 32 != 37, drop this branch.\n    |- Try 27 - 5 = 22. Add 22 to the number set. Current number set: [22, 1], target: 37, just two numbers left.\n     |- Try 22 + 1 = 23. Evaluate 23 != 37, drop this branch.\n     |- Try 22 - 1 = 21. Evaluate 21 != 37, drop this branch.\n     |- Try 22 * 1 = 22. Evaluate 22 != 37, drop this branch.\n     |- Try 22 \/ 1 = 22. Evaluate 22 != 37, drop this branch.\n    |- Try 27 * 5 = 135. Add 135 to the number set. Current number set: [135, 1], target: 37, just two numbers left.\n     |- Try 135 + 1 = 136. Evaluate 136 != 37, drop this branch.\n     |- Try 135 - 1 = 134. Evaluate 134 != 37, drop this branch.\n     |- Try 135 * 1 = 135. Evaluate 135 != 37, drop this branch.\n     |- Try 135 \/ 1 = 135. Evaluate 135 != 37, drop this branch.\n    |- Try 27 \/ 5 = 5.4. 5.4 is a decimal, drop this branch.\n   |- Pick two numbers (1, 27) (numbers left: [5]). Try possible operations.\n    |- Try 27 + 1 = 28. Add 28 to the number set. Current number set: [28, 5], target: 37, just two numbers left.\n     |- Try 28 + 5 = 33. Evaluate 33 != 37, drop this branch.\n     |- Try 28 - 5 = 23. Evaluate 23 != 37, drop this branch.\n     |- Try 28 * 5 = 140. Evaluate 140 != 37, drop this branch.\n     |- Try 28 \/ 5 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 27 - 1 = 26. Add 26 to the number set. Current number set: [26, 5], target: 37, just two numbers left.\n     |- Try 26 + 5 = 31. Evaluate 31 != 37, drop this branch.\n     |- Try 26 - 5 = 21. Evaluate 21 != 37, drop this branch.\n     |- Try 26 * 5 = 130. Evaluate 130 != 37, drop this branch.\n     |- Try 26 \/ 5 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 27 * 1 = 27. Add 27 to the number set. Current number set: [27, 5], target: 37, just two numbers left.\n     |- Try 27 + 5 = 32. Evaluate 32 != 37, drop this branch.\n     |- Try 27 - 5 = 22. Evaluate 22 != 37, drop this branch.\n     |- Try 27 * 5 = 135. Evaluate 135 != 37, drop this branch.\n     |- Try 27 \/ 5 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 27 \/ 1 = 27. Add 27 to the number set. Current number set: [27, 5], target: 37, just two numbers left.\n     |- Try 27 + 5 = 32. Evaluate 32 != 37, drop this branch.\n     |- Try 27 - 5 = 22. Evaluate 22 != 37, drop this branch.\n     |- Try 27 * 5 = 135. Evaluate 135 != 37, drop this branch.\n     |- Try 27 \/ 5 = 5.4. 5.4 is a decimal, drop this branch.\n |- Pick two numbers (1, 1) (numbers left: [5, 27]). Try possible operations.\n  |- Try 1 + 1 = 2. Add 2 to the number set. Current number set: [2, 5, 27], target: 37. Options for choosing two numbers: [(2, 5), (2, 27), (5, 27)].\n   |- Pick two numbers (2, 5) (numbers left: [27]). Try possible operations.\n    |- Try 5 + 2 = 7. Add 7 to the number set. Current number set: [7, 27], target: 37, just two numbers left.\n     |- Try 27 + 7 = 34. Evaluate 34 != 37, drop this branch.\n     |- Try 27 - 7 = 20. Evaluate 20 != 37, drop this branch.\n     |- Try 27 * 7 = 189. Evaluate 189 != 37, drop this branch.\n     |- Try 27 \/ 7 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 5 - 2 = 3. Add 3 to the number set. Current number set: [3, 27], target: 37, just two numbers left.\n     |- Try 27 + 3 = 30. Evaluate 30 != 37, drop this branch.\n     |- Try 27 - 3 = 24. Evaluate 24 != 37, drop this branch.\n     |- Try 27 * 3 = 81. Evaluate 81 != 37, drop this branch.\n     |- Try 27 \/ 3 = 9. Evaluate 9 != 37, drop this branch.\n    |- Try 5 * 2 = 10. Add 10 to the number set. Current number set: [10, 27], target: 37, just two numbers left.\n     |- Try 27 + 10 = 37. Evaluate 37 == 37, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 27 + 10 = 37\nThe step before: 5 * 2 = 10\nThe first step: 1 + 1 = 2\n\nOutput the solution in the required format:\n<Solution>\n1 + 1 = 2\n5 * 2 = 10\n27 + 10 = 37\n<\/Solution>\n","item":{"nums":[1,5,1,27],"solution":["1 + 1 = 2","5 * 2 = 10","27 + 10 = 37"],"target":37}}
+{"instance_id":"countdown_8k_89","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [29, 2, 32, 10]\nTarget: 14","reference_output":"# Search Procedure\nInitial number set: [29, 2, 32, 10], target: 14. Options for choosing two numbers: [(29, 2), (29, 32), (29, 10), (2, 32), (2, 10), (32, 10)].\n |- Pick two numbers (29, 2) (numbers left: [32, 10]). Try possible operations.\n  |- Try 29 + 2 = 31. Add 31 to the number set. Current number set: [31, 32, 10], target: 14. Options for choosing two numbers: [(31, 32), (31, 10), (32, 10)].\n   |- Pick two numbers (31, 32) (numbers left: [10]). Try possible operations.\n    |- Try 32 + 31 = 63. Add 63 to the number set. Current number set: [63, 10], target: 14, just two numbers left.\n     |- Try 63 + 10 = 73. Evaluate 73 != 14, drop this branch.\n     |- Try 63 - 10 = 53. Evaluate 53 != 14, drop this branch.\n     |- Try 63 * 10 = 630. Evaluate 630 != 14, drop this branch.\n     |- Try 63 \/ 10 = 6.3. 6.3 is a decimal, drop this branch.\n    |- Try 32 - 31 = 1. Add 1 to the number set. Current number set: [1, 10], target: 14, just two numbers left.\n     |- Try 10 + 1 = 11. Evaluate 11 != 14, drop this branch.\n     |- Try 10 - 1 = 9. Evaluate 9 != 14, drop this branch.\n     |- Try 10 * 1 = 10. Evaluate 10 != 14, drop this branch.\n     |- Try 10 \/ 1 = 10. Evaluate 10 != 14, drop this branch.\n    |- Try 32 * 31 = 992. Add 992 to the number set. Current number set: [992, 10], target: 14, just two numbers left.\n     |- Try 992 + 10 = 1002. Evaluate 1002 != 14, drop this branch.\n     |- Try 992 - 10 = 982. Evaluate 982 != 14, drop this branch.\n     |- Try 992 * 10 = 9920. 9920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 992 \/ 10 = 99.2. 99.2 is a decimal, drop this branch.\n    |- Try 32 \/ 31 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (31, 10) (numbers left: [32]). Try possible operations.\n    |- Try 31 + 10 = 41. Add 41 to the number set. Current number set: [41, 32], target: 14, just two numbers left.\n     |- Try 41 + 32 = 73. Evaluate 73 != 14, drop this branch.\n     |- Try 41 - 32 = 9. Evaluate 9 != 14, drop this branch.\n     |- Try 41 * 32 = 1312. Evaluate 1312 != 14, drop this branch.\n     |- Try 41 \/ 32 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 31 - 10 = 21. Add 21 to the number set. Current number set: [21, 32], target: 14, just two numbers left.\n     |- Try 32 + 21 = 53. Evaluate 53 != 14, drop this branch.\n     |- Try 32 - 21 = 11. Evaluate 11 != 14, drop this branch.\n     |- Try 32 * 21 = 672. Evaluate 672 != 14, drop this branch.\n     |- Try 32 \/ 21 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 31 * 10 = 310. Add 310 to the number set. Current number set: [310, 32], target: 14, just two numbers left.\n     |- Try 310 + 32 = 342. Evaluate 342 != 14, drop this branch.\n     |- Try 310 - 32 = 278. Evaluate 278 != 14, drop this branch.\n     |- Try 310 * 32 = 9920. 9920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 310 \/ 32 = 9.7. 9.7 is a decimal, drop this branch.\n    |- Try 31 \/ 10 = 3.1. 3.1 is a decimal, drop this branch.\n   |- Pick two numbers (32, 10) (numbers left: [31]). Try possible operations.\n    |- Try 32 + 10 = 42. Add 42 to the number set. Current number set: [42, 31], target: 14, just two numbers left.\n     |- Try 42 + 31 = 73. Evaluate 73 != 14, drop this branch.\n     |- Try 42 - 31 = 11. Evaluate 11 != 14, drop this branch.\n     |- Try 42 * 31 = 1302. Evaluate 1302 != 14, drop this branch.\n     |- Try 42 \/ 31 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 32 - 10 = 22. Add 22 to the number set. Current number set: [22, 31], target: 14, just two numbers left.\n     |- Try 31 + 22 = 53. Evaluate 53 != 14, drop this branch.\n     |- Try 31 - 22 = 9. Evaluate 9 != 14, drop this branch.\n     |- Try 31 * 22 = 682. Evaluate 682 != 14, drop this branch.\n     |- Try 31 \/ 22 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 32 * 10 = 320. Add 320 to the number set. Current number set: [320, 31], target: 14, just two numbers left.\n     |- Try 320 + 31 = 351. Evaluate 351 != 14, drop this branch.\n     |- Try 320 - 31 = 289. Evaluate 289 != 14, drop this branch.\n     |- Try 320 * 31 = 9920. 9920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 320 \/ 31 = 10.3. 10.3 is a decimal, drop this branch.\n    |- Try 32 \/ 10 = 3.2. 3.2 is a decimal, drop this branch.\n  |- Try 29 - 2 = 27. Add 27 to the number set. Current number set: [27, 32, 10], target: 14. Options for choosing two numbers: [(27, 32), (27, 10), (32, 10)].\n   |- Pick two numbers (27, 32) (numbers left: [10]). Try possible operations.\n    |- Try 32 + 27 = 59. Add 59 to the number set. Current number set: [59, 10], target: 14, just two numbers left.\n     |- Try 59 + 10 = 69. Evaluate 69 != 14, drop this branch.\n     |- Try 59 - 10 = 49. Evaluate 49 != 14, drop this branch.\n     |- Try 59 * 10 = 590. Evaluate 590 != 14, drop this branch.\n     |- Try 59 \/ 10 = 5.9. 5.9 is a decimal, drop this branch.\n    |- Try 32 - 27 = 5. Add 5 to the number set. Current number set: [5, 10], target: 14, just two numbers left.\n     |- Try 10 + 5 = 15. Evaluate 15 != 14, drop this branch.\n     |- Try 10 - 5 = 5. Evaluate 5 != 14, drop this branch.\n     |- Try 10 * 5 = 50. Evaluate 50 != 14, drop this branch.\n     |- Try 10 \/ 5 = 2. Evaluate 2 != 14, drop this branch.\n    |- Try 32 * 27 = 864. Add 864 to the number set. Current number set: [864, 10], target: 14, just two numbers left.\n     |- Try 864 + 10 = 874. Evaluate 874 != 14, drop this branch.\n     |- Try 864 - 10 = 854. Evaluate 854 != 14, drop this branch.\n     |- Try 864 * 10 = 8640. 8640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 10 = 86.4. 86.4 is a decimal, drop this branch.\n    |- Try 32 \/ 27 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (27, 10) (numbers left: [32]). Try possible operations.\n    |- Try 27 + 10 = 37. Add 37 to the number set. Current number set: [37, 32], target: 14, just two numbers left.\n     |- Try 37 + 32 = 69. Evaluate 69 != 14, drop this branch.\n     |- Try 37 - 32 = 5. Evaluate 5 != 14, drop this branch.\n     |- Try 37 * 32 = 1184. Evaluate 1184 != 14, drop this branch.\n     |- Try 37 \/ 32 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 27 - 10 = 17. Add 17 to the number set. Current number set: [17, 32], target: 14, just two numbers left.\n     |- Try 32 + 17 = 49. Evaluate 49 != 14, drop this branch.\n     |- Try 32 - 17 = 15. Evaluate 15 != 14, drop this branch.\n     |- Try 32 * 17 = 544. Evaluate 544 != 14, drop this branch.\n     |- Try 32 \/ 17 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 27 * 10 = 270. Add 270 to the number set. Current number set: [270, 32], target: 14, just two numbers left.\n     |- Try 270 + 32 = 302. Evaluate 302 != 14, drop this branch.\n     |- Try 270 - 32 = 238. Evaluate 238 != 14, drop this branch.\n     |- Try 270 * 32 = 8640. 8640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 270 \/ 32 = 8.4. 8.4 is a decimal, drop this branch.\n    |- Try 27 \/ 10 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (32, 10) (numbers left: [27]). Try possible operations.\n    |- Try 32 + 10 = 42. Add 42 to the number set. Current number set: [42, 27], target: 14, just two numbers left.\n     |- Try 42 + 27 = 69. Evaluate 69 != 14, drop this branch.\n     |- Try 42 - 27 = 15. Evaluate 15 != 14, drop this branch.\n     |- Try 42 * 27 = 1134. Evaluate 1134 != 14, drop this branch.\n     |- Try 42 \/ 27 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 32 - 10 = 22. Add 22 to the number set. Current number set: [22, 27], target: 14, just two numbers left.\n     |- Try 27 + 22 = 49. Evaluate 49 != 14, drop this branch.\n     |- Try 27 - 22 = 5. Evaluate 5 != 14, drop this branch.\n     |- Try 27 * 22 = 594. Evaluate 594 != 14, drop this branch.\n     |- Try 27 \/ 22 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 32 * 10 = 320. Add 320 to the number set. Current number set: [320, 27], target: 14, just two numbers left.\n     |- Try 320 + 27 = 347. Evaluate 347 != 14, drop this branch.\n     |- Try 320 - 27 = 293. Evaluate 293 != 14, drop this branch.\n     |- Try 320 * 27 = 8640. 8640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 320 \/ 27 = 11.9. 11.9 is a decimal, drop this branch.\n    |- Try 32 \/ 10 = 3.2. 3.2 is a decimal, drop this branch.\n  |- Try 29 * 2 = 58. Add 58 to the number set. Current number set: [58, 32, 10], target: 14. Options for choosing two numbers: [(58, 32), (58, 10), (32, 10)].\n   |- Pick two numbers (58, 32) (numbers left: [10]). Try possible operations.\n    |- Try 58 + 32 = 90. Add 90 to the number set. Current number set: [90, 10], target: 14, just two numbers left.\n     |- Try 90 + 10 = 100. Evaluate 100 != 14, drop this branch.\n     |- Try 90 - 10 = 80. Evaluate 80 != 14, drop this branch.\n     |- Try 90 * 10 = 900. Evaluate 900 != 14, drop this branch.\n     |- Try 90 \/ 10 = 9. Evaluate 9 != 14, drop this branch.\n    |- Try 58 - 32 = 26. Add 26 to the number set. Current number set: [26, 10], target: 14, just two numbers left.\n     |- Try 26 + 10 = 36. Evaluate 36 != 14, drop this branch.\n     |- Try 26 - 10 = 16. Evaluate 16 != 14, drop this branch.\n     |- Try 26 * 10 = 260. Evaluate 260 != 14, drop this branch.\n     |- Try 26 \/ 10 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 58 * 32 = 1856. Add 1856 to the number set. Current number set: [1856, 10], target: 14, just two numbers left.\n     |- Try 1856 + 10 = 1866. Evaluate 1866 != 14, drop this branch.\n     |- Try 1856 - 10 = 1846. Evaluate 1846 != 14, drop this branch.\n     |- Try 1856 * 10 = 18560. 18560 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1856 \/ 10 = 185.6. 185.6 is a decimal, drop this branch.\n    |- Try 58 \/ 32 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (58, 10) (numbers left: [32]). Try possible operations.\n    |- Try 58 + 10 = 68. Add 68 to the number set. Current number set: [68, 32], target: 14, just two numbers left.\n     |- Try 68 + 32 = 100. Evaluate 100 != 14, drop this branch.\n     |- Try 68 - 32 = 36. Evaluate 36 != 14, drop this branch.\n     |- Try 68 * 32 = 2176. 2176 exceeds the maximum intermediate result, drop this branch.\n     |- Try 68 \/ 32 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 58 - 10 = 48. Add 48 to the number set. Current number set: [48, 32], target: 14, just two numbers left.\n     |- Try 48 + 32 = 80. Evaluate 80 != 14, drop this branch.\n     |- Try 48 - 32 = 16. Evaluate 16 != 14, drop this branch.\n     |- Try 48 * 32 = 1536. Evaluate 1536 != 14, drop this branch.\n     |- Try 48 \/ 32 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 58 * 10 = 580. Add 580 to the number set. Current number set: [580, 32], target: 14, just two numbers left.\n     |- Try 580 + 32 = 612. Evaluate 612 != 14, drop this branch.\n     |- Try 580 - 32 = 548. Evaluate 548 != 14, drop this branch.\n     |- Try 580 * 32 = 18560. 18560 exceeds the maximum intermediate result, drop this branch.\n     |- Try 580 \/ 32 = 18.1. 18.1 is a decimal, drop this branch.\n    |- Try 58 \/ 10 = 5.8. 5.8 is a decimal, drop this branch.\n   |- Pick two numbers (32, 10) (numbers left: [58]). Try possible operations.\n    |- Try 32 + 10 = 42. Add 42 to the number set. Current number set: [42, 58], target: 14, just two numbers left.\n     |- Try 58 + 42 = 100. Evaluate 100 != 14, drop this branch.\n     |- Try 58 - 42 = 16. Evaluate 16 != 14, drop this branch.\n     |- Try 58 * 42 = 2436. 2436 exceeds the maximum intermediate result, drop this branch.\n     |- Try 58 \/ 42 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 32 - 10 = 22. Add 22 to the number set. Current number set: [22, 58], target: 14, just two numbers left.\n     |- Try 58 + 22 = 80. Evaluate 80 != 14, drop this branch.\n     |- Try 58 - 22 = 36. Evaluate 36 != 14, drop this branch.\n     |- Try 58 * 22 = 1276. Evaluate 1276 != 14, drop this branch.\n     |- Try 58 \/ 22 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 32 * 10 = 320. Add 320 to the number set. Current number set: [320, 58], target: 14, just two numbers left.\n     |- Try 320 + 58 = 378. Evaluate 378 != 14, drop this branch.\n     |- Try 320 - 58 = 262. Evaluate 262 != 14, drop this branch.\n     |- Try 320 * 58 = 18560. 18560 exceeds the maximum intermediate result, drop this branch.\n     |- Try 320 \/ 58 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 32 \/ 10 = 3.2. 3.2 is a decimal, drop this branch.\n  |- Try 29 \/ 2 = 14.5. 14.5 is a decimal, drop this branch.\n |- Pick two numbers (29, 32) (numbers left: [2, 10]). Try possible operations.\n  |- Try 32 + 29 = 61. Add 61 to the number set. Current number set: [61, 2, 10], target: 14. Options for choosing two numbers: [(61, 2), (61, 10), (2, 10)].\n   |- Pick two numbers (61, 2) (numbers left: [10]). Try possible operations.\n    |- Try 61 + 2 = 63. Add 63 to the number set. Current number set: [63, 10], target: 14, just two numbers left.\n     |- Try 63 + 10 = 73. Evaluate 73 != 14, drop this branch.\n     |- Try 63 - 10 = 53. Evaluate 53 != 14, drop this branch.\n     |- Try 63 * 10 = 630. Evaluate 630 != 14, drop this branch.\n     |- Try 63 \/ 10 = 6.3. 6.3 is a decimal, drop this branch.\n    |- Try 61 - 2 = 59. Add 59 to the number set. Current number set: [59, 10], target: 14, just two numbers left.\n     |- Try 59 + 10 = 69. Evaluate 69 != 14, drop this branch.\n     |- Try 59 - 10 = 49. Evaluate 49 != 14, drop this branch.\n     |- Try 59 * 10 = 590. Evaluate 590 != 14, drop this branch.\n     |- Try 59 \/ 10 = 5.9. 5.9 is a decimal, drop this branch.\n    |- Try 61 * 2 = 122. Add 122 to the number set. Current number set: [122, 10], target: 14, just two numbers left.\n     |- Try 122 + 10 = 132. Evaluate 132 != 14, drop this branch.\n     |- Try 122 - 10 = 112. Evaluate 112 != 14, drop this branch.\n     |- Try 122 * 10 = 1220. Evaluate 1220 != 14, drop this branch.\n     |- Try 122 \/ 10 = 12.2. 12.2 is a decimal, drop this branch.\n    |- Try 61 \/ 2 = 30.5. 30.5 is a decimal, drop this branch.\n   |- Pick two numbers (61, 10) (numbers left: [2]). Try possible operations.\n    |- Try 61 + 10 = 71. Add 71 to the number set. Current number set: [71, 2], target: 14, just two numbers left.\n     |- Try 71 + 2 = 73. Evaluate 73 != 14, drop this branch.\n     |- Try 71 - 2 = 69. Evaluate 69 != 14, drop this branch.\n     |- Try 71 * 2 = 142. Evaluate 142 != 14, drop this branch.\n     |- Try 71 \/ 2 = 35.5. 35.5 is a decimal, drop this branch.\n    |- Try 61 - 10 = 51. Add 51 to the number set. Current number set: [51, 2], target: 14, just two numbers left.\n     |- Try 51 + 2 = 53. Evaluate 53 != 14, drop this branch.\n     |- Try 51 - 2 = 49. Evaluate 49 != 14, drop this branch.\n     |- Try 51 * 2 = 102. Evaluate 102 != 14, drop this branch.\n     |- Try 51 \/ 2 = 25.5. 25.5 is a decimal, drop this branch.\n    |- Try 61 * 10 = 610. Add 610 to the number set. Current number set: [610, 2], target: 14, just two numbers left.\n     |- Try 610 + 2 = 612. Evaluate 612 != 14, drop this branch.\n     |- Try 610 - 2 = 608. Evaluate 608 != 14, drop this branch.\n     |- Try 610 * 2 = 1220. Evaluate 1220 != 14, drop this branch.\n     |- Try 610 \/ 2 = 305. Evaluate 305 != 14, drop this branch.\n    |- Try 61 \/ 10 = 6.1. 6.1 is a decimal, drop this branch.\n   |- Pick two numbers (2, 10) (numbers left: [61]). Try possible operations.\n    |- Try 10 + 2 = 12. Add 12 to the number set. Current number set: [12, 61], target: 14, just two numbers left.\n     |- Try 61 + 12 = 73. Evaluate 73 != 14, drop this branch.\n     |- Try 61 - 12 = 49. Evaluate 49 != 14, drop this branch.\n     |- Try 61 * 12 = 732. Evaluate 732 != 14, drop this branch.\n     |- Try 61 \/ 12 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 10 - 2 = 8. Add 8 to the number set. Current number set: [8, 61], target: 14, just two numbers left.\n     |- Try 61 + 8 = 69. Evaluate 69 != 14, drop this branch.\n     |- Try 61 - 8 = 53. Evaluate 53 != 14, drop this branch.\n     |- Try 61 * 8 = 488. Evaluate 488 != 14, drop this branch.\n     |- Try 61 \/ 8 = 7.6. 7.6 is a decimal, drop this branch.\n    |- Try 10 * 2 = 20. Add 20 to the number set. Current number set: [20, 61], target: 14, just two numbers left.\n     |- Try 61 + 20 = 81. Evaluate 81 != 14, drop this branch.\n     |- Try 61 - 20 = 41. Evaluate 41 != 14, drop this branch.\n     |- Try 61 * 20 = 1220. Evaluate 1220 != 14, drop this branch.\n     |- Try 61 \/ 20 = 3.0. 3.0 is a decimal, drop this branch.\n    |- Try 10 \/ 2 = 5. Add 5 to the number set. Current number set: [5, 61], target: 14, just two numbers left.\n     |- Try 61 + 5 = 66. Evaluate 66 != 14, drop this branch.\n     |- Try 61 - 5 = 56. Evaluate 56 != 14, drop this branch.\n     |- Try 61 * 5 = 305. Evaluate 305 != 14, drop this branch.\n     |- Try 61 \/ 5 = 12.2. 12.2 is a decimal, drop this branch.\n  |- Try 32 - 29 = 3. Add 3 to the number set. Current number set: [3, 2, 10], target: 14. Options for choosing two numbers: [(3, 2), (3, 10), (2, 10)].\n   |- Pick two numbers (3, 2) (numbers left: [10]). Try possible operations.\n    |- Try 3 + 2 = 5. Add 5 to the number set. Current number set: [5, 10], target: 14, just two numbers left.\n     |- Try 10 + 5 = 15. Evaluate 15 != 14, drop this branch.\n     |- Try 10 - 5 = 5. Evaluate 5 != 14, drop this branch.\n     |- Try 10 * 5 = 50. Evaluate 50 != 14, drop this branch.\n     |- Try 10 \/ 5 = 2. Evaluate 2 != 14, drop this branch.\n    |- Try 3 - 2 = 1. Add 1 to the number set. Current number set: [1, 10], target: 14, just two numbers left.\n     |- Try 10 + 1 = 11. Evaluate 11 != 14, drop this branch.\n     |- Try 10 - 1 = 9. Evaluate 9 != 14, drop this branch.\n     |- Try 10 * 1 = 10. Evaluate 10 != 14, drop this branch.\n     |- Try 10 \/ 1 = 10. Evaluate 10 != 14, drop this branch.\n    |- Try 3 * 2 = 6. Add 6 to the number set. Current number set: [6, 10], target: 14, just two numbers left.\n     |- Try 10 + 6 = 16. Evaluate 16 != 14, drop this branch.\n     |- Try 10 - 6 = 4. Evaluate 4 != 14, drop this branch.\n     |- Try 10 * 6 = 60. Evaluate 60 != 14, drop this branch.\n     |- Try 10 \/ 6 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 3 \/ 2 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (3, 10) (numbers left: [2]). Try possible operations.\n    |- Try 10 + 3 = 13. Add 13 to the number set. Current number set: [13, 2], target: 14, just two numbers left.\n     |- Try 13 + 2 = 15. Evaluate 15 != 14, drop this branch.\n     |- Try 13 - 2 = 11. Evaluate 11 != 14, drop this branch.\n     |- Try 13 * 2 = 26. Evaluate 26 != 14, drop this branch.\n     |- Try 13 \/ 2 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 10 - 3 = 7. Add 7 to the number set. Current number set: [7, 2], target: 14, just two numbers left.\n     |- Try 7 + 2 = 9. Evaluate 9 != 14, drop this branch.\n     |- Try 7 - 2 = 5. Evaluate 5 != 14, drop this branch.\n     |- Try 7 * 2 = 14. Evaluate 14 == 14, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 7 * 2 = 14\nThe step before: 10 - 3 = 7\nThe first step: 32 - 29 = 3\n\nOutput the solution in the required format:\n<Solution>\n32 - 29 = 3\n10 - 3 = 7\n7 * 2 = 14\n<\/Solution>\n","item":{"nums":[29,2,32,10],"solution":["32 - 29 = 3","10 - 3 = 7","7 * 2 = 14"],"target":14}}
+{"instance_id":"countdown_8k_90","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [18, 10, 45, 22]\nTarget: 50","reference_output":"# Search Procedure\nInitial number set: [18, 10, 45, 22], target: 50. Options for choosing two numbers: [(18, 10), (18, 45), (18, 22), (10, 45), (10, 22), (45, 22)].\n |- Pick two numbers (18, 10) (numbers left: [45, 22]). Try possible operations.\n  |- Try 18 + 10 = 28. Add 28 to the number set. Current number set: [28, 45, 22], target: 50. Options for choosing two numbers: [(28, 45), (28, 22), (45, 22)].\n   |- Pick two numbers (28, 45) (numbers left: [22]). Try possible operations.\n    |- Try 45 + 28 = 73. Add 73 to the number set. Current number set: [73, 22], target: 50, just two numbers left.\n     |- Try 73 + 22 = 95. Evaluate 95 != 50, drop this branch.\n     |- Try 73 - 22 = 51. Evaluate 51 != 50, drop this branch.\n     |- Try 73 * 22 = 1606. Evaluate 1606 != 50, drop this branch.\n     |- Try 73 \/ 22 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 45 - 28 = 17. Add 17 to the number set. Current number set: [17, 22], target: 50, just two numbers left.\n     |- Try 22 + 17 = 39. Evaluate 39 != 50, drop this branch.\n     |- Try 22 - 17 = 5. Evaluate 5 != 50, drop this branch.\n     |- Try 22 * 17 = 374. Evaluate 374 != 50, drop this branch.\n     |- Try 22 \/ 17 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 45 * 28 = 1260. Add 1260 to the number set. Current number set: [1260, 22], target: 50, just two numbers left.\n     |- Try 1260 + 22 = 1282. Evaluate 1282 != 50, drop this branch.\n     |- Try 1260 - 22 = 1238. Evaluate 1238 != 50, drop this branch.\n     |- Try 1260 * 22 = 27720. 27720 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1260 \/ 22 = 57.3. 57.3 is a decimal, drop this branch.\n    |- Try 45 \/ 28 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (28, 22) (numbers left: [45]). Try possible operations.\n    |- Try 28 + 22 = 50. Add 50 to the number set. Current number set: [50, 45], target: 50, just two numbers left.\n     |- Try 50 + 45 = 95. Evaluate 95 != 50, drop this branch.\n     |- Try 50 - 45 = 5. Evaluate 5 != 50, drop this branch.\n     |- Try 50 * 45 = 2250. 2250 exceeds the maximum intermediate result, drop this branch.\n     |- Try 50 \/ 45 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 28 - 22 = 6. Add 6 to the number set. Current number set: [6, 45], target: 50, just two numbers left.\n     |- Try 45 + 6 = 51. Evaluate 51 != 50, drop this branch.\n     |- Try 45 - 6 = 39. Evaluate 39 != 50, drop this branch.\n     |- Try 45 * 6 = 270. Evaluate 270 != 50, drop this branch.\n     |- Try 45 \/ 6 = 7.5. 7.5 is a decimal, drop this branch.\n    |- Try 28 * 22 = 616. Add 616 to the number set. Current number set: [616, 45], target: 50, just two numbers left.\n     |- Try 616 + 45 = 661. Evaluate 661 != 50, drop this branch.\n     |- Try 616 - 45 = 571. Evaluate 571 != 50, drop this branch.\n     |- Try 616 * 45 = 27720. 27720 exceeds the maximum intermediate result, drop this branch.\n     |- Try 616 \/ 45 = 13.7. 13.7 is a decimal, drop this branch.\n    |- Try 28 \/ 22 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (45, 22) (numbers left: [28]). Try possible operations.\n    |- Try 45 + 22 = 67. Add 67 to the number set. Current number set: [67, 28], target: 50, just two numbers left.\n     |- Try 67 + 28 = 95. Evaluate 95 != 50, drop this branch.\n     |- Try 67 - 28 = 39. Evaluate 39 != 50, drop this branch.\n     |- Try 67 * 28 = 1876. Evaluate 1876 != 50, drop this branch.\n     |- Try 67 \/ 28 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 45 - 22 = 23. Add 23 to the number set. Current number set: [23, 28], target: 50, just two numbers left.\n     |- Try 28 + 23 = 51. Evaluate 51 != 50, drop this branch.\n     |- Try 28 - 23 = 5. Evaluate 5 != 50, drop this branch.\n     |- Try 28 * 23 = 644. Evaluate 644 != 50, drop this branch.\n     |- Try 28 \/ 23 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 45 * 22 = 990. Add 990 to the number set. Current number set: [990, 28], target: 50, just two numbers left.\n     |- Try 990 + 28 = 1018. Evaluate 1018 != 50, drop this branch.\n     |- Try 990 - 28 = 962. Evaluate 962 != 50, drop this branch.\n     |- Try 990 * 28 = 27720. 27720 exceeds the maximum intermediate result, drop this branch.\n     |- Try 990 \/ 28 = 35.4. 35.4 is a decimal, drop this branch.\n    |- Try 45 \/ 22 = 2.0. 2.0 is a decimal, drop this branch.\n  |- Try 18 - 10 = 8. Add 8 to the number set. Current number set: [8, 45, 22], target: 50. Options for choosing two numbers: [(8, 45), (8, 22), (45, 22)].\n   |- Pick two numbers (8, 45) (numbers left: [22]). Try possible operations.\n    |- Try 45 + 8 = 53. Add 53 to the number set. Current number set: [53, 22], target: 50, just two numbers left.\n     |- Try 53 + 22 = 75. Evaluate 75 != 50, drop this branch.\n     |- Try 53 - 22 = 31. Evaluate 31 != 50, drop this branch.\n     |- Try 53 * 22 = 1166. Evaluate 1166 != 50, drop this branch.\n     |- Try 53 \/ 22 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 45 - 8 = 37. Add 37 to the number set. Current number set: [37, 22], target: 50, just two numbers left.\n     |- Try 37 + 22 = 59. Evaluate 59 != 50, drop this branch.\n     |- Try 37 - 22 = 15. Evaluate 15 != 50, drop this branch.\n     |- Try 37 * 22 = 814. Evaluate 814 != 50, drop this branch.\n     |- Try 37 \/ 22 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 45 * 8 = 360. Add 360 to the number set. Current number set: [360, 22], target: 50, just two numbers left.\n     |- Try 360 + 22 = 382. Evaluate 382 != 50, drop this branch.\n     |- Try 360 - 22 = 338. Evaluate 338 != 50, drop this branch.\n     |- Try 360 * 22 = 7920. 7920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 360 \/ 22 = 16.4. 16.4 is a decimal, drop this branch.\n    |- Try 45 \/ 8 = 5.6. 5.6 is a decimal, drop this branch.\n   |- Pick two numbers (8, 22) (numbers left: [45]). Try possible operations.\n    |- Try 22 + 8 = 30. Add 30 to the number set. Current number set: [30, 45], target: 50, just two numbers left.\n     |- Try 45 + 30 = 75. Evaluate 75 != 50, drop this branch.\n     |- Try 45 - 30 = 15. Evaluate 15 != 50, drop this branch.\n     |- Try 45 * 30 = 1350. Evaluate 1350 != 50, drop this branch.\n     |- Try 45 \/ 30 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 22 - 8 = 14. Add 14 to the number set. Current number set: [14, 45], target: 50, just two numbers left.\n     |- Try 45 + 14 = 59. Evaluate 59 != 50, drop this branch.\n     |- Try 45 - 14 = 31. Evaluate 31 != 50, drop this branch.\n     |- Try 45 * 14 = 630. Evaluate 630 != 50, drop this branch.\n     |- Try 45 \/ 14 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 22 * 8 = 176. Add 176 to the number set. Current number set: [176, 45], target: 50, just two numbers left.\n     |- Try 176 + 45 = 221. Evaluate 221 != 50, drop this branch.\n     |- Try 176 - 45 = 131. Evaluate 131 != 50, drop this branch.\n     |- Try 176 * 45 = 7920. 7920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 176 \/ 45 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 22 \/ 8 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (45, 22) (numbers left: [8]). Try possible operations.\n    |- Try 45 + 22 = 67. Add 67 to the number set. Current number set: [67, 8], target: 50, just two numbers left.\n     |- Try 67 + 8 = 75. Evaluate 75 != 50, drop this branch.\n     |- Try 67 - 8 = 59. Evaluate 59 != 50, drop this branch.\n     |- Try 67 * 8 = 536. Evaluate 536 != 50, drop this branch.\n     |- Try 67 \/ 8 = 8.4. 8.4 is a decimal, drop this branch.\n    |- Try 45 - 22 = 23. Add 23 to the number set. Current number set: [23, 8], target: 50, just two numbers left.\n     |- Try 23 + 8 = 31. Evaluate 31 != 50, drop this branch.\n     |- Try 23 - 8 = 15. Evaluate 15 != 50, drop this branch.\n     |- Try 23 * 8 = 184. Evaluate 184 != 50, drop this branch.\n     |- Try 23 \/ 8 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 45 * 22 = 990. Add 990 to the number set. Current number set: [990, 8], target: 50, just two numbers left.\n     |- Try 990 + 8 = 998. Evaluate 998 != 50, drop this branch.\n     |- Try 990 - 8 = 982. Evaluate 982 != 50, drop this branch.\n     |- Try 990 * 8 = 7920. 7920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 990 \/ 8 = 123.8. 123.8 is a decimal, drop this branch.\n    |- Try 45 \/ 22 = 2.0. 2.0 is a decimal, drop this branch.\n  |- Try 18 * 10 = 180. Add 180 to the number set. Current number set: [180, 45, 22], target: 50. Options for choosing two numbers: [(180, 45), (180, 22), (45, 22)].\n   |- Pick two numbers (180, 45) (numbers left: [22]). Try possible operations.\n    |- Try 180 + 45 = 225. Add 225 to the number set. Current number set: [225, 22], target: 50, just two numbers left.\n     |- Try 225 + 22 = 247. Evaluate 247 != 50, drop this branch.\n     |- Try 225 - 22 = 203. Evaluate 203 != 50, drop this branch.\n     |- Try 225 * 22 = 4950. 4950 exceeds the maximum intermediate result, drop this branch.\n     |- Try 225 \/ 22 = 10.2. 10.2 is a decimal, drop this branch.\n    |- Try 180 - 45 = 135. Add 135 to the number set. Current number set: [135, 22], target: 50, just two numbers left.\n     |- Try 135 + 22 = 157. Evaluate 157 != 50, drop this branch.\n     |- Try 135 - 22 = 113. Evaluate 113 != 50, drop this branch.\n     |- Try 135 * 22 = 2970. 2970 exceeds the maximum intermediate result, drop this branch.\n     |- Try 135 \/ 22 = 6.1. 6.1 is a decimal, drop this branch.\n    |- Try 180 * 45 = 8100. 8100 exceeds the maximum intermediate result, drop this branch.\n    |- Try 180 \/ 45 = 4. Add 4 to the number set. Current number set: [4, 22], target: 50, just two numbers left.\n     |- Try 22 + 4 = 26. Evaluate 26 != 50, drop this branch.\n     |- Try 22 - 4 = 18. Evaluate 18 != 50, drop this branch.\n     |- Try 22 * 4 = 88. Evaluate 88 != 50, drop this branch.\n     |- Try 22 \/ 4 = 5.5. 5.5 is a decimal, drop this branch.\n   |- Pick two numbers (180, 22) (numbers left: [45]). Try possible operations.\n    |- Try 180 + 22 = 202. Add 202 to the number set. Current number set: [202, 45], target: 50, just two numbers left.\n     |- Try 202 + 45 = 247. Evaluate 247 != 50, drop this branch.\n     |- Try 202 - 45 = 157. Evaluate 157 != 50, drop this branch.\n     |- Try 202 * 45 = 9090. 9090 exceeds the maximum intermediate result, drop this branch.\n     |- Try 202 \/ 45 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 180 - 22 = 158. Add 158 to the number set. Current number set: [158, 45], target: 50, just two numbers left.\n     |- Try 158 + 45 = 203. Evaluate 203 != 50, drop this branch.\n     |- Try 158 - 45 = 113. Evaluate 113 != 50, drop this branch.\n     |- Try 158 * 45 = 7110. 7110 exceeds the maximum intermediate result, drop this branch.\n     |- Try 158 \/ 45 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 180 * 22 = 3960. 3960 exceeds the maximum intermediate result, drop this branch.\n    |- Try 180 \/ 22 = 8.2. 8.2 is a decimal, drop this branch.\n   |- Pick two numbers (45, 22) (numbers left: [180]). Try possible operations.\n    |- Try 45 + 22 = 67. Add 67 to the number set. Current number set: [67, 180], target: 50, just two numbers left.\n     |- Try 180 + 67 = 247. Evaluate 247 != 50, drop this branch.\n     |- Try 180 - 67 = 113. Evaluate 113 != 50, drop this branch.\n     |- Try 180 * 67 = 12060. 12060 exceeds the maximum intermediate result, drop this branch.\n     |- Try 180 \/ 67 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 45 - 22 = 23. Add 23 to the number set. Current number set: [23, 180], target: 50, just two numbers left.\n     |- Try 180 + 23 = 203. Evaluate 203 != 50, drop this branch.\n     |- Try 180 - 23 = 157. Evaluate 157 != 50, drop this branch.\n     |- Try 180 * 23 = 4140. 4140 exceeds the maximum intermediate result, drop this branch.\n     |- Try 180 \/ 23 = 7.8. 7.8 is a decimal, drop this branch.\n    |- Try 45 * 22 = 990. Add 990 to the number set. Current number set: [990, 180], target: 50, just two numbers left.\n     |- Try 990 + 180 = 1170. Evaluate 1170 != 50, drop this branch.\n     |- Try 990 - 180 = 810. Evaluate 810 != 50, drop this branch.\n     |- Try 990 * 180 = 178200. 178200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 990 \/ 180 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 45 \/ 22 = 2.0. 2.0 is a decimal, drop this branch.\n  |- Try 18 \/ 10 = 1.8. 1.8 is a decimal, drop this branch.\n |- Pick two numbers (18, 45) (numbers left: [10, 22]). Try possible operations.\n  |- Try 45 + 18 = 63. Add 63 to the number set. Current number set: [63, 10, 22], target: 50. Options for choosing two numbers: [(63, 10), (63, 22), (10, 22)].\n   |- Pick two numbers (63, 10) (numbers left: [22]). Try possible operations.\n    |- Try 63 + 10 = 73. Add 73 to the number set. Current number set: [73, 22], target: 50, just two numbers left.\n     |- Try 73 + 22 = 95. Evaluate 95 != 50, drop this branch.\n     |- Try 73 - 22 = 51. Evaluate 51 != 50, drop this branch.\n     |- Try 73 * 22 = 1606. Evaluate 1606 != 50, drop this branch.\n     |- Try 73 \/ 22 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 63 - 10 = 53. Add 53 to the number set. Current number set: [53, 22], target: 50, just two numbers left.\n     |- Try 53 + 22 = 75. Evaluate 75 != 50, drop this branch.\n     |- Try 53 - 22 = 31. Evaluate 31 != 50, drop this branch.\n     |- Try 53 * 22 = 1166. Evaluate 1166 != 50, drop this branch.\n     |- Try 53 \/ 22 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 63 * 10 = 630. Add 630 to the number set. Current number set: [630, 22], target: 50, just two numbers left.\n     |- Try 630 + 22 = 652. Evaluate 652 != 50, drop this branch.\n     |- Try 630 - 22 = 608. Evaluate 608 != 50, drop this branch.\n     |- Try 630 * 22 = 13860. 13860 exceeds the maximum intermediate result, drop this branch.\n     |- Try 630 \/ 22 = 28.6. 28.6 is a decimal, drop this branch.\n    |- Try 63 \/ 10 = 6.3. 6.3 is a decimal, drop this branch.\n   |- Pick two numbers (63, 22) (numbers left: [10]). Try possible operations.\n    |- Try 63 + 22 = 85. Add 85 to the number set. Current number set: [85, 10], target: 50, just two numbers left.\n     |- Try 85 + 10 = 95. Evaluate 95 != 50, drop this branch.\n     |- Try 85 - 10 = 75. Evaluate 75 != 50, drop this branch.\n     |- Try 85 * 10 = 850. Evaluate 850 != 50, drop this branch.\n     |- Try 85 \/ 10 = 8.5. 8.5 is a decimal, drop this branch.\n    |- Try 63 - 22 = 41. Add 41 to the number set. Current number set: [41, 10], target: 50, just two numbers left.\n     |- Try 41 + 10 = 51. Evaluate 51 != 50, drop this branch.\n     |- Try 41 - 10 = 31. Evaluate 31 != 50, drop this branch.\n     |- Try 41 * 10 = 410. Evaluate 410 != 50, drop this branch.\n     |- Try 41 \/ 10 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 63 * 22 = 1386. Add 1386 to the number set. Current number set: [1386, 10], target: 50, just two numbers left.\n     |- Try 1386 + 10 = 1396. Evaluate 1396 != 50, drop this branch.\n     |- Try 1386 - 10 = 1376. Evaluate 1376 != 50, drop this branch.\n     |- Try 1386 * 10 = 13860. 13860 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1386 \/ 10 = 138.6. 138.6 is a decimal, drop this branch.\n    |- Try 63 \/ 22 = 2.9. 2.9 is a decimal, drop this branch.\n   |- Pick two numbers (10, 22) (numbers left: [63]). Try possible operations.\n    |- Try 22 + 10 = 32. Add 32 to the number set. Current number set: [32, 63], target: 50, just two numbers left.\n     |- Try 63 + 32 = 95. Evaluate 95 != 50, drop this branch.\n     |- Try 63 - 32 = 31. Evaluate 31 != 50, drop this branch.\n     |- Try 63 * 32 = 2016. 2016 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 32 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 22 - 10 = 12. Add 12 to the number set. Current number set: [12, 63], target: 50, just two numbers left.\n     |- Try 63 + 12 = 75. Evaluate 75 != 50, drop this branch.\n     |- Try 63 - 12 = 51. Evaluate 51 != 50, drop this branch.\n     |- Try 63 * 12 = 756. Evaluate 756 != 50, drop this branch.\n     |- Try 63 \/ 12 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 22 * 10 = 220. Add 220 to the number set. Current number set: [220, 63], target: 50, just two numbers left.\n     |- Try 220 + 63 = 283. Evaluate 283 != 50, drop this branch.\n     |- Try 220 - 63 = 157. Evaluate 157 != 50, drop this branch.\n     |- Try 220 * 63 = 13860. 13860 exceeds the maximum intermediate result, drop this branch.\n     |- Try 220 \/ 63 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 22 \/ 10 = 2.2. 2.2 is a decimal, drop this branch.\n  |- Try 45 - 18 = 27. Add 27 to the number set. Current number set: [27, 10, 22], target: 50. Options for choosing two numbers: [(27, 10), (27, 22), (10, 22)].\n   |- Pick two numbers (27, 10) (numbers left: [22]). Try possible operations.\n    |- Try 27 + 10 = 37. Add 37 to the number set. Current number set: [37, 22], target: 50, just two numbers left.\n     |- Try 37 + 22 = 59. Evaluate 59 != 50, drop this branch.\n     |- Try 37 - 22 = 15. Evaluate 15 != 50, drop this branch.\n     |- Try 37 * 22 = 814. Evaluate 814 != 50, drop this branch.\n     |- Try 37 \/ 22 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 27 - 10 = 17. Add 17 to the number set. Current number set: [17, 22], target: 50, just two numbers left.\n     |- Try 22 + 17 = 39. Evaluate 39 != 50, drop this branch.\n     |- Try 22 - 17 = 5. Evaluate 5 != 50, drop this branch.\n     |- Try 22 * 17 = 374. Evaluate 374 != 50, drop this branch.\n     |- Try 22 \/ 17 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 27 * 10 = 270. Add 270 to the number set. Current number set: [270, 22], target: 50, just two numbers left.\n     |- Try 270 + 22 = 292. Evaluate 292 != 50, drop this branch.\n     |- Try 270 - 22 = 248. Evaluate 248 != 50, drop this branch.\n     |- Try 270 * 22 = 5940. 5940 exceeds the maximum intermediate result, drop this branch.\n     |- Try 270 \/ 22 = 12.3. 12.3 is a decimal, drop this branch.\n    |- Try 27 \/ 10 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (27, 22) (numbers left: [10]). Try possible operations.\n    |- Try 27 + 22 = 49. Add 49 to the number set. Current number set: [49, 10], target: 50, just two numbers left.\n     |- Try 49 + 10 = 59. Evaluate 59 != 50, drop this branch.\n     |- Try 49 - 10 = 39. Evaluate 39 != 50, drop this branch.\n     |- Try 49 * 10 = 490. Evaluate 490 != 50, drop this branch.\n     |- Try 49 \/ 10 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 27 - 22 = 5. Add 5 to the number set. Current number set: [5, 10], target: 50, just two numbers left.\n     |- Try 10 + 5 = 15. Evaluate 15 != 50, drop this branch.\n     |- Try 10 - 5 = 5. Evaluate 5 != 50, drop this branch.\n     |- Try 10 * 5 = 50. Evaluate 50 == 50, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 10 * 5 = 50\nThe step before: 27 - 22 = 5\nThe first step: 45 - 18 = 27\n\nOutput the solution in the required format:\n<Solution>\n45 - 18 = 27\n27 - 22 = 5\n10 * 5 = 50\n<\/Solution>\n","item":{"nums":[18,10,45,22],"solution":["45 - 18 = 27","27 - 22 = 5","10 * 5 = 50"],"target":50}}
+{"instance_id":"countdown_8k_91","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [9, 3, 13, 2]\nTarget: 29","reference_output":"# Search Procedure\nInitial number set: [9, 3, 13, 2], target: 29. Options for choosing two numbers: [(9, 3), (9, 13), (9, 2), (3, 13), (3, 2), (13, 2)].\n |- Pick two numbers (9, 3) (numbers left: [13, 2]). Try possible operations.\n  |- Try 9 + 3 = 12. Add 12 to the number set. Current number set: [12, 13, 2], target: 29. Options for choosing two numbers: [(12, 13), (12, 2), (13, 2)].\n   |- Pick two numbers (12, 13) (numbers left: [2]). Try possible operations.\n    |- Try 13 + 12 = 25. Add 25 to the number set. Current number set: [25, 2], target: 29, just two numbers left.\n     |- Try 25 + 2 = 27. Evaluate 27 != 29, drop this branch.\n     |- Try 25 - 2 = 23. Evaluate 23 != 29, drop this branch.\n     |- Try 25 * 2 = 50. Evaluate 50 != 29, drop this branch.\n     |- Try 25 \/ 2 = 12.5. 12.5 is a decimal, drop this branch.\n    |- Try 13 - 12 = 1. Add 1 to the number set. Current number set: [1, 2], target: 29, just two numbers left.\n     |- Try 2 + 1 = 3. Evaluate 3 != 29, drop this branch.\n     |- Try 2 - 1 = 1. Evaluate 1 != 29, drop this branch.\n     |- Try 2 * 1 = 2. Evaluate 2 != 29, drop this branch.\n     |- Try 2 \/ 1 = 2. Evaluate 2 != 29, drop this branch.\n    |- Try 13 * 12 = 156. Add 156 to the number set. Current number set: [156, 2], target: 29, just two numbers left.\n     |- Try 156 + 2 = 158. Evaluate 158 != 29, drop this branch.\n     |- Try 156 - 2 = 154. Evaluate 154 != 29, drop this branch.\n     |- Try 156 * 2 = 312. Evaluate 312 != 29, drop this branch.\n     |- Try 156 \/ 2 = 78. Evaluate 78 != 29, drop this branch.\n    |- Try 13 \/ 12 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (12, 2) (numbers left: [13]). Try possible operations.\n    |- Try 12 + 2 = 14. Add 14 to the number set. Current number set: [14, 13], target: 29, just two numbers left.\n     |- Try 14 + 13 = 27. Evaluate 27 != 29, drop this branch.\n     |- Try 14 - 13 = 1. Evaluate 1 != 29, drop this branch.\n     |- Try 14 * 13 = 182. Evaluate 182 != 29, drop this branch.\n     |- Try 14 \/ 13 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 12 - 2 = 10. Add 10 to the number set. Current number set: [10, 13], target: 29, just two numbers left.\n     |- Try 13 + 10 = 23. Evaluate 23 != 29, drop this branch.\n     |- Try 13 - 10 = 3. Evaluate 3 != 29, drop this branch.\n     |- Try 13 * 10 = 130. Evaluate 130 != 29, drop this branch.\n     |- Try 13 \/ 10 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 12 * 2 = 24. Add 24 to the number set. Current number set: [24, 13], target: 29, just two numbers left.\n     |- Try 24 + 13 = 37. Evaluate 37 != 29, drop this branch.\n     |- Try 24 - 13 = 11. Evaluate 11 != 29, drop this branch.\n     |- Try 24 * 13 = 312. Evaluate 312 != 29, drop this branch.\n     |- Try 24 \/ 13 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 12 \/ 2 = 6. Add 6 to the number set. Current number set: [6, 13], target: 29, just two numbers left.\n     |- Try 13 + 6 = 19. Evaluate 19 != 29, drop this branch.\n     |- Try 13 - 6 = 7. Evaluate 7 != 29, drop this branch.\n     |- Try 13 * 6 = 78. Evaluate 78 != 29, drop this branch.\n     |- Try 13 \/ 6 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (13, 2) (numbers left: [12]). Try possible operations.\n    |- Try 13 + 2 = 15. Add 15 to the number set. Current number set: [15, 12], target: 29, just two numbers left.\n     |- Try 15 + 12 = 27. Evaluate 27 != 29, drop this branch.\n     |- Try 15 - 12 = 3. Evaluate 3 != 29, drop this branch.\n     |- Try 15 * 12 = 180. Evaluate 180 != 29, drop this branch.\n     |- Try 15 \/ 12 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 13 - 2 = 11. Add 11 to the number set. Current number set: [11, 12], target: 29, just two numbers left.\n     |- Try 12 + 11 = 23. Evaluate 23 != 29, drop this branch.\n     |- Try 12 - 11 = 1. Evaluate 1 != 29, drop this branch.\n     |- Try 12 * 11 = 132. Evaluate 132 != 29, drop this branch.\n     |- Try 12 \/ 11 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 13 * 2 = 26. Add 26 to the number set. Current number set: [26, 12], target: 29, just two numbers left.\n     |- Try 26 + 12 = 38. Evaluate 38 != 29, drop this branch.\n     |- Try 26 - 12 = 14. Evaluate 14 != 29, drop this branch.\n     |- Try 26 * 12 = 312. Evaluate 312 != 29, drop this branch.\n     |- Try 26 \/ 12 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 13 \/ 2 = 6.5. 6.5 is a decimal, drop this branch.\n  |- Try 9 - 3 = 6. Add 6 to the number set. Current number set: [6, 13, 2], target: 29. Options for choosing two numbers: [(6, 13), (6, 2), (13, 2)].\n   |- Pick two numbers (6, 13) (numbers left: [2]). Try possible operations.\n    |- Try 13 + 6 = 19. Add 19 to the number set. Current number set: [19, 2], target: 29, just two numbers left.\n     |- Try 19 + 2 = 21. Evaluate 21 != 29, drop this branch.\n     |- Try 19 - 2 = 17. Evaluate 17 != 29, drop this branch.\n     |- Try 19 * 2 = 38. Evaluate 38 != 29, drop this branch.\n     |- Try 19 \/ 2 = 9.5. 9.5 is a decimal, drop this branch.\n    |- Try 13 - 6 = 7. Add 7 to the number set. Current number set: [7, 2], target: 29, just two numbers left.\n     |- Try 7 + 2 = 9. Evaluate 9 != 29, drop this branch.\n     |- Try 7 - 2 = 5. Evaluate 5 != 29, drop this branch.\n     |- Try 7 * 2 = 14. Evaluate 14 != 29, drop this branch.\n     |- Try 7 \/ 2 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 13 * 6 = 78. Add 78 to the number set. Current number set: [78, 2], target: 29, just two numbers left.\n     |- Try 78 + 2 = 80. Evaluate 80 != 29, drop this branch.\n     |- Try 78 - 2 = 76. Evaluate 76 != 29, drop this branch.\n     |- Try 78 * 2 = 156. Evaluate 156 != 29, drop this branch.\n     |- Try 78 \/ 2 = 39. Evaluate 39 != 29, drop this branch.\n    |- Try 13 \/ 6 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (6, 2) (numbers left: [13]). Try possible operations.\n    |- Try 6 + 2 = 8. Add 8 to the number set. Current number set: [8, 13], target: 29, just two numbers left.\n     |- Try 13 + 8 = 21. Evaluate 21 != 29, drop this branch.\n     |- Try 13 - 8 = 5. Evaluate 5 != 29, drop this branch.\n     |- Try 13 * 8 = 104. Evaluate 104 != 29, drop this branch.\n     |- Try 13 \/ 8 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 6 - 2 = 4. Add 4 to the number set. Current number set: [4, 13], target: 29, just two numbers left.\n     |- Try 13 + 4 = 17. Evaluate 17 != 29, drop this branch.\n     |- Try 13 - 4 = 9. Evaluate 9 != 29, drop this branch.\n     |- Try 13 * 4 = 52. Evaluate 52 != 29, drop this branch.\n     |- Try 13 \/ 4 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 6 * 2 = 12. Add 12 to the number set. Current number set: [12, 13], target: 29, just two numbers left.\n     |- Try 13 + 12 = 25. Evaluate 25 != 29, drop this branch.\n     |- Try 13 - 12 = 1. Evaluate 1 != 29, drop this branch.\n     |- Try 13 * 12 = 156. Evaluate 156 != 29, drop this branch.\n     |- Try 13 \/ 12 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 6 \/ 2 = 3. Add 3 to the number set. Current number set: [3, 13], target: 29, just two numbers left.\n     |- Try 13 + 3 = 16. Evaluate 16 != 29, drop this branch.\n     |- Try 13 - 3 = 10. Evaluate 10 != 29, drop this branch.\n     |- Try 13 * 3 = 39. Evaluate 39 != 29, drop this branch.\n     |- Try 13 \/ 3 = 4.3. 4.3 is a decimal, drop this branch.\n   |- Pick two numbers (13, 2) (numbers left: [6]). Try possible operations.\n    |- Try 13 + 2 = 15. Add 15 to the number set. Current number set: [15, 6], target: 29, just two numbers left.\n     |- Try 15 + 6 = 21. Evaluate 21 != 29, drop this branch.\n     |- Try 15 - 6 = 9. Evaluate 9 != 29, drop this branch.\n     |- Try 15 * 6 = 90. Evaluate 90 != 29, drop this branch.\n     |- Try 15 \/ 6 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 13 - 2 = 11. Add 11 to the number set. Current number set: [11, 6], target: 29, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 29, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 29, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 29, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 13 * 2 = 26. Add 26 to the number set. Current number set: [26, 6], target: 29, just two numbers left.\n     |- Try 26 + 6 = 32. Evaluate 32 != 29, drop this branch.\n     |- Try 26 - 6 = 20. Evaluate 20 != 29, drop this branch.\n     |- Try 26 * 6 = 156. Evaluate 156 != 29, drop this branch.\n     |- Try 26 \/ 6 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 13 \/ 2 = 6.5. 6.5 is a decimal, drop this branch.\n  |- Try 9 * 3 = 27. Add 27 to the number set. Current number set: [27, 13, 2], target: 29. Options for choosing two numbers: [(27, 13), (27, 2), (13, 2)].\n   |- Pick two numbers (27, 13) (numbers left: [2]). Try possible operations.\n    |- Try 27 + 13 = 40. Add 40 to the number set. Current number set: [40, 2], target: 29, just two numbers left.\n     |- Try 40 + 2 = 42. Evaluate 42 != 29, drop this branch.\n     |- Try 40 - 2 = 38. Evaluate 38 != 29, drop this branch.\n     |- Try 40 * 2 = 80. Evaluate 80 != 29, drop this branch.\n     |- Try 40 \/ 2 = 20. Evaluate 20 != 29, drop this branch.\n    |- Try 27 - 13 = 14. Add 14 to the number set. Current number set: [14, 2], target: 29, just two numbers left.\n     |- Try 14 + 2 = 16. Evaluate 16 != 29, drop this branch.\n     |- Try 14 - 2 = 12. Evaluate 12 != 29, drop this branch.\n     |- Try 14 * 2 = 28. Evaluate 28 != 29, drop this branch.\n     |- Try 14 \/ 2 = 7. Evaluate 7 != 29, drop this branch.\n    |- Try 27 * 13 = 351. Add 351 to the number set. Current number set: [351, 2], target: 29, just two numbers left.\n     |- Try 351 + 2 = 353. Evaluate 353 != 29, drop this branch.\n     |- Try 351 - 2 = 349. Evaluate 349 != 29, drop this branch.\n     |- Try 351 * 2 = 702. Evaluate 702 != 29, drop this branch.\n     |- Try 351 \/ 2 = 175.5. 175.5 is a decimal, drop this branch.\n    |- Try 27 \/ 13 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (27, 2) (numbers left: [13]). Try possible operations.\n    |- Try 27 + 2 = 29. Add 29 to the number set. Current number set: [29, 13], target: 29, just two numbers left.\n     |- Try 29 + 13 = 42. Evaluate 42 != 29, drop this branch.\n     |- Try 29 - 13 = 16. Evaluate 16 != 29, drop this branch.\n     |- Try 29 * 13 = 377. Evaluate 377 != 29, drop this branch.\n     |- Try 29 \/ 13 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 27 - 2 = 25. Add 25 to the number set. Current number set: [25, 13], target: 29, just two numbers left.\n     |- Try 25 + 13 = 38. Evaluate 38 != 29, drop this branch.\n     |- Try 25 - 13 = 12. Evaluate 12 != 29, drop this branch.\n     |- Try 25 * 13 = 325. Evaluate 325 != 29, drop this branch.\n     |- Try 25 \/ 13 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 27 * 2 = 54. Add 54 to the number set. Current number set: [54, 13], target: 29, just two numbers left.\n     |- Try 54 + 13 = 67. Evaluate 67 != 29, drop this branch.\n     |- Try 54 - 13 = 41. Evaluate 41 != 29, drop this branch.\n     |- Try 54 * 13 = 702. Evaluate 702 != 29, drop this branch.\n     |- Try 54 \/ 13 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 27 \/ 2 = 13.5. 13.5 is a decimal, drop this branch.\n   |- Pick two numbers (13, 2) (numbers left: [27]). Try possible operations.\n    |- Try 13 + 2 = 15. Add 15 to the number set. Current number set: [15, 27], target: 29, just two numbers left.\n     |- Try 27 + 15 = 42. Evaluate 42 != 29, drop this branch.\n     |- Try 27 - 15 = 12. Evaluate 12 != 29, drop this branch.\n     |- Try 27 * 15 = 405. Evaluate 405 != 29, drop this branch.\n     |- Try 27 \/ 15 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 13 - 2 = 11. Add 11 to the number set. Current number set: [11, 27], target: 29, just two numbers left.\n     |- Try 27 + 11 = 38. Evaluate 38 != 29, drop this branch.\n     |- Try 27 - 11 = 16. Evaluate 16 != 29, drop this branch.\n     |- Try 27 * 11 = 297. Evaluate 297 != 29, drop this branch.\n     |- Try 27 \/ 11 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 13 * 2 = 26. Add 26 to the number set. Current number set: [26, 27], target: 29, just two numbers left.\n     |- Try 27 + 26 = 53. Evaluate 53 != 29, drop this branch.\n     |- Try 27 - 26 = 1. Evaluate 1 != 29, drop this branch.\n     |- Try 27 * 26 = 702. Evaluate 702 != 29, drop this branch.\n     |- Try 27 \/ 26 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 13 \/ 2 = 6.5. 6.5 is a decimal, drop this branch.\n  |- Try 9 \/ 3 = 3. Add 3 to the number set. Current number set: [3, 13, 2], target: 29. Options for choosing two numbers: [(3, 13), (3, 2), (13, 2)].\n   |- Pick two numbers (3, 13) (numbers left: [2]). Try possible operations.\n    |- Try 13 + 3 = 16. Add 16 to the number set. Current number set: [16, 2], target: 29, just two numbers left.\n     |- Try 16 + 2 = 18. Evaluate 18 != 29, drop this branch.\n     |- Try 16 - 2 = 14. Evaluate 14 != 29, drop this branch.\n     |- Try 16 * 2 = 32. Evaluate 32 != 29, drop this branch.\n     |- Try 16 \/ 2 = 8. Evaluate 8 != 29, drop this branch.\n    |- Try 13 - 3 = 10. Add 10 to the number set. Current number set: [10, 2], target: 29, just two numbers left.\n     |- Try 10 + 2 = 12. Evaluate 12 != 29, drop this branch.\n     |- Try 10 - 2 = 8. Evaluate 8 != 29, drop this branch.\n     |- Try 10 * 2 = 20. Evaluate 20 != 29, drop this branch.\n     |- Try 10 \/ 2 = 5. Evaluate 5 != 29, drop this branch.\n    |- Try 13 * 3 = 39. Add 39 to the number set. Current number set: [39, 2], target: 29, just two numbers left.\n     |- Try 39 + 2 = 41. Evaluate 41 != 29, drop this branch.\n     |- Try 39 - 2 = 37. Evaluate 37 != 29, drop this branch.\n     |- Try 39 * 2 = 78. Evaluate 78 != 29, drop this branch.\n     |- Try 39 \/ 2 = 19.5. 19.5 is a decimal, drop this branch.\n    |- Try 13 \/ 3 = 4.3. 4.3 is a decimal, drop this branch.\n   |- Pick two numbers (3, 2) (numbers left: [13]). Try possible operations.\n    |- Try 3 + 2 = 5. Add 5 to the number set. Current number set: [5, 13], target: 29, just two numbers left.\n     |- Try 13 + 5 = 18. Evaluate 18 != 29, drop this branch.\n     |- Try 13 - 5 = 8. Evaluate 8 != 29, drop this branch.\n     |- Try 13 * 5 = 65. Evaluate 65 != 29, drop this branch.\n     |- Try 13 \/ 5 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 3 - 2 = 1. Add 1 to the number set. Current number set: [1, 13], target: 29, just two numbers left.\n     |- Try 13 + 1 = 14. Evaluate 14 != 29, drop this branch.\n     |- Try 13 - 1 = 12. Evaluate 12 != 29, drop this branch.\n     |- Try 13 * 1 = 13. Evaluate 13 != 29, drop this branch.\n     |- Try 13 \/ 1 = 13. Evaluate 13 != 29, drop this branch.\n    |- Try 3 * 2 = 6. Add 6 to the number set. Current number set: [6, 13], target: 29, just two numbers left.\n     |- Try 13 + 6 = 19. Evaluate 19 != 29, drop this branch.\n     |- Try 13 - 6 = 7. Evaluate 7 != 29, drop this branch.\n     |- Try 13 * 6 = 78. Evaluate 78 != 29, drop this branch.\n     |- Try 13 \/ 6 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 3 \/ 2 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (13, 2) (numbers left: [3]). Try possible operations.\n    |- Try 13 + 2 = 15. Add 15 to the number set. Current number set: [15, 3], target: 29, just two numbers left.\n     |- Try 15 + 3 = 18. Evaluate 18 != 29, drop this branch.\n     |- Try 15 - 3 = 12. Evaluate 12 != 29, drop this branch.\n     |- Try 15 * 3 = 45. Evaluate 45 != 29, drop this branch.\n     |- Try 15 \/ 3 = 5. Evaluate 5 != 29, drop this branch.\n    |- Try 13 - 2 = 11. Add 11 to the number set. Current number set: [11, 3], target: 29, just two numbers left.\n     |- Try 11 + 3 = 14. Evaluate 14 != 29, drop this branch.\n     |- Try 11 - 3 = 8. Evaluate 8 != 29, drop this branch.\n     |- Try 11 * 3 = 33. Evaluate 33 != 29, drop this branch.\n     |- Try 11 \/ 3 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 13 * 2 = 26. Add 26 to the number set. Current number set: [26, 3], target: 29, just two numbers left.\n     |- Try 26 + 3 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 26 + 3 = 29\nThe step before: 13 * 2 = 26\nThe first step: 9 \/ 3 = 3\n\nOutput the solution in the required format:\n<Solution>\n9 \/ 3 = 3\n13 * 2 = 26\n26 + 3 = 29\n<\/Solution>\n","item":{"nums":[9,3,13,2],"solution":["9 \/ 3 = 3","13 * 2 = 26","26 + 3 = 29"],"target":29}}
+{"instance_id":"countdown_8k_92","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [13, 28, 22, 48]\nTarget: 14","reference_output":"# Search Procedure\nInitial number set: [13, 28, 22, 48], target: 14. Options for choosing two numbers: [(13, 28), (13, 22), (13, 48), (28, 22), (28, 48), (22, 48)].\n |- Pick two numbers (13, 28) (numbers left: [22, 48]). Try possible operations.\n  |- Try 28 + 13 = 41. Add 41 to the number set. Current number set: [41, 22, 48], target: 14. Options for choosing two numbers: [(41, 22), (41, 48), (22, 48)].\n   |- Pick two numbers (41, 22) (numbers left: [48]). Try possible operations.\n    |- Try 41 + 22 = 63. Add 63 to the number set. Current number set: [63, 48], target: 14, just two numbers left.\n     |- Try 63 + 48 = 111. Evaluate 111 != 14, drop this branch.\n     |- Try 63 - 48 = 15. Evaluate 15 != 14, drop this branch.\n     |- Try 63 * 48 = 3024. 3024 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 48 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 41 - 22 = 19. Add 19 to the number set. Current number set: [19, 48], target: 14, just two numbers left.\n     |- Try 48 + 19 = 67. Evaluate 67 != 14, drop this branch.\n     |- Try 48 - 19 = 29. Evaluate 29 != 14, drop this branch.\n     |- Try 48 * 19 = 912. Evaluate 912 != 14, drop this branch.\n     |- Try 48 \/ 19 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 41 * 22 = 902. Add 902 to the number set. Current number set: [902, 48], target: 14, just two numbers left.\n     |- Try 902 + 48 = 950. Evaluate 950 != 14, drop this branch.\n     |- Try 902 - 48 = 854. Evaluate 854 != 14, drop this branch.\n     |- Try 902 * 48 = 43296. 43296 exceeds the maximum intermediate result, drop this branch.\n     |- Try 902 \/ 48 = 18.8. 18.8 is a decimal, drop this branch.\n    |- Try 41 \/ 22 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (41, 48) (numbers left: [22]). Try possible operations.\n    |- Try 48 + 41 = 89. Add 89 to the number set. Current number set: [89, 22], target: 14, just two numbers left.\n     |- Try 89 + 22 = 111. Evaluate 111 != 14, drop this branch.\n     |- Try 89 - 22 = 67. Evaluate 67 != 14, drop this branch.\n     |- Try 89 * 22 = 1958. Evaluate 1958 != 14, drop this branch.\n     |- Try 89 \/ 22 = 4.0. 4.0 is a decimal, drop this branch.\n    |- Try 48 - 41 = 7. Add 7 to the number set. Current number set: [7, 22], target: 14, just two numbers left.\n     |- Try 22 + 7 = 29. Evaluate 29 != 14, drop this branch.\n     |- Try 22 - 7 = 15. Evaluate 15 != 14, drop this branch.\n     |- Try 22 * 7 = 154. Evaluate 154 != 14, drop this branch.\n     |- Try 22 \/ 7 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 48 * 41 = 1968. Add 1968 to the number set. Current number set: [1968, 22], target: 14, just two numbers left.\n     |- Try 1968 + 22 = 1990. Evaluate 1990 != 14, drop this branch.\n     |- Try 1968 - 22 = 1946. Evaluate 1946 != 14, drop this branch.\n     |- Try 1968 * 22 = 43296. 43296 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1968 \/ 22 = 89.5. 89.5 is a decimal, drop this branch.\n    |- Try 48 \/ 41 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (22, 48) (numbers left: [41]). Try possible operations.\n    |- Try 48 + 22 = 70. Add 70 to the number set. Current number set: [70, 41], target: 14, just two numbers left.\n     |- Try 70 + 41 = 111. Evaluate 111 != 14, drop this branch.\n     |- Try 70 - 41 = 29. Evaluate 29 != 14, drop this branch.\n     |- Try 70 * 41 = 2870. 2870 exceeds the maximum intermediate result, drop this branch.\n     |- Try 70 \/ 41 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 48 - 22 = 26. Add 26 to the number set. Current number set: [26, 41], target: 14, just two numbers left.\n     |- Try 41 + 26 = 67. Evaluate 67 != 14, drop this branch.\n     |- Try 41 - 26 = 15. Evaluate 15 != 14, drop this branch.\n     |- Try 41 * 26 = 1066. Evaluate 1066 != 14, drop this branch.\n     |- Try 41 \/ 26 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 48 * 22 = 1056. Add 1056 to the number set. Current number set: [1056, 41], target: 14, just two numbers left.\n     |- Try 1056 + 41 = 1097. Evaluate 1097 != 14, drop this branch.\n     |- Try 1056 - 41 = 1015. Evaluate 1015 != 14, drop this branch.\n     |- Try 1056 * 41 = 43296. 43296 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1056 \/ 41 = 25.8. 25.8 is a decimal, drop this branch.\n    |- Try 48 \/ 22 = 2.2. 2.2 is a decimal, drop this branch.\n  |- Try 28 - 13 = 15. Add 15 to the number set. Current number set: [15, 22, 48], target: 14. Options for choosing two numbers: [(15, 22), (15, 48), (22, 48)].\n   |- Pick two numbers (15, 22) (numbers left: [48]). Try possible operations.\n    |- Try 22 + 15 = 37. Add 37 to the number set. Current number set: [37, 48], target: 14, just two numbers left.\n     |- Try 48 + 37 = 85. Evaluate 85 != 14, drop this branch.\n     |- Try 48 - 37 = 11. Evaluate 11 != 14, drop this branch.\n     |- Try 48 * 37 = 1776. Evaluate 1776 != 14, drop this branch.\n     |- Try 48 \/ 37 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 22 - 15 = 7. Add 7 to the number set. Current number set: [7, 48], target: 14, just two numbers left.\n     |- Try 48 + 7 = 55. Evaluate 55 != 14, drop this branch.\n     |- Try 48 - 7 = 41. Evaluate 41 != 14, drop this branch.\n     |- Try 48 * 7 = 336. Evaluate 336 != 14, drop this branch.\n     |- Try 48 \/ 7 = 6.9. 6.9 is a decimal, drop this branch.\n    |- Try 22 * 15 = 330. Add 330 to the number set. Current number set: [330, 48], target: 14, just two numbers left.\n     |- Try 330 + 48 = 378. Evaluate 378 != 14, drop this branch.\n     |- Try 330 - 48 = 282. Evaluate 282 != 14, drop this branch.\n     |- Try 330 * 48 = 15840. 15840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 330 \/ 48 = 6.9. 6.9 is a decimal, drop this branch.\n    |- Try 22 \/ 15 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (15, 48) (numbers left: [22]). Try possible operations.\n    |- Try 48 + 15 = 63. Add 63 to the number set. Current number set: [63, 22], target: 14, just two numbers left.\n     |- Try 63 + 22 = 85. Evaluate 85 != 14, drop this branch.\n     |- Try 63 - 22 = 41. Evaluate 41 != 14, drop this branch.\n     |- Try 63 * 22 = 1386. Evaluate 1386 != 14, drop this branch.\n     |- Try 63 \/ 22 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 48 - 15 = 33. Add 33 to the number set. Current number set: [33, 22], target: 14, just two numbers left.\n     |- Try 33 + 22 = 55. Evaluate 55 != 14, drop this branch.\n     |- Try 33 - 22 = 11. Evaluate 11 != 14, drop this branch.\n     |- Try 33 * 22 = 726. Evaluate 726 != 14, drop this branch.\n     |- Try 33 \/ 22 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 48 * 15 = 720. Add 720 to the number set. Current number set: [720, 22], target: 14, just two numbers left.\n     |- Try 720 + 22 = 742. Evaluate 742 != 14, drop this branch.\n     |- Try 720 - 22 = 698. Evaluate 698 != 14, drop this branch.\n     |- Try 720 * 22 = 15840. 15840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 720 \/ 22 = 32.7. 32.7 is a decimal, drop this branch.\n    |- Try 48 \/ 15 = 3.2. 3.2 is a decimal, drop this branch.\n   |- Pick two numbers (22, 48) (numbers left: [15]). Try possible operations.\n    |- Try 48 + 22 = 70. Add 70 to the number set. Current number set: [70, 15], target: 14, just two numbers left.\n     |- Try 70 + 15 = 85. Evaluate 85 != 14, drop this branch.\n     |- Try 70 - 15 = 55. Evaluate 55 != 14, drop this branch.\n     |- Try 70 * 15 = 1050. Evaluate 1050 != 14, drop this branch.\n     |- Try 70 \/ 15 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 48 - 22 = 26. Add 26 to the number set. Current number set: [26, 15], target: 14, just two numbers left.\n     |- Try 26 + 15 = 41. Evaluate 41 != 14, drop this branch.\n     |- Try 26 - 15 = 11. Evaluate 11 != 14, drop this branch.\n     |- Try 26 * 15 = 390. Evaluate 390 != 14, drop this branch.\n     |- Try 26 \/ 15 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 48 * 22 = 1056. Add 1056 to the number set. Current number set: [1056, 15], target: 14, just two numbers left.\n     |- Try 1056 + 15 = 1071. Evaluate 1071 != 14, drop this branch.\n     |- Try 1056 - 15 = 1041. Evaluate 1041 != 14, drop this branch.\n     |- Try 1056 * 15 = 15840. 15840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1056 \/ 15 = 70.4. 70.4 is a decimal, drop this branch.\n    |- Try 48 \/ 22 = 2.2. 2.2 is a decimal, drop this branch.\n  |- Try 28 * 13 = 364. Add 364 to the number set. Current number set: [364, 22, 48], target: 14. Options for choosing two numbers: [(364, 22), (364, 48), (22, 48)].\n   |- Pick two numbers (364, 22) (numbers left: [48]). Try possible operations.\n    |- Try 364 + 22 = 386. Add 386 to the number set. Current number set: [386, 48], target: 14, just two numbers left.\n     |- Try 386 + 48 = 434. Evaluate 434 != 14, drop this branch.\n     |- Try 386 - 48 = 338. Evaluate 338 != 14, drop this branch.\n     |- Try 386 * 48 = 18528. 18528 exceeds the maximum intermediate result, drop this branch.\n     |- Try 386 \/ 48 = 8.0. 8.0 is a decimal, drop this branch.\n    |- Try 364 - 22 = 342. Add 342 to the number set. Current number set: [342, 48], target: 14, just two numbers left.\n     |- Try 342 + 48 = 390. Evaluate 390 != 14, drop this branch.\n     |- Try 342 - 48 = 294. Evaluate 294 != 14, drop this branch.\n     |- Try 342 * 48 = 16416. 16416 exceeds the maximum intermediate result, drop this branch.\n     |- Try 342 \/ 48 = 7.1. 7.1 is a decimal, drop this branch.\n    |- Try 364 * 22 = 8008. 8008 exceeds the maximum intermediate result, drop this branch.\n    |- Try 364 \/ 22 = 16.5. 16.5 is a decimal, drop this branch.\n   |- Pick two numbers (364, 48) (numbers left: [22]). Try possible operations.\n    |- Try 364 + 48 = 412. Add 412 to the number set. Current number set: [412, 22], target: 14, just two numbers left.\n     |- Try 412 + 22 = 434. Evaluate 434 != 14, drop this branch.\n     |- Try 412 - 22 = 390. Evaluate 390 != 14, drop this branch.\n     |- Try 412 * 22 = 9064. 9064 exceeds the maximum intermediate result, drop this branch.\n     |- Try 412 \/ 22 = 18.7. 18.7 is a decimal, drop this branch.\n    |- Try 364 - 48 = 316. Add 316 to the number set. Current number set: [316, 22], target: 14, just two numbers left.\n     |- Try 316 + 22 = 338. Evaluate 338 != 14, drop this branch.\n     |- Try 316 - 22 = 294. Evaluate 294 != 14, drop this branch.\n     |- Try 316 * 22 = 6952. 6952 exceeds the maximum intermediate result, drop this branch.\n     |- Try 316 \/ 22 = 14.4. 14.4 is a decimal, drop this branch.\n    |- Try 364 * 48 = 17472. 17472 exceeds the maximum intermediate result, drop this branch.\n    |- Try 364 \/ 48 = 7.6. 7.6 is a decimal, drop this branch.\n   |- Pick two numbers (22, 48) (numbers left: [364]). Try possible operations.\n    |- Try 48 + 22 = 70. Add 70 to the number set. Current number set: [70, 364], target: 14, just two numbers left.\n     |- Try 364 + 70 = 434. Evaluate 434 != 14, drop this branch.\n     |- Try 364 - 70 = 294. Evaluate 294 != 14, drop this branch.\n     |- Try 364 * 70 = 25480. 25480 exceeds the maximum intermediate result, drop this branch.\n     |- Try 364 \/ 70 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 48 - 22 = 26. Add 26 to the number set. Current number set: [26, 364], target: 14, just two numbers left.\n     |- Try 364 + 26 = 390. Evaluate 390 != 14, drop this branch.\n     |- Try 364 - 26 = 338. Evaluate 338 != 14, drop this branch.\n     |- Try 364 * 26 = 9464. 9464 exceeds the maximum intermediate result, drop this branch.\n     |- Try 364 \/ 26 = 14. Evaluate 14 == 14, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 364 \/ 26 = 14\nThe step before: 48 - 22 = 26\nThe first step: 28 * 13 = 364\n\nOutput the solution in the required format:\n<Solution>\n28 * 13 = 364\n48 - 22 = 26\n364 \/ 26 = 14\n<\/Solution>\n","item":{"nums":[13,28,22,48],"solution":["28 * 13 = 364","48 - 22 = 26","364 \/ 26 = 14"],"target":14}}
+{"instance_id":"countdown_8k_93","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [3, 38, 12, 22]\nTarget: 44","reference_output":"# Search Procedure\nInitial number set: [3, 38, 12, 22], target: 44. Options for choosing two numbers: [(3, 38), (3, 12), (3, 22), (38, 12), (38, 22), (12, 22)].\n |- Pick two numbers (3, 38) (numbers left: [12, 22]). Try possible operations.\n  |- Try 38 + 3 = 41. Add 41 to the number set. Current number set: [41, 12, 22], target: 44. Options for choosing two numbers: [(41, 12), (41, 22), (12, 22)].\n   |- Pick two numbers (41, 12) (numbers left: [22]). Try possible operations.\n    |- Try 41 + 12 = 53. Add 53 to the number set. Current number set: [53, 22], target: 44, just two numbers left.\n     |- Try 53 + 22 = 75. Evaluate 75 != 44, drop this branch.\n     |- Try 53 - 22 = 31. Evaluate 31 != 44, drop this branch.\n     |- Try 53 * 22 = 1166. Evaluate 1166 != 44, drop this branch.\n     |- Try 53 \/ 22 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 41 - 12 = 29. Add 29 to the number set. Current number set: [29, 22], target: 44, just two numbers left.\n     |- Try 29 + 22 = 51. Evaluate 51 != 44, drop this branch.\n     |- Try 29 - 22 = 7. Evaluate 7 != 44, drop this branch.\n     |- Try 29 * 22 = 638. Evaluate 638 != 44, drop this branch.\n     |- Try 29 \/ 22 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 41 * 12 = 492. Add 492 to the number set. Current number set: [492, 22], target: 44, just two numbers left.\n     |- Try 492 + 22 = 514. Evaluate 514 != 44, drop this branch.\n     |- Try 492 - 22 = 470. Evaluate 470 != 44, drop this branch.\n     |- Try 492 * 22 = 10824. 10824 exceeds the maximum intermediate result, drop this branch.\n     |- Try 492 \/ 22 = 22.4. 22.4 is a decimal, drop this branch.\n    |- Try 41 \/ 12 = 3.4. 3.4 is a decimal, drop this branch.\n   |- Pick two numbers (41, 22) (numbers left: [12]). Try possible operations.\n    |- Try 41 + 22 = 63. Add 63 to the number set. Current number set: [63, 12], target: 44, just two numbers left.\n     |- Try 63 + 12 = 75. Evaluate 75 != 44, drop this branch.\n     |- Try 63 - 12 = 51. Evaluate 51 != 44, drop this branch.\n     |- Try 63 * 12 = 756. Evaluate 756 != 44, drop this branch.\n     |- Try 63 \/ 12 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 41 - 22 = 19. Add 19 to the number set. Current number set: [19, 12], target: 44, just two numbers left.\n     |- Try 19 + 12 = 31. Evaluate 31 != 44, drop this branch.\n     |- Try 19 - 12 = 7. Evaluate 7 != 44, drop this branch.\n     |- Try 19 * 12 = 228. Evaluate 228 != 44, drop this branch.\n     |- Try 19 \/ 12 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 41 * 22 = 902. Add 902 to the number set. Current number set: [902, 12], target: 44, just two numbers left.\n     |- Try 902 + 12 = 914. Evaluate 914 != 44, drop this branch.\n     |- Try 902 - 12 = 890. Evaluate 890 != 44, drop this branch.\n     |- Try 902 * 12 = 10824. 10824 exceeds the maximum intermediate result, drop this branch.\n     |- Try 902 \/ 12 = 75.2. 75.2 is a decimal, drop this branch.\n    |- Try 41 \/ 22 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (12, 22) (numbers left: [41]). Try possible operations.\n    |- Try 22 + 12 = 34. Add 34 to the number set. Current number set: [34, 41], target: 44, just two numbers left.\n     |- Try 41 + 34 = 75. Evaluate 75 != 44, drop this branch.\n     |- Try 41 - 34 = 7. Evaluate 7 != 44, drop this branch.\n     |- Try 41 * 34 = 1394. Evaluate 1394 != 44, drop this branch.\n     |- Try 41 \/ 34 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 22 - 12 = 10. Add 10 to the number set. Current number set: [10, 41], target: 44, just two numbers left.\n     |- Try 41 + 10 = 51. Evaluate 51 != 44, drop this branch.\n     |- Try 41 - 10 = 31. Evaluate 31 != 44, drop this branch.\n     |- Try 41 * 10 = 410. Evaluate 410 != 44, drop this branch.\n     |- Try 41 \/ 10 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 22 * 12 = 264. Add 264 to the number set. Current number set: [264, 41], target: 44, just two numbers left.\n     |- Try 264 + 41 = 305. Evaluate 305 != 44, drop this branch.\n     |- Try 264 - 41 = 223. Evaluate 223 != 44, drop this branch.\n     |- Try 264 * 41 = 10824. 10824 exceeds the maximum intermediate result, drop this branch.\n     |- Try 264 \/ 41 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 22 \/ 12 = 1.8. 1.8 is a decimal, drop this branch.\n  |- Try 38 - 3 = 35. Add 35 to the number set. Current number set: [35, 12, 22], target: 44. Options for choosing two numbers: [(35, 12), (35, 22), (12, 22)].\n   |- Pick two numbers (35, 12) (numbers left: [22]). Try possible operations.\n    |- Try 35 + 12 = 47. Add 47 to the number set. Current number set: [47, 22], target: 44, just two numbers left.\n     |- Try 47 + 22 = 69. Evaluate 69 != 44, drop this branch.\n     |- Try 47 - 22 = 25. Evaluate 25 != 44, drop this branch.\n     |- Try 47 * 22 = 1034. Evaluate 1034 != 44, drop this branch.\n     |- Try 47 \/ 22 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 35 - 12 = 23. Add 23 to the number set. Current number set: [23, 22], target: 44, just two numbers left.\n     |- Try 23 + 22 = 45. Evaluate 45 != 44, drop this branch.\n     |- Try 23 - 22 = 1. Evaluate 1 != 44, drop this branch.\n     |- Try 23 * 22 = 506. Evaluate 506 != 44, drop this branch.\n     |- Try 23 \/ 22 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 35 * 12 = 420. Add 420 to the number set. Current number set: [420, 22], target: 44, just two numbers left.\n     |- Try 420 + 22 = 442. Evaluate 442 != 44, drop this branch.\n     |- Try 420 - 22 = 398. Evaluate 398 != 44, drop this branch.\n     |- Try 420 * 22 = 9240. 9240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 420 \/ 22 = 19.1. 19.1 is a decimal, drop this branch.\n    |- Try 35 \/ 12 = 2.9. 2.9 is a decimal, drop this branch.\n   |- Pick two numbers (35, 22) (numbers left: [12]). Try possible operations.\n    |- Try 35 + 22 = 57. Add 57 to the number set. Current number set: [57, 12], target: 44, just two numbers left.\n     |- Try 57 + 12 = 69. Evaluate 69 != 44, drop this branch.\n     |- Try 57 - 12 = 45. Evaluate 45 != 44, drop this branch.\n     |- Try 57 * 12 = 684. Evaluate 684 != 44, drop this branch.\n     |- Try 57 \/ 12 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 35 - 22 = 13. Add 13 to the number set. Current number set: [13, 12], target: 44, just two numbers left.\n     |- Try 13 + 12 = 25. Evaluate 25 != 44, drop this branch.\n     |- Try 13 - 12 = 1. Evaluate 1 != 44, drop this branch.\n     |- Try 13 * 12 = 156. Evaluate 156 != 44, drop this branch.\n     |- Try 13 \/ 12 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 35 * 22 = 770. Add 770 to the number set. Current number set: [770, 12], target: 44, just two numbers left.\n     |- Try 770 + 12 = 782. Evaluate 782 != 44, drop this branch.\n     |- Try 770 - 12 = 758. Evaluate 758 != 44, drop this branch.\n     |- Try 770 * 12 = 9240. 9240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 770 \/ 12 = 64.2. 64.2 is a decimal, drop this branch.\n    |- Try 35 \/ 22 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (12, 22) (numbers left: [35]). Try possible operations.\n    |- Try 22 + 12 = 34. Add 34 to the number set. Current number set: [34, 35], target: 44, just two numbers left.\n     |- Try 35 + 34 = 69. Evaluate 69 != 44, drop this branch.\n     |- Try 35 - 34 = 1. Evaluate 1 != 44, drop this branch.\n     |- Try 35 * 34 = 1190. Evaluate 1190 != 44, drop this branch.\n     |- Try 35 \/ 34 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 22 - 12 = 10. Add 10 to the number set. Current number set: [10, 35], target: 44, just two numbers left.\n     |- Try 35 + 10 = 45. Evaluate 45 != 44, drop this branch.\n     |- Try 35 - 10 = 25. Evaluate 25 != 44, drop this branch.\n     |- Try 35 * 10 = 350. Evaluate 350 != 44, drop this branch.\n     |- Try 35 \/ 10 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 22 * 12 = 264. Add 264 to the number set. Current number set: [264, 35], target: 44, just two numbers left.\n     |- Try 264 + 35 = 299. Evaluate 299 != 44, drop this branch.\n     |- Try 264 - 35 = 229. Evaluate 229 != 44, drop this branch.\n     |- Try 264 * 35 = 9240. 9240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 264 \/ 35 = 7.5. 7.5 is a decimal, drop this branch.\n    |- Try 22 \/ 12 = 1.8. 1.8 is a decimal, drop this branch.\n  |- Try 38 * 3 = 114. Add 114 to the number set. Current number set: [114, 12, 22], target: 44. Options for choosing two numbers: [(114, 12), (114, 22), (12, 22)].\n   |- Pick two numbers (114, 12) (numbers left: [22]). Try possible operations.\n    |- Try 114 + 12 = 126. Add 126 to the number set. Current number set: [126, 22], target: 44, just two numbers left.\n     |- Try 126 + 22 = 148. Evaluate 148 != 44, drop this branch.\n     |- Try 126 - 22 = 104. Evaluate 104 != 44, drop this branch.\n     |- Try 126 * 22 = 2772. 2772 exceeds the maximum intermediate result, drop this branch.\n     |- Try 126 \/ 22 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 114 - 12 = 102. Add 102 to the number set. Current number set: [102, 22], target: 44, just two numbers left.\n     |- Try 102 + 22 = 124. Evaluate 124 != 44, drop this branch.\n     |- Try 102 - 22 = 80. Evaluate 80 != 44, drop this branch.\n     |- Try 102 * 22 = 2244. 2244 exceeds the maximum intermediate result, drop this branch.\n     |- Try 102 \/ 22 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 114 * 12 = 1368. Add 1368 to the number set. Current number set: [1368, 22], target: 44, just two numbers left.\n     |- Try 1368 + 22 = 1390. Evaluate 1390 != 44, drop this branch.\n     |- Try 1368 - 22 = 1346. Evaluate 1346 != 44, drop this branch.\n     |- Try 1368 * 22 = 30096. 30096 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1368 \/ 22 = 62.2. 62.2 is a decimal, drop this branch.\n    |- Try 114 \/ 12 = 9.5. 9.5 is a decimal, drop this branch.\n   |- Pick two numbers (114, 22) (numbers left: [12]). Try possible operations.\n    |- Try 114 + 22 = 136. Add 136 to the number set. Current number set: [136, 12], target: 44, just two numbers left.\n     |- Try 136 + 12 = 148. Evaluate 148 != 44, drop this branch.\n     |- Try 136 - 12 = 124. Evaluate 124 != 44, drop this branch.\n     |- Try 136 * 12 = 1632. Evaluate 1632 != 44, drop this branch.\n     |- Try 136 \/ 12 = 11.3. 11.3 is a decimal, drop this branch.\n    |- Try 114 - 22 = 92. Add 92 to the number set. Current number set: [92, 12], target: 44, just two numbers left.\n     |- Try 92 + 12 = 104. Evaluate 104 != 44, drop this branch.\n     |- Try 92 - 12 = 80. Evaluate 80 != 44, drop this branch.\n     |- Try 92 * 12 = 1104. Evaluate 1104 != 44, drop this branch.\n     |- Try 92 \/ 12 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 114 * 22 = 2508. 2508 exceeds the maximum intermediate result, drop this branch.\n    |- Try 114 \/ 22 = 5.2. 5.2 is a decimal, drop this branch.\n   |- Pick two numbers (12, 22) (numbers left: [114]). Try possible operations.\n    |- Try 22 + 12 = 34. Add 34 to the number set. Current number set: [34, 114], target: 44, just two numbers left.\n     |- Try 114 + 34 = 148. Evaluate 148 != 44, drop this branch.\n     |- Try 114 - 34 = 80. Evaluate 80 != 44, drop this branch.\n     |- Try 114 * 34 = 3876. 3876 exceeds the maximum intermediate result, drop this branch.\n     |- Try 114 \/ 34 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 22 - 12 = 10. Add 10 to the number set. Current number set: [10, 114], target: 44, just two numbers left.\n     |- Try 114 + 10 = 124. Evaluate 124 != 44, drop this branch.\n     |- Try 114 - 10 = 104. Evaluate 104 != 44, drop this branch.\n     |- Try 114 * 10 = 1140. Evaluate 1140 != 44, drop this branch.\n     |- Try 114 \/ 10 = 11.4. 11.4 is a decimal, drop this branch.\n    |- Try 22 * 12 = 264. Add 264 to the number set. Current number set: [264, 114], target: 44, just two numbers left.\n     |- Try 264 + 114 = 378. Evaluate 378 != 44, drop this branch.\n     |- Try 264 - 114 = 150. Evaluate 150 != 44, drop this branch.\n     |- Try 264 * 114 = 30096. 30096 exceeds the maximum intermediate result, drop this branch.\n     |- Try 264 \/ 114 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 22 \/ 12 = 1.8. 1.8 is a decimal, drop this branch.\n  |- Try 38 \/ 3 = 12.7. 12.7 is a decimal, drop this branch.\n |- Pick two numbers (3, 12) (numbers left: [38, 22]). Try possible operations.\n  |- Try 12 + 3 = 15. Add 15 to the number set. Current number set: [15, 38, 22], target: 44. Options for choosing two numbers: [(15, 38), (15, 22), (38, 22)].\n   |- Pick two numbers (15, 38) (numbers left: [22]). Try possible operations.\n    |- Try 38 + 15 = 53. Add 53 to the number set. Current number set: [53, 22], target: 44, just two numbers left.\n     |- Try 53 + 22 = 75. Evaluate 75 != 44, drop this branch.\n     |- Try 53 - 22 = 31. Evaluate 31 != 44, drop this branch.\n     |- Try 53 * 22 = 1166. Evaluate 1166 != 44, drop this branch.\n     |- Try 53 \/ 22 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 38 - 15 = 23. Add 23 to the number set. Current number set: [23, 22], target: 44, just two numbers left.\n     |- Try 23 + 22 = 45. Evaluate 45 != 44, drop this branch.\n     |- Try 23 - 22 = 1. Evaluate 1 != 44, drop this branch.\n     |- Try 23 * 22 = 506. Evaluate 506 != 44, drop this branch.\n     |- Try 23 \/ 22 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 38 * 15 = 570. Add 570 to the number set. Current number set: [570, 22], target: 44, just two numbers left.\n     |- Try 570 + 22 = 592. Evaluate 592 != 44, drop this branch.\n     |- Try 570 - 22 = 548. Evaluate 548 != 44, drop this branch.\n     |- Try 570 * 22 = 12540. 12540 exceeds the maximum intermediate result, drop this branch.\n     |- Try 570 \/ 22 = 25.9. 25.9 is a decimal, drop this branch.\n    |- Try 38 \/ 15 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (15, 22) (numbers left: [38]). Try possible operations.\n    |- Try 22 + 15 = 37. Add 37 to the number set. Current number set: [37, 38], target: 44, just two numbers left.\n     |- Try 38 + 37 = 75. Evaluate 75 != 44, drop this branch.\n     |- Try 38 - 37 = 1. Evaluate 1 != 44, drop this branch.\n     |- Try 38 * 37 = 1406. Evaluate 1406 != 44, drop this branch.\n     |- Try 38 \/ 37 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 22 - 15 = 7. Add 7 to the number set. Current number set: [7, 38], target: 44, just two numbers left.\n     |- Try 38 + 7 = 45. Evaluate 45 != 44, drop this branch.\n     |- Try 38 - 7 = 31. Evaluate 31 != 44, drop this branch.\n     |- Try 38 * 7 = 266. Evaluate 266 != 44, drop this branch.\n     |- Try 38 \/ 7 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 22 * 15 = 330. Add 330 to the number set. Current number set: [330, 38], target: 44, just two numbers left.\n     |- Try 330 + 38 = 368. Evaluate 368 != 44, drop this branch.\n     |- Try 330 - 38 = 292. Evaluate 292 != 44, drop this branch.\n     |- Try 330 * 38 = 12540. 12540 exceeds the maximum intermediate result, drop this branch.\n     |- Try 330 \/ 38 = 8.7. 8.7 is a decimal, drop this branch.\n    |- Try 22 \/ 15 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (38, 22) (numbers left: [15]). Try possible operations.\n    |- Try 38 + 22 = 60. Add 60 to the number set. Current number set: [60, 15], target: 44, just two numbers left.\n     |- Try 60 + 15 = 75. Evaluate 75 != 44, drop this branch.\n     |- Try 60 - 15 = 45. Evaluate 45 != 44, drop this branch.\n     |- Try 60 * 15 = 900. Evaluate 900 != 44, drop this branch.\n     |- Try 60 \/ 15 = 4. Evaluate 4 != 44, drop this branch.\n    |- Try 38 - 22 = 16. Add 16 to the number set. Current number set: [16, 15], target: 44, just two numbers left.\n     |- Try 16 + 15 = 31. Evaluate 31 != 44, drop this branch.\n     |- Try 16 - 15 = 1. Evaluate 1 != 44, drop this branch.\n     |- Try 16 * 15 = 240. Evaluate 240 != 44, drop this branch.\n     |- Try 16 \/ 15 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 38 * 22 = 836. Add 836 to the number set. Current number set: [836, 15], target: 44, just two numbers left.\n     |- Try 836 + 15 = 851. Evaluate 851 != 44, drop this branch.\n     |- Try 836 - 15 = 821. Evaluate 821 != 44, drop this branch.\n     |- Try 836 * 15 = 12540. 12540 exceeds the maximum intermediate result, drop this branch.\n     |- Try 836 \/ 15 = 55.7. 55.7 is a decimal, drop this branch.\n    |- Try 38 \/ 22 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 12 - 3 = 9. Add 9 to the number set. Current number set: [9, 38, 22], target: 44. Options for choosing two numbers: [(9, 38), (9, 22), (38, 22)].\n   |- Pick two numbers (9, 38) (numbers left: [22]). Try possible operations.\n    |- Try 38 + 9 = 47. Add 47 to the number set. Current number set: [47, 22], target: 44, just two numbers left.\n     |- Try 47 + 22 = 69. Evaluate 69 != 44, drop this branch.\n     |- Try 47 - 22 = 25. Evaluate 25 != 44, drop this branch.\n     |- Try 47 * 22 = 1034. Evaluate 1034 != 44, drop this branch.\n     |- Try 47 \/ 22 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 38 - 9 = 29. Add 29 to the number set. Current number set: [29, 22], target: 44, just two numbers left.\n     |- Try 29 + 22 = 51. Evaluate 51 != 44, drop this branch.\n     |- Try 29 - 22 = 7. Evaluate 7 != 44, drop this branch.\n     |- Try 29 * 22 = 638. Evaluate 638 != 44, drop this branch.\n     |- Try 29 \/ 22 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 38 * 9 = 342. Add 342 to the number set. Current number set: [342, 22], target: 44, just two numbers left.\n     |- Try 342 + 22 = 364. Evaluate 364 != 44, drop this branch.\n     |- Try 342 - 22 = 320. Evaluate 320 != 44, drop this branch.\n     |- Try 342 * 22 = 7524. 7524 exceeds the maximum intermediate result, drop this branch.\n     |- Try 342 \/ 22 = 15.5. 15.5 is a decimal, drop this branch.\n    |- Try 38 \/ 9 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (9, 22) (numbers left: [38]). Try possible operations.\n    |- Try 22 + 9 = 31. Add 31 to the number set. Current number set: [31, 38], target: 44, just two numbers left.\n     |- Try 38 + 31 = 69. Evaluate 69 != 44, drop this branch.\n     |- Try 38 - 31 = 7. Evaluate 7 != 44, drop this branch.\n     |- Try 38 * 31 = 1178. Evaluate 1178 != 44, drop this branch.\n     |- Try 38 \/ 31 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 22 - 9 = 13. Add 13 to the number set. Current number set: [13, 38], target: 44, just two numbers left.\n     |- Try 38 + 13 = 51. Evaluate 51 != 44, drop this branch.\n     |- Try 38 - 13 = 25. Evaluate 25 != 44, drop this branch.\n     |- Try 38 * 13 = 494. Evaluate 494 != 44, drop this branch.\n     |- Try 38 \/ 13 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 22 * 9 = 198. Add 198 to the number set. Current number set: [198, 38], target: 44, just two numbers left.\n     |- Try 198 + 38 = 236. Evaluate 236 != 44, drop this branch.\n     |- Try 198 - 38 = 160. Evaluate 160 != 44, drop this branch.\n     |- Try 198 * 38 = 7524. 7524 exceeds the maximum intermediate result, drop this branch.\n     |- Try 198 \/ 38 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 22 \/ 9 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (38, 22) (numbers left: [9]). Try possible operations.\n    |- Try 38 + 22 = 60. Add 60 to the number set. Current number set: [60, 9], target: 44, just two numbers left.\n     |- Try 60 + 9 = 69. Evaluate 69 != 44, drop this branch.\n     |- Try 60 - 9 = 51. Evaluate 51 != 44, drop this branch.\n     |- Try 60 * 9 = 540. Evaluate 540 != 44, drop this branch.\n     |- Try 60 \/ 9 = 6.7. 6.7 is a decimal, drop this branch.\n    |- Try 38 - 22 = 16. Add 16 to the number set. Current number set: [16, 9], target: 44, just two numbers left.\n     |- Try 16 + 9 = 25. Evaluate 25 != 44, drop this branch.\n     |- Try 16 - 9 = 7. Evaluate 7 != 44, drop this branch.\n     |- Try 16 * 9 = 144. Evaluate 144 != 44, drop this branch.\n     |- Try 16 \/ 9 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 38 * 22 = 836. Add 836 to the number set. Current number set: [836, 9], target: 44, just two numbers left.\n     |- Try 836 + 9 = 845. Evaluate 845 != 44, drop this branch.\n     |- Try 836 - 9 = 827. Evaluate 827 != 44, drop this branch.\n     |- Try 836 * 9 = 7524. 7524 exceeds the maximum intermediate result, drop this branch.\n     |- Try 836 \/ 9 = 92.9. 92.9 is a decimal, drop this branch.\n    |- Try 38 \/ 22 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 12 * 3 = 36. Add 36 to the number set. Current number set: [36, 38, 22], target: 44. Options for choosing two numbers: [(36, 38), (36, 22), (38, 22)].\n   |- Pick two numbers (36, 38) (numbers left: [22]). Try possible operations.\n    |- Try 38 + 36 = 74. Add 74 to the number set. Current number set: [74, 22], target: 44, just two numbers left.\n     |- Try 74 + 22 = 96. Evaluate 96 != 44, drop this branch.\n     |- Try 74 - 22 = 52. Evaluate 52 != 44, drop this branch.\n     |- Try 74 * 22 = 1628. Evaluate 1628 != 44, drop this branch.\n     |- Try 74 \/ 22 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 38 - 36 = 2. Add 2 to the number set. Current number set: [2, 22], target: 44, just two numbers left.\n     |- Try 22 + 2 = 24. Evaluate 24 != 44, drop this branch.\n     |- Try 22 - 2 = 20. Evaluate 20 != 44, drop this branch.\n     |- Try 22 * 2 = 44. Evaluate 44 == 44, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 22 * 2 = 44\nThe step before: 38 - 36 = 2\nThe first step: 12 * 3 = 36\n\nOutput the solution in the required format:\n<Solution>\n12 * 3 = 36\n38 - 36 = 2\n22 * 2 = 44\n<\/Solution>\n","item":{"nums":[3,38,12,22],"solution":["12 * 3 = 36","38 - 36 = 2","22 * 2 = 44"],"target":44}}
+{"instance_id":"countdown_8k_94","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [13, 8, 34, 7]\nTarget: 21","reference_output":"# Search Procedure\nInitial number set: [13, 8, 34, 7], target: 21. Options for choosing two numbers: [(13, 8), (13, 34), (13, 7), (8, 34), (8, 7), (34, 7)].\n |- Pick two numbers (13, 8) (numbers left: [34, 7]). Try possible operations.\n  |- Try 13 + 8 = 21. Add 21 to the number set. Current number set: [21, 34, 7], target: 21. Options for choosing two numbers: [(21, 34), (21, 7), (34, 7)].\n   |- Pick two numbers (21, 34) (numbers left: [7]). Try possible operations.\n    |- Try 34 + 21 = 55. Add 55 to the number set. Current number set: [55, 7], target: 21, just two numbers left.\n     |- Try 55 + 7 = 62. Evaluate 62 != 21, drop this branch.\n     |- Try 55 - 7 = 48. Evaluate 48 != 21, drop this branch.\n     |- Try 55 * 7 = 385. Evaluate 385 != 21, drop this branch.\n     |- Try 55 \/ 7 = 7.9. 7.9 is a decimal, drop this branch.\n    |- Try 34 - 21 = 13. Add 13 to the number set. Current number set: [13, 7], target: 21, just two numbers left.\n     |- Try 13 + 7 = 20. Evaluate 20 != 21, drop this branch.\n     |- Try 13 - 7 = 6. Evaluate 6 != 21, drop this branch.\n     |- Try 13 * 7 = 91. Evaluate 91 != 21, drop this branch.\n     |- Try 13 \/ 7 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 34 * 21 = 714. Add 714 to the number set. Current number set: [714, 7], target: 21, just two numbers left.\n     |- Try 714 + 7 = 721. Evaluate 721 != 21, drop this branch.\n     |- Try 714 - 7 = 707. Evaluate 707 != 21, drop this branch.\n     |- Try 714 * 7 = 4998. 4998 exceeds the maximum intermediate result, drop this branch.\n     |- Try 714 \/ 7 = 102. Evaluate 102 != 21, drop this branch.\n    |- Try 34 \/ 21 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (21, 7) (numbers left: [34]). Try possible operations.\n    |- Try 21 + 7 = 28. Add 28 to the number set. Current number set: [28, 34], target: 21, just two numbers left.\n     |- Try 34 + 28 = 62. Evaluate 62 != 21, drop this branch.\n     |- Try 34 - 28 = 6. Evaluate 6 != 21, drop this branch.\n     |- Try 34 * 28 = 952. Evaluate 952 != 21, drop this branch.\n     |- Try 34 \/ 28 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 21 - 7 = 14. Add 14 to the number set. Current number set: [14, 34], target: 21, just two numbers left.\n     |- Try 34 + 14 = 48. Evaluate 48 != 21, drop this branch.\n     |- Try 34 - 14 = 20. Evaluate 20 != 21, drop this branch.\n     |- Try 34 * 14 = 476. Evaluate 476 != 21, drop this branch.\n     |- Try 34 \/ 14 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 21 * 7 = 147. Add 147 to the number set. Current number set: [147, 34], target: 21, just two numbers left.\n     |- Try 147 + 34 = 181. Evaluate 181 != 21, drop this branch.\n     |- Try 147 - 34 = 113. Evaluate 113 != 21, drop this branch.\n     |- Try 147 * 34 = 4998. 4998 exceeds the maximum intermediate result, drop this branch.\n     |- Try 147 \/ 34 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 21 \/ 7 = 3. Add 3 to the number set. Current number set: [3, 34], target: 21, just two numbers left.\n     |- Try 34 + 3 = 37. Evaluate 37 != 21, drop this branch.\n     |- Try 34 - 3 = 31. Evaluate 31 != 21, drop this branch.\n     |- Try 34 * 3 = 102. Evaluate 102 != 21, drop this branch.\n     |- Try 34 \/ 3 = 11.3. 11.3 is a decimal, drop this branch.\n   |- Pick two numbers (34, 7) (numbers left: [21]). Try possible operations.\n    |- Try 34 + 7 = 41. Add 41 to the number set. Current number set: [41, 21], target: 21, just two numbers left.\n     |- Try 41 + 21 = 62. Evaluate 62 != 21, drop this branch.\n     |- Try 41 - 21 = 20. Evaluate 20 != 21, drop this branch.\n     |- Try 41 * 21 = 861. Evaluate 861 != 21, drop this branch.\n     |- Try 41 \/ 21 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 34 - 7 = 27. Add 27 to the number set. Current number set: [27, 21], target: 21, just two numbers left.\n     |- Try 27 + 21 = 48. Evaluate 48 != 21, drop this branch.\n     |- Try 27 - 21 = 6. Evaluate 6 != 21, drop this branch.\n     |- Try 27 * 21 = 567. Evaluate 567 != 21, drop this branch.\n     |- Try 27 \/ 21 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 34 * 7 = 238. Add 238 to the number set. Current number set: [238, 21], target: 21, just two numbers left.\n     |- Try 238 + 21 = 259. Evaluate 259 != 21, drop this branch.\n     |- Try 238 - 21 = 217. Evaluate 217 != 21, drop this branch.\n     |- Try 238 * 21 = 4998. 4998 exceeds the maximum intermediate result, drop this branch.\n     |- Try 238 \/ 21 = 11.3. 11.3 is a decimal, drop this branch.\n    |- Try 34 \/ 7 = 4.9. 4.9 is a decimal, drop this branch.\n  |- Try 13 - 8 = 5. Add 5 to the number set. Current number set: [5, 34, 7], target: 21. Options for choosing two numbers: [(5, 34), (5, 7), (34, 7)].\n   |- Pick two numbers (5, 34) (numbers left: [7]). Try possible operations.\n    |- Try 34 + 5 = 39. Add 39 to the number set. Current number set: [39, 7], target: 21, just two numbers left.\n     |- Try 39 + 7 = 46. Evaluate 46 != 21, drop this branch.\n     |- Try 39 - 7 = 32. Evaluate 32 != 21, drop this branch.\n     |- Try 39 * 7 = 273. Evaluate 273 != 21, drop this branch.\n     |- Try 39 \/ 7 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 34 - 5 = 29. Add 29 to the number set. Current number set: [29, 7], target: 21, just two numbers left.\n     |- Try 29 + 7 = 36. Evaluate 36 != 21, drop this branch.\n     |- Try 29 - 7 = 22. Evaluate 22 != 21, drop this branch.\n     |- Try 29 * 7 = 203. Evaluate 203 != 21, drop this branch.\n     |- Try 29 \/ 7 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 34 * 5 = 170. Add 170 to the number set. Current number set: [170, 7], target: 21, just two numbers left.\n     |- Try 170 + 7 = 177. Evaluate 177 != 21, drop this branch.\n     |- Try 170 - 7 = 163. Evaluate 163 != 21, drop this branch.\n     |- Try 170 * 7 = 1190. Evaluate 1190 != 21, drop this branch.\n     |- Try 170 \/ 7 = 24.3. 24.3 is a decimal, drop this branch.\n    |- Try 34 \/ 5 = 6.8. 6.8 is a decimal, drop this branch.\n   |- Pick two numbers (5, 7) (numbers left: [34]). Try possible operations.\n    |- Try 7 + 5 = 12. Add 12 to the number set. Current number set: [12, 34], target: 21, just two numbers left.\n     |- Try 34 + 12 = 46. Evaluate 46 != 21, drop this branch.\n     |- Try 34 - 12 = 22. Evaluate 22 != 21, drop this branch.\n     |- Try 34 * 12 = 408. Evaluate 408 != 21, drop this branch.\n     |- Try 34 \/ 12 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 7 - 5 = 2. Add 2 to the number set. Current number set: [2, 34], target: 21, just two numbers left.\n     |- Try 34 + 2 = 36. Evaluate 36 != 21, drop this branch.\n     |- Try 34 - 2 = 32. Evaluate 32 != 21, drop this branch.\n     |- Try 34 * 2 = 68. Evaluate 68 != 21, drop this branch.\n     |- Try 34 \/ 2 = 17. Evaluate 17 != 21, drop this branch.\n    |- Try 7 * 5 = 35. Add 35 to the number set. Current number set: [35, 34], target: 21, just two numbers left.\n     |- Try 35 + 34 = 69. Evaluate 69 != 21, drop this branch.\n     |- Try 35 - 34 = 1. Evaluate 1 != 21, drop this branch.\n     |- Try 35 * 34 = 1190. Evaluate 1190 != 21, drop this branch.\n     |- Try 35 \/ 34 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 7 \/ 5 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (34, 7) (numbers left: [5]). Try possible operations.\n    |- Try 34 + 7 = 41. Add 41 to the number set. Current number set: [41, 5], target: 21, just two numbers left.\n     |- Try 41 + 5 = 46. Evaluate 46 != 21, drop this branch.\n     |- Try 41 - 5 = 36. Evaluate 36 != 21, drop this branch.\n     |- Try 41 * 5 = 205. Evaluate 205 != 21, drop this branch.\n     |- Try 41 \/ 5 = 8.2. 8.2 is a decimal, drop this branch.\n    |- Try 34 - 7 = 27. Add 27 to the number set. Current number set: [27, 5], target: 21, just two numbers left.\n     |- Try 27 + 5 = 32. Evaluate 32 != 21, drop this branch.\n     |- Try 27 - 5 = 22. Evaluate 22 != 21, drop this branch.\n     |- Try 27 * 5 = 135. Evaluate 135 != 21, drop this branch.\n     |- Try 27 \/ 5 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 34 * 7 = 238. Add 238 to the number set. Current number set: [238, 5], target: 21, just two numbers left.\n     |- Try 238 + 5 = 243. Evaluate 243 != 21, drop this branch.\n     |- Try 238 - 5 = 233. Evaluate 233 != 21, drop this branch.\n     |- Try 238 * 5 = 1190. Evaluate 1190 != 21, drop this branch.\n     |- Try 238 \/ 5 = 47.6. 47.6 is a decimal, drop this branch.\n    |- Try 34 \/ 7 = 4.9. 4.9 is a decimal, drop this branch.\n  |- Try 13 * 8 = 104. Add 104 to the number set. Current number set: [104, 34, 7], target: 21. Options for choosing two numbers: [(104, 34), (104, 7), (34, 7)].\n   |- Pick two numbers (104, 34) (numbers left: [7]). Try possible operations.\n    |- Try 104 + 34 = 138. Add 138 to the number set. Current number set: [138, 7], target: 21, just two numbers left.\n     |- Try 138 + 7 = 145. Evaluate 145 != 21, drop this branch.\n     |- Try 138 - 7 = 131. Evaluate 131 != 21, drop this branch.\n     |- Try 138 * 7 = 966. Evaluate 966 != 21, drop this branch.\n     |- Try 138 \/ 7 = 19.7. 19.7 is a decimal, drop this branch.\n    |- Try 104 - 34 = 70. Add 70 to the number set. Current number set: [70, 7], target: 21, just two numbers left.\n     |- Try 70 + 7 = 77. Evaluate 77 != 21, drop this branch.\n     |- Try 70 - 7 = 63. Evaluate 63 != 21, drop this branch.\n     |- Try 70 * 7 = 490. Evaluate 490 != 21, drop this branch.\n     |- Try 70 \/ 7 = 10. Evaluate 10 != 21, drop this branch.\n    |- Try 104 * 34 = 3536. 3536 exceeds the maximum intermediate result, drop this branch.\n    |- Try 104 \/ 34 = 3.1. 3.1 is a decimal, drop this branch.\n   |- Pick two numbers (104, 7) (numbers left: [34]). Try possible operations.\n    |- Try 104 + 7 = 111. Add 111 to the number set. Current number set: [111, 34], target: 21, just two numbers left.\n     |- Try 111 + 34 = 145. Evaluate 145 != 21, drop this branch.\n     |- Try 111 - 34 = 77. Evaluate 77 != 21, drop this branch.\n     |- Try 111 * 34 = 3774. 3774 exceeds the maximum intermediate result, drop this branch.\n     |- Try 111 \/ 34 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 104 - 7 = 97. Add 97 to the number set. Current number set: [97, 34], target: 21, just two numbers left.\n     |- Try 97 + 34 = 131. Evaluate 131 != 21, drop this branch.\n     |- Try 97 - 34 = 63. Evaluate 63 != 21, drop this branch.\n     |- Try 97 * 34 = 3298. 3298 exceeds the maximum intermediate result, drop this branch.\n     |- Try 97 \/ 34 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 104 * 7 = 728. Add 728 to the number set. Current number set: [728, 34], target: 21, just two numbers left.\n     |- Try 728 + 34 = 762. Evaluate 762 != 21, drop this branch.\n     |- Try 728 - 34 = 694. Evaluate 694 != 21, drop this branch.\n     |- Try 728 * 34 = 24752. 24752 exceeds the maximum intermediate result, drop this branch.\n     |- Try 728 \/ 34 = 21.4. 21.4 is a decimal, drop this branch.\n    |- Try 104 \/ 7 = 14.9. 14.9 is a decimal, drop this branch.\n   |- Pick two numbers (34, 7) (numbers left: [104]). Try possible operations.\n    |- Try 34 + 7 = 41. Add 41 to the number set. Current number set: [41, 104], target: 21, just two numbers left.\n     |- Try 104 + 41 = 145. Evaluate 145 != 21, drop this branch.\n     |- Try 104 - 41 = 63. Evaluate 63 != 21, drop this branch.\n     |- Try 104 * 41 = 4264. 4264 exceeds the maximum intermediate result, drop this branch.\n     |- Try 104 \/ 41 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 34 - 7 = 27. Add 27 to the number set. Current number set: [27, 104], target: 21, just two numbers left.\n     |- Try 104 + 27 = 131. Evaluate 131 != 21, drop this branch.\n     |- Try 104 - 27 = 77. Evaluate 77 != 21, drop this branch.\n     |- Try 104 * 27 = 2808. 2808 exceeds the maximum intermediate result, drop this branch.\n     |- Try 104 \/ 27 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 34 * 7 = 238. Add 238 to the number set. Current number set: [238, 104], target: 21, just two numbers left.\n     |- Try 238 + 104 = 342. Evaluate 342 != 21, drop this branch.\n     |- Try 238 - 104 = 134. Evaluate 134 != 21, drop this branch.\n     |- Try 238 * 104 = 24752. 24752 exceeds the maximum intermediate result, drop this branch.\n     |- Try 238 \/ 104 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 34 \/ 7 = 4.9. 4.9 is a decimal, drop this branch.\n  |- Try 13 \/ 8 = 1.6. 1.6 is a decimal, drop this branch.\n |- Pick two numbers (13, 34) (numbers left: [8, 7]). Try possible operations.\n  |- Try 34 + 13 = 47. Add 47 to the number set. Current number set: [47, 8, 7], target: 21. Options for choosing two numbers: [(47, 8), (47, 7), (8, 7)].\n   |- Pick two numbers (47, 8) (numbers left: [7]). Try possible operations.\n    |- Try 47 + 8 = 55. Add 55 to the number set. Current number set: [55, 7], target: 21, just two numbers left.\n     |- Try 55 + 7 = 62. Evaluate 62 != 21, drop this branch.\n     |- Try 55 - 7 = 48. Evaluate 48 != 21, drop this branch.\n     |- Try 55 * 7 = 385. Evaluate 385 != 21, drop this branch.\n     |- Try 55 \/ 7 = 7.9. 7.9 is a decimal, drop this branch.\n    |- Try 47 - 8 = 39. Add 39 to the number set. Current number set: [39, 7], target: 21, just two numbers left.\n     |- Try 39 + 7 = 46. Evaluate 46 != 21, drop this branch.\n     |- Try 39 - 7 = 32. Evaluate 32 != 21, drop this branch.\n     |- Try 39 * 7 = 273. Evaluate 273 != 21, drop this branch.\n     |- Try 39 \/ 7 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 47 * 8 = 376. Add 376 to the number set. Current number set: [376, 7], target: 21, just two numbers left.\n     |- Try 376 + 7 = 383. Evaluate 383 != 21, drop this branch.\n     |- Try 376 - 7 = 369. Evaluate 369 != 21, drop this branch.\n     |- Try 376 * 7 = 2632. 2632 exceeds the maximum intermediate result, drop this branch.\n     |- Try 376 \/ 7 = 53.7. 53.7 is a decimal, drop this branch.\n    |- Try 47 \/ 8 = 5.9. 5.9 is a decimal, drop this branch.\n   |- Pick two numbers (47, 7) (numbers left: [8]). Try possible operations.\n    |- Try 47 + 7 = 54. Add 54 to the number set. Current number set: [54, 8], target: 21, just two numbers left.\n     |- Try 54 + 8 = 62. Evaluate 62 != 21, drop this branch.\n     |- Try 54 - 8 = 46. Evaluate 46 != 21, drop this branch.\n     |- Try 54 * 8 = 432. Evaluate 432 != 21, drop this branch.\n     |- Try 54 \/ 8 = 6.8. 6.8 is a decimal, drop this branch.\n    |- Try 47 - 7 = 40. Add 40 to the number set. Current number set: [40, 8], target: 21, just two numbers left.\n     |- Try 40 + 8 = 48. Evaluate 48 != 21, drop this branch.\n     |- Try 40 - 8 = 32. Evaluate 32 != 21, drop this branch.\n     |- Try 40 * 8 = 320. Evaluate 320 != 21, drop this branch.\n     |- Try 40 \/ 8 = 5. Evaluate 5 != 21, drop this branch.\n    |- Try 47 * 7 = 329. Add 329 to the number set. Current number set: [329, 8], target: 21, just two numbers left.\n     |- Try 329 + 8 = 337. Evaluate 337 != 21, drop this branch.\n     |- Try 329 - 8 = 321. Evaluate 321 != 21, drop this branch.\n     |- Try 329 * 8 = 2632. 2632 exceeds the maximum intermediate result, drop this branch.\n     |- Try 329 \/ 8 = 41.1. 41.1 is a decimal, drop this branch.\n    |- Try 47 \/ 7 = 6.7. 6.7 is a decimal, drop this branch.\n   |- Pick two numbers (8, 7) (numbers left: [47]). Try possible operations.\n    |- Try 8 + 7 = 15. Add 15 to the number set. Current number set: [15, 47], target: 21, just two numbers left.\n     |- Try 47 + 15 = 62. Evaluate 62 != 21, drop this branch.\n     |- Try 47 - 15 = 32. Evaluate 32 != 21, drop this branch.\n     |- Try 47 * 15 = 705. Evaluate 705 != 21, drop this branch.\n     |- Try 47 \/ 15 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 8 - 7 = 1. Add 1 to the number set. Current number set: [1, 47], target: 21, just two numbers left.\n     |- Try 47 + 1 = 48. Evaluate 48 != 21, drop this branch.\n     |- Try 47 - 1 = 46. Evaluate 46 != 21, drop this branch.\n     |- Try 47 * 1 = 47. Evaluate 47 != 21, drop this branch.\n     |- Try 47 \/ 1 = 47. Evaluate 47 != 21, drop this branch.\n    |- Try 8 * 7 = 56. Add 56 to the number set. Current number set: [56, 47], target: 21, just two numbers left.\n     |- Try 56 + 47 = 103. Evaluate 103 != 21, drop this branch.\n     |- Try 56 - 47 = 9. Evaluate 9 != 21, drop this branch.\n     |- Try 56 * 47 = 2632. 2632 exceeds the maximum intermediate result, drop this branch.\n     |- Try 56 \/ 47 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 8 \/ 7 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 34 - 13 = 21. Add 21 to the number set. Current number set: [21, 8, 7], target: 21. Options for choosing two numbers: [(21, 8), (21, 7), (8, 7)].\n   |- Pick two numbers (21, 8) (numbers left: [7]). Try possible operations.\n    |- Try 21 + 8 = 29. Add 29 to the number set. Current number set: [29, 7], target: 21, just two numbers left.\n     |- Try 29 + 7 = 36. Evaluate 36 != 21, drop this branch.\n     |- Try 29 - 7 = 22. Evaluate 22 != 21, drop this branch.\n     |- Try 29 * 7 = 203. Evaluate 203 != 21, drop this branch.\n     |- Try 29 \/ 7 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 21 - 8 = 13. Add 13 to the number set. Current number set: [13, 7], target: 21, just two numbers left.\n     |- Try 13 + 7 = 20. Evaluate 20 != 21, drop this branch.\n     |- Try 13 - 7 = 6. Evaluate 6 != 21, drop this branch.\n     |- Try 13 * 7 = 91. Evaluate 91 != 21, drop this branch.\n     |- Try 13 \/ 7 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 21 * 8 = 168. Add 168 to the number set. Current number set: [168, 7], target: 21, just two numbers left.\n     |- Try 168 + 7 = 175. Evaluate 175 != 21, drop this branch.\n     |- Try 168 - 7 = 161. Evaluate 161 != 21, drop this branch.\n     |- Try 168 * 7 = 1176. Evaluate 1176 != 21, drop this branch.\n     |- Try 168 \/ 7 = 24. Evaluate 24 != 21, drop this branch.\n    |- Try 21 \/ 8 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (21, 7) (numbers left: [8]). Try possible operations.\n    |- Try 21 + 7 = 28. Add 28 to the number set. Current number set: [28, 8], target: 21, just two numbers left.\n     |- Try 28 + 8 = 36. Evaluate 36 != 21, drop this branch.\n     |- Try 28 - 8 = 20. Evaluate 20 != 21, drop this branch.\n     |- Try 28 * 8 = 224. Evaluate 224 != 21, drop this branch.\n     |- Try 28 \/ 8 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 21 - 7 = 14. Add 14 to the number set. Current number set: [14, 8], target: 21, just two numbers left.\n     |- Try 14 + 8 = 22. Evaluate 22 != 21, drop this branch.\n     |- Try 14 - 8 = 6. Evaluate 6 != 21, drop this branch.\n     |- Try 14 * 8 = 112. Evaluate 112 != 21, drop this branch.\n     |- Try 14 \/ 8 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 21 * 7 = 147. Add 147 to the number set. Current number set: [147, 8], target: 21, just two numbers left.\n     |- Try 147 + 8 = 155. Evaluate 155 != 21, drop this branch.\n     |- Try 147 - 8 = 139. Evaluate 139 != 21, drop this branch.\n     |- Try 147 * 8 = 1176. Evaluate 1176 != 21, drop this branch.\n     |- Try 147 \/ 8 = 18.4. 18.4 is a decimal, drop this branch.\n    |- Try 21 \/ 7 = 3. Add 3 to the number set. Current number set: [3, 8], target: 21, just two numbers left.\n     |- Try 8 + 3 = 11. Evaluate 11 != 21, drop this branch.\n     |- Try 8 - 3 = 5. Evaluate 5 != 21, drop this branch.\n     |- Try 8 * 3 = 24. Evaluate 24 != 21, drop this branch.\n     |- Try 8 \/ 3 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (8, 7) (numbers left: [21]). Try possible operations.\n    |- Try 8 + 7 = 15. Add 15 to the number set. Current number set: [15, 21], target: 21, just two numbers left.\n     |- Try 21 + 15 = 36. Evaluate 36 != 21, drop this branch.\n     |- Try 21 - 15 = 6. Evaluate 6 != 21, drop this branch.\n     |- Try 21 * 15 = 315. Evaluate 315 != 21, drop this branch.\n     |- Try 21 \/ 15 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 8 - 7 = 1. Add 1 to the number set. Current number set: [1, 21], target: 21, just two numbers left.\n     |- Try 21 + 1 = 22. Evaluate 22 != 21, drop this branch.\n     |- Try 21 - 1 = 20. Evaluate 20 != 21, drop this branch.\n     |- Try 21 * 1 = 21. Evaluate 21 == 21, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 21 * 1 = 21\nThe step before: 8 - 7 = 1\nThe first step: 34 - 13 = 21\n\nOutput the solution in the required format:\n<Solution>\n34 - 13 = 21\n8 - 7 = 1\n21 * 1 = 21\n<\/Solution>\n","item":{"nums":[13,8,34,7],"solution":["34 - 13 = 21","8 - 7 = 1","21 * 1 = 21"],"target":21}}
+{"instance_id":"countdown_8k_95","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [27, 3, 3, 31]\nTarget: 43","reference_output":"# Search Procedure\nInitial number set: [27, 3, 3, 31], target: 43. Options for choosing two numbers: [(27, 3), (27, 3), (27, 31), (3, 3), (3, 31), (3, 31)].\n |- Pick two numbers (27, 3) (numbers left: [3, 31]). Try possible operations.\n  |- Try 27 + 3 = 30. Add 30 to the number set. Current number set: [30, 3, 31], target: 43. Options for choosing two numbers: [(30, 3), (30, 31), (3, 31)].\n   |- Pick two numbers (30, 3) (numbers left: [31]). Try possible operations.\n    |- Try 30 + 3 = 33. Add 33 to the number set. Current number set: [33, 31], target: 43, just two numbers left.\n     |- Try 33 + 31 = 64. Evaluate 64 != 43, drop this branch.\n     |- Try 33 - 31 = 2. Evaluate 2 != 43, drop this branch.\n     |- Try 33 * 31 = 1023. Evaluate 1023 != 43, drop this branch.\n     |- Try 33 \/ 31 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 30 - 3 = 27. Add 27 to the number set. Current number set: [27, 31], target: 43, just two numbers left.\n     |- Try 31 + 27 = 58. Evaluate 58 != 43, drop this branch.\n     |- Try 31 - 27 = 4. Evaluate 4 != 43, drop this branch.\n     |- Try 31 * 27 = 837. Evaluate 837 != 43, drop this branch.\n     |- Try 31 \/ 27 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 30 * 3 = 90. Add 90 to the number set. Current number set: [90, 31], target: 43, just two numbers left.\n     |- Try 90 + 31 = 121. Evaluate 121 != 43, drop this branch.\n     |- Try 90 - 31 = 59. Evaluate 59 != 43, drop this branch.\n     |- Try 90 * 31 = 2790. 2790 exceeds the maximum intermediate result, drop this branch.\n     |- Try 90 \/ 31 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 30 \/ 3 = 10. Add 10 to the number set. Current number set: [10, 31], target: 43, just two numbers left.\n     |- Try 31 + 10 = 41. Evaluate 41 != 43, drop this branch.\n     |- Try 31 - 10 = 21. Evaluate 21 != 43, drop this branch.\n     |- Try 31 * 10 = 310. Evaluate 310 != 43, drop this branch.\n     |- Try 31 \/ 10 = 3.1. 3.1 is a decimal, drop this branch.\n   |- Pick two numbers (30, 31) (numbers left: [3]). Try possible operations.\n    |- Try 31 + 30 = 61. Add 61 to the number set. Current number set: [61, 3], target: 43, just two numbers left.\n     |- Try 61 + 3 = 64. Evaluate 64 != 43, drop this branch.\n     |- Try 61 - 3 = 58. Evaluate 58 != 43, drop this branch.\n     |- Try 61 * 3 = 183. Evaluate 183 != 43, drop this branch.\n     |- Try 61 \/ 3 = 20.3. 20.3 is a decimal, drop this branch.\n    |- Try 31 - 30 = 1. Add 1 to the number set. Current number set: [1, 3], target: 43, just two numbers left.\n     |- Try 3 + 1 = 4. Evaluate 4 != 43, drop this branch.\n     |- Try 3 - 1 = 2. Evaluate 2 != 43, drop this branch.\n     |- Try 3 * 1 = 3. Evaluate 3 != 43, drop this branch.\n     |- Try 3 \/ 1 = 3. Evaluate 3 != 43, drop this branch.\n    |- Try 31 * 30 = 930. Add 930 to the number set. Current number set: [930, 3], target: 43, just two numbers left.\n     |- Try 930 + 3 = 933. Evaluate 933 != 43, drop this branch.\n     |- Try 930 - 3 = 927. Evaluate 927 != 43, drop this branch.\n     |- Try 930 * 3 = 2790. 2790 exceeds the maximum intermediate result, drop this branch.\n     |- Try 930 \/ 3 = 310. Evaluate 310 != 43, drop this branch.\n    |- Try 31 \/ 30 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (3, 31) (numbers left: [30]). Try possible operations.\n    |- Try 31 + 3 = 34. Add 34 to the number set. Current number set: [34, 30], target: 43, just two numbers left.\n     |- Try 34 + 30 = 64. Evaluate 64 != 43, drop this branch.\n     |- Try 34 - 30 = 4. Evaluate 4 != 43, drop this branch.\n     |- Try 34 * 30 = 1020. Evaluate 1020 != 43, drop this branch.\n     |- Try 34 \/ 30 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 31 - 3 = 28. Add 28 to the number set. Current number set: [28, 30], target: 43, just two numbers left.\n     |- Try 30 + 28 = 58. Evaluate 58 != 43, drop this branch.\n     |- Try 30 - 28 = 2. Evaluate 2 != 43, drop this branch.\n     |- Try 30 * 28 = 840. Evaluate 840 != 43, drop this branch.\n     |- Try 30 \/ 28 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 31 * 3 = 93. Add 93 to the number set. Current number set: [93, 30], target: 43, just two numbers left.\n     |- Try 93 + 30 = 123. Evaluate 123 != 43, drop this branch.\n     |- Try 93 - 30 = 63. Evaluate 63 != 43, drop this branch.\n     |- Try 93 * 30 = 2790. 2790 exceeds the maximum intermediate result, drop this branch.\n     |- Try 93 \/ 30 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 31 \/ 3 = 10.3. 10.3 is a decimal, drop this branch.\n  |- Try 27 - 3 = 24. Add 24 to the number set. Current number set: [24, 3, 31], target: 43. Options for choosing two numbers: [(24, 3), (24, 31), (3, 31)].\n   |- Pick two numbers (24, 3) (numbers left: [31]). Try possible operations.\n    |- Try 24 + 3 = 27. Add 27 to the number set. Current number set: [27, 31], target: 43, just two numbers left.\n     |- Try 31 + 27 = 58. Evaluate 58 != 43, drop this branch.\n     |- Try 31 - 27 = 4. Evaluate 4 != 43, drop this branch.\n     |- Try 31 * 27 = 837. Evaluate 837 != 43, drop this branch.\n     |- Try 31 \/ 27 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 24 - 3 = 21. Add 21 to the number set. Current number set: [21, 31], target: 43, just two numbers left.\n     |- Try 31 + 21 = 52. Evaluate 52 != 43, drop this branch.\n     |- Try 31 - 21 = 10. Evaluate 10 != 43, drop this branch.\n     |- Try 31 * 21 = 651. Evaluate 651 != 43, drop this branch.\n     |- Try 31 \/ 21 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 24 * 3 = 72. Add 72 to the number set. Current number set: [72, 31], target: 43, just two numbers left.\n     |- Try 72 + 31 = 103. Evaluate 103 != 43, drop this branch.\n     |- Try 72 - 31 = 41. Evaluate 41 != 43, drop this branch.\n     |- Try 72 * 31 = 2232. 2232 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 31 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 24 \/ 3 = 8. Add 8 to the number set. Current number set: [8, 31], target: 43, just two numbers left.\n     |- Try 31 + 8 = 39. Evaluate 39 != 43, drop this branch.\n     |- Try 31 - 8 = 23. Evaluate 23 != 43, drop this branch.\n     |- Try 31 * 8 = 248. Evaluate 248 != 43, drop this branch.\n     |- Try 31 \/ 8 = 3.9. 3.9 is a decimal, drop this branch.\n   |- Pick two numbers (24, 31) (numbers left: [3]). Try possible operations.\n    |- Try 31 + 24 = 55. Add 55 to the number set. Current number set: [55, 3], target: 43, just two numbers left.\n     |- Try 55 + 3 = 58. Evaluate 58 != 43, drop this branch.\n     |- Try 55 - 3 = 52. Evaluate 52 != 43, drop this branch.\n     |- Try 55 * 3 = 165. Evaluate 165 != 43, drop this branch.\n     |- Try 55 \/ 3 = 18.3. 18.3 is a decimal, drop this branch.\n    |- Try 31 - 24 = 7. Add 7 to the number set. Current number set: [7, 3], target: 43, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 43, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 43, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 43, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 31 * 24 = 744. Add 744 to the number set. Current number set: [744, 3], target: 43, just two numbers left.\n     |- Try 744 + 3 = 747. Evaluate 747 != 43, drop this branch.\n     |- Try 744 - 3 = 741. Evaluate 741 != 43, drop this branch.\n     |- Try 744 * 3 = 2232. 2232 exceeds the maximum intermediate result, drop this branch.\n     |- Try 744 \/ 3 = 248. Evaluate 248 != 43, drop this branch.\n    |- Try 31 \/ 24 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (3, 31) (numbers left: [24]). Try possible operations.\n    |- Try 31 + 3 = 34. Add 34 to the number set. Current number set: [34, 24], target: 43, just two numbers left.\n     |- Try 34 + 24 = 58. Evaluate 58 != 43, drop this branch.\n     |- Try 34 - 24 = 10. Evaluate 10 != 43, drop this branch.\n     |- Try 34 * 24 = 816. Evaluate 816 != 43, drop this branch.\n     |- Try 34 \/ 24 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 31 - 3 = 28. Add 28 to the number set. Current number set: [28, 24], target: 43, just two numbers left.\n     |- Try 28 + 24 = 52. Evaluate 52 != 43, drop this branch.\n     |- Try 28 - 24 = 4. Evaluate 4 != 43, drop this branch.\n     |- Try 28 * 24 = 672. Evaluate 672 != 43, drop this branch.\n     |- Try 28 \/ 24 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 31 * 3 = 93. Add 93 to the number set. Current number set: [93, 24], target: 43, just two numbers left.\n     |- Try 93 + 24 = 117. Evaluate 117 != 43, drop this branch.\n     |- Try 93 - 24 = 69. Evaluate 69 != 43, drop this branch.\n     |- Try 93 * 24 = 2232. 2232 exceeds the maximum intermediate result, drop this branch.\n     |- Try 93 \/ 24 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 31 \/ 3 = 10.3. 10.3 is a decimal, drop this branch.\n  |- Try 27 * 3 = 81. Add 81 to the number set. Current number set: [81, 3, 31], target: 43. Options for choosing two numbers: [(81, 3), (81, 31), (3, 31)].\n   |- Pick two numbers (81, 3) (numbers left: [31]). Try possible operations.\n    |- Try 81 + 3 = 84. Add 84 to the number set. Current number set: [84, 31], target: 43, just two numbers left.\n     |- Try 84 + 31 = 115. Evaluate 115 != 43, drop this branch.\n     |- Try 84 - 31 = 53. Evaluate 53 != 43, drop this branch.\n     |- Try 84 * 31 = 2604. 2604 exceeds the maximum intermediate result, drop this branch.\n     |- Try 84 \/ 31 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 81 - 3 = 78. Add 78 to the number set. Current number set: [78, 31], target: 43, just two numbers left.\n     |- Try 78 + 31 = 109. Evaluate 109 != 43, drop this branch.\n     |- Try 78 - 31 = 47. Evaluate 47 != 43, drop this branch.\n     |- Try 78 * 31 = 2418. 2418 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 31 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 81 * 3 = 243. Add 243 to the number set. Current number set: [243, 31], target: 43, just two numbers left.\n     |- Try 243 + 31 = 274. Evaluate 274 != 43, drop this branch.\n     |- Try 243 - 31 = 212. Evaluate 212 != 43, drop this branch.\n     |- Try 243 * 31 = 7533. 7533 exceeds the maximum intermediate result, drop this branch.\n     |- Try 243 \/ 31 = 7.8. 7.8 is a decimal, drop this branch.\n    |- Try 81 \/ 3 = 27. Add 27 to the number set. Current number set: [27, 31], target: 43, just two numbers left.\n     |- Try 31 + 27 = 58. Evaluate 58 != 43, drop this branch.\n     |- Try 31 - 27 = 4. Evaluate 4 != 43, drop this branch.\n     |- Try 31 * 27 = 837. Evaluate 837 != 43, drop this branch.\n     |- Try 31 \/ 27 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (81, 31) (numbers left: [3]). Try possible operations.\n    |- Try 81 + 31 = 112. Add 112 to the number set. Current number set: [112, 3], target: 43, just two numbers left.\n     |- Try 112 + 3 = 115. Evaluate 115 != 43, drop this branch.\n     |- Try 112 - 3 = 109. Evaluate 109 != 43, drop this branch.\n     |- Try 112 * 3 = 336. Evaluate 336 != 43, drop this branch.\n     |- Try 112 \/ 3 = 37.3. 37.3 is a decimal, drop this branch.\n    |- Try 81 - 31 = 50. Add 50 to the number set. Current number set: [50, 3], target: 43, just two numbers left.\n     |- Try 50 + 3 = 53. Evaluate 53 != 43, drop this branch.\n     |- Try 50 - 3 = 47. Evaluate 47 != 43, drop this branch.\n     |- Try 50 * 3 = 150. Evaluate 150 != 43, drop this branch.\n     |- Try 50 \/ 3 = 16.7. 16.7 is a decimal, drop this branch.\n    |- Try 81 * 31 = 2511. 2511 exceeds the maximum intermediate result, drop this branch.\n    |- Try 81 \/ 31 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (3, 31) (numbers left: [81]). Try possible operations.\n    |- Try 31 + 3 = 34. Add 34 to the number set. Current number set: [34, 81], target: 43, just two numbers left.\n     |- Try 81 + 34 = 115. Evaluate 115 != 43, drop this branch.\n     |- Try 81 - 34 = 47. Evaluate 47 != 43, drop this branch.\n     |- Try 81 * 34 = 2754. 2754 exceeds the maximum intermediate result, drop this branch.\n     |- Try 81 \/ 34 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 31 - 3 = 28. Add 28 to the number set. Current number set: [28, 81], target: 43, just two numbers left.\n     |- Try 81 + 28 = 109. Evaluate 109 != 43, drop this branch.\n     |- Try 81 - 28 = 53. Evaluate 53 != 43, drop this branch.\n     |- Try 81 * 28 = 2268. 2268 exceeds the maximum intermediate result, drop this branch.\n     |- Try 81 \/ 28 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 31 * 3 = 93. Add 93 to the number set. Current number set: [93, 81], target: 43, just two numbers left.\n     |- Try 93 + 81 = 174. Evaluate 174 != 43, drop this branch.\n     |- Try 93 - 81 = 12. Evaluate 12 != 43, drop this branch.\n     |- Try 93 * 81 = 7533. 7533 exceeds the maximum intermediate result, drop this branch.\n     |- Try 93 \/ 81 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 31 \/ 3 = 10.3. 10.3 is a decimal, drop this branch.\n  |- Try 27 \/ 3 = 9. Add 9 to the number set. Current number set: [9, 3, 31], target: 43. Options for choosing two numbers: [(9, 3), (9, 31), (3, 31)].\n   |- Pick two numbers (9, 3) (numbers left: [31]). Try possible operations.\n    |- Try 9 + 3 = 12. Add 12 to the number set. Current number set: [12, 31], target: 43, just two numbers left.\n     |- Try 31 + 12 = 43. Evaluate 43 == 43, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 31 + 12 = 43\nThe step before: 9 + 3 = 12\nThe first step: 27 \/ 3 = 9\n\nOutput the solution in the required format:\n<Solution>\n27 \/ 3 = 9\n9 + 3 = 12\n31 + 12 = 43\n<\/Solution>\n","item":{"nums":[27,3,3,31],"solution":["27 \/ 3 = 9","9 + 3 = 12","31 + 12 = 43"],"target":43}}
+{"instance_id":"countdown_8k_96","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [27, 44, 35, 9]\nTarget: 28","reference_output":"# Search Procedure\nInitial number set: [27, 44, 35, 9], target: 28. Options for choosing two numbers: [(27, 44), (27, 35), (27, 9), (44, 35), (44, 9), (35, 9)].\n |- Pick two numbers (27, 44) (numbers left: [35, 9]). Try possible operations.\n  |- Try 44 + 27 = 71. Add 71 to the number set. Current number set: [71, 35, 9], target: 28. Options for choosing two numbers: [(71, 35), (71, 9), (35, 9)].\n   |- Pick two numbers (71, 35) (numbers left: [9]). Try possible operations.\n    |- Try 71 + 35 = 106. Add 106 to the number set. Current number set: [106, 9], target: 28, just two numbers left.\n     |- Try 106 + 9 = 115. Evaluate 115 != 28, drop this branch.\n     |- Try 106 - 9 = 97. Evaluate 97 != 28, drop this branch.\n     |- Try 106 * 9 = 954. Evaluate 954 != 28, drop this branch.\n     |- Try 106 \/ 9 = 11.8. 11.8 is a decimal, drop this branch.\n    |- Try 71 - 35 = 36. Add 36 to the number set. Current number set: [36, 9], target: 28, just two numbers left.\n     |- Try 36 + 9 = 45. Evaluate 45 != 28, drop this branch.\n     |- Try 36 - 9 = 27. Evaluate 27 != 28, drop this branch.\n     |- Try 36 * 9 = 324. Evaluate 324 != 28, drop this branch.\n     |- Try 36 \/ 9 = 4. Evaluate 4 != 28, drop this branch.\n    |- Try 71 * 35 = 2485. 2485 exceeds the maximum intermediate result, drop this branch.\n    |- Try 71 \/ 35 = 2.0. 2.0 is a decimal, drop this branch.\n   |- Pick two numbers (71, 9) (numbers left: [35]). Try possible operations.\n    |- Try 71 + 9 = 80. Add 80 to the number set. Current number set: [80, 35], target: 28, just two numbers left.\n     |- Try 80 + 35 = 115. Evaluate 115 != 28, drop this branch.\n     |- Try 80 - 35 = 45. Evaluate 45 != 28, drop this branch.\n     |- Try 80 * 35 = 2800. 2800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 80 \/ 35 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 71 - 9 = 62. Add 62 to the number set. Current number set: [62, 35], target: 28, just two numbers left.\n     |- Try 62 + 35 = 97. Evaluate 97 != 28, drop this branch.\n     |- Try 62 - 35 = 27. Evaluate 27 != 28, drop this branch.\n     |- Try 62 * 35 = 2170. 2170 exceeds the maximum intermediate result, drop this branch.\n     |- Try 62 \/ 35 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 71 * 9 = 639. Add 639 to the number set. Current number set: [639, 35], target: 28, just two numbers left.\n     |- Try 639 + 35 = 674. Evaluate 674 != 28, drop this branch.\n     |- Try 639 - 35 = 604. Evaluate 604 != 28, drop this branch.\n     |- Try 639 * 35 = 22365. 22365 exceeds the maximum intermediate result, drop this branch.\n     |- Try 639 \/ 35 = 18.3. 18.3 is a decimal, drop this branch.\n    |- Try 71 \/ 9 = 7.9. 7.9 is a decimal, drop this branch.\n   |- Pick two numbers (35, 9) (numbers left: [71]). Try possible operations.\n    |- Try 35 + 9 = 44. Add 44 to the number set. Current number set: [44, 71], target: 28, just two numbers left.\n     |- Try 71 + 44 = 115. Evaluate 115 != 28, drop this branch.\n     |- Try 71 - 44 = 27. Evaluate 27 != 28, drop this branch.\n     |- Try 71 * 44 = 3124. 3124 exceeds the maximum intermediate result, drop this branch.\n     |- Try 71 \/ 44 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 35 - 9 = 26. Add 26 to the number set. Current number set: [26, 71], target: 28, just two numbers left.\n     |- Try 71 + 26 = 97. Evaluate 97 != 28, drop this branch.\n     |- Try 71 - 26 = 45. Evaluate 45 != 28, drop this branch.\n     |- Try 71 * 26 = 1846. Evaluate 1846 != 28, drop this branch.\n     |- Try 71 \/ 26 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 35 * 9 = 315. Add 315 to the number set. Current number set: [315, 71], target: 28, just two numbers left.\n     |- Try 315 + 71 = 386. Evaluate 386 != 28, drop this branch.\n     |- Try 315 - 71 = 244. Evaluate 244 != 28, drop this branch.\n     |- Try 315 * 71 = 22365. 22365 exceeds the maximum intermediate result, drop this branch.\n     |- Try 315 \/ 71 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 35 \/ 9 = 3.9. 3.9 is a decimal, drop this branch.\n  |- Try 44 - 27 = 17. Add 17 to the number set. Current number set: [17, 35, 9], target: 28. Options for choosing two numbers: [(17, 35), (17, 9), (35, 9)].\n   |- Pick two numbers (17, 35) (numbers left: [9]). Try possible operations.\n    |- Try 35 + 17 = 52. Add 52 to the number set. Current number set: [52, 9], target: 28, just two numbers left.\n     |- Try 52 + 9 = 61. Evaluate 61 != 28, drop this branch.\n     |- Try 52 - 9 = 43. Evaluate 43 != 28, drop this branch.\n     |- Try 52 * 9 = 468. Evaluate 468 != 28, drop this branch.\n     |- Try 52 \/ 9 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 35 - 17 = 18. Add 18 to the number set. Current number set: [18, 9], target: 28, just two numbers left.\n     |- Try 18 + 9 = 27. Evaluate 27 != 28, drop this branch.\n     |- Try 18 - 9 = 9. Evaluate 9 != 28, drop this branch.\n     |- Try 18 * 9 = 162. Evaluate 162 != 28, drop this branch.\n     |- Try 18 \/ 9 = 2. Evaluate 2 != 28, drop this branch.\n    |- Try 35 * 17 = 595. Add 595 to the number set. Current number set: [595, 9], target: 28, just two numbers left.\n     |- Try 595 + 9 = 604. Evaluate 604 != 28, drop this branch.\n     |- Try 595 - 9 = 586. Evaluate 586 != 28, drop this branch.\n     |- Try 595 * 9 = 5355. 5355 exceeds the maximum intermediate result, drop this branch.\n     |- Try 595 \/ 9 = 66.1. 66.1 is a decimal, drop this branch.\n    |- Try 35 \/ 17 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (17, 9) (numbers left: [35]). Try possible operations.\n    |- Try 17 + 9 = 26. Add 26 to the number set. Current number set: [26, 35], target: 28, just two numbers left.\n     |- Try 35 + 26 = 61. Evaluate 61 != 28, drop this branch.\n     |- Try 35 - 26 = 9. Evaluate 9 != 28, drop this branch.\n     |- Try 35 * 26 = 910. Evaluate 910 != 28, drop this branch.\n     |- Try 35 \/ 26 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 17 - 9 = 8. Add 8 to the number set. Current number set: [8, 35], target: 28, just two numbers left.\n     |- Try 35 + 8 = 43. Evaluate 43 != 28, drop this branch.\n     |- Try 35 - 8 = 27. Evaluate 27 != 28, drop this branch.\n     |- Try 35 * 8 = 280. Evaluate 280 != 28, drop this branch.\n     |- Try 35 \/ 8 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 17 * 9 = 153. Add 153 to the number set. Current number set: [153, 35], target: 28, just two numbers left.\n     |- Try 153 + 35 = 188. Evaluate 188 != 28, drop this branch.\n     |- Try 153 - 35 = 118. Evaluate 118 != 28, drop this branch.\n     |- Try 153 * 35 = 5355. 5355 exceeds the maximum intermediate result, drop this branch.\n     |- Try 153 \/ 35 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 17 \/ 9 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (35, 9) (numbers left: [17]). Try possible operations.\n    |- Try 35 + 9 = 44. Add 44 to the number set. Current number set: [44, 17], target: 28, just two numbers left.\n     |- Try 44 + 17 = 61. Evaluate 61 != 28, drop this branch.\n     |- Try 44 - 17 = 27. Evaluate 27 != 28, drop this branch.\n     |- Try 44 * 17 = 748. Evaluate 748 != 28, drop this branch.\n     |- Try 44 \/ 17 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 35 - 9 = 26. Add 26 to the number set. Current number set: [26, 17], target: 28, just two numbers left.\n     |- Try 26 + 17 = 43. Evaluate 43 != 28, drop this branch.\n     |- Try 26 - 17 = 9. Evaluate 9 != 28, drop this branch.\n     |- Try 26 * 17 = 442. Evaluate 442 != 28, drop this branch.\n     |- Try 26 \/ 17 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 35 * 9 = 315. Add 315 to the number set. Current number set: [315, 17], target: 28, just two numbers left.\n     |- Try 315 + 17 = 332. Evaluate 332 != 28, drop this branch.\n     |- Try 315 - 17 = 298. Evaluate 298 != 28, drop this branch.\n     |- Try 315 * 17 = 5355. 5355 exceeds the maximum intermediate result, drop this branch.\n     |- Try 315 \/ 17 = 18.5. 18.5 is a decimal, drop this branch.\n    |- Try 35 \/ 9 = 3.9. 3.9 is a decimal, drop this branch.\n  |- Try 44 * 27 = 1188. Add 1188 to the number set. Current number set: [1188, 35, 9], target: 28. Options for choosing two numbers: [(1188, 35), (1188, 9), (35, 9)].\n   |- Pick two numbers (1188, 35) (numbers left: [9]). Try possible operations.\n    |- Try 1188 + 35 = 1223. Add 1223 to the number set. Current number set: [1223, 9], target: 28, just two numbers left.\n     |- Try 1223 + 9 = 1232. Evaluate 1232 != 28, drop this branch.\n     |- Try 1223 - 9 = 1214. Evaluate 1214 != 28, drop this branch.\n     |- Try 1223 * 9 = 11007. 11007 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1223 \/ 9 = 135.9. 135.9 is a decimal, drop this branch.\n    |- Try 1188 - 35 = 1153. Add 1153 to the number set. Current number set: [1153, 9], target: 28, just two numbers left.\n     |- Try 1153 + 9 = 1162. Evaluate 1162 != 28, drop this branch.\n     |- Try 1153 - 9 = 1144. Evaluate 1144 != 28, drop this branch.\n     |- Try 1153 * 9 = 10377. 10377 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1153 \/ 9 = 128.1. 128.1 is a decimal, drop this branch.\n    |- Try 1188 * 35 = 41580. 41580 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1188 \/ 35 = 33.9. 33.9 is a decimal, drop this branch.\n   |- Pick two numbers (1188, 9) (numbers left: [35]). Try possible operations.\n    |- Try 1188 + 9 = 1197. Add 1197 to the number set. Current number set: [1197, 35], target: 28, just two numbers left.\n     |- Try 1197 + 35 = 1232. Evaluate 1232 != 28, drop this branch.\n     |- Try 1197 - 35 = 1162. Evaluate 1162 != 28, drop this branch.\n     |- Try 1197 * 35 = 41895. 41895 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1197 \/ 35 = 34.2. 34.2 is a decimal, drop this branch.\n    |- Try 1188 - 9 = 1179. Add 1179 to the number set. Current number set: [1179, 35], target: 28, just two numbers left.\n     |- Try 1179 + 35 = 1214. Evaluate 1214 != 28, drop this branch.\n     |- Try 1179 - 35 = 1144. Evaluate 1144 != 28, drop this branch.\n     |- Try 1179 * 35 = 41265. 41265 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1179 \/ 35 = 33.7. 33.7 is a decimal, drop this branch.\n    |- Try 1188 * 9 = 10692. 10692 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1188 \/ 9 = 132. Add 132 to the number set. Current number set: [132, 35], target: 28, just two numbers left.\n     |- Try 132 + 35 = 167. Evaluate 167 != 28, drop this branch.\n     |- Try 132 - 35 = 97. Evaluate 97 != 28, drop this branch.\n     |- Try 132 * 35 = 4620. 4620 exceeds the maximum intermediate result, drop this branch.\n     |- Try 132 \/ 35 = 3.8. 3.8 is a decimal, drop this branch.\n   |- Pick two numbers (35, 9) (numbers left: [1188]). Try possible operations.\n    |- Try 35 + 9 = 44. Add 44 to the number set. Current number set: [44, 1188], target: 28, just two numbers left.\n     |- Try 1188 + 44 = 1232. Evaluate 1232 != 28, drop this branch.\n     |- Try 1188 - 44 = 1144. Evaluate 1144 != 28, drop this branch.\n     |- Try 1188 * 44 = 52272. 52272 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1188 \/ 44 = 27. Evaluate 27 != 28, drop this branch.\n    |- Try 35 - 9 = 26. Add 26 to the number set. Current number set: [26, 1188], target: 28, just two numbers left.\n     |- Try 1188 + 26 = 1214. Evaluate 1214 != 28, drop this branch.\n     |- Try 1188 - 26 = 1162. Evaluate 1162 != 28, drop this branch.\n     |- Try 1188 * 26 = 30888. 30888 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1188 \/ 26 = 45.7. 45.7 is a decimal, drop this branch.\n    |- Try 35 * 9 = 315. Add 315 to the number set. Current number set: [315, 1188], target: 28, just two numbers left.\n     |- Try 1188 + 315 = 1503. Evaluate 1503 != 28, drop this branch.\n     |- Try 1188 - 315 = 873. Evaluate 873 != 28, drop this branch.\n     |- Try 1188 * 315 = 374220. 374220 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1188 \/ 315 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 35 \/ 9 = 3.9. 3.9 is a decimal, drop this branch.\n  |- Try 44 \/ 27 = 1.6. 1.6 is a decimal, drop this branch.\n |- Pick two numbers (27, 35) (numbers left: [44, 9]). Try possible operations.\n  |- Try 35 + 27 = 62. Add 62 to the number set. Current number set: [62, 44, 9], target: 28. Options for choosing two numbers: [(62, 44), (62, 9), (44, 9)].\n   |- Pick two numbers (62, 44) (numbers left: [9]). Try possible operations.\n    |- Try 62 + 44 = 106. Add 106 to the number set. Current number set: [106, 9], target: 28, just two numbers left.\n     |- Try 106 + 9 = 115. Evaluate 115 != 28, drop this branch.\n     |- Try 106 - 9 = 97. Evaluate 97 != 28, drop this branch.\n     |- Try 106 * 9 = 954. Evaluate 954 != 28, drop this branch.\n     |- Try 106 \/ 9 = 11.8. 11.8 is a decimal, drop this branch.\n    |- Try 62 - 44 = 18. Add 18 to the number set. Current number set: [18, 9], target: 28, just two numbers left.\n     |- Try 18 + 9 = 27. Evaluate 27 != 28, drop this branch.\n     |- Try 18 - 9 = 9. Evaluate 9 != 28, drop this branch.\n     |- Try 18 * 9 = 162. Evaluate 162 != 28, drop this branch.\n     |- Try 18 \/ 9 = 2. Evaluate 2 != 28, drop this branch.\n    |- Try 62 * 44 = 2728. 2728 exceeds the maximum intermediate result, drop this branch.\n    |- Try 62 \/ 44 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (62, 9) (numbers left: [44]). Try possible operations.\n    |- Try 62 + 9 = 71. Add 71 to the number set. Current number set: [71, 44], target: 28, just two numbers left.\n     |- Try 71 + 44 = 115. Evaluate 115 != 28, drop this branch.\n     |- Try 71 - 44 = 27. Evaluate 27 != 28, drop this branch.\n     |- Try 71 * 44 = 3124. 3124 exceeds the maximum intermediate result, drop this branch.\n     |- Try 71 \/ 44 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 62 - 9 = 53. Add 53 to the number set. Current number set: [53, 44], target: 28, just two numbers left.\n     |- Try 53 + 44 = 97. Evaluate 97 != 28, drop this branch.\n     |- Try 53 - 44 = 9. Evaluate 9 != 28, drop this branch.\n     |- Try 53 * 44 = 2332. 2332 exceeds the maximum intermediate result, drop this branch.\n     |- Try 53 \/ 44 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 62 * 9 = 558. Add 558 to the number set. Current number set: [558, 44], target: 28, just two numbers left.\n     |- Try 558 + 44 = 602. Evaluate 602 != 28, drop this branch.\n     |- Try 558 - 44 = 514. Evaluate 514 != 28, drop this branch.\n     |- Try 558 * 44 = 24552. 24552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 558 \/ 44 = 12.7. 12.7 is a decimal, drop this branch.\n    |- Try 62 \/ 9 = 6.9. 6.9 is a decimal, drop this branch.\n   |- Pick two numbers (44, 9) (numbers left: [62]). Try possible operations.\n    |- Try 44 + 9 = 53. Add 53 to the number set. Current number set: [53, 62], target: 28, just two numbers left.\n     |- Try 62 + 53 = 115. Evaluate 115 != 28, drop this branch.\n     |- Try 62 - 53 = 9. Evaluate 9 != 28, drop this branch.\n     |- Try 62 * 53 = 3286. 3286 exceeds the maximum intermediate result, drop this branch.\n     |- Try 62 \/ 53 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 44 - 9 = 35. Add 35 to the number set. Current number set: [35, 62], target: 28, just two numbers left.\n     |- Try 62 + 35 = 97. Evaluate 97 != 28, drop this branch.\n     |- Try 62 - 35 = 27. Evaluate 27 != 28, drop this branch.\n     |- Try 62 * 35 = 2170. 2170 exceeds the maximum intermediate result, drop this branch.\n     |- Try 62 \/ 35 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 44 * 9 = 396. Add 396 to the number set. Current number set: [396, 62], target: 28, just two numbers left.\n     |- Try 396 + 62 = 458. Evaluate 458 != 28, drop this branch.\n     |- Try 396 - 62 = 334. Evaluate 334 != 28, drop this branch.\n     |- Try 396 * 62 = 24552. 24552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 396 \/ 62 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 44 \/ 9 = 4.9. 4.9 is a decimal, drop this branch.\n  |- Try 35 - 27 = 8. Add 8 to the number set. Current number set: [8, 44, 9], target: 28. Options for choosing two numbers: [(8, 44), (8, 9), (44, 9)].\n   |- Pick two numbers (8, 44) (numbers left: [9]). Try possible operations.\n    |- Try 44 + 8 = 52. Add 52 to the number set. Current number set: [52, 9], target: 28, just two numbers left.\n     |- Try 52 + 9 = 61. Evaluate 61 != 28, drop this branch.\n     |- Try 52 - 9 = 43. Evaluate 43 != 28, drop this branch.\n     |- Try 52 * 9 = 468. Evaluate 468 != 28, drop this branch.\n     |- Try 52 \/ 9 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 44 - 8 = 36. Add 36 to the number set. Current number set: [36, 9], target: 28, just two numbers left.\n     |- Try 36 + 9 = 45. Evaluate 45 != 28, drop this branch.\n     |- Try 36 - 9 = 27. Evaluate 27 != 28, drop this branch.\n     |- Try 36 * 9 = 324. Evaluate 324 != 28, drop this branch.\n     |- Try 36 \/ 9 = 4. Evaluate 4 != 28, drop this branch.\n    |- Try 44 * 8 = 352. Add 352 to the number set. Current number set: [352, 9], target: 28, just two numbers left.\n     |- Try 352 + 9 = 361. Evaluate 361 != 28, drop this branch.\n     |- Try 352 - 9 = 343. Evaluate 343 != 28, drop this branch.\n     |- Try 352 * 9 = 3168. 3168 exceeds the maximum intermediate result, drop this branch.\n     |- Try 352 \/ 9 = 39.1. 39.1 is a decimal, drop this branch.\n    |- Try 44 \/ 8 = 5.5. 5.5 is a decimal, drop this branch.\n   |- Pick two numbers (8, 9) (numbers left: [44]). Try possible operations.\n    |- Try 9 + 8 = 17. Add 17 to the number set. Current number set: [17, 44], target: 28, just two numbers left.\n     |- Try 44 + 17 = 61. Evaluate 61 != 28, drop this branch.\n     |- Try 44 - 17 = 27. Evaluate 27 != 28, drop this branch.\n     |- Try 44 * 17 = 748. Evaluate 748 != 28, drop this branch.\n     |- Try 44 \/ 17 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 9 - 8 = 1. Add 1 to the number set. Current number set: [1, 44], target: 28, just two numbers left.\n     |- Try 44 + 1 = 45. Evaluate 45 != 28, drop this branch.\n     |- Try 44 - 1 = 43. Evaluate 43 != 28, drop this branch.\n     |- Try 44 * 1 = 44. Evaluate 44 != 28, drop this branch.\n     |- Try 44 \/ 1 = 44. Evaluate 44 != 28, drop this branch.\n    |- Try 9 * 8 = 72. Add 72 to the number set. Current number set: [72, 44], target: 28, just two numbers left.\n     |- Try 72 + 44 = 116. Evaluate 116 != 28, drop this branch.\n     |- Try 72 - 44 = 28. Evaluate 28 == 28, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 72 - 44 = 28\nThe step before: 9 * 8 = 72\nThe first step: 35 - 27 = 8\n\nOutput the solution in the required format:\n<Solution>\n35 - 27 = 8\n9 * 8 = 72\n72 - 44 = 28\n<\/Solution>\n","item":{"nums":[27,44,35,9],"solution":["35 - 27 = 8","9 * 8 = 72","72 - 44 = 28"],"target":28}}
+{"instance_id":"countdown_8k_97","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [34, 36, 29, 30]\nTarget: 30","reference_output":"# Search Procedure\nInitial number set: [34, 36, 29, 30], target: 30. Options for choosing two numbers: [(34, 36), (34, 29), (34, 30), (36, 29), (36, 30), (29, 30)].\n |- Pick two numbers (34, 36) (numbers left: [29, 30]). Try possible operations.\n  |- Try 36 + 34 = 70. Add 70 to the number set. Current number set: [70, 29, 30], target: 30. Options for choosing two numbers: [(70, 29), (70, 30), (29, 30)].\n   |- Pick two numbers (70, 29) (numbers left: [30]). Try possible operations.\n    |- Try 70 + 29 = 99. Add 99 to the number set. Current number set: [99, 30], target: 30, just two numbers left.\n     |- Try 99 + 30 = 129. Evaluate 129 != 30, drop this branch.\n     |- Try 99 - 30 = 69. Evaluate 69 != 30, drop this branch.\n     |- Try 99 * 30 = 2970. 2970 exceeds the maximum intermediate result, drop this branch.\n     |- Try 99 \/ 30 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 70 - 29 = 41. Add 41 to the number set. Current number set: [41, 30], target: 30, just two numbers left.\n     |- Try 41 + 30 = 71. Evaluate 71 != 30, drop this branch.\n     |- Try 41 - 30 = 11. Evaluate 11 != 30, drop this branch.\n     |- Try 41 * 30 = 1230. Evaluate 1230 != 30, drop this branch.\n     |- Try 41 \/ 30 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 70 * 29 = 2030. 2030 exceeds the maximum intermediate result, drop this branch.\n    |- Try 70 \/ 29 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (70, 30) (numbers left: [29]). Try possible operations.\n    |- Try 70 + 30 = 100. Add 100 to the number set. Current number set: [100, 29], target: 30, just two numbers left.\n     |- Try 100 + 29 = 129. Evaluate 129 != 30, drop this branch.\n     |- Try 100 - 29 = 71. Evaluate 71 != 30, drop this branch.\n     |- Try 100 * 29 = 2900. 2900 exceeds the maximum intermediate result, drop this branch.\n     |- Try 100 \/ 29 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 70 - 30 = 40. Add 40 to the number set. Current number set: [40, 29], target: 30, just two numbers left.\n     |- Try 40 + 29 = 69. Evaluate 69 != 30, drop this branch.\n     |- Try 40 - 29 = 11. Evaluate 11 != 30, drop this branch.\n     |- Try 40 * 29 = 1160. Evaluate 1160 != 30, drop this branch.\n     |- Try 40 \/ 29 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 70 * 30 = 2100. 2100 exceeds the maximum intermediate result, drop this branch.\n    |- Try 70 \/ 30 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (29, 30) (numbers left: [70]). Try possible operations.\n    |- Try 30 + 29 = 59. Add 59 to the number set. Current number set: [59, 70], target: 30, just two numbers left.\n     |- Try 70 + 59 = 129. Evaluate 129 != 30, drop this branch.\n     |- Try 70 - 59 = 11. Evaluate 11 != 30, drop this branch.\n     |- Try 70 * 59 = 4130. 4130 exceeds the maximum intermediate result, drop this branch.\n     |- Try 70 \/ 59 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 30 - 29 = 1. Add 1 to the number set. Current number set: [1, 70], target: 30, just two numbers left.\n     |- Try 70 + 1 = 71. Evaluate 71 != 30, drop this branch.\n     |- Try 70 - 1 = 69. Evaluate 69 != 30, drop this branch.\n     |- Try 70 * 1 = 70. Evaluate 70 != 30, drop this branch.\n     |- Try 70 \/ 1 = 70. Evaluate 70 != 30, drop this branch.\n    |- Try 30 * 29 = 870. Add 870 to the number set. Current number set: [870, 70], target: 30, just two numbers left.\n     |- Try 870 + 70 = 940. Evaluate 940 != 30, drop this branch.\n     |- Try 870 - 70 = 800. Evaluate 800 != 30, drop this branch.\n     |- Try 870 * 70 = 60900. 60900 exceeds the maximum intermediate result, drop this branch.\n     |- Try 870 \/ 70 = 12.4. 12.4 is a decimal, drop this branch.\n    |- Try 30 \/ 29 = 1.0. 1.0 is a decimal, drop this branch.\n  |- Try 36 - 34 = 2. Add 2 to the number set. Current number set: [2, 29, 30], target: 30. Options for choosing two numbers: [(2, 29), (2, 30), (29, 30)].\n   |- Pick two numbers (2, 29) (numbers left: [30]). Try possible operations.\n    |- Try 29 + 2 = 31. Add 31 to the number set. Current number set: [31, 30], target: 30, just two numbers left.\n     |- Try 31 + 30 = 61. Evaluate 61 != 30, drop this branch.\n     |- Try 31 - 30 = 1. Evaluate 1 != 30, drop this branch.\n     |- Try 31 * 30 = 930. Evaluate 930 != 30, drop this branch.\n     |- Try 31 \/ 30 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 29 - 2 = 27. Add 27 to the number set. Current number set: [27, 30], target: 30, just two numbers left.\n     |- Try 30 + 27 = 57. Evaluate 57 != 30, drop this branch.\n     |- Try 30 - 27 = 3. Evaluate 3 != 30, drop this branch.\n     |- Try 30 * 27 = 810. Evaluate 810 != 30, drop this branch.\n     |- Try 30 \/ 27 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 29 * 2 = 58. Add 58 to the number set. Current number set: [58, 30], target: 30, just two numbers left.\n     |- Try 58 + 30 = 88. Evaluate 88 != 30, drop this branch.\n     |- Try 58 - 30 = 28. Evaluate 28 != 30, drop this branch.\n     |- Try 58 * 30 = 1740. Evaluate 1740 != 30, drop this branch.\n     |- Try 58 \/ 30 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 29 \/ 2 = 14.5. 14.5 is a decimal, drop this branch.\n   |- Pick two numbers (2, 30) (numbers left: [29]). Try possible operations.\n    |- Try 30 + 2 = 32. Add 32 to the number set. Current number set: [32, 29], target: 30, just two numbers left.\n     |- Try 32 + 29 = 61. Evaluate 61 != 30, drop this branch.\n     |- Try 32 - 29 = 3. Evaluate 3 != 30, drop this branch.\n     |- Try 32 * 29 = 928. Evaluate 928 != 30, drop this branch.\n     |- Try 32 \/ 29 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 30 - 2 = 28. Add 28 to the number set. Current number set: [28, 29], target: 30, just two numbers left.\n     |- Try 29 + 28 = 57. Evaluate 57 != 30, drop this branch.\n     |- Try 29 - 28 = 1. Evaluate 1 != 30, drop this branch.\n     |- Try 29 * 28 = 812. Evaluate 812 != 30, drop this branch.\n     |- Try 29 \/ 28 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 30 * 2 = 60. Add 60 to the number set. Current number set: [60, 29], target: 30, just two numbers left.\n     |- Try 60 + 29 = 89. Evaluate 89 != 30, drop this branch.\n     |- Try 60 - 29 = 31. Evaluate 31 != 30, drop this branch.\n     |- Try 60 * 29 = 1740. Evaluate 1740 != 30, drop this branch.\n     |- Try 60 \/ 29 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 30 \/ 2 = 15. Add 15 to the number set. Current number set: [15, 29], target: 30, just two numbers left.\n     |- Try 29 + 15 = 44. Evaluate 44 != 30, drop this branch.\n     |- Try 29 - 15 = 14. Evaluate 14 != 30, drop this branch.\n     |- Try 29 * 15 = 435. Evaluate 435 != 30, drop this branch.\n     |- Try 29 \/ 15 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (29, 30) (numbers left: [2]). Try possible operations.\n    |- Try 30 + 29 = 59. Add 59 to the number set. Current number set: [59, 2], target: 30, just two numbers left.\n     |- Try 59 + 2 = 61. Evaluate 61 != 30, drop this branch.\n     |- Try 59 - 2 = 57. Evaluate 57 != 30, drop this branch.\n     |- Try 59 * 2 = 118. Evaluate 118 != 30, drop this branch.\n     |- Try 59 \/ 2 = 29.5. 29.5 is a decimal, drop this branch.\n    |- Try 30 - 29 = 1. Add 1 to the number set. Current number set: [1, 2], target: 30, just two numbers left.\n     |- Try 2 + 1 = 3. Evaluate 3 != 30, drop this branch.\n     |- Try 2 - 1 = 1. Evaluate 1 != 30, drop this branch.\n     |- Try 2 * 1 = 2. Evaluate 2 != 30, drop this branch.\n     |- Try 2 \/ 1 = 2. Evaluate 2 != 30, drop this branch.\n    |- Try 30 * 29 = 870. Add 870 to the number set. Current number set: [870, 2], target: 30, just two numbers left.\n     |- Try 870 + 2 = 872. Evaluate 872 != 30, drop this branch.\n     |- Try 870 - 2 = 868. Evaluate 868 != 30, drop this branch.\n     |- Try 870 * 2 = 1740. Evaluate 1740 != 30, drop this branch.\n     |- Try 870 \/ 2 = 435. Evaluate 435 != 30, drop this branch.\n    |- Try 30 \/ 29 = 1.0. 1.0 is a decimal, drop this branch.\n  |- Try 36 * 34 = 1224. Add 1224 to the number set. Current number set: [1224, 29, 30], target: 30. Options for choosing two numbers: [(1224, 29), (1224, 30), (29, 30)].\n   |- Pick two numbers (1224, 29) (numbers left: [30]). Try possible operations.\n    |- Try 1224 + 29 = 1253. Add 1253 to the number set. Current number set: [1253, 30], target: 30, just two numbers left.\n     |- Try 1253 + 30 = 1283. Evaluate 1283 != 30, drop this branch.\n     |- Try 1253 - 30 = 1223. Evaluate 1223 != 30, drop this branch.\n     |- Try 1253 * 30 = 37590. 37590 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1253 \/ 30 = 41.8. 41.8 is a decimal, drop this branch.\n    |- Try 1224 - 29 = 1195. Add 1195 to the number set. Current number set: [1195, 30], target: 30, just two numbers left.\n     |- Try 1195 + 30 = 1225. Evaluate 1225 != 30, drop this branch.\n     |- Try 1195 - 30 = 1165. Evaluate 1165 != 30, drop this branch.\n     |- Try 1195 * 30 = 35850. 35850 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1195 \/ 30 = 39.8. 39.8 is a decimal, drop this branch.\n    |- Try 1224 * 29 = 35496. 35496 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1224 \/ 29 = 42.2. 42.2 is a decimal, drop this branch.\n   |- Pick two numbers (1224, 30) (numbers left: [29]). Try possible operations.\n    |- Try 1224 + 30 = 1254. Add 1254 to the number set. Current number set: [1254, 29], target: 30, just two numbers left.\n     |- Try 1254 + 29 = 1283. Evaluate 1283 != 30, drop this branch.\n     |- Try 1254 - 29 = 1225. Evaluate 1225 != 30, drop this branch.\n     |- Try 1254 * 29 = 36366. 36366 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1254 \/ 29 = 43.2. 43.2 is a decimal, drop this branch.\n    |- Try 1224 - 30 = 1194. Add 1194 to the number set. Current number set: [1194, 29], target: 30, just two numbers left.\n     |- Try 1194 + 29 = 1223. Evaluate 1223 != 30, drop this branch.\n     |- Try 1194 - 29 = 1165. Evaluate 1165 != 30, drop this branch.\n     |- Try 1194 * 29 = 34626. 34626 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1194 \/ 29 = 41.2. 41.2 is a decimal, drop this branch.\n    |- Try 1224 * 30 = 36720. 36720 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1224 \/ 30 = 40.8. 40.8 is a decimal, drop this branch.\n   |- Pick two numbers (29, 30) (numbers left: [1224]). Try possible operations.\n    |- Try 30 + 29 = 59. Add 59 to the number set. Current number set: [59, 1224], target: 30, just two numbers left.\n     |- Try 1224 + 59 = 1283. Evaluate 1283 != 30, drop this branch.\n     |- Try 1224 - 59 = 1165. Evaluate 1165 != 30, drop this branch.\n     |- Try 1224 * 59 = 72216. 72216 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1224 \/ 59 = 20.7. 20.7 is a decimal, drop this branch.\n    |- Try 30 - 29 = 1. Add 1 to the number set. Current number set: [1, 1224], target: 30, just two numbers left.\n     |- Try 1224 + 1 = 1225. Evaluate 1225 != 30, drop this branch.\n     |- Try 1224 - 1 = 1223. Evaluate 1223 != 30, drop this branch.\n     |- Try 1224 * 1 = 1224. Evaluate 1224 != 30, drop this branch.\n     |- Try 1224 \/ 1 = 1224. Evaluate 1224 != 30, drop this branch.\n    |- Try 30 * 29 = 870. Add 870 to the number set. Current number set: [870, 1224], target: 30, just two numbers left.\n     |- Try 1224 + 870 = 2094. 2094 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1224 - 870 = 354. Evaluate 354 != 30, drop this branch.\n     |- Try 1224 * 870 = 1064880. 1064880 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1224 \/ 870 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 30 \/ 29 = 1.0. 1.0 is a decimal, drop this branch.\n  |- Try 36 \/ 34 = 1.1. 1.1 is a decimal, drop this branch.\n |- Pick two numbers (34, 29) (numbers left: [36, 30]). Try possible operations.\n  |- Try 34 + 29 = 63. Add 63 to the number set. Current number set: [63, 36, 30], target: 30. Options for choosing two numbers: [(63, 36), (63, 30), (36, 30)].\n   |- Pick two numbers (63, 36) (numbers left: [30]). Try possible operations.\n    |- Try 63 + 36 = 99. Add 99 to the number set. Current number set: [99, 30], target: 30, just two numbers left.\n     |- Try 99 + 30 = 129. Evaluate 129 != 30, drop this branch.\n     |- Try 99 - 30 = 69. Evaluate 69 != 30, drop this branch.\n     |- Try 99 * 30 = 2970. 2970 exceeds the maximum intermediate result, drop this branch.\n     |- Try 99 \/ 30 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 63 - 36 = 27. Add 27 to the number set. Current number set: [27, 30], target: 30, just two numbers left.\n     |- Try 30 + 27 = 57. Evaluate 57 != 30, drop this branch.\n     |- Try 30 - 27 = 3. Evaluate 3 != 30, drop this branch.\n     |- Try 30 * 27 = 810. Evaluate 810 != 30, drop this branch.\n     |- Try 30 \/ 27 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 63 * 36 = 2268. 2268 exceeds the maximum intermediate result, drop this branch.\n    |- Try 63 \/ 36 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (63, 30) (numbers left: [36]). Try possible operations.\n    |- Try 63 + 30 = 93. Add 93 to the number set. Current number set: [93, 36], target: 30, just two numbers left.\n     |- Try 93 + 36 = 129. Evaluate 129 != 30, drop this branch.\n     |- Try 93 - 36 = 57. Evaluate 57 != 30, drop this branch.\n     |- Try 93 * 36 = 3348. 3348 exceeds the maximum intermediate result, drop this branch.\n     |- Try 93 \/ 36 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 63 - 30 = 33. Add 33 to the number set. Current number set: [33, 36], target: 30, just two numbers left.\n     |- Try 36 + 33 = 69. Evaluate 69 != 30, drop this branch.\n     |- Try 36 - 33 = 3. Evaluate 3 != 30, drop this branch.\n     |- Try 36 * 33 = 1188. Evaluate 1188 != 30, drop this branch.\n     |- Try 36 \/ 33 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 63 * 30 = 1890. Add 1890 to the number set. Current number set: [1890, 36], target: 30, just two numbers left.\n     |- Try 1890 + 36 = 1926. Evaluate 1926 != 30, drop this branch.\n     |- Try 1890 - 36 = 1854. Evaluate 1854 != 30, drop this branch.\n     |- Try 1890 * 36 = 68040. 68040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1890 \/ 36 = 52.5. 52.5 is a decimal, drop this branch.\n    |- Try 63 \/ 30 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (36, 30) (numbers left: [63]). Try possible operations.\n    |- Try 36 + 30 = 66. Add 66 to the number set. Current number set: [66, 63], target: 30, just two numbers left.\n     |- Try 66 + 63 = 129. Evaluate 129 != 30, drop this branch.\n     |- Try 66 - 63 = 3. Evaluate 3 != 30, drop this branch.\n     |- Try 66 * 63 = 4158. 4158 exceeds the maximum intermediate result, drop this branch.\n     |- Try 66 \/ 63 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 36 - 30 = 6. Add 6 to the number set. Current number set: [6, 63], target: 30, just two numbers left.\n     |- Try 63 + 6 = 69. Evaluate 69 != 30, drop this branch.\n     |- Try 63 - 6 = 57. Evaluate 57 != 30, drop this branch.\n     |- Try 63 * 6 = 378. Evaluate 378 != 30, drop this branch.\n     |- Try 63 \/ 6 = 10.5. 10.5 is a decimal, drop this branch.\n    |- Try 36 * 30 = 1080. Add 1080 to the number set. Current number set: [1080, 63], target: 30, just two numbers left.\n     |- Try 1080 + 63 = 1143. Evaluate 1143 != 30, drop this branch.\n     |- Try 1080 - 63 = 1017. Evaluate 1017 != 30, drop this branch.\n     |- Try 1080 * 63 = 68040. 68040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1080 \/ 63 = 17.1. 17.1 is a decimal, drop this branch.\n    |- Try 36 \/ 30 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 34 - 29 = 5. Add 5 to the number set. Current number set: [5, 36, 30], target: 30. Options for choosing two numbers: [(5, 36), (5, 30), (36, 30)].\n   |- Pick two numbers (5, 36) (numbers left: [30]). Try possible operations.\n    |- Try 36 + 5 = 41. Add 41 to the number set. Current number set: [41, 30], target: 30, just two numbers left.\n     |- Try 41 + 30 = 71. Evaluate 71 != 30, drop this branch.\n     |- Try 41 - 30 = 11. Evaluate 11 != 30, drop this branch.\n     |- Try 41 * 30 = 1230. Evaluate 1230 != 30, drop this branch.\n     |- Try 41 \/ 30 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 36 - 5 = 31. Add 31 to the number set. Current number set: [31, 30], target: 30, just two numbers left.\n     |- Try 31 + 30 = 61. Evaluate 61 != 30, drop this branch.\n     |- Try 31 - 30 = 1. Evaluate 1 != 30, drop this branch.\n     |- Try 31 * 30 = 930. Evaluate 930 != 30, drop this branch.\n     |- Try 31 \/ 30 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 36 * 5 = 180. Add 180 to the number set. Current number set: [180, 30], target: 30, just two numbers left.\n     |- Try 180 + 30 = 210. Evaluate 210 != 30, drop this branch.\n     |- Try 180 - 30 = 150. Evaluate 150 != 30, drop this branch.\n     |- Try 180 * 30 = 5400. 5400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 180 \/ 30 = 6. Evaluate 6 != 30, drop this branch.\n    |- Try 36 \/ 5 = 7.2. 7.2 is a decimal, drop this branch.\n   |- Pick two numbers (5, 30) (numbers left: [36]). Try possible operations.\n    |- Try 30 + 5 = 35. Add 35 to the number set. Current number set: [35, 36], target: 30, just two numbers left.\n     |- Try 36 + 35 = 71. Evaluate 71 != 30, drop this branch.\n     |- Try 36 - 35 = 1. Evaluate 1 != 30, drop this branch.\n     |- Try 36 * 35 = 1260. Evaluate 1260 != 30, drop this branch.\n     |- Try 36 \/ 35 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 30 - 5 = 25. Add 25 to the number set. Current number set: [25, 36], target: 30, just two numbers left.\n     |- Try 36 + 25 = 61. Evaluate 61 != 30, drop this branch.\n     |- Try 36 - 25 = 11. Evaluate 11 != 30, drop this branch.\n     |- Try 36 * 25 = 900. Evaluate 900 != 30, drop this branch.\n     |- Try 36 \/ 25 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 30 * 5 = 150. Add 150 to the number set. Current number set: [150, 36], target: 30, just two numbers left.\n     |- Try 150 + 36 = 186. Evaluate 186 != 30, drop this branch.\n     |- Try 150 - 36 = 114. Evaluate 114 != 30, drop this branch.\n     |- Try 150 * 36 = 5400. 5400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 36 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 30 \/ 5 = 6. Add 6 to the number set. Current number set: [6, 36], target: 30, just two numbers left.\n     |- Try 36 + 6 = 42. Evaluate 42 != 30, drop this branch.\n     |- Try 36 - 6 = 30. Evaluate 30 == 30, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 6 = 30\nThe step before: 30 \/ 5 = 6\nThe first step: 34 - 29 = 5\n\nOutput the solution in the required format:\n<Solution>\n34 - 29 = 5\n30 \/ 5 = 6\n36 - 6 = 30\n<\/Solution>\n","item":{"nums":[34,36,29,30],"solution":["34 - 29 = 5","30 \/ 5 = 6","36 - 6 = 30"],"target":30}}
+{"instance_id":"countdown_8k_98","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [9, 44, 36, 8]\nTarget: 35","reference_output":"# Search Procedure\nInitial number set: [9, 44, 36, 8], target: 35. Options for choosing two numbers: [(9, 44), (9, 36), (9, 8), (44, 36), (44, 8), (36, 8)].\n |- Pick two numbers (9, 44) (numbers left: [36, 8]). Try possible operations.\n  |- Try 44 + 9 = 53. Add 53 to the number set. Current number set: [53, 36, 8], target: 35. Options for choosing two numbers: [(53, 36), (53, 8), (36, 8)].\n   |- Pick two numbers (53, 36) (numbers left: [8]). Try possible operations.\n    |- Try 53 + 36 = 89. Add 89 to the number set. Current number set: [89, 8], target: 35, just two numbers left.\n     |- Try 89 + 8 = 97. Evaluate 97 != 35, drop this branch.\n     |- Try 89 - 8 = 81. Evaluate 81 != 35, drop this branch.\n     |- Try 89 * 8 = 712. Evaluate 712 != 35, drop this branch.\n     |- Try 89 \/ 8 = 11.1. 11.1 is a decimal, drop this branch.\n    |- Try 53 - 36 = 17. Add 17 to the number set. Current number set: [17, 8], target: 35, just two numbers left.\n     |- Try 17 + 8 = 25. Evaluate 25 != 35, drop this branch.\n     |- Try 17 - 8 = 9. Evaluate 9 != 35, drop this branch.\n     |- Try 17 * 8 = 136. Evaluate 136 != 35, drop this branch.\n     |- Try 17 \/ 8 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 53 * 36 = 1908. Add 1908 to the number set. Current number set: [1908, 8], target: 35, just two numbers left.\n     |- Try 1908 + 8 = 1916. Evaluate 1916 != 35, drop this branch.\n     |- Try 1908 - 8 = 1900. Evaluate 1900 != 35, drop this branch.\n     |- Try 1908 * 8 = 15264. 15264 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1908 \/ 8 = 238.5. 238.5 is a decimal, drop this branch.\n    |- Try 53 \/ 36 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (53, 8) (numbers left: [36]). Try possible operations.\n    |- Try 53 + 8 = 61. Add 61 to the number set. Current number set: [61, 36], target: 35, just two numbers left.\n     |- Try 61 + 36 = 97. Evaluate 97 != 35, drop this branch.\n     |- Try 61 - 36 = 25. Evaluate 25 != 35, drop this branch.\n     |- Try 61 * 36 = 2196. 2196 exceeds the maximum intermediate result, drop this branch.\n     |- Try 61 \/ 36 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 53 - 8 = 45. Add 45 to the number set. Current number set: [45, 36], target: 35, just two numbers left.\n     |- Try 45 + 36 = 81. Evaluate 81 != 35, drop this branch.\n     |- Try 45 - 36 = 9. Evaluate 9 != 35, drop this branch.\n     |- Try 45 * 36 = 1620. Evaluate 1620 != 35, drop this branch.\n     |- Try 45 \/ 36 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 53 * 8 = 424. Add 424 to the number set. Current number set: [424, 36], target: 35, just two numbers left.\n     |- Try 424 + 36 = 460. Evaluate 460 != 35, drop this branch.\n     |- Try 424 - 36 = 388. Evaluate 388 != 35, drop this branch.\n     |- Try 424 * 36 = 15264. 15264 exceeds the maximum intermediate result, drop this branch.\n     |- Try 424 \/ 36 = 11.8. 11.8 is a decimal, drop this branch.\n    |- Try 53 \/ 8 = 6.6. 6.6 is a decimal, drop this branch.\n   |- Pick two numbers (36, 8) (numbers left: [53]). Try possible operations.\n    |- Try 36 + 8 = 44. Add 44 to the number set. Current number set: [44, 53], target: 35, just two numbers left.\n     |- Try 53 + 44 = 97. Evaluate 97 != 35, drop this branch.\n     |- Try 53 - 44 = 9. Evaluate 9 != 35, drop this branch.\n     |- Try 53 * 44 = 2332. 2332 exceeds the maximum intermediate result, drop this branch.\n     |- Try 53 \/ 44 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 36 - 8 = 28. Add 28 to the number set. Current number set: [28, 53], target: 35, just two numbers left.\n     |- Try 53 + 28 = 81. Evaluate 81 != 35, drop this branch.\n     |- Try 53 - 28 = 25. Evaluate 25 != 35, drop this branch.\n     |- Try 53 * 28 = 1484. Evaluate 1484 != 35, drop this branch.\n     |- Try 53 \/ 28 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 36 * 8 = 288. Add 288 to the number set. Current number set: [288, 53], target: 35, just two numbers left.\n     |- Try 288 + 53 = 341. Evaluate 341 != 35, drop this branch.\n     |- Try 288 - 53 = 235. Evaluate 235 != 35, drop this branch.\n     |- Try 288 * 53 = 15264. 15264 exceeds the maximum intermediate result, drop this branch.\n     |- Try 288 \/ 53 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 36 \/ 8 = 4.5. 4.5 is a decimal, drop this branch.\n  |- Try 44 - 9 = 35. Add 35 to the number set. Current number set: [35, 36, 8], target: 35. Options for choosing two numbers: [(35, 36), (35, 8), (36, 8)].\n   |- Pick two numbers (35, 36) (numbers left: [8]). Try possible operations.\n    |- Try 36 + 35 = 71. Add 71 to the number set. Current number set: [71, 8], target: 35, just two numbers left.\n     |- Try 71 + 8 = 79. Evaluate 79 != 35, drop this branch.\n     |- Try 71 - 8 = 63. Evaluate 63 != 35, drop this branch.\n     |- Try 71 * 8 = 568. Evaluate 568 != 35, drop this branch.\n     |- Try 71 \/ 8 = 8.9. 8.9 is a decimal, drop this branch.\n    |- Try 36 - 35 = 1. Add 1 to the number set. Current number set: [1, 8], target: 35, just two numbers left.\n     |- Try 8 + 1 = 9. Evaluate 9 != 35, drop this branch.\n     |- Try 8 - 1 = 7. Evaluate 7 != 35, drop this branch.\n     |- Try 8 * 1 = 8. Evaluate 8 != 35, drop this branch.\n     |- Try 8 \/ 1 = 8. Evaluate 8 != 35, drop this branch.\n    |- Try 36 * 35 = 1260. Add 1260 to the number set. Current number set: [1260, 8], target: 35, just two numbers left.\n     |- Try 1260 + 8 = 1268. Evaluate 1268 != 35, drop this branch.\n     |- Try 1260 - 8 = 1252. Evaluate 1252 != 35, drop this branch.\n     |- Try 1260 * 8 = 10080. 10080 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1260 \/ 8 = 157.5. 157.5 is a decimal, drop this branch.\n    |- Try 36 \/ 35 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (35, 8) (numbers left: [36]). Try possible operations.\n    |- Try 35 + 8 = 43. Add 43 to the number set. Current number set: [43, 36], target: 35, just two numbers left.\n     |- Try 43 + 36 = 79. Evaluate 79 != 35, drop this branch.\n     |- Try 43 - 36 = 7. Evaluate 7 != 35, drop this branch.\n     |- Try 43 * 36 = 1548. Evaluate 1548 != 35, drop this branch.\n     |- Try 43 \/ 36 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 35 - 8 = 27. Add 27 to the number set. Current number set: [27, 36], target: 35, just two numbers left.\n     |- Try 36 + 27 = 63. Evaluate 63 != 35, drop this branch.\n     |- Try 36 - 27 = 9. Evaluate 9 != 35, drop this branch.\n     |- Try 36 * 27 = 972. Evaluate 972 != 35, drop this branch.\n     |- Try 36 \/ 27 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 35 * 8 = 280. Add 280 to the number set. Current number set: [280, 36], target: 35, just two numbers left.\n     |- Try 280 + 36 = 316. Evaluate 316 != 35, drop this branch.\n     |- Try 280 - 36 = 244. Evaluate 244 != 35, drop this branch.\n     |- Try 280 * 36 = 10080. 10080 exceeds the maximum intermediate result, drop this branch.\n     |- Try 280 \/ 36 = 7.8. 7.8 is a decimal, drop this branch.\n    |- Try 35 \/ 8 = 4.4. 4.4 is a decimal, drop this branch.\n   |- Pick two numbers (36, 8) (numbers left: [35]). Try possible operations.\n    |- Try 36 + 8 = 44. Add 44 to the number set. Current number set: [44, 35], target: 35, just two numbers left.\n     |- Try 44 + 35 = 79. Evaluate 79 != 35, drop this branch.\n     |- Try 44 - 35 = 9. Evaluate 9 != 35, drop this branch.\n     |- Try 44 * 35 = 1540. Evaluate 1540 != 35, drop this branch.\n     |- Try 44 \/ 35 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 36 - 8 = 28. Add 28 to the number set. Current number set: [28, 35], target: 35, just two numbers left.\n     |- Try 35 + 28 = 63. Evaluate 63 != 35, drop this branch.\n     |- Try 35 - 28 = 7. Evaluate 7 != 35, drop this branch.\n     |- Try 35 * 28 = 980. Evaluate 980 != 35, drop this branch.\n     |- Try 35 \/ 28 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 36 * 8 = 288. Add 288 to the number set. Current number set: [288, 35], target: 35, just two numbers left.\n     |- Try 288 + 35 = 323. Evaluate 323 != 35, drop this branch.\n     |- Try 288 - 35 = 253. Evaluate 253 != 35, drop this branch.\n     |- Try 288 * 35 = 10080. 10080 exceeds the maximum intermediate result, drop this branch.\n     |- Try 288 \/ 35 = 8.2. 8.2 is a decimal, drop this branch.\n    |- Try 36 \/ 8 = 4.5. 4.5 is a decimal, drop this branch.\n  |- Try 44 * 9 = 396. Add 396 to the number set. Current number set: [396, 36, 8], target: 35. Options for choosing two numbers: [(396, 36), (396, 8), (36, 8)].\n   |- Pick two numbers (396, 36) (numbers left: [8]). Try possible operations.\n    |- Try 396 + 36 = 432. Add 432 to the number set. Current number set: [432, 8], target: 35, just two numbers left.\n     |- Try 432 + 8 = 440. Evaluate 440 != 35, drop this branch.\n     |- Try 432 - 8 = 424. Evaluate 424 != 35, drop this branch.\n     |- Try 432 * 8 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 432 \/ 8 = 54. Evaluate 54 != 35, drop this branch.\n    |- Try 396 - 36 = 360. Add 360 to the number set. Current number set: [360, 8], target: 35, just two numbers left.\n     |- Try 360 + 8 = 368. Evaluate 368 != 35, drop this branch.\n     |- Try 360 - 8 = 352. Evaluate 352 != 35, drop this branch.\n     |- Try 360 * 8 = 2880. 2880 exceeds the maximum intermediate result, drop this branch.\n     |- Try 360 \/ 8 = 45. Evaluate 45 != 35, drop this branch.\n    |- Try 396 * 36 = 14256. 14256 exceeds the maximum intermediate result, drop this branch.\n    |- Try 396 \/ 36 = 11. Add 11 to the number set. Current number set: [11, 8], target: 35, just two numbers left.\n     |- Try 11 + 8 = 19. Evaluate 19 != 35, drop this branch.\n     |- Try 11 - 8 = 3. Evaluate 3 != 35, drop this branch.\n     |- Try 11 * 8 = 88. Evaluate 88 != 35, drop this branch.\n     |- Try 11 \/ 8 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (396, 8) (numbers left: [36]). Try possible operations.\n    |- Try 396 + 8 = 404. Add 404 to the number set. Current number set: [404, 36], target: 35, just two numbers left.\n     |- Try 404 + 36 = 440. Evaluate 440 != 35, drop this branch.\n     |- Try 404 - 36 = 368. Evaluate 368 != 35, drop this branch.\n     |- Try 404 * 36 = 14544. 14544 exceeds the maximum intermediate result, drop this branch.\n     |- Try 404 \/ 36 = 11.2. 11.2 is a decimal, drop this branch.\n    |- Try 396 - 8 = 388. Add 388 to the number set. Current number set: [388, 36], target: 35, just two numbers left.\n     |- Try 388 + 36 = 424. Evaluate 424 != 35, drop this branch.\n     |- Try 388 - 36 = 352. Evaluate 352 != 35, drop this branch.\n     |- Try 388 * 36 = 13968. 13968 exceeds the maximum intermediate result, drop this branch.\n     |- Try 388 \/ 36 = 10.8. 10.8 is a decimal, drop this branch.\n    |- Try 396 * 8 = 3168. 3168 exceeds the maximum intermediate result, drop this branch.\n    |- Try 396 \/ 8 = 49.5. 49.5 is a decimal, drop this branch.\n   |- Pick two numbers (36, 8) (numbers left: [396]). Try possible operations.\n    |- Try 36 + 8 = 44. Add 44 to the number set. Current number set: [44, 396], target: 35, just two numbers left.\n     |- Try 396 + 44 = 440. Evaluate 440 != 35, drop this branch.\n     |- Try 396 - 44 = 352. Evaluate 352 != 35, drop this branch.\n     |- Try 396 * 44 = 17424. 17424 exceeds the maximum intermediate result, drop this branch.\n     |- Try 396 \/ 44 = 9. Evaluate 9 != 35, drop this branch.\n    |- Try 36 - 8 = 28. Add 28 to the number set. Current number set: [28, 396], target: 35, just two numbers left.\n     |- Try 396 + 28 = 424. Evaluate 424 != 35, drop this branch.\n     |- Try 396 - 28 = 368. Evaluate 368 != 35, drop this branch.\n     |- Try 396 * 28 = 11088. 11088 exceeds the maximum intermediate result, drop this branch.\n     |- Try 396 \/ 28 = 14.1. 14.1 is a decimal, drop this branch.\n    |- Try 36 * 8 = 288. Add 288 to the number set. Current number set: [288, 396], target: 35, just two numbers left.\n     |- Try 396 + 288 = 684. Evaluate 684 != 35, drop this branch.\n     |- Try 396 - 288 = 108. Evaluate 108 != 35, drop this branch.\n     |- Try 396 * 288 = 114048. 114048 exceeds the maximum intermediate result, drop this branch.\n     |- Try 396 \/ 288 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 36 \/ 8 = 4.5. 4.5 is a decimal, drop this branch.\n  |- Try 44 \/ 9 = 4.9. 4.9 is a decimal, drop this branch.\n |- Pick two numbers (9, 36) (numbers left: [44, 8]). Try possible operations.\n  |- Try 36 + 9 = 45. Add 45 to the number set. Current number set: [45, 44, 8], target: 35. Options for choosing two numbers: [(45, 44), (45, 8), (44, 8)].\n   |- Pick two numbers (45, 44) (numbers left: [8]). Try possible operations.\n    |- Try 45 + 44 = 89. Add 89 to the number set. Current number set: [89, 8], target: 35, just two numbers left.\n     |- Try 89 + 8 = 97. Evaluate 97 != 35, drop this branch.\n     |- Try 89 - 8 = 81. Evaluate 81 != 35, drop this branch.\n     |- Try 89 * 8 = 712. Evaluate 712 != 35, drop this branch.\n     |- Try 89 \/ 8 = 11.1. 11.1 is a decimal, drop this branch.\n    |- Try 45 - 44 = 1. Add 1 to the number set. Current number set: [1, 8], target: 35, just two numbers left.\n     |- Try 8 + 1 = 9. Evaluate 9 != 35, drop this branch.\n     |- Try 8 - 1 = 7. Evaluate 7 != 35, drop this branch.\n     |- Try 8 * 1 = 8. Evaluate 8 != 35, drop this branch.\n     |- Try 8 \/ 1 = 8. Evaluate 8 != 35, drop this branch.\n    |- Try 45 * 44 = 1980. Add 1980 to the number set. Current number set: [1980, 8], target: 35, just two numbers left.\n     |- Try 1980 + 8 = 1988. Evaluate 1988 != 35, drop this branch.\n     |- Try 1980 - 8 = 1972. Evaluate 1972 != 35, drop this branch.\n     |- Try 1980 * 8 = 15840. 15840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1980 \/ 8 = 247.5. 247.5 is a decimal, drop this branch.\n    |- Try 45 \/ 44 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (45, 8) (numbers left: [44]). Try possible operations.\n    |- Try 45 + 8 = 53. Add 53 to the number set. Current number set: [53, 44], target: 35, just two numbers left.\n     |- Try 53 + 44 = 97. Evaluate 97 != 35, drop this branch.\n     |- Try 53 - 44 = 9. Evaluate 9 != 35, drop this branch.\n     |- Try 53 * 44 = 2332. 2332 exceeds the maximum intermediate result, drop this branch.\n     |- Try 53 \/ 44 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 45 - 8 = 37. Add 37 to the number set. Current number set: [37, 44], target: 35, just two numbers left.\n     |- Try 44 + 37 = 81. Evaluate 81 != 35, drop this branch.\n     |- Try 44 - 37 = 7. Evaluate 7 != 35, drop this branch.\n     |- Try 44 * 37 = 1628. Evaluate 1628 != 35, drop this branch.\n     |- Try 44 \/ 37 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 45 * 8 = 360. Add 360 to the number set. Current number set: [360, 44], target: 35, just two numbers left.\n     |- Try 360 + 44 = 404. Evaluate 404 != 35, drop this branch.\n     |- Try 360 - 44 = 316. Evaluate 316 != 35, drop this branch.\n     |- Try 360 * 44 = 15840. 15840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 360 \/ 44 = 8.2. 8.2 is a decimal, drop this branch.\n    |- Try 45 \/ 8 = 5.6. 5.6 is a decimal, drop this branch.\n   |- Pick two numbers (44, 8) (numbers left: [45]). Try possible operations.\n    |- Try 44 + 8 = 52. Add 52 to the number set. Current number set: [52, 45], target: 35, just two numbers left.\n     |- Try 52 + 45 = 97. Evaluate 97 != 35, drop this branch.\n     |- Try 52 - 45 = 7. Evaluate 7 != 35, drop this branch.\n     |- Try 52 * 45 = 2340. 2340 exceeds the maximum intermediate result, drop this branch.\n     |- Try 52 \/ 45 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 44 - 8 = 36. Add 36 to the number set. Current number set: [36, 45], target: 35, just two numbers left.\n     |- Try 45 + 36 = 81. Evaluate 81 != 35, drop this branch.\n     |- Try 45 - 36 = 9. Evaluate 9 != 35, drop this branch.\n     |- Try 45 * 36 = 1620. Evaluate 1620 != 35, drop this branch.\n     |- Try 45 \/ 36 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 44 * 8 = 352. Add 352 to the number set. Current number set: [352, 45], target: 35, just two numbers left.\n     |- Try 352 + 45 = 397. Evaluate 397 != 35, drop this branch.\n     |- Try 352 - 45 = 307. Evaluate 307 != 35, drop this branch.\n     |- Try 352 * 45 = 15840. 15840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 352 \/ 45 = 7.8. 7.8 is a decimal, drop this branch.\n    |- Try 44 \/ 8 = 5.5. 5.5 is a decimal, drop this branch.\n  |- Try 36 - 9 = 27. Add 27 to the number set. Current number set: [27, 44, 8], target: 35. Options for choosing two numbers: [(27, 44), (27, 8), (44, 8)].\n   |- Pick two numbers (27, 44) (numbers left: [8]). Try possible operations.\n    |- Try 44 + 27 = 71. Add 71 to the number set. Current number set: [71, 8], target: 35, just two numbers left.\n     |- Try 71 + 8 = 79. Evaluate 79 != 35, drop this branch.\n     |- Try 71 - 8 = 63. Evaluate 63 != 35, drop this branch.\n     |- Try 71 * 8 = 568. Evaluate 568 != 35, drop this branch.\n     |- Try 71 \/ 8 = 8.9. 8.9 is a decimal, drop this branch.\n    |- Try 44 - 27 = 17. Add 17 to the number set. Current number set: [17, 8], target: 35, just two numbers left.\n     |- Try 17 + 8 = 25. Evaluate 25 != 35, drop this branch.\n     |- Try 17 - 8 = 9. Evaluate 9 != 35, drop this branch.\n     |- Try 17 * 8 = 136. Evaluate 136 != 35, drop this branch.\n     |- Try 17 \/ 8 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 44 * 27 = 1188. Add 1188 to the number set. Current number set: [1188, 8], target: 35, just two numbers left.\n     |- Try 1188 + 8 = 1196. Evaluate 1196 != 35, drop this branch.\n     |- Try 1188 - 8 = 1180. Evaluate 1180 != 35, drop this branch.\n     |- Try 1188 * 8 = 9504. 9504 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1188 \/ 8 = 148.5. 148.5 is a decimal, drop this branch.\n    |- Try 44 \/ 27 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (27, 8) (numbers left: [44]). Try possible operations.\n    |- Try 27 + 8 = 35. Add 35 to the number set. Current number set: [35, 44], target: 35, just two numbers left.\n     |- Try 44 + 35 = 79. Evaluate 79 != 35, drop this branch.\n     |- Try 44 - 35 = 9. Evaluate 9 != 35, drop this branch.\n     |- Try 44 * 35 = 1540. Evaluate 1540 != 35, drop this branch.\n     |- Try 44 \/ 35 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 27 - 8 = 19. Add 19 to the number set. Current number set: [19, 44], target: 35, just two numbers left.\n     |- Try 44 + 19 = 63. Evaluate 63 != 35, drop this branch.\n     |- Try 44 - 19 = 25. Evaluate 25 != 35, drop this branch.\n     |- Try 44 * 19 = 836. Evaluate 836 != 35, drop this branch.\n     |- Try 44 \/ 19 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 27 * 8 = 216. Add 216 to the number set. Current number set: [216, 44], target: 35, just two numbers left.\n     |- Try 216 + 44 = 260. Evaluate 260 != 35, drop this branch.\n     |- Try 216 - 44 = 172. Evaluate 172 != 35, drop this branch.\n     |- Try 216 * 44 = 9504. 9504 exceeds the maximum intermediate result, drop this branch.\n     |- Try 216 \/ 44 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 27 \/ 8 = 3.4. 3.4 is a decimal, drop this branch.\n   |- Pick two numbers (44, 8) (numbers left: [27]). Try possible operations.\n    |- Try 44 + 8 = 52. Add 52 to the number set. Current number set: [52, 27], target: 35, just two numbers left.\n     |- Try 52 + 27 = 79. Evaluate 79 != 35, drop this branch.\n     |- Try 52 - 27 = 25. Evaluate 25 != 35, drop this branch.\n     |- Try 52 * 27 = 1404. Evaluate 1404 != 35, drop this branch.\n     |- Try 52 \/ 27 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 44 - 8 = 36. Add 36 to the number set. Current number set: [36, 27], target: 35, just two numbers left.\n     |- Try 36 + 27 = 63. Evaluate 63 != 35, drop this branch.\n     |- Try 36 - 27 = 9. Evaluate 9 != 35, drop this branch.\n     |- Try 36 * 27 = 972. Evaluate 972 != 35, drop this branch.\n     |- Try 36 \/ 27 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 44 * 8 = 352. Add 352 to the number set. Current number set: [352, 27], target: 35, just two numbers left.\n     |- Try 352 + 27 = 379. Evaluate 379 != 35, drop this branch.\n     |- Try 352 - 27 = 325. Evaluate 325 != 35, drop this branch.\n     |- Try 352 * 27 = 9504. 9504 exceeds the maximum intermediate result, drop this branch.\n     |- Try 352 \/ 27 = 13.0. 13.0 is a decimal, drop this branch.\n    |- Try 44 \/ 8 = 5.5. 5.5 is a decimal, drop this branch.\n  |- Try 36 * 9 = 324. Add 324 to the number set. Current number set: [324, 44, 8], target: 35. Options for choosing two numbers: [(324, 44), (324, 8), (44, 8)].\n   |- Pick two numbers (324, 44) (numbers left: [8]). Try possible operations.\n    |- Try 324 + 44 = 368. Add 368 to the number set. Current number set: [368, 8], target: 35, just two numbers left.\n     |- Try 368 + 8 = 376. Evaluate 376 != 35, drop this branch.\n     |- Try 368 - 8 = 360. Evaluate 360 != 35, drop this branch.\n     |- Try 368 * 8 = 2944. 2944 exceeds the maximum intermediate result, drop this branch.\n     |- Try 368 \/ 8 = 46. Evaluate 46 != 35, drop this branch.\n    |- Try 324 - 44 = 280. Add 280 to the number set. Current number set: [280, 8], target: 35, just two numbers left.\n     |- Try 280 + 8 = 288. Evaluate 288 != 35, drop this branch.\n     |- Try 280 - 8 = 272. Evaluate 272 != 35, drop this branch.\n     |- Try 280 * 8 = 2240. 2240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 280 \/ 8 = 35. Evaluate 35 == 35, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 280 \/ 8 = 35\nThe step before: 324 - 44 = 280\nThe first step: 36 * 9 = 324\n\nOutput the solution in the required format:\n<Solution>\n36 * 9 = 324\n324 - 44 = 280\n280 \/ 8 = 35\n<\/Solution>\n","item":{"nums":[9,44,36,8],"solution":["36 * 9 = 324","324 - 44 = 280","280 \/ 8 = 35"],"target":35}}
+{"instance_id":"countdown_8k_99","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [31, 37, 28, 17]\nTarget: 14","reference_output":"# Search Procedure\nInitial number set: [31, 37, 28, 17], target: 14. Options for choosing two numbers: [(31, 37), (31, 28), (31, 17), (37, 28), (37, 17), (28, 17)].\n |- Pick two numbers (31, 37) (numbers left: [28, 17]). Try possible operations.\n  |- Try 37 + 31 = 68. Add 68 to the number set. Current number set: [68, 28, 17], target: 14. Options for choosing two numbers: [(68, 28), (68, 17), (28, 17)].\n   |- Pick two numbers (68, 28) (numbers left: [17]). Try possible operations.\n    |- Try 68 + 28 = 96. Add 96 to the number set. Current number set: [96, 17], target: 14, just two numbers left.\n     |- Try 96 + 17 = 113. Evaluate 113 != 14, drop this branch.\n     |- Try 96 - 17 = 79. Evaluate 79 != 14, drop this branch.\n     |- Try 96 * 17 = 1632. Evaluate 1632 != 14, drop this branch.\n     |- Try 96 \/ 17 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 68 - 28 = 40. Add 40 to the number set. Current number set: [40, 17], target: 14, just two numbers left.\n     |- Try 40 + 17 = 57. Evaluate 57 != 14, drop this branch.\n     |- Try 40 - 17 = 23. Evaluate 23 != 14, drop this branch.\n     |- Try 40 * 17 = 680. Evaluate 680 != 14, drop this branch.\n     |- Try 40 \/ 17 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 68 * 28 = 1904. Add 1904 to the number set. Current number set: [1904, 17], target: 14, just two numbers left.\n     |- Try 1904 + 17 = 1921. Evaluate 1921 != 14, drop this branch.\n     |- Try 1904 - 17 = 1887. Evaluate 1887 != 14, drop this branch.\n     |- Try 1904 * 17 = 32368. 32368 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1904 \/ 17 = 112. Evaluate 112 != 14, drop this branch.\n    |- Try 68 \/ 28 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (68, 17) (numbers left: [28]). Try possible operations.\n    |- Try 68 + 17 = 85. Add 85 to the number set. Current number set: [85, 28], target: 14, just two numbers left.\n     |- Try 85 + 28 = 113. Evaluate 113 != 14, drop this branch.\n     |- Try 85 - 28 = 57. Evaluate 57 != 14, drop this branch.\n     |- Try 85 * 28 = 2380. 2380 exceeds the maximum intermediate result, drop this branch.\n     |- Try 85 \/ 28 = 3.0. 3.0 is a decimal, drop this branch.\n    |- Try 68 - 17 = 51. Add 51 to the number set. Current number set: [51, 28], target: 14, just two numbers left.\n     |- Try 51 + 28 = 79. Evaluate 79 != 14, drop this branch.\n     |- Try 51 - 28 = 23. Evaluate 23 != 14, drop this branch.\n     |- Try 51 * 28 = 1428. Evaluate 1428 != 14, drop this branch.\n     |- Try 51 \/ 28 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 68 * 17 = 1156. Add 1156 to the number set. Current number set: [1156, 28], target: 14, just two numbers left.\n     |- Try 1156 + 28 = 1184. Evaluate 1184 != 14, drop this branch.\n     |- Try 1156 - 28 = 1128. Evaluate 1128 != 14, drop this branch.\n     |- Try 1156 * 28 = 32368. 32368 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1156 \/ 28 = 41.3. 41.3 is a decimal, drop this branch.\n    |- Try 68 \/ 17 = 4. Add 4 to the number set. Current number set: [4, 28], target: 14, just two numbers left.\n     |- Try 28 + 4 = 32. Evaluate 32 != 14, drop this branch.\n     |- Try 28 - 4 = 24. Evaluate 24 != 14, drop this branch.\n     |- Try 28 * 4 = 112. Evaluate 112 != 14, drop this branch.\n     |- Try 28 \/ 4 = 7. Evaluate 7 != 14, drop this branch.\n   |- Pick two numbers (28, 17) (numbers left: [68]). Try possible operations.\n    |- Try 28 + 17 = 45. Add 45 to the number set. Current number set: [45, 68], target: 14, just two numbers left.\n     |- Try 68 + 45 = 113. Evaluate 113 != 14, drop this branch.\n     |- Try 68 - 45 = 23. Evaluate 23 != 14, drop this branch.\n     |- Try 68 * 45 = 3060. 3060 exceeds the maximum intermediate result, drop this branch.\n     |- Try 68 \/ 45 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 28 - 17 = 11. Add 11 to the number set. Current number set: [11, 68], target: 14, just two numbers left.\n     |- Try 68 + 11 = 79. Evaluate 79 != 14, drop this branch.\n     |- Try 68 - 11 = 57. Evaluate 57 != 14, drop this branch.\n     |- Try 68 * 11 = 748. Evaluate 748 != 14, drop this branch.\n     |- Try 68 \/ 11 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 28 * 17 = 476. Add 476 to the number set. Current number set: [476, 68], target: 14, just two numbers left.\n     |- Try 476 + 68 = 544. Evaluate 544 != 14, drop this branch.\n     |- Try 476 - 68 = 408. Evaluate 408 != 14, drop this branch.\n     |- Try 476 * 68 = 32368. 32368 exceeds the maximum intermediate result, drop this branch.\n     |- Try 476 \/ 68 = 7. Evaluate 7 != 14, drop this branch.\n    |- Try 28 \/ 17 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 37 - 31 = 6. Add 6 to the number set. Current number set: [6, 28, 17], target: 14. Options for choosing two numbers: [(6, 28), (6, 17), (28, 17)].\n   |- Pick two numbers (6, 28) (numbers left: [17]). Try possible operations.\n    |- Try 28 + 6 = 34. Add 34 to the number set. Current number set: [34, 17], target: 14, just two numbers left.\n     |- Try 34 + 17 = 51. Evaluate 51 != 14, drop this branch.\n     |- Try 34 - 17 = 17. Evaluate 17 != 14, drop this branch.\n     |- Try 34 * 17 = 578. Evaluate 578 != 14, drop this branch.\n     |- Try 34 \/ 17 = 2. Evaluate 2 != 14, drop this branch.\n    |- Try 28 - 6 = 22. Add 22 to the number set. Current number set: [22, 17], target: 14, just two numbers left.\n     |- Try 22 + 17 = 39. Evaluate 39 != 14, drop this branch.\n     |- Try 22 - 17 = 5. Evaluate 5 != 14, drop this branch.\n     |- Try 22 * 17 = 374. Evaluate 374 != 14, drop this branch.\n     |- Try 22 \/ 17 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 28 * 6 = 168. Add 168 to the number set. Current number set: [168, 17], target: 14, just two numbers left.\n     |- Try 168 + 17 = 185. Evaluate 185 != 14, drop this branch.\n     |- Try 168 - 17 = 151. Evaluate 151 != 14, drop this branch.\n     |- Try 168 * 17 = 2856. 2856 exceeds the maximum intermediate result, drop this branch.\n     |- Try 168 \/ 17 = 9.9. 9.9 is a decimal, drop this branch.\n    |- Try 28 \/ 6 = 4.7. 4.7 is a decimal, drop this branch.\n   |- Pick two numbers (6, 17) (numbers left: [28]). Try possible operations.\n    |- Try 17 + 6 = 23. Add 23 to the number set. Current number set: [23, 28], target: 14, just two numbers left.\n     |- Try 28 + 23 = 51. Evaluate 51 != 14, drop this branch.\n     |- Try 28 - 23 = 5. Evaluate 5 != 14, drop this branch.\n     |- Try 28 * 23 = 644. Evaluate 644 != 14, drop this branch.\n     |- Try 28 \/ 23 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 17 - 6 = 11. Add 11 to the number set. Current number set: [11, 28], target: 14, just two numbers left.\n     |- Try 28 + 11 = 39. Evaluate 39 != 14, drop this branch.\n     |- Try 28 - 11 = 17. Evaluate 17 != 14, drop this branch.\n     |- Try 28 * 11 = 308. Evaluate 308 != 14, drop this branch.\n     |- Try 28 \/ 11 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 17 * 6 = 102. Add 102 to the number set. Current number set: [102, 28], target: 14, just two numbers left.\n     |- Try 102 + 28 = 130. Evaluate 130 != 14, drop this branch.\n     |- Try 102 - 28 = 74. Evaluate 74 != 14, drop this branch.\n     |- Try 102 * 28 = 2856. 2856 exceeds the maximum intermediate result, drop this branch.\n     |- Try 102 \/ 28 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 17 \/ 6 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (28, 17) (numbers left: [6]). Try possible operations.\n    |- Try 28 + 17 = 45. Add 45 to the number set. Current number set: [45, 6], target: 14, just two numbers left.\n     |- Try 45 + 6 = 51. Evaluate 51 != 14, drop this branch.\n     |- Try 45 - 6 = 39. Evaluate 39 != 14, drop this branch.\n     |- Try 45 * 6 = 270. Evaluate 270 != 14, drop this branch.\n     |- Try 45 \/ 6 = 7.5. 7.5 is a decimal, drop this branch.\n    |- Try 28 - 17 = 11. Add 11 to the number set. Current number set: [11, 6], target: 14, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 14, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 14, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 14, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 28 * 17 = 476. Add 476 to the number set. Current number set: [476, 6], target: 14, just two numbers left.\n     |- Try 476 + 6 = 482. Evaluate 482 != 14, drop this branch.\n     |- Try 476 - 6 = 470. Evaluate 470 != 14, drop this branch.\n     |- Try 476 * 6 = 2856. 2856 exceeds the maximum intermediate result, drop this branch.\n     |- Try 476 \/ 6 = 79.3. 79.3 is a decimal, drop this branch.\n    |- Try 28 \/ 17 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 37 * 31 = 1147. Add 1147 to the number set. Current number set: [1147, 28, 17], target: 14. Options for choosing two numbers: [(1147, 28), (1147, 17), (28, 17)].\n   |- Pick two numbers (1147, 28) (numbers left: [17]). Try possible operations.\n    |- Try 1147 + 28 = 1175. Add 1175 to the number set. Current number set: [1175, 17], target: 14, just two numbers left.\n     |- Try 1175 + 17 = 1192. Evaluate 1192 != 14, drop this branch.\n     |- Try 1175 - 17 = 1158. Evaluate 1158 != 14, drop this branch.\n     |- Try 1175 * 17 = 19975. 19975 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1175 \/ 17 = 69.1. 69.1 is a decimal, drop this branch.\n    |- Try 1147 - 28 = 1119. Add 1119 to the number set. Current number set: [1119, 17], target: 14, just two numbers left.\n     |- Try 1119 + 17 = 1136. Evaluate 1136 != 14, drop this branch.\n     |- Try 1119 - 17 = 1102. Evaluate 1102 != 14, drop this branch.\n     |- Try 1119 * 17 = 19023. 19023 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1119 \/ 17 = 65.8. 65.8 is a decimal, drop this branch.\n    |- Try 1147 * 28 = 32116. 32116 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1147 \/ 28 = 41.0. 41.0 is a decimal, drop this branch.\n   |- Pick two numbers (1147, 17) (numbers left: [28]). Try possible operations.\n    |- Try 1147 + 17 = 1164. Add 1164 to the number set. Current number set: [1164, 28], target: 14, just two numbers left.\n     |- Try 1164 + 28 = 1192. Evaluate 1192 != 14, drop this branch.\n     |- Try 1164 - 28 = 1136. Evaluate 1136 != 14, drop this branch.\n     |- Try 1164 * 28 = 32592. 32592 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1164 \/ 28 = 41.6. 41.6 is a decimal, drop this branch.\n    |- Try 1147 - 17 = 1130. Add 1130 to the number set. Current number set: [1130, 28], target: 14, just two numbers left.\n     |- Try 1130 + 28 = 1158. Evaluate 1158 != 14, drop this branch.\n     |- Try 1130 - 28 = 1102. Evaluate 1102 != 14, drop this branch.\n     |- Try 1130 * 28 = 31640. 31640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1130 \/ 28 = 40.4. 40.4 is a decimal, drop this branch.\n    |- Try 1147 * 17 = 19499. 19499 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1147 \/ 17 = 67.5. 67.5 is a decimal, drop this branch.\n   |- Pick two numbers (28, 17) (numbers left: [1147]). Try possible operations.\n    |- Try 28 + 17 = 45. Add 45 to the number set. Current number set: [45, 1147], target: 14, just two numbers left.\n     |- Try 1147 + 45 = 1192. Evaluate 1192 != 14, drop this branch.\n     |- Try 1147 - 45 = 1102. Evaluate 1102 != 14, drop this branch.\n     |- Try 1147 * 45 = 51615. 51615 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1147 \/ 45 = 25.5. 25.5 is a decimal, drop this branch.\n    |- Try 28 - 17 = 11. Add 11 to the number set. Current number set: [11, 1147], target: 14, just two numbers left.\n     |- Try 1147 + 11 = 1158. Evaluate 1158 != 14, drop this branch.\n     |- Try 1147 - 11 = 1136. Evaluate 1136 != 14, drop this branch.\n     |- Try 1147 * 11 = 12617. 12617 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1147 \/ 11 = 104.3. 104.3 is a decimal, drop this branch.\n    |- Try 28 * 17 = 476. Add 476 to the number set. Current number set: [476, 1147], target: 14, just two numbers left.\n     |- Try 1147 + 476 = 1623. Evaluate 1623 != 14, drop this branch.\n     |- Try 1147 - 476 = 671. Evaluate 671 != 14, drop this branch.\n     |- Try 1147 * 476 = 545972. 545972 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1147 \/ 476 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 28 \/ 17 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 37 \/ 31 = 1.2. 1.2 is a decimal, drop this branch.\n |- Pick two numbers (31, 28) (numbers left: [37, 17]). Try possible operations.\n  |- Try 31 + 28 = 59. Add 59 to the number set. Current number set: [59, 37, 17], target: 14. Options for choosing two numbers: [(59, 37), (59, 17), (37, 17)].\n   |- Pick two numbers (59, 37) (numbers left: [17]). Try possible operations.\n    |- Try 59 + 37 = 96. Add 96 to the number set. Current number set: [96, 17], target: 14, just two numbers left.\n     |- Try 96 + 17 = 113. Evaluate 113 != 14, drop this branch.\n     |- Try 96 - 17 = 79. Evaluate 79 != 14, drop this branch.\n     |- Try 96 * 17 = 1632. Evaluate 1632 != 14, drop this branch.\n     |- Try 96 \/ 17 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 59 - 37 = 22. Add 22 to the number set. Current number set: [22, 17], target: 14, just two numbers left.\n     |- Try 22 + 17 = 39. Evaluate 39 != 14, drop this branch.\n     |- Try 22 - 17 = 5. Evaluate 5 != 14, drop this branch.\n     |- Try 22 * 17 = 374. Evaluate 374 != 14, drop this branch.\n     |- Try 22 \/ 17 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 59 * 37 = 2183. 2183 exceeds the maximum intermediate result, drop this branch.\n    |- Try 59 \/ 37 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (59, 17) (numbers left: [37]). Try possible operations.\n    |- Try 59 + 17 = 76. Add 76 to the number set. Current number set: [76, 37], target: 14, just two numbers left.\n     |- Try 76 + 37 = 113. Evaluate 113 != 14, drop this branch.\n     |- Try 76 - 37 = 39. Evaluate 39 != 14, drop this branch.\n     |- Try 76 * 37 = 2812. 2812 exceeds the maximum intermediate result, drop this branch.\n     |- Try 76 \/ 37 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 59 - 17 = 42. Add 42 to the number set. Current number set: [42, 37], target: 14, just two numbers left.\n     |- Try 42 + 37 = 79. Evaluate 79 != 14, drop this branch.\n     |- Try 42 - 37 = 5. Evaluate 5 != 14, drop this branch.\n     |- Try 42 * 37 = 1554. Evaluate 1554 != 14, drop this branch.\n     |- Try 42 \/ 37 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 59 * 17 = 1003. Add 1003 to the number set. Current number set: [1003, 37], target: 14, just two numbers left.\n     |- Try 1003 + 37 = 1040. Evaluate 1040 != 14, drop this branch.\n     |- Try 1003 - 37 = 966. Evaluate 966 != 14, drop this branch.\n     |- Try 1003 * 37 = 37111. 37111 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1003 \/ 37 = 27.1. 27.1 is a decimal, drop this branch.\n    |- Try 59 \/ 17 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (37, 17) (numbers left: [59]). Try possible operations.\n    |- Try 37 + 17 = 54. Add 54 to the number set. Current number set: [54, 59], target: 14, just two numbers left.\n     |- Try 59 + 54 = 113. Evaluate 113 != 14, drop this branch.\n     |- Try 59 - 54 = 5. Evaluate 5 != 14, drop this branch.\n     |- Try 59 * 54 = 3186. 3186 exceeds the maximum intermediate result, drop this branch.\n     |- Try 59 \/ 54 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 37 - 17 = 20. Add 20 to the number set. Current number set: [20, 59], target: 14, just two numbers left.\n     |- Try 59 + 20 = 79. Evaluate 79 != 14, drop this branch.\n     |- Try 59 - 20 = 39. Evaluate 39 != 14, drop this branch.\n     |- Try 59 * 20 = 1180. Evaluate 1180 != 14, drop this branch.\n     |- Try 59 \/ 20 = 3.0. 3.0 is a decimal, drop this branch.\n    |- Try 37 * 17 = 629. Add 629 to the number set. Current number set: [629, 59], target: 14, just two numbers left.\n     |- Try 629 + 59 = 688. Evaluate 688 != 14, drop this branch.\n     |- Try 629 - 59 = 570. Evaluate 570 != 14, drop this branch.\n     |- Try 629 * 59 = 37111. 37111 exceeds the maximum intermediate result, drop this branch.\n     |- Try 629 \/ 59 = 10.7. 10.7 is a decimal, drop this branch.\n    |- Try 37 \/ 17 = 2.2. 2.2 is a decimal, drop this branch.\n  |- Try 31 - 28 = 3. Add 3 to the number set. Current number set: [3, 37, 17], target: 14. Options for choosing two numbers: [(3, 37), (3, 17), (37, 17)].\n   |- Pick two numbers (3, 37) (numbers left: [17]). Try possible operations.\n    |- Try 37 + 3 = 40. Add 40 to the number set. Current number set: [40, 17], target: 14, just two numbers left.\n     |- Try 40 + 17 = 57. Evaluate 57 != 14, drop this branch.\n     |- Try 40 - 17 = 23. Evaluate 23 != 14, drop this branch.\n     |- Try 40 * 17 = 680. Evaluate 680 != 14, drop this branch.\n     |- Try 40 \/ 17 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 37 - 3 = 34. Add 34 to the number set. Current number set: [34, 17], target: 14, just two numbers left.\n     |- Try 34 + 17 = 51. Evaluate 51 != 14, drop this branch.\n     |- Try 34 - 17 = 17. Evaluate 17 != 14, drop this branch.\n     |- Try 34 * 17 = 578. Evaluate 578 != 14, drop this branch.\n     |- Try 34 \/ 17 = 2. Evaluate 2 != 14, drop this branch.\n    |- Try 37 * 3 = 111. Add 111 to the number set. Current number set: [111, 17], target: 14, just two numbers left.\n     |- Try 111 + 17 = 128. Evaluate 128 != 14, drop this branch.\n     |- Try 111 - 17 = 94. Evaluate 94 != 14, drop this branch.\n     |- Try 111 * 17 = 1887. Evaluate 1887 != 14, drop this branch.\n     |- Try 111 \/ 17 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 37 \/ 3 = 12.3. 12.3 is a decimal, drop this branch.\n   |- Pick two numbers (3, 17) (numbers left: [37]). Try possible operations.\n    |- Try 17 + 3 = 20. Add 20 to the number set. Current number set: [20, 37], target: 14, just two numbers left.\n     |- Try 37 + 20 = 57. Evaluate 57 != 14, drop this branch.\n     |- Try 37 - 20 = 17. Evaluate 17 != 14, drop this branch.\n     |- Try 37 * 20 = 740. Evaluate 740 != 14, drop this branch.\n     |- Try 37 \/ 20 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 17 - 3 = 14. Add 14 to the number set. Current number set: [14, 37], target: 14, just two numbers left.\n     |- Try 37 + 14 = 51. Evaluate 51 != 14, drop this branch.\n     |- Try 37 - 14 = 23. Evaluate 23 != 14, drop this branch.\n     |- Try 37 * 14 = 518. Evaluate 518 != 14, drop this branch.\n     |- Try 37 \/ 14 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 17 * 3 = 51. Add 51 to the number set. Current number set: [51, 37], target: 14, just two numbers left.\n     |- Try 51 + 37 = 88. Evaluate 88 != 14, drop this branch.\n     |- Try 51 - 37 = 14. Evaluate 14 == 14, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 51 - 37 = 14\nThe step before: 17 * 3 = 51\nThe first step: 31 - 28 = 3\n\nOutput the solution in the required format:\n<Solution>\n31 - 28 = 3\n17 * 3 = 51\n51 - 37 = 14\n<\/Solution>\n","item":{"nums":[31,37,28,17],"solution":["31 - 28 = 3","17 * 3 = 51","51 - 37 = 14"],"target":14}}
+{"instance_id":"countdown_8k_100","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [41, 5, 33, 13]\nTarget: 27","reference_output":"# Search Procedure\nInitial number set: [41, 5, 33, 13], target: 27. Options for choosing two numbers: [(41, 5), (41, 33), (41, 13), (5, 33), (5, 13), (33, 13)].\n |- Pick two numbers (41, 5) (numbers left: [33, 13]). Try possible operations.\n  |- Try 41 + 5 = 46. Add 46 to the number set. Current number set: [46, 33, 13], target: 27. Options for choosing two numbers: [(46, 33), (46, 13), (33, 13)].\n   |- Pick two numbers (46, 33) (numbers left: [13]). Try possible operations.\n    |- Try 46 + 33 = 79. Add 79 to the number set. Current number set: [79, 13], target: 27, just two numbers left.\n     |- Try 79 + 13 = 92. Evaluate 92 != 27, drop this branch.\n     |- Try 79 - 13 = 66. Evaluate 66 != 27, drop this branch.\n     |- Try 79 * 13 = 1027. Evaluate 1027 != 27, drop this branch.\n     |- Try 79 \/ 13 = 6.1. 6.1 is a decimal, drop this branch.\n    |- Try 46 - 33 = 13. Add 13 to the number set. Current number set: [13, 13], target: 27, just two numbers left.\n     |- Try 13 + 13 = 26. Evaluate 26 != 27, drop this branch.\n     |- Try 13 - 13 = 0. Evaluate 0 != 27, drop this branch.\n     |- Try 13 * 13 = 169. Evaluate 169 != 27, drop this branch.\n     |- Try 13 \/ 13 = 1. Evaluate 1 != 27, drop this branch.\n    |- Try 46 * 33 = 1518. Add 1518 to the number set. Current number set: [1518, 13], target: 27, just two numbers left.\n     |- Try 1518 + 13 = 1531. Evaluate 1531 != 27, drop this branch.\n     |- Try 1518 - 13 = 1505. Evaluate 1505 != 27, drop this branch.\n     |- Try 1518 * 13 = 19734. 19734 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1518 \/ 13 = 116.8. 116.8 is a decimal, drop this branch.\n    |- Try 46 \/ 33 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (46, 13) (numbers left: [33]). Try possible operations.\n    |- Try 46 + 13 = 59. Add 59 to the number set. Current number set: [59, 33], target: 27, just two numbers left.\n     |- Try 59 + 33 = 92. Evaluate 92 != 27, drop this branch.\n     |- Try 59 - 33 = 26. Evaluate 26 != 27, drop this branch.\n     |- Try 59 * 33 = 1947. Evaluate 1947 != 27, drop this branch.\n     |- Try 59 \/ 33 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 46 - 13 = 33. Add 33 to the number set. Current number set: [33, 33], target: 27, just two numbers left.\n     |- Try 33 + 33 = 66. Evaluate 66 != 27, drop this branch.\n     |- Try 33 - 33 = 0. Evaluate 0 != 27, drop this branch.\n     |- Try 33 * 33 = 1089. Evaluate 1089 != 27, drop this branch.\n     |- Try 33 \/ 33 = 1. Evaluate 1 != 27, drop this branch.\n    |- Try 46 * 13 = 598. Add 598 to the number set. Current number set: [598, 33], target: 27, just two numbers left.\n     |- Try 598 + 33 = 631. Evaluate 631 != 27, drop this branch.\n     |- Try 598 - 33 = 565. Evaluate 565 != 27, drop this branch.\n     |- Try 598 * 33 = 19734. 19734 exceeds the maximum intermediate result, drop this branch.\n     |- Try 598 \/ 33 = 18.1. 18.1 is a decimal, drop this branch.\n    |- Try 46 \/ 13 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (33, 13) (numbers left: [46]). Try possible operations.\n    |- Try 33 + 13 = 46. Add 46 to the number set. Current number set: [46, 46], target: 27, just two numbers left.\n     |- Try 46 + 46 = 92. Evaluate 92 != 27, drop this branch.\n     |- Try 46 - 46 = 0. Evaluate 0 != 27, drop this branch.\n     |- Try 46 * 46 = 2116. 2116 exceeds the maximum intermediate result, drop this branch.\n     |- Try 46 \/ 46 = 1. Evaluate 1 != 27, drop this branch.\n    |- Try 33 - 13 = 20. Add 20 to the number set. Current number set: [20, 46], target: 27, just two numbers left.\n     |- Try 46 + 20 = 66. Evaluate 66 != 27, drop this branch.\n     |- Try 46 - 20 = 26. Evaluate 26 != 27, drop this branch.\n     |- Try 46 * 20 = 920. Evaluate 920 != 27, drop this branch.\n     |- Try 46 \/ 20 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 33 * 13 = 429. Add 429 to the number set. Current number set: [429, 46], target: 27, just two numbers left.\n     |- Try 429 + 46 = 475. Evaluate 475 != 27, drop this branch.\n     |- Try 429 - 46 = 383. Evaluate 383 != 27, drop this branch.\n     |- Try 429 * 46 = 19734. 19734 exceeds the maximum intermediate result, drop this branch.\n     |- Try 429 \/ 46 = 9.3. 9.3 is a decimal, drop this branch.\n    |- Try 33 \/ 13 = 2.5. 2.5 is a decimal, drop this branch.\n  |- Try 41 - 5 = 36. Add 36 to the number set. Current number set: [36, 33, 13], target: 27. Options for choosing two numbers: [(36, 33), (36, 13), (33, 13)].\n   |- Pick two numbers (36, 33) (numbers left: [13]). Try possible operations.\n    |- Try 36 + 33 = 69. Add 69 to the number set. Current number set: [69, 13], target: 27, just two numbers left.\n     |- Try 69 + 13 = 82. Evaluate 82 != 27, drop this branch.\n     |- Try 69 - 13 = 56. Evaluate 56 != 27, drop this branch.\n     |- Try 69 * 13 = 897. Evaluate 897 != 27, drop this branch.\n     |- Try 69 \/ 13 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 36 - 33 = 3. Add 3 to the number set. Current number set: [3, 13], target: 27, just two numbers left.\n     |- Try 13 + 3 = 16. Evaluate 16 != 27, drop this branch.\n     |- Try 13 - 3 = 10. Evaluate 10 != 27, drop this branch.\n     |- Try 13 * 3 = 39. Evaluate 39 != 27, drop this branch.\n     |- Try 13 \/ 3 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 36 * 33 = 1188. Add 1188 to the number set. Current number set: [1188, 13], target: 27, just two numbers left.\n     |- Try 1188 + 13 = 1201. Evaluate 1201 != 27, drop this branch.\n     |- Try 1188 - 13 = 1175. Evaluate 1175 != 27, drop this branch.\n     |- Try 1188 * 13 = 15444. 15444 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1188 \/ 13 = 91.4. 91.4 is a decimal, drop this branch.\n    |- Try 36 \/ 33 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (36, 13) (numbers left: [33]). Try possible operations.\n    |- Try 36 + 13 = 49. Add 49 to the number set. Current number set: [49, 33], target: 27, just two numbers left.\n     |- Try 49 + 33 = 82. Evaluate 82 != 27, drop this branch.\n     |- Try 49 - 33 = 16. Evaluate 16 != 27, drop this branch.\n     |- Try 49 * 33 = 1617. Evaluate 1617 != 27, drop this branch.\n     |- Try 49 \/ 33 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 36 - 13 = 23. Add 23 to the number set. Current number set: [23, 33], target: 27, just two numbers left.\n     |- Try 33 + 23 = 56. Evaluate 56 != 27, drop this branch.\n     |- Try 33 - 23 = 10. Evaluate 10 != 27, drop this branch.\n     |- Try 33 * 23 = 759. Evaluate 759 != 27, drop this branch.\n     |- Try 33 \/ 23 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 36 * 13 = 468. Add 468 to the number set. Current number set: [468, 33], target: 27, just two numbers left.\n     |- Try 468 + 33 = 501. Evaluate 501 != 27, drop this branch.\n     |- Try 468 - 33 = 435. Evaluate 435 != 27, drop this branch.\n     |- Try 468 * 33 = 15444. 15444 exceeds the maximum intermediate result, drop this branch.\n     |- Try 468 \/ 33 = 14.2. 14.2 is a decimal, drop this branch.\n    |- Try 36 \/ 13 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (33, 13) (numbers left: [36]). Try possible operations.\n    |- Try 33 + 13 = 46. Add 46 to the number set. Current number set: [46, 36], target: 27, just two numbers left.\n     |- Try 46 + 36 = 82. Evaluate 82 != 27, drop this branch.\n     |- Try 46 - 36 = 10. Evaluate 10 != 27, drop this branch.\n     |- Try 46 * 36 = 1656. Evaluate 1656 != 27, drop this branch.\n     |- Try 46 \/ 36 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 33 - 13 = 20. Add 20 to the number set. Current number set: [20, 36], target: 27, just two numbers left.\n     |- Try 36 + 20 = 56. Evaluate 56 != 27, drop this branch.\n     |- Try 36 - 20 = 16. Evaluate 16 != 27, drop this branch.\n     |- Try 36 * 20 = 720. Evaluate 720 != 27, drop this branch.\n     |- Try 36 \/ 20 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 33 * 13 = 429. Add 429 to the number set. Current number set: [429, 36], target: 27, just two numbers left.\n     |- Try 429 + 36 = 465. Evaluate 465 != 27, drop this branch.\n     |- Try 429 - 36 = 393. Evaluate 393 != 27, drop this branch.\n     |- Try 429 * 36 = 15444. 15444 exceeds the maximum intermediate result, drop this branch.\n     |- Try 429 \/ 36 = 11.9. 11.9 is a decimal, drop this branch.\n    |- Try 33 \/ 13 = 2.5. 2.5 is a decimal, drop this branch.\n  |- Try 41 * 5 = 205. Add 205 to the number set. Current number set: [205, 33, 13], target: 27. Options for choosing two numbers: [(205, 33), (205, 13), (33, 13)].\n   |- Pick two numbers (205, 33) (numbers left: [13]). Try possible operations.\n    |- Try 205 + 33 = 238. Add 238 to the number set. Current number set: [238, 13], target: 27, just two numbers left.\n     |- Try 238 + 13 = 251. Evaluate 251 != 27, drop this branch.\n     |- Try 238 - 13 = 225. Evaluate 225 != 27, drop this branch.\n     |- Try 238 * 13 = 3094. 3094 exceeds the maximum intermediate result, drop this branch.\n     |- Try 238 \/ 13 = 18.3. 18.3 is a decimal, drop this branch.\n    |- Try 205 - 33 = 172. Add 172 to the number set. Current number set: [172, 13], target: 27, just two numbers left.\n     |- Try 172 + 13 = 185. Evaluate 185 != 27, drop this branch.\n     |- Try 172 - 13 = 159. Evaluate 159 != 27, drop this branch.\n     |- Try 172 * 13 = 2236. 2236 exceeds the maximum intermediate result, drop this branch.\n     |- Try 172 \/ 13 = 13.2. 13.2 is a decimal, drop this branch.\n    |- Try 205 * 33 = 6765. 6765 exceeds the maximum intermediate result, drop this branch.\n    |- Try 205 \/ 33 = 6.2. 6.2 is a decimal, drop this branch.\n   |- Pick two numbers (205, 13) (numbers left: [33]). Try possible operations.\n    |- Try 205 + 13 = 218. Add 218 to the number set. Current number set: [218, 33], target: 27, just two numbers left.\n     |- Try 218 + 33 = 251. Evaluate 251 != 27, drop this branch.\n     |- Try 218 - 33 = 185. Evaluate 185 != 27, drop this branch.\n     |- Try 218 * 33 = 7194. 7194 exceeds the maximum intermediate result, drop this branch.\n     |- Try 218 \/ 33 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 205 - 13 = 192. Add 192 to the number set. Current number set: [192, 33], target: 27, just two numbers left.\n     |- Try 192 + 33 = 225. Evaluate 225 != 27, drop this branch.\n     |- Try 192 - 33 = 159. Evaluate 159 != 27, drop this branch.\n     |- Try 192 * 33 = 6336. 6336 exceeds the maximum intermediate result, drop this branch.\n     |- Try 192 \/ 33 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 205 * 13 = 2665. 2665 exceeds the maximum intermediate result, drop this branch.\n    |- Try 205 \/ 13 = 15.8. 15.8 is a decimal, drop this branch.\n   |- Pick two numbers (33, 13) (numbers left: [205]). Try possible operations.\n    |- Try 33 + 13 = 46. Add 46 to the number set. Current number set: [46, 205], target: 27, just two numbers left.\n     |- Try 205 + 46 = 251. Evaluate 251 != 27, drop this branch.\n     |- Try 205 - 46 = 159. Evaluate 159 != 27, drop this branch.\n     |- Try 205 * 46 = 9430. 9430 exceeds the maximum intermediate result, drop this branch.\n     |- Try 205 \/ 46 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 33 - 13 = 20. Add 20 to the number set. Current number set: [20, 205], target: 27, just two numbers left.\n     |- Try 205 + 20 = 225. Evaluate 225 != 27, drop this branch.\n     |- Try 205 - 20 = 185. Evaluate 185 != 27, drop this branch.\n     |- Try 205 * 20 = 4100. 4100 exceeds the maximum intermediate result, drop this branch.\n     |- Try 205 \/ 20 = 10.2. 10.2 is a decimal, drop this branch.\n    |- Try 33 * 13 = 429. Add 429 to the number set. Current number set: [429, 205], target: 27, just two numbers left.\n     |- Try 429 + 205 = 634. Evaluate 634 != 27, drop this branch.\n     |- Try 429 - 205 = 224. Evaluate 224 != 27, drop this branch.\n     |- Try 429 * 205 = 87945. 87945 exceeds the maximum intermediate result, drop this branch.\n     |- Try 429 \/ 205 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 33 \/ 13 = 2.5. 2.5 is a decimal, drop this branch.\n  |- Try 41 \/ 5 = 8.2. 8.2 is a decimal, drop this branch.\n |- Pick two numbers (41, 33) (numbers left: [5, 13]). Try possible operations.\n  |- Try 41 + 33 = 74. Add 74 to the number set. Current number set: [74, 5, 13], target: 27. Options for choosing two numbers: [(74, 5), (74, 13), (5, 13)].\n   |- Pick two numbers (74, 5) (numbers left: [13]). Try possible operations.\n    |- Try 74 + 5 = 79. Add 79 to the number set. Current number set: [79, 13], target: 27, just two numbers left.\n     |- Try 79 + 13 = 92. Evaluate 92 != 27, drop this branch.\n     |- Try 79 - 13 = 66. Evaluate 66 != 27, drop this branch.\n     |- Try 79 * 13 = 1027. Evaluate 1027 != 27, drop this branch.\n     |- Try 79 \/ 13 = 6.1. 6.1 is a decimal, drop this branch.\n    |- Try 74 - 5 = 69. Add 69 to the number set. Current number set: [69, 13], target: 27, just two numbers left.\n     |- Try 69 + 13 = 82. Evaluate 82 != 27, drop this branch.\n     |- Try 69 - 13 = 56. Evaluate 56 != 27, drop this branch.\n     |- Try 69 * 13 = 897. Evaluate 897 != 27, drop this branch.\n     |- Try 69 \/ 13 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 74 * 5 = 370. Add 370 to the number set. Current number set: [370, 13], target: 27, just two numbers left.\n     |- Try 370 + 13 = 383. Evaluate 383 != 27, drop this branch.\n     |- Try 370 - 13 = 357. Evaluate 357 != 27, drop this branch.\n     |- Try 370 * 13 = 4810. 4810 exceeds the maximum intermediate result, drop this branch.\n     |- Try 370 \/ 13 = 28.5. 28.5 is a decimal, drop this branch.\n    |- Try 74 \/ 5 = 14.8. 14.8 is a decimal, drop this branch.\n   |- Pick two numbers (74, 13) (numbers left: [5]). Try possible operations.\n    |- Try 74 + 13 = 87. Add 87 to the number set. Current number set: [87, 5], target: 27, just two numbers left.\n     |- Try 87 + 5 = 92. Evaluate 92 != 27, drop this branch.\n     |- Try 87 - 5 = 82. Evaluate 82 != 27, drop this branch.\n     |- Try 87 * 5 = 435. Evaluate 435 != 27, drop this branch.\n     |- Try 87 \/ 5 = 17.4. 17.4 is a decimal, drop this branch.\n    |- Try 74 - 13 = 61. Add 61 to the number set. Current number set: [61, 5], target: 27, just two numbers left.\n     |- Try 61 + 5 = 66. Evaluate 66 != 27, drop this branch.\n     |- Try 61 - 5 = 56. Evaluate 56 != 27, drop this branch.\n     |- Try 61 * 5 = 305. Evaluate 305 != 27, drop this branch.\n     |- Try 61 \/ 5 = 12.2. 12.2 is a decimal, drop this branch.\n    |- Try 74 * 13 = 962. Add 962 to the number set. Current number set: [962, 5], target: 27, just two numbers left.\n     |- Try 962 + 5 = 967. Evaluate 967 != 27, drop this branch.\n     |- Try 962 - 5 = 957. Evaluate 957 != 27, drop this branch.\n     |- Try 962 * 5 = 4810. 4810 exceeds the maximum intermediate result, drop this branch.\n     |- Try 962 \/ 5 = 192.4. 192.4 is a decimal, drop this branch.\n    |- Try 74 \/ 13 = 5.7. 5.7 is a decimal, drop this branch.\n   |- Pick two numbers (5, 13) (numbers left: [74]). Try possible operations.\n    |- Try 13 + 5 = 18. Add 18 to the number set. Current number set: [18, 74], target: 27, just two numbers left.\n     |- Try 74 + 18 = 92. Evaluate 92 != 27, drop this branch.\n     |- Try 74 - 18 = 56. Evaluate 56 != 27, drop this branch.\n     |- Try 74 * 18 = 1332. Evaluate 1332 != 27, drop this branch.\n     |- Try 74 \/ 18 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 13 - 5 = 8. Add 8 to the number set. Current number set: [8, 74], target: 27, just two numbers left.\n     |- Try 74 + 8 = 82. Evaluate 82 != 27, drop this branch.\n     |- Try 74 - 8 = 66. Evaluate 66 != 27, drop this branch.\n     |- Try 74 * 8 = 592. Evaluate 592 != 27, drop this branch.\n     |- Try 74 \/ 8 = 9.2. 9.2 is a decimal, drop this branch.\n    |- Try 13 * 5 = 65. Add 65 to the number set. Current number set: [65, 74], target: 27, just two numbers left.\n     |- Try 74 + 65 = 139. Evaluate 139 != 27, drop this branch.\n     |- Try 74 - 65 = 9. Evaluate 9 != 27, drop this branch.\n     |- Try 74 * 65 = 4810. 4810 exceeds the maximum intermediate result, drop this branch.\n     |- Try 74 \/ 65 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 13 \/ 5 = 2.6. 2.6 is a decimal, drop this branch.\n  |- Try 41 - 33 = 8. Add 8 to the number set. Current number set: [8, 5, 13], target: 27. Options for choosing two numbers: [(8, 5), (8, 13), (5, 13)].\n   |- Pick two numbers (8, 5) (numbers left: [13]). Try possible operations.\n    |- Try 8 + 5 = 13. Add 13 to the number set. Current number set: [13, 13], target: 27, just two numbers left.\n     |- Try 13 + 13 = 26. Evaluate 26 != 27, drop this branch.\n     |- Try 13 - 13 = 0. Evaluate 0 != 27, drop this branch.\n     |- Try 13 * 13 = 169. Evaluate 169 != 27, drop this branch.\n     |- Try 13 \/ 13 = 1. Evaluate 1 != 27, drop this branch.\n    |- Try 8 - 5 = 3. Add 3 to the number set. Current number set: [3, 13], target: 27, just two numbers left.\n     |- Try 13 + 3 = 16. Evaluate 16 != 27, drop this branch.\n     |- Try 13 - 3 = 10. Evaluate 10 != 27, drop this branch.\n     |- Try 13 * 3 = 39. Evaluate 39 != 27, drop this branch.\n     |- Try 13 \/ 3 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 8 * 5 = 40. Add 40 to the number set. Current number set: [40, 13], target: 27, just two numbers left.\n     |- Try 40 + 13 = 53. Evaluate 53 != 27, drop this branch.\n     |- Try 40 - 13 = 27. Evaluate 27 == 27, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 40 - 13 = 27\nThe step before: 8 * 5 = 40\nThe first step: 41 - 33 = 8\n\nOutput the solution in the required format:\n<Solution>\n41 - 33 = 8\n8 * 5 = 40\n40 - 13 = 27\n<\/Solution>\n","item":{"nums":[41,5,33,13],"solution":["41 - 33 = 8","8 * 5 = 40","40 - 13 = 27"],"target":27}}
+{"instance_id":"countdown_8k_101","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [12, 49, 7, 39]\nTarget: 50","reference_output":"# Search Procedure\nInitial number set: [12, 49, 7, 39], target: 50. Options for choosing two numbers: [(12, 49), (12, 7), (12, 39), (49, 7), (49, 39), (7, 39)].\n |- Pick two numbers (12, 49) (numbers left: [7, 39]). Try possible operations.\n  |- Try 49 + 12 = 61. Add 61 to the number set. Current number set: [61, 7, 39], target: 50. Options for choosing two numbers: [(61, 7), (61, 39), (7, 39)].\n   |- Pick two numbers (61, 7) (numbers left: [39]). Try possible operations.\n    |- Try 61 + 7 = 68. Add 68 to the number set. Current number set: [68, 39], target: 50, just two numbers left.\n     |- Try 68 + 39 = 107. Evaluate 107 != 50, drop this branch.\n     |- Try 68 - 39 = 29. Evaluate 29 != 50, drop this branch.\n     |- Try 68 * 39 = 2652. 2652 exceeds the maximum intermediate result, drop this branch.\n     |- Try 68 \/ 39 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 61 - 7 = 54. Add 54 to the number set. Current number set: [54, 39], target: 50, just two numbers left.\n     |- Try 54 + 39 = 93. Evaluate 93 != 50, drop this branch.\n     |- Try 54 - 39 = 15. Evaluate 15 != 50, drop this branch.\n     |- Try 54 * 39 = 2106. 2106 exceeds the maximum intermediate result, drop this branch.\n     |- Try 54 \/ 39 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 61 * 7 = 427. Add 427 to the number set. Current number set: [427, 39], target: 50, just two numbers left.\n     |- Try 427 + 39 = 466. Evaluate 466 != 50, drop this branch.\n     |- Try 427 - 39 = 388. Evaluate 388 != 50, drop this branch.\n     |- Try 427 * 39 = 16653. 16653 exceeds the maximum intermediate result, drop this branch.\n     |- Try 427 \/ 39 = 10.9. 10.9 is a decimal, drop this branch.\n    |- Try 61 \/ 7 = 8.7. 8.7 is a decimal, drop this branch.\n   |- Pick two numbers (61, 39) (numbers left: [7]). Try possible operations.\n    |- Try 61 + 39 = 100. Add 100 to the number set. Current number set: [100, 7], target: 50, just two numbers left.\n     |- Try 100 + 7 = 107. Evaluate 107 != 50, drop this branch.\n     |- Try 100 - 7 = 93. Evaluate 93 != 50, drop this branch.\n     |- Try 100 * 7 = 700. Evaluate 700 != 50, drop this branch.\n     |- Try 100 \/ 7 = 14.3. 14.3 is a decimal, drop this branch.\n    |- Try 61 - 39 = 22. Add 22 to the number set. Current number set: [22, 7], target: 50, just two numbers left.\n     |- Try 22 + 7 = 29. Evaluate 29 != 50, drop this branch.\n     |- Try 22 - 7 = 15. Evaluate 15 != 50, drop this branch.\n     |- Try 22 * 7 = 154. Evaluate 154 != 50, drop this branch.\n     |- Try 22 \/ 7 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 61 * 39 = 2379. 2379 exceeds the maximum intermediate result, drop this branch.\n    |- Try 61 \/ 39 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (7, 39) (numbers left: [61]). Try possible operations.\n    |- Try 39 + 7 = 46. Add 46 to the number set. Current number set: [46, 61], target: 50, just two numbers left.\n     |- Try 61 + 46 = 107. Evaluate 107 != 50, drop this branch.\n     |- Try 61 - 46 = 15. Evaluate 15 != 50, drop this branch.\n     |- Try 61 * 46 = 2806. 2806 exceeds the maximum intermediate result, drop this branch.\n     |- Try 61 \/ 46 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 39 - 7 = 32. Add 32 to the number set. Current number set: [32, 61], target: 50, just two numbers left.\n     |- Try 61 + 32 = 93. Evaluate 93 != 50, drop this branch.\n     |- Try 61 - 32 = 29. Evaluate 29 != 50, drop this branch.\n     |- Try 61 * 32 = 1952. Evaluate 1952 != 50, drop this branch.\n     |- Try 61 \/ 32 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 39 * 7 = 273. Add 273 to the number set. Current number set: [273, 61], target: 50, just two numbers left.\n     |- Try 273 + 61 = 334. Evaluate 334 != 50, drop this branch.\n     |- Try 273 - 61 = 212. Evaluate 212 != 50, drop this branch.\n     |- Try 273 * 61 = 16653. 16653 exceeds the maximum intermediate result, drop this branch.\n     |- Try 273 \/ 61 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 39 \/ 7 = 5.6. 5.6 is a decimal, drop this branch.\n  |- Try 49 - 12 = 37. Add 37 to the number set. Current number set: [37, 7, 39], target: 50. Options for choosing two numbers: [(37, 7), (37, 39), (7, 39)].\n   |- Pick two numbers (37, 7) (numbers left: [39]). Try possible operations.\n    |- Try 37 + 7 = 44. Add 44 to the number set. Current number set: [44, 39], target: 50, just two numbers left.\n     |- Try 44 + 39 = 83. Evaluate 83 != 50, drop this branch.\n     |- Try 44 - 39 = 5. Evaluate 5 != 50, drop this branch.\n     |- Try 44 * 39 = 1716. Evaluate 1716 != 50, drop this branch.\n     |- Try 44 \/ 39 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 37 - 7 = 30. Add 30 to the number set. Current number set: [30, 39], target: 50, just two numbers left.\n     |- Try 39 + 30 = 69. Evaluate 69 != 50, drop this branch.\n     |- Try 39 - 30 = 9. Evaluate 9 != 50, drop this branch.\n     |- Try 39 * 30 = 1170. Evaluate 1170 != 50, drop this branch.\n     |- Try 39 \/ 30 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 37 * 7 = 259. Add 259 to the number set. Current number set: [259, 39], target: 50, just two numbers left.\n     |- Try 259 + 39 = 298. Evaluate 298 != 50, drop this branch.\n     |- Try 259 - 39 = 220. Evaluate 220 != 50, drop this branch.\n     |- Try 259 * 39 = 10101. 10101 exceeds the maximum intermediate result, drop this branch.\n     |- Try 259 \/ 39 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 37 \/ 7 = 5.3. 5.3 is a decimal, drop this branch.\n   |- Pick two numbers (37, 39) (numbers left: [7]). Try possible operations.\n    |- Try 39 + 37 = 76. Add 76 to the number set. Current number set: [76, 7], target: 50, just two numbers left.\n     |- Try 76 + 7 = 83. Evaluate 83 != 50, drop this branch.\n     |- Try 76 - 7 = 69. Evaluate 69 != 50, drop this branch.\n     |- Try 76 * 7 = 532. Evaluate 532 != 50, drop this branch.\n     |- Try 76 \/ 7 = 10.9. 10.9 is a decimal, drop this branch.\n    |- Try 39 - 37 = 2. Add 2 to the number set. Current number set: [2, 7], target: 50, just two numbers left.\n     |- Try 7 + 2 = 9. Evaluate 9 != 50, drop this branch.\n     |- Try 7 - 2 = 5. Evaluate 5 != 50, drop this branch.\n     |- Try 7 * 2 = 14. Evaluate 14 != 50, drop this branch.\n     |- Try 7 \/ 2 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 39 * 37 = 1443. Add 1443 to the number set. Current number set: [1443, 7], target: 50, just two numbers left.\n     |- Try 1443 + 7 = 1450. Evaluate 1450 != 50, drop this branch.\n     |- Try 1443 - 7 = 1436. Evaluate 1436 != 50, drop this branch.\n     |- Try 1443 * 7 = 10101. 10101 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1443 \/ 7 = 206.1. 206.1 is a decimal, drop this branch.\n    |- Try 39 \/ 37 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (7, 39) (numbers left: [37]). Try possible operations.\n    |- Try 39 + 7 = 46. Add 46 to the number set. Current number set: [46, 37], target: 50, just two numbers left.\n     |- Try 46 + 37 = 83. Evaluate 83 != 50, drop this branch.\n     |- Try 46 - 37 = 9. Evaluate 9 != 50, drop this branch.\n     |- Try 46 * 37 = 1702. Evaluate 1702 != 50, drop this branch.\n     |- Try 46 \/ 37 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 39 - 7 = 32. Add 32 to the number set. Current number set: [32, 37], target: 50, just two numbers left.\n     |- Try 37 + 32 = 69. Evaluate 69 != 50, drop this branch.\n     |- Try 37 - 32 = 5. Evaluate 5 != 50, drop this branch.\n     |- Try 37 * 32 = 1184. Evaluate 1184 != 50, drop this branch.\n     |- Try 37 \/ 32 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 39 * 7 = 273. Add 273 to the number set. Current number set: [273, 37], target: 50, just two numbers left.\n     |- Try 273 + 37 = 310. Evaluate 310 != 50, drop this branch.\n     |- Try 273 - 37 = 236. Evaluate 236 != 50, drop this branch.\n     |- Try 273 * 37 = 10101. 10101 exceeds the maximum intermediate result, drop this branch.\n     |- Try 273 \/ 37 = 7.4. 7.4 is a decimal, drop this branch.\n    |- Try 39 \/ 7 = 5.6. 5.6 is a decimal, drop this branch.\n  |- Try 49 * 12 = 588. Add 588 to the number set. Current number set: [588, 7, 39], target: 50. Options for choosing two numbers: [(588, 7), (588, 39), (7, 39)].\n   |- Pick two numbers (588, 7) (numbers left: [39]). Try possible operations.\n    |- Try 588 + 7 = 595. Add 595 to the number set. Current number set: [595, 39], target: 50, just two numbers left.\n     |- Try 595 + 39 = 634. Evaluate 634 != 50, drop this branch.\n     |- Try 595 - 39 = 556. Evaluate 556 != 50, drop this branch.\n     |- Try 595 * 39 = 23205. 23205 exceeds the maximum intermediate result, drop this branch.\n     |- Try 595 \/ 39 = 15.3. 15.3 is a decimal, drop this branch.\n    |- Try 588 - 7 = 581. Add 581 to the number set. Current number set: [581, 39], target: 50, just two numbers left.\n     |- Try 581 + 39 = 620. Evaluate 620 != 50, drop this branch.\n     |- Try 581 - 39 = 542. Evaluate 542 != 50, drop this branch.\n     |- Try 581 * 39 = 22659. 22659 exceeds the maximum intermediate result, drop this branch.\n     |- Try 581 \/ 39 = 14.9. 14.9 is a decimal, drop this branch.\n    |- Try 588 * 7 = 4116. 4116 exceeds the maximum intermediate result, drop this branch.\n    |- Try 588 \/ 7 = 84. Add 84 to the number set. Current number set: [84, 39], target: 50, just two numbers left.\n     |- Try 84 + 39 = 123. Evaluate 123 != 50, drop this branch.\n     |- Try 84 - 39 = 45. Evaluate 45 != 50, drop this branch.\n     |- Try 84 * 39 = 3276. 3276 exceeds the maximum intermediate result, drop this branch.\n     |- Try 84 \/ 39 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (588, 39) (numbers left: [7]). Try possible operations.\n    |- Try 588 + 39 = 627. Add 627 to the number set. Current number set: [627, 7], target: 50, just two numbers left.\n     |- Try 627 + 7 = 634. Evaluate 634 != 50, drop this branch.\n     |- Try 627 - 7 = 620. Evaluate 620 != 50, drop this branch.\n     |- Try 627 * 7 = 4389. 4389 exceeds the maximum intermediate result, drop this branch.\n     |- Try 627 \/ 7 = 89.6. 89.6 is a decimal, drop this branch.\n    |- Try 588 - 39 = 549. Add 549 to the number set. Current number set: [549, 7], target: 50, just two numbers left.\n     |- Try 549 + 7 = 556. Evaluate 556 != 50, drop this branch.\n     |- Try 549 - 7 = 542. Evaluate 542 != 50, drop this branch.\n     |- Try 549 * 7 = 3843. 3843 exceeds the maximum intermediate result, drop this branch.\n     |- Try 549 \/ 7 = 78.4. 78.4 is a decimal, drop this branch.\n    |- Try 588 * 39 = 22932. 22932 exceeds the maximum intermediate result, drop this branch.\n    |- Try 588 \/ 39 = 15.1. 15.1 is a decimal, drop this branch.\n   |- Pick two numbers (7, 39) (numbers left: [588]). Try possible operations.\n    |- Try 39 + 7 = 46. Add 46 to the number set. Current number set: [46, 588], target: 50, just two numbers left.\n     |- Try 588 + 46 = 634. Evaluate 634 != 50, drop this branch.\n     |- Try 588 - 46 = 542. Evaluate 542 != 50, drop this branch.\n     |- Try 588 * 46 = 27048. 27048 exceeds the maximum intermediate result, drop this branch.\n     |- Try 588 \/ 46 = 12.8. 12.8 is a decimal, drop this branch.\n    |- Try 39 - 7 = 32. Add 32 to the number set. Current number set: [32, 588], target: 50, just two numbers left.\n     |- Try 588 + 32 = 620. Evaluate 620 != 50, drop this branch.\n     |- Try 588 - 32 = 556. Evaluate 556 != 50, drop this branch.\n     |- Try 588 * 32 = 18816. 18816 exceeds the maximum intermediate result, drop this branch.\n     |- Try 588 \/ 32 = 18.4. 18.4 is a decimal, drop this branch.\n    |- Try 39 * 7 = 273. Add 273 to the number set. Current number set: [273, 588], target: 50, just two numbers left.\n     |- Try 588 + 273 = 861. Evaluate 861 != 50, drop this branch.\n     |- Try 588 - 273 = 315. Evaluate 315 != 50, drop this branch.\n     |- Try 588 * 273 = 160524. 160524 exceeds the maximum intermediate result, drop this branch.\n     |- Try 588 \/ 273 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 39 \/ 7 = 5.6. 5.6 is a decimal, drop this branch.\n  |- Try 49 \/ 12 = 4.1. 4.1 is a decimal, drop this branch.\n |- Pick two numbers (12, 7) (numbers left: [49, 39]). Try possible operations.\n  |- Try 12 + 7 = 19. Add 19 to the number set. Current number set: [19, 49, 39], target: 50. Options for choosing two numbers: [(19, 49), (19, 39), (49, 39)].\n   |- Pick two numbers (19, 49) (numbers left: [39]). Try possible operations.\n    |- Try 49 + 19 = 68. Add 68 to the number set. Current number set: [68, 39], target: 50, just two numbers left.\n     |- Try 68 + 39 = 107. Evaluate 107 != 50, drop this branch.\n     |- Try 68 - 39 = 29. Evaluate 29 != 50, drop this branch.\n     |- Try 68 * 39 = 2652. 2652 exceeds the maximum intermediate result, drop this branch.\n     |- Try 68 \/ 39 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 49 - 19 = 30. Add 30 to the number set. Current number set: [30, 39], target: 50, just two numbers left.\n     |- Try 39 + 30 = 69. Evaluate 69 != 50, drop this branch.\n     |- Try 39 - 30 = 9. Evaluate 9 != 50, drop this branch.\n     |- Try 39 * 30 = 1170. Evaluate 1170 != 50, drop this branch.\n     |- Try 39 \/ 30 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 49 * 19 = 931. Add 931 to the number set. Current number set: [931, 39], target: 50, just two numbers left.\n     |- Try 931 + 39 = 970. Evaluate 970 != 50, drop this branch.\n     |- Try 931 - 39 = 892. Evaluate 892 != 50, drop this branch.\n     |- Try 931 * 39 = 36309. 36309 exceeds the maximum intermediate result, drop this branch.\n     |- Try 931 \/ 39 = 23.9. 23.9 is a decimal, drop this branch.\n    |- Try 49 \/ 19 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (19, 39) (numbers left: [49]). Try possible operations.\n    |- Try 39 + 19 = 58. Add 58 to the number set. Current number set: [58, 49], target: 50, just two numbers left.\n     |- Try 58 + 49 = 107. Evaluate 107 != 50, drop this branch.\n     |- Try 58 - 49 = 9. Evaluate 9 != 50, drop this branch.\n     |- Try 58 * 49 = 2842. 2842 exceeds the maximum intermediate result, drop this branch.\n     |- Try 58 \/ 49 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 39 - 19 = 20. Add 20 to the number set. Current number set: [20, 49], target: 50, just two numbers left.\n     |- Try 49 + 20 = 69. Evaluate 69 != 50, drop this branch.\n     |- Try 49 - 20 = 29. Evaluate 29 != 50, drop this branch.\n     |- Try 49 * 20 = 980. Evaluate 980 != 50, drop this branch.\n     |- Try 49 \/ 20 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 39 * 19 = 741. Add 741 to the number set. Current number set: [741, 49], target: 50, just two numbers left.\n     |- Try 741 + 49 = 790. Evaluate 790 != 50, drop this branch.\n     |- Try 741 - 49 = 692. Evaluate 692 != 50, drop this branch.\n     |- Try 741 * 49 = 36309. 36309 exceeds the maximum intermediate result, drop this branch.\n     |- Try 741 \/ 49 = 15.1. 15.1 is a decimal, drop this branch.\n    |- Try 39 \/ 19 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (49, 39) (numbers left: [19]). Try possible operations.\n    |- Try 49 + 39 = 88. Add 88 to the number set. Current number set: [88, 19], target: 50, just two numbers left.\n     |- Try 88 + 19 = 107. Evaluate 107 != 50, drop this branch.\n     |- Try 88 - 19 = 69. Evaluate 69 != 50, drop this branch.\n     |- Try 88 * 19 = 1672. Evaluate 1672 != 50, drop this branch.\n     |- Try 88 \/ 19 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 49 - 39 = 10. Add 10 to the number set. Current number set: [10, 19], target: 50, just two numbers left.\n     |- Try 19 + 10 = 29. Evaluate 29 != 50, drop this branch.\n     |- Try 19 - 10 = 9. Evaluate 9 != 50, drop this branch.\n     |- Try 19 * 10 = 190. Evaluate 190 != 50, drop this branch.\n     |- Try 19 \/ 10 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 49 * 39 = 1911. Add 1911 to the number set. Current number set: [1911, 19], target: 50, just two numbers left.\n     |- Try 1911 + 19 = 1930. Evaluate 1930 != 50, drop this branch.\n     |- Try 1911 - 19 = 1892. Evaluate 1892 != 50, drop this branch.\n     |- Try 1911 * 19 = 36309. 36309 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1911 \/ 19 = 100.6. 100.6 is a decimal, drop this branch.\n    |- Try 49 \/ 39 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 12 - 7 = 5. Add 5 to the number set. Current number set: [5, 49, 39], target: 50. Options for choosing two numbers: [(5, 49), (5, 39), (49, 39)].\n   |- Pick two numbers (5, 49) (numbers left: [39]). Try possible operations.\n    |- Try 49 + 5 = 54. Add 54 to the number set. Current number set: [54, 39], target: 50, just two numbers left.\n     |- Try 54 + 39 = 93. Evaluate 93 != 50, drop this branch.\n     |- Try 54 - 39 = 15. Evaluate 15 != 50, drop this branch.\n     |- Try 54 * 39 = 2106. 2106 exceeds the maximum intermediate result, drop this branch.\n     |- Try 54 \/ 39 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 49 - 5 = 44. Add 44 to the number set. Current number set: [44, 39], target: 50, just two numbers left.\n     |- Try 44 + 39 = 83. Evaluate 83 != 50, drop this branch.\n     |- Try 44 - 39 = 5. Evaluate 5 != 50, drop this branch.\n     |- Try 44 * 39 = 1716. Evaluate 1716 != 50, drop this branch.\n     |- Try 44 \/ 39 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 49 * 5 = 245. Add 245 to the number set. Current number set: [245, 39], target: 50, just two numbers left.\n     |- Try 245 + 39 = 284. Evaluate 284 != 50, drop this branch.\n     |- Try 245 - 39 = 206. Evaluate 206 != 50, drop this branch.\n     |- Try 245 * 39 = 9555. 9555 exceeds the maximum intermediate result, drop this branch.\n     |- Try 245 \/ 39 = 6.3. 6.3 is a decimal, drop this branch.\n    |- Try 49 \/ 5 = 9.8. 9.8 is a decimal, drop this branch.\n   |- Pick two numbers (5, 39) (numbers left: [49]). Try possible operations.\n    |- Try 39 + 5 = 44. Add 44 to the number set. Current number set: [44, 49], target: 50, just two numbers left.\n     |- Try 49 + 44 = 93. Evaluate 93 != 50, drop this branch.\n     |- Try 49 - 44 = 5. Evaluate 5 != 50, drop this branch.\n     |- Try 49 * 44 = 2156. 2156 exceeds the maximum intermediate result, drop this branch.\n     |- Try 49 \/ 44 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 39 - 5 = 34. Add 34 to the number set. Current number set: [34, 49], target: 50, just two numbers left.\n     |- Try 49 + 34 = 83. Evaluate 83 != 50, drop this branch.\n     |- Try 49 - 34 = 15. Evaluate 15 != 50, drop this branch.\n     |- Try 49 * 34 = 1666. Evaluate 1666 != 50, drop this branch.\n     |- Try 49 \/ 34 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 39 * 5 = 195. Add 195 to the number set. Current number set: [195, 49], target: 50, just two numbers left.\n     |- Try 195 + 49 = 244. Evaluate 244 != 50, drop this branch.\n     |- Try 195 - 49 = 146. Evaluate 146 != 50, drop this branch.\n     |- Try 195 * 49 = 9555. 9555 exceeds the maximum intermediate result, drop this branch.\n     |- Try 195 \/ 49 = 4.0. 4.0 is a decimal, drop this branch.\n    |- Try 39 \/ 5 = 7.8. 7.8 is a decimal, drop this branch.\n   |- Pick two numbers (49, 39) (numbers left: [5]). Try possible operations.\n    |- Try 49 + 39 = 88. Add 88 to the number set. Current number set: [88, 5], target: 50, just two numbers left.\n     |- Try 88 + 5 = 93. Evaluate 93 != 50, drop this branch.\n     |- Try 88 - 5 = 83. Evaluate 83 != 50, drop this branch.\n     |- Try 88 * 5 = 440. Evaluate 440 != 50, drop this branch.\n     |- Try 88 \/ 5 = 17.6. 17.6 is a decimal, drop this branch.\n    |- Try 49 - 39 = 10. Add 10 to the number set. Current number set: [10, 5], target: 50, just two numbers left.\n     |- Try 10 + 5 = 15. Evaluate 15 != 50, drop this branch.\n     |- Try 10 - 5 = 5. Evaluate 5 != 50, drop this branch.\n     |- Try 10 * 5 = 50. Evaluate 50 == 50, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 10 * 5 = 50\nThe step before: 49 - 39 = 10\nThe first step: 12 - 7 = 5\n\nOutput the solution in the required format:\n<Solution>\n12 - 7 = 5\n49 - 39 = 10\n10 * 5 = 50\n<\/Solution>\n","item":{"nums":[12,49,7,39],"solution":["12 - 7 = 5","49 - 39 = 10","10 * 5 = 50"],"target":50}}
+{"instance_id":"countdown_8k_102","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [20, 2, 48, 8]\nTarget: 43","reference_output":"# Search Procedure\nInitial number set: [20, 2, 48, 8], target: 43. Options for choosing two numbers: [(20, 2), (20, 48), (20, 8), (2, 48), (2, 8), (48, 8)].\n |- Pick two numbers (20, 2) (numbers left: [48, 8]). Try possible operations.\n  |- Try 20 + 2 = 22. Add 22 to the number set. Current number set: [22, 48, 8], target: 43. Options for choosing two numbers: [(22, 48), (22, 8), (48, 8)].\n   |- Pick two numbers (22, 48) (numbers left: [8]). Try possible operations.\n    |- Try 48 + 22 = 70. Add 70 to the number set. Current number set: [70, 8], target: 43, just two numbers left.\n     |- Try 70 + 8 = 78. Evaluate 78 != 43, drop this branch.\n     |- Try 70 - 8 = 62. Evaluate 62 != 43, drop this branch.\n     |- Try 70 * 8 = 560. Evaluate 560 != 43, drop this branch.\n     |- Try 70 \/ 8 = 8.8. 8.8 is a decimal, drop this branch.\n    |- Try 48 - 22 = 26. Add 26 to the number set. Current number set: [26, 8], target: 43, just two numbers left.\n     |- Try 26 + 8 = 34. Evaluate 34 != 43, drop this branch.\n     |- Try 26 - 8 = 18. Evaluate 18 != 43, drop this branch.\n     |- Try 26 * 8 = 208. Evaluate 208 != 43, drop this branch.\n     |- Try 26 \/ 8 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 48 * 22 = 1056. Add 1056 to the number set. Current number set: [1056, 8], target: 43, just two numbers left.\n     |- Try 1056 + 8 = 1064. Evaluate 1064 != 43, drop this branch.\n     |- Try 1056 - 8 = 1048. Evaluate 1048 != 43, drop this branch.\n     |- Try 1056 * 8 = 8448. 8448 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1056 \/ 8 = 132. Evaluate 132 != 43, drop this branch.\n    |- Try 48 \/ 22 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (22, 8) (numbers left: [48]). Try possible operations.\n    |- Try 22 + 8 = 30. Add 30 to the number set. Current number set: [30, 48], target: 43, just two numbers left.\n     |- Try 48 + 30 = 78. Evaluate 78 != 43, drop this branch.\n     |- Try 48 - 30 = 18. Evaluate 18 != 43, drop this branch.\n     |- Try 48 * 30 = 1440. Evaluate 1440 != 43, drop this branch.\n     |- Try 48 \/ 30 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 22 - 8 = 14. Add 14 to the number set. Current number set: [14, 48], target: 43, just two numbers left.\n     |- Try 48 + 14 = 62. Evaluate 62 != 43, drop this branch.\n     |- Try 48 - 14 = 34. Evaluate 34 != 43, drop this branch.\n     |- Try 48 * 14 = 672. Evaluate 672 != 43, drop this branch.\n     |- Try 48 \/ 14 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 22 * 8 = 176. Add 176 to the number set. Current number set: [176, 48], target: 43, just two numbers left.\n     |- Try 176 + 48 = 224. Evaluate 224 != 43, drop this branch.\n     |- Try 176 - 48 = 128. Evaluate 128 != 43, drop this branch.\n     |- Try 176 * 48 = 8448. 8448 exceeds the maximum intermediate result, drop this branch.\n     |- Try 176 \/ 48 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 22 \/ 8 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (48, 8) (numbers left: [22]). Try possible operations.\n    |- Try 48 + 8 = 56. Add 56 to the number set. Current number set: [56, 22], target: 43, just two numbers left.\n     |- Try 56 + 22 = 78. Evaluate 78 != 43, drop this branch.\n     |- Try 56 - 22 = 34. Evaluate 34 != 43, drop this branch.\n     |- Try 56 * 22 = 1232. Evaluate 1232 != 43, drop this branch.\n     |- Try 56 \/ 22 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 48 - 8 = 40. Add 40 to the number set. Current number set: [40, 22], target: 43, just two numbers left.\n     |- Try 40 + 22 = 62. Evaluate 62 != 43, drop this branch.\n     |- Try 40 - 22 = 18. Evaluate 18 != 43, drop this branch.\n     |- Try 40 * 22 = 880. Evaluate 880 != 43, drop this branch.\n     |- Try 40 \/ 22 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 48 * 8 = 384. Add 384 to the number set. Current number set: [384, 22], target: 43, just two numbers left.\n     |- Try 384 + 22 = 406. Evaluate 406 != 43, drop this branch.\n     |- Try 384 - 22 = 362. Evaluate 362 != 43, drop this branch.\n     |- Try 384 * 22 = 8448. 8448 exceeds the maximum intermediate result, drop this branch.\n     |- Try 384 \/ 22 = 17.5. 17.5 is a decimal, drop this branch.\n    |- Try 48 \/ 8 = 6. Add 6 to the number set. Current number set: [6, 22], target: 43, just two numbers left.\n     |- Try 22 + 6 = 28. Evaluate 28 != 43, drop this branch.\n     |- Try 22 - 6 = 16. Evaluate 16 != 43, drop this branch.\n     |- Try 22 * 6 = 132. Evaluate 132 != 43, drop this branch.\n     |- Try 22 \/ 6 = 3.7. 3.7 is a decimal, drop this branch.\n  |- Try 20 - 2 = 18. Add 18 to the number set. Current number set: [18, 48, 8], target: 43. Options for choosing two numbers: [(18, 48), (18, 8), (48, 8)].\n   |- Pick two numbers (18, 48) (numbers left: [8]). Try possible operations.\n    |- Try 48 + 18 = 66. Add 66 to the number set. Current number set: [66, 8], target: 43, just two numbers left.\n     |- Try 66 + 8 = 74. Evaluate 74 != 43, drop this branch.\n     |- Try 66 - 8 = 58. Evaluate 58 != 43, drop this branch.\n     |- Try 66 * 8 = 528. Evaluate 528 != 43, drop this branch.\n     |- Try 66 \/ 8 = 8.2. 8.2 is a decimal, drop this branch.\n    |- Try 48 - 18 = 30. Add 30 to the number set. Current number set: [30, 8], target: 43, just two numbers left.\n     |- Try 30 + 8 = 38. Evaluate 38 != 43, drop this branch.\n     |- Try 30 - 8 = 22. Evaluate 22 != 43, drop this branch.\n     |- Try 30 * 8 = 240. Evaluate 240 != 43, drop this branch.\n     |- Try 30 \/ 8 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 48 * 18 = 864. Add 864 to the number set. Current number set: [864, 8], target: 43, just two numbers left.\n     |- Try 864 + 8 = 872. Evaluate 872 != 43, drop this branch.\n     |- Try 864 - 8 = 856. Evaluate 856 != 43, drop this branch.\n     |- Try 864 * 8 = 6912. 6912 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 8 = 108. Evaluate 108 != 43, drop this branch.\n    |- Try 48 \/ 18 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (18, 8) (numbers left: [48]). Try possible operations.\n    |- Try 18 + 8 = 26. Add 26 to the number set. Current number set: [26, 48], target: 43, just two numbers left.\n     |- Try 48 + 26 = 74. Evaluate 74 != 43, drop this branch.\n     |- Try 48 - 26 = 22. Evaluate 22 != 43, drop this branch.\n     |- Try 48 * 26 = 1248. Evaluate 1248 != 43, drop this branch.\n     |- Try 48 \/ 26 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 - 8 = 10. Add 10 to the number set. Current number set: [10, 48], target: 43, just two numbers left.\n     |- Try 48 + 10 = 58. Evaluate 58 != 43, drop this branch.\n     |- Try 48 - 10 = 38. Evaluate 38 != 43, drop this branch.\n     |- Try 48 * 10 = 480. Evaluate 480 != 43, drop this branch.\n     |- Try 48 \/ 10 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 18 * 8 = 144. Add 144 to the number set. Current number set: [144, 48], target: 43, just two numbers left.\n     |- Try 144 + 48 = 192. Evaluate 192 != 43, drop this branch.\n     |- Try 144 - 48 = 96. Evaluate 96 != 43, drop this branch.\n     |- Try 144 * 48 = 6912. 6912 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 48 = 3. Evaluate 3 != 43, drop this branch.\n    |- Try 18 \/ 8 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (48, 8) (numbers left: [18]). Try possible operations.\n    |- Try 48 + 8 = 56. Add 56 to the number set. Current number set: [56, 18], target: 43, just two numbers left.\n     |- Try 56 + 18 = 74. Evaluate 74 != 43, drop this branch.\n     |- Try 56 - 18 = 38. Evaluate 38 != 43, drop this branch.\n     |- Try 56 * 18 = 1008. Evaluate 1008 != 43, drop this branch.\n     |- Try 56 \/ 18 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 48 - 8 = 40. Add 40 to the number set. Current number set: [40, 18], target: 43, just two numbers left.\n     |- Try 40 + 18 = 58. Evaluate 58 != 43, drop this branch.\n     |- Try 40 - 18 = 22. Evaluate 22 != 43, drop this branch.\n     |- Try 40 * 18 = 720. Evaluate 720 != 43, drop this branch.\n     |- Try 40 \/ 18 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 48 * 8 = 384. Add 384 to the number set. Current number set: [384, 18], target: 43, just two numbers left.\n     |- Try 384 + 18 = 402. Evaluate 402 != 43, drop this branch.\n     |- Try 384 - 18 = 366. Evaluate 366 != 43, drop this branch.\n     |- Try 384 * 18 = 6912. 6912 exceeds the maximum intermediate result, drop this branch.\n     |- Try 384 \/ 18 = 21.3. 21.3 is a decimal, drop this branch.\n    |- Try 48 \/ 8 = 6. Add 6 to the number set. Current number set: [6, 18], target: 43, just two numbers left.\n     |- Try 18 + 6 = 24. Evaluate 24 != 43, drop this branch.\n     |- Try 18 - 6 = 12. Evaluate 12 != 43, drop this branch.\n     |- Try 18 * 6 = 108. Evaluate 108 != 43, drop this branch.\n     |- Try 18 \/ 6 = 3. Evaluate 3 != 43, drop this branch.\n  |- Try 20 * 2 = 40. Add 40 to the number set. Current number set: [40, 48, 8], target: 43. Options for choosing two numbers: [(40, 48), (40, 8), (48, 8)].\n   |- Pick two numbers (40, 48) (numbers left: [8]). Try possible operations.\n    |- Try 48 + 40 = 88. Add 88 to the number set. Current number set: [88, 8], target: 43, just two numbers left.\n     |- Try 88 + 8 = 96. Evaluate 96 != 43, drop this branch.\n     |- Try 88 - 8 = 80. Evaluate 80 != 43, drop this branch.\n     |- Try 88 * 8 = 704. Evaluate 704 != 43, drop this branch.\n     |- Try 88 \/ 8 = 11. Evaluate 11 != 43, drop this branch.\n    |- Try 48 - 40 = 8. Add 8 to the number set. Current number set: [8, 8], target: 43, just two numbers left.\n     |- Try 8 + 8 = 16. Evaluate 16 != 43, drop this branch.\n     |- Try 8 - 8 = 0. Evaluate 0 != 43, drop this branch.\n     |- Try 8 * 8 = 64. Evaluate 64 != 43, drop this branch.\n     |- Try 8 \/ 8 = 1. Evaluate 1 != 43, drop this branch.\n    |- Try 48 * 40 = 1920. Add 1920 to the number set. Current number set: [1920, 8], target: 43, just two numbers left.\n     |- Try 1920 + 8 = 1928. Evaluate 1928 != 43, drop this branch.\n     |- Try 1920 - 8 = 1912. Evaluate 1912 != 43, drop this branch.\n     |- Try 1920 * 8 = 15360. 15360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1920 \/ 8 = 240. Evaluate 240 != 43, drop this branch.\n    |- Try 48 \/ 40 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (40, 8) (numbers left: [48]). Try possible operations.\n    |- Try 40 + 8 = 48. Add 48 to the number set. Current number set: [48, 48], target: 43, just two numbers left.\n     |- Try 48 + 48 = 96. Evaluate 96 != 43, drop this branch.\n     |- Try 48 - 48 = 0. Evaluate 0 != 43, drop this branch.\n     |- Try 48 * 48 = 2304. 2304 exceeds the maximum intermediate result, drop this branch.\n     |- Try 48 \/ 48 = 1. Evaluate 1 != 43, drop this branch.\n    |- Try 40 - 8 = 32. Add 32 to the number set. Current number set: [32, 48], target: 43, just two numbers left.\n     |- Try 48 + 32 = 80. Evaluate 80 != 43, drop this branch.\n     |- Try 48 - 32 = 16. Evaluate 16 != 43, drop this branch.\n     |- Try 48 * 32 = 1536. Evaluate 1536 != 43, drop this branch.\n     |- Try 48 \/ 32 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 40 * 8 = 320. Add 320 to the number set. Current number set: [320, 48], target: 43, just two numbers left.\n     |- Try 320 + 48 = 368. Evaluate 368 != 43, drop this branch.\n     |- Try 320 - 48 = 272. Evaluate 272 != 43, drop this branch.\n     |- Try 320 * 48 = 15360. 15360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 320 \/ 48 = 6.7. 6.7 is a decimal, drop this branch.\n    |- Try 40 \/ 8 = 5. Add 5 to the number set. Current number set: [5, 48], target: 43, just two numbers left.\n     |- Try 48 + 5 = 53. Evaluate 53 != 43, drop this branch.\n     |- Try 48 - 5 = 43. Evaluate 43 == 43, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 48 - 5 = 43\nThe step before: 40 \/ 8 = 5\nThe first step: 20 * 2 = 40\n\nOutput the solution in the required format:\n<Solution>\n20 * 2 = 40\n40 \/ 8 = 5\n48 - 5 = 43\n<\/Solution>\n","item":{"nums":[20,2,48,8],"solution":["20 * 2 = 40","40 \/ 8 = 5","48 - 5 = 43"],"target":43}}
+{"instance_id":"countdown_8k_103","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [19, 36, 47, 3]\nTarget: 16","reference_output":"# Search Procedure\nInitial number set: [19, 36, 47, 3], target: 16. Options for choosing two numbers: [(19, 36), (19, 47), (19, 3), (36, 47), (36, 3), (47, 3)].\n |- Pick two numbers (19, 36) (numbers left: [47, 3]). Try possible operations.\n  |- Try 36 + 19 = 55. Add 55 to the number set. Current number set: [55, 47, 3], target: 16. Options for choosing two numbers: [(55, 47), (55, 3), (47, 3)].\n   |- Pick two numbers (55, 47) (numbers left: [3]). Try possible operations.\n    |- Try 55 + 47 = 102. Add 102 to the number set. Current number set: [102, 3], target: 16, just two numbers left.\n     |- Try 102 + 3 = 105. Evaluate 105 != 16, drop this branch.\n     |- Try 102 - 3 = 99. Evaluate 99 != 16, drop this branch.\n     |- Try 102 * 3 = 306. Evaluate 306 != 16, drop this branch.\n     |- Try 102 \/ 3 = 34. Evaluate 34 != 16, drop this branch.\n    |- Try 55 - 47 = 8. Add 8 to the number set. Current number set: [8, 3], target: 16, just two numbers left.\n     |- Try 8 + 3 = 11. Evaluate 11 != 16, drop this branch.\n     |- Try 8 - 3 = 5. Evaluate 5 != 16, drop this branch.\n     |- Try 8 * 3 = 24. Evaluate 24 != 16, drop this branch.\n     |- Try 8 \/ 3 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 55 * 47 = 2585. 2585 exceeds the maximum intermediate result, drop this branch.\n    |- Try 55 \/ 47 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (55, 3) (numbers left: [47]). Try possible operations.\n    |- Try 55 + 3 = 58. Add 58 to the number set. Current number set: [58, 47], target: 16, just two numbers left.\n     |- Try 58 + 47 = 105. Evaluate 105 != 16, drop this branch.\n     |- Try 58 - 47 = 11. Evaluate 11 != 16, drop this branch.\n     |- Try 58 * 47 = 2726. 2726 exceeds the maximum intermediate result, drop this branch.\n     |- Try 58 \/ 47 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 55 - 3 = 52. Add 52 to the number set. Current number set: [52, 47], target: 16, just two numbers left.\n     |- Try 52 + 47 = 99. Evaluate 99 != 16, drop this branch.\n     |- Try 52 - 47 = 5. Evaluate 5 != 16, drop this branch.\n     |- Try 52 * 47 = 2444. 2444 exceeds the maximum intermediate result, drop this branch.\n     |- Try 52 \/ 47 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 55 * 3 = 165. Add 165 to the number set. Current number set: [165, 47], target: 16, just two numbers left.\n     |- Try 165 + 47 = 212. Evaluate 212 != 16, drop this branch.\n     |- Try 165 - 47 = 118. Evaluate 118 != 16, drop this branch.\n     |- Try 165 * 47 = 7755. 7755 exceeds the maximum intermediate result, drop this branch.\n     |- Try 165 \/ 47 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 55 \/ 3 = 18.3. 18.3 is a decimal, drop this branch.\n   |- Pick two numbers (47, 3) (numbers left: [55]). Try possible operations.\n    |- Try 47 + 3 = 50. Add 50 to the number set. Current number set: [50, 55], target: 16, just two numbers left.\n     |- Try 55 + 50 = 105. Evaluate 105 != 16, drop this branch.\n     |- Try 55 - 50 = 5. Evaluate 5 != 16, drop this branch.\n     |- Try 55 * 50 = 2750. 2750 exceeds the maximum intermediate result, drop this branch.\n     |- Try 55 \/ 50 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 47 - 3 = 44. Add 44 to the number set. Current number set: [44, 55], target: 16, just two numbers left.\n     |- Try 55 + 44 = 99. Evaluate 99 != 16, drop this branch.\n     |- Try 55 - 44 = 11. Evaluate 11 != 16, drop this branch.\n     |- Try 55 * 44 = 2420. 2420 exceeds the maximum intermediate result, drop this branch.\n     |- Try 55 \/ 44 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 47 * 3 = 141. Add 141 to the number set. Current number set: [141, 55], target: 16, just two numbers left.\n     |- Try 141 + 55 = 196. Evaluate 196 != 16, drop this branch.\n     |- Try 141 - 55 = 86. Evaluate 86 != 16, drop this branch.\n     |- Try 141 * 55 = 7755. 7755 exceeds the maximum intermediate result, drop this branch.\n     |- Try 141 \/ 55 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 47 \/ 3 = 15.7. 15.7 is a decimal, drop this branch.\n  |- Try 36 - 19 = 17. Add 17 to the number set. Current number set: [17, 47, 3], target: 16. Options for choosing two numbers: [(17, 47), (17, 3), (47, 3)].\n   |- Pick two numbers (17, 47) (numbers left: [3]). Try possible operations.\n    |- Try 47 + 17 = 64. Add 64 to the number set. Current number set: [64, 3], target: 16, just two numbers left.\n     |- Try 64 + 3 = 67. Evaluate 67 != 16, drop this branch.\n     |- Try 64 - 3 = 61. Evaluate 61 != 16, drop this branch.\n     |- Try 64 * 3 = 192. Evaluate 192 != 16, drop this branch.\n     |- Try 64 \/ 3 = 21.3. 21.3 is a decimal, drop this branch.\n    |- Try 47 - 17 = 30. Add 30 to the number set. Current number set: [30, 3], target: 16, just two numbers left.\n     |- Try 30 + 3 = 33. Evaluate 33 != 16, drop this branch.\n     |- Try 30 - 3 = 27. Evaluate 27 != 16, drop this branch.\n     |- Try 30 * 3 = 90. Evaluate 90 != 16, drop this branch.\n     |- Try 30 \/ 3 = 10. Evaluate 10 != 16, drop this branch.\n    |- Try 47 * 17 = 799. Add 799 to the number set. Current number set: [799, 3], target: 16, just two numbers left.\n     |- Try 799 + 3 = 802. Evaluate 802 != 16, drop this branch.\n     |- Try 799 - 3 = 796. Evaluate 796 != 16, drop this branch.\n     |- Try 799 * 3 = 2397. 2397 exceeds the maximum intermediate result, drop this branch.\n     |- Try 799 \/ 3 = 266.3. 266.3 is a decimal, drop this branch.\n    |- Try 47 \/ 17 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (17, 3) (numbers left: [47]). Try possible operations.\n    |- Try 17 + 3 = 20. Add 20 to the number set. Current number set: [20, 47], target: 16, just two numbers left.\n     |- Try 47 + 20 = 67. Evaluate 67 != 16, drop this branch.\n     |- Try 47 - 20 = 27. Evaluate 27 != 16, drop this branch.\n     |- Try 47 * 20 = 940. Evaluate 940 != 16, drop this branch.\n     |- Try 47 \/ 20 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 17 - 3 = 14. Add 14 to the number set. Current number set: [14, 47], target: 16, just two numbers left.\n     |- Try 47 + 14 = 61. Evaluate 61 != 16, drop this branch.\n     |- Try 47 - 14 = 33. Evaluate 33 != 16, drop this branch.\n     |- Try 47 * 14 = 658. Evaluate 658 != 16, drop this branch.\n     |- Try 47 \/ 14 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 17 * 3 = 51. Add 51 to the number set. Current number set: [51, 47], target: 16, just two numbers left.\n     |- Try 51 + 47 = 98. Evaluate 98 != 16, drop this branch.\n     |- Try 51 - 47 = 4. Evaluate 4 != 16, drop this branch.\n     |- Try 51 * 47 = 2397. 2397 exceeds the maximum intermediate result, drop this branch.\n     |- Try 51 \/ 47 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 17 \/ 3 = 5.7. 5.7 is a decimal, drop this branch.\n   |- Pick two numbers (47, 3) (numbers left: [17]). Try possible operations.\n    |- Try 47 + 3 = 50. Add 50 to the number set. Current number set: [50, 17], target: 16, just two numbers left.\n     |- Try 50 + 17 = 67. Evaluate 67 != 16, drop this branch.\n     |- Try 50 - 17 = 33. Evaluate 33 != 16, drop this branch.\n     |- Try 50 * 17 = 850. Evaluate 850 != 16, drop this branch.\n     |- Try 50 \/ 17 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 47 - 3 = 44. Add 44 to the number set. Current number set: [44, 17], target: 16, just two numbers left.\n     |- Try 44 + 17 = 61. Evaluate 61 != 16, drop this branch.\n     |- Try 44 - 17 = 27. Evaluate 27 != 16, drop this branch.\n     |- Try 44 * 17 = 748. Evaluate 748 != 16, drop this branch.\n     |- Try 44 \/ 17 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 47 * 3 = 141. Add 141 to the number set. Current number set: [141, 17], target: 16, just two numbers left.\n     |- Try 141 + 17 = 158. Evaluate 158 != 16, drop this branch.\n     |- Try 141 - 17 = 124. Evaluate 124 != 16, drop this branch.\n     |- Try 141 * 17 = 2397. 2397 exceeds the maximum intermediate result, drop this branch.\n     |- Try 141 \/ 17 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 47 \/ 3 = 15.7. 15.7 is a decimal, drop this branch.\n  |- Try 36 * 19 = 684. Add 684 to the number set. Current number set: [684, 47, 3], target: 16. Options for choosing two numbers: [(684, 47), (684, 3), (47, 3)].\n   |- Pick two numbers (684, 47) (numbers left: [3]). Try possible operations.\n    |- Try 684 + 47 = 731. Add 731 to the number set. Current number set: [731, 3], target: 16, just two numbers left.\n     |- Try 731 + 3 = 734. Evaluate 734 != 16, drop this branch.\n     |- Try 731 - 3 = 728. Evaluate 728 != 16, drop this branch.\n     |- Try 731 * 3 = 2193. 2193 exceeds the maximum intermediate result, drop this branch.\n     |- Try 731 \/ 3 = 243.7. 243.7 is a decimal, drop this branch.\n    |- Try 684 - 47 = 637. Add 637 to the number set. Current number set: [637, 3], target: 16, just two numbers left.\n     |- Try 637 + 3 = 640. Evaluate 640 != 16, drop this branch.\n     |- Try 637 - 3 = 634. Evaluate 634 != 16, drop this branch.\n     |- Try 637 * 3 = 1911. Evaluate 1911 != 16, drop this branch.\n     |- Try 637 \/ 3 = 212.3. 212.3 is a decimal, drop this branch.\n    |- Try 684 * 47 = 32148. 32148 exceeds the maximum intermediate result, drop this branch.\n    |- Try 684 \/ 47 = 14.6. 14.6 is a decimal, drop this branch.\n   |- Pick two numbers (684, 3) (numbers left: [47]). Try possible operations.\n    |- Try 684 + 3 = 687. Add 687 to the number set. Current number set: [687, 47], target: 16, just two numbers left.\n     |- Try 687 + 47 = 734. Evaluate 734 != 16, drop this branch.\n     |- Try 687 - 47 = 640. Evaluate 640 != 16, drop this branch.\n     |- Try 687 * 47 = 32289. 32289 exceeds the maximum intermediate result, drop this branch.\n     |- Try 687 \/ 47 = 14.6. 14.6 is a decimal, drop this branch.\n    |- Try 684 - 3 = 681. Add 681 to the number set. Current number set: [681, 47], target: 16, just two numbers left.\n     |- Try 681 + 47 = 728. Evaluate 728 != 16, drop this branch.\n     |- Try 681 - 47 = 634. Evaluate 634 != 16, drop this branch.\n     |- Try 681 * 47 = 32007. 32007 exceeds the maximum intermediate result, drop this branch.\n     |- Try 681 \/ 47 = 14.5. 14.5 is a decimal, drop this branch.\n    |- Try 684 * 3 = 2052. 2052 exceeds the maximum intermediate result, drop this branch.\n    |- Try 684 \/ 3 = 228. Add 228 to the number set. Current number set: [228, 47], target: 16, just two numbers left.\n     |- Try 228 + 47 = 275. Evaluate 275 != 16, drop this branch.\n     |- Try 228 - 47 = 181. Evaluate 181 != 16, drop this branch.\n     |- Try 228 * 47 = 10716. 10716 exceeds the maximum intermediate result, drop this branch.\n     |- Try 228 \/ 47 = 4.9. 4.9 is a decimal, drop this branch.\n   |- Pick two numbers (47, 3) (numbers left: [684]). Try possible operations.\n    |- Try 47 + 3 = 50. Add 50 to the number set. Current number set: [50, 684], target: 16, just two numbers left.\n     |- Try 684 + 50 = 734. Evaluate 734 != 16, drop this branch.\n     |- Try 684 - 50 = 634. Evaluate 634 != 16, drop this branch.\n     |- Try 684 * 50 = 34200. 34200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 684 \/ 50 = 13.7. 13.7 is a decimal, drop this branch.\n    |- Try 47 - 3 = 44. Add 44 to the number set. Current number set: [44, 684], target: 16, just two numbers left.\n     |- Try 684 + 44 = 728. Evaluate 728 != 16, drop this branch.\n     |- Try 684 - 44 = 640. Evaluate 640 != 16, drop this branch.\n     |- Try 684 * 44 = 30096. 30096 exceeds the maximum intermediate result, drop this branch.\n     |- Try 684 \/ 44 = 15.5. 15.5 is a decimal, drop this branch.\n    |- Try 47 * 3 = 141. Add 141 to the number set. Current number set: [141, 684], target: 16, just two numbers left.\n     |- Try 684 + 141 = 825. Evaluate 825 != 16, drop this branch.\n     |- Try 684 - 141 = 543. Evaluate 543 != 16, drop this branch.\n     |- Try 684 * 141 = 96444. 96444 exceeds the maximum intermediate result, drop this branch.\n     |- Try 684 \/ 141 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 47 \/ 3 = 15.7. 15.7 is a decimal, drop this branch.\n  |- Try 36 \/ 19 = 1.9. 1.9 is a decimal, drop this branch.\n |- Pick two numbers (19, 47) (numbers left: [36, 3]). Try possible operations.\n  |- Try 47 + 19 = 66. Add 66 to the number set. Current number set: [66, 36, 3], target: 16. Options for choosing two numbers: [(66, 36), (66, 3), (36, 3)].\n   |- Pick two numbers (66, 36) (numbers left: [3]). Try possible operations.\n    |- Try 66 + 36 = 102. Add 102 to the number set. Current number set: [102, 3], target: 16, just two numbers left.\n     |- Try 102 + 3 = 105. Evaluate 105 != 16, drop this branch.\n     |- Try 102 - 3 = 99. Evaluate 99 != 16, drop this branch.\n     |- Try 102 * 3 = 306. Evaluate 306 != 16, drop this branch.\n     |- Try 102 \/ 3 = 34. Evaluate 34 != 16, drop this branch.\n    |- Try 66 - 36 = 30. Add 30 to the number set. Current number set: [30, 3], target: 16, just two numbers left.\n     |- Try 30 + 3 = 33. Evaluate 33 != 16, drop this branch.\n     |- Try 30 - 3 = 27. Evaluate 27 != 16, drop this branch.\n     |- Try 30 * 3 = 90. Evaluate 90 != 16, drop this branch.\n     |- Try 30 \/ 3 = 10. Evaluate 10 != 16, drop this branch.\n    |- Try 66 * 36 = 2376. 2376 exceeds the maximum intermediate result, drop this branch.\n    |- Try 66 \/ 36 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (66, 3) (numbers left: [36]). Try possible operations.\n    |- Try 66 + 3 = 69. Add 69 to the number set. Current number set: [69, 36], target: 16, just two numbers left.\n     |- Try 69 + 36 = 105. Evaluate 105 != 16, drop this branch.\n     |- Try 69 - 36 = 33. Evaluate 33 != 16, drop this branch.\n     |- Try 69 * 36 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 69 \/ 36 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 66 - 3 = 63. Add 63 to the number set. Current number set: [63, 36], target: 16, just two numbers left.\n     |- Try 63 + 36 = 99. Evaluate 99 != 16, drop this branch.\n     |- Try 63 - 36 = 27. Evaluate 27 != 16, drop this branch.\n     |- Try 63 * 36 = 2268. 2268 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 36 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 66 * 3 = 198. Add 198 to the number set. Current number set: [198, 36], target: 16, just two numbers left.\n     |- Try 198 + 36 = 234. Evaluate 234 != 16, drop this branch.\n     |- Try 198 - 36 = 162. Evaluate 162 != 16, drop this branch.\n     |- Try 198 * 36 = 7128. 7128 exceeds the maximum intermediate result, drop this branch.\n     |- Try 198 \/ 36 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 66 \/ 3 = 22. Add 22 to the number set. Current number set: [22, 36], target: 16, just two numbers left.\n     |- Try 36 + 22 = 58. Evaluate 58 != 16, drop this branch.\n     |- Try 36 - 22 = 14. Evaluate 14 != 16, drop this branch.\n     |- Try 36 * 22 = 792. Evaluate 792 != 16, drop this branch.\n     |- Try 36 \/ 22 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (36, 3) (numbers left: [66]). Try possible operations.\n    |- Try 36 + 3 = 39. Add 39 to the number set. Current number set: [39, 66], target: 16, just two numbers left.\n     |- Try 66 + 39 = 105. Evaluate 105 != 16, drop this branch.\n     |- Try 66 - 39 = 27. Evaluate 27 != 16, drop this branch.\n     |- Try 66 * 39 = 2574. 2574 exceeds the maximum intermediate result, drop this branch.\n     |- Try 66 \/ 39 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 36 - 3 = 33. Add 33 to the number set. Current number set: [33, 66], target: 16, just two numbers left.\n     |- Try 66 + 33 = 99. Evaluate 99 != 16, drop this branch.\n     |- Try 66 - 33 = 33. Evaluate 33 != 16, drop this branch.\n     |- Try 66 * 33 = 2178. 2178 exceeds the maximum intermediate result, drop this branch.\n     |- Try 66 \/ 33 = 2. Evaluate 2 != 16, drop this branch.\n    |- Try 36 * 3 = 108. Add 108 to the number set. Current number set: [108, 66], target: 16, just two numbers left.\n     |- Try 108 + 66 = 174. Evaluate 174 != 16, drop this branch.\n     |- Try 108 - 66 = 42. Evaluate 42 != 16, drop this branch.\n     |- Try 108 * 66 = 7128. 7128 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 66 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 36 \/ 3 = 12. Add 12 to the number set. Current number set: [12, 66], target: 16, just two numbers left.\n     |- Try 66 + 12 = 78. Evaluate 78 != 16, drop this branch.\n     |- Try 66 - 12 = 54. Evaluate 54 != 16, drop this branch.\n     |- Try 66 * 12 = 792. Evaluate 792 != 16, drop this branch.\n     |- Try 66 \/ 12 = 5.5. 5.5 is a decimal, drop this branch.\n  |- Try 47 - 19 = 28. Add 28 to the number set. Current number set: [28, 36, 3], target: 16. Options for choosing two numbers: [(28, 36), (28, 3), (36, 3)].\n   |- Pick two numbers (28, 36) (numbers left: [3]). Try possible operations.\n    |- Try 36 + 28 = 64. Add 64 to the number set. Current number set: [64, 3], target: 16, just two numbers left.\n     |- Try 64 + 3 = 67. Evaluate 67 != 16, drop this branch.\n     |- Try 64 - 3 = 61. Evaluate 61 != 16, drop this branch.\n     |- Try 64 * 3 = 192. Evaluate 192 != 16, drop this branch.\n     |- Try 64 \/ 3 = 21.3. 21.3 is a decimal, drop this branch.\n    |- Try 36 - 28 = 8. Add 8 to the number set. Current number set: [8, 3], target: 16, just two numbers left.\n     |- Try 8 + 3 = 11. Evaluate 11 != 16, drop this branch.\n     |- Try 8 - 3 = 5. Evaluate 5 != 16, drop this branch.\n     |- Try 8 * 3 = 24. Evaluate 24 != 16, drop this branch.\n     |- Try 8 \/ 3 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 36 * 28 = 1008. Add 1008 to the number set. Current number set: [1008, 3], target: 16, just two numbers left.\n     |- Try 1008 + 3 = 1011. Evaluate 1011 != 16, drop this branch.\n     |- Try 1008 - 3 = 1005. Evaluate 1005 != 16, drop this branch.\n     |- Try 1008 * 3 = 3024. 3024 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1008 \/ 3 = 336. Evaluate 336 != 16, drop this branch.\n    |- Try 36 \/ 28 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (28, 3) (numbers left: [36]). Try possible operations.\n    |- Try 28 + 3 = 31. Add 31 to the number set. Current number set: [31, 36], target: 16, just two numbers left.\n     |- Try 36 + 31 = 67. Evaluate 67 != 16, drop this branch.\n     |- Try 36 - 31 = 5. Evaluate 5 != 16, drop this branch.\n     |- Try 36 * 31 = 1116. Evaluate 1116 != 16, drop this branch.\n     |- Try 36 \/ 31 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 28 - 3 = 25. Add 25 to the number set. Current number set: [25, 36], target: 16, just two numbers left.\n     |- Try 36 + 25 = 61. Evaluate 61 != 16, drop this branch.\n     |- Try 36 - 25 = 11. Evaluate 11 != 16, drop this branch.\n     |- Try 36 * 25 = 900. Evaluate 900 != 16, drop this branch.\n     |- Try 36 \/ 25 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 28 * 3 = 84. Add 84 to the number set. Current number set: [84, 36], target: 16, just two numbers left.\n     |- Try 84 + 36 = 120. Evaluate 120 != 16, drop this branch.\n     |- Try 84 - 36 = 48. Evaluate 48 != 16, drop this branch.\n     |- Try 84 * 36 = 3024. 3024 exceeds the maximum intermediate result, drop this branch.\n     |- Try 84 \/ 36 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 28 \/ 3 = 9.3. 9.3 is a decimal, drop this branch.\n   |- Pick two numbers (36, 3) (numbers left: [28]). Try possible operations.\n    |- Try 36 + 3 = 39. Add 39 to the number set. Current number set: [39, 28], target: 16, just two numbers left.\n     |- Try 39 + 28 = 67. Evaluate 67 != 16, drop this branch.\n     |- Try 39 - 28 = 11. Evaluate 11 != 16, drop this branch.\n     |- Try 39 * 28 = 1092. Evaluate 1092 != 16, drop this branch.\n     |- Try 39 \/ 28 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 36 - 3 = 33. Add 33 to the number set. Current number set: [33, 28], target: 16, just two numbers left.\n     |- Try 33 + 28 = 61. Evaluate 61 != 16, drop this branch.\n     |- Try 33 - 28 = 5. Evaluate 5 != 16, drop this branch.\n     |- Try 33 * 28 = 924. Evaluate 924 != 16, drop this branch.\n     |- Try 33 \/ 28 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 36 * 3 = 108. Add 108 to the number set. Current number set: [108, 28], target: 16, just two numbers left.\n     |- Try 108 + 28 = 136. Evaluate 136 != 16, drop this branch.\n     |- Try 108 - 28 = 80. Evaluate 80 != 16, drop this branch.\n     |- Try 108 * 28 = 3024. 3024 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 28 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 36 \/ 3 = 12. Add 12 to the number set. Current number set: [12, 28], target: 16, just two numbers left.\n     |- Try 28 + 12 = 40. Evaluate 40 != 16, drop this branch.\n     |- Try 28 - 12 = 16. Evaluate 16 == 16, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 28 - 12 = 16\nThe step before: 36 \/ 3 = 12\nThe first step: 47 - 19 = 28\n\nOutput the solution in the required format:\n<Solution>\n47 - 19 = 28\n36 \/ 3 = 12\n28 - 12 = 16\n<\/Solution>\n","item":{"nums":[19,36,47,3],"solution":["47 - 19 = 28","36 \/ 3 = 12","28 - 12 = 16"],"target":16}}
+{"instance_id":"countdown_8k_104","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [18, 10, 30, 7]\nTarget: 47","reference_output":"# Search Procedure\nInitial number set: [18, 10, 30, 7], target: 47. Options for choosing two numbers: [(18, 10), (18, 30), (18, 7), (10, 30), (10, 7), (30, 7)].\n |- Pick two numbers (18, 10) (numbers left: [30, 7]). Try possible operations.\n  |- Try 18 + 10 = 28. Add 28 to the number set. Current number set: [28, 30, 7], target: 47. Options for choosing two numbers: [(28, 30), (28, 7), (30, 7)].\n   |- Pick two numbers (28, 30) (numbers left: [7]). Try possible operations.\n    |- Try 30 + 28 = 58. Add 58 to the number set. Current number set: [58, 7], target: 47, just two numbers left.\n     |- Try 58 + 7 = 65. Evaluate 65 != 47, drop this branch.\n     |- Try 58 - 7 = 51. Evaluate 51 != 47, drop this branch.\n     |- Try 58 * 7 = 406. Evaluate 406 != 47, drop this branch.\n     |- Try 58 \/ 7 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 30 - 28 = 2. Add 2 to the number set. Current number set: [2, 7], target: 47, just two numbers left.\n     |- Try 7 + 2 = 9. Evaluate 9 != 47, drop this branch.\n     |- Try 7 - 2 = 5. Evaluate 5 != 47, drop this branch.\n     |- Try 7 * 2 = 14. Evaluate 14 != 47, drop this branch.\n     |- Try 7 \/ 2 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 30 * 28 = 840. Add 840 to the number set. Current number set: [840, 7], target: 47, just two numbers left.\n     |- Try 840 + 7 = 847. Evaluate 847 != 47, drop this branch.\n     |- Try 840 - 7 = 833. Evaluate 833 != 47, drop this branch.\n     |- Try 840 * 7 = 5880. 5880 exceeds the maximum intermediate result, drop this branch.\n     |- Try 840 \/ 7 = 120. Evaluate 120 != 47, drop this branch.\n    |- Try 30 \/ 28 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (28, 7) (numbers left: [30]). Try possible operations.\n    |- Try 28 + 7 = 35. Add 35 to the number set. Current number set: [35, 30], target: 47, just two numbers left.\n     |- Try 35 + 30 = 65. Evaluate 65 != 47, drop this branch.\n     |- Try 35 - 30 = 5. Evaluate 5 != 47, drop this branch.\n     |- Try 35 * 30 = 1050. Evaluate 1050 != 47, drop this branch.\n     |- Try 35 \/ 30 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 28 - 7 = 21. Add 21 to the number set. Current number set: [21, 30], target: 47, just two numbers left.\n     |- Try 30 + 21 = 51. Evaluate 51 != 47, drop this branch.\n     |- Try 30 - 21 = 9. Evaluate 9 != 47, drop this branch.\n     |- Try 30 * 21 = 630. Evaluate 630 != 47, drop this branch.\n     |- Try 30 \/ 21 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 28 * 7 = 196. Add 196 to the number set. Current number set: [196, 30], target: 47, just two numbers left.\n     |- Try 196 + 30 = 226. Evaluate 226 != 47, drop this branch.\n     |- Try 196 - 30 = 166. Evaluate 166 != 47, drop this branch.\n     |- Try 196 * 30 = 5880. 5880 exceeds the maximum intermediate result, drop this branch.\n     |- Try 196 \/ 30 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 28 \/ 7 = 4. Add 4 to the number set. Current number set: [4, 30], target: 47, just two numbers left.\n     |- Try 30 + 4 = 34. Evaluate 34 != 47, drop this branch.\n     |- Try 30 - 4 = 26. Evaluate 26 != 47, drop this branch.\n     |- Try 30 * 4 = 120. Evaluate 120 != 47, drop this branch.\n     |- Try 30 \/ 4 = 7.5. 7.5 is a decimal, drop this branch.\n   |- Pick two numbers (30, 7) (numbers left: [28]). Try possible operations.\n    |- Try 30 + 7 = 37. Add 37 to the number set. Current number set: [37, 28], target: 47, just two numbers left.\n     |- Try 37 + 28 = 65. Evaluate 65 != 47, drop this branch.\n     |- Try 37 - 28 = 9. Evaluate 9 != 47, drop this branch.\n     |- Try 37 * 28 = 1036. Evaluate 1036 != 47, drop this branch.\n     |- Try 37 \/ 28 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 30 - 7 = 23. Add 23 to the number set. Current number set: [23, 28], target: 47, just two numbers left.\n     |- Try 28 + 23 = 51. Evaluate 51 != 47, drop this branch.\n     |- Try 28 - 23 = 5. Evaluate 5 != 47, drop this branch.\n     |- Try 28 * 23 = 644. Evaluate 644 != 47, drop this branch.\n     |- Try 28 \/ 23 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 30 * 7 = 210. Add 210 to the number set. Current number set: [210, 28], target: 47, just two numbers left.\n     |- Try 210 + 28 = 238. Evaluate 238 != 47, drop this branch.\n     |- Try 210 - 28 = 182. Evaluate 182 != 47, drop this branch.\n     |- Try 210 * 28 = 5880. 5880 exceeds the maximum intermediate result, drop this branch.\n     |- Try 210 \/ 28 = 7.5. 7.5 is a decimal, drop this branch.\n    |- Try 30 \/ 7 = 4.3. 4.3 is a decimal, drop this branch.\n  |- Try 18 - 10 = 8. Add 8 to the number set. Current number set: [8, 30, 7], target: 47. Options for choosing two numbers: [(8, 30), (8, 7), (30, 7)].\n   |- Pick two numbers (8, 30) (numbers left: [7]). Try possible operations.\n    |- Try 30 + 8 = 38. Add 38 to the number set. Current number set: [38, 7], target: 47, just two numbers left.\n     |- Try 38 + 7 = 45. Evaluate 45 != 47, drop this branch.\n     |- Try 38 - 7 = 31. Evaluate 31 != 47, drop this branch.\n     |- Try 38 * 7 = 266. Evaluate 266 != 47, drop this branch.\n     |- Try 38 \/ 7 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 30 - 8 = 22. Add 22 to the number set. Current number set: [22, 7], target: 47, just two numbers left.\n     |- Try 22 + 7 = 29. Evaluate 29 != 47, drop this branch.\n     |- Try 22 - 7 = 15. Evaluate 15 != 47, drop this branch.\n     |- Try 22 * 7 = 154. Evaluate 154 != 47, drop this branch.\n     |- Try 22 \/ 7 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 30 * 8 = 240. Add 240 to the number set. Current number set: [240, 7], target: 47, just two numbers left.\n     |- Try 240 + 7 = 247. Evaluate 247 != 47, drop this branch.\n     |- Try 240 - 7 = 233. Evaluate 233 != 47, drop this branch.\n     |- Try 240 * 7 = 1680. Evaluate 1680 != 47, drop this branch.\n     |- Try 240 \/ 7 = 34.3. 34.3 is a decimal, drop this branch.\n    |- Try 30 \/ 8 = 3.8. 3.8 is a decimal, drop this branch.\n   |- Pick two numbers (8, 7) (numbers left: [30]). Try possible operations.\n    |- Try 8 + 7 = 15. Add 15 to the number set. Current number set: [15, 30], target: 47, just two numbers left.\n     |- Try 30 + 15 = 45. Evaluate 45 != 47, drop this branch.\n     |- Try 30 - 15 = 15. Evaluate 15 != 47, drop this branch.\n     |- Try 30 * 15 = 450. Evaluate 450 != 47, drop this branch.\n     |- Try 30 \/ 15 = 2. Evaluate 2 != 47, drop this branch.\n    |- Try 8 - 7 = 1. Add 1 to the number set. Current number set: [1, 30], target: 47, just two numbers left.\n     |- Try 30 + 1 = 31. Evaluate 31 != 47, drop this branch.\n     |- Try 30 - 1 = 29. Evaluate 29 != 47, drop this branch.\n     |- Try 30 * 1 = 30. Evaluate 30 != 47, drop this branch.\n     |- Try 30 \/ 1 = 30. Evaluate 30 != 47, drop this branch.\n    |- Try 8 * 7 = 56. Add 56 to the number set. Current number set: [56, 30], target: 47, just two numbers left.\n     |- Try 56 + 30 = 86. Evaluate 86 != 47, drop this branch.\n     |- Try 56 - 30 = 26. Evaluate 26 != 47, drop this branch.\n     |- Try 56 * 30 = 1680. Evaluate 1680 != 47, drop this branch.\n     |- Try 56 \/ 30 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 8 \/ 7 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (30, 7) (numbers left: [8]). Try possible operations.\n    |- Try 30 + 7 = 37. Add 37 to the number set. Current number set: [37, 8], target: 47, just two numbers left.\n     |- Try 37 + 8 = 45. Evaluate 45 != 47, drop this branch.\n     |- Try 37 - 8 = 29. Evaluate 29 != 47, drop this branch.\n     |- Try 37 * 8 = 296. Evaluate 296 != 47, drop this branch.\n     |- Try 37 \/ 8 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 30 - 7 = 23. Add 23 to the number set. Current number set: [23, 8], target: 47, just two numbers left.\n     |- Try 23 + 8 = 31. Evaluate 31 != 47, drop this branch.\n     |- Try 23 - 8 = 15. Evaluate 15 != 47, drop this branch.\n     |- Try 23 * 8 = 184. Evaluate 184 != 47, drop this branch.\n     |- Try 23 \/ 8 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 30 * 7 = 210. Add 210 to the number set. Current number set: [210, 8], target: 47, just two numbers left.\n     |- Try 210 + 8 = 218. Evaluate 218 != 47, drop this branch.\n     |- Try 210 - 8 = 202. Evaluate 202 != 47, drop this branch.\n     |- Try 210 * 8 = 1680. Evaluate 1680 != 47, drop this branch.\n     |- Try 210 \/ 8 = 26.2. 26.2 is a decimal, drop this branch.\n    |- Try 30 \/ 7 = 4.3. 4.3 is a decimal, drop this branch.\n  |- Try 18 * 10 = 180. Add 180 to the number set. Current number set: [180, 30, 7], target: 47. Options for choosing two numbers: [(180, 30), (180, 7), (30, 7)].\n   |- Pick two numbers (180, 30) (numbers left: [7]). Try possible operations.\n    |- Try 180 + 30 = 210. Add 210 to the number set. Current number set: [210, 7], target: 47, just two numbers left.\n     |- Try 210 + 7 = 217. Evaluate 217 != 47, drop this branch.\n     |- Try 210 - 7 = 203. Evaluate 203 != 47, drop this branch.\n     |- Try 210 * 7 = 1470. Evaluate 1470 != 47, drop this branch.\n     |- Try 210 \/ 7 = 30. Evaluate 30 != 47, drop this branch.\n    |- Try 180 - 30 = 150. Add 150 to the number set. Current number set: [150, 7], target: 47, just two numbers left.\n     |- Try 150 + 7 = 157. Evaluate 157 != 47, drop this branch.\n     |- Try 150 - 7 = 143. Evaluate 143 != 47, drop this branch.\n     |- Try 150 * 7 = 1050. Evaluate 1050 != 47, drop this branch.\n     |- Try 150 \/ 7 = 21.4. 21.4 is a decimal, drop this branch.\n    |- Try 180 * 30 = 5400. 5400 exceeds the maximum intermediate result, drop this branch.\n    |- Try 180 \/ 30 = 6. Add 6 to the number set. Current number set: [6, 7], target: 47, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 47, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 47, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 47, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (180, 7) (numbers left: [30]). Try possible operations.\n    |- Try 180 + 7 = 187. Add 187 to the number set. Current number set: [187, 30], target: 47, just two numbers left.\n     |- Try 187 + 30 = 217. Evaluate 217 != 47, drop this branch.\n     |- Try 187 - 30 = 157. Evaluate 157 != 47, drop this branch.\n     |- Try 187 * 30 = 5610. 5610 exceeds the maximum intermediate result, drop this branch.\n     |- Try 187 \/ 30 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 180 - 7 = 173. Add 173 to the number set. Current number set: [173, 30], target: 47, just two numbers left.\n     |- Try 173 + 30 = 203. Evaluate 203 != 47, drop this branch.\n     |- Try 173 - 30 = 143. Evaluate 143 != 47, drop this branch.\n     |- Try 173 * 30 = 5190. 5190 exceeds the maximum intermediate result, drop this branch.\n     |- Try 173 \/ 30 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 180 * 7 = 1260. Add 1260 to the number set. Current number set: [1260, 30], target: 47, just two numbers left.\n     |- Try 1260 + 30 = 1290. Evaluate 1290 != 47, drop this branch.\n     |- Try 1260 - 30 = 1230. Evaluate 1230 != 47, drop this branch.\n     |- Try 1260 * 30 = 37800. 37800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1260 \/ 30 = 42. Evaluate 42 != 47, drop this branch.\n    |- Try 180 \/ 7 = 25.7. 25.7 is a decimal, drop this branch.\n   |- Pick two numbers (30, 7) (numbers left: [180]). Try possible operations.\n    |- Try 30 + 7 = 37. Add 37 to the number set. Current number set: [37, 180], target: 47, just two numbers left.\n     |- Try 180 + 37 = 217. Evaluate 217 != 47, drop this branch.\n     |- Try 180 - 37 = 143. Evaluate 143 != 47, drop this branch.\n     |- Try 180 * 37 = 6660. 6660 exceeds the maximum intermediate result, drop this branch.\n     |- Try 180 \/ 37 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 30 - 7 = 23. Add 23 to the number set. Current number set: [23, 180], target: 47, just two numbers left.\n     |- Try 180 + 23 = 203. Evaluate 203 != 47, drop this branch.\n     |- Try 180 - 23 = 157. Evaluate 157 != 47, drop this branch.\n     |- Try 180 * 23 = 4140. 4140 exceeds the maximum intermediate result, drop this branch.\n     |- Try 180 \/ 23 = 7.8. 7.8 is a decimal, drop this branch.\n    |- Try 30 * 7 = 210. Add 210 to the number set. Current number set: [210, 180], target: 47, just two numbers left.\n     |- Try 210 + 180 = 390. Evaluate 390 != 47, drop this branch.\n     |- Try 210 - 180 = 30. Evaluate 30 != 47, drop this branch.\n     |- Try 210 * 180 = 37800. 37800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 210 \/ 180 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 30 \/ 7 = 4.3. 4.3 is a decimal, drop this branch.\n  |- Try 18 \/ 10 = 1.8. 1.8 is a decimal, drop this branch.\n |- Pick two numbers (18, 30) (numbers left: [10, 7]). Try possible operations.\n  |- Try 30 + 18 = 48. Add 48 to the number set. Current number set: [48, 10, 7], target: 47. Options for choosing two numbers: [(48, 10), (48, 7), (10, 7)].\n   |- Pick two numbers (48, 10) (numbers left: [7]). Try possible operations.\n    |- Try 48 + 10 = 58. Add 58 to the number set. Current number set: [58, 7], target: 47, just two numbers left.\n     |- Try 58 + 7 = 65. Evaluate 65 != 47, drop this branch.\n     |- Try 58 - 7 = 51. Evaluate 51 != 47, drop this branch.\n     |- Try 58 * 7 = 406. Evaluate 406 != 47, drop this branch.\n     |- Try 58 \/ 7 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 48 - 10 = 38. Add 38 to the number set. Current number set: [38, 7], target: 47, just two numbers left.\n     |- Try 38 + 7 = 45. Evaluate 45 != 47, drop this branch.\n     |- Try 38 - 7 = 31. Evaluate 31 != 47, drop this branch.\n     |- Try 38 * 7 = 266. Evaluate 266 != 47, drop this branch.\n     |- Try 38 \/ 7 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 48 * 10 = 480. Add 480 to the number set. Current number set: [480, 7], target: 47, just two numbers left.\n     |- Try 480 + 7 = 487. Evaluate 487 != 47, drop this branch.\n     |- Try 480 - 7 = 473. Evaluate 473 != 47, drop this branch.\n     |- Try 480 * 7 = 3360. 3360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 480 \/ 7 = 68.6. 68.6 is a decimal, drop this branch.\n    |- Try 48 \/ 10 = 4.8. 4.8 is a decimal, drop this branch.\n   |- Pick two numbers (48, 7) (numbers left: [10]). Try possible operations.\n    |- Try 48 + 7 = 55. Add 55 to the number set. Current number set: [55, 10], target: 47, just two numbers left.\n     |- Try 55 + 10 = 65. Evaluate 65 != 47, drop this branch.\n     |- Try 55 - 10 = 45. Evaluate 45 != 47, drop this branch.\n     |- Try 55 * 10 = 550. Evaluate 550 != 47, drop this branch.\n     |- Try 55 \/ 10 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 48 - 7 = 41. Add 41 to the number set. Current number set: [41, 10], target: 47, just two numbers left.\n     |- Try 41 + 10 = 51. Evaluate 51 != 47, drop this branch.\n     |- Try 41 - 10 = 31. Evaluate 31 != 47, drop this branch.\n     |- Try 41 * 10 = 410. Evaluate 410 != 47, drop this branch.\n     |- Try 41 \/ 10 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 48 * 7 = 336. Add 336 to the number set. Current number set: [336, 10], target: 47, just two numbers left.\n     |- Try 336 + 10 = 346. Evaluate 346 != 47, drop this branch.\n     |- Try 336 - 10 = 326. Evaluate 326 != 47, drop this branch.\n     |- Try 336 * 10 = 3360. 3360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 336 \/ 10 = 33.6. 33.6 is a decimal, drop this branch.\n    |- Try 48 \/ 7 = 6.9. 6.9 is a decimal, drop this branch.\n   |- Pick two numbers (10, 7) (numbers left: [48]). Try possible operations.\n    |- Try 10 + 7 = 17. Add 17 to the number set. Current number set: [17, 48], target: 47, just two numbers left.\n     |- Try 48 + 17 = 65. Evaluate 65 != 47, drop this branch.\n     |- Try 48 - 17 = 31. Evaluate 31 != 47, drop this branch.\n     |- Try 48 * 17 = 816. Evaluate 816 != 47, drop this branch.\n     |- Try 48 \/ 17 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 10 - 7 = 3. Add 3 to the number set. Current number set: [3, 48], target: 47, just two numbers left.\n     |- Try 48 + 3 = 51. Evaluate 51 != 47, drop this branch.\n     |- Try 48 - 3 = 45. Evaluate 45 != 47, drop this branch.\n     |- Try 48 * 3 = 144. Evaluate 144 != 47, drop this branch.\n     |- Try 48 \/ 3 = 16. Evaluate 16 != 47, drop this branch.\n    |- Try 10 * 7 = 70. Add 70 to the number set. Current number set: [70, 48], target: 47, just two numbers left.\n     |- Try 70 + 48 = 118. Evaluate 118 != 47, drop this branch.\n     |- Try 70 - 48 = 22. Evaluate 22 != 47, drop this branch.\n     |- Try 70 * 48 = 3360. 3360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 70 \/ 48 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 10 \/ 7 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 30 - 18 = 12. Add 12 to the number set. Current number set: [12, 10, 7], target: 47. Options for choosing two numbers: [(12, 10), (12, 7), (10, 7)].\n   |- Pick two numbers (12, 10) (numbers left: [7]). Try possible operations.\n    |- Try 12 + 10 = 22. Add 22 to the number set. Current number set: [22, 7], target: 47, just two numbers left.\n     |- Try 22 + 7 = 29. Evaluate 29 != 47, drop this branch.\n     |- Try 22 - 7 = 15. Evaluate 15 != 47, drop this branch.\n     |- Try 22 * 7 = 154. Evaluate 154 != 47, drop this branch.\n     |- Try 22 \/ 7 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 12 - 10 = 2. Add 2 to the number set. Current number set: [2, 7], target: 47, just two numbers left.\n     |- Try 7 + 2 = 9. Evaluate 9 != 47, drop this branch.\n     |- Try 7 - 2 = 5. Evaluate 5 != 47, drop this branch.\n     |- Try 7 * 2 = 14. Evaluate 14 != 47, drop this branch.\n     |- Try 7 \/ 2 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 12 * 10 = 120. Add 120 to the number set. Current number set: [120, 7], target: 47, just two numbers left.\n     |- Try 120 + 7 = 127. Evaluate 127 != 47, drop this branch.\n     |- Try 120 - 7 = 113. Evaluate 113 != 47, drop this branch.\n     |- Try 120 * 7 = 840. Evaluate 840 != 47, drop this branch.\n     |- Try 120 \/ 7 = 17.1. 17.1 is a decimal, drop this branch.\n    |- Try 12 \/ 10 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (12, 7) (numbers left: [10]). Try possible operations.\n    |- Try 12 + 7 = 19. Add 19 to the number set. Current number set: [19, 10], target: 47, just two numbers left.\n     |- Try 19 + 10 = 29. Evaluate 29 != 47, drop this branch.\n     |- Try 19 - 10 = 9. Evaluate 9 != 47, drop this branch.\n     |- Try 19 * 10 = 190. Evaluate 190 != 47, drop this branch.\n     |- Try 19 \/ 10 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 12 - 7 = 5. Add 5 to the number set. Current number set: [5, 10], target: 47, just two numbers left.\n     |- Try 10 + 5 = 15. Evaluate 15 != 47, drop this branch.\n     |- Try 10 - 5 = 5. Evaluate 5 != 47, drop this branch.\n     |- Try 10 * 5 = 50. Evaluate 50 != 47, drop this branch.\n     |- Try 10 \/ 5 = 2. Evaluate 2 != 47, drop this branch.\n    |- Try 12 * 7 = 84. Add 84 to the number set. Current number set: [84, 10], target: 47, just two numbers left.\n     |- Try 84 + 10 = 94. Evaluate 94 != 47, drop this branch.\n     |- Try 84 - 10 = 74. Evaluate 74 != 47, drop this branch.\n     |- Try 84 * 10 = 840. Evaluate 840 != 47, drop this branch.\n     |- Try 84 \/ 10 = 8.4. 8.4 is a decimal, drop this branch.\n    |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (10, 7) (numbers left: [12]). Try possible operations.\n    |- Try 10 + 7 = 17. Add 17 to the number set. Current number set: [17, 12], target: 47, just two numbers left.\n     |- Try 17 + 12 = 29. Evaluate 29 != 47, drop this branch.\n     |- Try 17 - 12 = 5. Evaluate 5 != 47, drop this branch.\n     |- Try 17 * 12 = 204. Evaluate 204 != 47, drop this branch.\n     |- Try 17 \/ 12 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 10 - 7 = 3. Add 3 to the number set. Current number set: [3, 12], target: 47, just two numbers left.\n     |- Try 12 + 3 = 15. Evaluate 15 != 47, drop this branch.\n     |- Try 12 - 3 = 9. Evaluate 9 != 47, drop this branch.\n     |- Try 12 * 3 = 36. Evaluate 36 != 47, drop this branch.\n     |- Try 12 \/ 3 = 4. Evaluate 4 != 47, drop this branch.\n    |- Try 10 * 7 = 70. Add 70 to the number set. Current number set: [70, 12], target: 47, just two numbers left.\n     |- Try 70 + 12 = 82. Evaluate 82 != 47, drop this branch.\n     |- Try 70 - 12 = 58. Evaluate 58 != 47, drop this branch.\n     |- Try 70 * 12 = 840. Evaluate 840 != 47, drop this branch.\n     |- Try 70 \/ 12 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 10 \/ 7 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 30 * 18 = 540. Add 540 to the number set. Current number set: [540, 10, 7], target: 47. Options for choosing two numbers: [(540, 10), (540, 7), (10, 7)].\n   |- Pick two numbers (540, 10) (numbers left: [7]). Try possible operations.\n    |- Try 540 + 10 = 550. Add 550 to the number set. Current number set: [550, 7], target: 47, just two numbers left.\n     |- Try 550 + 7 = 557. Evaluate 557 != 47, drop this branch.\n     |- Try 550 - 7 = 543. Evaluate 543 != 47, drop this branch.\n     |- Try 550 * 7 = 3850. 3850 exceeds the maximum intermediate result, drop this branch.\n     |- Try 550 \/ 7 = 78.6. 78.6 is a decimal, drop this branch.\n    |- Try 540 - 10 = 530. Add 530 to the number set. Current number set: [530, 7], target: 47, just two numbers left.\n     |- Try 530 + 7 = 537. Evaluate 537 != 47, drop this branch.\n     |- Try 530 - 7 = 523. Evaluate 523 != 47, drop this branch.\n     |- Try 530 * 7 = 3710. 3710 exceeds the maximum intermediate result, drop this branch.\n     |- Try 530 \/ 7 = 75.7. 75.7 is a decimal, drop this branch.\n    |- Try 540 * 10 = 5400. 5400 exceeds the maximum intermediate result, drop this branch.\n    |- Try 540 \/ 10 = 54. Add 54 to the number set. Current number set: [54, 7], target: 47, just two numbers left.\n     |- Try 54 + 7 = 61. Evaluate 61 != 47, drop this branch.\n     |- Try 54 - 7 = 47. Evaluate 47 == 47, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 54 - 7 = 47\nThe step before: 540 \/ 10 = 54\nThe first step: 30 * 18 = 540\n\nOutput the solution in the required format:\n<Solution>\n30 * 18 = 540\n540 \/ 10 = 54\n54 - 7 = 47\n<\/Solution>\n","item":{"nums":[18,10,30,7],"solution":["30 * 18 = 540","540 \/ 10 = 54","54 - 7 = 47"],"target":47}}
+{"instance_id":"countdown_8k_105","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [17, 35, 22, 35]\nTarget: 28","reference_output":"# Search Procedure\nInitial number set: [17, 35, 22, 35], target: 28. Options for choosing two numbers: [(17, 35), (17, 22), (17, 35), (35, 22), (35, 35), (22, 35)].\n |- Pick two numbers (17, 35) (numbers left: [22, 35]). Try possible operations.\n  |- Try 35 + 17 = 52. Add 52 to the number set. Current number set: [52, 22, 35], target: 28. Options for choosing two numbers: [(52, 22), (52, 35), (22, 35)].\n   |- Pick two numbers (52, 22) (numbers left: [35]). Try possible operations.\n    |- Try 52 + 22 = 74. Add 74 to the number set. Current number set: [74, 35], target: 28, just two numbers left.\n     |- Try 74 + 35 = 109. Evaluate 109 != 28, drop this branch.\n     |- Try 74 - 35 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 74 * 35 = 2590. 2590 exceeds the maximum intermediate result, drop this branch.\n     |- Try 74 \/ 35 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 52 - 22 = 30. Add 30 to the number set. Current number set: [30, 35], target: 28, just two numbers left.\n     |- Try 35 + 30 = 65. Evaluate 65 != 28, drop this branch.\n     |- Try 35 - 30 = 5. Evaluate 5 != 28, drop this branch.\n     |- Try 35 * 30 = 1050. Evaluate 1050 != 28, drop this branch.\n     |- Try 35 \/ 30 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 52 * 22 = 1144. Add 1144 to the number set. Current number set: [1144, 35], target: 28, just two numbers left.\n     |- Try 1144 + 35 = 1179. Evaluate 1179 != 28, drop this branch.\n     |- Try 1144 - 35 = 1109. Evaluate 1109 != 28, drop this branch.\n     |- Try 1144 * 35 = 40040. 40040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1144 \/ 35 = 32.7. 32.7 is a decimal, drop this branch.\n    |- Try 52 \/ 22 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (52, 35) (numbers left: [22]). Try possible operations.\n    |- Try 52 + 35 = 87. Add 87 to the number set. Current number set: [87, 22], target: 28, just two numbers left.\n     |- Try 87 + 22 = 109. Evaluate 109 != 28, drop this branch.\n     |- Try 87 - 22 = 65. Evaluate 65 != 28, drop this branch.\n     |- Try 87 * 22 = 1914. Evaluate 1914 != 28, drop this branch.\n     |- Try 87 \/ 22 = 4.0. 4.0 is a decimal, drop this branch.\n    |- Try 52 - 35 = 17. Add 17 to the number set. Current number set: [17, 22], target: 28, just two numbers left.\n     |- Try 22 + 17 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 22 - 17 = 5. Evaluate 5 != 28, drop this branch.\n     |- Try 22 * 17 = 374. Evaluate 374 != 28, drop this branch.\n     |- Try 22 \/ 17 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 52 * 35 = 1820. Add 1820 to the number set. Current number set: [1820, 22], target: 28, just two numbers left.\n     |- Try 1820 + 22 = 1842. Evaluate 1842 != 28, drop this branch.\n     |- Try 1820 - 22 = 1798. Evaluate 1798 != 28, drop this branch.\n     |- Try 1820 * 22 = 40040. 40040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1820 \/ 22 = 82.7. 82.7 is a decimal, drop this branch.\n    |- Try 52 \/ 35 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (22, 35) (numbers left: [52]). Try possible operations.\n    |- Try 35 + 22 = 57. Add 57 to the number set. Current number set: [57, 52], target: 28, just two numbers left.\n     |- Try 57 + 52 = 109. Evaluate 109 != 28, drop this branch.\n     |- Try 57 - 52 = 5. Evaluate 5 != 28, drop this branch.\n     |- Try 57 * 52 = 2964. 2964 exceeds the maximum intermediate result, drop this branch.\n     |- Try 57 \/ 52 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 35 - 22 = 13. Add 13 to the number set. Current number set: [13, 52], target: 28, just two numbers left.\n     |- Try 52 + 13 = 65. Evaluate 65 != 28, drop this branch.\n     |- Try 52 - 13 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 52 * 13 = 676. Evaluate 676 != 28, drop this branch.\n     |- Try 52 \/ 13 = 4. Evaluate 4 != 28, drop this branch.\n    |- Try 35 * 22 = 770. Add 770 to the number set. Current number set: [770, 52], target: 28, just two numbers left.\n     |- Try 770 + 52 = 822. Evaluate 822 != 28, drop this branch.\n     |- Try 770 - 52 = 718. Evaluate 718 != 28, drop this branch.\n     |- Try 770 * 52 = 40040. 40040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 770 \/ 52 = 14.8. 14.8 is a decimal, drop this branch.\n    |- Try 35 \/ 22 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 35 - 17 = 18. Add 18 to the number set. Current number set: [18, 22, 35], target: 28. Options for choosing two numbers: [(18, 22), (18, 35), (22, 35)].\n   |- Pick two numbers (18, 22) (numbers left: [35]). Try possible operations.\n    |- Try 22 + 18 = 40. Add 40 to the number set. Current number set: [40, 35], target: 28, just two numbers left.\n     |- Try 40 + 35 = 75. Evaluate 75 != 28, drop this branch.\n     |- Try 40 - 35 = 5. Evaluate 5 != 28, drop this branch.\n     |- Try 40 * 35 = 1400. Evaluate 1400 != 28, drop this branch.\n     |- Try 40 \/ 35 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 22 - 18 = 4. Add 4 to the number set. Current number set: [4, 35], target: 28, just two numbers left.\n     |- Try 35 + 4 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 35 - 4 = 31. Evaluate 31 != 28, drop this branch.\n     |- Try 35 * 4 = 140. Evaluate 140 != 28, drop this branch.\n     |- Try 35 \/ 4 = 8.8. 8.8 is a decimal, drop this branch.\n    |- Try 22 * 18 = 396. Add 396 to the number set. Current number set: [396, 35], target: 28, just two numbers left.\n     |- Try 396 + 35 = 431. Evaluate 431 != 28, drop this branch.\n     |- Try 396 - 35 = 361. Evaluate 361 != 28, drop this branch.\n     |- Try 396 * 35 = 13860. 13860 exceeds the maximum intermediate result, drop this branch.\n     |- Try 396 \/ 35 = 11.3. 11.3 is a decimal, drop this branch.\n    |- Try 22 \/ 18 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (18, 35) (numbers left: [22]). Try possible operations.\n    |- Try 35 + 18 = 53. Add 53 to the number set. Current number set: [53, 22], target: 28, just two numbers left.\n     |- Try 53 + 22 = 75. Evaluate 75 != 28, drop this branch.\n     |- Try 53 - 22 = 31. Evaluate 31 != 28, drop this branch.\n     |- Try 53 * 22 = 1166. Evaluate 1166 != 28, drop this branch.\n     |- Try 53 \/ 22 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 35 - 18 = 17. Add 17 to the number set. Current number set: [17, 22], target: 28, just two numbers left.\n     |- Try 22 + 17 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 22 - 17 = 5. Evaluate 5 != 28, drop this branch.\n     |- Try 22 * 17 = 374. Evaluate 374 != 28, drop this branch.\n     |- Try 22 \/ 17 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 35 * 18 = 630. Add 630 to the number set. Current number set: [630, 22], target: 28, just two numbers left.\n     |- Try 630 + 22 = 652. Evaluate 652 != 28, drop this branch.\n     |- Try 630 - 22 = 608. Evaluate 608 != 28, drop this branch.\n     |- Try 630 * 22 = 13860. 13860 exceeds the maximum intermediate result, drop this branch.\n     |- Try 630 \/ 22 = 28.6. 28.6 is a decimal, drop this branch.\n    |- Try 35 \/ 18 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (22, 35) (numbers left: [18]). Try possible operations.\n    |- Try 35 + 22 = 57. Add 57 to the number set. Current number set: [57, 18], target: 28, just two numbers left.\n     |- Try 57 + 18 = 75. Evaluate 75 != 28, drop this branch.\n     |- Try 57 - 18 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 57 * 18 = 1026. Evaluate 1026 != 28, drop this branch.\n     |- Try 57 \/ 18 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 35 - 22 = 13. Add 13 to the number set. Current number set: [13, 18], target: 28, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 28, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 28, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 28, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 35 * 22 = 770. Add 770 to the number set. Current number set: [770, 18], target: 28, just two numbers left.\n     |- Try 770 + 18 = 788. Evaluate 788 != 28, drop this branch.\n     |- Try 770 - 18 = 752. Evaluate 752 != 28, drop this branch.\n     |- Try 770 * 18 = 13860. 13860 exceeds the maximum intermediate result, drop this branch.\n     |- Try 770 \/ 18 = 42.8. 42.8 is a decimal, drop this branch.\n    |- Try 35 \/ 22 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 35 * 17 = 595. Add 595 to the number set. Current number set: [595, 22, 35], target: 28. Options for choosing two numbers: [(595, 22), (595, 35), (22, 35)].\n   |- Pick two numbers (595, 22) (numbers left: [35]). Try possible operations.\n    |- Try 595 + 22 = 617. Add 617 to the number set. Current number set: [617, 35], target: 28, just two numbers left.\n     |- Try 617 + 35 = 652. Evaluate 652 != 28, drop this branch.\n     |- Try 617 - 35 = 582. Evaluate 582 != 28, drop this branch.\n     |- Try 617 * 35 = 21595. 21595 exceeds the maximum intermediate result, drop this branch.\n     |- Try 617 \/ 35 = 17.6. 17.6 is a decimal, drop this branch.\n    |- Try 595 - 22 = 573. Add 573 to the number set. Current number set: [573, 35], target: 28, just two numbers left.\n     |- Try 573 + 35 = 608. Evaluate 608 != 28, drop this branch.\n     |- Try 573 - 35 = 538. Evaluate 538 != 28, drop this branch.\n     |- Try 573 * 35 = 20055. 20055 exceeds the maximum intermediate result, drop this branch.\n     |- Try 573 \/ 35 = 16.4. 16.4 is a decimal, drop this branch.\n    |- Try 595 * 22 = 13090. 13090 exceeds the maximum intermediate result, drop this branch.\n    |- Try 595 \/ 22 = 27.0. 27.0 is a decimal, drop this branch.\n   |- Pick two numbers (595, 35) (numbers left: [22]). Try possible operations.\n    |- Try 595 + 35 = 630. Add 630 to the number set. Current number set: [630, 22], target: 28, just two numbers left.\n     |- Try 630 + 22 = 652. Evaluate 652 != 28, drop this branch.\n     |- Try 630 - 22 = 608. Evaluate 608 != 28, drop this branch.\n     |- Try 630 * 22 = 13860. 13860 exceeds the maximum intermediate result, drop this branch.\n     |- Try 630 \/ 22 = 28.6. 28.6 is a decimal, drop this branch.\n    |- Try 595 - 35 = 560. Add 560 to the number set. Current number set: [560, 22], target: 28, just two numbers left.\n     |- Try 560 + 22 = 582. Evaluate 582 != 28, drop this branch.\n     |- Try 560 - 22 = 538. Evaluate 538 != 28, drop this branch.\n     |- Try 560 * 22 = 12320. 12320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 560 \/ 22 = 25.5. 25.5 is a decimal, drop this branch.\n    |- Try 595 * 35 = 20825. 20825 exceeds the maximum intermediate result, drop this branch.\n    |- Try 595 \/ 35 = 17. Add 17 to the number set. Current number set: [17, 22], target: 28, just two numbers left.\n     |- Try 22 + 17 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 22 - 17 = 5. Evaluate 5 != 28, drop this branch.\n     |- Try 22 * 17 = 374. Evaluate 374 != 28, drop this branch.\n     |- Try 22 \/ 17 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (22, 35) (numbers left: [595]). Try possible operations.\n    |- Try 35 + 22 = 57. Add 57 to the number set. Current number set: [57, 595], target: 28, just two numbers left.\n     |- Try 595 + 57 = 652. Evaluate 652 != 28, drop this branch.\n     |- Try 595 - 57 = 538. Evaluate 538 != 28, drop this branch.\n     |- Try 595 * 57 = 33915. 33915 exceeds the maximum intermediate result, drop this branch.\n     |- Try 595 \/ 57 = 10.4. 10.4 is a decimal, drop this branch.\n    |- Try 35 - 22 = 13. Add 13 to the number set. Current number set: [13, 595], target: 28, just two numbers left.\n     |- Try 595 + 13 = 608. Evaluate 608 != 28, drop this branch.\n     |- Try 595 - 13 = 582. Evaluate 582 != 28, drop this branch.\n     |- Try 595 * 13 = 7735. 7735 exceeds the maximum intermediate result, drop this branch.\n     |- Try 595 \/ 13 = 45.8. 45.8 is a decimal, drop this branch.\n    |- Try 35 * 22 = 770. Add 770 to the number set. Current number set: [770, 595], target: 28, just two numbers left.\n     |- Try 770 + 595 = 1365. Evaluate 1365 != 28, drop this branch.\n     |- Try 770 - 595 = 175. Evaluate 175 != 28, drop this branch.\n     |- Try 770 * 595 = 458150. 458150 exceeds the maximum intermediate result, drop this branch.\n     |- Try 770 \/ 595 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 35 \/ 22 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 35 \/ 17 = 2.1. 2.1 is a decimal, drop this branch.\n |- Pick two numbers (17, 22) (numbers left: [35, 35]). Try possible operations.\n  |- Try 22 + 17 = 39. Add 39 to the number set. Current number set: [39, 35, 35], target: 28. Options for choosing two numbers: [(39, 35), (39, 35), (35, 35)].\n   |- Pick two numbers (39, 35) (numbers left: [35]). Try possible operations.\n    |- Try 39 + 35 = 74. Add 74 to the number set. Current number set: [74, 35], target: 28, just two numbers left.\n     |- Try 74 + 35 = 109. Evaluate 109 != 28, drop this branch.\n     |- Try 74 - 35 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 74 * 35 = 2590. 2590 exceeds the maximum intermediate result, drop this branch.\n     |- Try 74 \/ 35 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 39 - 35 = 4. Add 4 to the number set. Current number set: [4, 35], target: 28, just two numbers left.\n     |- Try 35 + 4 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 35 - 4 = 31. Evaluate 31 != 28, drop this branch.\n     |- Try 35 * 4 = 140. Evaluate 140 != 28, drop this branch.\n     |- Try 35 \/ 4 = 8.8. 8.8 is a decimal, drop this branch.\n    |- Try 39 * 35 = 1365. Add 1365 to the number set. Current number set: [1365, 35], target: 28, just two numbers left.\n     |- Try 1365 + 35 = 1400. Evaluate 1400 != 28, drop this branch.\n     |- Try 1365 - 35 = 1330. Evaluate 1330 != 28, drop this branch.\n     |- Try 1365 * 35 = 47775. 47775 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1365 \/ 35 = 39. Evaluate 39 != 28, drop this branch.\n    |- Try 39 \/ 35 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (39, 35) (numbers left: [35]). Try possible operations.\n    |- Try 39 + 35 = 74. Add 74 to the number set. Current number set: [74, 35], target: 28, just two numbers left.\n     |- Try 74 + 35 = 109. Evaluate 109 != 28, drop this branch.\n     |- Try 74 - 35 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 74 * 35 = 2590. 2590 exceeds the maximum intermediate result, drop this branch.\n     |- Try 74 \/ 35 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 39 - 35 = 4. Add 4 to the number set. Current number set: [4, 35], target: 28, just two numbers left.\n     |- Try 35 + 4 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 35 - 4 = 31. Evaluate 31 != 28, drop this branch.\n     |- Try 35 * 4 = 140. Evaluate 140 != 28, drop this branch.\n     |- Try 35 \/ 4 = 8.8. 8.8 is a decimal, drop this branch.\n    |- Try 39 * 35 = 1365. Add 1365 to the number set. Current number set: [1365, 35], target: 28, just two numbers left.\n     |- Try 1365 + 35 = 1400. Evaluate 1400 != 28, drop this branch.\n     |- Try 1365 - 35 = 1330. Evaluate 1330 != 28, drop this branch.\n     |- Try 1365 * 35 = 47775. 47775 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1365 \/ 35 = 39. Evaluate 39 != 28, drop this branch.\n    |- Try 39 \/ 35 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (35, 35) (numbers left: [39]). Try possible operations.\n    |- Try 35 + 35 = 70. Add 70 to the number set. Current number set: [70, 39], target: 28, just two numbers left.\n     |- Try 70 + 39 = 109. Evaluate 109 != 28, drop this branch.\n     |- Try 70 - 39 = 31. Evaluate 31 != 28, drop this branch.\n     |- Try 70 * 39 = 2730. 2730 exceeds the maximum intermediate result, drop this branch.\n     |- Try 70 \/ 39 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 35 - 35 = 0. Add 0 to the number set. Current number set: [0, 39], target: 28, just two numbers left.\n     |- Try 39 + 0 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 39 - 0 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 39 * 0 = 0. Evaluate 0 != 28, drop this branch.\n     |- Try 39 \/ 0 (invalid operation). drop this branch.\n    |- Try 35 * 35 = 1225. Add 1225 to the number set. Current number set: [1225, 39], target: 28, just two numbers left.\n     |- Try 1225 + 39 = 1264. Evaluate 1264 != 28, drop this branch.\n     |- Try 1225 - 39 = 1186. Evaluate 1186 != 28, drop this branch.\n     |- Try 1225 * 39 = 47775. 47775 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1225 \/ 39 = 31.4. 31.4 is a decimal, drop this branch.\n    |- Try 35 \/ 35 = 1. Add 1 to the number set. Current number set: [1, 39], target: 28, just two numbers left.\n     |- Try 39 + 1 = 40. Evaluate 40 != 28, drop this branch.\n     |- Try 39 - 1 = 38. Evaluate 38 != 28, drop this branch.\n     |- Try 39 * 1 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 39 \/ 1 = 39. Evaluate 39 != 28, drop this branch.\n  |- Try 22 - 17 = 5. Add 5 to the number set. Current number set: [5, 35, 35], target: 28. Options for choosing two numbers: [(5, 35), (5, 35), (35, 35)].\n   |- Pick two numbers (5, 35) (numbers left: [35]). Try possible operations.\n    |- Try 35 + 5 = 40. Add 40 to the number set. Current number set: [40, 35], target: 28, just two numbers left.\n     |- Try 40 + 35 = 75. Evaluate 75 != 28, drop this branch.\n     |- Try 40 - 35 = 5. Evaluate 5 != 28, drop this branch.\n     |- Try 40 * 35 = 1400. Evaluate 1400 != 28, drop this branch.\n     |- Try 40 \/ 35 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 35 - 5 = 30. Add 30 to the number set. Current number set: [30, 35], target: 28, just two numbers left.\n     |- Try 35 + 30 = 65. Evaluate 65 != 28, drop this branch.\n     |- Try 35 - 30 = 5. Evaluate 5 != 28, drop this branch.\n     |- Try 35 * 30 = 1050. Evaluate 1050 != 28, drop this branch.\n     |- Try 35 \/ 30 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 35 * 5 = 175. Add 175 to the number set. Current number set: [175, 35], target: 28, just two numbers left.\n     |- Try 175 + 35 = 210. Evaluate 210 != 28, drop this branch.\n     |- Try 175 - 35 = 140. Evaluate 140 != 28, drop this branch.\n     |- Try 175 * 35 = 6125. 6125 exceeds the maximum intermediate result, drop this branch.\n     |- Try 175 \/ 35 = 5. Evaluate 5 != 28, drop this branch.\n    |- Try 35 \/ 5 = 7. Add 7 to the number set. Current number set: [7, 35], target: 28, just two numbers left.\n     |- Try 35 + 7 = 42. Evaluate 42 != 28, drop this branch.\n     |- Try 35 - 7 = 28. Evaluate 28 == 28, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 35 - 7 = 28\nThe step before: 35 \/ 5 = 7\nThe first step: 22 - 17 = 5\n\nOutput the solution in the required format:\n<Solution>\n22 - 17 = 5\n35 \/ 5 = 7\n35 - 7 = 28\n<\/Solution>\n","item":{"nums":[17,35,22,35],"solution":["22 - 17 = 5","35 \/ 5 = 7","35 - 7 = 28"],"target":28}}
+{"instance_id":"countdown_8k_106","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [35, 14, 19, 17]\nTarget: 14","reference_output":"# Search Procedure\nInitial number set: [35, 14, 19, 17], target: 14. Options for choosing two numbers: [(35, 14), (35, 19), (35, 17), (14, 19), (14, 17), (19, 17)].\n |- Pick two numbers (35, 14) (numbers left: [19, 17]). Try possible operations.\n  |- Try 35 + 14 = 49. Add 49 to the number set. Current number set: [49, 19, 17], target: 14. Options for choosing two numbers: [(49, 19), (49, 17), (19, 17)].\n   |- Pick two numbers (49, 19) (numbers left: [17]). Try possible operations.\n    |- Try 49 + 19 = 68. Add 68 to the number set. Current number set: [68, 17], target: 14, just two numbers left.\n     |- Try 68 + 17 = 85. Evaluate 85 != 14, drop this branch.\n     |- Try 68 - 17 = 51. Evaluate 51 != 14, drop this branch.\n     |- Try 68 * 17 = 1156. Evaluate 1156 != 14, drop this branch.\n     |- Try 68 \/ 17 = 4. Evaluate 4 != 14, drop this branch.\n    |- Try 49 - 19 = 30. Add 30 to the number set. Current number set: [30, 17], target: 14, just two numbers left.\n     |- Try 30 + 17 = 47. Evaluate 47 != 14, drop this branch.\n     |- Try 30 - 17 = 13. Evaluate 13 != 14, drop this branch.\n     |- Try 30 * 17 = 510. Evaluate 510 != 14, drop this branch.\n     |- Try 30 \/ 17 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 49 * 19 = 931. Add 931 to the number set. Current number set: [931, 17], target: 14, just two numbers left.\n     |- Try 931 + 17 = 948. Evaluate 948 != 14, drop this branch.\n     |- Try 931 - 17 = 914. Evaluate 914 != 14, drop this branch.\n     |- Try 931 * 17 = 15827. 15827 exceeds the maximum intermediate result, drop this branch.\n     |- Try 931 \/ 17 = 54.8. 54.8 is a decimal, drop this branch.\n    |- Try 49 \/ 19 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (49, 17) (numbers left: [19]). Try possible operations.\n    |- Try 49 + 17 = 66. Add 66 to the number set. Current number set: [66, 19], target: 14, just two numbers left.\n     |- Try 66 + 19 = 85. Evaluate 85 != 14, drop this branch.\n     |- Try 66 - 19 = 47. Evaluate 47 != 14, drop this branch.\n     |- Try 66 * 19 = 1254. Evaluate 1254 != 14, drop this branch.\n     |- Try 66 \/ 19 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 49 - 17 = 32. Add 32 to the number set. Current number set: [32, 19], target: 14, just two numbers left.\n     |- Try 32 + 19 = 51. Evaluate 51 != 14, drop this branch.\n     |- Try 32 - 19 = 13. Evaluate 13 != 14, drop this branch.\n     |- Try 32 * 19 = 608. Evaluate 608 != 14, drop this branch.\n     |- Try 32 \/ 19 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 49 * 17 = 833. Add 833 to the number set. Current number set: [833, 19], target: 14, just two numbers left.\n     |- Try 833 + 19 = 852. Evaluate 852 != 14, drop this branch.\n     |- Try 833 - 19 = 814. Evaluate 814 != 14, drop this branch.\n     |- Try 833 * 19 = 15827. 15827 exceeds the maximum intermediate result, drop this branch.\n     |- Try 833 \/ 19 = 43.8. 43.8 is a decimal, drop this branch.\n    |- Try 49 \/ 17 = 2.9. 2.9 is a decimal, drop this branch.\n   |- Pick two numbers (19, 17) (numbers left: [49]). Try possible operations.\n    |- Try 19 + 17 = 36. Add 36 to the number set. Current number set: [36, 49], target: 14, just two numbers left.\n     |- Try 49 + 36 = 85. Evaluate 85 != 14, drop this branch.\n     |- Try 49 - 36 = 13. Evaluate 13 != 14, drop this branch.\n     |- Try 49 * 36 = 1764. Evaluate 1764 != 14, drop this branch.\n     |- Try 49 \/ 36 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 19 - 17 = 2. Add 2 to the number set. Current number set: [2, 49], target: 14, just two numbers left.\n     |- Try 49 + 2 = 51. Evaluate 51 != 14, drop this branch.\n     |- Try 49 - 2 = 47. Evaluate 47 != 14, drop this branch.\n     |- Try 49 * 2 = 98. Evaluate 98 != 14, drop this branch.\n     |- Try 49 \/ 2 = 24.5. 24.5 is a decimal, drop this branch.\n    |- Try 19 * 17 = 323. Add 323 to the number set. Current number set: [323, 49], target: 14, just two numbers left.\n     |- Try 323 + 49 = 372. Evaluate 372 != 14, drop this branch.\n     |- Try 323 - 49 = 274. Evaluate 274 != 14, drop this branch.\n     |- Try 323 * 49 = 15827. 15827 exceeds the maximum intermediate result, drop this branch.\n     |- Try 323 \/ 49 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 19 \/ 17 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 35 - 14 = 21. Add 21 to the number set. Current number set: [21, 19, 17], target: 14. Options for choosing two numbers: [(21, 19), (21, 17), (19, 17)].\n   |- Pick two numbers (21, 19) (numbers left: [17]). Try possible operations.\n    |- Try 21 + 19 = 40. Add 40 to the number set. Current number set: [40, 17], target: 14, just two numbers left.\n     |- Try 40 + 17 = 57. Evaluate 57 != 14, drop this branch.\n     |- Try 40 - 17 = 23. Evaluate 23 != 14, drop this branch.\n     |- Try 40 * 17 = 680. Evaluate 680 != 14, drop this branch.\n     |- Try 40 \/ 17 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 21 - 19 = 2. Add 2 to the number set. Current number set: [2, 17], target: 14, just two numbers left.\n     |- Try 17 + 2 = 19. Evaluate 19 != 14, drop this branch.\n     |- Try 17 - 2 = 15. Evaluate 15 != 14, drop this branch.\n     |- Try 17 * 2 = 34. Evaluate 34 != 14, drop this branch.\n     |- Try 17 \/ 2 = 8.5. 8.5 is a decimal, drop this branch.\n    |- Try 21 * 19 = 399. Add 399 to the number set. Current number set: [399, 17], target: 14, just two numbers left.\n     |- Try 399 + 17 = 416. Evaluate 416 != 14, drop this branch.\n     |- Try 399 - 17 = 382. Evaluate 382 != 14, drop this branch.\n     |- Try 399 * 17 = 6783. 6783 exceeds the maximum intermediate result, drop this branch.\n     |- Try 399 \/ 17 = 23.5. 23.5 is a decimal, drop this branch.\n    |- Try 21 \/ 19 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (21, 17) (numbers left: [19]). Try possible operations.\n    |- Try 21 + 17 = 38. Add 38 to the number set. Current number set: [38, 19], target: 14, just two numbers left.\n     |- Try 38 + 19 = 57. Evaluate 57 != 14, drop this branch.\n     |- Try 38 - 19 = 19. Evaluate 19 != 14, drop this branch.\n     |- Try 38 * 19 = 722. Evaluate 722 != 14, drop this branch.\n     |- Try 38 \/ 19 = 2. Evaluate 2 != 14, drop this branch.\n    |- Try 21 - 17 = 4. Add 4 to the number set. Current number set: [4, 19], target: 14, just two numbers left.\n     |- Try 19 + 4 = 23. Evaluate 23 != 14, drop this branch.\n     |- Try 19 - 4 = 15. Evaluate 15 != 14, drop this branch.\n     |- Try 19 * 4 = 76. Evaluate 76 != 14, drop this branch.\n     |- Try 19 \/ 4 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 21 * 17 = 357. Add 357 to the number set. Current number set: [357, 19], target: 14, just two numbers left.\n     |- Try 357 + 19 = 376. Evaluate 376 != 14, drop this branch.\n     |- Try 357 - 19 = 338. Evaluate 338 != 14, drop this branch.\n     |- Try 357 * 19 = 6783. 6783 exceeds the maximum intermediate result, drop this branch.\n     |- Try 357 \/ 19 = 18.8. 18.8 is a decimal, drop this branch.\n    |- Try 21 \/ 17 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (19, 17) (numbers left: [21]). Try possible operations.\n    |- Try 19 + 17 = 36. Add 36 to the number set. Current number set: [36, 21], target: 14, just two numbers left.\n     |- Try 36 + 21 = 57. Evaluate 57 != 14, drop this branch.\n     |- Try 36 - 21 = 15. Evaluate 15 != 14, drop this branch.\n     |- Try 36 * 21 = 756. Evaluate 756 != 14, drop this branch.\n     |- Try 36 \/ 21 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 19 - 17 = 2. Add 2 to the number set. Current number set: [2, 21], target: 14, just two numbers left.\n     |- Try 21 + 2 = 23. Evaluate 23 != 14, drop this branch.\n     |- Try 21 - 2 = 19. Evaluate 19 != 14, drop this branch.\n     |- Try 21 * 2 = 42. Evaluate 42 != 14, drop this branch.\n     |- Try 21 \/ 2 = 10.5. 10.5 is a decimal, drop this branch.\n    |- Try 19 * 17 = 323. Add 323 to the number set. Current number set: [323, 21], target: 14, just two numbers left.\n     |- Try 323 + 21 = 344. Evaluate 344 != 14, drop this branch.\n     |- Try 323 - 21 = 302. Evaluate 302 != 14, drop this branch.\n     |- Try 323 * 21 = 6783. 6783 exceeds the maximum intermediate result, drop this branch.\n     |- Try 323 \/ 21 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 19 \/ 17 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 35 * 14 = 490. Add 490 to the number set. Current number set: [490, 19, 17], target: 14. Options for choosing two numbers: [(490, 19), (490, 17), (19, 17)].\n   |- Pick two numbers (490, 19) (numbers left: [17]). Try possible operations.\n    |- Try 490 + 19 = 509. Add 509 to the number set. Current number set: [509, 17], target: 14, just two numbers left.\n     |- Try 509 + 17 = 526. Evaluate 526 != 14, drop this branch.\n     |- Try 509 - 17 = 492. Evaluate 492 != 14, drop this branch.\n     |- Try 509 * 17 = 8653. 8653 exceeds the maximum intermediate result, drop this branch.\n     |- Try 509 \/ 17 = 29.9. 29.9 is a decimal, drop this branch.\n    |- Try 490 - 19 = 471. Add 471 to the number set. Current number set: [471, 17], target: 14, just two numbers left.\n     |- Try 471 + 17 = 488. Evaluate 488 != 14, drop this branch.\n     |- Try 471 - 17 = 454. Evaluate 454 != 14, drop this branch.\n     |- Try 471 * 17 = 8007. 8007 exceeds the maximum intermediate result, drop this branch.\n     |- Try 471 \/ 17 = 27.7. 27.7 is a decimal, drop this branch.\n    |- Try 490 * 19 = 9310. 9310 exceeds the maximum intermediate result, drop this branch.\n    |- Try 490 \/ 19 = 25.8. 25.8 is a decimal, drop this branch.\n   |- Pick two numbers (490, 17) (numbers left: [19]). Try possible operations.\n    |- Try 490 + 17 = 507. Add 507 to the number set. Current number set: [507, 19], target: 14, just two numbers left.\n     |- Try 507 + 19 = 526. Evaluate 526 != 14, drop this branch.\n     |- Try 507 - 19 = 488. Evaluate 488 != 14, drop this branch.\n     |- Try 507 * 19 = 9633. 9633 exceeds the maximum intermediate result, drop this branch.\n     |- Try 507 \/ 19 = 26.7. 26.7 is a decimal, drop this branch.\n    |- Try 490 - 17 = 473. Add 473 to the number set. Current number set: [473, 19], target: 14, just two numbers left.\n     |- Try 473 + 19 = 492. Evaluate 492 != 14, drop this branch.\n     |- Try 473 - 19 = 454. Evaluate 454 != 14, drop this branch.\n     |- Try 473 * 19 = 8987. 8987 exceeds the maximum intermediate result, drop this branch.\n     |- Try 473 \/ 19 = 24.9. 24.9 is a decimal, drop this branch.\n    |- Try 490 * 17 = 8330. 8330 exceeds the maximum intermediate result, drop this branch.\n    |- Try 490 \/ 17 = 28.8. 28.8 is a decimal, drop this branch.\n   |- Pick two numbers (19, 17) (numbers left: [490]). Try possible operations.\n    |- Try 19 + 17 = 36. Add 36 to the number set. Current number set: [36, 490], target: 14, just two numbers left.\n     |- Try 490 + 36 = 526. Evaluate 526 != 14, drop this branch.\n     |- Try 490 - 36 = 454. Evaluate 454 != 14, drop this branch.\n     |- Try 490 * 36 = 17640. 17640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 490 \/ 36 = 13.6. 13.6 is a decimal, drop this branch.\n    |- Try 19 - 17 = 2. Add 2 to the number set. Current number set: [2, 490], target: 14, just two numbers left.\n     |- Try 490 + 2 = 492. Evaluate 492 != 14, drop this branch.\n     |- Try 490 - 2 = 488. Evaluate 488 != 14, drop this branch.\n     |- Try 490 * 2 = 980. Evaluate 980 != 14, drop this branch.\n     |- Try 490 \/ 2 = 245. Evaluate 245 != 14, drop this branch.\n    |- Try 19 * 17 = 323. Add 323 to the number set. Current number set: [323, 490], target: 14, just two numbers left.\n     |- Try 490 + 323 = 813. Evaluate 813 != 14, drop this branch.\n     |- Try 490 - 323 = 167. Evaluate 167 != 14, drop this branch.\n     |- Try 490 * 323 = 158270. 158270 exceeds the maximum intermediate result, drop this branch.\n     |- Try 490 \/ 323 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 19 \/ 17 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 35 \/ 14 = 2.5. 2.5 is a decimal, drop this branch.\n |- Pick two numbers (35, 19) (numbers left: [14, 17]). Try possible operations.\n  |- Try 35 + 19 = 54. Add 54 to the number set. Current number set: [54, 14, 17], target: 14. Options for choosing two numbers: [(54, 14), (54, 17), (14, 17)].\n   |- Pick two numbers (54, 14) (numbers left: [17]). Try possible operations.\n    |- Try 54 + 14 = 68. Add 68 to the number set. Current number set: [68, 17], target: 14, just two numbers left.\n     |- Try 68 + 17 = 85. Evaluate 85 != 14, drop this branch.\n     |- Try 68 - 17 = 51. Evaluate 51 != 14, drop this branch.\n     |- Try 68 * 17 = 1156. Evaluate 1156 != 14, drop this branch.\n     |- Try 68 \/ 17 = 4. Evaluate 4 != 14, drop this branch.\n    |- Try 54 - 14 = 40. Add 40 to the number set. Current number set: [40, 17], target: 14, just two numbers left.\n     |- Try 40 + 17 = 57. Evaluate 57 != 14, drop this branch.\n     |- Try 40 - 17 = 23. Evaluate 23 != 14, drop this branch.\n     |- Try 40 * 17 = 680. Evaluate 680 != 14, drop this branch.\n     |- Try 40 \/ 17 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 54 * 14 = 756. Add 756 to the number set. Current number set: [756, 17], target: 14, just two numbers left.\n     |- Try 756 + 17 = 773. Evaluate 773 != 14, drop this branch.\n     |- Try 756 - 17 = 739. Evaluate 739 != 14, drop this branch.\n     |- Try 756 * 17 = 12852. 12852 exceeds the maximum intermediate result, drop this branch.\n     |- Try 756 \/ 17 = 44.5. 44.5 is a decimal, drop this branch.\n    |- Try 54 \/ 14 = 3.9. 3.9 is a decimal, drop this branch.\n   |- Pick two numbers (54, 17) (numbers left: [14]). Try possible operations.\n    |- Try 54 + 17 = 71. Add 71 to the number set. Current number set: [71, 14], target: 14, just two numbers left.\n     |- Try 71 + 14 = 85. Evaluate 85 != 14, drop this branch.\n     |- Try 71 - 14 = 57. Evaluate 57 != 14, drop this branch.\n     |- Try 71 * 14 = 994. Evaluate 994 != 14, drop this branch.\n     |- Try 71 \/ 14 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 54 - 17 = 37. Add 37 to the number set. Current number set: [37, 14], target: 14, just two numbers left.\n     |- Try 37 + 14 = 51. Evaluate 51 != 14, drop this branch.\n     |- Try 37 - 14 = 23. Evaluate 23 != 14, drop this branch.\n     |- Try 37 * 14 = 518. Evaluate 518 != 14, drop this branch.\n     |- Try 37 \/ 14 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 54 * 17 = 918. Add 918 to the number set. Current number set: [918, 14], target: 14, just two numbers left.\n     |- Try 918 + 14 = 932. Evaluate 932 != 14, drop this branch.\n     |- Try 918 - 14 = 904. Evaluate 904 != 14, drop this branch.\n     |- Try 918 * 14 = 12852. 12852 exceeds the maximum intermediate result, drop this branch.\n     |- Try 918 \/ 14 = 65.6. 65.6 is a decimal, drop this branch.\n    |- Try 54 \/ 17 = 3.2. 3.2 is a decimal, drop this branch.\n   |- Pick two numbers (14, 17) (numbers left: [54]). Try possible operations.\n    |- Try 17 + 14 = 31. Add 31 to the number set. Current number set: [31, 54], target: 14, just two numbers left.\n     |- Try 54 + 31 = 85. Evaluate 85 != 14, drop this branch.\n     |- Try 54 - 31 = 23. Evaluate 23 != 14, drop this branch.\n     |- Try 54 * 31 = 1674. Evaluate 1674 != 14, drop this branch.\n     |- Try 54 \/ 31 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 17 - 14 = 3. Add 3 to the number set. Current number set: [3, 54], target: 14, just two numbers left.\n     |- Try 54 + 3 = 57. Evaluate 57 != 14, drop this branch.\n     |- Try 54 - 3 = 51. Evaluate 51 != 14, drop this branch.\n     |- Try 54 * 3 = 162. Evaluate 162 != 14, drop this branch.\n     |- Try 54 \/ 3 = 18. Evaluate 18 != 14, drop this branch.\n    |- Try 17 * 14 = 238. Add 238 to the number set. Current number set: [238, 54], target: 14, just two numbers left.\n     |- Try 238 + 54 = 292. Evaluate 292 != 14, drop this branch.\n     |- Try 238 - 54 = 184. Evaluate 184 != 14, drop this branch.\n     |- Try 238 * 54 = 12852. 12852 exceeds the maximum intermediate result, drop this branch.\n     |- Try 238 \/ 54 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 17 \/ 14 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 35 - 19 = 16. Add 16 to the number set. Current number set: [16, 14, 17], target: 14. Options for choosing two numbers: [(16, 14), (16, 17), (14, 17)].\n   |- Pick two numbers (16, 14) (numbers left: [17]). Try possible operations.\n    |- Try 16 + 14 = 30. Add 30 to the number set. Current number set: [30, 17], target: 14, just two numbers left.\n     |- Try 30 + 17 = 47. Evaluate 47 != 14, drop this branch.\n     |- Try 30 - 17 = 13. Evaluate 13 != 14, drop this branch.\n     |- Try 30 * 17 = 510. Evaluate 510 != 14, drop this branch.\n     |- Try 30 \/ 17 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 16 - 14 = 2. Add 2 to the number set. Current number set: [2, 17], target: 14, just two numbers left.\n     |- Try 17 + 2 = 19. Evaluate 19 != 14, drop this branch.\n     |- Try 17 - 2 = 15. Evaluate 15 != 14, drop this branch.\n     |- Try 17 * 2 = 34. Evaluate 34 != 14, drop this branch.\n     |- Try 17 \/ 2 = 8.5. 8.5 is a decimal, drop this branch.\n    |- Try 16 * 14 = 224. Add 224 to the number set. Current number set: [224, 17], target: 14, just two numbers left.\n     |- Try 224 + 17 = 241. Evaluate 241 != 14, drop this branch.\n     |- Try 224 - 17 = 207. Evaluate 207 != 14, drop this branch.\n     |- Try 224 * 17 = 3808. 3808 exceeds the maximum intermediate result, drop this branch.\n     |- Try 224 \/ 17 = 13.2. 13.2 is a decimal, drop this branch.\n    |- Try 16 \/ 14 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (16, 17) (numbers left: [14]). Try possible operations.\n    |- Try 17 + 16 = 33. Add 33 to the number set. Current number set: [33, 14], target: 14, just two numbers left.\n     |- Try 33 + 14 = 47. Evaluate 47 != 14, drop this branch.\n     |- Try 33 - 14 = 19. Evaluate 19 != 14, drop this branch.\n     |- Try 33 * 14 = 462. Evaluate 462 != 14, drop this branch.\n     |- Try 33 \/ 14 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 17 - 16 = 1. Add 1 to the number set. Current number set: [1, 14], target: 14, just two numbers left.\n     |- Try 14 + 1 = 15. Evaluate 15 != 14, drop this branch.\n     |- Try 14 - 1 = 13. Evaluate 13 != 14, drop this branch.\n     |- Try 14 * 1 = 14. Evaluate 14 == 14, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 14 * 1 = 14\nThe step before: 17 - 16 = 1\nThe first step: 35 - 19 = 16\n\nOutput the solution in the required format:\n<Solution>\n35 - 19 = 16\n17 - 16 = 1\n14 * 1 = 14\n<\/Solution>\n","item":{"nums":[35,14,19,17],"solution":["35 - 19 = 16","17 - 16 = 1","14 * 1 = 14"],"target":14}}
+{"instance_id":"countdown_8k_107","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [37, 34, 31, 28]\nTarget: 14","reference_output":"# Search Procedure\nInitial number set: [37, 34, 31, 28], target: 14. Options for choosing two numbers: [(37, 34), (37, 31), (37, 28), (34, 31), (34, 28), (31, 28)].\n |- Pick two numbers (37, 34) (numbers left: [31, 28]). Try possible operations.\n  |- Try 37 + 34 = 71. Add 71 to the number set. Current number set: [71, 31, 28], target: 14. Options for choosing two numbers: [(71, 31), (71, 28), (31, 28)].\n   |- Pick two numbers (71, 31) (numbers left: [28]). Try possible operations.\n    |- Try 71 + 31 = 102. Add 102 to the number set. Current number set: [102, 28], target: 14, just two numbers left.\n     |- Try 102 + 28 = 130. Evaluate 130 != 14, drop this branch.\n     |- Try 102 - 28 = 74. Evaluate 74 != 14, drop this branch.\n     |- Try 102 * 28 = 2856. 2856 exceeds the maximum intermediate result, drop this branch.\n     |- Try 102 \/ 28 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 71 - 31 = 40. Add 40 to the number set. Current number set: [40, 28], target: 14, just two numbers left.\n     |- Try 40 + 28 = 68. Evaluate 68 != 14, drop this branch.\n     |- Try 40 - 28 = 12. Evaluate 12 != 14, drop this branch.\n     |- Try 40 * 28 = 1120. Evaluate 1120 != 14, drop this branch.\n     |- Try 40 \/ 28 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 71 * 31 = 2201. 2201 exceeds the maximum intermediate result, drop this branch.\n    |- Try 71 \/ 31 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (71, 28) (numbers left: [31]). Try possible operations.\n    |- Try 71 + 28 = 99. Add 99 to the number set. Current number set: [99, 31], target: 14, just two numbers left.\n     |- Try 99 + 31 = 130. Evaluate 130 != 14, drop this branch.\n     |- Try 99 - 31 = 68. Evaluate 68 != 14, drop this branch.\n     |- Try 99 * 31 = 3069. 3069 exceeds the maximum intermediate result, drop this branch.\n     |- Try 99 \/ 31 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 71 - 28 = 43. Add 43 to the number set. Current number set: [43, 31], target: 14, just two numbers left.\n     |- Try 43 + 31 = 74. Evaluate 74 != 14, drop this branch.\n     |- Try 43 - 31 = 12. Evaluate 12 != 14, drop this branch.\n     |- Try 43 * 31 = 1333. Evaluate 1333 != 14, drop this branch.\n     |- Try 43 \/ 31 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 71 * 28 = 1988. Add 1988 to the number set. Current number set: [1988, 31], target: 14, just two numbers left.\n     |- Try 1988 + 31 = 2019. 2019 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1988 - 31 = 1957. Evaluate 1957 != 14, drop this branch.\n     |- Try 1988 * 31 = 61628. 61628 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1988 \/ 31 = 64.1. 64.1 is a decimal, drop this branch.\n    |- Try 71 \/ 28 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (31, 28) (numbers left: [71]). Try possible operations.\n    |- Try 31 + 28 = 59. Add 59 to the number set. Current number set: [59, 71], target: 14, just two numbers left.\n     |- Try 71 + 59 = 130. Evaluate 130 != 14, drop this branch.\n     |- Try 71 - 59 = 12. Evaluate 12 != 14, drop this branch.\n     |- Try 71 * 59 = 4189. 4189 exceeds the maximum intermediate result, drop this branch.\n     |- Try 71 \/ 59 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 31 - 28 = 3. Add 3 to the number set. Current number set: [3, 71], target: 14, just two numbers left.\n     |- Try 71 + 3 = 74. Evaluate 74 != 14, drop this branch.\n     |- Try 71 - 3 = 68. Evaluate 68 != 14, drop this branch.\n     |- Try 71 * 3 = 213. Evaluate 213 != 14, drop this branch.\n     |- Try 71 \/ 3 = 23.7. 23.7 is a decimal, drop this branch.\n    |- Try 31 * 28 = 868. Add 868 to the number set. Current number set: [868, 71], target: 14, just two numbers left.\n     |- Try 868 + 71 = 939. Evaluate 939 != 14, drop this branch.\n     |- Try 868 - 71 = 797. Evaluate 797 != 14, drop this branch.\n     |- Try 868 * 71 = 61628. 61628 exceeds the maximum intermediate result, drop this branch.\n     |- Try 868 \/ 71 = 12.2. 12.2 is a decimal, drop this branch.\n    |- Try 31 \/ 28 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 37 - 34 = 3. Add 3 to the number set. Current number set: [3, 31, 28], target: 14. Options for choosing two numbers: [(3, 31), (3, 28), (31, 28)].\n   |- Pick two numbers (3, 31) (numbers left: [28]). Try possible operations.\n    |- Try 31 + 3 = 34. Add 34 to the number set. Current number set: [34, 28], target: 14, just two numbers left.\n     |- Try 34 + 28 = 62. Evaluate 62 != 14, drop this branch.\n     |- Try 34 - 28 = 6. Evaluate 6 != 14, drop this branch.\n     |- Try 34 * 28 = 952. Evaluate 952 != 14, drop this branch.\n     |- Try 34 \/ 28 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 31 - 3 = 28. Add 28 to the number set. Current number set: [28, 28], target: 14, just two numbers left.\n     |- Try 28 + 28 = 56. Evaluate 56 != 14, drop this branch.\n     |- Try 28 - 28 = 0. Evaluate 0 != 14, drop this branch.\n     |- Try 28 * 28 = 784. Evaluate 784 != 14, drop this branch.\n     |- Try 28 \/ 28 = 1. Evaluate 1 != 14, drop this branch.\n    |- Try 31 * 3 = 93. Add 93 to the number set. Current number set: [93, 28], target: 14, just two numbers left.\n     |- Try 93 + 28 = 121. Evaluate 121 != 14, drop this branch.\n     |- Try 93 - 28 = 65. Evaluate 65 != 14, drop this branch.\n     |- Try 93 * 28 = 2604. 2604 exceeds the maximum intermediate result, drop this branch.\n     |- Try 93 \/ 28 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 31 \/ 3 = 10.3. 10.3 is a decimal, drop this branch.\n   |- Pick two numbers (3, 28) (numbers left: [31]). Try possible operations.\n    |- Try 28 + 3 = 31. Add 31 to the number set. Current number set: [31, 31], target: 14, just two numbers left.\n     |- Try 31 + 31 = 62. Evaluate 62 != 14, drop this branch.\n     |- Try 31 - 31 = 0. Evaluate 0 != 14, drop this branch.\n     |- Try 31 * 31 = 961. Evaluate 961 != 14, drop this branch.\n     |- Try 31 \/ 31 = 1. Evaluate 1 != 14, drop this branch.\n    |- Try 28 - 3 = 25. Add 25 to the number set. Current number set: [25, 31], target: 14, just two numbers left.\n     |- Try 31 + 25 = 56. Evaluate 56 != 14, drop this branch.\n     |- Try 31 - 25 = 6. Evaluate 6 != 14, drop this branch.\n     |- Try 31 * 25 = 775. Evaluate 775 != 14, drop this branch.\n     |- Try 31 \/ 25 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 28 * 3 = 84. Add 84 to the number set. Current number set: [84, 31], target: 14, just two numbers left.\n     |- Try 84 + 31 = 115. Evaluate 115 != 14, drop this branch.\n     |- Try 84 - 31 = 53. Evaluate 53 != 14, drop this branch.\n     |- Try 84 * 31 = 2604. 2604 exceeds the maximum intermediate result, drop this branch.\n     |- Try 84 \/ 31 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 28 \/ 3 = 9.3. 9.3 is a decimal, drop this branch.\n   |- Pick two numbers (31, 28) (numbers left: [3]). Try possible operations.\n    |- Try 31 + 28 = 59. Add 59 to the number set. Current number set: [59, 3], target: 14, just two numbers left.\n     |- Try 59 + 3 = 62. Evaluate 62 != 14, drop this branch.\n     |- Try 59 - 3 = 56. Evaluate 56 != 14, drop this branch.\n     |- Try 59 * 3 = 177. Evaluate 177 != 14, drop this branch.\n     |- Try 59 \/ 3 = 19.7. 19.7 is a decimal, drop this branch.\n    |- Try 31 - 28 = 3. Add 3 to the number set. Current number set: [3, 3], target: 14, just two numbers left.\n     |- Try 3 + 3 = 6. Evaluate 6 != 14, drop this branch.\n     |- Try 3 - 3 = 0. Evaluate 0 != 14, drop this branch.\n     |- Try 3 * 3 = 9. Evaluate 9 != 14, drop this branch.\n     |- Try 3 \/ 3 = 1. Evaluate 1 != 14, drop this branch.\n    |- Try 31 * 28 = 868. Add 868 to the number set. Current number set: [868, 3], target: 14, just two numbers left.\n     |- Try 868 + 3 = 871. Evaluate 871 != 14, drop this branch.\n     |- Try 868 - 3 = 865. Evaluate 865 != 14, drop this branch.\n     |- Try 868 * 3 = 2604. 2604 exceeds the maximum intermediate result, drop this branch.\n     |- Try 868 \/ 3 = 289.3. 289.3 is a decimal, drop this branch.\n    |- Try 31 \/ 28 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 37 * 34 = 1258. Add 1258 to the number set. Current number set: [1258, 31, 28], target: 14. Options for choosing two numbers: [(1258, 31), (1258, 28), (31, 28)].\n   |- Pick two numbers (1258, 31) (numbers left: [28]). Try possible operations.\n    |- Try 1258 + 31 = 1289. Add 1289 to the number set. Current number set: [1289, 28], target: 14, just two numbers left.\n     |- Try 1289 + 28 = 1317. Evaluate 1317 != 14, drop this branch.\n     |- Try 1289 - 28 = 1261. Evaluate 1261 != 14, drop this branch.\n     |- Try 1289 * 28 = 36092. 36092 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1289 \/ 28 = 46.0. 46.0 is a decimal, drop this branch.\n    |- Try 1258 - 31 = 1227. Add 1227 to the number set. Current number set: [1227, 28], target: 14, just two numbers left.\n     |- Try 1227 + 28 = 1255. Evaluate 1255 != 14, drop this branch.\n     |- Try 1227 - 28 = 1199. Evaluate 1199 != 14, drop this branch.\n     |- Try 1227 * 28 = 34356. 34356 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1227 \/ 28 = 43.8. 43.8 is a decimal, drop this branch.\n    |- Try 1258 * 31 = 38998. 38998 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1258 \/ 31 = 40.6. 40.6 is a decimal, drop this branch.\n   |- Pick two numbers (1258, 28) (numbers left: [31]). Try possible operations.\n    |- Try 1258 + 28 = 1286. Add 1286 to the number set. Current number set: [1286, 31], target: 14, just two numbers left.\n     |- Try 1286 + 31 = 1317. Evaluate 1317 != 14, drop this branch.\n     |- Try 1286 - 31 = 1255. Evaluate 1255 != 14, drop this branch.\n     |- Try 1286 * 31 = 39866. 39866 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1286 \/ 31 = 41.5. 41.5 is a decimal, drop this branch.\n    |- Try 1258 - 28 = 1230. Add 1230 to the number set. Current number set: [1230, 31], target: 14, just two numbers left.\n     |- Try 1230 + 31 = 1261. Evaluate 1261 != 14, drop this branch.\n     |- Try 1230 - 31 = 1199. Evaluate 1199 != 14, drop this branch.\n     |- Try 1230 * 31 = 38130. 38130 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1230 \/ 31 = 39.7. 39.7 is a decimal, drop this branch.\n    |- Try 1258 * 28 = 35224. 35224 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1258 \/ 28 = 44.9. 44.9 is a decimal, drop this branch.\n   |- Pick two numbers (31, 28) (numbers left: [1258]). Try possible operations.\n    |- Try 31 + 28 = 59. Add 59 to the number set. Current number set: [59, 1258], target: 14, just two numbers left.\n     |- Try 1258 + 59 = 1317. Evaluate 1317 != 14, drop this branch.\n     |- Try 1258 - 59 = 1199. Evaluate 1199 != 14, drop this branch.\n     |- Try 1258 * 59 = 74222. 74222 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1258 \/ 59 = 21.3. 21.3 is a decimal, drop this branch.\n    |- Try 31 - 28 = 3. Add 3 to the number set. Current number set: [3, 1258], target: 14, just two numbers left.\n     |- Try 1258 + 3 = 1261. Evaluate 1261 != 14, drop this branch.\n     |- Try 1258 - 3 = 1255. Evaluate 1255 != 14, drop this branch.\n     |- Try 1258 * 3 = 3774. 3774 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1258 \/ 3 = 419.3. 419.3 is a decimal, drop this branch.\n    |- Try 31 * 28 = 868. Add 868 to the number set. Current number set: [868, 1258], target: 14, just two numbers left.\n     |- Try 1258 + 868 = 2126. 2126 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1258 - 868 = 390. Evaluate 390 != 14, drop this branch.\n     |- Try 1258 * 868 = 1091944. 1091944 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1258 \/ 868 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 31 \/ 28 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 37 \/ 34 = 1.1. 1.1 is a decimal, drop this branch.\n |- Pick two numbers (37, 31) (numbers left: [34, 28]). Try possible operations.\n  |- Try 37 + 31 = 68. Add 68 to the number set. Current number set: [68, 34, 28], target: 14. Options for choosing two numbers: [(68, 34), (68, 28), (34, 28)].\n   |- Pick two numbers (68, 34) (numbers left: [28]). Try possible operations.\n    |- Try 68 + 34 = 102. Add 102 to the number set. Current number set: [102, 28], target: 14, just two numbers left.\n     |- Try 102 + 28 = 130. Evaluate 130 != 14, drop this branch.\n     |- Try 102 - 28 = 74. Evaluate 74 != 14, drop this branch.\n     |- Try 102 * 28 = 2856. 2856 exceeds the maximum intermediate result, drop this branch.\n     |- Try 102 \/ 28 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 68 - 34 = 34. Add 34 to the number set. Current number set: [34, 28], target: 14, just two numbers left.\n     |- Try 34 + 28 = 62. Evaluate 62 != 14, drop this branch.\n     |- Try 34 - 28 = 6. Evaluate 6 != 14, drop this branch.\n     |- Try 34 * 28 = 952. Evaluate 952 != 14, drop this branch.\n     |- Try 34 \/ 28 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 68 * 34 = 2312. 2312 exceeds the maximum intermediate result, drop this branch.\n    |- Try 68 \/ 34 = 2. Add 2 to the number set. Current number set: [2, 28], target: 14, just two numbers left.\n     |- Try 28 + 2 = 30. Evaluate 30 != 14, drop this branch.\n     |- Try 28 - 2 = 26. Evaluate 26 != 14, drop this branch.\n     |- Try 28 * 2 = 56. Evaluate 56 != 14, drop this branch.\n     |- Try 28 \/ 2 = 14. Evaluate 14 == 14, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 28 \/ 2 = 14\nThe step before: 68 \/ 34 = 2\nThe first step: 37 + 31 = 68\n\nOutput the solution in the required format:\n<Solution>\n37 + 31 = 68\n68 \/ 34 = 2\n28 \/ 2 = 14\n<\/Solution>\n","item":{"nums":[37,34,31,28],"solution":["37 + 31 = 68","68 \/ 34 = 2","28 \/ 2 = 14"],"target":14}}
+{"instance_id":"countdown_8k_108","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [23, 5, 42, 20]\nTarget: 23","reference_output":"# Search Procedure\nInitial number set: [23, 5, 42, 20], target: 23. Options for choosing two numbers: [(23, 5), (23, 42), (23, 20), (5, 42), (5, 20), (42, 20)].\n |- Pick two numbers (23, 5) (numbers left: [42, 20]). Try possible operations.\n  |- Try 23 + 5 = 28. Add 28 to the number set. Current number set: [28, 42, 20], target: 23. Options for choosing two numbers: [(28, 42), (28, 20), (42, 20)].\n   |- Pick two numbers (28, 42) (numbers left: [20]). Try possible operations.\n    |- Try 42 + 28 = 70. Add 70 to the number set. Current number set: [70, 20], target: 23, just two numbers left.\n     |- Try 70 + 20 = 90. Evaluate 90 != 23, drop this branch.\n     |- Try 70 - 20 = 50. Evaluate 50 != 23, drop this branch.\n     |- Try 70 * 20 = 1400. Evaluate 1400 != 23, drop this branch.\n     |- Try 70 \/ 20 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 42 - 28 = 14. Add 14 to the number set. Current number set: [14, 20], target: 23, just two numbers left.\n     |- Try 20 + 14 = 34. Evaluate 34 != 23, drop this branch.\n     |- Try 20 - 14 = 6. Evaluate 6 != 23, drop this branch.\n     |- Try 20 * 14 = 280. Evaluate 280 != 23, drop this branch.\n     |- Try 20 \/ 14 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 42 * 28 = 1176. Add 1176 to the number set. Current number set: [1176, 20], target: 23, just two numbers left.\n     |- Try 1176 + 20 = 1196. Evaluate 1196 != 23, drop this branch.\n     |- Try 1176 - 20 = 1156. Evaluate 1156 != 23, drop this branch.\n     |- Try 1176 * 20 = 23520. 23520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1176 \/ 20 = 58.8. 58.8 is a decimal, drop this branch.\n    |- Try 42 \/ 28 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (28, 20) (numbers left: [42]). Try possible operations.\n    |- Try 28 + 20 = 48. Add 48 to the number set. Current number set: [48, 42], target: 23, just two numbers left.\n     |- Try 48 + 42 = 90. Evaluate 90 != 23, drop this branch.\n     |- Try 48 - 42 = 6. Evaluate 6 != 23, drop this branch.\n     |- Try 48 * 42 = 2016. 2016 exceeds the maximum intermediate result, drop this branch.\n     |- Try 48 \/ 42 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 28 - 20 = 8. Add 8 to the number set. Current number set: [8, 42], target: 23, just two numbers left.\n     |- Try 42 + 8 = 50. Evaluate 50 != 23, drop this branch.\n     |- Try 42 - 8 = 34. Evaluate 34 != 23, drop this branch.\n     |- Try 42 * 8 = 336. Evaluate 336 != 23, drop this branch.\n     |- Try 42 \/ 8 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 28 * 20 = 560. Add 560 to the number set. Current number set: [560, 42], target: 23, just two numbers left.\n     |- Try 560 + 42 = 602. Evaluate 602 != 23, drop this branch.\n     |- Try 560 - 42 = 518. Evaluate 518 != 23, drop this branch.\n     |- Try 560 * 42 = 23520. 23520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 560 \/ 42 = 13.3. 13.3 is a decimal, drop this branch.\n    |- Try 28 \/ 20 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (42, 20) (numbers left: [28]). Try possible operations.\n    |- Try 42 + 20 = 62. Add 62 to the number set. Current number set: [62, 28], target: 23, just two numbers left.\n     |- Try 62 + 28 = 90. Evaluate 90 != 23, drop this branch.\n     |- Try 62 - 28 = 34. Evaluate 34 != 23, drop this branch.\n     |- Try 62 * 28 = 1736. Evaluate 1736 != 23, drop this branch.\n     |- Try 62 \/ 28 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 42 - 20 = 22. Add 22 to the number set. Current number set: [22, 28], target: 23, just two numbers left.\n     |- Try 28 + 22 = 50. Evaluate 50 != 23, drop this branch.\n     |- Try 28 - 22 = 6. Evaluate 6 != 23, drop this branch.\n     |- Try 28 * 22 = 616. Evaluate 616 != 23, drop this branch.\n     |- Try 28 \/ 22 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 42 * 20 = 840. Add 840 to the number set. Current number set: [840, 28], target: 23, just two numbers left.\n     |- Try 840 + 28 = 868. Evaluate 868 != 23, drop this branch.\n     |- Try 840 - 28 = 812. Evaluate 812 != 23, drop this branch.\n     |- Try 840 * 28 = 23520. 23520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 840 \/ 28 = 30. Evaluate 30 != 23, drop this branch.\n    |- Try 42 \/ 20 = 2.1. 2.1 is a decimal, drop this branch.\n  |- Try 23 - 5 = 18. Add 18 to the number set. Current number set: [18, 42, 20], target: 23. Options for choosing two numbers: [(18, 42), (18, 20), (42, 20)].\n   |- Pick two numbers (18, 42) (numbers left: [20]). Try possible operations.\n    |- Try 42 + 18 = 60. Add 60 to the number set. Current number set: [60, 20], target: 23, just two numbers left.\n     |- Try 60 + 20 = 80. Evaluate 80 != 23, drop this branch.\n     |- Try 60 - 20 = 40. Evaluate 40 != 23, drop this branch.\n     |- Try 60 * 20 = 1200. Evaluate 1200 != 23, drop this branch.\n     |- Try 60 \/ 20 = 3. Evaluate 3 != 23, drop this branch.\n    |- Try 42 - 18 = 24. Add 24 to the number set. Current number set: [24, 20], target: 23, just two numbers left.\n     |- Try 24 + 20 = 44. Evaluate 44 != 23, drop this branch.\n     |- Try 24 - 20 = 4. Evaluate 4 != 23, drop this branch.\n     |- Try 24 * 20 = 480. Evaluate 480 != 23, drop this branch.\n     |- Try 24 \/ 20 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 42 * 18 = 756. Add 756 to the number set. Current number set: [756, 20], target: 23, just two numbers left.\n     |- Try 756 + 20 = 776. Evaluate 776 != 23, drop this branch.\n     |- Try 756 - 20 = 736. Evaluate 736 != 23, drop this branch.\n     |- Try 756 * 20 = 15120. 15120 exceeds the maximum intermediate result, drop this branch.\n     |- Try 756 \/ 20 = 37.8. 37.8 is a decimal, drop this branch.\n    |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (18, 20) (numbers left: [42]). Try possible operations.\n    |- Try 20 + 18 = 38. Add 38 to the number set. Current number set: [38, 42], target: 23, just two numbers left.\n     |- Try 42 + 38 = 80. Evaluate 80 != 23, drop this branch.\n     |- Try 42 - 38 = 4. Evaluate 4 != 23, drop this branch.\n     |- Try 42 * 38 = 1596. Evaluate 1596 != 23, drop this branch.\n     |- Try 42 \/ 38 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 20 - 18 = 2. Add 2 to the number set. Current number set: [2, 42], target: 23, just two numbers left.\n     |- Try 42 + 2 = 44. Evaluate 44 != 23, drop this branch.\n     |- Try 42 - 2 = 40. Evaluate 40 != 23, drop this branch.\n     |- Try 42 * 2 = 84. Evaluate 84 != 23, drop this branch.\n     |- Try 42 \/ 2 = 21. Evaluate 21 != 23, drop this branch.\n    |- Try 20 * 18 = 360. Add 360 to the number set. Current number set: [360, 42], target: 23, just two numbers left.\n     |- Try 360 + 42 = 402. Evaluate 402 != 23, drop this branch.\n     |- Try 360 - 42 = 318. Evaluate 318 != 23, drop this branch.\n     |- Try 360 * 42 = 15120. 15120 exceeds the maximum intermediate result, drop this branch.\n     |- Try 360 \/ 42 = 8.6. 8.6 is a decimal, drop this branch.\n    |- Try 20 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (42, 20) (numbers left: [18]). Try possible operations.\n    |- Try 42 + 20 = 62. Add 62 to the number set. Current number set: [62, 18], target: 23, just two numbers left.\n     |- Try 62 + 18 = 80. Evaluate 80 != 23, drop this branch.\n     |- Try 62 - 18 = 44. Evaluate 44 != 23, drop this branch.\n     |- Try 62 * 18 = 1116. Evaluate 1116 != 23, drop this branch.\n     |- Try 62 \/ 18 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 42 - 20 = 22. Add 22 to the number set. Current number set: [22, 18], target: 23, just two numbers left.\n     |- Try 22 + 18 = 40. Evaluate 40 != 23, drop this branch.\n     |- Try 22 - 18 = 4. Evaluate 4 != 23, drop this branch.\n     |- Try 22 * 18 = 396. Evaluate 396 != 23, drop this branch.\n     |- Try 22 \/ 18 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 42 * 20 = 840. Add 840 to the number set. Current number set: [840, 18], target: 23, just two numbers left.\n     |- Try 840 + 18 = 858. Evaluate 858 != 23, drop this branch.\n     |- Try 840 - 18 = 822. Evaluate 822 != 23, drop this branch.\n     |- Try 840 * 18 = 15120. 15120 exceeds the maximum intermediate result, drop this branch.\n     |- Try 840 \/ 18 = 46.7. 46.7 is a decimal, drop this branch.\n    |- Try 42 \/ 20 = 2.1. 2.1 is a decimal, drop this branch.\n  |- Try 23 * 5 = 115. Add 115 to the number set. Current number set: [115, 42, 20], target: 23. Options for choosing two numbers: [(115, 42), (115, 20), (42, 20)].\n   |- Pick two numbers (115, 42) (numbers left: [20]). Try possible operations.\n    |- Try 115 + 42 = 157. Add 157 to the number set. Current number set: [157, 20], target: 23, just two numbers left.\n     |- Try 157 + 20 = 177. Evaluate 177 != 23, drop this branch.\n     |- Try 157 - 20 = 137. Evaluate 137 != 23, drop this branch.\n     |- Try 157 * 20 = 3140. 3140 exceeds the maximum intermediate result, drop this branch.\n     |- Try 157 \/ 20 = 7.8. 7.8 is a decimal, drop this branch.\n    |- Try 115 - 42 = 73. Add 73 to the number set. Current number set: [73, 20], target: 23, just two numbers left.\n     |- Try 73 + 20 = 93. Evaluate 93 != 23, drop this branch.\n     |- Try 73 - 20 = 53. Evaluate 53 != 23, drop this branch.\n     |- Try 73 * 20 = 1460. Evaluate 1460 != 23, drop this branch.\n     |- Try 73 \/ 20 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 115 * 42 = 4830. 4830 exceeds the maximum intermediate result, drop this branch.\n    |- Try 115 \/ 42 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (115, 20) (numbers left: [42]). Try possible operations.\n    |- Try 115 + 20 = 135. Add 135 to the number set. Current number set: [135, 42], target: 23, just two numbers left.\n     |- Try 135 + 42 = 177. Evaluate 177 != 23, drop this branch.\n     |- Try 135 - 42 = 93. Evaluate 93 != 23, drop this branch.\n     |- Try 135 * 42 = 5670. 5670 exceeds the maximum intermediate result, drop this branch.\n     |- Try 135 \/ 42 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 115 - 20 = 95. Add 95 to the number set. Current number set: [95, 42], target: 23, just two numbers left.\n     |- Try 95 + 42 = 137. Evaluate 137 != 23, drop this branch.\n     |- Try 95 - 42 = 53. Evaluate 53 != 23, drop this branch.\n     |- Try 95 * 42 = 3990. 3990 exceeds the maximum intermediate result, drop this branch.\n     |- Try 95 \/ 42 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 115 * 20 = 2300. 2300 exceeds the maximum intermediate result, drop this branch.\n    |- Try 115 \/ 20 = 5.8. 5.8 is a decimal, drop this branch.\n   |- Pick two numbers (42, 20) (numbers left: [115]). Try possible operations.\n    |- Try 42 + 20 = 62. Add 62 to the number set. Current number set: [62, 115], target: 23, just two numbers left.\n     |- Try 115 + 62 = 177. Evaluate 177 != 23, drop this branch.\n     |- Try 115 - 62 = 53. Evaluate 53 != 23, drop this branch.\n     |- Try 115 * 62 = 7130. 7130 exceeds the maximum intermediate result, drop this branch.\n     |- Try 115 \/ 62 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 42 - 20 = 22. Add 22 to the number set. Current number set: [22, 115], target: 23, just two numbers left.\n     |- Try 115 + 22 = 137. Evaluate 137 != 23, drop this branch.\n     |- Try 115 - 22 = 93. Evaluate 93 != 23, drop this branch.\n     |- Try 115 * 22 = 2530. 2530 exceeds the maximum intermediate result, drop this branch.\n     |- Try 115 \/ 22 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 42 * 20 = 840. Add 840 to the number set. Current number set: [840, 115], target: 23, just two numbers left.\n     |- Try 840 + 115 = 955. Evaluate 955 != 23, drop this branch.\n     |- Try 840 - 115 = 725. Evaluate 725 != 23, drop this branch.\n     |- Try 840 * 115 = 96600. 96600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 840 \/ 115 = 7.3. 7.3 is a decimal, drop this branch.\n    |- Try 42 \/ 20 = 2.1. 2.1 is a decimal, drop this branch.\n  |- Try 23 \/ 5 = 4.6. 4.6 is a decimal, drop this branch.\n |- Pick two numbers (23, 42) (numbers left: [5, 20]). Try possible operations.\n  |- Try 42 + 23 = 65. Add 65 to the number set. Current number set: [65, 5, 20], target: 23. Options for choosing two numbers: [(65, 5), (65, 20), (5, 20)].\n   |- Pick two numbers (65, 5) (numbers left: [20]). Try possible operations.\n    |- Try 65 + 5 = 70. Add 70 to the number set. Current number set: [70, 20], target: 23, just two numbers left.\n     |- Try 70 + 20 = 90. Evaluate 90 != 23, drop this branch.\n     |- Try 70 - 20 = 50. Evaluate 50 != 23, drop this branch.\n     |- Try 70 * 20 = 1400. Evaluate 1400 != 23, drop this branch.\n     |- Try 70 \/ 20 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 65 - 5 = 60. Add 60 to the number set. Current number set: [60, 20], target: 23, just two numbers left.\n     |- Try 60 + 20 = 80. Evaluate 80 != 23, drop this branch.\n     |- Try 60 - 20 = 40. Evaluate 40 != 23, drop this branch.\n     |- Try 60 * 20 = 1200. Evaluate 1200 != 23, drop this branch.\n     |- Try 60 \/ 20 = 3. Evaluate 3 != 23, drop this branch.\n    |- Try 65 * 5 = 325. Add 325 to the number set. Current number set: [325, 20], target: 23, just two numbers left.\n     |- Try 325 + 20 = 345. Evaluate 345 != 23, drop this branch.\n     |- Try 325 - 20 = 305. Evaluate 305 != 23, drop this branch.\n     |- Try 325 * 20 = 6500. 6500 exceeds the maximum intermediate result, drop this branch.\n     |- Try 325 \/ 20 = 16.2. 16.2 is a decimal, drop this branch.\n    |- Try 65 \/ 5 = 13. Add 13 to the number set. Current number set: [13, 20], target: 23, just two numbers left.\n     |- Try 20 + 13 = 33. Evaluate 33 != 23, drop this branch.\n     |- Try 20 - 13 = 7. Evaluate 7 != 23, drop this branch.\n     |- Try 20 * 13 = 260. Evaluate 260 != 23, drop this branch.\n     |- Try 20 \/ 13 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (65, 20) (numbers left: [5]). Try possible operations.\n    |- Try 65 + 20 = 85. Add 85 to the number set. Current number set: [85, 5], target: 23, just two numbers left.\n     |- Try 85 + 5 = 90. Evaluate 90 != 23, drop this branch.\n     |- Try 85 - 5 = 80. Evaluate 80 != 23, drop this branch.\n     |- Try 85 * 5 = 425. Evaluate 425 != 23, drop this branch.\n     |- Try 85 \/ 5 = 17. Evaluate 17 != 23, drop this branch.\n    |- Try 65 - 20 = 45. Add 45 to the number set. Current number set: [45, 5], target: 23, just two numbers left.\n     |- Try 45 + 5 = 50. Evaluate 50 != 23, drop this branch.\n     |- Try 45 - 5 = 40. Evaluate 40 != 23, drop this branch.\n     |- Try 45 * 5 = 225. Evaluate 225 != 23, drop this branch.\n     |- Try 45 \/ 5 = 9. Evaluate 9 != 23, drop this branch.\n    |- Try 65 * 20 = 1300. Add 1300 to the number set. Current number set: [1300, 5], target: 23, just two numbers left.\n     |- Try 1300 + 5 = 1305. Evaluate 1305 != 23, drop this branch.\n     |- Try 1300 - 5 = 1295. Evaluate 1295 != 23, drop this branch.\n     |- Try 1300 * 5 = 6500. 6500 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1300 \/ 5 = 260. Evaluate 260 != 23, drop this branch.\n    |- Try 65 \/ 20 = 3.2. 3.2 is a decimal, drop this branch.\n   |- Pick two numbers (5, 20) (numbers left: [65]). Try possible operations.\n    |- Try 20 + 5 = 25. Add 25 to the number set. Current number set: [25, 65], target: 23, just two numbers left.\n     |- Try 65 + 25 = 90. Evaluate 90 != 23, drop this branch.\n     |- Try 65 - 25 = 40. Evaluate 40 != 23, drop this branch.\n     |- Try 65 * 25 = 1625. Evaluate 1625 != 23, drop this branch.\n     |- Try 65 \/ 25 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 20 - 5 = 15. Add 15 to the number set. Current number set: [15, 65], target: 23, just two numbers left.\n     |- Try 65 + 15 = 80. Evaluate 80 != 23, drop this branch.\n     |- Try 65 - 15 = 50. Evaluate 50 != 23, drop this branch.\n     |- Try 65 * 15 = 975. Evaluate 975 != 23, drop this branch.\n     |- Try 65 \/ 15 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 20 * 5 = 100. Add 100 to the number set. Current number set: [100, 65], target: 23, just two numbers left.\n     |- Try 100 + 65 = 165. Evaluate 165 != 23, drop this branch.\n     |- Try 100 - 65 = 35. Evaluate 35 != 23, drop this branch.\n     |- Try 100 * 65 = 6500. 6500 exceeds the maximum intermediate result, drop this branch.\n     |- Try 100 \/ 65 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 20 \/ 5 = 4. Add 4 to the number set. Current number set: [4, 65], target: 23, just two numbers left.\n     |- Try 65 + 4 = 69. Evaluate 69 != 23, drop this branch.\n     |- Try 65 - 4 = 61. Evaluate 61 != 23, drop this branch.\n     |- Try 65 * 4 = 260. Evaluate 260 != 23, drop this branch.\n     |- Try 65 \/ 4 = 16.2. 16.2 is a decimal, drop this branch.\n  |- Try 42 - 23 = 19. Add 19 to the number set. Current number set: [19, 5, 20], target: 23. Options for choosing two numbers: [(19, 5), (19, 20), (5, 20)].\n   |- Pick two numbers (19, 5) (numbers left: [20]). Try possible operations.\n    |- Try 19 + 5 = 24. Add 24 to the number set. Current number set: [24, 20], target: 23, just two numbers left.\n     |- Try 24 + 20 = 44. Evaluate 44 != 23, drop this branch.\n     |- Try 24 - 20 = 4. Evaluate 4 != 23, drop this branch.\n     |- Try 24 * 20 = 480. Evaluate 480 != 23, drop this branch.\n     |- Try 24 \/ 20 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 19 - 5 = 14. Add 14 to the number set. Current number set: [14, 20], target: 23, just two numbers left.\n     |- Try 20 + 14 = 34. Evaluate 34 != 23, drop this branch.\n     |- Try 20 - 14 = 6. Evaluate 6 != 23, drop this branch.\n     |- Try 20 * 14 = 280. Evaluate 280 != 23, drop this branch.\n     |- Try 20 \/ 14 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 19 * 5 = 95. Add 95 to the number set. Current number set: [95, 20], target: 23, just two numbers left.\n     |- Try 95 + 20 = 115. Evaluate 115 != 23, drop this branch.\n     |- Try 95 - 20 = 75. Evaluate 75 != 23, drop this branch.\n     |- Try 95 * 20 = 1900. Evaluate 1900 != 23, drop this branch.\n     |- Try 95 \/ 20 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 19 \/ 5 = 3.8. 3.8 is a decimal, drop this branch.\n   |- Pick two numbers (19, 20) (numbers left: [5]). Try possible operations.\n    |- Try 20 + 19 = 39. Add 39 to the number set. Current number set: [39, 5], target: 23, just two numbers left.\n     |- Try 39 + 5 = 44. Evaluate 44 != 23, drop this branch.\n     |- Try 39 - 5 = 34. Evaluate 34 != 23, drop this branch.\n     |- Try 39 * 5 = 195. Evaluate 195 != 23, drop this branch.\n     |- Try 39 \/ 5 = 7.8. 7.8 is a decimal, drop this branch.\n    |- Try 20 - 19 = 1. Add 1 to the number set. Current number set: [1, 5], target: 23, just two numbers left.\n     |- Try 5 + 1 = 6. Evaluate 6 != 23, drop this branch.\n     |- Try 5 - 1 = 4. Evaluate 4 != 23, drop this branch.\n     |- Try 5 * 1 = 5. Evaluate 5 != 23, drop this branch.\n     |- Try 5 \/ 1 = 5. Evaluate 5 != 23, drop this branch.\n    |- Try 20 * 19 = 380. Add 380 to the number set. Current number set: [380, 5], target: 23, just two numbers left.\n     |- Try 380 + 5 = 385. Evaluate 385 != 23, drop this branch.\n     |- Try 380 - 5 = 375. Evaluate 375 != 23, drop this branch.\n     |- Try 380 * 5 = 1900. Evaluate 1900 != 23, drop this branch.\n     |- Try 380 \/ 5 = 76. Evaluate 76 != 23, drop this branch.\n    |- Try 20 \/ 19 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (5, 20) (numbers left: [19]). Try possible operations.\n    |- Try 20 + 5 = 25. Add 25 to the number set. Current number set: [25, 19], target: 23, just two numbers left.\n     |- Try 25 + 19 = 44. Evaluate 44 != 23, drop this branch.\n     |- Try 25 - 19 = 6. Evaluate 6 != 23, drop this branch.\n     |- Try 25 * 19 = 475. Evaluate 475 != 23, drop this branch.\n     |- Try 25 \/ 19 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 20 - 5 = 15. Add 15 to the number set. Current number set: [15, 19], target: 23, just two numbers left.\n     |- Try 19 + 15 = 34. Evaluate 34 != 23, drop this branch.\n     |- Try 19 - 15 = 4. Evaluate 4 != 23, drop this branch.\n     |- Try 19 * 15 = 285. Evaluate 285 != 23, drop this branch.\n     |- Try 19 \/ 15 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 20 * 5 = 100. Add 100 to the number set. Current number set: [100, 19], target: 23, just two numbers left.\n     |- Try 100 + 19 = 119. Evaluate 119 != 23, drop this branch.\n     |- Try 100 - 19 = 81. Evaluate 81 != 23, drop this branch.\n     |- Try 100 * 19 = 1900. Evaluate 1900 != 23, drop this branch.\n     |- Try 100 \/ 19 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 20 \/ 5 = 4. Add 4 to the number set. Current number set: [4, 19], target: 23, just two numbers left.\n     |- Try 19 + 4 = 23. Evaluate 23 == 23, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 19 + 4 = 23\nThe step before: 20 \/ 5 = 4\nThe first step: 42 - 23 = 19\n\nOutput the solution in the required format:\n<Solution>\n42 - 23 = 19\n20 \/ 5 = 4\n19 + 4 = 23\n<\/Solution>\n","item":{"nums":[23,5,42,20],"solution":["42 - 23 = 19","20 \/ 5 = 4","19 + 4 = 23"],"target":23}}
+{"instance_id":"countdown_8k_109","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [35, 40, 28, 37]\nTarget: 11","reference_output":"# Search Procedure\nInitial number set: [35, 40, 28, 37], target: 11. Options for choosing two numbers: [(35, 40), (35, 28), (35, 37), (40, 28), (40, 37), (28, 37)].\n |- Pick two numbers (35, 40) (numbers left: [28, 37]). Try possible operations.\n  |- Try 40 + 35 = 75. Add 75 to the number set. Current number set: [75, 28, 37], target: 11. Options for choosing two numbers: [(75, 28), (75, 37), (28, 37)].\n   |- Pick two numbers (75, 28) (numbers left: [37]). Try possible operations.\n    |- Try 75 + 28 = 103. Add 103 to the number set. Current number set: [103, 37], target: 11, just two numbers left.\n     |- Try 103 + 37 = 140. Evaluate 140 != 11, drop this branch.\n     |- Try 103 - 37 = 66. Evaluate 66 != 11, drop this branch.\n     |- Try 103 * 37 = 3811. 3811 exceeds the maximum intermediate result, drop this branch.\n     |- Try 103 \/ 37 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 75 - 28 = 47. Add 47 to the number set. Current number set: [47, 37], target: 11, just two numbers left.\n     |- Try 47 + 37 = 84. Evaluate 84 != 11, drop this branch.\n     |- Try 47 - 37 = 10. Evaluate 10 != 11, drop this branch.\n     |- Try 47 * 37 = 1739. Evaluate 1739 != 11, drop this branch.\n     |- Try 47 \/ 37 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 75 * 28 = 2100. 2100 exceeds the maximum intermediate result, drop this branch.\n    |- Try 75 \/ 28 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (75, 37) (numbers left: [28]). Try possible operations.\n    |- Try 75 + 37 = 112. Add 112 to the number set. Current number set: [112, 28], target: 11, just two numbers left.\n     |- Try 112 + 28 = 140. Evaluate 140 != 11, drop this branch.\n     |- Try 112 - 28 = 84. Evaluate 84 != 11, drop this branch.\n     |- Try 112 * 28 = 3136. 3136 exceeds the maximum intermediate result, drop this branch.\n     |- Try 112 \/ 28 = 4. Evaluate 4 != 11, drop this branch.\n    |- Try 75 - 37 = 38. Add 38 to the number set. Current number set: [38, 28], target: 11, just two numbers left.\n     |- Try 38 + 28 = 66. Evaluate 66 != 11, drop this branch.\n     |- Try 38 - 28 = 10. Evaluate 10 != 11, drop this branch.\n     |- Try 38 * 28 = 1064. Evaluate 1064 != 11, drop this branch.\n     |- Try 38 \/ 28 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 75 * 37 = 2775. 2775 exceeds the maximum intermediate result, drop this branch.\n    |- Try 75 \/ 37 = 2.0. 2.0 is a decimal, drop this branch.\n   |- Pick two numbers (28, 37) (numbers left: [75]). Try possible operations.\n    |- Try 37 + 28 = 65. Add 65 to the number set. Current number set: [65, 75], target: 11, just two numbers left.\n     |- Try 75 + 65 = 140. Evaluate 140 != 11, drop this branch.\n     |- Try 75 - 65 = 10. Evaluate 10 != 11, drop this branch.\n     |- Try 75 * 65 = 4875. 4875 exceeds the maximum intermediate result, drop this branch.\n     |- Try 75 \/ 65 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 37 - 28 = 9. Add 9 to the number set. Current number set: [9, 75], target: 11, just two numbers left.\n     |- Try 75 + 9 = 84. Evaluate 84 != 11, drop this branch.\n     |- Try 75 - 9 = 66. Evaluate 66 != 11, drop this branch.\n     |- Try 75 * 9 = 675. Evaluate 675 != 11, drop this branch.\n     |- Try 75 \/ 9 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 37 * 28 = 1036. Add 1036 to the number set. Current number set: [1036, 75], target: 11, just two numbers left.\n     |- Try 1036 + 75 = 1111. Evaluate 1111 != 11, drop this branch.\n     |- Try 1036 - 75 = 961. Evaluate 961 != 11, drop this branch.\n     |- Try 1036 * 75 = 77700. 77700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1036 \/ 75 = 13.8. 13.8 is a decimal, drop this branch.\n    |- Try 37 \/ 28 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 40 - 35 = 5. Add 5 to the number set. Current number set: [5, 28, 37], target: 11. Options for choosing two numbers: [(5, 28), (5, 37), (28, 37)].\n   |- Pick two numbers (5, 28) (numbers left: [37]). Try possible operations.\n    |- Try 28 + 5 = 33. Add 33 to the number set. Current number set: [33, 37], target: 11, just two numbers left.\n     |- Try 37 + 33 = 70. Evaluate 70 != 11, drop this branch.\n     |- Try 37 - 33 = 4. Evaluate 4 != 11, drop this branch.\n     |- Try 37 * 33 = 1221. Evaluate 1221 != 11, drop this branch.\n     |- Try 37 \/ 33 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 28 - 5 = 23. Add 23 to the number set. Current number set: [23, 37], target: 11, just two numbers left.\n     |- Try 37 + 23 = 60. Evaluate 60 != 11, drop this branch.\n     |- Try 37 - 23 = 14. Evaluate 14 != 11, drop this branch.\n     |- Try 37 * 23 = 851. Evaluate 851 != 11, drop this branch.\n     |- Try 37 \/ 23 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 28 * 5 = 140. Add 140 to the number set. Current number set: [140, 37], target: 11, just two numbers left.\n     |- Try 140 + 37 = 177. Evaluate 177 != 11, drop this branch.\n     |- Try 140 - 37 = 103. Evaluate 103 != 11, drop this branch.\n     |- Try 140 * 37 = 5180. 5180 exceeds the maximum intermediate result, drop this branch.\n     |- Try 140 \/ 37 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 28 \/ 5 = 5.6. 5.6 is a decimal, drop this branch.\n   |- Pick two numbers (5, 37) (numbers left: [28]). Try possible operations.\n    |- Try 37 + 5 = 42. Add 42 to the number set. Current number set: [42, 28], target: 11, just two numbers left.\n     |- Try 42 + 28 = 70. Evaluate 70 != 11, drop this branch.\n     |- Try 42 - 28 = 14. Evaluate 14 != 11, drop this branch.\n     |- Try 42 * 28 = 1176. Evaluate 1176 != 11, drop this branch.\n     |- Try 42 \/ 28 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 37 - 5 = 32. Add 32 to the number set. Current number set: [32, 28], target: 11, just two numbers left.\n     |- Try 32 + 28 = 60. Evaluate 60 != 11, drop this branch.\n     |- Try 32 - 28 = 4. Evaluate 4 != 11, drop this branch.\n     |- Try 32 * 28 = 896. Evaluate 896 != 11, drop this branch.\n     |- Try 32 \/ 28 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 37 * 5 = 185. Add 185 to the number set. Current number set: [185, 28], target: 11, just two numbers left.\n     |- Try 185 + 28 = 213. Evaluate 213 != 11, drop this branch.\n     |- Try 185 - 28 = 157. Evaluate 157 != 11, drop this branch.\n     |- Try 185 * 28 = 5180. 5180 exceeds the maximum intermediate result, drop this branch.\n     |- Try 185 \/ 28 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 37 \/ 5 = 7.4. 7.4 is a decimal, drop this branch.\n   |- Pick two numbers (28, 37) (numbers left: [5]). Try possible operations.\n    |- Try 37 + 28 = 65. Add 65 to the number set. Current number set: [65, 5], target: 11, just two numbers left.\n     |- Try 65 + 5 = 70. Evaluate 70 != 11, drop this branch.\n     |- Try 65 - 5 = 60. Evaluate 60 != 11, drop this branch.\n     |- Try 65 * 5 = 325. Evaluate 325 != 11, drop this branch.\n     |- Try 65 \/ 5 = 13. Evaluate 13 != 11, drop this branch.\n    |- Try 37 - 28 = 9. Add 9 to the number set. Current number set: [9, 5], target: 11, just two numbers left.\n     |- Try 9 + 5 = 14. Evaluate 14 != 11, drop this branch.\n     |- Try 9 - 5 = 4. Evaluate 4 != 11, drop this branch.\n     |- Try 9 * 5 = 45. Evaluate 45 != 11, drop this branch.\n     |- Try 9 \/ 5 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 37 * 28 = 1036. Add 1036 to the number set. Current number set: [1036, 5], target: 11, just two numbers left.\n     |- Try 1036 + 5 = 1041. Evaluate 1041 != 11, drop this branch.\n     |- Try 1036 - 5 = 1031. Evaluate 1031 != 11, drop this branch.\n     |- Try 1036 * 5 = 5180. 5180 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1036 \/ 5 = 207.2. 207.2 is a decimal, drop this branch.\n    |- Try 37 \/ 28 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 40 * 35 = 1400. Add 1400 to the number set. Current number set: [1400, 28, 37], target: 11. Options for choosing two numbers: [(1400, 28), (1400, 37), (28, 37)].\n   |- Pick two numbers (1400, 28) (numbers left: [37]). Try possible operations.\n    |- Try 1400 + 28 = 1428. Add 1428 to the number set. Current number set: [1428, 37], target: 11, just two numbers left.\n     |- Try 1428 + 37 = 1465. Evaluate 1465 != 11, drop this branch.\n     |- Try 1428 - 37 = 1391. Evaluate 1391 != 11, drop this branch.\n     |- Try 1428 * 37 = 52836. 52836 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1428 \/ 37 = 38.6. 38.6 is a decimal, drop this branch.\n    |- Try 1400 - 28 = 1372. Add 1372 to the number set. Current number set: [1372, 37], target: 11, just two numbers left.\n     |- Try 1372 + 37 = 1409. Evaluate 1409 != 11, drop this branch.\n     |- Try 1372 - 37 = 1335. Evaluate 1335 != 11, drop this branch.\n     |- Try 1372 * 37 = 50764. 50764 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1372 \/ 37 = 37.1. 37.1 is a decimal, drop this branch.\n    |- Try 1400 * 28 = 39200. 39200 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1400 \/ 28 = 50. Add 50 to the number set. Current number set: [50, 37], target: 11, just two numbers left.\n     |- Try 50 + 37 = 87. Evaluate 87 != 11, drop this branch.\n     |- Try 50 - 37 = 13. Evaluate 13 != 11, drop this branch.\n     |- Try 50 * 37 = 1850. Evaluate 1850 != 11, drop this branch.\n     |- Try 50 \/ 37 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (1400, 37) (numbers left: [28]). Try possible operations.\n    |- Try 1400 + 37 = 1437. Add 1437 to the number set. Current number set: [1437, 28], target: 11, just two numbers left.\n     |- Try 1437 + 28 = 1465. Evaluate 1465 != 11, drop this branch.\n     |- Try 1437 - 28 = 1409. Evaluate 1409 != 11, drop this branch.\n     |- Try 1437 * 28 = 40236. 40236 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1437 \/ 28 = 51.3. 51.3 is a decimal, drop this branch.\n    |- Try 1400 - 37 = 1363. Add 1363 to the number set. Current number set: [1363, 28], target: 11, just two numbers left.\n     |- Try 1363 + 28 = 1391. Evaluate 1391 != 11, drop this branch.\n     |- Try 1363 - 28 = 1335. Evaluate 1335 != 11, drop this branch.\n     |- Try 1363 * 28 = 38164. 38164 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1363 \/ 28 = 48.7. 48.7 is a decimal, drop this branch.\n    |- Try 1400 * 37 = 51800. 51800 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1400 \/ 37 = 37.8. 37.8 is a decimal, drop this branch.\n   |- Pick two numbers (28, 37) (numbers left: [1400]). Try possible operations.\n    |- Try 37 + 28 = 65. Add 65 to the number set. Current number set: [65, 1400], target: 11, just two numbers left.\n     |- Try 1400 + 65 = 1465. Evaluate 1465 != 11, drop this branch.\n     |- Try 1400 - 65 = 1335. Evaluate 1335 != 11, drop this branch.\n     |- Try 1400 * 65 = 91000. 91000 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1400 \/ 65 = 21.5. 21.5 is a decimal, drop this branch.\n    |- Try 37 - 28 = 9. Add 9 to the number set. Current number set: [9, 1400], target: 11, just two numbers left.\n     |- Try 1400 + 9 = 1409. Evaluate 1409 != 11, drop this branch.\n     |- Try 1400 - 9 = 1391. Evaluate 1391 != 11, drop this branch.\n     |- Try 1400 * 9 = 12600. 12600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1400 \/ 9 = 155.6. 155.6 is a decimal, drop this branch.\n    |- Try 37 * 28 = 1036. Add 1036 to the number set. Current number set: [1036, 1400], target: 11, just two numbers left.\n     |- Try 1400 + 1036 = 2436. 2436 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1400 - 1036 = 364. Evaluate 364 != 11, drop this branch.\n     |- Try 1400 * 1036 = 1450400. 1450400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1400 \/ 1036 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 37 \/ 28 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 40 \/ 35 = 1.1. 1.1 is a decimal, drop this branch.\n |- Pick two numbers (35, 28) (numbers left: [40, 37]). Try possible operations.\n  |- Try 35 + 28 = 63. Add 63 to the number set. Current number set: [63, 40, 37], target: 11. Options for choosing two numbers: [(63, 40), (63, 37), (40, 37)].\n   |- Pick two numbers (63, 40) (numbers left: [37]). Try possible operations.\n    |- Try 63 + 40 = 103. Add 103 to the number set. Current number set: [103, 37], target: 11, just two numbers left.\n     |- Try 103 + 37 = 140. Evaluate 140 != 11, drop this branch.\n     |- Try 103 - 37 = 66. Evaluate 66 != 11, drop this branch.\n     |- Try 103 * 37 = 3811. 3811 exceeds the maximum intermediate result, drop this branch.\n     |- Try 103 \/ 37 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 63 - 40 = 23. Add 23 to the number set. Current number set: [23, 37], target: 11, just two numbers left.\n     |- Try 37 + 23 = 60. Evaluate 60 != 11, drop this branch.\n     |- Try 37 - 23 = 14. Evaluate 14 != 11, drop this branch.\n     |- Try 37 * 23 = 851. Evaluate 851 != 11, drop this branch.\n     |- Try 37 \/ 23 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 63 * 40 = 2520. 2520 exceeds the maximum intermediate result, drop this branch.\n    |- Try 63 \/ 40 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (63, 37) (numbers left: [40]). Try possible operations.\n    |- Try 63 + 37 = 100. Add 100 to the number set. Current number set: [100, 40], target: 11, just two numbers left.\n     |- Try 100 + 40 = 140. Evaluate 140 != 11, drop this branch.\n     |- Try 100 - 40 = 60. Evaluate 60 != 11, drop this branch.\n     |- Try 100 * 40 = 4000. 4000 exceeds the maximum intermediate result, drop this branch.\n     |- Try 100 \/ 40 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 63 - 37 = 26. Add 26 to the number set. Current number set: [26, 40], target: 11, just two numbers left.\n     |- Try 40 + 26 = 66. Evaluate 66 != 11, drop this branch.\n     |- Try 40 - 26 = 14. Evaluate 14 != 11, drop this branch.\n     |- Try 40 * 26 = 1040. Evaluate 1040 != 11, drop this branch.\n     |- Try 40 \/ 26 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 63 * 37 = 2331. 2331 exceeds the maximum intermediate result, drop this branch.\n    |- Try 63 \/ 37 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (40, 37) (numbers left: [63]). Try possible operations.\n    |- Try 40 + 37 = 77. Add 77 to the number set. Current number set: [77, 63], target: 11, just two numbers left.\n     |- Try 77 + 63 = 140. Evaluate 140 != 11, drop this branch.\n     |- Try 77 - 63 = 14. Evaluate 14 != 11, drop this branch.\n     |- Try 77 * 63 = 4851. 4851 exceeds the maximum intermediate result, drop this branch.\n     |- Try 77 \/ 63 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 40 - 37 = 3. Add 3 to the number set. Current number set: [3, 63], target: 11, just two numbers left.\n     |- Try 63 + 3 = 66. Evaluate 66 != 11, drop this branch.\n     |- Try 63 - 3 = 60. Evaluate 60 != 11, drop this branch.\n     |- Try 63 * 3 = 189. Evaluate 189 != 11, drop this branch.\n     |- Try 63 \/ 3 = 21. Evaluate 21 != 11, drop this branch.\n    |- Try 40 * 37 = 1480. Add 1480 to the number set. Current number set: [1480, 63], target: 11, just two numbers left.\n     |- Try 1480 + 63 = 1543. Evaluate 1543 != 11, drop this branch.\n     |- Try 1480 - 63 = 1417. Evaluate 1417 != 11, drop this branch.\n     |- Try 1480 * 63 = 93240. 93240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1480 \/ 63 = 23.5. 23.5 is a decimal, drop this branch.\n    |- Try 40 \/ 37 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 35 - 28 = 7. Add 7 to the number set. Current number set: [7, 40, 37], target: 11. Options for choosing two numbers: [(7, 40), (7, 37), (40, 37)].\n   |- Pick two numbers (7, 40) (numbers left: [37]). Try possible operations.\n    |- Try 40 + 7 = 47. Add 47 to the number set. Current number set: [47, 37], target: 11, just two numbers left.\n     |- Try 47 + 37 = 84. Evaluate 84 != 11, drop this branch.\n     |- Try 47 - 37 = 10. Evaluate 10 != 11, drop this branch.\n     |- Try 47 * 37 = 1739. Evaluate 1739 != 11, drop this branch.\n     |- Try 47 \/ 37 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 40 - 7 = 33. Add 33 to the number set. Current number set: [33, 37], target: 11, just two numbers left.\n     |- Try 37 + 33 = 70. Evaluate 70 != 11, drop this branch.\n     |- Try 37 - 33 = 4. Evaluate 4 != 11, drop this branch.\n     |- Try 37 * 33 = 1221. Evaluate 1221 != 11, drop this branch.\n     |- Try 37 \/ 33 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 40 * 7 = 280. Add 280 to the number set. Current number set: [280, 37], target: 11, just two numbers left.\n     |- Try 280 + 37 = 317. Evaluate 317 != 11, drop this branch.\n     |- Try 280 - 37 = 243. Evaluate 243 != 11, drop this branch.\n     |- Try 280 * 37 = 10360. 10360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 280 \/ 37 = 7.6. 7.6 is a decimal, drop this branch.\n    |- Try 40 \/ 7 = 5.7. 5.7 is a decimal, drop this branch.\n   |- Pick two numbers (7, 37) (numbers left: [40]). Try possible operations.\n    |- Try 37 + 7 = 44. Add 44 to the number set. Current number set: [44, 40], target: 11, just two numbers left.\n     |- Try 44 + 40 = 84. Evaluate 84 != 11, drop this branch.\n     |- Try 44 - 40 = 4. Evaluate 4 != 11, drop this branch.\n     |- Try 44 * 40 = 1760. Evaluate 1760 != 11, drop this branch.\n     |- Try 44 \/ 40 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 37 - 7 = 30. Add 30 to the number set. Current number set: [30, 40], target: 11, just two numbers left.\n     |- Try 40 + 30 = 70. Evaluate 70 != 11, drop this branch.\n     |- Try 40 - 30 = 10. Evaluate 10 != 11, drop this branch.\n     |- Try 40 * 30 = 1200. Evaluate 1200 != 11, drop this branch.\n     |- Try 40 \/ 30 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 37 * 7 = 259. Add 259 to the number set. Current number set: [259, 40], target: 11, just two numbers left.\n     |- Try 259 + 40 = 299. Evaluate 299 != 11, drop this branch.\n     |- Try 259 - 40 = 219. Evaluate 219 != 11, drop this branch.\n     |- Try 259 * 40 = 10360. 10360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 259 \/ 40 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 37 \/ 7 = 5.3. 5.3 is a decimal, drop this branch.\n   |- Pick two numbers (40, 37) (numbers left: [7]). Try possible operations.\n    |- Try 40 + 37 = 77. Add 77 to the number set. Current number set: [77, 7], target: 11, just two numbers left.\n     |- Try 77 + 7 = 84. Evaluate 84 != 11, drop this branch.\n     |- Try 77 - 7 = 70. Evaluate 70 != 11, drop this branch.\n     |- Try 77 * 7 = 539. Evaluate 539 != 11, drop this branch.\n     |- Try 77 \/ 7 = 11. Evaluate 11 == 11, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 77 \/ 7 = 11\nThe step before: 40 + 37 = 77\nThe first step: 35 - 28 = 7\n\nOutput the solution in the required format:\n<Solution>\n35 - 28 = 7\n40 + 37 = 77\n77 \/ 7 = 11\n<\/Solution>\n","item":{"nums":[35,40,28,37],"solution":["35 - 28 = 7","40 + 37 = 77","77 \/ 7 = 11"],"target":11}}
+{"instance_id":"countdown_8k_110","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [30, 10, 16, 10]\nTarget: 50","reference_output":"# Search Procedure\nInitial number set: [30, 10, 16, 10], target: 50. Options for choosing two numbers: [(30, 10), (30, 16), (30, 10), (10, 16), (10, 10), (16, 10)].\n |- Pick two numbers (30, 10) (numbers left: [16, 10]). Try possible operations.\n  |- Try 30 + 10 = 40. Add 40 to the number set. Current number set: [40, 16, 10], target: 50. Options for choosing two numbers: [(40, 16), (40, 10), (16, 10)].\n   |- Pick two numbers (40, 16) (numbers left: [10]). Try possible operations.\n    |- Try 40 + 16 = 56. Add 56 to the number set. Current number set: [56, 10], target: 50, just two numbers left.\n     |- Try 56 + 10 = 66. Evaluate 66 != 50, drop this branch.\n     |- Try 56 - 10 = 46. Evaluate 46 != 50, drop this branch.\n     |- Try 56 * 10 = 560. Evaluate 560 != 50, drop this branch.\n     |- Try 56 \/ 10 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 40 - 16 = 24. Add 24 to the number set. Current number set: [24, 10], target: 50, just two numbers left.\n     |- Try 24 + 10 = 34. Evaluate 34 != 50, drop this branch.\n     |- Try 24 - 10 = 14. Evaluate 14 != 50, drop this branch.\n     |- Try 24 * 10 = 240. Evaluate 240 != 50, drop this branch.\n     |- Try 24 \/ 10 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 40 * 16 = 640. Add 640 to the number set. Current number set: [640, 10], target: 50, just two numbers left.\n     |- Try 640 + 10 = 650. Evaluate 650 != 50, drop this branch.\n     |- Try 640 - 10 = 630. Evaluate 630 != 50, drop this branch.\n     |- Try 640 * 10 = 6400. 6400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 640 \/ 10 = 64. Evaluate 64 != 50, drop this branch.\n    |- Try 40 \/ 16 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (40, 10) (numbers left: [16]). Try possible operations.\n    |- Try 40 + 10 = 50. Add 50 to the number set. Current number set: [50, 16], target: 50, just two numbers left.\n     |- Try 50 + 16 = 66. Evaluate 66 != 50, drop this branch.\n     |- Try 50 - 16 = 34. Evaluate 34 != 50, drop this branch.\n     |- Try 50 * 16 = 800. Evaluate 800 != 50, drop this branch.\n     |- Try 50 \/ 16 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 40 - 10 = 30. Add 30 to the number set. Current number set: [30, 16], target: 50, just two numbers left.\n     |- Try 30 + 16 = 46. Evaluate 46 != 50, drop this branch.\n     |- Try 30 - 16 = 14. Evaluate 14 != 50, drop this branch.\n     |- Try 30 * 16 = 480. Evaluate 480 != 50, drop this branch.\n     |- Try 30 \/ 16 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 40 * 10 = 400. Add 400 to the number set. Current number set: [400, 16], target: 50, just two numbers left.\n     |- Try 400 + 16 = 416. Evaluate 416 != 50, drop this branch.\n     |- Try 400 - 16 = 384. Evaluate 384 != 50, drop this branch.\n     |- Try 400 * 16 = 6400. 6400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 400 \/ 16 = 25. Evaluate 25 != 50, drop this branch.\n    |- Try 40 \/ 10 = 4. Add 4 to the number set. Current number set: [4, 16], target: 50, just two numbers left.\n     |- Try 16 + 4 = 20. Evaluate 20 != 50, drop this branch.\n     |- Try 16 - 4 = 12. Evaluate 12 != 50, drop this branch.\n     |- Try 16 * 4 = 64. Evaluate 64 != 50, drop this branch.\n     |- Try 16 \/ 4 = 4. Evaluate 4 != 50, drop this branch.\n   |- Pick two numbers (16, 10) (numbers left: [40]). Try possible operations.\n    |- Try 16 + 10 = 26. Add 26 to the number set. Current number set: [26, 40], target: 50, just two numbers left.\n     |- Try 40 + 26 = 66. Evaluate 66 != 50, drop this branch.\n     |- Try 40 - 26 = 14. Evaluate 14 != 50, drop this branch.\n     |- Try 40 * 26 = 1040. Evaluate 1040 != 50, drop this branch.\n     |- Try 40 \/ 26 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 16 - 10 = 6. Add 6 to the number set. Current number set: [6, 40], target: 50, just two numbers left.\n     |- Try 40 + 6 = 46. Evaluate 46 != 50, drop this branch.\n     |- Try 40 - 6 = 34. Evaluate 34 != 50, drop this branch.\n     |- Try 40 * 6 = 240. Evaluate 240 != 50, drop this branch.\n     |- Try 40 \/ 6 = 6.7. 6.7 is a decimal, drop this branch.\n    |- Try 16 * 10 = 160. Add 160 to the number set. Current number set: [160, 40], target: 50, just two numbers left.\n     |- Try 160 + 40 = 200. Evaluate 200 != 50, drop this branch.\n     |- Try 160 - 40 = 120. Evaluate 120 != 50, drop this branch.\n     |- Try 160 * 40 = 6400. 6400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 160 \/ 40 = 4. Evaluate 4 != 50, drop this branch.\n    |- Try 16 \/ 10 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 30 - 10 = 20. Add 20 to the number set. Current number set: [20, 16, 10], target: 50. Options for choosing two numbers: [(20, 16), (20, 10), (16, 10)].\n   |- Pick two numbers (20, 16) (numbers left: [10]). Try possible operations.\n    |- Try 20 + 16 = 36. Add 36 to the number set. Current number set: [36, 10], target: 50, just two numbers left.\n     |- Try 36 + 10 = 46. Evaluate 46 != 50, drop this branch.\n     |- Try 36 - 10 = 26. Evaluate 26 != 50, drop this branch.\n     |- Try 36 * 10 = 360. Evaluate 360 != 50, drop this branch.\n     |- Try 36 \/ 10 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 20 - 16 = 4. Add 4 to the number set. Current number set: [4, 10], target: 50, just two numbers left.\n     |- Try 10 + 4 = 14. Evaluate 14 != 50, drop this branch.\n     |- Try 10 - 4 = 6. Evaluate 6 != 50, drop this branch.\n     |- Try 10 * 4 = 40. Evaluate 40 != 50, drop this branch.\n     |- Try 10 \/ 4 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 20 * 16 = 320. Add 320 to the number set. Current number set: [320, 10], target: 50, just two numbers left.\n     |- Try 320 + 10 = 330. Evaluate 330 != 50, drop this branch.\n     |- Try 320 - 10 = 310. Evaluate 310 != 50, drop this branch.\n     |- Try 320 * 10 = 3200. 3200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 320 \/ 10 = 32. Evaluate 32 != 50, drop this branch.\n    |- Try 20 \/ 16 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (20, 10) (numbers left: [16]). Try possible operations.\n    |- Try 20 + 10 = 30. Add 30 to the number set. Current number set: [30, 16], target: 50, just two numbers left.\n     |- Try 30 + 16 = 46. Evaluate 46 != 50, drop this branch.\n     |- Try 30 - 16 = 14. Evaluate 14 != 50, drop this branch.\n     |- Try 30 * 16 = 480. Evaluate 480 != 50, drop this branch.\n     |- Try 30 \/ 16 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 20 - 10 = 10. Add 10 to the number set. Current number set: [10, 16], target: 50, just two numbers left.\n     |- Try 16 + 10 = 26. Evaluate 26 != 50, drop this branch.\n     |- Try 16 - 10 = 6. Evaluate 6 != 50, drop this branch.\n     |- Try 16 * 10 = 160. Evaluate 160 != 50, drop this branch.\n     |- Try 16 \/ 10 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 20 * 10 = 200. Add 200 to the number set. Current number set: [200, 16], target: 50, just two numbers left.\n     |- Try 200 + 16 = 216. Evaluate 216 != 50, drop this branch.\n     |- Try 200 - 16 = 184. Evaluate 184 != 50, drop this branch.\n     |- Try 200 * 16 = 3200. 3200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 200 \/ 16 = 12.5. 12.5 is a decimal, drop this branch.\n    |- Try 20 \/ 10 = 2. Add 2 to the number set. Current number set: [2, 16], target: 50, just two numbers left.\n     |- Try 16 + 2 = 18. Evaluate 18 != 50, drop this branch.\n     |- Try 16 - 2 = 14. Evaluate 14 != 50, drop this branch.\n     |- Try 16 * 2 = 32. Evaluate 32 != 50, drop this branch.\n     |- Try 16 \/ 2 = 8. Evaluate 8 != 50, drop this branch.\n   |- Pick two numbers (16, 10) (numbers left: [20]). Try possible operations.\n    |- Try 16 + 10 = 26. Add 26 to the number set. Current number set: [26, 20], target: 50, just two numbers left.\n     |- Try 26 + 20 = 46. Evaluate 46 != 50, drop this branch.\n     |- Try 26 - 20 = 6. Evaluate 6 != 50, drop this branch.\n     |- Try 26 * 20 = 520. Evaluate 520 != 50, drop this branch.\n     |- Try 26 \/ 20 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 16 - 10 = 6. Add 6 to the number set. Current number set: [6, 20], target: 50, just two numbers left.\n     |- Try 20 + 6 = 26. Evaluate 26 != 50, drop this branch.\n     |- Try 20 - 6 = 14. Evaluate 14 != 50, drop this branch.\n     |- Try 20 * 6 = 120. Evaluate 120 != 50, drop this branch.\n     |- Try 20 \/ 6 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 16 * 10 = 160. Add 160 to the number set. Current number set: [160, 20], target: 50, just two numbers left.\n     |- Try 160 + 20 = 180. Evaluate 180 != 50, drop this branch.\n     |- Try 160 - 20 = 140. Evaluate 140 != 50, drop this branch.\n     |- Try 160 * 20 = 3200. 3200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 160 \/ 20 = 8. Evaluate 8 != 50, drop this branch.\n    |- Try 16 \/ 10 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 30 * 10 = 300. Add 300 to the number set. Current number set: [300, 16, 10], target: 50. Options for choosing two numbers: [(300, 16), (300, 10), (16, 10)].\n   |- Pick two numbers (300, 16) (numbers left: [10]). Try possible operations.\n    |- Try 300 + 16 = 316. Add 316 to the number set. Current number set: [316, 10], target: 50, just two numbers left.\n     |- Try 316 + 10 = 326. Evaluate 326 != 50, drop this branch.\n     |- Try 316 - 10 = 306. Evaluate 306 != 50, drop this branch.\n     |- Try 316 * 10 = 3160. 3160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 316 \/ 10 = 31.6. 31.6 is a decimal, drop this branch.\n    |- Try 300 - 16 = 284. Add 284 to the number set. Current number set: [284, 10], target: 50, just two numbers left.\n     |- Try 284 + 10 = 294. Evaluate 294 != 50, drop this branch.\n     |- Try 284 - 10 = 274. Evaluate 274 != 50, drop this branch.\n     |- Try 284 * 10 = 2840. 2840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 284 \/ 10 = 28.4. 28.4 is a decimal, drop this branch.\n    |- Try 300 * 16 = 4800. 4800 exceeds the maximum intermediate result, drop this branch.\n    |- Try 300 \/ 16 = 18.8. 18.8 is a decimal, drop this branch.\n   |- Pick two numbers (300, 10) (numbers left: [16]). Try possible operations.\n    |- Try 300 + 10 = 310. Add 310 to the number set. Current number set: [310, 16], target: 50, just two numbers left.\n     |- Try 310 + 16 = 326. Evaluate 326 != 50, drop this branch.\n     |- Try 310 - 16 = 294. Evaluate 294 != 50, drop this branch.\n     |- Try 310 * 16 = 4960. 4960 exceeds the maximum intermediate result, drop this branch.\n     |- Try 310 \/ 16 = 19.4. 19.4 is a decimal, drop this branch.\n    |- Try 300 - 10 = 290. Add 290 to the number set. Current number set: [290, 16], target: 50, just two numbers left.\n     |- Try 290 + 16 = 306. Evaluate 306 != 50, drop this branch.\n     |- Try 290 - 16 = 274. Evaluate 274 != 50, drop this branch.\n     |- Try 290 * 16 = 4640. 4640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 290 \/ 16 = 18.1. 18.1 is a decimal, drop this branch.\n    |- Try 300 * 10 = 3000. 3000 exceeds the maximum intermediate result, drop this branch.\n    |- Try 300 \/ 10 = 30. Add 30 to the number set. Current number set: [30, 16], target: 50, just two numbers left.\n     |- Try 30 + 16 = 46. Evaluate 46 != 50, drop this branch.\n     |- Try 30 - 16 = 14. Evaluate 14 != 50, drop this branch.\n     |- Try 30 * 16 = 480. Evaluate 480 != 50, drop this branch.\n     |- Try 30 \/ 16 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (16, 10) (numbers left: [300]). Try possible operations.\n    |- Try 16 + 10 = 26. Add 26 to the number set. Current number set: [26, 300], target: 50, just two numbers left.\n     |- Try 300 + 26 = 326. Evaluate 326 != 50, drop this branch.\n     |- Try 300 - 26 = 274. Evaluate 274 != 50, drop this branch.\n     |- Try 300 * 26 = 7800. 7800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 300 \/ 26 = 11.5. 11.5 is a decimal, drop this branch.\n    |- Try 16 - 10 = 6. Add 6 to the number set. Current number set: [6, 300], target: 50, just two numbers left.\n     |- Try 300 + 6 = 306. Evaluate 306 != 50, drop this branch.\n     |- Try 300 - 6 = 294. Evaluate 294 != 50, drop this branch.\n     |- Try 300 * 6 = 1800. Evaluate 1800 != 50, drop this branch.\n     |- Try 300 \/ 6 = 50. Evaluate 50 == 50, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 300 \/ 6 = 50\nThe step before: 16 - 10 = 6\nThe first step: 30 * 10 = 300\n\nOutput the solution in the required format:\n<Solution>\n30 * 10 = 300\n16 - 10 = 6\n300 \/ 6 = 50\n<\/Solution>\n","item":{"nums":[30,10,16,10],"solution":["30 * 10 = 300","16 - 10 = 6","300 \/ 6 = 50"],"target":50}}
+{"instance_id":"countdown_8k_111","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [42, 10, 8, 20]\nTarget: 15","reference_output":"# Search Procedure\nInitial number set: [42, 10, 8, 20], target: 15. Options for choosing two numbers: [(42, 10), (42, 8), (42, 20), (10, 8), (10, 20), (8, 20)].\n |- Pick two numbers (42, 10) (numbers left: [8, 20]). Try possible operations.\n  |- Try 42 + 10 = 52. Add 52 to the number set. Current number set: [52, 8, 20], target: 15. Options for choosing two numbers: [(52, 8), (52, 20), (8, 20)].\n   |- Pick two numbers (52, 8) (numbers left: [20]). Try possible operations.\n    |- Try 52 + 8 = 60. Add 60 to the number set. Current number set: [60, 20], target: 15, just two numbers left.\n     |- Try 60 + 20 = 80. Evaluate 80 != 15, drop this branch.\n     |- Try 60 - 20 = 40. Evaluate 40 != 15, drop this branch.\n     |- Try 60 * 20 = 1200. Evaluate 1200 != 15, drop this branch.\n     |- Try 60 \/ 20 = 3. Evaluate 3 != 15, drop this branch.\n    |- Try 52 - 8 = 44. Add 44 to the number set. Current number set: [44, 20], target: 15, just two numbers left.\n     |- Try 44 + 20 = 64. Evaluate 64 != 15, drop this branch.\n     |- Try 44 - 20 = 24. Evaluate 24 != 15, drop this branch.\n     |- Try 44 * 20 = 880. Evaluate 880 != 15, drop this branch.\n     |- Try 44 \/ 20 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 52 * 8 = 416. Add 416 to the number set. Current number set: [416, 20], target: 15, just two numbers left.\n     |- Try 416 + 20 = 436. Evaluate 436 != 15, drop this branch.\n     |- Try 416 - 20 = 396. Evaluate 396 != 15, drop this branch.\n     |- Try 416 * 20 = 8320. 8320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 416 \/ 20 = 20.8. 20.8 is a decimal, drop this branch.\n    |- Try 52 \/ 8 = 6.5. 6.5 is a decimal, drop this branch.\n   |- Pick two numbers (52, 20) (numbers left: [8]). Try possible operations.\n    |- Try 52 + 20 = 72. Add 72 to the number set. Current number set: [72, 8], target: 15, just two numbers left.\n     |- Try 72 + 8 = 80. Evaluate 80 != 15, drop this branch.\n     |- Try 72 - 8 = 64. Evaluate 64 != 15, drop this branch.\n     |- Try 72 * 8 = 576. Evaluate 576 != 15, drop this branch.\n     |- Try 72 \/ 8 = 9. Evaluate 9 != 15, drop this branch.\n    |- Try 52 - 20 = 32. Add 32 to the number set. Current number set: [32, 8], target: 15, just two numbers left.\n     |- Try 32 + 8 = 40. Evaluate 40 != 15, drop this branch.\n     |- Try 32 - 8 = 24. Evaluate 24 != 15, drop this branch.\n     |- Try 32 * 8 = 256. Evaluate 256 != 15, drop this branch.\n     |- Try 32 \/ 8 = 4. Evaluate 4 != 15, drop this branch.\n    |- Try 52 * 20 = 1040. Add 1040 to the number set. Current number set: [1040, 8], target: 15, just two numbers left.\n     |- Try 1040 + 8 = 1048. Evaluate 1048 != 15, drop this branch.\n     |- Try 1040 - 8 = 1032. Evaluate 1032 != 15, drop this branch.\n     |- Try 1040 * 8 = 8320. 8320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1040 \/ 8 = 130. Evaluate 130 != 15, drop this branch.\n    |- Try 52 \/ 20 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (8, 20) (numbers left: [52]). Try possible operations.\n    |- Try 20 + 8 = 28. Add 28 to the number set. Current number set: [28, 52], target: 15, just two numbers left.\n     |- Try 52 + 28 = 80. Evaluate 80 != 15, drop this branch.\n     |- Try 52 - 28 = 24. Evaluate 24 != 15, drop this branch.\n     |- Try 52 * 28 = 1456. Evaluate 1456 != 15, drop this branch.\n     |- Try 52 \/ 28 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 20 - 8 = 12. Add 12 to the number set. Current number set: [12, 52], target: 15, just two numbers left.\n     |- Try 52 + 12 = 64. Evaluate 64 != 15, drop this branch.\n     |- Try 52 - 12 = 40. Evaluate 40 != 15, drop this branch.\n     |- Try 52 * 12 = 624. Evaluate 624 != 15, drop this branch.\n     |- Try 52 \/ 12 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 20 * 8 = 160. Add 160 to the number set. Current number set: [160, 52], target: 15, just two numbers left.\n     |- Try 160 + 52 = 212. Evaluate 212 != 15, drop this branch.\n     |- Try 160 - 52 = 108. Evaluate 108 != 15, drop this branch.\n     |- Try 160 * 52 = 8320. 8320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 160 \/ 52 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 20 \/ 8 = 2.5. 2.5 is a decimal, drop this branch.\n  |- Try 42 - 10 = 32. Add 32 to the number set. Current number set: [32, 8, 20], target: 15. Options for choosing two numbers: [(32, 8), (32, 20), (8, 20)].\n   |- Pick two numbers (32, 8) (numbers left: [20]). Try possible operations.\n    |- Try 32 + 8 = 40. Add 40 to the number set. Current number set: [40, 20], target: 15, just two numbers left.\n     |- Try 40 + 20 = 60. Evaluate 60 != 15, drop this branch.\n     |- Try 40 - 20 = 20. Evaluate 20 != 15, drop this branch.\n     |- Try 40 * 20 = 800. Evaluate 800 != 15, drop this branch.\n     |- Try 40 \/ 20 = 2. Evaluate 2 != 15, drop this branch.\n    |- Try 32 - 8 = 24. Add 24 to the number set. Current number set: [24, 20], target: 15, just two numbers left.\n     |- Try 24 + 20 = 44. Evaluate 44 != 15, drop this branch.\n     |- Try 24 - 20 = 4. Evaluate 4 != 15, drop this branch.\n     |- Try 24 * 20 = 480. Evaluate 480 != 15, drop this branch.\n     |- Try 24 \/ 20 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 32 * 8 = 256. Add 256 to the number set. Current number set: [256, 20], target: 15, just two numbers left.\n     |- Try 256 + 20 = 276. Evaluate 276 != 15, drop this branch.\n     |- Try 256 - 20 = 236. Evaluate 236 != 15, drop this branch.\n     |- Try 256 * 20 = 5120. 5120 exceeds the maximum intermediate result, drop this branch.\n     |- Try 256 \/ 20 = 12.8. 12.8 is a decimal, drop this branch.\n    |- Try 32 \/ 8 = 4. Add 4 to the number set. Current number set: [4, 20], target: 15, just two numbers left.\n     |- Try 20 + 4 = 24. Evaluate 24 != 15, drop this branch.\n     |- Try 20 - 4 = 16. Evaluate 16 != 15, drop this branch.\n     |- Try 20 * 4 = 80. Evaluate 80 != 15, drop this branch.\n     |- Try 20 \/ 4 = 5. Evaluate 5 != 15, drop this branch.\n   |- Pick two numbers (32, 20) (numbers left: [8]). Try possible operations.\n    |- Try 32 + 20 = 52. Add 52 to the number set. Current number set: [52, 8], target: 15, just two numbers left.\n     |- Try 52 + 8 = 60. Evaluate 60 != 15, drop this branch.\n     |- Try 52 - 8 = 44. Evaluate 44 != 15, drop this branch.\n     |- Try 52 * 8 = 416. Evaluate 416 != 15, drop this branch.\n     |- Try 52 \/ 8 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 32 - 20 = 12. Add 12 to the number set. Current number set: [12, 8], target: 15, just two numbers left.\n     |- Try 12 + 8 = 20. Evaluate 20 != 15, drop this branch.\n     |- Try 12 - 8 = 4. Evaluate 4 != 15, drop this branch.\n     |- Try 12 * 8 = 96. Evaluate 96 != 15, drop this branch.\n     |- Try 12 \/ 8 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 32 * 20 = 640. Add 640 to the number set. Current number set: [640, 8], target: 15, just two numbers left.\n     |- Try 640 + 8 = 648. Evaluate 648 != 15, drop this branch.\n     |- Try 640 - 8 = 632. Evaluate 632 != 15, drop this branch.\n     |- Try 640 * 8 = 5120. 5120 exceeds the maximum intermediate result, drop this branch.\n     |- Try 640 \/ 8 = 80. Evaluate 80 != 15, drop this branch.\n    |- Try 32 \/ 20 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (8, 20) (numbers left: [32]). Try possible operations.\n    |- Try 20 + 8 = 28. Add 28 to the number set. Current number set: [28, 32], target: 15, just two numbers left.\n     |- Try 32 + 28 = 60. Evaluate 60 != 15, drop this branch.\n     |- Try 32 - 28 = 4. Evaluate 4 != 15, drop this branch.\n     |- Try 32 * 28 = 896. Evaluate 896 != 15, drop this branch.\n     |- Try 32 \/ 28 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 20 - 8 = 12. Add 12 to the number set. Current number set: [12, 32], target: 15, just two numbers left.\n     |- Try 32 + 12 = 44. Evaluate 44 != 15, drop this branch.\n     |- Try 32 - 12 = 20. Evaluate 20 != 15, drop this branch.\n     |- Try 32 * 12 = 384. Evaluate 384 != 15, drop this branch.\n     |- Try 32 \/ 12 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 20 * 8 = 160. Add 160 to the number set. Current number set: [160, 32], target: 15, just two numbers left.\n     |- Try 160 + 32 = 192. Evaluate 192 != 15, drop this branch.\n     |- Try 160 - 32 = 128. Evaluate 128 != 15, drop this branch.\n     |- Try 160 * 32 = 5120. 5120 exceeds the maximum intermediate result, drop this branch.\n     |- Try 160 \/ 32 = 5. Evaluate 5 != 15, drop this branch.\n    |- Try 20 \/ 8 = 2.5. 2.5 is a decimal, drop this branch.\n  |- Try 42 * 10 = 420. Add 420 to the number set. Current number set: [420, 8, 20], target: 15. Options for choosing two numbers: [(420, 8), (420, 20), (8, 20)].\n   |- Pick two numbers (420, 8) (numbers left: [20]). Try possible operations.\n    |- Try 420 + 8 = 428. Add 428 to the number set. Current number set: [428, 20], target: 15, just two numbers left.\n     |- Try 428 + 20 = 448. Evaluate 448 != 15, drop this branch.\n     |- Try 428 - 20 = 408. Evaluate 408 != 15, drop this branch.\n     |- Try 428 * 20 = 8560. 8560 exceeds the maximum intermediate result, drop this branch.\n     |- Try 428 \/ 20 = 21.4. 21.4 is a decimal, drop this branch.\n    |- Try 420 - 8 = 412. Add 412 to the number set. Current number set: [412, 20], target: 15, just two numbers left.\n     |- Try 412 + 20 = 432. Evaluate 432 != 15, drop this branch.\n     |- Try 412 - 20 = 392. Evaluate 392 != 15, drop this branch.\n     |- Try 412 * 20 = 8240. 8240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 412 \/ 20 = 20.6. 20.6 is a decimal, drop this branch.\n    |- Try 420 * 8 = 3360. 3360 exceeds the maximum intermediate result, drop this branch.\n    |- Try 420 \/ 8 = 52.5. 52.5 is a decimal, drop this branch.\n   |- Pick two numbers (420, 20) (numbers left: [8]). Try possible operations.\n    |- Try 420 + 20 = 440. Add 440 to the number set. Current number set: [440, 8], target: 15, just two numbers left.\n     |- Try 440 + 8 = 448. Evaluate 448 != 15, drop this branch.\n     |- Try 440 - 8 = 432. Evaluate 432 != 15, drop this branch.\n     |- Try 440 * 8 = 3520. 3520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 440 \/ 8 = 55. Evaluate 55 != 15, drop this branch.\n    |- Try 420 - 20 = 400. Add 400 to the number set. Current number set: [400, 8], target: 15, just two numbers left.\n     |- Try 400 + 8 = 408. Evaluate 408 != 15, drop this branch.\n     |- Try 400 - 8 = 392. Evaluate 392 != 15, drop this branch.\n     |- Try 400 * 8 = 3200. 3200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 400 \/ 8 = 50. Evaluate 50 != 15, drop this branch.\n    |- Try 420 * 20 = 8400. 8400 exceeds the maximum intermediate result, drop this branch.\n    |- Try 420 \/ 20 = 21. Add 21 to the number set. Current number set: [21, 8], target: 15, just two numbers left.\n     |- Try 21 + 8 = 29. Evaluate 29 != 15, drop this branch.\n     |- Try 21 - 8 = 13. Evaluate 13 != 15, drop this branch.\n     |- Try 21 * 8 = 168. Evaluate 168 != 15, drop this branch.\n     |- Try 21 \/ 8 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (8, 20) (numbers left: [420]). Try possible operations.\n    |- Try 20 + 8 = 28. Add 28 to the number set. Current number set: [28, 420], target: 15, just two numbers left.\n     |- Try 420 + 28 = 448. Evaluate 448 != 15, drop this branch.\n     |- Try 420 - 28 = 392. Evaluate 392 != 15, drop this branch.\n     |- Try 420 * 28 = 11760. 11760 exceeds the maximum intermediate result, drop this branch.\n     |- Try 420 \/ 28 = 15. Evaluate 15 == 15, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 420 \/ 28 = 15\nThe step before: 20 + 8 = 28\nThe first step: 42 * 10 = 420\n\nOutput the solution in the required format:\n<Solution>\n42 * 10 = 420\n20 + 8 = 28\n420 \/ 28 = 15\n<\/Solution>\n","item":{"nums":[42,10,8,20],"solution":["42 * 10 = 420","20 + 8 = 28","420 \/ 28 = 15"],"target":15}}
+{"instance_id":"countdown_8k_112","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [3, 33, 22, 30]\nTarget: 15","reference_output":"# Search Procedure\nInitial number set: [3, 33, 22, 30], target: 15. Options for choosing two numbers: [(3, 33), (3, 22), (3, 30), (33, 22), (33, 30), (22, 30)].\n |- Pick two numbers (3, 33) (numbers left: [22, 30]). Try possible operations.\n  |- Try 33 + 3 = 36. Add 36 to the number set. Current number set: [36, 22, 30], target: 15. Options for choosing two numbers: [(36, 22), (36, 30), (22, 30)].\n   |- Pick two numbers (36, 22) (numbers left: [30]). Try possible operations.\n    |- Try 36 + 22 = 58. Add 58 to the number set. Current number set: [58, 30], target: 15, just two numbers left.\n     |- Try 58 + 30 = 88. Evaluate 88 != 15, drop this branch.\n     |- Try 58 - 30 = 28. Evaluate 28 != 15, drop this branch.\n     |- Try 58 * 30 = 1740. Evaluate 1740 != 15, drop this branch.\n     |- Try 58 \/ 30 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 36 - 22 = 14. Add 14 to the number set. Current number set: [14, 30], target: 15, just two numbers left.\n     |- Try 30 + 14 = 44. Evaluate 44 != 15, drop this branch.\n     |- Try 30 - 14 = 16. Evaluate 16 != 15, drop this branch.\n     |- Try 30 * 14 = 420. Evaluate 420 != 15, drop this branch.\n     |- Try 30 \/ 14 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 36 * 22 = 792. Add 792 to the number set. Current number set: [792, 30], target: 15, just two numbers left.\n     |- Try 792 + 30 = 822. Evaluate 822 != 15, drop this branch.\n     |- Try 792 - 30 = 762. Evaluate 762 != 15, drop this branch.\n     |- Try 792 * 30 = 23760. 23760 exceeds the maximum intermediate result, drop this branch.\n     |- Try 792 \/ 30 = 26.4. 26.4 is a decimal, drop this branch.\n    |- Try 36 \/ 22 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (36, 30) (numbers left: [22]). Try possible operations.\n    |- Try 36 + 30 = 66. Add 66 to the number set. Current number set: [66, 22], target: 15, just two numbers left.\n     |- Try 66 + 22 = 88. Evaluate 88 != 15, drop this branch.\n     |- Try 66 - 22 = 44. Evaluate 44 != 15, drop this branch.\n     |- Try 66 * 22 = 1452. Evaluate 1452 != 15, drop this branch.\n     |- Try 66 \/ 22 = 3. Evaluate 3 != 15, drop this branch.\n    |- Try 36 - 30 = 6. Add 6 to the number set. Current number set: [6, 22], target: 15, just two numbers left.\n     |- Try 22 + 6 = 28. Evaluate 28 != 15, drop this branch.\n     |- Try 22 - 6 = 16. Evaluate 16 != 15, drop this branch.\n     |- Try 22 * 6 = 132. Evaluate 132 != 15, drop this branch.\n     |- Try 22 \/ 6 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 36 * 30 = 1080. Add 1080 to the number set. Current number set: [1080, 22], target: 15, just two numbers left.\n     |- Try 1080 + 22 = 1102. Evaluate 1102 != 15, drop this branch.\n     |- Try 1080 - 22 = 1058. Evaluate 1058 != 15, drop this branch.\n     |- Try 1080 * 22 = 23760. 23760 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1080 \/ 22 = 49.1. 49.1 is a decimal, drop this branch.\n    |- Try 36 \/ 30 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (22, 30) (numbers left: [36]). Try possible operations.\n    |- Try 30 + 22 = 52. Add 52 to the number set. Current number set: [52, 36], target: 15, just two numbers left.\n     |- Try 52 + 36 = 88. Evaluate 88 != 15, drop this branch.\n     |- Try 52 - 36 = 16. Evaluate 16 != 15, drop this branch.\n     |- Try 52 * 36 = 1872. Evaluate 1872 != 15, drop this branch.\n     |- Try 52 \/ 36 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 30 - 22 = 8. Add 8 to the number set. Current number set: [8, 36], target: 15, just two numbers left.\n     |- Try 36 + 8 = 44. Evaluate 44 != 15, drop this branch.\n     |- Try 36 - 8 = 28. Evaluate 28 != 15, drop this branch.\n     |- Try 36 * 8 = 288. Evaluate 288 != 15, drop this branch.\n     |- Try 36 \/ 8 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 30 * 22 = 660. Add 660 to the number set. Current number set: [660, 36], target: 15, just two numbers left.\n     |- Try 660 + 36 = 696. Evaluate 696 != 15, drop this branch.\n     |- Try 660 - 36 = 624. Evaluate 624 != 15, drop this branch.\n     |- Try 660 * 36 = 23760. 23760 exceeds the maximum intermediate result, drop this branch.\n     |- Try 660 \/ 36 = 18.3. 18.3 is a decimal, drop this branch.\n    |- Try 30 \/ 22 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 33 - 3 = 30. Add 30 to the number set. Current number set: [30, 22, 30], target: 15. Options for choosing two numbers: [(30, 22), (30, 30), (22, 30)].\n   |- Pick two numbers (30, 22) (numbers left: [30]). Try possible operations.\n    |- Try 30 + 22 = 52. Add 52 to the number set. Current number set: [52, 30], target: 15, just two numbers left.\n     |- Try 52 + 30 = 82. Evaluate 82 != 15, drop this branch.\n     |- Try 52 - 30 = 22. Evaluate 22 != 15, drop this branch.\n     |- Try 52 * 30 = 1560. Evaluate 1560 != 15, drop this branch.\n     |- Try 52 \/ 30 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 30 - 22 = 8. Add 8 to the number set. Current number set: [8, 30], target: 15, just two numbers left.\n     |- Try 30 + 8 = 38. Evaluate 38 != 15, drop this branch.\n     |- Try 30 - 8 = 22. Evaluate 22 != 15, drop this branch.\n     |- Try 30 * 8 = 240. Evaluate 240 != 15, drop this branch.\n     |- Try 30 \/ 8 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 30 * 22 = 660. Add 660 to the number set. Current number set: [660, 30], target: 15, just two numbers left.\n     |- Try 660 + 30 = 690. Evaluate 690 != 15, drop this branch.\n     |- Try 660 - 30 = 630. Evaluate 630 != 15, drop this branch.\n     |- Try 660 * 30 = 19800. 19800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 660 \/ 30 = 22. Evaluate 22 != 15, drop this branch.\n    |- Try 30 \/ 22 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (30, 30) (numbers left: [22]). Try possible operations.\n    |- Try 30 + 30 = 60. Add 60 to the number set. Current number set: [60, 22], target: 15, just two numbers left.\n     |- Try 60 + 22 = 82. Evaluate 82 != 15, drop this branch.\n     |- Try 60 - 22 = 38. Evaluate 38 != 15, drop this branch.\n     |- Try 60 * 22 = 1320. Evaluate 1320 != 15, drop this branch.\n     |- Try 60 \/ 22 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 30 - 30 = 0. Add 0 to the number set. Current number set: [0, 22], target: 15, just two numbers left.\n     |- Try 22 + 0 = 22. Evaluate 22 != 15, drop this branch.\n     |- Try 22 - 0 = 22. Evaluate 22 != 15, drop this branch.\n     |- Try 22 * 0 = 0. Evaluate 0 != 15, drop this branch.\n     |- Try 22 \/ 0 (invalid operation). drop this branch.\n    |- Try 30 * 30 = 900. Add 900 to the number set. Current number set: [900, 22], target: 15, just two numbers left.\n     |- Try 900 + 22 = 922. Evaluate 922 != 15, drop this branch.\n     |- Try 900 - 22 = 878. Evaluate 878 != 15, drop this branch.\n     |- Try 900 * 22 = 19800. 19800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 900 \/ 22 = 40.9. 40.9 is a decimal, drop this branch.\n    |- Try 30 \/ 30 = 1. Add 1 to the number set. Current number set: [1, 22], target: 15, just two numbers left.\n     |- Try 22 + 1 = 23. Evaluate 23 != 15, drop this branch.\n     |- Try 22 - 1 = 21. Evaluate 21 != 15, drop this branch.\n     |- Try 22 * 1 = 22. Evaluate 22 != 15, drop this branch.\n     |- Try 22 \/ 1 = 22. Evaluate 22 != 15, drop this branch.\n   |- Pick two numbers (22, 30) (numbers left: [30]). Try possible operations.\n    |- Try 30 + 22 = 52. Add 52 to the number set. Current number set: [52, 30], target: 15, just two numbers left.\n     |- Try 52 + 30 = 82. Evaluate 82 != 15, drop this branch.\n     |- Try 52 - 30 = 22. Evaluate 22 != 15, drop this branch.\n     |- Try 52 * 30 = 1560. Evaluate 1560 != 15, drop this branch.\n     |- Try 52 \/ 30 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 30 - 22 = 8. Add 8 to the number set. Current number set: [8, 30], target: 15, just two numbers left.\n     |- Try 30 + 8 = 38. Evaluate 38 != 15, drop this branch.\n     |- Try 30 - 8 = 22. Evaluate 22 != 15, drop this branch.\n     |- Try 30 * 8 = 240. Evaluate 240 != 15, drop this branch.\n     |- Try 30 \/ 8 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 30 * 22 = 660. Add 660 to the number set. Current number set: [660, 30], target: 15, just two numbers left.\n     |- Try 660 + 30 = 690. Evaluate 690 != 15, drop this branch.\n     |- Try 660 - 30 = 630. Evaluate 630 != 15, drop this branch.\n     |- Try 660 * 30 = 19800. 19800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 660 \/ 30 = 22. Evaluate 22 != 15, drop this branch.\n    |- Try 30 \/ 22 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 33 * 3 = 99. Add 99 to the number set. Current number set: [99, 22, 30], target: 15. Options for choosing two numbers: [(99, 22), (99, 30), (22, 30)].\n   |- Pick two numbers (99, 22) (numbers left: [30]). Try possible operations.\n    |- Try 99 + 22 = 121. Add 121 to the number set. Current number set: [121, 30], target: 15, just two numbers left.\n     |- Try 121 + 30 = 151. Evaluate 151 != 15, drop this branch.\n     |- Try 121 - 30 = 91. Evaluate 91 != 15, drop this branch.\n     |- Try 121 * 30 = 3630. 3630 exceeds the maximum intermediate result, drop this branch.\n     |- Try 121 \/ 30 = 4.0. 4.0 is a decimal, drop this branch.\n    |- Try 99 - 22 = 77. Add 77 to the number set. Current number set: [77, 30], target: 15, just two numbers left.\n     |- Try 77 + 30 = 107. Evaluate 107 != 15, drop this branch.\n     |- Try 77 - 30 = 47. Evaluate 47 != 15, drop this branch.\n     |- Try 77 * 30 = 2310. 2310 exceeds the maximum intermediate result, drop this branch.\n     |- Try 77 \/ 30 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 99 * 22 = 2178. 2178 exceeds the maximum intermediate result, drop this branch.\n    |- Try 99 \/ 22 = 4.5. 4.5 is a decimal, drop this branch.\n   |- Pick two numbers (99, 30) (numbers left: [22]). Try possible operations.\n    |- Try 99 + 30 = 129. Add 129 to the number set. Current number set: [129, 22], target: 15, just two numbers left.\n     |- Try 129 + 22 = 151. Evaluate 151 != 15, drop this branch.\n     |- Try 129 - 22 = 107. Evaluate 107 != 15, drop this branch.\n     |- Try 129 * 22 = 2838. 2838 exceeds the maximum intermediate result, drop this branch.\n     |- Try 129 \/ 22 = 5.9. 5.9 is a decimal, drop this branch.\n    |- Try 99 - 30 = 69. Add 69 to the number set. Current number set: [69, 22], target: 15, just two numbers left.\n     |- Try 69 + 22 = 91. Evaluate 91 != 15, drop this branch.\n     |- Try 69 - 22 = 47. Evaluate 47 != 15, drop this branch.\n     |- Try 69 * 22 = 1518. Evaluate 1518 != 15, drop this branch.\n     |- Try 69 \/ 22 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 99 * 30 = 2970. 2970 exceeds the maximum intermediate result, drop this branch.\n    |- Try 99 \/ 30 = 3.3. 3.3 is a decimal, drop this branch.\n   |- Pick two numbers (22, 30) (numbers left: [99]). Try possible operations.\n    |- Try 30 + 22 = 52. Add 52 to the number set. Current number set: [52, 99], target: 15, just two numbers left.\n     |- Try 99 + 52 = 151. Evaluate 151 != 15, drop this branch.\n     |- Try 99 - 52 = 47. Evaluate 47 != 15, drop this branch.\n     |- Try 99 * 52 = 5148. 5148 exceeds the maximum intermediate result, drop this branch.\n     |- Try 99 \/ 52 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 30 - 22 = 8. Add 8 to the number set. Current number set: [8, 99], target: 15, just two numbers left.\n     |- Try 99 + 8 = 107. Evaluate 107 != 15, drop this branch.\n     |- Try 99 - 8 = 91. Evaluate 91 != 15, drop this branch.\n     |- Try 99 * 8 = 792. Evaluate 792 != 15, drop this branch.\n     |- Try 99 \/ 8 = 12.4. 12.4 is a decimal, drop this branch.\n    |- Try 30 * 22 = 660. Add 660 to the number set. Current number set: [660, 99], target: 15, just two numbers left.\n     |- Try 660 + 99 = 759. Evaluate 759 != 15, drop this branch.\n     |- Try 660 - 99 = 561. Evaluate 561 != 15, drop this branch.\n     |- Try 660 * 99 = 65340. 65340 exceeds the maximum intermediate result, drop this branch.\n     |- Try 660 \/ 99 = 6.7. 6.7 is a decimal, drop this branch.\n    |- Try 30 \/ 22 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 33 \/ 3 = 11. Add 11 to the number set. Current number set: [11, 22, 30], target: 15. Options for choosing two numbers: [(11, 22), (11, 30), (22, 30)].\n   |- Pick two numbers (11, 22) (numbers left: [30]). Try possible operations.\n    |- Try 22 + 11 = 33. Add 33 to the number set. Current number set: [33, 30], target: 15, just two numbers left.\n     |- Try 33 + 30 = 63. Evaluate 63 != 15, drop this branch.\n     |- Try 33 - 30 = 3. Evaluate 3 != 15, drop this branch.\n     |- Try 33 * 30 = 990. Evaluate 990 != 15, drop this branch.\n     |- Try 33 \/ 30 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 22 - 11 = 11. Add 11 to the number set. Current number set: [11, 30], target: 15, just two numbers left.\n     |- Try 30 + 11 = 41. Evaluate 41 != 15, drop this branch.\n     |- Try 30 - 11 = 19. Evaluate 19 != 15, drop this branch.\n     |- Try 30 * 11 = 330. Evaluate 330 != 15, drop this branch.\n     |- Try 30 \/ 11 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 22 * 11 = 242. Add 242 to the number set. Current number set: [242, 30], target: 15, just two numbers left.\n     |- Try 242 + 30 = 272. Evaluate 272 != 15, drop this branch.\n     |- Try 242 - 30 = 212. Evaluate 212 != 15, drop this branch.\n     |- Try 242 * 30 = 7260. 7260 exceeds the maximum intermediate result, drop this branch.\n     |- Try 242 \/ 30 = 8.1. 8.1 is a decimal, drop this branch.\n    |- Try 22 \/ 11 = 2. Add 2 to the number set. Current number set: [2, 30], target: 15, just two numbers left.\n     |- Try 30 + 2 = 32. Evaluate 32 != 15, drop this branch.\n     |- Try 30 - 2 = 28. Evaluate 28 != 15, drop this branch.\n     |- Try 30 * 2 = 60. Evaluate 60 != 15, drop this branch.\n     |- Try 30 \/ 2 = 15. Evaluate 15 == 15, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 30 \/ 2 = 15\nThe step before: 22 \/ 11 = 2\nThe first step: 33 \/ 3 = 11\n\nOutput the solution in the required format:\n<Solution>\n33 \/ 3 = 11\n22 \/ 11 = 2\n30 \/ 2 = 15\n<\/Solution>\n","item":{"nums":[3,33,22,30],"solution":["33 \/ 3 = 11","22 \/ 11 = 2","30 \/ 2 = 15"],"target":15}}
+{"instance_id":"countdown_8k_113","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [38, 6, 33, 2]\nTarget: 42","reference_output":"# Search Procedure\nInitial number set: [38, 6, 33, 2], target: 42. Options for choosing two numbers: [(38, 6), (38, 33), (38, 2), (6, 33), (6, 2), (33, 2)].\n |- Pick two numbers (38, 6) (numbers left: [33, 2]). Try possible operations.\n  |- Try 38 + 6 = 44. Add 44 to the number set. Current number set: [44, 33, 2], target: 42. Options for choosing two numbers: [(44, 33), (44, 2), (33, 2)].\n   |- Pick two numbers (44, 33) (numbers left: [2]). Try possible operations.\n    |- Try 44 + 33 = 77. Add 77 to the number set. Current number set: [77, 2], target: 42, just two numbers left.\n     |- Try 77 + 2 = 79. Evaluate 79 != 42, drop this branch.\n     |- Try 77 - 2 = 75. Evaluate 75 != 42, drop this branch.\n     |- Try 77 * 2 = 154. Evaluate 154 != 42, drop this branch.\n     |- Try 77 \/ 2 = 38.5. 38.5 is a decimal, drop this branch.\n    |- Try 44 - 33 = 11. Add 11 to the number set. Current number set: [11, 2], target: 42, just two numbers left.\n     |- Try 11 + 2 = 13. Evaluate 13 != 42, drop this branch.\n     |- Try 11 - 2 = 9. Evaluate 9 != 42, drop this branch.\n     |- Try 11 * 2 = 22. Evaluate 22 != 42, drop this branch.\n     |- Try 11 \/ 2 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 44 * 33 = 1452. Add 1452 to the number set. Current number set: [1452, 2], target: 42, just two numbers left.\n     |- Try 1452 + 2 = 1454. Evaluate 1454 != 42, drop this branch.\n     |- Try 1452 - 2 = 1450. Evaluate 1450 != 42, drop this branch.\n     |- Try 1452 * 2 = 2904. 2904 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1452 \/ 2 = 726. Evaluate 726 != 42, drop this branch.\n    |- Try 44 \/ 33 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (44, 2) (numbers left: [33]). Try possible operations.\n    |- Try 44 + 2 = 46. Add 46 to the number set. Current number set: [46, 33], target: 42, just two numbers left.\n     |- Try 46 + 33 = 79. Evaluate 79 != 42, drop this branch.\n     |- Try 46 - 33 = 13. Evaluate 13 != 42, drop this branch.\n     |- Try 46 * 33 = 1518. Evaluate 1518 != 42, drop this branch.\n     |- Try 46 \/ 33 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 44 - 2 = 42. Add 42 to the number set. Current number set: [42, 33], target: 42, just two numbers left.\n     |- Try 42 + 33 = 75. Evaluate 75 != 42, drop this branch.\n     |- Try 42 - 33 = 9. Evaluate 9 != 42, drop this branch.\n     |- Try 42 * 33 = 1386. Evaluate 1386 != 42, drop this branch.\n     |- Try 42 \/ 33 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 44 * 2 = 88. Add 88 to the number set. Current number set: [88, 33], target: 42, just two numbers left.\n     |- Try 88 + 33 = 121. Evaluate 121 != 42, drop this branch.\n     |- Try 88 - 33 = 55. Evaluate 55 != 42, drop this branch.\n     |- Try 88 * 33 = 2904. 2904 exceeds the maximum intermediate result, drop this branch.\n     |- Try 88 \/ 33 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 44 \/ 2 = 22. Add 22 to the number set. Current number set: [22, 33], target: 42, just two numbers left.\n     |- Try 33 + 22 = 55. Evaluate 55 != 42, drop this branch.\n     |- Try 33 - 22 = 11. Evaluate 11 != 42, drop this branch.\n     |- Try 33 * 22 = 726. Evaluate 726 != 42, drop this branch.\n     |- Try 33 \/ 22 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (33, 2) (numbers left: [44]). Try possible operations.\n    |- Try 33 + 2 = 35. Add 35 to the number set. Current number set: [35, 44], target: 42, just two numbers left.\n     |- Try 44 + 35 = 79. Evaluate 79 != 42, drop this branch.\n     |- Try 44 - 35 = 9. Evaluate 9 != 42, drop this branch.\n     |- Try 44 * 35 = 1540. Evaluate 1540 != 42, drop this branch.\n     |- Try 44 \/ 35 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 33 - 2 = 31. Add 31 to the number set. Current number set: [31, 44], target: 42, just two numbers left.\n     |- Try 44 + 31 = 75. Evaluate 75 != 42, drop this branch.\n     |- Try 44 - 31 = 13. Evaluate 13 != 42, drop this branch.\n     |- Try 44 * 31 = 1364. Evaluate 1364 != 42, drop this branch.\n     |- Try 44 \/ 31 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 33 * 2 = 66. Add 66 to the number set. Current number set: [66, 44], target: 42, just two numbers left.\n     |- Try 66 + 44 = 110. Evaluate 110 != 42, drop this branch.\n     |- Try 66 - 44 = 22. Evaluate 22 != 42, drop this branch.\n     |- Try 66 * 44 = 2904. 2904 exceeds the maximum intermediate result, drop this branch.\n     |- Try 66 \/ 44 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 33 \/ 2 = 16.5. 16.5 is a decimal, drop this branch.\n  |- Try 38 - 6 = 32. Add 32 to the number set. Current number set: [32, 33, 2], target: 42. Options for choosing two numbers: [(32, 33), (32, 2), (33, 2)].\n   |- Pick two numbers (32, 33) (numbers left: [2]). Try possible operations.\n    |- Try 33 + 32 = 65. Add 65 to the number set. Current number set: [65, 2], target: 42, just two numbers left.\n     |- Try 65 + 2 = 67. Evaluate 67 != 42, drop this branch.\n     |- Try 65 - 2 = 63. Evaluate 63 != 42, drop this branch.\n     |- Try 65 * 2 = 130. Evaluate 130 != 42, drop this branch.\n     |- Try 65 \/ 2 = 32.5. 32.5 is a decimal, drop this branch.\n    |- Try 33 - 32 = 1. Add 1 to the number set. Current number set: [1, 2], target: 42, just two numbers left.\n     |- Try 2 + 1 = 3. Evaluate 3 != 42, drop this branch.\n     |- Try 2 - 1 = 1. Evaluate 1 != 42, drop this branch.\n     |- Try 2 * 1 = 2. Evaluate 2 != 42, drop this branch.\n     |- Try 2 \/ 1 = 2. Evaluate 2 != 42, drop this branch.\n    |- Try 33 * 32 = 1056. Add 1056 to the number set. Current number set: [1056, 2], target: 42, just two numbers left.\n     |- Try 1056 + 2 = 1058. Evaluate 1058 != 42, drop this branch.\n     |- Try 1056 - 2 = 1054. Evaluate 1054 != 42, drop this branch.\n     |- Try 1056 * 2 = 2112. 2112 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1056 \/ 2 = 528. Evaluate 528 != 42, drop this branch.\n    |- Try 33 \/ 32 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (32, 2) (numbers left: [33]). Try possible operations.\n    |- Try 32 + 2 = 34. Add 34 to the number set. Current number set: [34, 33], target: 42, just two numbers left.\n     |- Try 34 + 33 = 67. Evaluate 67 != 42, drop this branch.\n     |- Try 34 - 33 = 1. Evaluate 1 != 42, drop this branch.\n     |- Try 34 * 33 = 1122. Evaluate 1122 != 42, drop this branch.\n     |- Try 34 \/ 33 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 32 - 2 = 30. Add 30 to the number set. Current number set: [30, 33], target: 42, just two numbers left.\n     |- Try 33 + 30 = 63. Evaluate 63 != 42, drop this branch.\n     |- Try 33 - 30 = 3. Evaluate 3 != 42, drop this branch.\n     |- Try 33 * 30 = 990. Evaluate 990 != 42, drop this branch.\n     |- Try 33 \/ 30 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 32 * 2 = 64. Add 64 to the number set. Current number set: [64, 33], target: 42, just two numbers left.\n     |- Try 64 + 33 = 97. Evaluate 97 != 42, drop this branch.\n     |- Try 64 - 33 = 31. Evaluate 31 != 42, drop this branch.\n     |- Try 64 * 33 = 2112. 2112 exceeds the maximum intermediate result, drop this branch.\n     |- Try 64 \/ 33 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 32 \/ 2 = 16. Add 16 to the number set. Current number set: [16, 33], target: 42, just two numbers left.\n     |- Try 33 + 16 = 49. Evaluate 49 != 42, drop this branch.\n     |- Try 33 - 16 = 17. Evaluate 17 != 42, drop this branch.\n     |- Try 33 * 16 = 528. Evaluate 528 != 42, drop this branch.\n     |- Try 33 \/ 16 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (33, 2) (numbers left: [32]). Try possible operations.\n    |- Try 33 + 2 = 35. Add 35 to the number set. Current number set: [35, 32], target: 42, just two numbers left.\n     |- Try 35 + 32 = 67. Evaluate 67 != 42, drop this branch.\n     |- Try 35 - 32 = 3. Evaluate 3 != 42, drop this branch.\n     |- Try 35 * 32 = 1120. Evaluate 1120 != 42, drop this branch.\n     |- Try 35 \/ 32 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 33 - 2 = 31. Add 31 to the number set. Current number set: [31, 32], target: 42, just two numbers left.\n     |- Try 32 + 31 = 63. Evaluate 63 != 42, drop this branch.\n     |- Try 32 - 31 = 1. Evaluate 1 != 42, drop this branch.\n     |- Try 32 * 31 = 992. Evaluate 992 != 42, drop this branch.\n     |- Try 32 \/ 31 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 33 * 2 = 66. Add 66 to the number set. Current number set: [66, 32], target: 42, just two numbers left.\n     |- Try 66 + 32 = 98. Evaluate 98 != 42, drop this branch.\n     |- Try 66 - 32 = 34. Evaluate 34 != 42, drop this branch.\n     |- Try 66 * 32 = 2112. 2112 exceeds the maximum intermediate result, drop this branch.\n     |- Try 66 \/ 32 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 33 \/ 2 = 16.5. 16.5 is a decimal, drop this branch.\n  |- Try 38 * 6 = 228. Add 228 to the number set. Current number set: [228, 33, 2], target: 42. Options for choosing two numbers: [(228, 33), (228, 2), (33, 2)].\n   |- Pick two numbers (228, 33) (numbers left: [2]). Try possible operations.\n    |- Try 228 + 33 = 261. Add 261 to the number set. Current number set: [261, 2], target: 42, just two numbers left.\n     |- Try 261 + 2 = 263. Evaluate 263 != 42, drop this branch.\n     |- Try 261 - 2 = 259. Evaluate 259 != 42, drop this branch.\n     |- Try 261 * 2 = 522. Evaluate 522 != 42, drop this branch.\n     |- Try 261 \/ 2 = 130.5. 130.5 is a decimal, drop this branch.\n    |- Try 228 - 33 = 195. Add 195 to the number set. Current number set: [195, 2], target: 42, just two numbers left.\n     |- Try 195 + 2 = 197. Evaluate 197 != 42, drop this branch.\n     |- Try 195 - 2 = 193. Evaluate 193 != 42, drop this branch.\n     |- Try 195 * 2 = 390. Evaluate 390 != 42, drop this branch.\n     |- Try 195 \/ 2 = 97.5. 97.5 is a decimal, drop this branch.\n    |- Try 228 * 33 = 7524. 7524 exceeds the maximum intermediate result, drop this branch.\n    |- Try 228 \/ 33 = 6.9. 6.9 is a decimal, drop this branch.\n   |- Pick two numbers (228, 2) (numbers left: [33]). Try possible operations.\n    |- Try 228 + 2 = 230. Add 230 to the number set. Current number set: [230, 33], target: 42, just two numbers left.\n     |- Try 230 + 33 = 263. Evaluate 263 != 42, drop this branch.\n     |- Try 230 - 33 = 197. Evaluate 197 != 42, drop this branch.\n     |- Try 230 * 33 = 7590. 7590 exceeds the maximum intermediate result, drop this branch.\n     |- Try 230 \/ 33 = 7.0. 7.0 is a decimal, drop this branch.\n    |- Try 228 - 2 = 226. Add 226 to the number set. Current number set: [226, 33], target: 42, just two numbers left.\n     |- Try 226 + 33 = 259. Evaluate 259 != 42, drop this branch.\n     |- Try 226 - 33 = 193. Evaluate 193 != 42, drop this branch.\n     |- Try 226 * 33 = 7458. 7458 exceeds the maximum intermediate result, drop this branch.\n     |- Try 226 \/ 33 = 6.8. 6.8 is a decimal, drop this branch.\n    |- Try 228 * 2 = 456. Add 456 to the number set. Current number set: [456, 33], target: 42, just two numbers left.\n     |- Try 456 + 33 = 489. Evaluate 489 != 42, drop this branch.\n     |- Try 456 - 33 = 423. Evaluate 423 != 42, drop this branch.\n     |- Try 456 * 33 = 15048. 15048 exceeds the maximum intermediate result, drop this branch.\n     |- Try 456 \/ 33 = 13.8. 13.8 is a decimal, drop this branch.\n    |- Try 228 \/ 2 = 114. Add 114 to the number set. Current number set: [114, 33], target: 42, just two numbers left.\n     |- Try 114 + 33 = 147. Evaluate 147 != 42, drop this branch.\n     |- Try 114 - 33 = 81. Evaluate 81 != 42, drop this branch.\n     |- Try 114 * 33 = 3762. 3762 exceeds the maximum intermediate result, drop this branch.\n     |- Try 114 \/ 33 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (33, 2) (numbers left: [228]). Try possible operations.\n    |- Try 33 + 2 = 35. Add 35 to the number set. Current number set: [35, 228], target: 42, just two numbers left.\n     |- Try 228 + 35 = 263. Evaluate 263 != 42, drop this branch.\n     |- Try 228 - 35 = 193. Evaluate 193 != 42, drop this branch.\n     |- Try 228 * 35 = 7980. 7980 exceeds the maximum intermediate result, drop this branch.\n     |- Try 228 \/ 35 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 33 - 2 = 31. Add 31 to the number set. Current number set: [31, 228], target: 42, just two numbers left.\n     |- Try 228 + 31 = 259. Evaluate 259 != 42, drop this branch.\n     |- Try 228 - 31 = 197. Evaluate 197 != 42, drop this branch.\n     |- Try 228 * 31 = 7068. 7068 exceeds the maximum intermediate result, drop this branch.\n     |- Try 228 \/ 31 = 7.4. 7.4 is a decimal, drop this branch.\n    |- Try 33 * 2 = 66. Add 66 to the number set. Current number set: [66, 228], target: 42, just two numbers left.\n     |- Try 228 + 66 = 294. Evaluate 294 != 42, drop this branch.\n     |- Try 228 - 66 = 162. Evaluate 162 != 42, drop this branch.\n     |- Try 228 * 66 = 15048. 15048 exceeds the maximum intermediate result, drop this branch.\n     |- Try 228 \/ 66 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 33 \/ 2 = 16.5. 16.5 is a decimal, drop this branch.\n  |- Try 38 \/ 6 = 6.3. 6.3 is a decimal, drop this branch.\n |- Pick two numbers (38, 33) (numbers left: [6, 2]). Try possible operations.\n  |- Try 38 + 33 = 71. Add 71 to the number set. Current number set: [71, 6, 2], target: 42. Options for choosing two numbers: [(71, 6), (71, 2), (6, 2)].\n   |- Pick two numbers (71, 6) (numbers left: [2]). Try possible operations.\n    |- Try 71 + 6 = 77. Add 77 to the number set. Current number set: [77, 2], target: 42, just two numbers left.\n     |- Try 77 + 2 = 79. Evaluate 79 != 42, drop this branch.\n     |- Try 77 - 2 = 75. Evaluate 75 != 42, drop this branch.\n     |- Try 77 * 2 = 154. Evaluate 154 != 42, drop this branch.\n     |- Try 77 \/ 2 = 38.5. 38.5 is a decimal, drop this branch.\n    |- Try 71 - 6 = 65. Add 65 to the number set. Current number set: [65, 2], target: 42, just two numbers left.\n     |- Try 65 + 2 = 67. Evaluate 67 != 42, drop this branch.\n     |- Try 65 - 2 = 63. Evaluate 63 != 42, drop this branch.\n     |- Try 65 * 2 = 130. Evaluate 130 != 42, drop this branch.\n     |- Try 65 \/ 2 = 32.5. 32.5 is a decimal, drop this branch.\n    |- Try 71 * 6 = 426. Add 426 to the number set. Current number set: [426, 2], target: 42, just two numbers left.\n     |- Try 426 + 2 = 428. Evaluate 428 != 42, drop this branch.\n     |- Try 426 - 2 = 424. Evaluate 424 != 42, drop this branch.\n     |- Try 426 * 2 = 852. Evaluate 852 != 42, drop this branch.\n     |- Try 426 \/ 2 = 213. Evaluate 213 != 42, drop this branch.\n    |- Try 71 \/ 6 = 11.8. 11.8 is a decimal, drop this branch.\n   |- Pick two numbers (71, 2) (numbers left: [6]). Try possible operations.\n    |- Try 71 + 2 = 73. Add 73 to the number set. Current number set: [73, 6], target: 42, just two numbers left.\n     |- Try 73 + 6 = 79. Evaluate 79 != 42, drop this branch.\n     |- Try 73 - 6 = 67. Evaluate 67 != 42, drop this branch.\n     |- Try 73 * 6 = 438. Evaluate 438 != 42, drop this branch.\n     |- Try 73 \/ 6 = 12.2. 12.2 is a decimal, drop this branch.\n    |- Try 71 - 2 = 69. Add 69 to the number set. Current number set: [69, 6], target: 42, just two numbers left.\n     |- Try 69 + 6 = 75. Evaluate 75 != 42, drop this branch.\n     |- Try 69 - 6 = 63. Evaluate 63 != 42, drop this branch.\n     |- Try 69 * 6 = 414. Evaluate 414 != 42, drop this branch.\n     |- Try 69 \/ 6 = 11.5. 11.5 is a decimal, drop this branch.\n    |- Try 71 * 2 = 142. Add 142 to the number set. Current number set: [142, 6], target: 42, just two numbers left.\n     |- Try 142 + 6 = 148. Evaluate 148 != 42, drop this branch.\n     |- Try 142 - 6 = 136. Evaluate 136 != 42, drop this branch.\n     |- Try 142 * 6 = 852. Evaluate 852 != 42, drop this branch.\n     |- Try 142 \/ 6 = 23.7. 23.7 is a decimal, drop this branch.\n    |- Try 71 \/ 2 = 35.5. 35.5 is a decimal, drop this branch.\n   |- Pick two numbers (6, 2) (numbers left: [71]). Try possible operations.\n    |- Try 6 + 2 = 8. Add 8 to the number set. Current number set: [8, 71], target: 42, just two numbers left.\n     |- Try 71 + 8 = 79. Evaluate 79 != 42, drop this branch.\n     |- Try 71 - 8 = 63. Evaluate 63 != 42, drop this branch.\n     |- Try 71 * 8 = 568. Evaluate 568 != 42, drop this branch.\n     |- Try 71 \/ 8 = 8.9. 8.9 is a decimal, drop this branch.\n    |- Try 6 - 2 = 4. Add 4 to the number set. Current number set: [4, 71], target: 42, just two numbers left.\n     |- Try 71 + 4 = 75. Evaluate 75 != 42, drop this branch.\n     |- Try 71 - 4 = 67. Evaluate 67 != 42, drop this branch.\n     |- Try 71 * 4 = 284. Evaluate 284 != 42, drop this branch.\n     |- Try 71 \/ 4 = 17.8. 17.8 is a decimal, drop this branch.\n    |- Try 6 * 2 = 12. Add 12 to the number set. Current number set: [12, 71], target: 42, just two numbers left.\n     |- Try 71 + 12 = 83. Evaluate 83 != 42, drop this branch.\n     |- Try 71 - 12 = 59. Evaluate 59 != 42, drop this branch.\n     |- Try 71 * 12 = 852. Evaluate 852 != 42, drop this branch.\n     |- Try 71 \/ 12 = 5.9. 5.9 is a decimal, drop this branch.\n    |- Try 6 \/ 2 = 3. Add 3 to the number set. Current number set: [3, 71], target: 42, just two numbers left.\n     |- Try 71 + 3 = 74. Evaluate 74 != 42, drop this branch.\n     |- Try 71 - 3 = 68. Evaluate 68 != 42, drop this branch.\n     |- Try 71 * 3 = 213. Evaluate 213 != 42, drop this branch.\n     |- Try 71 \/ 3 = 23.7. 23.7 is a decimal, drop this branch.\n  |- Try 38 - 33 = 5. Add 5 to the number set. Current number set: [5, 6, 2], target: 42. Options for choosing two numbers: [(5, 6), (5, 2), (6, 2)].\n   |- Pick two numbers (5, 6) (numbers left: [2]). Try possible operations.\n    |- Try 6 + 5 = 11. Add 11 to the number set. Current number set: [11, 2], target: 42, just two numbers left.\n     |- Try 11 + 2 = 13. Evaluate 13 != 42, drop this branch.\n     |- Try 11 - 2 = 9. Evaluate 9 != 42, drop this branch.\n     |- Try 11 * 2 = 22. Evaluate 22 != 42, drop this branch.\n     |- Try 11 \/ 2 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 6 - 5 = 1. Add 1 to the number set. Current number set: [1, 2], target: 42, just two numbers left.\n     |- Try 2 + 1 = 3. Evaluate 3 != 42, drop this branch.\n     |- Try 2 - 1 = 1. Evaluate 1 != 42, drop this branch.\n     |- Try 2 * 1 = 2. Evaluate 2 != 42, drop this branch.\n     |- Try 2 \/ 1 = 2. Evaluate 2 != 42, drop this branch.\n    |- Try 6 * 5 = 30. Add 30 to the number set. Current number set: [30, 2], target: 42, just two numbers left.\n     |- Try 30 + 2 = 32. Evaluate 32 != 42, drop this branch.\n     |- Try 30 - 2 = 28. Evaluate 28 != 42, drop this branch.\n     |- Try 30 * 2 = 60. Evaluate 60 != 42, drop this branch.\n     |- Try 30 \/ 2 = 15. Evaluate 15 != 42, drop this branch.\n    |- Try 6 \/ 5 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (5, 2) (numbers left: [6]). Try possible operations.\n    |- Try 5 + 2 = 7. Add 7 to the number set. Current number set: [7, 6], target: 42, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 42, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 42, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 == 42, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 7 * 6 = 42\nThe step before: 5 + 2 = 7\nThe first step: 38 - 33 = 5\n\nOutput the solution in the required format:\n<Solution>\n38 - 33 = 5\n5 + 2 = 7\n7 * 6 = 42\n<\/Solution>\n","item":{"nums":[38,6,33,2],"solution":["38 - 33 = 5","5 + 2 = 7","7 * 6 = 42"],"target":42}}
+{"instance_id":"countdown_8k_114","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [26, 3, 6, 27]\nTarget: 21","reference_output":"# Search Procedure\nInitial number set: [26, 3, 6, 27], target: 21. Options for choosing two numbers: [(26, 3), (26, 6), (26, 27), (3, 6), (3, 27), (6, 27)].\n |- Pick two numbers (26, 3) (numbers left: [6, 27]). Try possible operations.\n  |- Try 26 + 3 = 29. Add 29 to the number set. Current number set: [29, 6, 27], target: 21. Options for choosing two numbers: [(29, 6), (29, 27), (6, 27)].\n   |- Pick two numbers (29, 6) (numbers left: [27]). Try possible operations.\n    |- Try 29 + 6 = 35. Add 35 to the number set. Current number set: [35, 27], target: 21, just two numbers left.\n     |- Try 35 + 27 = 62. Evaluate 62 != 21, drop this branch.\n     |- Try 35 - 27 = 8. Evaluate 8 != 21, drop this branch.\n     |- Try 35 * 27 = 945. Evaluate 945 != 21, drop this branch.\n     |- Try 35 \/ 27 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 29 - 6 = 23. Add 23 to the number set. Current number set: [23, 27], target: 21, just two numbers left.\n     |- Try 27 + 23 = 50. Evaluate 50 != 21, drop this branch.\n     |- Try 27 - 23 = 4. Evaluate 4 != 21, drop this branch.\n     |- Try 27 * 23 = 621. Evaluate 621 != 21, drop this branch.\n     |- Try 27 \/ 23 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 29 * 6 = 174. Add 174 to the number set. Current number set: [174, 27], target: 21, just two numbers left.\n     |- Try 174 + 27 = 201. Evaluate 201 != 21, drop this branch.\n     |- Try 174 - 27 = 147. Evaluate 147 != 21, drop this branch.\n     |- Try 174 * 27 = 4698. 4698 exceeds the maximum intermediate result, drop this branch.\n     |- Try 174 \/ 27 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 29 \/ 6 = 4.8. 4.8 is a decimal, drop this branch.\n   |- Pick two numbers (29, 27) (numbers left: [6]). Try possible operations.\n    |- Try 29 + 27 = 56. Add 56 to the number set. Current number set: [56, 6], target: 21, just two numbers left.\n     |- Try 56 + 6 = 62. Evaluate 62 != 21, drop this branch.\n     |- Try 56 - 6 = 50. Evaluate 50 != 21, drop this branch.\n     |- Try 56 * 6 = 336. Evaluate 336 != 21, drop this branch.\n     |- Try 56 \/ 6 = 9.3. 9.3 is a decimal, drop this branch.\n    |- Try 29 - 27 = 2. Add 2 to the number set. Current number set: [2, 6], target: 21, just two numbers left.\n     |- Try 6 + 2 = 8. Evaluate 8 != 21, drop this branch.\n     |- Try 6 - 2 = 4. Evaluate 4 != 21, drop this branch.\n     |- Try 6 * 2 = 12. Evaluate 12 != 21, drop this branch.\n     |- Try 6 \/ 2 = 3. Evaluate 3 != 21, drop this branch.\n    |- Try 29 * 27 = 783. Add 783 to the number set. Current number set: [783, 6], target: 21, just two numbers left.\n     |- Try 783 + 6 = 789. Evaluate 789 != 21, drop this branch.\n     |- Try 783 - 6 = 777. Evaluate 777 != 21, drop this branch.\n     |- Try 783 * 6 = 4698. 4698 exceeds the maximum intermediate result, drop this branch.\n     |- Try 783 \/ 6 = 130.5. 130.5 is a decimal, drop this branch.\n    |- Try 29 \/ 27 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (6, 27) (numbers left: [29]). Try possible operations.\n    |- Try 27 + 6 = 33. Add 33 to the number set. Current number set: [33, 29], target: 21, just two numbers left.\n     |- Try 33 + 29 = 62. Evaluate 62 != 21, drop this branch.\n     |- Try 33 - 29 = 4. Evaluate 4 != 21, drop this branch.\n     |- Try 33 * 29 = 957. Evaluate 957 != 21, drop this branch.\n     |- Try 33 \/ 29 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 27 - 6 = 21. Add 21 to the number set. Current number set: [21, 29], target: 21, just two numbers left.\n     |- Try 29 + 21 = 50. Evaluate 50 != 21, drop this branch.\n     |- Try 29 - 21 = 8. Evaluate 8 != 21, drop this branch.\n     |- Try 29 * 21 = 609. Evaluate 609 != 21, drop this branch.\n     |- Try 29 \/ 21 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 27 * 6 = 162. Add 162 to the number set. Current number set: [162, 29], target: 21, just two numbers left.\n     |- Try 162 + 29 = 191. Evaluate 191 != 21, drop this branch.\n     |- Try 162 - 29 = 133. Evaluate 133 != 21, drop this branch.\n     |- Try 162 * 29 = 4698. 4698 exceeds the maximum intermediate result, drop this branch.\n     |- Try 162 \/ 29 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 27 \/ 6 = 4.5. 4.5 is a decimal, drop this branch.\n  |- Try 26 - 3 = 23. Add 23 to the number set. Current number set: [23, 6, 27], target: 21. Options for choosing two numbers: [(23, 6), (23, 27), (6, 27)].\n   |- Pick two numbers (23, 6) (numbers left: [27]). Try possible operations.\n    |- Try 23 + 6 = 29. Add 29 to the number set. Current number set: [29, 27], target: 21, just two numbers left.\n     |- Try 29 + 27 = 56. Evaluate 56 != 21, drop this branch.\n     |- Try 29 - 27 = 2. Evaluate 2 != 21, drop this branch.\n     |- Try 29 * 27 = 783. Evaluate 783 != 21, drop this branch.\n     |- Try 29 \/ 27 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 23 - 6 = 17. Add 17 to the number set. Current number set: [17, 27], target: 21, just two numbers left.\n     |- Try 27 + 17 = 44. Evaluate 44 != 21, drop this branch.\n     |- Try 27 - 17 = 10. Evaluate 10 != 21, drop this branch.\n     |- Try 27 * 17 = 459. Evaluate 459 != 21, drop this branch.\n     |- Try 27 \/ 17 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 23 * 6 = 138. Add 138 to the number set. Current number set: [138, 27], target: 21, just two numbers left.\n     |- Try 138 + 27 = 165. Evaluate 165 != 21, drop this branch.\n     |- Try 138 - 27 = 111. Evaluate 111 != 21, drop this branch.\n     |- Try 138 * 27 = 3726. 3726 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 27 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 23 \/ 6 = 3.8. 3.8 is a decimal, drop this branch.\n   |- Pick two numbers (23, 27) (numbers left: [6]). Try possible operations.\n    |- Try 27 + 23 = 50. Add 50 to the number set. Current number set: [50, 6], target: 21, just two numbers left.\n     |- Try 50 + 6 = 56. Evaluate 56 != 21, drop this branch.\n     |- Try 50 - 6 = 44. Evaluate 44 != 21, drop this branch.\n     |- Try 50 * 6 = 300. Evaluate 300 != 21, drop this branch.\n     |- Try 50 \/ 6 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 27 - 23 = 4. Add 4 to the number set. Current number set: [4, 6], target: 21, just two numbers left.\n     |- Try 6 + 4 = 10. Evaluate 10 != 21, drop this branch.\n     |- Try 6 - 4 = 2. Evaluate 2 != 21, drop this branch.\n     |- Try 6 * 4 = 24. Evaluate 24 != 21, drop this branch.\n     |- Try 6 \/ 4 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 27 * 23 = 621. Add 621 to the number set. Current number set: [621, 6], target: 21, just two numbers left.\n     |- Try 621 + 6 = 627. Evaluate 627 != 21, drop this branch.\n     |- Try 621 - 6 = 615. Evaluate 615 != 21, drop this branch.\n     |- Try 621 * 6 = 3726. 3726 exceeds the maximum intermediate result, drop this branch.\n     |- Try 621 \/ 6 = 103.5. 103.5 is a decimal, drop this branch.\n    |- Try 27 \/ 23 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (6, 27) (numbers left: [23]). Try possible operations.\n    |- Try 27 + 6 = 33. Add 33 to the number set. Current number set: [33, 23], target: 21, just two numbers left.\n     |- Try 33 + 23 = 56. Evaluate 56 != 21, drop this branch.\n     |- Try 33 - 23 = 10. Evaluate 10 != 21, drop this branch.\n     |- Try 33 * 23 = 759. Evaluate 759 != 21, drop this branch.\n     |- Try 33 \/ 23 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 27 - 6 = 21. Add 21 to the number set. Current number set: [21, 23], target: 21, just two numbers left.\n     |- Try 23 + 21 = 44. Evaluate 44 != 21, drop this branch.\n     |- Try 23 - 21 = 2. Evaluate 2 != 21, drop this branch.\n     |- Try 23 * 21 = 483. Evaluate 483 != 21, drop this branch.\n     |- Try 23 \/ 21 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 27 * 6 = 162. Add 162 to the number set. Current number set: [162, 23], target: 21, just two numbers left.\n     |- Try 162 + 23 = 185. Evaluate 185 != 21, drop this branch.\n     |- Try 162 - 23 = 139. Evaluate 139 != 21, drop this branch.\n     |- Try 162 * 23 = 3726. 3726 exceeds the maximum intermediate result, drop this branch.\n     |- Try 162 \/ 23 = 7.0. 7.0 is a decimal, drop this branch.\n    |- Try 27 \/ 6 = 4.5. 4.5 is a decimal, drop this branch.\n  |- Try 26 * 3 = 78. Add 78 to the number set. Current number set: [78, 6, 27], target: 21. Options for choosing two numbers: [(78, 6), (78, 27), (6, 27)].\n   |- Pick two numbers (78, 6) (numbers left: [27]). Try possible operations.\n    |- Try 78 + 6 = 84. Add 84 to the number set. Current number set: [84, 27], target: 21, just two numbers left.\n     |- Try 84 + 27 = 111. Evaluate 111 != 21, drop this branch.\n     |- Try 84 - 27 = 57. Evaluate 57 != 21, drop this branch.\n     |- Try 84 * 27 = 2268. 2268 exceeds the maximum intermediate result, drop this branch.\n     |- Try 84 \/ 27 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 78 - 6 = 72. Add 72 to the number set. Current number set: [72, 27], target: 21, just two numbers left.\n     |- Try 72 + 27 = 99. Evaluate 99 != 21, drop this branch.\n     |- Try 72 - 27 = 45. Evaluate 45 != 21, drop this branch.\n     |- Try 72 * 27 = 1944. Evaluate 1944 != 21, drop this branch.\n     |- Try 72 \/ 27 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 78 * 6 = 468. Add 468 to the number set. Current number set: [468, 27], target: 21, just two numbers left.\n     |- Try 468 + 27 = 495. Evaluate 495 != 21, drop this branch.\n     |- Try 468 - 27 = 441. Evaluate 441 != 21, drop this branch.\n     |- Try 468 * 27 = 12636. 12636 exceeds the maximum intermediate result, drop this branch.\n     |- Try 468 \/ 27 = 17.3. 17.3 is a decimal, drop this branch.\n    |- Try 78 \/ 6 = 13. Add 13 to the number set. Current number set: [13, 27], target: 21, just two numbers left.\n     |- Try 27 + 13 = 40. Evaluate 40 != 21, drop this branch.\n     |- Try 27 - 13 = 14. Evaluate 14 != 21, drop this branch.\n     |- Try 27 * 13 = 351. Evaluate 351 != 21, drop this branch.\n     |- Try 27 \/ 13 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (78, 27) (numbers left: [6]). Try possible operations.\n    |- Try 78 + 27 = 105. Add 105 to the number set. Current number set: [105, 6], target: 21, just two numbers left.\n     |- Try 105 + 6 = 111. Evaluate 111 != 21, drop this branch.\n     |- Try 105 - 6 = 99. Evaluate 99 != 21, drop this branch.\n     |- Try 105 * 6 = 630. Evaluate 630 != 21, drop this branch.\n     |- Try 105 \/ 6 = 17.5. 17.5 is a decimal, drop this branch.\n    |- Try 78 - 27 = 51. Add 51 to the number set. Current number set: [51, 6], target: 21, just two numbers left.\n     |- Try 51 + 6 = 57. Evaluate 57 != 21, drop this branch.\n     |- Try 51 - 6 = 45. Evaluate 45 != 21, drop this branch.\n     |- Try 51 * 6 = 306. Evaluate 306 != 21, drop this branch.\n     |- Try 51 \/ 6 = 8.5. 8.5 is a decimal, drop this branch.\n    |- Try 78 * 27 = 2106. 2106 exceeds the maximum intermediate result, drop this branch.\n    |- Try 78 \/ 27 = 2.9. 2.9 is a decimal, drop this branch.\n   |- Pick two numbers (6, 27) (numbers left: [78]). Try possible operations.\n    |- Try 27 + 6 = 33. Add 33 to the number set. Current number set: [33, 78], target: 21, just two numbers left.\n     |- Try 78 + 33 = 111. Evaluate 111 != 21, drop this branch.\n     |- Try 78 - 33 = 45. Evaluate 45 != 21, drop this branch.\n     |- Try 78 * 33 = 2574. 2574 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 33 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 27 - 6 = 21. Add 21 to the number set. Current number set: [21, 78], target: 21, just two numbers left.\n     |- Try 78 + 21 = 99. Evaluate 99 != 21, drop this branch.\n     |- Try 78 - 21 = 57. Evaluate 57 != 21, drop this branch.\n     |- Try 78 * 21 = 1638. Evaluate 1638 != 21, drop this branch.\n     |- Try 78 \/ 21 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 27 * 6 = 162. Add 162 to the number set. Current number set: [162, 78], target: 21, just two numbers left.\n     |- Try 162 + 78 = 240. Evaluate 240 != 21, drop this branch.\n     |- Try 162 - 78 = 84. Evaluate 84 != 21, drop this branch.\n     |- Try 162 * 78 = 12636. 12636 exceeds the maximum intermediate result, drop this branch.\n     |- Try 162 \/ 78 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 27 \/ 6 = 4.5. 4.5 is a decimal, drop this branch.\n  |- Try 26 \/ 3 = 8.7. 8.7 is a decimal, drop this branch.\n |- Pick two numbers (26, 6) (numbers left: [3, 27]). Try possible operations.\n  |- Try 26 + 6 = 32. Add 32 to the number set. Current number set: [32, 3, 27], target: 21. Options for choosing two numbers: [(32, 3), (32, 27), (3, 27)].\n   |- Pick two numbers (32, 3) (numbers left: [27]). Try possible operations.\n    |- Try 32 + 3 = 35. Add 35 to the number set. Current number set: [35, 27], target: 21, just two numbers left.\n     |- Try 35 + 27 = 62. Evaluate 62 != 21, drop this branch.\n     |- Try 35 - 27 = 8. Evaluate 8 != 21, drop this branch.\n     |- Try 35 * 27 = 945. Evaluate 945 != 21, drop this branch.\n     |- Try 35 \/ 27 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 32 - 3 = 29. Add 29 to the number set. Current number set: [29, 27], target: 21, just two numbers left.\n     |- Try 29 + 27 = 56. Evaluate 56 != 21, drop this branch.\n     |- Try 29 - 27 = 2. Evaluate 2 != 21, drop this branch.\n     |- Try 29 * 27 = 783. Evaluate 783 != 21, drop this branch.\n     |- Try 29 \/ 27 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 32 * 3 = 96. Add 96 to the number set. Current number set: [96, 27], target: 21, just two numbers left.\n     |- Try 96 + 27 = 123. Evaluate 123 != 21, drop this branch.\n     |- Try 96 - 27 = 69. Evaluate 69 != 21, drop this branch.\n     |- Try 96 * 27 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n     |- Try 96 \/ 27 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 32 \/ 3 = 10.7. 10.7 is a decimal, drop this branch.\n   |- Pick two numbers (32, 27) (numbers left: [3]). Try possible operations.\n    |- Try 32 + 27 = 59. Add 59 to the number set. Current number set: [59, 3], target: 21, just two numbers left.\n     |- Try 59 + 3 = 62. Evaluate 62 != 21, drop this branch.\n     |- Try 59 - 3 = 56. Evaluate 56 != 21, drop this branch.\n     |- Try 59 * 3 = 177. Evaluate 177 != 21, drop this branch.\n     |- Try 59 \/ 3 = 19.7. 19.7 is a decimal, drop this branch.\n    |- Try 32 - 27 = 5. Add 5 to the number set. Current number set: [5, 3], target: 21, just two numbers left.\n     |- Try 5 + 3 = 8. Evaluate 8 != 21, drop this branch.\n     |- Try 5 - 3 = 2. Evaluate 2 != 21, drop this branch.\n     |- Try 5 * 3 = 15. Evaluate 15 != 21, drop this branch.\n     |- Try 5 \/ 3 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 32 * 27 = 864. Add 864 to the number set. Current number set: [864, 3], target: 21, just two numbers left.\n     |- Try 864 + 3 = 867. Evaluate 867 != 21, drop this branch.\n     |- Try 864 - 3 = 861. Evaluate 861 != 21, drop this branch.\n     |- Try 864 * 3 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 3 = 288. Evaluate 288 != 21, drop this branch.\n    |- Try 32 \/ 27 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (3, 27) (numbers left: [32]). Try possible operations.\n    |- Try 27 + 3 = 30. Add 30 to the number set. Current number set: [30, 32], target: 21, just two numbers left.\n     |- Try 32 + 30 = 62. Evaluate 62 != 21, drop this branch.\n     |- Try 32 - 30 = 2. Evaluate 2 != 21, drop this branch.\n     |- Try 32 * 30 = 960. Evaluate 960 != 21, drop this branch.\n     |- Try 32 \/ 30 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 27 - 3 = 24. Add 24 to the number set. Current number set: [24, 32], target: 21, just two numbers left.\n     |- Try 32 + 24 = 56. Evaluate 56 != 21, drop this branch.\n     |- Try 32 - 24 = 8. Evaluate 8 != 21, drop this branch.\n     |- Try 32 * 24 = 768. Evaluate 768 != 21, drop this branch.\n     |- Try 32 \/ 24 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 27 * 3 = 81. Add 81 to the number set. Current number set: [81, 32], target: 21, just two numbers left.\n     |- Try 81 + 32 = 113. Evaluate 113 != 21, drop this branch.\n     |- Try 81 - 32 = 49. Evaluate 49 != 21, drop this branch.\n     |- Try 81 * 32 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n     |- Try 81 \/ 32 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 27 \/ 3 = 9. Add 9 to the number set. Current number set: [9, 32], target: 21, just two numbers left.\n     |- Try 32 + 9 = 41. Evaluate 41 != 21, drop this branch.\n     |- Try 32 - 9 = 23. Evaluate 23 != 21, drop this branch.\n     |- Try 32 * 9 = 288. Evaluate 288 != 21, drop this branch.\n     |- Try 32 \/ 9 = 3.6. 3.6 is a decimal, drop this branch.\n  |- Try 26 - 6 = 20. Add 20 to the number set. Current number set: [20, 3, 27], target: 21. Options for choosing two numbers: [(20, 3), (20, 27), (3, 27)].\n   |- Pick two numbers (20, 3) (numbers left: [27]). Try possible operations.\n    |- Try 20 + 3 = 23. Add 23 to the number set. Current number set: [23, 27], target: 21, just two numbers left.\n     |- Try 27 + 23 = 50. Evaluate 50 != 21, drop this branch.\n     |- Try 27 - 23 = 4. Evaluate 4 != 21, drop this branch.\n     |- Try 27 * 23 = 621. Evaluate 621 != 21, drop this branch.\n     |- Try 27 \/ 23 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 20 - 3 = 17. Add 17 to the number set. Current number set: [17, 27], target: 21, just two numbers left.\n     |- Try 27 + 17 = 44. Evaluate 44 != 21, drop this branch.\n     |- Try 27 - 17 = 10. Evaluate 10 != 21, drop this branch.\n     |- Try 27 * 17 = 459. Evaluate 459 != 21, drop this branch.\n     |- Try 27 \/ 17 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 20 * 3 = 60. Add 60 to the number set. Current number set: [60, 27], target: 21, just two numbers left.\n     |- Try 60 + 27 = 87. Evaluate 87 != 21, drop this branch.\n     |- Try 60 - 27 = 33. Evaluate 33 != 21, drop this branch.\n     |- Try 60 * 27 = 1620. Evaluate 1620 != 21, drop this branch.\n     |- Try 60 \/ 27 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 20 \/ 3 = 6.7. 6.7 is a decimal, drop this branch.\n   |- Pick two numbers (20, 27) (numbers left: [3]). Try possible operations.\n    |- Try 27 + 20 = 47. Add 47 to the number set. Current number set: [47, 3], target: 21, just two numbers left.\n     |- Try 47 + 3 = 50. Evaluate 50 != 21, drop this branch.\n     |- Try 47 - 3 = 44. Evaluate 44 != 21, drop this branch.\n     |- Try 47 * 3 = 141. Evaluate 141 != 21, drop this branch.\n     |- Try 47 \/ 3 = 15.7. 15.7 is a decimal, drop this branch.\n    |- Try 27 - 20 = 7. Add 7 to the number set. Current number set: [7, 3], target: 21, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 21, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 21, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 == 21, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 7 * 3 = 21\nThe step before: 27 - 20 = 7\nThe first step: 26 - 6 = 20\n\nOutput the solution in the required format:\n<Solution>\n26 - 6 = 20\n27 - 20 = 7\n7 * 3 = 21\n<\/Solution>\n","item":{"nums":[26,3,6,27],"solution":["26 - 6 = 20","27 - 20 = 7","7 * 3 = 21"],"target":21}}
+{"instance_id":"countdown_8k_115","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [12, 6, 48, 39]\nTarget: 29","reference_output":"# Search Procedure\nInitial number set: [12, 6, 48, 39], target: 29. Options for choosing two numbers: [(12, 6), (12, 48), (12, 39), (6, 48), (6, 39), (48, 39)].\n |- Pick two numbers (12, 6) (numbers left: [48, 39]). Try possible operations.\n  |- Try 12 + 6 = 18. Add 18 to the number set. Current number set: [18, 48, 39], target: 29. Options for choosing two numbers: [(18, 48), (18, 39), (48, 39)].\n   |- Pick two numbers (18, 48) (numbers left: [39]). Try possible operations.\n    |- Try 48 + 18 = 66. Add 66 to the number set. Current number set: [66, 39], target: 29, just two numbers left.\n     |- Try 66 + 39 = 105. Evaluate 105 != 29, drop this branch.\n     |- Try 66 - 39 = 27. Evaluate 27 != 29, drop this branch.\n     |- Try 66 * 39 = 2574. 2574 exceeds the maximum intermediate result, drop this branch.\n     |- Try 66 \/ 39 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 48 - 18 = 30. Add 30 to the number set. Current number set: [30, 39], target: 29, just two numbers left.\n     |- Try 39 + 30 = 69. Evaluate 69 != 29, drop this branch.\n     |- Try 39 - 30 = 9. Evaluate 9 != 29, drop this branch.\n     |- Try 39 * 30 = 1170. Evaluate 1170 != 29, drop this branch.\n     |- Try 39 \/ 30 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 48 * 18 = 864. Add 864 to the number set. Current number set: [864, 39], target: 29, just two numbers left.\n     |- Try 864 + 39 = 903. Evaluate 903 != 29, drop this branch.\n     |- Try 864 - 39 = 825. Evaluate 825 != 29, drop this branch.\n     |- Try 864 * 39 = 33696. 33696 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 39 = 22.2. 22.2 is a decimal, drop this branch.\n    |- Try 48 \/ 18 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (18, 39) (numbers left: [48]). Try possible operations.\n    |- Try 39 + 18 = 57. Add 57 to the number set. Current number set: [57, 48], target: 29, just two numbers left.\n     |- Try 57 + 48 = 105. Evaluate 105 != 29, drop this branch.\n     |- Try 57 - 48 = 9. Evaluate 9 != 29, drop this branch.\n     |- Try 57 * 48 = 2736. 2736 exceeds the maximum intermediate result, drop this branch.\n     |- Try 57 \/ 48 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 39 - 18 = 21. Add 21 to the number set. Current number set: [21, 48], target: 29, just two numbers left.\n     |- Try 48 + 21 = 69. Evaluate 69 != 29, drop this branch.\n     |- Try 48 - 21 = 27. Evaluate 27 != 29, drop this branch.\n     |- Try 48 * 21 = 1008. Evaluate 1008 != 29, drop this branch.\n     |- Try 48 \/ 21 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 39 * 18 = 702. Add 702 to the number set. Current number set: [702, 48], target: 29, just two numbers left.\n     |- Try 702 + 48 = 750. Evaluate 750 != 29, drop this branch.\n     |- Try 702 - 48 = 654. Evaluate 654 != 29, drop this branch.\n     |- Try 702 * 48 = 33696. 33696 exceeds the maximum intermediate result, drop this branch.\n     |- Try 702 \/ 48 = 14.6. 14.6 is a decimal, drop this branch.\n    |- Try 39 \/ 18 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (48, 39) (numbers left: [18]). Try possible operations.\n    |- Try 48 + 39 = 87. Add 87 to the number set. Current number set: [87, 18], target: 29, just two numbers left.\n     |- Try 87 + 18 = 105. Evaluate 105 != 29, drop this branch.\n     |- Try 87 - 18 = 69. Evaluate 69 != 29, drop this branch.\n     |- Try 87 * 18 = 1566. Evaluate 1566 != 29, drop this branch.\n     |- Try 87 \/ 18 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 48 - 39 = 9. Add 9 to the number set. Current number set: [9, 18], target: 29, just two numbers left.\n     |- Try 18 + 9 = 27. Evaluate 27 != 29, drop this branch.\n     |- Try 18 - 9 = 9. Evaluate 9 != 29, drop this branch.\n     |- Try 18 * 9 = 162. Evaluate 162 != 29, drop this branch.\n     |- Try 18 \/ 9 = 2. Evaluate 2 != 29, drop this branch.\n    |- Try 48 * 39 = 1872. Add 1872 to the number set. Current number set: [1872, 18], target: 29, just two numbers left.\n     |- Try 1872 + 18 = 1890. Evaluate 1890 != 29, drop this branch.\n     |- Try 1872 - 18 = 1854. Evaluate 1854 != 29, drop this branch.\n     |- Try 1872 * 18 = 33696. 33696 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1872 \/ 18 = 104. Evaluate 104 != 29, drop this branch.\n    |- Try 48 \/ 39 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 12 - 6 = 6. Add 6 to the number set. Current number set: [6, 48, 39], target: 29. Options for choosing two numbers: [(6, 48), (6, 39), (48, 39)].\n   |- Pick two numbers (6, 48) (numbers left: [39]). Try possible operations.\n    |- Try 48 + 6 = 54. Add 54 to the number set. Current number set: [54, 39], target: 29, just two numbers left.\n     |- Try 54 + 39 = 93. Evaluate 93 != 29, drop this branch.\n     |- Try 54 - 39 = 15. Evaluate 15 != 29, drop this branch.\n     |- Try 54 * 39 = 2106. 2106 exceeds the maximum intermediate result, drop this branch.\n     |- Try 54 \/ 39 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 48 - 6 = 42. Add 42 to the number set. Current number set: [42, 39], target: 29, just two numbers left.\n     |- Try 42 + 39 = 81. Evaluate 81 != 29, drop this branch.\n     |- Try 42 - 39 = 3. Evaluate 3 != 29, drop this branch.\n     |- Try 42 * 39 = 1638. Evaluate 1638 != 29, drop this branch.\n     |- Try 42 \/ 39 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 48 * 6 = 288. Add 288 to the number set. Current number set: [288, 39], target: 29, just two numbers left.\n     |- Try 288 + 39 = 327. Evaluate 327 != 29, drop this branch.\n     |- Try 288 - 39 = 249. Evaluate 249 != 29, drop this branch.\n     |- Try 288 * 39 = 11232. 11232 exceeds the maximum intermediate result, drop this branch.\n     |- Try 288 \/ 39 = 7.4. 7.4 is a decimal, drop this branch.\n    |- Try 48 \/ 6 = 8. Add 8 to the number set. Current number set: [8, 39], target: 29, just two numbers left.\n     |- Try 39 + 8 = 47. Evaluate 47 != 29, drop this branch.\n     |- Try 39 - 8 = 31. Evaluate 31 != 29, drop this branch.\n     |- Try 39 * 8 = 312. Evaluate 312 != 29, drop this branch.\n     |- Try 39 \/ 8 = 4.9. 4.9 is a decimal, drop this branch.\n   |- Pick two numbers (6, 39) (numbers left: [48]). Try possible operations.\n    |- Try 39 + 6 = 45. Add 45 to the number set. Current number set: [45, 48], target: 29, just two numbers left.\n     |- Try 48 + 45 = 93. Evaluate 93 != 29, drop this branch.\n     |- Try 48 - 45 = 3. Evaluate 3 != 29, drop this branch.\n     |- Try 48 * 45 = 2160. 2160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 48 \/ 45 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 39 - 6 = 33. Add 33 to the number set. Current number set: [33, 48], target: 29, just two numbers left.\n     |- Try 48 + 33 = 81. Evaluate 81 != 29, drop this branch.\n     |- Try 48 - 33 = 15. Evaluate 15 != 29, drop this branch.\n     |- Try 48 * 33 = 1584. Evaluate 1584 != 29, drop this branch.\n     |- Try 48 \/ 33 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 39 * 6 = 234. Add 234 to the number set. Current number set: [234, 48], target: 29, just two numbers left.\n     |- Try 234 + 48 = 282. Evaluate 282 != 29, drop this branch.\n     |- Try 234 - 48 = 186. Evaluate 186 != 29, drop this branch.\n     |- Try 234 * 48 = 11232. 11232 exceeds the maximum intermediate result, drop this branch.\n     |- Try 234 \/ 48 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 39 \/ 6 = 6.5. 6.5 is a decimal, drop this branch.\n   |- Pick two numbers (48, 39) (numbers left: [6]). Try possible operations.\n    |- Try 48 + 39 = 87. Add 87 to the number set. Current number set: [87, 6], target: 29, just two numbers left.\n     |- Try 87 + 6 = 93. Evaluate 93 != 29, drop this branch.\n     |- Try 87 - 6 = 81. Evaluate 81 != 29, drop this branch.\n     |- Try 87 * 6 = 522. Evaluate 522 != 29, drop this branch.\n     |- Try 87 \/ 6 = 14.5. 14.5 is a decimal, drop this branch.\n    |- Try 48 - 39 = 9. Add 9 to the number set. Current number set: [9, 6], target: 29, just two numbers left.\n     |- Try 9 + 6 = 15. Evaluate 15 != 29, drop this branch.\n     |- Try 9 - 6 = 3. Evaluate 3 != 29, drop this branch.\n     |- Try 9 * 6 = 54. Evaluate 54 != 29, drop this branch.\n     |- Try 9 \/ 6 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 48 * 39 = 1872. Add 1872 to the number set. Current number set: [1872, 6], target: 29, just two numbers left.\n     |- Try 1872 + 6 = 1878. Evaluate 1878 != 29, drop this branch.\n     |- Try 1872 - 6 = 1866. Evaluate 1866 != 29, drop this branch.\n     |- Try 1872 * 6 = 11232. 11232 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1872 \/ 6 = 312. Evaluate 312 != 29, drop this branch.\n    |- Try 48 \/ 39 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 12 * 6 = 72. Add 72 to the number set. Current number set: [72, 48, 39], target: 29. Options for choosing two numbers: [(72, 48), (72, 39), (48, 39)].\n   |- Pick two numbers (72, 48) (numbers left: [39]). Try possible operations.\n    |- Try 72 + 48 = 120. Add 120 to the number set. Current number set: [120, 39], target: 29, just two numbers left.\n     |- Try 120 + 39 = 159. Evaluate 159 != 29, drop this branch.\n     |- Try 120 - 39 = 81. Evaluate 81 != 29, drop this branch.\n     |- Try 120 * 39 = 4680. 4680 exceeds the maximum intermediate result, drop this branch.\n     |- Try 120 \/ 39 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 72 - 48 = 24. Add 24 to the number set. Current number set: [24, 39], target: 29, just two numbers left.\n     |- Try 39 + 24 = 63. Evaluate 63 != 29, drop this branch.\n     |- Try 39 - 24 = 15. Evaluate 15 != 29, drop this branch.\n     |- Try 39 * 24 = 936. Evaluate 936 != 29, drop this branch.\n     |- Try 39 \/ 24 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 72 * 48 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n    |- Try 72 \/ 48 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (72, 39) (numbers left: [48]). Try possible operations.\n    |- Try 72 + 39 = 111. Add 111 to the number set. Current number set: [111, 48], target: 29, just two numbers left.\n     |- Try 111 + 48 = 159. Evaluate 159 != 29, drop this branch.\n     |- Try 111 - 48 = 63. Evaluate 63 != 29, drop this branch.\n     |- Try 111 * 48 = 5328. 5328 exceeds the maximum intermediate result, drop this branch.\n     |- Try 111 \/ 48 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 72 - 39 = 33. Add 33 to the number set. Current number set: [33, 48], target: 29, just two numbers left.\n     |- Try 48 + 33 = 81. Evaluate 81 != 29, drop this branch.\n     |- Try 48 - 33 = 15. Evaluate 15 != 29, drop this branch.\n     |- Try 48 * 33 = 1584. Evaluate 1584 != 29, drop this branch.\n     |- Try 48 \/ 33 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 72 * 39 = 2808. 2808 exceeds the maximum intermediate result, drop this branch.\n    |- Try 72 \/ 39 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (48, 39) (numbers left: [72]). Try possible operations.\n    |- Try 48 + 39 = 87. Add 87 to the number set. Current number set: [87, 72], target: 29, just two numbers left.\n     |- Try 87 + 72 = 159. Evaluate 159 != 29, drop this branch.\n     |- Try 87 - 72 = 15. Evaluate 15 != 29, drop this branch.\n     |- Try 87 * 72 = 6264. 6264 exceeds the maximum intermediate result, drop this branch.\n     |- Try 87 \/ 72 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 48 - 39 = 9. Add 9 to the number set. Current number set: [9, 72], target: 29, just two numbers left.\n     |- Try 72 + 9 = 81. Evaluate 81 != 29, drop this branch.\n     |- Try 72 - 9 = 63. Evaluate 63 != 29, drop this branch.\n     |- Try 72 * 9 = 648. Evaluate 648 != 29, drop this branch.\n     |- Try 72 \/ 9 = 8. Evaluate 8 != 29, drop this branch.\n    |- Try 48 * 39 = 1872. Add 1872 to the number set. Current number set: [1872, 72], target: 29, just two numbers left.\n     |- Try 1872 + 72 = 1944. Evaluate 1944 != 29, drop this branch.\n     |- Try 1872 - 72 = 1800. Evaluate 1800 != 29, drop this branch.\n     |- Try 1872 * 72 = 134784. 134784 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1872 \/ 72 = 26. Evaluate 26 != 29, drop this branch.\n    |- Try 48 \/ 39 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 12 \/ 6 = 2. Add 2 to the number set. Current number set: [2, 48, 39], target: 29. Options for choosing two numbers: [(2, 48), (2, 39), (48, 39)].\n   |- Pick two numbers (2, 48) (numbers left: [39]). Try possible operations.\n    |- Try 48 + 2 = 50. Add 50 to the number set. Current number set: [50, 39], target: 29, just two numbers left.\n     |- Try 50 + 39 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 50 - 39 = 11. Evaluate 11 != 29, drop this branch.\n     |- Try 50 * 39 = 1950. Evaluate 1950 != 29, drop this branch.\n     |- Try 50 \/ 39 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 48 - 2 = 46. Add 46 to the number set. Current number set: [46, 39], target: 29, just two numbers left.\n     |- Try 46 + 39 = 85. Evaluate 85 != 29, drop this branch.\n     |- Try 46 - 39 = 7. Evaluate 7 != 29, drop this branch.\n     |- Try 46 * 39 = 1794. Evaluate 1794 != 29, drop this branch.\n     |- Try 46 \/ 39 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 48 * 2 = 96. Add 96 to the number set. Current number set: [96, 39], target: 29, just two numbers left.\n     |- Try 96 + 39 = 135. Evaluate 135 != 29, drop this branch.\n     |- Try 96 - 39 = 57. Evaluate 57 != 29, drop this branch.\n     |- Try 96 * 39 = 3744. 3744 exceeds the maximum intermediate result, drop this branch.\n     |- Try 96 \/ 39 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 48 \/ 2 = 24. Add 24 to the number set. Current number set: [24, 39], target: 29, just two numbers left.\n     |- Try 39 + 24 = 63. Evaluate 63 != 29, drop this branch.\n     |- Try 39 - 24 = 15. Evaluate 15 != 29, drop this branch.\n     |- Try 39 * 24 = 936. Evaluate 936 != 29, drop this branch.\n     |- Try 39 \/ 24 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (2, 39) (numbers left: [48]). Try possible operations.\n    |- Try 39 + 2 = 41. Add 41 to the number set. Current number set: [41, 48], target: 29, just two numbers left.\n     |- Try 48 + 41 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 48 - 41 = 7. Evaluate 7 != 29, drop this branch.\n     |- Try 48 * 41 = 1968. Evaluate 1968 != 29, drop this branch.\n     |- Try 48 \/ 41 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 39 - 2 = 37. Add 37 to the number set. Current number set: [37, 48], target: 29, just two numbers left.\n     |- Try 48 + 37 = 85. Evaluate 85 != 29, drop this branch.\n     |- Try 48 - 37 = 11. Evaluate 11 != 29, drop this branch.\n     |- Try 48 * 37 = 1776. Evaluate 1776 != 29, drop this branch.\n     |- Try 48 \/ 37 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 39 * 2 = 78. Add 78 to the number set. Current number set: [78, 48], target: 29, just two numbers left.\n     |- Try 78 + 48 = 126. Evaluate 126 != 29, drop this branch.\n     |- Try 78 - 48 = 30. Evaluate 30 != 29, drop this branch.\n     |- Try 78 * 48 = 3744. 3744 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 48 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 39 \/ 2 = 19.5. 19.5 is a decimal, drop this branch.\n   |- Pick two numbers (48, 39) (numbers left: [2]). Try possible operations.\n    |- Try 48 + 39 = 87. Add 87 to the number set. Current number set: [87, 2], target: 29, just two numbers left.\n     |- Try 87 + 2 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 87 - 2 = 85. Evaluate 85 != 29, drop this branch.\n     |- Try 87 * 2 = 174. Evaluate 174 != 29, drop this branch.\n     |- Try 87 \/ 2 = 43.5. 43.5 is a decimal, drop this branch.\n    |- Try 48 - 39 = 9. Add 9 to the number set. Current number set: [9, 2], target: 29, just two numbers left.\n     |- Try 9 + 2 = 11. Evaluate 11 != 29, drop this branch.\n     |- Try 9 - 2 = 7. Evaluate 7 != 29, drop this branch.\n     |- Try 9 * 2 = 18. Evaluate 18 != 29, drop this branch.\n     |- Try 9 \/ 2 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 48 * 39 = 1872. Add 1872 to the number set. Current number set: [1872, 2], target: 29, just two numbers left.\n     |- Try 1872 + 2 = 1874. Evaluate 1874 != 29, drop this branch.\n     |- Try 1872 - 2 = 1870. Evaluate 1870 != 29, drop this branch.\n     |- Try 1872 * 2 = 3744. 3744 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1872 \/ 2 = 936. Evaluate 936 != 29, drop this branch.\n    |- Try 48 \/ 39 = 1.2. 1.2 is a decimal, drop this branch.\n |- Pick two numbers (12, 48) (numbers left: [6, 39]). Try possible operations.\n  |- Try 48 + 12 = 60. Add 60 to the number set. Current number set: [60, 6, 39], target: 29. Options for choosing two numbers: [(60, 6), (60, 39), (6, 39)].\n   |- Pick two numbers (60, 6) (numbers left: [39]). Try possible operations.\n    |- Try 60 + 6 = 66. Add 66 to the number set. Current number set: [66, 39], target: 29, just two numbers left.\n     |- Try 66 + 39 = 105. Evaluate 105 != 29, drop this branch.\n     |- Try 66 - 39 = 27. Evaluate 27 != 29, drop this branch.\n     |- Try 66 * 39 = 2574. 2574 exceeds the maximum intermediate result, drop this branch.\n     |- Try 66 \/ 39 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 60 - 6 = 54. Add 54 to the number set. Current number set: [54, 39], target: 29, just two numbers left.\n     |- Try 54 + 39 = 93. Evaluate 93 != 29, drop this branch.\n     |- Try 54 - 39 = 15. Evaluate 15 != 29, drop this branch.\n     |- Try 54 * 39 = 2106. 2106 exceeds the maximum intermediate result, drop this branch.\n     |- Try 54 \/ 39 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 60 * 6 = 360. Add 360 to the number set. Current number set: [360, 39], target: 29, just two numbers left.\n     |- Try 360 + 39 = 399. Evaluate 399 != 29, drop this branch.\n     |- Try 360 - 39 = 321. Evaluate 321 != 29, drop this branch.\n     |- Try 360 * 39 = 14040. 14040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 360 \/ 39 = 9.2. 9.2 is a decimal, drop this branch.\n    |- Try 60 \/ 6 = 10. Add 10 to the number set. Current number set: [10, 39], target: 29, just two numbers left.\n     |- Try 39 + 10 = 49. Evaluate 49 != 29, drop this branch.\n     |- Try 39 - 10 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 39 - 10 = 29\nThe step before: 60 \/ 6 = 10\nThe first step: 48 + 12 = 60\n\nOutput the solution in the required format:\n<Solution>\n48 + 12 = 60\n60 \/ 6 = 10\n39 - 10 = 29\n<\/Solution>\n","item":{"nums":[12,6,48,39],"solution":["48 + 12 = 60","60 \/ 6 = 10","39 - 10 = 29"],"target":29}}
+{"instance_id":"countdown_8k_116","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [45, 26, 43, 48]\nTarget: 11","reference_output":"# Search Procedure\nInitial number set: [45, 26, 43, 48], target: 11. Options for choosing two numbers: [(45, 26), (45, 43), (45, 48), (26, 43), (26, 48), (43, 48)].\n |- Pick two numbers (45, 26) (numbers left: [43, 48]). Try possible operations.\n  |- Try 45 + 26 = 71. Add 71 to the number set. Current number set: [71, 43, 48], target: 11. Options for choosing two numbers: [(71, 43), (71, 48), (43, 48)].\n   |- Pick two numbers (71, 43) (numbers left: [48]). Try possible operations.\n    |- Try 71 + 43 = 114. Add 114 to the number set. Current number set: [114, 48], target: 11, just two numbers left.\n     |- Try 114 + 48 = 162. Evaluate 162 != 11, drop this branch.\n     |- Try 114 - 48 = 66. Evaluate 66 != 11, drop this branch.\n     |- Try 114 * 48 = 5472. 5472 exceeds the maximum intermediate result, drop this branch.\n     |- Try 114 \/ 48 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 71 - 43 = 28. Add 28 to the number set. Current number set: [28, 48], target: 11, just two numbers left.\n     |- Try 48 + 28 = 76. Evaluate 76 != 11, drop this branch.\n     |- Try 48 - 28 = 20. Evaluate 20 != 11, drop this branch.\n     |- Try 48 * 28 = 1344. Evaluate 1344 != 11, drop this branch.\n     |- Try 48 \/ 28 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 71 * 43 = 3053. 3053 exceeds the maximum intermediate result, drop this branch.\n    |- Try 71 \/ 43 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (71, 48) (numbers left: [43]). Try possible operations.\n    |- Try 71 + 48 = 119. Add 119 to the number set. Current number set: [119, 43], target: 11, just two numbers left.\n     |- Try 119 + 43 = 162. Evaluate 162 != 11, drop this branch.\n     |- Try 119 - 43 = 76. Evaluate 76 != 11, drop this branch.\n     |- Try 119 * 43 = 5117. 5117 exceeds the maximum intermediate result, drop this branch.\n     |- Try 119 \/ 43 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 71 - 48 = 23. Add 23 to the number set. Current number set: [23, 43], target: 11, just two numbers left.\n     |- Try 43 + 23 = 66. Evaluate 66 != 11, drop this branch.\n     |- Try 43 - 23 = 20. Evaluate 20 != 11, drop this branch.\n     |- Try 43 * 23 = 989. Evaluate 989 != 11, drop this branch.\n     |- Try 43 \/ 23 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 71 * 48 = 3408. 3408 exceeds the maximum intermediate result, drop this branch.\n    |- Try 71 \/ 48 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (43, 48) (numbers left: [71]). Try possible operations.\n    |- Try 48 + 43 = 91. Add 91 to the number set. Current number set: [91, 71], target: 11, just two numbers left.\n     |- Try 91 + 71 = 162. Evaluate 162 != 11, drop this branch.\n     |- Try 91 - 71 = 20. Evaluate 20 != 11, drop this branch.\n     |- Try 91 * 71 = 6461. 6461 exceeds the maximum intermediate result, drop this branch.\n     |- Try 91 \/ 71 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 48 - 43 = 5. Add 5 to the number set. Current number set: [5, 71], target: 11, just two numbers left.\n     |- Try 71 + 5 = 76. Evaluate 76 != 11, drop this branch.\n     |- Try 71 - 5 = 66. Evaluate 66 != 11, drop this branch.\n     |- Try 71 * 5 = 355. Evaluate 355 != 11, drop this branch.\n     |- Try 71 \/ 5 = 14.2. 14.2 is a decimal, drop this branch.\n    |- Try 48 * 43 = 2064. 2064 exceeds the maximum intermediate result, drop this branch.\n    |- Try 48 \/ 43 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 45 - 26 = 19. Add 19 to the number set. Current number set: [19, 43, 48], target: 11. Options for choosing two numbers: [(19, 43), (19, 48), (43, 48)].\n   |- Pick two numbers (19, 43) (numbers left: [48]). Try possible operations.\n    |- Try 43 + 19 = 62. Add 62 to the number set. Current number set: [62, 48], target: 11, just two numbers left.\n     |- Try 62 + 48 = 110. Evaluate 110 != 11, drop this branch.\n     |- Try 62 - 48 = 14. Evaluate 14 != 11, drop this branch.\n     |- Try 62 * 48 = 2976. 2976 exceeds the maximum intermediate result, drop this branch.\n     |- Try 62 \/ 48 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 43 - 19 = 24. Add 24 to the number set. Current number set: [24, 48], target: 11, just two numbers left.\n     |- Try 48 + 24 = 72. Evaluate 72 != 11, drop this branch.\n     |- Try 48 - 24 = 24. Evaluate 24 != 11, drop this branch.\n     |- Try 48 * 24 = 1152. Evaluate 1152 != 11, drop this branch.\n     |- Try 48 \/ 24 = 2. Evaluate 2 != 11, drop this branch.\n    |- Try 43 * 19 = 817. Add 817 to the number set. Current number set: [817, 48], target: 11, just two numbers left.\n     |- Try 817 + 48 = 865. Evaluate 865 != 11, drop this branch.\n     |- Try 817 - 48 = 769. Evaluate 769 != 11, drop this branch.\n     |- Try 817 * 48 = 39216. 39216 exceeds the maximum intermediate result, drop this branch.\n     |- Try 817 \/ 48 = 17.0. 17.0 is a decimal, drop this branch.\n    |- Try 43 \/ 19 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (19, 48) (numbers left: [43]). Try possible operations.\n    |- Try 48 + 19 = 67. Add 67 to the number set. Current number set: [67, 43], target: 11, just two numbers left.\n     |- Try 67 + 43 = 110. Evaluate 110 != 11, drop this branch.\n     |- Try 67 - 43 = 24. Evaluate 24 != 11, drop this branch.\n     |- Try 67 * 43 = 2881. 2881 exceeds the maximum intermediate result, drop this branch.\n     |- Try 67 \/ 43 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 48 - 19 = 29. Add 29 to the number set. Current number set: [29, 43], target: 11, just two numbers left.\n     |- Try 43 + 29 = 72. Evaluate 72 != 11, drop this branch.\n     |- Try 43 - 29 = 14. Evaluate 14 != 11, drop this branch.\n     |- Try 43 * 29 = 1247. Evaluate 1247 != 11, drop this branch.\n     |- Try 43 \/ 29 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 48 * 19 = 912. Add 912 to the number set. Current number set: [912, 43], target: 11, just two numbers left.\n     |- Try 912 + 43 = 955. Evaluate 955 != 11, drop this branch.\n     |- Try 912 - 43 = 869. Evaluate 869 != 11, drop this branch.\n     |- Try 912 * 43 = 39216. 39216 exceeds the maximum intermediate result, drop this branch.\n     |- Try 912 \/ 43 = 21.2. 21.2 is a decimal, drop this branch.\n    |- Try 48 \/ 19 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (43, 48) (numbers left: [19]). Try possible operations.\n    |- Try 48 + 43 = 91. Add 91 to the number set. Current number set: [91, 19], target: 11, just two numbers left.\n     |- Try 91 + 19 = 110. Evaluate 110 != 11, drop this branch.\n     |- Try 91 - 19 = 72. Evaluate 72 != 11, drop this branch.\n     |- Try 91 * 19 = 1729. Evaluate 1729 != 11, drop this branch.\n     |- Try 91 \/ 19 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 48 - 43 = 5. Add 5 to the number set. Current number set: [5, 19], target: 11, just two numbers left.\n     |- Try 19 + 5 = 24. Evaluate 24 != 11, drop this branch.\n     |- Try 19 - 5 = 14. Evaluate 14 != 11, drop this branch.\n     |- Try 19 * 5 = 95. Evaluate 95 != 11, drop this branch.\n     |- Try 19 \/ 5 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 48 * 43 = 2064. 2064 exceeds the maximum intermediate result, drop this branch.\n    |- Try 48 \/ 43 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 45 * 26 = 1170. Add 1170 to the number set. Current number set: [1170, 43, 48], target: 11. Options for choosing two numbers: [(1170, 43), (1170, 48), (43, 48)].\n   |- Pick two numbers (1170, 43) (numbers left: [48]). Try possible operations.\n    |- Try 1170 + 43 = 1213. Add 1213 to the number set. Current number set: [1213, 48], target: 11, just two numbers left.\n     |- Try 1213 + 48 = 1261. Evaluate 1261 != 11, drop this branch.\n     |- Try 1213 - 48 = 1165. Evaluate 1165 != 11, drop this branch.\n     |- Try 1213 * 48 = 58224. 58224 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1213 \/ 48 = 25.3. 25.3 is a decimal, drop this branch.\n    |- Try 1170 - 43 = 1127. Add 1127 to the number set. Current number set: [1127, 48], target: 11, just two numbers left.\n     |- Try 1127 + 48 = 1175. Evaluate 1175 != 11, drop this branch.\n     |- Try 1127 - 48 = 1079. Evaluate 1079 != 11, drop this branch.\n     |- Try 1127 * 48 = 54096. 54096 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1127 \/ 48 = 23.5. 23.5 is a decimal, drop this branch.\n    |- Try 1170 * 43 = 50310. 50310 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1170 \/ 43 = 27.2. 27.2 is a decimal, drop this branch.\n   |- Pick two numbers (1170, 48) (numbers left: [43]). Try possible operations.\n    |- Try 1170 + 48 = 1218. Add 1218 to the number set. Current number set: [1218, 43], target: 11, just two numbers left.\n     |- Try 1218 + 43 = 1261. Evaluate 1261 != 11, drop this branch.\n     |- Try 1218 - 43 = 1175. Evaluate 1175 != 11, drop this branch.\n     |- Try 1218 * 43 = 52374. 52374 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1218 \/ 43 = 28.3. 28.3 is a decimal, drop this branch.\n    |- Try 1170 - 48 = 1122. Add 1122 to the number set. Current number set: [1122, 43], target: 11, just two numbers left.\n     |- Try 1122 + 43 = 1165. Evaluate 1165 != 11, drop this branch.\n     |- Try 1122 - 43 = 1079. Evaluate 1079 != 11, drop this branch.\n     |- Try 1122 * 43 = 48246. 48246 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1122 \/ 43 = 26.1. 26.1 is a decimal, drop this branch.\n    |- Try 1170 * 48 = 56160. 56160 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1170 \/ 48 = 24.4. 24.4 is a decimal, drop this branch.\n   |- Pick two numbers (43, 48) (numbers left: [1170]). Try possible operations.\n    |- Try 48 + 43 = 91. Add 91 to the number set. Current number set: [91, 1170], target: 11, just two numbers left.\n     |- Try 1170 + 91 = 1261. Evaluate 1261 != 11, drop this branch.\n     |- Try 1170 - 91 = 1079. Evaluate 1079 != 11, drop this branch.\n     |- Try 1170 * 91 = 106470. 106470 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1170 \/ 91 = 12.9. 12.9 is a decimal, drop this branch.\n    |- Try 48 - 43 = 5. Add 5 to the number set. Current number set: [5, 1170], target: 11, just two numbers left.\n     |- Try 1170 + 5 = 1175. Evaluate 1175 != 11, drop this branch.\n     |- Try 1170 - 5 = 1165. Evaluate 1165 != 11, drop this branch.\n     |- Try 1170 * 5 = 5850. 5850 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1170 \/ 5 = 234. Evaluate 234 != 11, drop this branch.\n    |- Try 48 * 43 = 2064. 2064 exceeds the maximum intermediate result, drop this branch.\n    |- Try 48 \/ 43 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 45 \/ 26 = 1.7. 1.7 is a decimal, drop this branch.\n |- Pick two numbers (45, 43) (numbers left: [26, 48]). Try possible operations.\n  |- Try 45 + 43 = 88. Add 88 to the number set. Current number set: [88, 26, 48], target: 11. Options for choosing two numbers: [(88, 26), (88, 48), (26, 48)].\n   |- Pick two numbers (88, 26) (numbers left: [48]). Try possible operations.\n    |- Try 88 + 26 = 114. Add 114 to the number set. Current number set: [114, 48], target: 11, just two numbers left.\n     |- Try 114 + 48 = 162. Evaluate 162 != 11, drop this branch.\n     |- Try 114 - 48 = 66. Evaluate 66 != 11, drop this branch.\n     |- Try 114 * 48 = 5472. 5472 exceeds the maximum intermediate result, drop this branch.\n     |- Try 114 \/ 48 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 88 - 26 = 62. Add 62 to the number set. Current number set: [62, 48], target: 11, just two numbers left.\n     |- Try 62 + 48 = 110. Evaluate 110 != 11, drop this branch.\n     |- Try 62 - 48 = 14. Evaluate 14 != 11, drop this branch.\n     |- Try 62 * 48 = 2976. 2976 exceeds the maximum intermediate result, drop this branch.\n     |- Try 62 \/ 48 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 88 * 26 = 2288. 2288 exceeds the maximum intermediate result, drop this branch.\n    |- Try 88 \/ 26 = 3.4. 3.4 is a decimal, drop this branch.\n   |- Pick two numbers (88, 48) (numbers left: [26]). Try possible operations.\n    |- Try 88 + 48 = 136. Add 136 to the number set. Current number set: [136, 26], target: 11, just two numbers left.\n     |- Try 136 + 26 = 162. Evaluate 162 != 11, drop this branch.\n     |- Try 136 - 26 = 110. Evaluate 110 != 11, drop this branch.\n     |- Try 136 * 26 = 3536. 3536 exceeds the maximum intermediate result, drop this branch.\n     |- Try 136 \/ 26 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 88 - 48 = 40. Add 40 to the number set. Current number set: [40, 26], target: 11, just two numbers left.\n     |- Try 40 + 26 = 66. Evaluate 66 != 11, drop this branch.\n     |- Try 40 - 26 = 14. Evaluate 14 != 11, drop this branch.\n     |- Try 40 * 26 = 1040. Evaluate 1040 != 11, drop this branch.\n     |- Try 40 \/ 26 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 88 * 48 = 4224. 4224 exceeds the maximum intermediate result, drop this branch.\n    |- Try 88 \/ 48 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (26, 48) (numbers left: [88]). Try possible operations.\n    |- Try 48 + 26 = 74. Add 74 to the number set. Current number set: [74, 88], target: 11, just two numbers left.\n     |- Try 88 + 74 = 162. Evaluate 162 != 11, drop this branch.\n     |- Try 88 - 74 = 14. Evaluate 14 != 11, drop this branch.\n     |- Try 88 * 74 = 6512. 6512 exceeds the maximum intermediate result, drop this branch.\n     |- Try 88 \/ 74 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 48 - 26 = 22. Add 22 to the number set. Current number set: [22, 88], target: 11, just two numbers left.\n     |- Try 88 + 22 = 110. Evaluate 110 != 11, drop this branch.\n     |- Try 88 - 22 = 66. Evaluate 66 != 11, drop this branch.\n     |- Try 88 * 22 = 1936. Evaluate 1936 != 11, drop this branch.\n     |- Try 88 \/ 22 = 4. Evaluate 4 != 11, drop this branch.\n    |- Try 48 * 26 = 1248. Add 1248 to the number set. Current number set: [1248, 88], target: 11, just two numbers left.\n     |- Try 1248 + 88 = 1336. Evaluate 1336 != 11, drop this branch.\n     |- Try 1248 - 88 = 1160. Evaluate 1160 != 11, drop this branch.\n     |- Try 1248 * 88 = 109824. 109824 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1248 \/ 88 = 14.2. 14.2 is a decimal, drop this branch.\n    |- Try 48 \/ 26 = 1.8. 1.8 is a decimal, drop this branch.\n  |- Try 45 - 43 = 2. Add 2 to the number set. Current number set: [2, 26, 48], target: 11. Options for choosing two numbers: [(2, 26), (2, 48), (26, 48)].\n   |- Pick two numbers (2, 26) (numbers left: [48]). Try possible operations.\n    |- Try 26 + 2 = 28. Add 28 to the number set. Current number set: [28, 48], target: 11, just two numbers left.\n     |- Try 48 + 28 = 76. Evaluate 76 != 11, drop this branch.\n     |- Try 48 - 28 = 20. Evaluate 20 != 11, drop this branch.\n     |- Try 48 * 28 = 1344. Evaluate 1344 != 11, drop this branch.\n     |- Try 48 \/ 28 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 26 - 2 = 24. Add 24 to the number set. Current number set: [24, 48], target: 11, just two numbers left.\n     |- Try 48 + 24 = 72. Evaluate 72 != 11, drop this branch.\n     |- Try 48 - 24 = 24. Evaluate 24 != 11, drop this branch.\n     |- Try 48 * 24 = 1152. Evaluate 1152 != 11, drop this branch.\n     |- Try 48 \/ 24 = 2. Evaluate 2 != 11, drop this branch.\n    |- Try 26 * 2 = 52. Add 52 to the number set. Current number set: [52, 48], target: 11, just two numbers left.\n     |- Try 52 + 48 = 100. Evaluate 100 != 11, drop this branch.\n     |- Try 52 - 48 = 4. Evaluate 4 != 11, drop this branch.\n     |- Try 52 * 48 = 2496. 2496 exceeds the maximum intermediate result, drop this branch.\n     |- Try 52 \/ 48 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 26 \/ 2 = 13. Add 13 to the number set. Current number set: [13, 48], target: 11, just two numbers left.\n     |- Try 48 + 13 = 61. Evaluate 61 != 11, drop this branch.\n     |- Try 48 - 13 = 35. Evaluate 35 != 11, drop this branch.\n     |- Try 48 * 13 = 624. Evaluate 624 != 11, drop this branch.\n     |- Try 48 \/ 13 = 3.7. 3.7 is a decimal, drop this branch.\n   |- Pick two numbers (2, 48) (numbers left: [26]). Try possible operations.\n    |- Try 48 + 2 = 50. Add 50 to the number set. Current number set: [50, 26], target: 11, just two numbers left.\n     |- Try 50 + 26 = 76. Evaluate 76 != 11, drop this branch.\n     |- Try 50 - 26 = 24. Evaluate 24 != 11, drop this branch.\n     |- Try 50 * 26 = 1300. Evaluate 1300 != 11, drop this branch.\n     |- Try 50 \/ 26 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 48 - 2 = 46. Add 46 to the number set. Current number set: [46, 26], target: 11, just two numbers left.\n     |- Try 46 + 26 = 72. Evaluate 72 != 11, drop this branch.\n     |- Try 46 - 26 = 20. Evaluate 20 != 11, drop this branch.\n     |- Try 46 * 26 = 1196. Evaluate 1196 != 11, drop this branch.\n     |- Try 46 \/ 26 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 48 * 2 = 96. Add 96 to the number set. Current number set: [96, 26], target: 11, just two numbers left.\n     |- Try 96 + 26 = 122. Evaluate 122 != 11, drop this branch.\n     |- Try 96 - 26 = 70. Evaluate 70 != 11, drop this branch.\n     |- Try 96 * 26 = 2496. 2496 exceeds the maximum intermediate result, drop this branch.\n     |- Try 96 \/ 26 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 48 \/ 2 = 24. Add 24 to the number set. Current number set: [24, 26], target: 11, just two numbers left.\n     |- Try 26 + 24 = 50. Evaluate 50 != 11, drop this branch.\n     |- Try 26 - 24 = 2. Evaluate 2 != 11, drop this branch.\n     |- Try 26 * 24 = 624. Evaluate 624 != 11, drop this branch.\n     |- Try 26 \/ 24 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (26, 48) (numbers left: [2]). Try possible operations.\n    |- Try 48 + 26 = 74. Add 74 to the number set. Current number set: [74, 2], target: 11, just two numbers left.\n     |- Try 74 + 2 = 76. Evaluate 76 != 11, drop this branch.\n     |- Try 74 - 2 = 72. Evaluate 72 != 11, drop this branch.\n     |- Try 74 * 2 = 148. Evaluate 148 != 11, drop this branch.\n     |- Try 74 \/ 2 = 37. Evaluate 37 != 11, drop this branch.\n    |- Try 48 - 26 = 22. Add 22 to the number set. Current number set: [22, 2], target: 11, just two numbers left.\n     |- Try 22 + 2 = 24. Evaluate 24 != 11, drop this branch.\n     |- Try 22 - 2 = 20. Evaluate 20 != 11, drop this branch.\n     |- Try 22 * 2 = 44. Evaluate 44 != 11, drop this branch.\n     |- Try 22 \/ 2 = 11. Evaluate 11 == 11, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 22 \/ 2 = 11\nThe step before: 48 - 26 = 22\nThe first step: 45 - 43 = 2\n\nOutput the solution in the required format:\n<Solution>\n45 - 43 = 2\n48 - 26 = 22\n22 \/ 2 = 11\n<\/Solution>\n","item":{"nums":[45,26,43,48],"solution":["45 - 43 = 2","48 - 26 = 22","22 \/ 2 = 11"],"target":11}}
+{"instance_id":"countdown_8k_117","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [47, 36, 19, 3]\nTarget: 48","reference_output":"# Search Procedure\nInitial number set: [47, 36, 19, 3], target: 48. Options for choosing two numbers: [(47, 36), (47, 19), (47, 3), (36, 19), (36, 3), (19, 3)].\n |- Pick two numbers (47, 36) (numbers left: [19, 3]). Try possible operations.\n  |- Try 47 + 36 = 83. Add 83 to the number set. Current number set: [83, 19, 3], target: 48. Options for choosing two numbers: [(83, 19), (83, 3), (19, 3)].\n   |- Pick two numbers (83, 19) (numbers left: [3]). Try possible operations.\n    |- Try 83 + 19 = 102. Add 102 to the number set. Current number set: [102, 3], target: 48, just two numbers left.\n     |- Try 102 + 3 = 105. Evaluate 105 != 48, drop this branch.\n     |- Try 102 - 3 = 99. Evaluate 99 != 48, drop this branch.\n     |- Try 102 * 3 = 306. Evaluate 306 != 48, drop this branch.\n     |- Try 102 \/ 3 = 34. Evaluate 34 != 48, drop this branch.\n    |- Try 83 - 19 = 64. Add 64 to the number set. Current number set: [64, 3], target: 48, just two numbers left.\n     |- Try 64 + 3 = 67. Evaluate 67 != 48, drop this branch.\n     |- Try 64 - 3 = 61. Evaluate 61 != 48, drop this branch.\n     |- Try 64 * 3 = 192. Evaluate 192 != 48, drop this branch.\n     |- Try 64 \/ 3 = 21.3. 21.3 is a decimal, drop this branch.\n    |- Try 83 * 19 = 1577. Add 1577 to the number set. Current number set: [1577, 3], target: 48, just two numbers left.\n     |- Try 1577 + 3 = 1580. Evaluate 1580 != 48, drop this branch.\n     |- Try 1577 - 3 = 1574. Evaluate 1574 != 48, drop this branch.\n     |- Try 1577 * 3 = 4731. 4731 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1577 \/ 3 = 525.7. 525.7 is a decimal, drop this branch.\n    |- Try 83 \/ 19 = 4.4. 4.4 is a decimal, drop this branch.\n   |- Pick two numbers (83, 3) (numbers left: [19]). Try possible operations.\n    |- Try 83 + 3 = 86. Add 86 to the number set. Current number set: [86, 19], target: 48, just two numbers left.\n     |- Try 86 + 19 = 105. Evaluate 105 != 48, drop this branch.\n     |- Try 86 - 19 = 67. Evaluate 67 != 48, drop this branch.\n     |- Try 86 * 19 = 1634. Evaluate 1634 != 48, drop this branch.\n     |- Try 86 \/ 19 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 83 - 3 = 80. Add 80 to the number set. Current number set: [80, 19], target: 48, just two numbers left.\n     |- Try 80 + 19 = 99. Evaluate 99 != 48, drop this branch.\n     |- Try 80 - 19 = 61. Evaluate 61 != 48, drop this branch.\n     |- Try 80 * 19 = 1520. Evaluate 1520 != 48, drop this branch.\n     |- Try 80 \/ 19 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 83 * 3 = 249. Add 249 to the number set. Current number set: [249, 19], target: 48, just two numbers left.\n     |- Try 249 + 19 = 268. Evaluate 268 != 48, drop this branch.\n     |- Try 249 - 19 = 230. Evaluate 230 != 48, drop this branch.\n     |- Try 249 * 19 = 4731. 4731 exceeds the maximum intermediate result, drop this branch.\n     |- Try 249 \/ 19 = 13.1. 13.1 is a decimal, drop this branch.\n    |- Try 83 \/ 3 = 27.7. 27.7 is a decimal, drop this branch.\n   |- Pick two numbers (19, 3) (numbers left: [83]). Try possible operations.\n    |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 83], target: 48, just two numbers left.\n     |- Try 83 + 22 = 105. Evaluate 105 != 48, drop this branch.\n     |- Try 83 - 22 = 61. Evaluate 61 != 48, drop this branch.\n     |- Try 83 * 22 = 1826. Evaluate 1826 != 48, drop this branch.\n     |- Try 83 \/ 22 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 83], target: 48, just two numbers left.\n     |- Try 83 + 16 = 99. Evaluate 99 != 48, drop this branch.\n     |- Try 83 - 16 = 67. Evaluate 67 != 48, drop this branch.\n     |- Try 83 * 16 = 1328. Evaluate 1328 != 48, drop this branch.\n     |- Try 83 \/ 16 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 19 * 3 = 57. Add 57 to the number set. Current number set: [57, 83], target: 48, just two numbers left.\n     |- Try 83 + 57 = 140. Evaluate 140 != 48, drop this branch.\n     |- Try 83 - 57 = 26. Evaluate 26 != 48, drop this branch.\n     |- Try 83 * 57 = 4731. 4731 exceeds the maximum intermediate result, drop this branch.\n     |- Try 83 \/ 57 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 19 \/ 3 = 6.3. 6.3 is a decimal, drop this branch.\n  |- Try 47 - 36 = 11. Add 11 to the number set. Current number set: [11, 19, 3], target: 48. Options for choosing two numbers: [(11, 19), (11, 3), (19, 3)].\n   |- Pick two numbers (11, 19) (numbers left: [3]). Try possible operations.\n    |- Try 19 + 11 = 30. Add 30 to the number set. Current number set: [30, 3], target: 48, just two numbers left.\n     |- Try 30 + 3 = 33. Evaluate 33 != 48, drop this branch.\n     |- Try 30 - 3 = 27. Evaluate 27 != 48, drop this branch.\n     |- Try 30 * 3 = 90. Evaluate 90 != 48, drop this branch.\n     |- Try 30 \/ 3 = 10. Evaluate 10 != 48, drop this branch.\n    |- Try 19 - 11 = 8. Add 8 to the number set. Current number set: [8, 3], target: 48, just two numbers left.\n     |- Try 8 + 3 = 11. Evaluate 11 != 48, drop this branch.\n     |- Try 8 - 3 = 5. Evaluate 5 != 48, drop this branch.\n     |- Try 8 * 3 = 24. Evaluate 24 != 48, drop this branch.\n     |- Try 8 \/ 3 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 19 * 11 = 209. Add 209 to the number set. Current number set: [209, 3], target: 48, just two numbers left.\n     |- Try 209 + 3 = 212. Evaluate 212 != 48, drop this branch.\n     |- Try 209 - 3 = 206. Evaluate 206 != 48, drop this branch.\n     |- Try 209 * 3 = 627. Evaluate 627 != 48, drop this branch.\n     |- Try 209 \/ 3 = 69.7. 69.7 is a decimal, drop this branch.\n    |- Try 19 \/ 11 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (11, 3) (numbers left: [19]). Try possible operations.\n    |- Try 11 + 3 = 14. Add 14 to the number set. Current number set: [14, 19], target: 48, just two numbers left.\n     |- Try 19 + 14 = 33. Evaluate 33 != 48, drop this branch.\n     |- Try 19 - 14 = 5. Evaluate 5 != 48, drop this branch.\n     |- Try 19 * 14 = 266. Evaluate 266 != 48, drop this branch.\n     |- Try 19 \/ 14 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 11 - 3 = 8. Add 8 to the number set. Current number set: [8, 19], target: 48, just two numbers left.\n     |- Try 19 + 8 = 27. Evaluate 27 != 48, drop this branch.\n     |- Try 19 - 8 = 11. Evaluate 11 != 48, drop this branch.\n     |- Try 19 * 8 = 152. Evaluate 152 != 48, drop this branch.\n     |- Try 19 \/ 8 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 11 * 3 = 33. Add 33 to the number set. Current number set: [33, 19], target: 48, just two numbers left.\n     |- Try 33 + 19 = 52. Evaluate 52 != 48, drop this branch.\n     |- Try 33 - 19 = 14. Evaluate 14 != 48, drop this branch.\n     |- Try 33 * 19 = 627. Evaluate 627 != 48, drop this branch.\n     |- Try 33 \/ 19 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 11 \/ 3 = 3.7. 3.7 is a decimal, drop this branch.\n   |- Pick two numbers (19, 3) (numbers left: [11]). Try possible operations.\n    |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 11], target: 48, just two numbers left.\n     |- Try 22 + 11 = 33. Evaluate 33 != 48, drop this branch.\n     |- Try 22 - 11 = 11. Evaluate 11 != 48, drop this branch.\n     |- Try 22 * 11 = 242. Evaluate 242 != 48, drop this branch.\n     |- Try 22 \/ 11 = 2. Evaluate 2 != 48, drop this branch.\n    |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 11], target: 48, just two numbers left.\n     |- Try 16 + 11 = 27. Evaluate 27 != 48, drop this branch.\n     |- Try 16 - 11 = 5. Evaluate 5 != 48, drop this branch.\n     |- Try 16 * 11 = 176. Evaluate 176 != 48, drop this branch.\n     |- Try 16 \/ 11 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 19 * 3 = 57. Add 57 to the number set. Current number set: [57, 11], target: 48, just two numbers left.\n     |- Try 57 + 11 = 68. Evaluate 68 != 48, drop this branch.\n     |- Try 57 - 11 = 46. Evaluate 46 != 48, drop this branch.\n     |- Try 57 * 11 = 627. Evaluate 627 != 48, drop this branch.\n     |- Try 57 \/ 11 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 19 \/ 3 = 6.3. 6.3 is a decimal, drop this branch.\n  |- Try 47 * 36 = 1692. Add 1692 to the number set. Current number set: [1692, 19, 3], target: 48. Options for choosing two numbers: [(1692, 19), (1692, 3), (19, 3)].\n   |- Pick two numbers (1692, 19) (numbers left: [3]). Try possible operations.\n    |- Try 1692 + 19 = 1711. Add 1711 to the number set. Current number set: [1711, 3], target: 48, just two numbers left.\n     |- Try 1711 + 3 = 1714. Evaluate 1714 != 48, drop this branch.\n     |- Try 1711 - 3 = 1708. Evaluate 1708 != 48, drop this branch.\n     |- Try 1711 * 3 = 5133. 5133 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1711 \/ 3 = 570.3. 570.3 is a decimal, drop this branch.\n    |- Try 1692 - 19 = 1673. Add 1673 to the number set. Current number set: [1673, 3], target: 48, just two numbers left.\n     |- Try 1673 + 3 = 1676. Evaluate 1676 != 48, drop this branch.\n     |- Try 1673 - 3 = 1670. Evaluate 1670 != 48, drop this branch.\n     |- Try 1673 * 3 = 5019. 5019 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1673 \/ 3 = 557.7. 557.7 is a decimal, drop this branch.\n    |- Try 1692 * 19 = 32148. 32148 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1692 \/ 19 = 89.1. 89.1 is a decimal, drop this branch.\n   |- Pick two numbers (1692, 3) (numbers left: [19]). Try possible operations.\n    |- Try 1692 + 3 = 1695. Add 1695 to the number set. Current number set: [1695, 19], target: 48, just two numbers left.\n     |- Try 1695 + 19 = 1714. Evaluate 1714 != 48, drop this branch.\n     |- Try 1695 - 19 = 1676. Evaluate 1676 != 48, drop this branch.\n     |- Try 1695 * 19 = 32205. 32205 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1695 \/ 19 = 89.2. 89.2 is a decimal, drop this branch.\n    |- Try 1692 - 3 = 1689. Add 1689 to the number set. Current number set: [1689, 19], target: 48, just two numbers left.\n     |- Try 1689 + 19 = 1708. Evaluate 1708 != 48, drop this branch.\n     |- Try 1689 - 19 = 1670. Evaluate 1670 != 48, drop this branch.\n     |- Try 1689 * 19 = 32091. 32091 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1689 \/ 19 = 88.9. 88.9 is a decimal, drop this branch.\n    |- Try 1692 * 3 = 5076. 5076 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1692 \/ 3 = 564. Add 564 to the number set. Current number set: [564, 19], target: 48, just two numbers left.\n     |- Try 564 + 19 = 583. Evaluate 583 != 48, drop this branch.\n     |- Try 564 - 19 = 545. Evaluate 545 != 48, drop this branch.\n     |- Try 564 * 19 = 10716. 10716 exceeds the maximum intermediate result, drop this branch.\n     |- Try 564 \/ 19 = 29.7. 29.7 is a decimal, drop this branch.\n   |- Pick two numbers (19, 3) (numbers left: [1692]). Try possible operations.\n    |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 1692], target: 48, just two numbers left.\n     |- Try 1692 + 22 = 1714. Evaluate 1714 != 48, drop this branch.\n     |- Try 1692 - 22 = 1670. Evaluate 1670 != 48, drop this branch.\n     |- Try 1692 * 22 = 37224. 37224 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1692 \/ 22 = 76.9. 76.9 is a decimal, drop this branch.\n    |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 1692], target: 48, just two numbers left.\n     |- Try 1692 + 16 = 1708. Evaluate 1708 != 48, drop this branch.\n     |- Try 1692 - 16 = 1676. Evaluate 1676 != 48, drop this branch.\n     |- Try 1692 * 16 = 27072. 27072 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1692 \/ 16 = 105.8. 105.8 is a decimal, drop this branch.\n    |- Try 19 * 3 = 57. Add 57 to the number set. Current number set: [57, 1692], target: 48, just two numbers left.\n     |- Try 1692 + 57 = 1749. Evaluate 1749 != 48, drop this branch.\n     |- Try 1692 - 57 = 1635. Evaluate 1635 != 48, drop this branch.\n     |- Try 1692 * 57 = 96444. 96444 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1692 \/ 57 = 29.7. 29.7 is a decimal, drop this branch.\n    |- Try 19 \/ 3 = 6.3. 6.3 is a decimal, drop this branch.\n  |- Try 47 \/ 36 = 1.3. 1.3 is a decimal, drop this branch.\n |- Pick two numbers (47, 19) (numbers left: [36, 3]). Try possible operations.\n  |- Try 47 + 19 = 66. Add 66 to the number set. Current number set: [66, 36, 3], target: 48. Options for choosing two numbers: [(66, 36), (66, 3), (36, 3)].\n   |- Pick two numbers (66, 36) (numbers left: [3]). Try possible operations.\n    |- Try 66 + 36 = 102. Add 102 to the number set. Current number set: [102, 3], target: 48, just two numbers left.\n     |- Try 102 + 3 = 105. Evaluate 105 != 48, drop this branch.\n     |- Try 102 - 3 = 99. Evaluate 99 != 48, drop this branch.\n     |- Try 102 * 3 = 306. Evaluate 306 != 48, drop this branch.\n     |- Try 102 \/ 3 = 34. Evaluate 34 != 48, drop this branch.\n    |- Try 66 - 36 = 30. Add 30 to the number set. Current number set: [30, 3], target: 48, just two numbers left.\n     |- Try 30 + 3 = 33. Evaluate 33 != 48, drop this branch.\n     |- Try 30 - 3 = 27. Evaluate 27 != 48, drop this branch.\n     |- Try 30 * 3 = 90. Evaluate 90 != 48, drop this branch.\n     |- Try 30 \/ 3 = 10. Evaluate 10 != 48, drop this branch.\n    |- Try 66 * 36 = 2376. 2376 exceeds the maximum intermediate result, drop this branch.\n    |- Try 66 \/ 36 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (66, 3) (numbers left: [36]). Try possible operations.\n    |- Try 66 + 3 = 69. Add 69 to the number set. Current number set: [69, 36], target: 48, just two numbers left.\n     |- Try 69 + 36 = 105. Evaluate 105 != 48, drop this branch.\n     |- Try 69 - 36 = 33. Evaluate 33 != 48, drop this branch.\n     |- Try 69 * 36 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 69 \/ 36 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 66 - 3 = 63. Add 63 to the number set. Current number set: [63, 36], target: 48, just two numbers left.\n     |- Try 63 + 36 = 99. Evaluate 99 != 48, drop this branch.\n     |- Try 63 - 36 = 27. Evaluate 27 != 48, drop this branch.\n     |- Try 63 * 36 = 2268. 2268 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 36 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 66 * 3 = 198. Add 198 to the number set. Current number set: [198, 36], target: 48, just two numbers left.\n     |- Try 198 + 36 = 234. Evaluate 234 != 48, drop this branch.\n     |- Try 198 - 36 = 162. Evaluate 162 != 48, drop this branch.\n     |- Try 198 * 36 = 7128. 7128 exceeds the maximum intermediate result, drop this branch.\n     |- Try 198 \/ 36 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 66 \/ 3 = 22. Add 22 to the number set. Current number set: [22, 36], target: 48, just two numbers left.\n     |- Try 36 + 22 = 58. Evaluate 58 != 48, drop this branch.\n     |- Try 36 - 22 = 14. Evaluate 14 != 48, drop this branch.\n     |- Try 36 * 22 = 792. Evaluate 792 != 48, drop this branch.\n     |- Try 36 \/ 22 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (36, 3) (numbers left: [66]). Try possible operations.\n    |- Try 36 + 3 = 39. Add 39 to the number set. Current number set: [39, 66], target: 48, just two numbers left.\n     |- Try 66 + 39 = 105. Evaluate 105 != 48, drop this branch.\n     |- Try 66 - 39 = 27. Evaluate 27 != 48, drop this branch.\n     |- Try 66 * 39 = 2574. 2574 exceeds the maximum intermediate result, drop this branch.\n     |- Try 66 \/ 39 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 36 - 3 = 33. Add 33 to the number set. Current number set: [33, 66], target: 48, just two numbers left.\n     |- Try 66 + 33 = 99. Evaluate 99 != 48, drop this branch.\n     |- Try 66 - 33 = 33. Evaluate 33 != 48, drop this branch.\n     |- Try 66 * 33 = 2178. 2178 exceeds the maximum intermediate result, drop this branch.\n     |- Try 66 \/ 33 = 2. Evaluate 2 != 48, drop this branch.\n    |- Try 36 * 3 = 108. Add 108 to the number set. Current number set: [108, 66], target: 48, just two numbers left.\n     |- Try 108 + 66 = 174. Evaluate 174 != 48, drop this branch.\n     |- Try 108 - 66 = 42. Evaluate 42 != 48, drop this branch.\n     |- Try 108 * 66 = 7128. 7128 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 66 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 36 \/ 3 = 12. Add 12 to the number set. Current number set: [12, 66], target: 48, just two numbers left.\n     |- Try 66 + 12 = 78. Evaluate 78 != 48, drop this branch.\n     |- Try 66 - 12 = 54. Evaluate 54 != 48, drop this branch.\n     |- Try 66 * 12 = 792. Evaluate 792 != 48, drop this branch.\n     |- Try 66 \/ 12 = 5.5. 5.5 is a decimal, drop this branch.\n  |- Try 47 - 19 = 28. Add 28 to the number set. Current number set: [28, 36, 3], target: 48. Options for choosing two numbers: [(28, 36), (28, 3), (36, 3)].\n   |- Pick two numbers (28, 36) (numbers left: [3]). Try possible operations.\n    |- Try 36 + 28 = 64. Add 64 to the number set. Current number set: [64, 3], target: 48, just two numbers left.\n     |- Try 64 + 3 = 67. Evaluate 67 != 48, drop this branch.\n     |- Try 64 - 3 = 61. Evaluate 61 != 48, drop this branch.\n     |- Try 64 * 3 = 192. Evaluate 192 != 48, drop this branch.\n     |- Try 64 \/ 3 = 21.3. 21.3 is a decimal, drop this branch.\n    |- Try 36 - 28 = 8. Add 8 to the number set. Current number set: [8, 3], target: 48, just two numbers left.\n     |- Try 8 + 3 = 11. Evaluate 11 != 48, drop this branch.\n     |- Try 8 - 3 = 5. Evaluate 5 != 48, drop this branch.\n     |- Try 8 * 3 = 24. Evaluate 24 != 48, drop this branch.\n     |- Try 8 \/ 3 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 36 * 28 = 1008. Add 1008 to the number set. Current number set: [1008, 3], target: 48, just two numbers left.\n     |- Try 1008 + 3 = 1011. Evaluate 1011 != 48, drop this branch.\n     |- Try 1008 - 3 = 1005. Evaluate 1005 != 48, drop this branch.\n     |- Try 1008 * 3 = 3024. 3024 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1008 \/ 3 = 336. Evaluate 336 != 48, drop this branch.\n    |- Try 36 \/ 28 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (28, 3) (numbers left: [36]). Try possible operations.\n    |- Try 28 + 3 = 31. Add 31 to the number set. Current number set: [31, 36], target: 48, just two numbers left.\n     |- Try 36 + 31 = 67. Evaluate 67 != 48, drop this branch.\n     |- Try 36 - 31 = 5. Evaluate 5 != 48, drop this branch.\n     |- Try 36 * 31 = 1116. Evaluate 1116 != 48, drop this branch.\n     |- Try 36 \/ 31 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 28 - 3 = 25. Add 25 to the number set. Current number set: [25, 36], target: 48, just two numbers left.\n     |- Try 36 + 25 = 61. Evaluate 61 != 48, drop this branch.\n     |- Try 36 - 25 = 11. Evaluate 11 != 48, drop this branch.\n     |- Try 36 * 25 = 900. Evaluate 900 != 48, drop this branch.\n     |- Try 36 \/ 25 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 28 * 3 = 84. Add 84 to the number set. Current number set: [84, 36], target: 48, just two numbers left.\n     |- Try 84 + 36 = 120. Evaluate 120 != 48, drop this branch.\n     |- Try 84 - 36 = 48. Evaluate 48 == 48, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 84 - 36 = 48\nThe step before: 28 * 3 = 84\nThe first step: 47 - 19 = 28\n\nOutput the solution in the required format:\n<Solution>\n47 - 19 = 28\n28 * 3 = 84\n84 - 36 = 48\n<\/Solution>\n","item":{"nums":[47,36,19,3],"solution":["47 - 19 = 28","28 * 3 = 84","84 - 36 = 48"],"target":48}}
+{"instance_id":"countdown_8k_118","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [45, 23, 42, 26]\nTarget: 43","reference_output":"# Search Procedure\nInitial number set: [45, 23, 42, 26], target: 43. Options for choosing two numbers: [(45, 23), (45, 42), (45, 26), (23, 42), (23, 26), (42, 26)].\n |- Pick two numbers (45, 23) (numbers left: [42, 26]). Try possible operations.\n  |- Try 45 + 23 = 68. Add 68 to the number set. Current number set: [68, 42, 26], target: 43. Options for choosing two numbers: [(68, 42), (68, 26), (42, 26)].\n   |- Pick two numbers (68, 42) (numbers left: [26]). Try possible operations.\n    |- Try 68 + 42 = 110. Add 110 to the number set. Current number set: [110, 26], target: 43, just two numbers left.\n     |- Try 110 + 26 = 136. Evaluate 136 != 43, drop this branch.\n     |- Try 110 - 26 = 84. Evaluate 84 != 43, drop this branch.\n     |- Try 110 * 26 = 2860. 2860 exceeds the maximum intermediate result, drop this branch.\n     |- Try 110 \/ 26 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 68 - 42 = 26. Add 26 to the number set. Current number set: [26, 26], target: 43, just two numbers left.\n     |- Try 26 + 26 = 52. Evaluate 52 != 43, drop this branch.\n     |- Try 26 - 26 = 0. Evaluate 0 != 43, drop this branch.\n     |- Try 26 * 26 = 676. Evaluate 676 != 43, drop this branch.\n     |- Try 26 \/ 26 = 1. Evaluate 1 != 43, drop this branch.\n    |- Try 68 * 42 = 2856. 2856 exceeds the maximum intermediate result, drop this branch.\n    |- Try 68 \/ 42 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (68, 26) (numbers left: [42]). Try possible operations.\n    |- Try 68 + 26 = 94. Add 94 to the number set. Current number set: [94, 42], target: 43, just two numbers left.\n     |- Try 94 + 42 = 136. Evaluate 136 != 43, drop this branch.\n     |- Try 94 - 42 = 52. Evaluate 52 != 43, drop this branch.\n     |- Try 94 * 42 = 3948. 3948 exceeds the maximum intermediate result, drop this branch.\n     |- Try 94 \/ 42 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 68 - 26 = 42. Add 42 to the number set. Current number set: [42, 42], target: 43, just two numbers left.\n     |- Try 42 + 42 = 84. Evaluate 84 != 43, drop this branch.\n     |- Try 42 - 42 = 0. Evaluate 0 != 43, drop this branch.\n     |- Try 42 * 42 = 1764. Evaluate 1764 != 43, drop this branch.\n     |- Try 42 \/ 42 = 1. Evaluate 1 != 43, drop this branch.\n    |- Try 68 * 26 = 1768. Add 1768 to the number set. Current number set: [1768, 42], target: 43, just two numbers left.\n     |- Try 1768 + 42 = 1810. Evaluate 1810 != 43, drop this branch.\n     |- Try 1768 - 42 = 1726. Evaluate 1726 != 43, drop this branch.\n     |- Try 1768 * 42 = 74256. 74256 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1768 \/ 42 = 42.1. 42.1 is a decimal, drop this branch.\n    |- Try 68 \/ 26 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (42, 26) (numbers left: [68]). Try possible operations.\n    |- Try 42 + 26 = 68. Add 68 to the number set. Current number set: [68, 68], target: 43, just two numbers left.\n     |- Try 68 + 68 = 136. Evaluate 136 != 43, drop this branch.\n     |- Try 68 - 68 = 0. Evaluate 0 != 43, drop this branch.\n     |- Try 68 * 68 = 4624. 4624 exceeds the maximum intermediate result, drop this branch.\n     |- Try 68 \/ 68 = 1. Evaluate 1 != 43, drop this branch.\n    |- Try 42 - 26 = 16. Add 16 to the number set. Current number set: [16, 68], target: 43, just two numbers left.\n     |- Try 68 + 16 = 84. Evaluate 84 != 43, drop this branch.\n     |- Try 68 - 16 = 52. Evaluate 52 != 43, drop this branch.\n     |- Try 68 * 16 = 1088. Evaluate 1088 != 43, drop this branch.\n     |- Try 68 \/ 16 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 42 * 26 = 1092. Add 1092 to the number set. Current number set: [1092, 68], target: 43, just two numbers left.\n     |- Try 1092 + 68 = 1160. Evaluate 1160 != 43, drop this branch.\n     |- Try 1092 - 68 = 1024. Evaluate 1024 != 43, drop this branch.\n     |- Try 1092 * 68 = 74256. 74256 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1092 \/ 68 = 16.1. 16.1 is a decimal, drop this branch.\n    |- Try 42 \/ 26 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 45 - 23 = 22. Add 22 to the number set. Current number set: [22, 42, 26], target: 43. Options for choosing two numbers: [(22, 42), (22, 26), (42, 26)].\n   |- Pick two numbers (22, 42) (numbers left: [26]). Try possible operations.\n    |- Try 42 + 22 = 64. Add 64 to the number set. Current number set: [64, 26], target: 43, just two numbers left.\n     |- Try 64 + 26 = 90. Evaluate 90 != 43, drop this branch.\n     |- Try 64 - 26 = 38. Evaluate 38 != 43, drop this branch.\n     |- Try 64 * 26 = 1664. Evaluate 1664 != 43, drop this branch.\n     |- Try 64 \/ 26 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 42 - 22 = 20. Add 20 to the number set. Current number set: [20, 26], target: 43, just two numbers left.\n     |- Try 26 + 20 = 46. Evaluate 46 != 43, drop this branch.\n     |- Try 26 - 20 = 6. Evaluate 6 != 43, drop this branch.\n     |- Try 26 * 20 = 520. Evaluate 520 != 43, drop this branch.\n     |- Try 26 \/ 20 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 42 * 22 = 924. Add 924 to the number set. Current number set: [924, 26], target: 43, just two numbers left.\n     |- Try 924 + 26 = 950. Evaluate 950 != 43, drop this branch.\n     |- Try 924 - 26 = 898. Evaluate 898 != 43, drop this branch.\n     |- Try 924 * 26 = 24024. 24024 exceeds the maximum intermediate result, drop this branch.\n     |- Try 924 \/ 26 = 35.5. 35.5 is a decimal, drop this branch.\n    |- Try 42 \/ 22 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (22, 26) (numbers left: [42]). Try possible operations.\n    |- Try 26 + 22 = 48. Add 48 to the number set. Current number set: [48, 42], target: 43, just two numbers left.\n     |- Try 48 + 42 = 90. Evaluate 90 != 43, drop this branch.\n     |- Try 48 - 42 = 6. Evaluate 6 != 43, drop this branch.\n     |- Try 48 * 42 = 2016. 2016 exceeds the maximum intermediate result, drop this branch.\n     |- Try 48 \/ 42 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 26 - 22 = 4. Add 4 to the number set. Current number set: [4, 42], target: 43, just two numbers left.\n     |- Try 42 + 4 = 46. Evaluate 46 != 43, drop this branch.\n     |- Try 42 - 4 = 38. Evaluate 38 != 43, drop this branch.\n     |- Try 42 * 4 = 168. Evaluate 168 != 43, drop this branch.\n     |- Try 42 \/ 4 = 10.5. 10.5 is a decimal, drop this branch.\n    |- Try 26 * 22 = 572. Add 572 to the number set. Current number set: [572, 42], target: 43, just two numbers left.\n     |- Try 572 + 42 = 614. Evaluate 614 != 43, drop this branch.\n     |- Try 572 - 42 = 530. Evaluate 530 != 43, drop this branch.\n     |- Try 572 * 42 = 24024. 24024 exceeds the maximum intermediate result, drop this branch.\n     |- Try 572 \/ 42 = 13.6. 13.6 is a decimal, drop this branch.\n    |- Try 26 \/ 22 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (42, 26) (numbers left: [22]). Try possible operations.\n    |- Try 42 + 26 = 68. Add 68 to the number set. Current number set: [68, 22], target: 43, just two numbers left.\n     |- Try 68 + 22 = 90. Evaluate 90 != 43, drop this branch.\n     |- Try 68 - 22 = 46. Evaluate 46 != 43, drop this branch.\n     |- Try 68 * 22 = 1496. Evaluate 1496 != 43, drop this branch.\n     |- Try 68 \/ 22 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 42 - 26 = 16. Add 16 to the number set. Current number set: [16, 22], target: 43, just two numbers left.\n     |- Try 22 + 16 = 38. Evaluate 38 != 43, drop this branch.\n     |- Try 22 - 16 = 6. Evaluate 6 != 43, drop this branch.\n     |- Try 22 * 16 = 352. Evaluate 352 != 43, drop this branch.\n     |- Try 22 \/ 16 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 42 * 26 = 1092. Add 1092 to the number set. Current number set: [1092, 22], target: 43, just two numbers left.\n     |- Try 1092 + 22 = 1114. Evaluate 1114 != 43, drop this branch.\n     |- Try 1092 - 22 = 1070. Evaluate 1070 != 43, drop this branch.\n     |- Try 1092 * 22 = 24024. 24024 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1092 \/ 22 = 49.6. 49.6 is a decimal, drop this branch.\n    |- Try 42 \/ 26 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 45 * 23 = 1035. Add 1035 to the number set. Current number set: [1035, 42, 26], target: 43. Options for choosing two numbers: [(1035, 42), (1035, 26), (42, 26)].\n   |- Pick two numbers (1035, 42) (numbers left: [26]). Try possible operations.\n    |- Try 1035 + 42 = 1077. Add 1077 to the number set. Current number set: [1077, 26], target: 43, just two numbers left.\n     |- Try 1077 + 26 = 1103. Evaluate 1103 != 43, drop this branch.\n     |- Try 1077 - 26 = 1051. Evaluate 1051 != 43, drop this branch.\n     |- Try 1077 * 26 = 28002. 28002 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1077 \/ 26 = 41.4. 41.4 is a decimal, drop this branch.\n    |- Try 1035 - 42 = 993. Add 993 to the number set. Current number set: [993, 26], target: 43, just two numbers left.\n     |- Try 993 + 26 = 1019. Evaluate 1019 != 43, drop this branch.\n     |- Try 993 - 26 = 967. Evaluate 967 != 43, drop this branch.\n     |- Try 993 * 26 = 25818. 25818 exceeds the maximum intermediate result, drop this branch.\n     |- Try 993 \/ 26 = 38.2. 38.2 is a decimal, drop this branch.\n    |- Try 1035 * 42 = 43470. 43470 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1035 \/ 42 = 24.6. 24.6 is a decimal, drop this branch.\n   |- Pick two numbers (1035, 26) (numbers left: [42]). Try possible operations.\n    |- Try 1035 + 26 = 1061. Add 1061 to the number set. Current number set: [1061, 42], target: 43, just two numbers left.\n     |- Try 1061 + 42 = 1103. Evaluate 1103 != 43, drop this branch.\n     |- Try 1061 - 42 = 1019. Evaluate 1019 != 43, drop this branch.\n     |- Try 1061 * 42 = 44562. 44562 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1061 \/ 42 = 25.3. 25.3 is a decimal, drop this branch.\n    |- Try 1035 - 26 = 1009. Add 1009 to the number set. Current number set: [1009, 42], target: 43, just two numbers left.\n     |- Try 1009 + 42 = 1051. Evaluate 1051 != 43, drop this branch.\n     |- Try 1009 - 42 = 967. Evaluate 967 != 43, drop this branch.\n     |- Try 1009 * 42 = 42378. 42378 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1009 \/ 42 = 24.0. 24.0 is a decimal, drop this branch.\n    |- Try 1035 * 26 = 26910. 26910 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1035 \/ 26 = 39.8. 39.8 is a decimal, drop this branch.\n   |- Pick two numbers (42, 26) (numbers left: [1035]). Try possible operations.\n    |- Try 42 + 26 = 68. Add 68 to the number set. Current number set: [68, 1035], target: 43, just two numbers left.\n     |- Try 1035 + 68 = 1103. Evaluate 1103 != 43, drop this branch.\n     |- Try 1035 - 68 = 967. Evaluate 967 != 43, drop this branch.\n     |- Try 1035 * 68 = 70380. 70380 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1035 \/ 68 = 15.2. 15.2 is a decimal, drop this branch.\n    |- Try 42 - 26 = 16. Add 16 to the number set. Current number set: [16, 1035], target: 43, just two numbers left.\n     |- Try 1035 + 16 = 1051. Evaluate 1051 != 43, drop this branch.\n     |- Try 1035 - 16 = 1019. Evaluate 1019 != 43, drop this branch.\n     |- Try 1035 * 16 = 16560. 16560 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1035 \/ 16 = 64.7. 64.7 is a decimal, drop this branch.\n    |- Try 42 * 26 = 1092. Add 1092 to the number set. Current number set: [1092, 1035], target: 43, just two numbers left.\n     |- Try 1092 + 1035 = 2127. 2127 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1092 - 1035 = 57. Evaluate 57 != 43, drop this branch.\n     |- Try 1092 * 1035 = 1130220. 1130220 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1092 \/ 1035 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 42 \/ 26 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 45 \/ 23 = 2.0. 2.0 is a decimal, drop this branch.\n |- Pick two numbers (45, 42) (numbers left: [23, 26]). Try possible operations.\n  |- Try 45 + 42 = 87. Add 87 to the number set. Current number set: [87, 23, 26], target: 43. Options for choosing two numbers: [(87, 23), (87, 26), (23, 26)].\n   |- Pick two numbers (87, 23) (numbers left: [26]). Try possible operations.\n    |- Try 87 + 23 = 110. Add 110 to the number set. Current number set: [110, 26], target: 43, just two numbers left.\n     |- Try 110 + 26 = 136. Evaluate 136 != 43, drop this branch.\n     |- Try 110 - 26 = 84. Evaluate 84 != 43, drop this branch.\n     |- Try 110 * 26 = 2860. 2860 exceeds the maximum intermediate result, drop this branch.\n     |- Try 110 \/ 26 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 87 - 23 = 64. Add 64 to the number set. Current number set: [64, 26], target: 43, just two numbers left.\n     |- Try 64 + 26 = 90. Evaluate 90 != 43, drop this branch.\n     |- Try 64 - 26 = 38. Evaluate 38 != 43, drop this branch.\n     |- Try 64 * 26 = 1664. Evaluate 1664 != 43, drop this branch.\n     |- Try 64 \/ 26 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 87 * 23 = 2001. 2001 exceeds the maximum intermediate result, drop this branch.\n    |- Try 87 \/ 23 = 3.8. 3.8 is a decimal, drop this branch.\n   |- Pick two numbers (87, 26) (numbers left: [23]). Try possible operations.\n    |- Try 87 + 26 = 113. Add 113 to the number set. Current number set: [113, 23], target: 43, just two numbers left.\n     |- Try 113 + 23 = 136. Evaluate 136 != 43, drop this branch.\n     |- Try 113 - 23 = 90. Evaluate 90 != 43, drop this branch.\n     |- Try 113 * 23 = 2599. 2599 exceeds the maximum intermediate result, drop this branch.\n     |- Try 113 \/ 23 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 87 - 26 = 61. Add 61 to the number set. Current number set: [61, 23], target: 43, just two numbers left.\n     |- Try 61 + 23 = 84. Evaluate 84 != 43, drop this branch.\n     |- Try 61 - 23 = 38. Evaluate 38 != 43, drop this branch.\n     |- Try 61 * 23 = 1403. Evaluate 1403 != 43, drop this branch.\n     |- Try 61 \/ 23 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 87 * 26 = 2262. 2262 exceeds the maximum intermediate result, drop this branch.\n    |- Try 87 \/ 26 = 3.3. 3.3 is a decimal, drop this branch.\n   |- Pick two numbers (23, 26) (numbers left: [87]). Try possible operations.\n    |- Try 26 + 23 = 49. Add 49 to the number set. Current number set: [49, 87], target: 43, just two numbers left.\n     |- Try 87 + 49 = 136. Evaluate 136 != 43, drop this branch.\n     |- Try 87 - 49 = 38. Evaluate 38 != 43, drop this branch.\n     |- Try 87 * 49 = 4263. 4263 exceeds the maximum intermediate result, drop this branch.\n     |- Try 87 \/ 49 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 26 - 23 = 3. Add 3 to the number set. Current number set: [3, 87], target: 43, just two numbers left.\n     |- Try 87 + 3 = 90. Evaluate 90 != 43, drop this branch.\n     |- Try 87 - 3 = 84. Evaluate 84 != 43, drop this branch.\n     |- Try 87 * 3 = 261. Evaluate 261 != 43, drop this branch.\n     |- Try 87 \/ 3 = 29. Evaluate 29 != 43, drop this branch.\n    |- Try 26 * 23 = 598. Add 598 to the number set. Current number set: [598, 87], target: 43, just two numbers left.\n     |- Try 598 + 87 = 685. Evaluate 685 != 43, drop this branch.\n     |- Try 598 - 87 = 511. Evaluate 511 != 43, drop this branch.\n     |- Try 598 * 87 = 52026. 52026 exceeds the maximum intermediate result, drop this branch.\n     |- Try 598 \/ 87 = 6.9. 6.9 is a decimal, drop this branch.\n    |- Try 26 \/ 23 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 45 - 42 = 3. Add 3 to the number set. Current number set: [3, 23, 26], target: 43. Options for choosing two numbers: [(3, 23), (3, 26), (23, 26)].\n   |- Pick two numbers (3, 23) (numbers left: [26]). Try possible operations.\n    |- Try 23 + 3 = 26. Add 26 to the number set. Current number set: [26, 26], target: 43, just two numbers left.\n     |- Try 26 + 26 = 52. Evaluate 52 != 43, drop this branch.\n     |- Try 26 - 26 = 0. Evaluate 0 != 43, drop this branch.\n     |- Try 26 * 26 = 676. Evaluate 676 != 43, drop this branch.\n     |- Try 26 \/ 26 = 1. Evaluate 1 != 43, drop this branch.\n    |- Try 23 - 3 = 20. Add 20 to the number set. Current number set: [20, 26], target: 43, just two numbers left.\n     |- Try 26 + 20 = 46. Evaluate 46 != 43, drop this branch.\n     |- Try 26 - 20 = 6. Evaluate 6 != 43, drop this branch.\n     |- Try 26 * 20 = 520. Evaluate 520 != 43, drop this branch.\n     |- Try 26 \/ 20 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 23 * 3 = 69. Add 69 to the number set. Current number set: [69, 26], target: 43, just two numbers left.\n     |- Try 69 + 26 = 95. Evaluate 95 != 43, drop this branch.\n     |- Try 69 - 26 = 43. Evaluate 43 == 43, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 69 - 26 = 43\nThe step before: 23 * 3 = 69\nThe first step: 45 - 42 = 3\n\nOutput the solution in the required format:\n<Solution>\n45 - 42 = 3\n23 * 3 = 69\n69 - 26 = 43\n<\/Solution>\n","item":{"nums":[45,23,42,26],"solution":["45 - 42 = 3","23 * 3 = 69","69 - 26 = 43"],"target":43}}
+{"instance_id":"countdown_8k_119","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [15, 23, 20, 19]\nTarget: 17","reference_output":"# Search Procedure\nInitial number set: [15, 23, 20, 19], target: 17. Options for choosing two numbers: [(15, 23), (15, 20), (15, 19), (23, 20), (23, 19), (20, 19)].\n |- Pick two numbers (15, 23) (numbers left: [20, 19]). Try possible operations.\n  |- Try 23 + 15 = 38. Add 38 to the number set. Current number set: [38, 20, 19], target: 17. Options for choosing two numbers: [(38, 20), (38, 19), (20, 19)].\n   |- Pick two numbers (38, 20) (numbers left: [19]). Try possible operations.\n    |- Try 38 + 20 = 58. Add 58 to the number set. Current number set: [58, 19], target: 17, just two numbers left.\n     |- Try 58 + 19 = 77. Evaluate 77 != 17, drop this branch.\n     |- Try 58 - 19 = 39. Evaluate 39 != 17, drop this branch.\n     |- Try 58 * 19 = 1102. Evaluate 1102 != 17, drop this branch.\n     |- Try 58 \/ 19 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 38 - 20 = 18. Add 18 to the number set. Current number set: [18, 19], target: 17, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 17, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 17, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 17, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 38 * 20 = 760. Add 760 to the number set. Current number set: [760, 19], target: 17, just two numbers left.\n     |- Try 760 + 19 = 779. Evaluate 779 != 17, drop this branch.\n     |- Try 760 - 19 = 741. Evaluate 741 != 17, drop this branch.\n     |- Try 760 * 19 = 14440. 14440 exceeds the maximum intermediate result, drop this branch.\n     |- Try 760 \/ 19 = 40. Evaluate 40 != 17, drop this branch.\n    |- Try 38 \/ 20 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (38, 19) (numbers left: [20]). Try possible operations.\n    |- Try 38 + 19 = 57. Add 57 to the number set. Current number set: [57, 20], target: 17, just two numbers left.\n     |- Try 57 + 20 = 77. Evaluate 77 != 17, drop this branch.\n     |- Try 57 - 20 = 37. Evaluate 37 != 17, drop this branch.\n     |- Try 57 * 20 = 1140. Evaluate 1140 != 17, drop this branch.\n     |- Try 57 \/ 20 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 38 - 19 = 19. Add 19 to the number set. Current number set: [19, 20], target: 17, just two numbers left.\n     |- Try 20 + 19 = 39. Evaluate 39 != 17, drop this branch.\n     |- Try 20 - 19 = 1. Evaluate 1 != 17, drop this branch.\n     |- Try 20 * 19 = 380. Evaluate 380 != 17, drop this branch.\n     |- Try 20 \/ 19 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 38 * 19 = 722. Add 722 to the number set. Current number set: [722, 20], target: 17, just two numbers left.\n     |- Try 722 + 20 = 742. Evaluate 742 != 17, drop this branch.\n     |- Try 722 - 20 = 702. Evaluate 702 != 17, drop this branch.\n     |- Try 722 * 20 = 14440. 14440 exceeds the maximum intermediate result, drop this branch.\n     |- Try 722 \/ 20 = 36.1. 36.1 is a decimal, drop this branch.\n    |- Try 38 \/ 19 = 2. Add 2 to the number set. Current number set: [2, 20], target: 17, just two numbers left.\n     |- Try 20 + 2 = 22. Evaluate 22 != 17, drop this branch.\n     |- Try 20 - 2 = 18. Evaluate 18 != 17, drop this branch.\n     |- Try 20 * 2 = 40. Evaluate 40 != 17, drop this branch.\n     |- Try 20 \/ 2 = 10. Evaluate 10 != 17, drop this branch.\n   |- Pick two numbers (20, 19) (numbers left: [38]). Try possible operations.\n    |- Try 20 + 19 = 39. Add 39 to the number set. Current number set: [39, 38], target: 17, just two numbers left.\n     |- Try 39 + 38 = 77. Evaluate 77 != 17, drop this branch.\n     |- Try 39 - 38 = 1. Evaluate 1 != 17, drop this branch.\n     |- Try 39 * 38 = 1482. Evaluate 1482 != 17, drop this branch.\n     |- Try 39 \/ 38 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 20 - 19 = 1. Add 1 to the number set. Current number set: [1, 38], target: 17, just two numbers left.\n     |- Try 38 + 1 = 39. Evaluate 39 != 17, drop this branch.\n     |- Try 38 - 1 = 37. Evaluate 37 != 17, drop this branch.\n     |- Try 38 * 1 = 38. Evaluate 38 != 17, drop this branch.\n     |- Try 38 \/ 1 = 38. Evaluate 38 != 17, drop this branch.\n    |- Try 20 * 19 = 380. Add 380 to the number set. Current number set: [380, 38], target: 17, just two numbers left.\n     |- Try 380 + 38 = 418. Evaluate 418 != 17, drop this branch.\n     |- Try 380 - 38 = 342. Evaluate 342 != 17, drop this branch.\n     |- Try 380 * 38 = 14440. 14440 exceeds the maximum intermediate result, drop this branch.\n     |- Try 380 \/ 38 = 10. Evaluate 10 != 17, drop this branch.\n    |- Try 20 \/ 19 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 23 - 15 = 8. Add 8 to the number set. Current number set: [8, 20, 19], target: 17. Options for choosing two numbers: [(8, 20), (8, 19), (20, 19)].\n   |- Pick two numbers (8, 20) (numbers left: [19]). Try possible operations.\n    |- Try 20 + 8 = 28. Add 28 to the number set. Current number set: [28, 19], target: 17, just two numbers left.\n     |- Try 28 + 19 = 47. Evaluate 47 != 17, drop this branch.\n     |- Try 28 - 19 = 9. Evaluate 9 != 17, drop this branch.\n     |- Try 28 * 19 = 532. Evaluate 532 != 17, drop this branch.\n     |- Try 28 \/ 19 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 20 - 8 = 12. Add 12 to the number set. Current number set: [12, 19], target: 17, just two numbers left.\n     |- Try 19 + 12 = 31. Evaluate 31 != 17, drop this branch.\n     |- Try 19 - 12 = 7. Evaluate 7 != 17, drop this branch.\n     |- Try 19 * 12 = 228. Evaluate 228 != 17, drop this branch.\n     |- Try 19 \/ 12 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 20 * 8 = 160. Add 160 to the number set. Current number set: [160, 19], target: 17, just two numbers left.\n     |- Try 160 + 19 = 179. Evaluate 179 != 17, drop this branch.\n     |- Try 160 - 19 = 141. Evaluate 141 != 17, drop this branch.\n     |- Try 160 * 19 = 3040. 3040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 160 \/ 19 = 8.4. 8.4 is a decimal, drop this branch.\n    |- Try 20 \/ 8 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (8, 19) (numbers left: [20]). Try possible operations.\n    |- Try 19 + 8 = 27. Add 27 to the number set. Current number set: [27, 20], target: 17, just two numbers left.\n     |- Try 27 + 20 = 47. Evaluate 47 != 17, drop this branch.\n     |- Try 27 - 20 = 7. Evaluate 7 != 17, drop this branch.\n     |- Try 27 * 20 = 540. Evaluate 540 != 17, drop this branch.\n     |- Try 27 \/ 20 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 19 - 8 = 11. Add 11 to the number set. Current number set: [11, 20], target: 17, just two numbers left.\n     |- Try 20 + 11 = 31. Evaluate 31 != 17, drop this branch.\n     |- Try 20 - 11 = 9. Evaluate 9 != 17, drop this branch.\n     |- Try 20 * 11 = 220. Evaluate 220 != 17, drop this branch.\n     |- Try 20 \/ 11 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 19 * 8 = 152. Add 152 to the number set. Current number set: [152, 20], target: 17, just two numbers left.\n     |- Try 152 + 20 = 172. Evaluate 172 != 17, drop this branch.\n     |- Try 152 - 20 = 132. Evaluate 132 != 17, drop this branch.\n     |- Try 152 * 20 = 3040. 3040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 152 \/ 20 = 7.6. 7.6 is a decimal, drop this branch.\n    |- Try 19 \/ 8 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (20, 19) (numbers left: [8]). Try possible operations.\n    |- Try 20 + 19 = 39. Add 39 to the number set. Current number set: [39, 8], target: 17, just two numbers left.\n     |- Try 39 + 8 = 47. Evaluate 47 != 17, drop this branch.\n     |- Try 39 - 8 = 31. Evaluate 31 != 17, drop this branch.\n     |- Try 39 * 8 = 312. Evaluate 312 != 17, drop this branch.\n     |- Try 39 \/ 8 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 20 - 19 = 1. Add 1 to the number set. Current number set: [1, 8], target: 17, just two numbers left.\n     |- Try 8 + 1 = 9. Evaluate 9 != 17, drop this branch.\n     |- Try 8 - 1 = 7. Evaluate 7 != 17, drop this branch.\n     |- Try 8 * 1 = 8. Evaluate 8 != 17, drop this branch.\n     |- Try 8 \/ 1 = 8. Evaluate 8 != 17, drop this branch.\n    |- Try 20 * 19 = 380. Add 380 to the number set. Current number set: [380, 8], target: 17, just two numbers left.\n     |- Try 380 + 8 = 388. Evaluate 388 != 17, drop this branch.\n     |- Try 380 - 8 = 372. Evaluate 372 != 17, drop this branch.\n     |- Try 380 * 8 = 3040. 3040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 380 \/ 8 = 47.5. 47.5 is a decimal, drop this branch.\n    |- Try 20 \/ 19 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 23 * 15 = 345. Add 345 to the number set. Current number set: [345, 20, 19], target: 17. Options for choosing two numbers: [(345, 20), (345, 19), (20, 19)].\n   |- Pick two numbers (345, 20) (numbers left: [19]). Try possible operations.\n    |- Try 345 + 20 = 365. Add 365 to the number set. Current number set: [365, 19], target: 17, just two numbers left.\n     |- Try 365 + 19 = 384. Evaluate 384 != 17, drop this branch.\n     |- Try 365 - 19 = 346. Evaluate 346 != 17, drop this branch.\n     |- Try 365 * 19 = 6935. 6935 exceeds the maximum intermediate result, drop this branch.\n     |- Try 365 \/ 19 = 19.2. 19.2 is a decimal, drop this branch.\n    |- Try 345 - 20 = 325. Add 325 to the number set. Current number set: [325, 19], target: 17, just two numbers left.\n     |- Try 325 + 19 = 344. Evaluate 344 != 17, drop this branch.\n     |- Try 325 - 19 = 306. Evaluate 306 != 17, drop this branch.\n     |- Try 325 * 19 = 6175. 6175 exceeds the maximum intermediate result, drop this branch.\n     |- Try 325 \/ 19 = 17.1. 17.1 is a decimal, drop this branch.\n    |- Try 345 * 20 = 6900. 6900 exceeds the maximum intermediate result, drop this branch.\n    |- Try 345 \/ 20 = 17.2. 17.2 is a decimal, drop this branch.\n   |- Pick two numbers (345, 19) (numbers left: [20]). Try possible operations.\n    |- Try 345 + 19 = 364. Add 364 to the number set. Current number set: [364, 20], target: 17, just two numbers left.\n     |- Try 364 + 20 = 384. Evaluate 384 != 17, drop this branch.\n     |- Try 364 - 20 = 344. Evaluate 344 != 17, drop this branch.\n     |- Try 364 * 20 = 7280. 7280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 364 \/ 20 = 18.2. 18.2 is a decimal, drop this branch.\n    |- Try 345 - 19 = 326. Add 326 to the number set. Current number set: [326, 20], target: 17, just two numbers left.\n     |- Try 326 + 20 = 346. Evaluate 346 != 17, drop this branch.\n     |- Try 326 - 20 = 306. Evaluate 306 != 17, drop this branch.\n     |- Try 326 * 20 = 6520. 6520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 326 \/ 20 = 16.3. 16.3 is a decimal, drop this branch.\n    |- Try 345 * 19 = 6555. 6555 exceeds the maximum intermediate result, drop this branch.\n    |- Try 345 \/ 19 = 18.2. 18.2 is a decimal, drop this branch.\n   |- Pick two numbers (20, 19) (numbers left: [345]). Try possible operations.\n    |- Try 20 + 19 = 39. Add 39 to the number set. Current number set: [39, 345], target: 17, just two numbers left.\n     |- Try 345 + 39 = 384. Evaluate 384 != 17, drop this branch.\n     |- Try 345 - 39 = 306. Evaluate 306 != 17, drop this branch.\n     |- Try 345 * 39 = 13455. 13455 exceeds the maximum intermediate result, drop this branch.\n     |- Try 345 \/ 39 = 8.8. 8.8 is a decimal, drop this branch.\n    |- Try 20 - 19 = 1. Add 1 to the number set. Current number set: [1, 345], target: 17, just two numbers left.\n     |- Try 345 + 1 = 346. Evaluate 346 != 17, drop this branch.\n     |- Try 345 - 1 = 344. Evaluate 344 != 17, drop this branch.\n     |- Try 345 * 1 = 345. Evaluate 345 != 17, drop this branch.\n     |- Try 345 \/ 1 = 345. Evaluate 345 != 17, drop this branch.\n    |- Try 20 * 19 = 380. Add 380 to the number set. Current number set: [380, 345], target: 17, just two numbers left.\n     |- Try 380 + 345 = 725. Evaluate 725 != 17, drop this branch.\n     |- Try 380 - 345 = 35. Evaluate 35 != 17, drop this branch.\n     |- Try 380 * 345 = 131100. 131100 exceeds the maximum intermediate result, drop this branch.\n     |- Try 380 \/ 345 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 20 \/ 19 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 23 \/ 15 = 1.5. 1.5 is a decimal, drop this branch.\n |- Pick two numbers (15, 20) (numbers left: [23, 19]). Try possible operations.\n  |- Try 20 + 15 = 35. Add 35 to the number set. Current number set: [35, 23, 19], target: 17. Options for choosing two numbers: [(35, 23), (35, 19), (23, 19)].\n   |- Pick two numbers (35, 23) (numbers left: [19]). Try possible operations.\n    |- Try 35 + 23 = 58. Add 58 to the number set. Current number set: [58, 19], target: 17, just two numbers left.\n     |- Try 58 + 19 = 77. Evaluate 77 != 17, drop this branch.\n     |- Try 58 - 19 = 39. Evaluate 39 != 17, drop this branch.\n     |- Try 58 * 19 = 1102. Evaluate 1102 != 17, drop this branch.\n     |- Try 58 \/ 19 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 35 - 23 = 12. Add 12 to the number set. Current number set: [12, 19], target: 17, just two numbers left.\n     |- Try 19 + 12 = 31. Evaluate 31 != 17, drop this branch.\n     |- Try 19 - 12 = 7. Evaluate 7 != 17, drop this branch.\n     |- Try 19 * 12 = 228. Evaluate 228 != 17, drop this branch.\n     |- Try 19 \/ 12 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 35 * 23 = 805. Add 805 to the number set. Current number set: [805, 19], target: 17, just two numbers left.\n     |- Try 805 + 19 = 824. Evaluate 824 != 17, drop this branch.\n     |- Try 805 - 19 = 786. Evaluate 786 != 17, drop this branch.\n     |- Try 805 * 19 = 15295. 15295 exceeds the maximum intermediate result, drop this branch.\n     |- Try 805 \/ 19 = 42.4. 42.4 is a decimal, drop this branch.\n    |- Try 35 \/ 23 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (35, 19) (numbers left: [23]). Try possible operations.\n    |- Try 35 + 19 = 54. Add 54 to the number set. Current number set: [54, 23], target: 17, just two numbers left.\n     |- Try 54 + 23 = 77. Evaluate 77 != 17, drop this branch.\n     |- Try 54 - 23 = 31. Evaluate 31 != 17, drop this branch.\n     |- Try 54 * 23 = 1242. Evaluate 1242 != 17, drop this branch.\n     |- Try 54 \/ 23 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 35 - 19 = 16. Add 16 to the number set. Current number set: [16, 23], target: 17, just two numbers left.\n     |- Try 23 + 16 = 39. Evaluate 39 != 17, drop this branch.\n     |- Try 23 - 16 = 7. Evaluate 7 != 17, drop this branch.\n     |- Try 23 * 16 = 368. Evaluate 368 != 17, drop this branch.\n     |- Try 23 \/ 16 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 35 * 19 = 665. Add 665 to the number set. Current number set: [665, 23], target: 17, just two numbers left.\n     |- Try 665 + 23 = 688. Evaluate 688 != 17, drop this branch.\n     |- Try 665 - 23 = 642. Evaluate 642 != 17, drop this branch.\n     |- Try 665 * 23 = 15295. 15295 exceeds the maximum intermediate result, drop this branch.\n     |- Try 665 \/ 23 = 28.9. 28.9 is a decimal, drop this branch.\n    |- Try 35 \/ 19 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (23, 19) (numbers left: [35]). Try possible operations.\n    |- Try 23 + 19 = 42. Add 42 to the number set. Current number set: [42, 35], target: 17, just two numbers left.\n     |- Try 42 + 35 = 77. Evaluate 77 != 17, drop this branch.\n     |- Try 42 - 35 = 7. Evaluate 7 != 17, drop this branch.\n     |- Try 42 * 35 = 1470. Evaluate 1470 != 17, drop this branch.\n     |- Try 42 \/ 35 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 23 - 19 = 4. Add 4 to the number set. Current number set: [4, 35], target: 17, just two numbers left.\n     |- Try 35 + 4 = 39. Evaluate 39 != 17, drop this branch.\n     |- Try 35 - 4 = 31. Evaluate 31 != 17, drop this branch.\n     |- Try 35 * 4 = 140. Evaluate 140 != 17, drop this branch.\n     |- Try 35 \/ 4 = 8.8. 8.8 is a decimal, drop this branch.\n    |- Try 23 * 19 = 437. Add 437 to the number set. Current number set: [437, 35], target: 17, just two numbers left.\n     |- Try 437 + 35 = 472. Evaluate 472 != 17, drop this branch.\n     |- Try 437 - 35 = 402. Evaluate 402 != 17, drop this branch.\n     |- Try 437 * 35 = 15295. 15295 exceeds the maximum intermediate result, drop this branch.\n     |- Try 437 \/ 35 = 12.5. 12.5 is a decimal, drop this branch.\n    |- Try 23 \/ 19 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 20 - 15 = 5. Add 5 to the number set. Current number set: [5, 23, 19], target: 17. Options for choosing two numbers: [(5, 23), (5, 19), (23, 19)].\n   |- Pick two numbers (5, 23) (numbers left: [19]). Try possible operations.\n    |- Try 23 + 5 = 28. Add 28 to the number set. Current number set: [28, 19], target: 17, just two numbers left.\n     |- Try 28 + 19 = 47. Evaluate 47 != 17, drop this branch.\n     |- Try 28 - 19 = 9. Evaluate 9 != 17, drop this branch.\n     |- Try 28 * 19 = 532. Evaluate 532 != 17, drop this branch.\n     |- Try 28 \/ 19 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 23 - 5 = 18. Add 18 to the number set. Current number set: [18, 19], target: 17, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 17, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 17, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 17, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 23 * 5 = 115. Add 115 to the number set. Current number set: [115, 19], target: 17, just two numbers left.\n     |- Try 115 + 19 = 134. Evaluate 134 != 17, drop this branch.\n     |- Try 115 - 19 = 96. Evaluate 96 != 17, drop this branch.\n     |- Try 115 * 19 = 2185. 2185 exceeds the maximum intermediate result, drop this branch.\n     |- Try 115 \/ 19 = 6.1. 6.1 is a decimal, drop this branch.\n    |- Try 23 \/ 5 = 4.6. 4.6 is a decimal, drop this branch.\n   |- Pick two numbers (5, 19) (numbers left: [23]). Try possible operations.\n    |- Try 19 + 5 = 24. Add 24 to the number set. Current number set: [24, 23], target: 17, just two numbers left.\n     |- Try 24 + 23 = 47. Evaluate 47 != 17, drop this branch.\n     |- Try 24 - 23 = 1. Evaluate 1 != 17, drop this branch.\n     |- Try 24 * 23 = 552. Evaluate 552 != 17, drop this branch.\n     |- Try 24 \/ 23 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 19 - 5 = 14. Add 14 to the number set. Current number set: [14, 23], target: 17, just two numbers left.\n     |- Try 23 + 14 = 37. Evaluate 37 != 17, drop this branch.\n     |- Try 23 - 14 = 9. Evaluate 9 != 17, drop this branch.\n     |- Try 23 * 14 = 322. Evaluate 322 != 17, drop this branch.\n     |- Try 23 \/ 14 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 19 * 5 = 95. Add 95 to the number set. Current number set: [95, 23], target: 17, just two numbers left.\n     |- Try 95 + 23 = 118. Evaluate 118 != 17, drop this branch.\n     |- Try 95 - 23 = 72. Evaluate 72 != 17, drop this branch.\n     |- Try 95 * 23 = 2185. 2185 exceeds the maximum intermediate result, drop this branch.\n     |- Try 95 \/ 23 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 19 \/ 5 = 3.8. 3.8 is a decimal, drop this branch.\n   |- Pick two numbers (23, 19) (numbers left: [5]). Try possible operations.\n    |- Try 23 + 19 = 42. Add 42 to the number set. Current number set: [42, 5], target: 17, just two numbers left.\n     |- Try 42 + 5 = 47. Evaluate 47 != 17, drop this branch.\n     |- Try 42 - 5 = 37. Evaluate 37 != 17, drop this branch.\n     |- Try 42 * 5 = 210. Evaluate 210 != 17, drop this branch.\n     |- Try 42 \/ 5 = 8.4. 8.4 is a decimal, drop this branch.\n    |- Try 23 - 19 = 4. Add 4 to the number set. Current number set: [4, 5], target: 17, just two numbers left.\n     |- Try 5 + 4 = 9. Evaluate 9 != 17, drop this branch.\n     |- Try 5 - 4 = 1. Evaluate 1 != 17, drop this branch.\n     |- Try 5 * 4 = 20. Evaluate 20 != 17, drop this branch.\n     |- Try 5 \/ 4 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 23 * 19 = 437. Add 437 to the number set. Current number set: [437, 5], target: 17, just two numbers left.\n     |- Try 437 + 5 = 442. Evaluate 442 != 17, drop this branch.\n     |- Try 437 - 5 = 432. Evaluate 432 != 17, drop this branch.\n     |- Try 437 * 5 = 2185. 2185 exceeds the maximum intermediate result, drop this branch.\n     |- Try 437 \/ 5 = 87.4. 87.4 is a decimal, drop this branch.\n    |- Try 23 \/ 19 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 20 * 15 = 300. Add 300 to the number set. Current number set: [300, 23, 19], target: 17. Options for choosing two numbers: [(300, 23), (300, 19), (23, 19)].\n   |- Pick two numbers (300, 23) (numbers left: [19]). Try possible operations.\n    |- Try 300 + 23 = 323. Add 323 to the number set. Current number set: [323, 19], target: 17, just two numbers left.\n     |- Try 323 + 19 = 342. Evaluate 342 != 17, drop this branch.\n     |- Try 323 - 19 = 304. Evaluate 304 != 17, drop this branch.\n     |- Try 323 * 19 = 6137. 6137 exceeds the maximum intermediate result, drop this branch.\n     |- Try 323 \/ 19 = 17. Evaluate 17 == 17, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 323 \/ 19 = 17\nThe step before: 300 + 23 = 323\nThe first step: 20 * 15 = 300\n\nOutput the solution in the required format:\n<Solution>\n20 * 15 = 300\n300 + 23 = 323\n323 \/ 19 = 17\n<\/Solution>\n","item":{"nums":[15,23,20,19],"solution":["20 * 15 = 300","300 + 23 = 323","323 \/ 19 = 17"],"target":17}}
+{"instance_id":"countdown_8k_120","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [27, 11, 10, 33]\nTarget: 40","reference_output":"# Search Procedure\nInitial number set: [27, 11, 10, 33], target: 40. Options for choosing two numbers: [(27, 11), (27, 10), (27, 33), (11, 10), (11, 33), (10, 33)].\n |- Pick two numbers (27, 11) (numbers left: [10, 33]). Try possible operations.\n  |- Try 27 + 11 = 38. Add 38 to the number set. Current number set: [38, 10, 33], target: 40. Options for choosing two numbers: [(38, 10), (38, 33), (10, 33)].\n   |- Pick two numbers (38, 10) (numbers left: [33]). Try possible operations.\n    |- Try 38 + 10 = 48. Add 48 to the number set. Current number set: [48, 33], target: 40, just two numbers left.\n     |- Try 48 + 33 = 81. Evaluate 81 != 40, drop this branch.\n     |- Try 48 - 33 = 15. Evaluate 15 != 40, drop this branch.\n     |- Try 48 * 33 = 1584. Evaluate 1584 != 40, drop this branch.\n     |- Try 48 \/ 33 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 38 - 10 = 28. Add 28 to the number set. Current number set: [28, 33], target: 40, just two numbers left.\n     |- Try 33 + 28 = 61. Evaluate 61 != 40, drop this branch.\n     |- Try 33 - 28 = 5. Evaluate 5 != 40, drop this branch.\n     |- Try 33 * 28 = 924. Evaluate 924 != 40, drop this branch.\n     |- Try 33 \/ 28 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 38 * 10 = 380. Add 380 to the number set. Current number set: [380, 33], target: 40, just two numbers left.\n     |- Try 380 + 33 = 413. Evaluate 413 != 40, drop this branch.\n     |- Try 380 - 33 = 347. Evaluate 347 != 40, drop this branch.\n     |- Try 380 * 33 = 12540. 12540 exceeds the maximum intermediate result, drop this branch.\n     |- Try 380 \/ 33 = 11.5. 11.5 is a decimal, drop this branch.\n    |- Try 38 \/ 10 = 3.8. 3.8 is a decimal, drop this branch.\n   |- Pick two numbers (38, 33) (numbers left: [10]). Try possible operations.\n    |- Try 38 + 33 = 71. Add 71 to the number set. Current number set: [71, 10], target: 40, just two numbers left.\n     |- Try 71 + 10 = 81. Evaluate 81 != 40, drop this branch.\n     |- Try 71 - 10 = 61. Evaluate 61 != 40, drop this branch.\n     |- Try 71 * 10 = 710. Evaluate 710 != 40, drop this branch.\n     |- Try 71 \/ 10 = 7.1. 7.1 is a decimal, drop this branch.\n    |- Try 38 - 33 = 5. Add 5 to the number set. Current number set: [5, 10], target: 40, just two numbers left.\n     |- Try 10 + 5 = 15. Evaluate 15 != 40, drop this branch.\n     |- Try 10 - 5 = 5. Evaluate 5 != 40, drop this branch.\n     |- Try 10 * 5 = 50. Evaluate 50 != 40, drop this branch.\n     |- Try 10 \/ 5 = 2. Evaluate 2 != 40, drop this branch.\n    |- Try 38 * 33 = 1254. Add 1254 to the number set. Current number set: [1254, 10], target: 40, just two numbers left.\n     |- Try 1254 + 10 = 1264. Evaluate 1264 != 40, drop this branch.\n     |- Try 1254 - 10 = 1244. Evaluate 1244 != 40, drop this branch.\n     |- Try 1254 * 10 = 12540. 12540 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1254 \/ 10 = 125.4. 125.4 is a decimal, drop this branch.\n    |- Try 38 \/ 33 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (10, 33) (numbers left: [38]). Try possible operations.\n    |- Try 33 + 10 = 43. Add 43 to the number set. Current number set: [43, 38], target: 40, just two numbers left.\n     |- Try 43 + 38 = 81. Evaluate 81 != 40, drop this branch.\n     |- Try 43 - 38 = 5. Evaluate 5 != 40, drop this branch.\n     |- Try 43 * 38 = 1634. Evaluate 1634 != 40, drop this branch.\n     |- Try 43 \/ 38 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 33 - 10 = 23. Add 23 to the number set. Current number set: [23, 38], target: 40, just two numbers left.\n     |- Try 38 + 23 = 61. Evaluate 61 != 40, drop this branch.\n     |- Try 38 - 23 = 15. Evaluate 15 != 40, drop this branch.\n     |- Try 38 * 23 = 874. Evaluate 874 != 40, drop this branch.\n     |- Try 38 \/ 23 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 33 * 10 = 330. Add 330 to the number set. Current number set: [330, 38], target: 40, just two numbers left.\n     |- Try 330 + 38 = 368. Evaluate 368 != 40, drop this branch.\n     |- Try 330 - 38 = 292. Evaluate 292 != 40, drop this branch.\n     |- Try 330 * 38 = 12540. 12540 exceeds the maximum intermediate result, drop this branch.\n     |- Try 330 \/ 38 = 8.7. 8.7 is a decimal, drop this branch.\n    |- Try 33 \/ 10 = 3.3. 3.3 is a decimal, drop this branch.\n  |- Try 27 - 11 = 16. Add 16 to the number set. Current number set: [16, 10, 33], target: 40. Options for choosing two numbers: [(16, 10), (16, 33), (10, 33)].\n   |- Pick two numbers (16, 10) (numbers left: [33]). Try possible operations.\n    |- Try 16 + 10 = 26. Add 26 to the number set. Current number set: [26, 33], target: 40, just two numbers left.\n     |- Try 33 + 26 = 59. Evaluate 59 != 40, drop this branch.\n     |- Try 33 - 26 = 7. Evaluate 7 != 40, drop this branch.\n     |- Try 33 * 26 = 858. Evaluate 858 != 40, drop this branch.\n     |- Try 33 \/ 26 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 16 - 10 = 6. Add 6 to the number set. Current number set: [6, 33], target: 40, just two numbers left.\n     |- Try 33 + 6 = 39. Evaluate 39 != 40, drop this branch.\n     |- Try 33 - 6 = 27. Evaluate 27 != 40, drop this branch.\n     |- Try 33 * 6 = 198. Evaluate 198 != 40, drop this branch.\n     |- Try 33 \/ 6 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 16 * 10 = 160. Add 160 to the number set. Current number set: [160, 33], target: 40, just two numbers left.\n     |- Try 160 + 33 = 193. Evaluate 193 != 40, drop this branch.\n     |- Try 160 - 33 = 127. Evaluate 127 != 40, drop this branch.\n     |- Try 160 * 33 = 5280. 5280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 160 \/ 33 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 16 \/ 10 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (16, 33) (numbers left: [10]). Try possible operations.\n    |- Try 33 + 16 = 49. Add 49 to the number set. Current number set: [49, 10], target: 40, just two numbers left.\n     |- Try 49 + 10 = 59. Evaluate 59 != 40, drop this branch.\n     |- Try 49 - 10 = 39. Evaluate 39 != 40, drop this branch.\n     |- Try 49 * 10 = 490. Evaluate 490 != 40, drop this branch.\n     |- Try 49 \/ 10 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 33 - 16 = 17. Add 17 to the number set. Current number set: [17, 10], target: 40, just two numbers left.\n     |- Try 17 + 10 = 27. Evaluate 27 != 40, drop this branch.\n     |- Try 17 - 10 = 7. Evaluate 7 != 40, drop this branch.\n     |- Try 17 * 10 = 170. Evaluate 170 != 40, drop this branch.\n     |- Try 17 \/ 10 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 33 * 16 = 528. Add 528 to the number set. Current number set: [528, 10], target: 40, just two numbers left.\n     |- Try 528 + 10 = 538. Evaluate 538 != 40, drop this branch.\n     |- Try 528 - 10 = 518. Evaluate 518 != 40, drop this branch.\n     |- Try 528 * 10 = 5280. 5280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 528 \/ 10 = 52.8. 52.8 is a decimal, drop this branch.\n    |- Try 33 \/ 16 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (10, 33) (numbers left: [16]). Try possible operations.\n    |- Try 33 + 10 = 43. Add 43 to the number set. Current number set: [43, 16], target: 40, just two numbers left.\n     |- Try 43 + 16 = 59. Evaluate 59 != 40, drop this branch.\n     |- Try 43 - 16 = 27. Evaluate 27 != 40, drop this branch.\n     |- Try 43 * 16 = 688. Evaluate 688 != 40, drop this branch.\n     |- Try 43 \/ 16 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 33 - 10 = 23. Add 23 to the number set. Current number set: [23, 16], target: 40, just two numbers left.\n     |- Try 23 + 16 = 39. Evaluate 39 != 40, drop this branch.\n     |- Try 23 - 16 = 7. Evaluate 7 != 40, drop this branch.\n     |- Try 23 * 16 = 368. Evaluate 368 != 40, drop this branch.\n     |- Try 23 \/ 16 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 33 * 10 = 330. Add 330 to the number set. Current number set: [330, 16], target: 40, just two numbers left.\n     |- Try 330 + 16 = 346. Evaluate 346 != 40, drop this branch.\n     |- Try 330 - 16 = 314. Evaluate 314 != 40, drop this branch.\n     |- Try 330 * 16 = 5280. 5280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 330 \/ 16 = 20.6. 20.6 is a decimal, drop this branch.\n    |- Try 33 \/ 10 = 3.3. 3.3 is a decimal, drop this branch.\n  |- Try 27 * 11 = 297. Add 297 to the number set. Current number set: [297, 10, 33], target: 40. Options for choosing two numbers: [(297, 10), (297, 33), (10, 33)].\n   |- Pick two numbers (297, 10) (numbers left: [33]). Try possible operations.\n    |- Try 297 + 10 = 307. Add 307 to the number set. Current number set: [307, 33], target: 40, just two numbers left.\n     |- Try 307 + 33 = 340. Evaluate 340 != 40, drop this branch.\n     |- Try 307 - 33 = 274. Evaluate 274 != 40, drop this branch.\n     |- Try 307 * 33 = 10131. 10131 exceeds the maximum intermediate result, drop this branch.\n     |- Try 307 \/ 33 = 9.3. 9.3 is a decimal, drop this branch.\n    |- Try 297 - 10 = 287. Add 287 to the number set. Current number set: [287, 33], target: 40, just two numbers left.\n     |- Try 287 + 33 = 320. Evaluate 320 != 40, drop this branch.\n     |- Try 287 - 33 = 254. Evaluate 254 != 40, drop this branch.\n     |- Try 287 * 33 = 9471. 9471 exceeds the maximum intermediate result, drop this branch.\n     |- Try 287 \/ 33 = 8.7. 8.7 is a decimal, drop this branch.\n    |- Try 297 * 10 = 2970. 2970 exceeds the maximum intermediate result, drop this branch.\n    |- Try 297 \/ 10 = 29.7. 29.7 is a decimal, drop this branch.\n   |- Pick two numbers (297, 33) (numbers left: [10]). Try possible operations.\n    |- Try 297 + 33 = 330. Add 330 to the number set. Current number set: [330, 10], target: 40, just two numbers left.\n     |- Try 330 + 10 = 340. Evaluate 340 != 40, drop this branch.\n     |- Try 330 - 10 = 320. Evaluate 320 != 40, drop this branch.\n     |- Try 330 * 10 = 3300. 3300 exceeds the maximum intermediate result, drop this branch.\n     |- Try 330 \/ 10 = 33. Evaluate 33 != 40, drop this branch.\n    |- Try 297 - 33 = 264. Add 264 to the number set. Current number set: [264, 10], target: 40, just two numbers left.\n     |- Try 264 + 10 = 274. Evaluate 274 != 40, drop this branch.\n     |- Try 264 - 10 = 254. Evaluate 254 != 40, drop this branch.\n     |- Try 264 * 10 = 2640. 2640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 264 \/ 10 = 26.4. 26.4 is a decimal, drop this branch.\n    |- Try 297 * 33 = 9801. 9801 exceeds the maximum intermediate result, drop this branch.\n    |- Try 297 \/ 33 = 9. Add 9 to the number set. Current number set: [9, 10], target: 40, just two numbers left.\n     |- Try 10 + 9 = 19. Evaluate 19 != 40, drop this branch.\n     |- Try 10 - 9 = 1. Evaluate 1 != 40, drop this branch.\n     |- Try 10 * 9 = 90. Evaluate 90 != 40, drop this branch.\n     |- Try 10 \/ 9 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (10, 33) (numbers left: [297]). Try possible operations.\n    |- Try 33 + 10 = 43. Add 43 to the number set. Current number set: [43, 297], target: 40, just two numbers left.\n     |- Try 297 + 43 = 340. Evaluate 340 != 40, drop this branch.\n     |- Try 297 - 43 = 254. Evaluate 254 != 40, drop this branch.\n     |- Try 297 * 43 = 12771. 12771 exceeds the maximum intermediate result, drop this branch.\n     |- Try 297 \/ 43 = 6.9. 6.9 is a decimal, drop this branch.\n    |- Try 33 - 10 = 23. Add 23 to the number set. Current number set: [23, 297], target: 40, just two numbers left.\n     |- Try 297 + 23 = 320. Evaluate 320 != 40, drop this branch.\n     |- Try 297 - 23 = 274. Evaluate 274 != 40, drop this branch.\n     |- Try 297 * 23 = 6831. 6831 exceeds the maximum intermediate result, drop this branch.\n     |- Try 297 \/ 23 = 12.9. 12.9 is a decimal, drop this branch.\n    |- Try 33 * 10 = 330. Add 330 to the number set. Current number set: [330, 297], target: 40, just two numbers left.\n     |- Try 330 + 297 = 627. Evaluate 627 != 40, drop this branch.\n     |- Try 330 - 297 = 33. Evaluate 33 != 40, drop this branch.\n     |- Try 330 * 297 = 98010. 98010 exceeds the maximum intermediate result, drop this branch.\n     |- Try 330 \/ 297 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 33 \/ 10 = 3.3. 3.3 is a decimal, drop this branch.\n  |- Try 27 \/ 11 = 2.5. 2.5 is a decimal, drop this branch.\n |- Pick two numbers (27, 10) (numbers left: [11, 33]). Try possible operations.\n  |- Try 27 + 10 = 37. Add 37 to the number set. Current number set: [37, 11, 33], target: 40. Options for choosing two numbers: [(37, 11), (37, 33), (11, 33)].\n   |- Pick two numbers (37, 11) (numbers left: [33]). Try possible operations.\n    |- Try 37 + 11 = 48. Add 48 to the number set. Current number set: [48, 33], target: 40, just two numbers left.\n     |- Try 48 + 33 = 81. Evaluate 81 != 40, drop this branch.\n     |- Try 48 - 33 = 15. Evaluate 15 != 40, drop this branch.\n     |- Try 48 * 33 = 1584. Evaluate 1584 != 40, drop this branch.\n     |- Try 48 \/ 33 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 37 - 11 = 26. Add 26 to the number set. Current number set: [26, 33], target: 40, just two numbers left.\n     |- Try 33 + 26 = 59. Evaluate 59 != 40, drop this branch.\n     |- Try 33 - 26 = 7. Evaluate 7 != 40, drop this branch.\n     |- Try 33 * 26 = 858. Evaluate 858 != 40, drop this branch.\n     |- Try 33 \/ 26 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 37 * 11 = 407. Add 407 to the number set. Current number set: [407, 33], target: 40, just two numbers left.\n     |- Try 407 + 33 = 440. Evaluate 440 != 40, drop this branch.\n     |- Try 407 - 33 = 374. Evaluate 374 != 40, drop this branch.\n     |- Try 407 * 33 = 13431. 13431 exceeds the maximum intermediate result, drop this branch.\n     |- Try 407 \/ 33 = 12.3. 12.3 is a decimal, drop this branch.\n    |- Try 37 \/ 11 = 3.4. 3.4 is a decimal, drop this branch.\n   |- Pick two numbers (37, 33) (numbers left: [11]). Try possible operations.\n    |- Try 37 + 33 = 70. Add 70 to the number set. Current number set: [70, 11], target: 40, just two numbers left.\n     |- Try 70 + 11 = 81. Evaluate 81 != 40, drop this branch.\n     |- Try 70 - 11 = 59. Evaluate 59 != 40, drop this branch.\n     |- Try 70 * 11 = 770. Evaluate 770 != 40, drop this branch.\n     |- Try 70 \/ 11 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 37 - 33 = 4. Add 4 to the number set. Current number set: [4, 11], target: 40, just two numbers left.\n     |- Try 11 + 4 = 15. Evaluate 15 != 40, drop this branch.\n     |- Try 11 - 4 = 7. Evaluate 7 != 40, drop this branch.\n     |- Try 11 * 4 = 44. Evaluate 44 != 40, drop this branch.\n     |- Try 11 \/ 4 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 37 * 33 = 1221. Add 1221 to the number set. Current number set: [1221, 11], target: 40, just two numbers left.\n     |- Try 1221 + 11 = 1232. Evaluate 1232 != 40, drop this branch.\n     |- Try 1221 - 11 = 1210. Evaluate 1210 != 40, drop this branch.\n     |- Try 1221 * 11 = 13431. 13431 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1221 \/ 11 = 111. Evaluate 111 != 40, drop this branch.\n    |- Try 37 \/ 33 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (11, 33) (numbers left: [37]). Try possible operations.\n    |- Try 33 + 11 = 44. Add 44 to the number set. Current number set: [44, 37], target: 40, just two numbers left.\n     |- Try 44 + 37 = 81. Evaluate 81 != 40, drop this branch.\n     |- Try 44 - 37 = 7. Evaluate 7 != 40, drop this branch.\n     |- Try 44 * 37 = 1628. Evaluate 1628 != 40, drop this branch.\n     |- Try 44 \/ 37 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 33 - 11 = 22. Add 22 to the number set. Current number set: [22, 37], target: 40, just two numbers left.\n     |- Try 37 + 22 = 59. Evaluate 59 != 40, drop this branch.\n     |- Try 37 - 22 = 15. Evaluate 15 != 40, drop this branch.\n     |- Try 37 * 22 = 814. Evaluate 814 != 40, drop this branch.\n     |- Try 37 \/ 22 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 33 * 11 = 363. Add 363 to the number set. Current number set: [363, 37], target: 40, just two numbers left.\n     |- Try 363 + 37 = 400. Evaluate 400 != 40, drop this branch.\n     |- Try 363 - 37 = 326. Evaluate 326 != 40, drop this branch.\n     |- Try 363 * 37 = 13431. 13431 exceeds the maximum intermediate result, drop this branch.\n     |- Try 363 \/ 37 = 9.8. 9.8 is a decimal, drop this branch.\n    |- Try 33 \/ 11 = 3. Add 3 to the number set. Current number set: [3, 37], target: 40, just two numbers left.\n     |- Try 37 + 3 = 40. Evaluate 40 == 40, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 37 + 3 = 40\nThe step before: 33 \/ 11 = 3\nThe first step: 27 + 10 = 37\n\nOutput the solution in the required format:\n<Solution>\n27 + 10 = 37\n33 \/ 11 = 3\n37 + 3 = 40\n<\/Solution>\n","item":{"nums":[27,11,10,33],"solution":["27 + 10 = 37","33 \/ 11 = 3","37 + 3 = 40"],"target":40}}
+{"instance_id":"countdown_8k_121","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [12, 48, 32, 1]\nTarget: 36","reference_output":"# Search Procedure\nInitial number set: [12, 48, 32, 1], target: 36. Options for choosing two numbers: [(12, 48), (12, 32), (12, 1), (48, 32), (48, 1), (32, 1)].\n |- Pick two numbers (12, 48) (numbers left: [32, 1]). Try possible operations.\n  |- Try 48 + 12 = 60. Add 60 to the number set. Current number set: [60, 32, 1], target: 36. Options for choosing two numbers: [(60, 32), (60, 1), (32, 1)].\n   |- Pick two numbers (60, 32) (numbers left: [1]). Try possible operations.\n    |- Try 60 + 32 = 92. Add 92 to the number set. Current number set: [92, 1], target: 36, just two numbers left.\n     |- Try 92 + 1 = 93. Evaluate 93 != 36, drop this branch.\n     |- Try 92 - 1 = 91. Evaluate 91 != 36, drop this branch.\n     |- Try 92 * 1 = 92. Evaluate 92 != 36, drop this branch.\n     |- Try 92 \/ 1 = 92. Evaluate 92 != 36, drop this branch.\n    |- Try 60 - 32 = 28. Add 28 to the number set. Current number set: [28, 1], target: 36, just two numbers left.\n     |- Try 28 + 1 = 29. Evaluate 29 != 36, drop this branch.\n     |- Try 28 - 1 = 27. Evaluate 27 != 36, drop this branch.\n     |- Try 28 * 1 = 28. Evaluate 28 != 36, drop this branch.\n     |- Try 28 \/ 1 = 28. Evaluate 28 != 36, drop this branch.\n    |- Try 60 * 32 = 1920. Add 1920 to the number set. Current number set: [1920, 1], target: 36, just two numbers left.\n     |- Try 1920 + 1 = 1921. Evaluate 1921 != 36, drop this branch.\n     |- Try 1920 - 1 = 1919. Evaluate 1919 != 36, drop this branch.\n     |- Try 1920 * 1 = 1920. Evaluate 1920 != 36, drop this branch.\n     |- Try 1920 \/ 1 = 1920. Evaluate 1920 != 36, drop this branch.\n    |- Try 60 \/ 32 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (60, 1) (numbers left: [32]). Try possible operations.\n    |- Try 60 + 1 = 61. Add 61 to the number set. Current number set: [61, 32], target: 36, just two numbers left.\n     |- Try 61 + 32 = 93. Evaluate 93 != 36, drop this branch.\n     |- Try 61 - 32 = 29. Evaluate 29 != 36, drop this branch.\n     |- Try 61 * 32 = 1952. Evaluate 1952 != 36, drop this branch.\n     |- Try 61 \/ 32 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 60 - 1 = 59. Add 59 to the number set. Current number set: [59, 32], target: 36, just two numbers left.\n     |- Try 59 + 32 = 91. Evaluate 91 != 36, drop this branch.\n     |- Try 59 - 32 = 27. Evaluate 27 != 36, drop this branch.\n     |- Try 59 * 32 = 1888. Evaluate 1888 != 36, drop this branch.\n     |- Try 59 \/ 32 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 60 * 1 = 60. Add 60 to the number set. Current number set: [60, 32], target: 36, just two numbers left.\n     |- Try 60 + 32 = 92. Evaluate 92 != 36, drop this branch.\n     |- Try 60 - 32 = 28. Evaluate 28 != 36, drop this branch.\n     |- Try 60 * 32 = 1920. Evaluate 1920 != 36, drop this branch.\n     |- Try 60 \/ 32 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 60 \/ 1 = 60. Add 60 to the number set. Current number set: [60, 32], target: 36, just two numbers left.\n     |- Try 60 + 32 = 92. Evaluate 92 != 36, drop this branch.\n     |- Try 60 - 32 = 28. Evaluate 28 != 36, drop this branch.\n     |- Try 60 * 32 = 1920. Evaluate 1920 != 36, drop this branch.\n     |- Try 60 \/ 32 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (32, 1) (numbers left: [60]). Try possible operations.\n    |- Try 32 + 1 = 33. Add 33 to the number set. Current number set: [33, 60], target: 36, just two numbers left.\n     |- Try 60 + 33 = 93. Evaluate 93 != 36, drop this branch.\n     |- Try 60 - 33 = 27. Evaluate 27 != 36, drop this branch.\n     |- Try 60 * 33 = 1980. Evaluate 1980 != 36, drop this branch.\n     |- Try 60 \/ 33 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 32 - 1 = 31. Add 31 to the number set. Current number set: [31, 60], target: 36, just two numbers left.\n     |- Try 60 + 31 = 91. Evaluate 91 != 36, drop this branch.\n     |- Try 60 - 31 = 29. Evaluate 29 != 36, drop this branch.\n     |- Try 60 * 31 = 1860. Evaluate 1860 != 36, drop this branch.\n     |- Try 60 \/ 31 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 32 * 1 = 32. Add 32 to the number set. Current number set: [32, 60], target: 36, just two numbers left.\n     |- Try 60 + 32 = 92. Evaluate 92 != 36, drop this branch.\n     |- Try 60 - 32 = 28. Evaluate 28 != 36, drop this branch.\n     |- Try 60 * 32 = 1920. Evaluate 1920 != 36, drop this branch.\n     |- Try 60 \/ 32 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 32 \/ 1 = 32. Add 32 to the number set. Current number set: [32, 60], target: 36, just two numbers left.\n     |- Try 60 + 32 = 92. Evaluate 92 != 36, drop this branch.\n     |- Try 60 - 32 = 28. Evaluate 28 != 36, drop this branch.\n     |- Try 60 * 32 = 1920. Evaluate 1920 != 36, drop this branch.\n     |- Try 60 \/ 32 = 1.9. 1.9 is a decimal, drop this branch.\n  |- Try 48 - 12 = 36. Add 36 to the number set. Current number set: [36, 32, 1], target: 36. Options for choosing two numbers: [(36, 32), (36, 1), (32, 1)].\n   |- Pick two numbers (36, 32) (numbers left: [1]). Try possible operations.\n    |- Try 36 + 32 = 68. Add 68 to the number set. Current number set: [68, 1], target: 36, just two numbers left.\n     |- Try 68 + 1 = 69. Evaluate 69 != 36, drop this branch.\n     |- Try 68 - 1 = 67. Evaluate 67 != 36, drop this branch.\n     |- Try 68 * 1 = 68. Evaluate 68 != 36, drop this branch.\n     |- Try 68 \/ 1 = 68. Evaluate 68 != 36, drop this branch.\n    |- Try 36 - 32 = 4. Add 4 to the number set. Current number set: [4, 1], target: 36, just two numbers left.\n     |- Try 4 + 1 = 5. Evaluate 5 != 36, drop this branch.\n     |- Try 4 - 1 = 3. Evaluate 3 != 36, drop this branch.\n     |- Try 4 * 1 = 4. Evaluate 4 != 36, drop this branch.\n     |- Try 4 \/ 1 = 4. Evaluate 4 != 36, drop this branch.\n    |- Try 36 * 32 = 1152. Add 1152 to the number set. Current number set: [1152, 1], target: 36, just two numbers left.\n     |- Try 1152 + 1 = 1153. Evaluate 1153 != 36, drop this branch.\n     |- Try 1152 - 1 = 1151. Evaluate 1151 != 36, drop this branch.\n     |- Try 1152 * 1 = 1152. Evaluate 1152 != 36, drop this branch.\n     |- Try 1152 \/ 1 = 1152. Evaluate 1152 != 36, drop this branch.\n    |- Try 36 \/ 32 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (36, 1) (numbers left: [32]). Try possible operations.\n    |- Try 36 + 1 = 37. Add 37 to the number set. Current number set: [37, 32], target: 36, just two numbers left.\n     |- Try 37 + 32 = 69. Evaluate 69 != 36, drop this branch.\n     |- Try 37 - 32 = 5. Evaluate 5 != 36, drop this branch.\n     |- Try 37 * 32 = 1184. Evaluate 1184 != 36, drop this branch.\n     |- Try 37 \/ 32 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 36 - 1 = 35. Add 35 to the number set. Current number set: [35, 32], target: 36, just two numbers left.\n     |- Try 35 + 32 = 67. Evaluate 67 != 36, drop this branch.\n     |- Try 35 - 32 = 3. Evaluate 3 != 36, drop this branch.\n     |- Try 35 * 32 = 1120. Evaluate 1120 != 36, drop this branch.\n     |- Try 35 \/ 32 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 36 * 1 = 36. Add 36 to the number set. Current number set: [36, 32], target: 36, just two numbers left.\n     |- Try 36 + 32 = 68. Evaluate 68 != 36, drop this branch.\n     |- Try 36 - 32 = 4. Evaluate 4 != 36, drop this branch.\n     |- Try 36 * 32 = 1152. Evaluate 1152 != 36, drop this branch.\n     |- Try 36 \/ 32 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 36 \/ 1 = 36. Add 36 to the number set. Current number set: [36, 32], target: 36, just two numbers left.\n     |- Try 36 + 32 = 68. Evaluate 68 != 36, drop this branch.\n     |- Try 36 - 32 = 4. Evaluate 4 != 36, drop this branch.\n     |- Try 36 * 32 = 1152. Evaluate 1152 != 36, drop this branch.\n     |- Try 36 \/ 32 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (32, 1) (numbers left: [36]). Try possible operations.\n    |- Try 32 + 1 = 33. Add 33 to the number set. Current number set: [33, 36], target: 36, just two numbers left.\n     |- Try 36 + 33 = 69. Evaluate 69 != 36, drop this branch.\n     |- Try 36 - 33 = 3. Evaluate 3 != 36, drop this branch.\n     |- Try 36 * 33 = 1188. Evaluate 1188 != 36, drop this branch.\n     |- Try 36 \/ 33 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 32 - 1 = 31. Add 31 to the number set. Current number set: [31, 36], target: 36, just two numbers left.\n     |- Try 36 + 31 = 67. Evaluate 67 != 36, drop this branch.\n     |- Try 36 - 31 = 5. Evaluate 5 != 36, drop this branch.\n     |- Try 36 * 31 = 1116. Evaluate 1116 != 36, drop this branch.\n     |- Try 36 \/ 31 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 32 * 1 = 32. Add 32 to the number set. Current number set: [32, 36], target: 36, just two numbers left.\n     |- Try 36 + 32 = 68. Evaluate 68 != 36, drop this branch.\n     |- Try 36 - 32 = 4. Evaluate 4 != 36, drop this branch.\n     |- Try 36 * 32 = 1152. Evaluate 1152 != 36, drop this branch.\n     |- Try 36 \/ 32 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 32 \/ 1 = 32. Add 32 to the number set. Current number set: [32, 36], target: 36, just two numbers left.\n     |- Try 36 + 32 = 68. Evaluate 68 != 36, drop this branch.\n     |- Try 36 - 32 = 4. Evaluate 4 != 36, drop this branch.\n     |- Try 36 * 32 = 1152. Evaluate 1152 != 36, drop this branch.\n     |- Try 36 \/ 32 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 48 * 12 = 576. Add 576 to the number set. Current number set: [576, 32, 1], target: 36. Options for choosing two numbers: [(576, 32), (576, 1), (32, 1)].\n   |- Pick two numbers (576, 32) (numbers left: [1]). Try possible operations.\n    |- Try 576 + 32 = 608. Add 608 to the number set. Current number set: [608, 1], target: 36, just two numbers left.\n     |- Try 608 + 1 = 609. Evaluate 609 != 36, drop this branch.\n     |- Try 608 - 1 = 607. Evaluate 607 != 36, drop this branch.\n     |- Try 608 * 1 = 608. Evaluate 608 != 36, drop this branch.\n     |- Try 608 \/ 1 = 608. Evaluate 608 != 36, drop this branch.\n    |- Try 576 - 32 = 544. Add 544 to the number set. Current number set: [544, 1], target: 36, just two numbers left.\n     |- Try 544 + 1 = 545. Evaluate 545 != 36, drop this branch.\n     |- Try 544 - 1 = 543. Evaluate 543 != 36, drop this branch.\n     |- Try 544 * 1 = 544. Evaluate 544 != 36, drop this branch.\n     |- Try 544 \/ 1 = 544. Evaluate 544 != 36, drop this branch.\n    |- Try 576 * 32 = 18432. 18432 exceeds the maximum intermediate result, drop this branch.\n    |- Try 576 \/ 32 = 18. Add 18 to the number set. Current number set: [18, 1], target: 36, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 36, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 36, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 36, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 36, drop this branch.\n   |- Pick two numbers (576, 1) (numbers left: [32]). Try possible operations.\n    |- Try 576 + 1 = 577. Add 577 to the number set. Current number set: [577, 32], target: 36, just two numbers left.\n     |- Try 577 + 32 = 609. Evaluate 609 != 36, drop this branch.\n     |- Try 577 - 32 = 545. Evaluate 545 != 36, drop this branch.\n     |- Try 577 * 32 = 18464. 18464 exceeds the maximum intermediate result, drop this branch.\n     |- Try 577 \/ 32 = 18.0. 18.0 is a decimal, drop this branch.\n    |- Try 576 - 1 = 575. Add 575 to the number set. Current number set: [575, 32], target: 36, just two numbers left.\n     |- Try 575 + 32 = 607. Evaluate 607 != 36, drop this branch.\n     |- Try 575 - 32 = 543. Evaluate 543 != 36, drop this branch.\n     |- Try 575 * 32 = 18400. 18400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 575 \/ 32 = 18.0. 18.0 is a decimal, drop this branch.\n    |- Try 576 * 1 = 576. Add 576 to the number set. Current number set: [576, 32], target: 36, just two numbers left.\n     |- Try 576 + 32 = 608. Evaluate 608 != 36, drop this branch.\n     |- Try 576 - 32 = 544. Evaluate 544 != 36, drop this branch.\n     |- Try 576 * 32 = 18432. 18432 exceeds the maximum intermediate result, drop this branch.\n     |- Try 576 \/ 32 = 18. Evaluate 18 != 36, drop this branch.\n    |- Try 576 \/ 1 = 576. Add 576 to the number set. Current number set: [576, 32], target: 36, just two numbers left.\n     |- Try 576 + 32 = 608. Evaluate 608 != 36, drop this branch.\n     |- Try 576 - 32 = 544. Evaluate 544 != 36, drop this branch.\n     |- Try 576 * 32 = 18432. 18432 exceeds the maximum intermediate result, drop this branch.\n     |- Try 576 \/ 32 = 18. Evaluate 18 != 36, drop this branch.\n   |- Pick two numbers (32, 1) (numbers left: [576]). Try possible operations.\n    |- Try 32 + 1 = 33. Add 33 to the number set. Current number set: [33, 576], target: 36, just two numbers left.\n     |- Try 576 + 33 = 609. Evaluate 609 != 36, drop this branch.\n     |- Try 576 - 33 = 543. Evaluate 543 != 36, drop this branch.\n     |- Try 576 * 33 = 19008. 19008 exceeds the maximum intermediate result, drop this branch.\n     |- Try 576 \/ 33 = 17.5. 17.5 is a decimal, drop this branch.\n    |- Try 32 - 1 = 31. Add 31 to the number set. Current number set: [31, 576], target: 36, just two numbers left.\n     |- Try 576 + 31 = 607. Evaluate 607 != 36, drop this branch.\n     |- Try 576 - 31 = 545. Evaluate 545 != 36, drop this branch.\n     |- Try 576 * 31 = 17856. 17856 exceeds the maximum intermediate result, drop this branch.\n     |- Try 576 \/ 31 = 18.6. 18.6 is a decimal, drop this branch.\n    |- Try 32 * 1 = 32. Add 32 to the number set. Current number set: [32, 576], target: 36, just two numbers left.\n     |- Try 576 + 32 = 608. Evaluate 608 != 36, drop this branch.\n     |- Try 576 - 32 = 544. Evaluate 544 != 36, drop this branch.\n     |- Try 576 * 32 = 18432. 18432 exceeds the maximum intermediate result, drop this branch.\n     |- Try 576 \/ 32 = 18. Evaluate 18 != 36, drop this branch.\n    |- Try 32 \/ 1 = 32. Add 32 to the number set. Current number set: [32, 576], target: 36, just two numbers left.\n     |- Try 576 + 32 = 608. Evaluate 608 != 36, drop this branch.\n     |- Try 576 - 32 = 544. Evaluate 544 != 36, drop this branch.\n     |- Try 576 * 32 = 18432. 18432 exceeds the maximum intermediate result, drop this branch.\n     |- Try 576 \/ 32 = 18. Evaluate 18 != 36, drop this branch.\n  |- Try 48 \/ 12 = 4. Add 4 to the number set. Current number set: [4, 32, 1], target: 36. Options for choosing two numbers: [(4, 32), (4, 1), (32, 1)].\n   |- Pick two numbers (4, 32) (numbers left: [1]). Try possible operations.\n    |- Try 32 + 4 = 36. Add 36 to the number set. Current number set: [36, 1], target: 36, just two numbers left.\n     |- Try 36 + 1 = 37. Evaluate 37 != 36, drop this branch.\n     |- Try 36 - 1 = 35. Evaluate 35 != 36, drop this branch.\n     |- Try 36 * 1 = 36. Evaluate 36 == 36, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 * 1 = 36\nThe step before: 32 + 4 = 36\nThe first step: 48 \/ 12 = 4\n\nOutput the solution in the required format:\n<Solution>\n48 \/ 12 = 4\n32 + 4 = 36\n36 * 1 = 36\n<\/Solution>\n","item":{"nums":[12,48,32,1],"solution":["48 \/ 12 = 4","32 + 4 = 36","36 * 1 = 36"],"target":36}}
+{"instance_id":"countdown_8k_122","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [29, 22, 25, 31]\nTarget: 36","reference_output":"# Search Procedure\nInitial number set: [29, 22, 25, 31], target: 36. Options for choosing two numbers: [(29, 22), (29, 25), (29, 31), (22, 25), (22, 31), (25, 31)].\n |- Pick two numbers (29, 22) (numbers left: [25, 31]). Try possible operations.\n  |- Try 29 + 22 = 51. Add 51 to the number set. Current number set: [51, 25, 31], target: 36. Options for choosing two numbers: [(51, 25), (51, 31), (25, 31)].\n   |- Pick two numbers (51, 25) (numbers left: [31]). Try possible operations.\n    |- Try 51 + 25 = 76. Add 76 to the number set. Current number set: [76, 31], target: 36, just two numbers left.\n     |- Try 76 + 31 = 107. Evaluate 107 != 36, drop this branch.\n     |- Try 76 - 31 = 45. Evaluate 45 != 36, drop this branch.\n     |- Try 76 * 31 = 2356. 2356 exceeds the maximum intermediate result, drop this branch.\n     |- Try 76 \/ 31 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 51 - 25 = 26. Add 26 to the number set. Current number set: [26, 31], target: 36, just two numbers left.\n     |- Try 31 + 26 = 57. Evaluate 57 != 36, drop this branch.\n     |- Try 31 - 26 = 5. Evaluate 5 != 36, drop this branch.\n     |- Try 31 * 26 = 806. Evaluate 806 != 36, drop this branch.\n     |- Try 31 \/ 26 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 51 * 25 = 1275. Add 1275 to the number set. Current number set: [1275, 31], target: 36, just two numbers left.\n     |- Try 1275 + 31 = 1306. Evaluate 1306 != 36, drop this branch.\n     |- Try 1275 - 31 = 1244. Evaluate 1244 != 36, drop this branch.\n     |- Try 1275 * 31 = 39525. 39525 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1275 \/ 31 = 41.1. 41.1 is a decimal, drop this branch.\n    |- Try 51 \/ 25 = 2.0. 2.0 is a decimal, drop this branch.\n   |- Pick two numbers (51, 31) (numbers left: [25]). Try possible operations.\n    |- Try 51 + 31 = 82. Add 82 to the number set. Current number set: [82, 25], target: 36, just two numbers left.\n     |- Try 82 + 25 = 107. Evaluate 107 != 36, drop this branch.\n     |- Try 82 - 25 = 57. Evaluate 57 != 36, drop this branch.\n     |- Try 82 * 25 = 2050. 2050 exceeds the maximum intermediate result, drop this branch.\n     |- Try 82 \/ 25 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 51 - 31 = 20. Add 20 to the number set. Current number set: [20, 25], target: 36, just two numbers left.\n     |- Try 25 + 20 = 45. Evaluate 45 != 36, drop this branch.\n     |- Try 25 - 20 = 5. Evaluate 5 != 36, drop this branch.\n     |- Try 25 * 20 = 500. Evaluate 500 != 36, drop this branch.\n     |- Try 25 \/ 20 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 51 * 31 = 1581. Add 1581 to the number set. Current number set: [1581, 25], target: 36, just two numbers left.\n     |- Try 1581 + 25 = 1606. Evaluate 1606 != 36, drop this branch.\n     |- Try 1581 - 25 = 1556. Evaluate 1556 != 36, drop this branch.\n     |- Try 1581 * 25 = 39525. 39525 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1581 \/ 25 = 63.2. 63.2 is a decimal, drop this branch.\n    |- Try 51 \/ 31 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (25, 31) (numbers left: [51]). Try possible operations.\n    |- Try 31 + 25 = 56. Add 56 to the number set. Current number set: [56, 51], target: 36, just two numbers left.\n     |- Try 56 + 51 = 107. Evaluate 107 != 36, drop this branch.\n     |- Try 56 - 51 = 5. Evaluate 5 != 36, drop this branch.\n     |- Try 56 * 51 = 2856. 2856 exceeds the maximum intermediate result, drop this branch.\n     |- Try 56 \/ 51 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 31 - 25 = 6. Add 6 to the number set. Current number set: [6, 51], target: 36, just two numbers left.\n     |- Try 51 + 6 = 57. Evaluate 57 != 36, drop this branch.\n     |- Try 51 - 6 = 45. Evaluate 45 != 36, drop this branch.\n     |- Try 51 * 6 = 306. Evaluate 306 != 36, drop this branch.\n     |- Try 51 \/ 6 = 8.5. 8.5 is a decimal, drop this branch.\n    |- Try 31 * 25 = 775. Add 775 to the number set. Current number set: [775, 51], target: 36, just two numbers left.\n     |- Try 775 + 51 = 826. Evaluate 826 != 36, drop this branch.\n     |- Try 775 - 51 = 724. Evaluate 724 != 36, drop this branch.\n     |- Try 775 * 51 = 39525. 39525 exceeds the maximum intermediate result, drop this branch.\n     |- Try 775 \/ 51 = 15.2. 15.2 is a decimal, drop this branch.\n    |- Try 31 \/ 25 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 29 - 22 = 7. Add 7 to the number set. Current number set: [7, 25, 31], target: 36. Options for choosing two numbers: [(7, 25), (7, 31), (25, 31)].\n   |- Pick two numbers (7, 25) (numbers left: [31]). Try possible operations.\n    |- Try 25 + 7 = 32. Add 32 to the number set. Current number set: [32, 31], target: 36, just two numbers left.\n     |- Try 32 + 31 = 63. Evaluate 63 != 36, drop this branch.\n     |- Try 32 - 31 = 1. Evaluate 1 != 36, drop this branch.\n     |- Try 32 * 31 = 992. Evaluate 992 != 36, drop this branch.\n     |- Try 32 \/ 31 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 25 - 7 = 18. Add 18 to the number set. Current number set: [18, 31], target: 36, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 36, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 36, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 36, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 * 7 = 175. Add 175 to the number set. Current number set: [175, 31], target: 36, just two numbers left.\n     |- Try 175 + 31 = 206. Evaluate 206 != 36, drop this branch.\n     |- Try 175 - 31 = 144. Evaluate 144 != 36, drop this branch.\n     |- Try 175 * 31 = 5425. 5425 exceeds the maximum intermediate result, drop this branch.\n     |- Try 175 \/ 31 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 25 \/ 7 = 3.6. 3.6 is a decimal, drop this branch.\n   |- Pick two numbers (7, 31) (numbers left: [25]). Try possible operations.\n    |- Try 31 + 7 = 38. Add 38 to the number set. Current number set: [38, 25], target: 36, just two numbers left.\n     |- Try 38 + 25 = 63. Evaluate 63 != 36, drop this branch.\n     |- Try 38 - 25 = 13. Evaluate 13 != 36, drop this branch.\n     |- Try 38 * 25 = 950. Evaluate 950 != 36, drop this branch.\n     |- Try 38 \/ 25 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 31 - 7 = 24. Add 24 to the number set. Current number set: [24, 25], target: 36, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 36, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 36, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 36, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 31 * 7 = 217. Add 217 to the number set. Current number set: [217, 25], target: 36, just two numbers left.\n     |- Try 217 + 25 = 242. Evaluate 242 != 36, drop this branch.\n     |- Try 217 - 25 = 192. Evaluate 192 != 36, drop this branch.\n     |- Try 217 * 25 = 5425. 5425 exceeds the maximum intermediate result, drop this branch.\n     |- Try 217 \/ 25 = 8.7. 8.7 is a decimal, drop this branch.\n    |- Try 31 \/ 7 = 4.4. 4.4 is a decimal, drop this branch.\n   |- Pick two numbers (25, 31) (numbers left: [7]). Try possible operations.\n    |- Try 31 + 25 = 56. Add 56 to the number set. Current number set: [56, 7], target: 36, just two numbers left.\n     |- Try 56 + 7 = 63. Evaluate 63 != 36, drop this branch.\n     |- Try 56 - 7 = 49. Evaluate 49 != 36, drop this branch.\n     |- Try 56 * 7 = 392. Evaluate 392 != 36, drop this branch.\n     |- Try 56 \/ 7 = 8. Evaluate 8 != 36, drop this branch.\n    |- Try 31 - 25 = 6. Add 6 to the number set. Current number set: [6, 7], target: 36, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 36, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 36, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 36, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 31 * 25 = 775. Add 775 to the number set. Current number set: [775, 7], target: 36, just two numbers left.\n     |- Try 775 + 7 = 782. Evaluate 782 != 36, drop this branch.\n     |- Try 775 - 7 = 768. Evaluate 768 != 36, drop this branch.\n     |- Try 775 * 7 = 5425. 5425 exceeds the maximum intermediate result, drop this branch.\n     |- Try 775 \/ 7 = 110.7. 110.7 is a decimal, drop this branch.\n    |- Try 31 \/ 25 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 29 * 22 = 638. Add 638 to the number set. Current number set: [638, 25, 31], target: 36. Options for choosing two numbers: [(638, 25), (638, 31), (25, 31)].\n   |- Pick two numbers (638, 25) (numbers left: [31]). Try possible operations.\n    |- Try 638 + 25 = 663. Add 663 to the number set. Current number set: [663, 31], target: 36, just two numbers left.\n     |- Try 663 + 31 = 694. Evaluate 694 != 36, drop this branch.\n     |- Try 663 - 31 = 632. Evaluate 632 != 36, drop this branch.\n     |- Try 663 * 31 = 20553. 20553 exceeds the maximum intermediate result, drop this branch.\n     |- Try 663 \/ 31 = 21.4. 21.4 is a decimal, drop this branch.\n    |- Try 638 - 25 = 613. Add 613 to the number set. Current number set: [613, 31], target: 36, just two numbers left.\n     |- Try 613 + 31 = 644. Evaluate 644 != 36, drop this branch.\n     |- Try 613 - 31 = 582. Evaluate 582 != 36, drop this branch.\n     |- Try 613 * 31 = 19003. 19003 exceeds the maximum intermediate result, drop this branch.\n     |- Try 613 \/ 31 = 19.8. 19.8 is a decimal, drop this branch.\n    |- Try 638 * 25 = 15950. 15950 exceeds the maximum intermediate result, drop this branch.\n    |- Try 638 \/ 25 = 25.5. 25.5 is a decimal, drop this branch.\n   |- Pick two numbers (638, 31) (numbers left: [25]). Try possible operations.\n    |- Try 638 + 31 = 669. Add 669 to the number set. Current number set: [669, 25], target: 36, just two numbers left.\n     |- Try 669 + 25 = 694. Evaluate 694 != 36, drop this branch.\n     |- Try 669 - 25 = 644. Evaluate 644 != 36, drop this branch.\n     |- Try 669 * 25 = 16725. 16725 exceeds the maximum intermediate result, drop this branch.\n     |- Try 669 \/ 25 = 26.8. 26.8 is a decimal, drop this branch.\n    |- Try 638 - 31 = 607. Add 607 to the number set. Current number set: [607, 25], target: 36, just two numbers left.\n     |- Try 607 + 25 = 632. Evaluate 632 != 36, drop this branch.\n     |- Try 607 - 25 = 582. Evaluate 582 != 36, drop this branch.\n     |- Try 607 * 25 = 15175. 15175 exceeds the maximum intermediate result, drop this branch.\n     |- Try 607 \/ 25 = 24.3. 24.3 is a decimal, drop this branch.\n    |- Try 638 * 31 = 19778. 19778 exceeds the maximum intermediate result, drop this branch.\n    |- Try 638 \/ 31 = 20.6. 20.6 is a decimal, drop this branch.\n   |- Pick two numbers (25, 31) (numbers left: [638]). Try possible operations.\n    |- Try 31 + 25 = 56. Add 56 to the number set. Current number set: [56, 638], target: 36, just two numbers left.\n     |- Try 638 + 56 = 694. Evaluate 694 != 36, drop this branch.\n     |- Try 638 - 56 = 582. Evaluate 582 != 36, drop this branch.\n     |- Try 638 * 56 = 35728. 35728 exceeds the maximum intermediate result, drop this branch.\n     |- Try 638 \/ 56 = 11.4. 11.4 is a decimal, drop this branch.\n    |- Try 31 - 25 = 6. Add 6 to the number set. Current number set: [6, 638], target: 36, just two numbers left.\n     |- Try 638 + 6 = 644. Evaluate 644 != 36, drop this branch.\n     |- Try 638 - 6 = 632. Evaluate 632 != 36, drop this branch.\n     |- Try 638 * 6 = 3828. 3828 exceeds the maximum intermediate result, drop this branch.\n     |- Try 638 \/ 6 = 106.3. 106.3 is a decimal, drop this branch.\n    |- Try 31 * 25 = 775. Add 775 to the number set. Current number set: [775, 638], target: 36, just two numbers left.\n     |- Try 775 + 638 = 1413. Evaluate 1413 != 36, drop this branch.\n     |- Try 775 - 638 = 137. Evaluate 137 != 36, drop this branch.\n     |- Try 775 * 638 = 494450. 494450 exceeds the maximum intermediate result, drop this branch.\n     |- Try 775 \/ 638 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 31 \/ 25 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 29 \/ 22 = 1.3. 1.3 is a decimal, drop this branch.\n |- Pick two numbers (29, 25) (numbers left: [22, 31]). Try possible operations.\n  |- Try 29 + 25 = 54. Add 54 to the number set. Current number set: [54, 22, 31], target: 36. Options for choosing two numbers: [(54, 22), (54, 31), (22, 31)].\n   |- Pick two numbers (54, 22) (numbers left: [31]). Try possible operations.\n    |- Try 54 + 22 = 76. Add 76 to the number set. Current number set: [76, 31], target: 36, just two numbers left.\n     |- Try 76 + 31 = 107. Evaluate 107 != 36, drop this branch.\n     |- Try 76 - 31 = 45. Evaluate 45 != 36, drop this branch.\n     |- Try 76 * 31 = 2356. 2356 exceeds the maximum intermediate result, drop this branch.\n     |- Try 76 \/ 31 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 54 - 22 = 32. Add 32 to the number set. Current number set: [32, 31], target: 36, just two numbers left.\n     |- Try 32 + 31 = 63. Evaluate 63 != 36, drop this branch.\n     |- Try 32 - 31 = 1. Evaluate 1 != 36, drop this branch.\n     |- Try 32 * 31 = 992. Evaluate 992 != 36, drop this branch.\n     |- Try 32 \/ 31 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 54 * 22 = 1188. Add 1188 to the number set. Current number set: [1188, 31], target: 36, just two numbers left.\n     |- Try 1188 + 31 = 1219. Evaluate 1219 != 36, drop this branch.\n     |- Try 1188 - 31 = 1157. Evaluate 1157 != 36, drop this branch.\n     |- Try 1188 * 31 = 36828. 36828 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1188 \/ 31 = 38.3. 38.3 is a decimal, drop this branch.\n    |- Try 54 \/ 22 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (54, 31) (numbers left: [22]). Try possible operations.\n    |- Try 54 + 31 = 85. Add 85 to the number set. Current number set: [85, 22], target: 36, just two numbers left.\n     |- Try 85 + 22 = 107. Evaluate 107 != 36, drop this branch.\n     |- Try 85 - 22 = 63. Evaluate 63 != 36, drop this branch.\n     |- Try 85 * 22 = 1870. Evaluate 1870 != 36, drop this branch.\n     |- Try 85 \/ 22 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 54 - 31 = 23. Add 23 to the number set. Current number set: [23, 22], target: 36, just two numbers left.\n     |- Try 23 + 22 = 45. Evaluate 45 != 36, drop this branch.\n     |- Try 23 - 22 = 1. Evaluate 1 != 36, drop this branch.\n     |- Try 23 * 22 = 506. Evaluate 506 != 36, drop this branch.\n     |- Try 23 \/ 22 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 54 * 31 = 1674. Add 1674 to the number set. Current number set: [1674, 22], target: 36, just two numbers left.\n     |- Try 1674 + 22 = 1696. Evaluate 1696 != 36, drop this branch.\n     |- Try 1674 - 22 = 1652. Evaluate 1652 != 36, drop this branch.\n     |- Try 1674 * 22 = 36828. 36828 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1674 \/ 22 = 76.1. 76.1 is a decimal, drop this branch.\n    |- Try 54 \/ 31 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (22, 31) (numbers left: [54]). Try possible operations.\n    |- Try 31 + 22 = 53. Add 53 to the number set. Current number set: [53, 54], target: 36, just two numbers left.\n     |- Try 54 + 53 = 107. Evaluate 107 != 36, drop this branch.\n     |- Try 54 - 53 = 1. Evaluate 1 != 36, drop this branch.\n     |- Try 54 * 53 = 2862. 2862 exceeds the maximum intermediate result, drop this branch.\n     |- Try 54 \/ 53 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 31 - 22 = 9. Add 9 to the number set. Current number set: [9, 54], target: 36, just two numbers left.\n     |- Try 54 + 9 = 63. Evaluate 63 != 36, drop this branch.\n     |- Try 54 - 9 = 45. Evaluate 45 != 36, drop this branch.\n     |- Try 54 * 9 = 486. Evaluate 486 != 36, drop this branch.\n     |- Try 54 \/ 9 = 6. Evaluate 6 != 36, drop this branch.\n    |- Try 31 * 22 = 682. Add 682 to the number set. Current number set: [682, 54], target: 36, just two numbers left.\n     |- Try 682 + 54 = 736. Evaluate 736 != 36, drop this branch.\n     |- Try 682 - 54 = 628. Evaluate 628 != 36, drop this branch.\n     |- Try 682 * 54 = 36828. 36828 exceeds the maximum intermediate result, drop this branch.\n     |- Try 682 \/ 54 = 12.6. 12.6 is a decimal, drop this branch.\n    |- Try 31 \/ 22 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 29 - 25 = 4. Add 4 to the number set. Current number set: [4, 22, 31], target: 36. Options for choosing two numbers: [(4, 22), (4, 31), (22, 31)].\n   |- Pick two numbers (4, 22) (numbers left: [31]). Try possible operations.\n    |- Try 22 + 4 = 26. Add 26 to the number set. Current number set: [26, 31], target: 36, just two numbers left.\n     |- Try 31 + 26 = 57. Evaluate 57 != 36, drop this branch.\n     |- Try 31 - 26 = 5. Evaluate 5 != 36, drop this branch.\n     |- Try 31 * 26 = 806. Evaluate 806 != 36, drop this branch.\n     |- Try 31 \/ 26 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 22 - 4 = 18. Add 18 to the number set. Current number set: [18, 31], target: 36, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 36, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 36, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 36, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 22 * 4 = 88. Add 88 to the number set. Current number set: [88, 31], target: 36, just two numbers left.\n     |- Try 88 + 31 = 119. Evaluate 119 != 36, drop this branch.\n     |- Try 88 - 31 = 57. Evaluate 57 != 36, drop this branch.\n     |- Try 88 * 31 = 2728. 2728 exceeds the maximum intermediate result, drop this branch.\n     |- Try 88 \/ 31 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 22 \/ 4 = 5.5. 5.5 is a decimal, drop this branch.\n   |- Pick two numbers (4, 31) (numbers left: [22]). Try possible operations.\n    |- Try 31 + 4 = 35. Add 35 to the number set. Current number set: [35, 22], target: 36, just two numbers left.\n     |- Try 35 + 22 = 57. Evaluate 57 != 36, drop this branch.\n     |- Try 35 - 22 = 13. Evaluate 13 != 36, drop this branch.\n     |- Try 35 * 22 = 770. Evaluate 770 != 36, drop this branch.\n     |- Try 35 \/ 22 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 31 - 4 = 27. Add 27 to the number set. Current number set: [27, 22], target: 36, just two numbers left.\n     |- Try 27 + 22 = 49. Evaluate 49 != 36, drop this branch.\n     |- Try 27 - 22 = 5. Evaluate 5 != 36, drop this branch.\n     |- Try 27 * 22 = 594. Evaluate 594 != 36, drop this branch.\n     |- Try 27 \/ 22 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 31 * 4 = 124. Add 124 to the number set. Current number set: [124, 22], target: 36, just two numbers left.\n     |- Try 124 + 22 = 146. Evaluate 146 != 36, drop this branch.\n     |- Try 124 - 22 = 102. Evaluate 102 != 36, drop this branch.\n     |- Try 124 * 22 = 2728. 2728 exceeds the maximum intermediate result, drop this branch.\n     |- Try 124 \/ 22 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 31 \/ 4 = 7.8. 7.8 is a decimal, drop this branch.\n   |- Pick two numbers (22, 31) (numbers left: [4]). Try possible operations.\n    |- Try 31 + 22 = 53. Add 53 to the number set. Current number set: [53, 4], target: 36, just two numbers left.\n     |- Try 53 + 4 = 57. Evaluate 57 != 36, drop this branch.\n     |- Try 53 - 4 = 49. Evaluate 49 != 36, drop this branch.\n     |- Try 53 * 4 = 212. Evaluate 212 != 36, drop this branch.\n     |- Try 53 \/ 4 = 13.2. 13.2 is a decimal, drop this branch.\n    |- Try 31 - 22 = 9. Add 9 to the number set. Current number set: [9, 4], target: 36, just two numbers left.\n     |- Try 9 + 4 = 13. Evaluate 13 != 36, drop this branch.\n     |- Try 9 - 4 = 5. Evaluate 5 != 36, drop this branch.\n     |- Try 9 * 4 = 36. Evaluate 36 == 36, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 9 * 4 = 36\nThe step before: 31 - 22 = 9\nThe first step: 29 - 25 = 4\n\nOutput the solution in the required format:\n<Solution>\n29 - 25 = 4\n31 - 22 = 9\n9 * 4 = 36\n<\/Solution>\n","item":{"nums":[29,22,25,31],"solution":["29 - 25 = 4","31 - 22 = 9","9 * 4 = 36"],"target":36}}
+{"instance_id":"countdown_8k_123","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [2, 18, 14, 16]\nTarget: 21","reference_output":"# Search Procedure\nInitial number set: [2, 18, 14, 16], target: 21. Options for choosing two numbers: [(2, 18), (2, 14), (2, 16), (18, 14), (18, 16), (14, 16)].\n |- Pick two numbers (2, 18) (numbers left: [14, 16]). Try possible operations.\n  |- Try 18 + 2 = 20. Add 20 to the number set. Current number set: [20, 14, 16], target: 21. Options for choosing two numbers: [(20, 14), (20, 16), (14, 16)].\n   |- Pick two numbers (20, 14) (numbers left: [16]). Try possible operations.\n    |- Try 20 + 14 = 34. Add 34 to the number set. Current number set: [34, 16], target: 21, just two numbers left.\n     |- Try 34 + 16 = 50. Evaluate 50 != 21, drop this branch.\n     |- Try 34 - 16 = 18. Evaluate 18 != 21, drop this branch.\n     |- Try 34 * 16 = 544. Evaluate 544 != 21, drop this branch.\n     |- Try 34 \/ 16 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 20 - 14 = 6. Add 6 to the number set. Current number set: [6, 16], target: 21, just two numbers left.\n     |- Try 16 + 6 = 22. Evaluate 22 != 21, drop this branch.\n     |- Try 16 - 6 = 10. Evaluate 10 != 21, drop this branch.\n     |- Try 16 * 6 = 96. Evaluate 96 != 21, drop this branch.\n     |- Try 16 \/ 6 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 20 * 14 = 280. Add 280 to the number set. Current number set: [280, 16], target: 21, just two numbers left.\n     |- Try 280 + 16 = 296. Evaluate 296 != 21, drop this branch.\n     |- Try 280 - 16 = 264. Evaluate 264 != 21, drop this branch.\n     |- Try 280 * 16 = 4480. 4480 exceeds the maximum intermediate result, drop this branch.\n     |- Try 280 \/ 16 = 17.5. 17.5 is a decimal, drop this branch.\n    |- Try 20 \/ 14 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (20, 16) (numbers left: [14]). Try possible operations.\n    |- Try 20 + 16 = 36. Add 36 to the number set. Current number set: [36, 14], target: 21, just two numbers left.\n     |- Try 36 + 14 = 50. Evaluate 50 != 21, drop this branch.\n     |- Try 36 - 14 = 22. Evaluate 22 != 21, drop this branch.\n     |- Try 36 * 14 = 504. Evaluate 504 != 21, drop this branch.\n     |- Try 36 \/ 14 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 20 - 16 = 4. Add 4 to the number set. Current number set: [4, 14], target: 21, just two numbers left.\n     |- Try 14 + 4 = 18. Evaluate 18 != 21, drop this branch.\n     |- Try 14 - 4 = 10. Evaluate 10 != 21, drop this branch.\n     |- Try 14 * 4 = 56. Evaluate 56 != 21, drop this branch.\n     |- Try 14 \/ 4 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 20 * 16 = 320. Add 320 to the number set. Current number set: [320, 14], target: 21, just two numbers left.\n     |- Try 320 + 14 = 334. Evaluate 334 != 21, drop this branch.\n     |- Try 320 - 14 = 306. Evaluate 306 != 21, drop this branch.\n     |- Try 320 * 14 = 4480. 4480 exceeds the maximum intermediate result, drop this branch.\n     |- Try 320 \/ 14 = 22.9. 22.9 is a decimal, drop this branch.\n    |- Try 20 \/ 16 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (14, 16) (numbers left: [20]). Try possible operations.\n    |- Try 16 + 14 = 30. Add 30 to the number set. Current number set: [30, 20], target: 21, just two numbers left.\n     |- Try 30 + 20 = 50. Evaluate 50 != 21, drop this branch.\n     |- Try 30 - 20 = 10. Evaluate 10 != 21, drop this branch.\n     |- Try 30 * 20 = 600. Evaluate 600 != 21, drop this branch.\n     |- Try 30 \/ 20 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 16 - 14 = 2. Add 2 to the number set. Current number set: [2, 20], target: 21, just two numbers left.\n     |- Try 20 + 2 = 22. Evaluate 22 != 21, drop this branch.\n     |- Try 20 - 2 = 18. Evaluate 18 != 21, drop this branch.\n     |- Try 20 * 2 = 40. Evaluate 40 != 21, drop this branch.\n     |- Try 20 \/ 2 = 10. Evaluate 10 != 21, drop this branch.\n    |- Try 16 * 14 = 224. Add 224 to the number set. Current number set: [224, 20], target: 21, just two numbers left.\n     |- Try 224 + 20 = 244. Evaluate 244 != 21, drop this branch.\n     |- Try 224 - 20 = 204. Evaluate 204 != 21, drop this branch.\n     |- Try 224 * 20 = 4480. 4480 exceeds the maximum intermediate result, drop this branch.\n     |- Try 224 \/ 20 = 11.2. 11.2 is a decimal, drop this branch.\n    |- Try 16 \/ 14 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 18 - 2 = 16. Add 16 to the number set. Current number set: [16, 14, 16], target: 21. Options for choosing two numbers: [(16, 14), (16, 16), (14, 16)].\n   |- Pick two numbers (16, 14) (numbers left: [16]). Try possible operations.\n    |- Try 16 + 14 = 30. Add 30 to the number set. Current number set: [30, 16], target: 21, just two numbers left.\n     |- Try 30 + 16 = 46. Evaluate 46 != 21, drop this branch.\n     |- Try 30 - 16 = 14. Evaluate 14 != 21, drop this branch.\n     |- Try 30 * 16 = 480. Evaluate 480 != 21, drop this branch.\n     |- Try 30 \/ 16 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 16 - 14 = 2. Add 2 to the number set. Current number set: [2, 16], target: 21, just two numbers left.\n     |- Try 16 + 2 = 18. Evaluate 18 != 21, drop this branch.\n     |- Try 16 - 2 = 14. Evaluate 14 != 21, drop this branch.\n     |- Try 16 * 2 = 32. Evaluate 32 != 21, drop this branch.\n     |- Try 16 \/ 2 = 8. Evaluate 8 != 21, drop this branch.\n    |- Try 16 * 14 = 224. Add 224 to the number set. Current number set: [224, 16], target: 21, just two numbers left.\n     |- Try 224 + 16 = 240. Evaluate 240 != 21, drop this branch.\n     |- Try 224 - 16 = 208. Evaluate 208 != 21, drop this branch.\n     |- Try 224 * 16 = 3584. 3584 exceeds the maximum intermediate result, drop this branch.\n     |- Try 224 \/ 16 = 14. Evaluate 14 != 21, drop this branch.\n    |- Try 16 \/ 14 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (16, 16) (numbers left: [14]). Try possible operations.\n    |- Try 16 + 16 = 32. Add 32 to the number set. Current number set: [32, 14], target: 21, just two numbers left.\n     |- Try 32 + 14 = 46. Evaluate 46 != 21, drop this branch.\n     |- Try 32 - 14 = 18. Evaluate 18 != 21, drop this branch.\n     |- Try 32 * 14 = 448. Evaluate 448 != 21, drop this branch.\n     |- Try 32 \/ 14 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 16 - 16 = 0. Add 0 to the number set. Current number set: [0, 14], target: 21, just two numbers left.\n     |- Try 14 + 0 = 14. Evaluate 14 != 21, drop this branch.\n     |- Try 14 - 0 = 14. Evaluate 14 != 21, drop this branch.\n     |- Try 14 * 0 = 0. Evaluate 0 != 21, drop this branch.\n     |- Try 14 \/ 0 (invalid operation). drop this branch.\n    |- Try 16 * 16 = 256. Add 256 to the number set. Current number set: [256, 14], target: 21, just two numbers left.\n     |- Try 256 + 14 = 270. Evaluate 270 != 21, drop this branch.\n     |- Try 256 - 14 = 242. Evaluate 242 != 21, drop this branch.\n     |- Try 256 * 14 = 3584. 3584 exceeds the maximum intermediate result, drop this branch.\n     |- Try 256 \/ 14 = 18.3. 18.3 is a decimal, drop this branch.\n    |- Try 16 \/ 16 = 1. Add 1 to the number set. Current number set: [1, 14], target: 21, just two numbers left.\n     |- Try 14 + 1 = 15. Evaluate 15 != 21, drop this branch.\n     |- Try 14 - 1 = 13. Evaluate 13 != 21, drop this branch.\n     |- Try 14 * 1 = 14. Evaluate 14 != 21, drop this branch.\n     |- Try 14 \/ 1 = 14. Evaluate 14 != 21, drop this branch.\n   |- Pick two numbers (14, 16) (numbers left: [16]). Try possible operations.\n    |- Try 16 + 14 = 30. Add 30 to the number set. Current number set: [30, 16], target: 21, just two numbers left.\n     |- Try 30 + 16 = 46. Evaluate 46 != 21, drop this branch.\n     |- Try 30 - 16 = 14. Evaluate 14 != 21, drop this branch.\n     |- Try 30 * 16 = 480. Evaluate 480 != 21, drop this branch.\n     |- Try 30 \/ 16 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 16 - 14 = 2. Add 2 to the number set. Current number set: [2, 16], target: 21, just two numbers left.\n     |- Try 16 + 2 = 18. Evaluate 18 != 21, drop this branch.\n     |- Try 16 - 2 = 14. Evaluate 14 != 21, drop this branch.\n     |- Try 16 * 2 = 32. Evaluate 32 != 21, drop this branch.\n     |- Try 16 \/ 2 = 8. Evaluate 8 != 21, drop this branch.\n    |- Try 16 * 14 = 224. Add 224 to the number set. Current number set: [224, 16], target: 21, just two numbers left.\n     |- Try 224 + 16 = 240. Evaluate 240 != 21, drop this branch.\n     |- Try 224 - 16 = 208. Evaluate 208 != 21, drop this branch.\n     |- Try 224 * 16 = 3584. 3584 exceeds the maximum intermediate result, drop this branch.\n     |- Try 224 \/ 16 = 14. Evaluate 14 != 21, drop this branch.\n    |- Try 16 \/ 14 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 18 * 2 = 36. Add 36 to the number set. Current number set: [36, 14, 16], target: 21. Options for choosing two numbers: [(36, 14), (36, 16), (14, 16)].\n   |- Pick two numbers (36, 14) (numbers left: [16]). Try possible operations.\n    |- Try 36 + 14 = 50. Add 50 to the number set. Current number set: [50, 16], target: 21, just two numbers left.\n     |- Try 50 + 16 = 66. Evaluate 66 != 21, drop this branch.\n     |- Try 50 - 16 = 34. Evaluate 34 != 21, drop this branch.\n     |- Try 50 * 16 = 800. Evaluate 800 != 21, drop this branch.\n     |- Try 50 \/ 16 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 36 - 14 = 22. Add 22 to the number set. Current number set: [22, 16], target: 21, just two numbers left.\n     |- Try 22 + 16 = 38. Evaluate 38 != 21, drop this branch.\n     |- Try 22 - 16 = 6. Evaluate 6 != 21, drop this branch.\n     |- Try 22 * 16 = 352. Evaluate 352 != 21, drop this branch.\n     |- Try 22 \/ 16 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 36 * 14 = 504. Add 504 to the number set. Current number set: [504, 16], target: 21, just two numbers left.\n     |- Try 504 + 16 = 520. Evaluate 520 != 21, drop this branch.\n     |- Try 504 - 16 = 488. Evaluate 488 != 21, drop this branch.\n     |- Try 504 * 16 = 8064. 8064 exceeds the maximum intermediate result, drop this branch.\n     |- Try 504 \/ 16 = 31.5. 31.5 is a decimal, drop this branch.\n    |- Try 36 \/ 14 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (36, 16) (numbers left: [14]). Try possible operations.\n    |- Try 36 + 16 = 52. Add 52 to the number set. Current number set: [52, 14], target: 21, just two numbers left.\n     |- Try 52 + 14 = 66. Evaluate 66 != 21, drop this branch.\n     |- Try 52 - 14 = 38. Evaluate 38 != 21, drop this branch.\n     |- Try 52 * 14 = 728. Evaluate 728 != 21, drop this branch.\n     |- Try 52 \/ 14 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 36 - 16 = 20. Add 20 to the number set. Current number set: [20, 14], target: 21, just two numbers left.\n     |- Try 20 + 14 = 34. Evaluate 34 != 21, drop this branch.\n     |- Try 20 - 14 = 6. Evaluate 6 != 21, drop this branch.\n     |- Try 20 * 14 = 280. Evaluate 280 != 21, drop this branch.\n     |- Try 20 \/ 14 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 36 * 16 = 576. Add 576 to the number set. Current number set: [576, 14], target: 21, just two numbers left.\n     |- Try 576 + 14 = 590. Evaluate 590 != 21, drop this branch.\n     |- Try 576 - 14 = 562. Evaluate 562 != 21, drop this branch.\n     |- Try 576 * 14 = 8064. 8064 exceeds the maximum intermediate result, drop this branch.\n     |- Try 576 \/ 14 = 41.1. 41.1 is a decimal, drop this branch.\n    |- Try 36 \/ 16 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (14, 16) (numbers left: [36]). Try possible operations.\n    |- Try 16 + 14 = 30. Add 30 to the number set. Current number set: [30, 36], target: 21, just two numbers left.\n     |- Try 36 + 30 = 66. Evaluate 66 != 21, drop this branch.\n     |- Try 36 - 30 = 6. Evaluate 6 != 21, drop this branch.\n     |- Try 36 * 30 = 1080. Evaluate 1080 != 21, drop this branch.\n     |- Try 36 \/ 30 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 16 - 14 = 2. Add 2 to the number set. Current number set: [2, 36], target: 21, just two numbers left.\n     |- Try 36 + 2 = 38. Evaluate 38 != 21, drop this branch.\n     |- Try 36 - 2 = 34. Evaluate 34 != 21, drop this branch.\n     |- Try 36 * 2 = 72. Evaluate 72 != 21, drop this branch.\n     |- Try 36 \/ 2 = 18. Evaluate 18 != 21, drop this branch.\n    |- Try 16 * 14 = 224. Add 224 to the number set. Current number set: [224, 36], target: 21, just two numbers left.\n     |- Try 224 + 36 = 260. Evaluate 260 != 21, drop this branch.\n     |- Try 224 - 36 = 188. Evaluate 188 != 21, drop this branch.\n     |- Try 224 * 36 = 8064. 8064 exceeds the maximum intermediate result, drop this branch.\n     |- Try 224 \/ 36 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 16 \/ 14 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 18 \/ 2 = 9. Add 9 to the number set. Current number set: [9, 14, 16], target: 21. Options for choosing two numbers: [(9, 14), (9, 16), (14, 16)].\n   |- Pick two numbers (9, 14) (numbers left: [16]). Try possible operations.\n    |- Try 14 + 9 = 23. Add 23 to the number set. Current number set: [23, 16], target: 21, just two numbers left.\n     |- Try 23 + 16 = 39. Evaluate 39 != 21, drop this branch.\n     |- Try 23 - 16 = 7. Evaluate 7 != 21, drop this branch.\n     |- Try 23 * 16 = 368. Evaluate 368 != 21, drop this branch.\n     |- Try 23 \/ 16 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 14 - 9 = 5. Add 5 to the number set. Current number set: [5, 16], target: 21, just two numbers left.\n     |- Try 16 + 5 = 21. Evaluate 21 == 21, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 16 + 5 = 21\nThe step before: 14 - 9 = 5\nThe first step: 18 \/ 2 = 9\n\nOutput the solution in the required format:\n<Solution>\n18 \/ 2 = 9\n14 - 9 = 5\n16 + 5 = 21\n<\/Solution>\n","item":{"nums":[2,18,14,16],"solution":["18 \/ 2 = 9","14 - 9 = 5","16 + 5 = 21"],"target":21}}
+{"instance_id":"countdown_8k_124","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [4, 40, 21, 12]\nTarget: 19","reference_output":"# Search Procedure\nInitial number set: [4, 40, 21, 12], target: 19. Options for choosing two numbers: [(4, 40), (4, 21), (4, 12), (40, 21), (40, 12), (21, 12)].\n |- Pick two numbers (4, 40) (numbers left: [21, 12]). Try possible operations.\n  |- Try 40 + 4 = 44. Add 44 to the number set. Current number set: [44, 21, 12], target: 19. Options for choosing two numbers: [(44, 21), (44, 12), (21, 12)].\n   |- Pick two numbers (44, 21) (numbers left: [12]). Try possible operations.\n    |- Try 44 + 21 = 65. Add 65 to the number set. Current number set: [65, 12], target: 19, just two numbers left.\n     |- Try 65 + 12 = 77. Evaluate 77 != 19, drop this branch.\n     |- Try 65 - 12 = 53. Evaluate 53 != 19, drop this branch.\n     |- Try 65 * 12 = 780. Evaluate 780 != 19, drop this branch.\n     |- Try 65 \/ 12 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 44 - 21 = 23. Add 23 to the number set. Current number set: [23, 12], target: 19, just two numbers left.\n     |- Try 23 + 12 = 35. Evaluate 35 != 19, drop this branch.\n     |- Try 23 - 12 = 11. Evaluate 11 != 19, drop this branch.\n     |- Try 23 * 12 = 276. Evaluate 276 != 19, drop this branch.\n     |- Try 23 \/ 12 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 44 * 21 = 924. Add 924 to the number set. Current number set: [924, 12], target: 19, just two numbers left.\n     |- Try 924 + 12 = 936. Evaluate 936 != 19, drop this branch.\n     |- Try 924 - 12 = 912. Evaluate 912 != 19, drop this branch.\n     |- Try 924 * 12 = 11088. 11088 exceeds the maximum intermediate result, drop this branch.\n     |- Try 924 \/ 12 = 77. Evaluate 77 != 19, drop this branch.\n    |- Try 44 \/ 21 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (44, 12) (numbers left: [21]). Try possible operations.\n    |- Try 44 + 12 = 56. Add 56 to the number set. Current number set: [56, 21], target: 19, just two numbers left.\n     |- Try 56 + 21 = 77. Evaluate 77 != 19, drop this branch.\n     |- Try 56 - 21 = 35. Evaluate 35 != 19, drop this branch.\n     |- Try 56 * 21 = 1176. Evaluate 1176 != 19, drop this branch.\n     |- Try 56 \/ 21 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 44 - 12 = 32. Add 32 to the number set. Current number set: [32, 21], target: 19, just two numbers left.\n     |- Try 32 + 21 = 53. Evaluate 53 != 19, drop this branch.\n     |- Try 32 - 21 = 11. Evaluate 11 != 19, drop this branch.\n     |- Try 32 * 21 = 672. Evaluate 672 != 19, drop this branch.\n     |- Try 32 \/ 21 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 44 * 12 = 528. Add 528 to the number set. Current number set: [528, 21], target: 19, just two numbers left.\n     |- Try 528 + 21 = 549. Evaluate 549 != 19, drop this branch.\n     |- Try 528 - 21 = 507. Evaluate 507 != 19, drop this branch.\n     |- Try 528 * 21 = 11088. 11088 exceeds the maximum intermediate result, drop this branch.\n     |- Try 528 \/ 21 = 25.1. 25.1 is a decimal, drop this branch.\n    |- Try 44 \/ 12 = 3.7. 3.7 is a decimal, drop this branch.\n   |- Pick two numbers (21, 12) (numbers left: [44]). Try possible operations.\n    |- Try 21 + 12 = 33. Add 33 to the number set. Current number set: [33, 44], target: 19, just two numbers left.\n     |- Try 44 + 33 = 77. Evaluate 77 != 19, drop this branch.\n     |- Try 44 - 33 = 11. Evaluate 11 != 19, drop this branch.\n     |- Try 44 * 33 = 1452. Evaluate 1452 != 19, drop this branch.\n     |- Try 44 \/ 33 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 21 - 12 = 9. Add 9 to the number set. Current number set: [9, 44], target: 19, just two numbers left.\n     |- Try 44 + 9 = 53. Evaluate 53 != 19, drop this branch.\n     |- Try 44 - 9 = 35. Evaluate 35 != 19, drop this branch.\n     |- Try 44 * 9 = 396. Evaluate 396 != 19, drop this branch.\n     |- Try 44 \/ 9 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 21 * 12 = 252. Add 252 to the number set. Current number set: [252, 44], target: 19, just two numbers left.\n     |- Try 252 + 44 = 296. Evaluate 296 != 19, drop this branch.\n     |- Try 252 - 44 = 208. Evaluate 208 != 19, drop this branch.\n     |- Try 252 * 44 = 11088. 11088 exceeds the maximum intermediate result, drop this branch.\n     |- Try 252 \/ 44 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 21 \/ 12 = 1.8. 1.8 is a decimal, drop this branch.\n  |- Try 40 - 4 = 36. Add 36 to the number set. Current number set: [36, 21, 12], target: 19. Options for choosing two numbers: [(36, 21), (36, 12), (21, 12)].\n   |- Pick two numbers (36, 21) (numbers left: [12]). Try possible operations.\n    |- Try 36 + 21 = 57. Add 57 to the number set. Current number set: [57, 12], target: 19, just two numbers left.\n     |- Try 57 + 12 = 69. Evaluate 69 != 19, drop this branch.\n     |- Try 57 - 12 = 45. Evaluate 45 != 19, drop this branch.\n     |- Try 57 * 12 = 684. Evaluate 684 != 19, drop this branch.\n     |- Try 57 \/ 12 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 36 - 21 = 15. Add 15 to the number set. Current number set: [15, 12], target: 19, just two numbers left.\n     |- Try 15 + 12 = 27. Evaluate 27 != 19, drop this branch.\n     |- Try 15 - 12 = 3. Evaluate 3 != 19, drop this branch.\n     |- Try 15 * 12 = 180. Evaluate 180 != 19, drop this branch.\n     |- Try 15 \/ 12 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 36 * 21 = 756. Add 756 to the number set. Current number set: [756, 12], target: 19, just two numbers left.\n     |- Try 756 + 12 = 768. Evaluate 768 != 19, drop this branch.\n     |- Try 756 - 12 = 744. Evaluate 744 != 19, drop this branch.\n     |- Try 756 * 12 = 9072. 9072 exceeds the maximum intermediate result, drop this branch.\n     |- Try 756 \/ 12 = 63. Evaluate 63 != 19, drop this branch.\n    |- Try 36 \/ 21 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (36, 12) (numbers left: [21]). Try possible operations.\n    |- Try 36 + 12 = 48. Add 48 to the number set. Current number set: [48, 21], target: 19, just two numbers left.\n     |- Try 48 + 21 = 69. Evaluate 69 != 19, drop this branch.\n     |- Try 48 - 21 = 27. Evaluate 27 != 19, drop this branch.\n     |- Try 48 * 21 = 1008. Evaluate 1008 != 19, drop this branch.\n     |- Try 48 \/ 21 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 36 - 12 = 24. Add 24 to the number set. Current number set: [24, 21], target: 19, just two numbers left.\n     |- Try 24 + 21 = 45. Evaluate 45 != 19, drop this branch.\n     |- Try 24 - 21 = 3. Evaluate 3 != 19, drop this branch.\n     |- Try 24 * 21 = 504. Evaluate 504 != 19, drop this branch.\n     |- Try 24 \/ 21 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 36 * 12 = 432. Add 432 to the number set. Current number set: [432, 21], target: 19, just two numbers left.\n     |- Try 432 + 21 = 453. Evaluate 453 != 19, drop this branch.\n     |- Try 432 - 21 = 411. Evaluate 411 != 19, drop this branch.\n     |- Try 432 * 21 = 9072. 9072 exceeds the maximum intermediate result, drop this branch.\n     |- Try 432 \/ 21 = 20.6. 20.6 is a decimal, drop this branch.\n    |- Try 36 \/ 12 = 3. Add 3 to the number set. Current number set: [3, 21], target: 19, just two numbers left.\n     |- Try 21 + 3 = 24. Evaluate 24 != 19, drop this branch.\n     |- Try 21 - 3 = 18. Evaluate 18 != 19, drop this branch.\n     |- Try 21 * 3 = 63. Evaluate 63 != 19, drop this branch.\n     |- Try 21 \/ 3 = 7. Evaluate 7 != 19, drop this branch.\n   |- Pick two numbers (21, 12) (numbers left: [36]). Try possible operations.\n    |- Try 21 + 12 = 33. Add 33 to the number set. Current number set: [33, 36], target: 19, just two numbers left.\n     |- Try 36 + 33 = 69. Evaluate 69 != 19, drop this branch.\n     |- Try 36 - 33 = 3. Evaluate 3 != 19, drop this branch.\n     |- Try 36 * 33 = 1188. Evaluate 1188 != 19, drop this branch.\n     |- Try 36 \/ 33 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 21 - 12 = 9. Add 9 to the number set. Current number set: [9, 36], target: 19, just two numbers left.\n     |- Try 36 + 9 = 45. Evaluate 45 != 19, drop this branch.\n     |- Try 36 - 9 = 27. Evaluate 27 != 19, drop this branch.\n     |- Try 36 * 9 = 324. Evaluate 324 != 19, drop this branch.\n     |- Try 36 \/ 9 = 4. Evaluate 4 != 19, drop this branch.\n    |- Try 21 * 12 = 252. Add 252 to the number set. Current number set: [252, 36], target: 19, just two numbers left.\n     |- Try 252 + 36 = 288. Evaluate 288 != 19, drop this branch.\n     |- Try 252 - 36 = 216. Evaluate 216 != 19, drop this branch.\n     |- Try 252 * 36 = 9072. 9072 exceeds the maximum intermediate result, drop this branch.\n     |- Try 252 \/ 36 = 7. Evaluate 7 != 19, drop this branch.\n    |- Try 21 \/ 12 = 1.8. 1.8 is a decimal, drop this branch.\n  |- Try 40 * 4 = 160. Add 160 to the number set. Current number set: [160, 21, 12], target: 19. Options for choosing two numbers: [(160, 21), (160, 12), (21, 12)].\n   |- Pick two numbers (160, 21) (numbers left: [12]). Try possible operations.\n    |- Try 160 + 21 = 181. Add 181 to the number set. Current number set: [181, 12], target: 19, just two numbers left.\n     |- Try 181 + 12 = 193. Evaluate 193 != 19, drop this branch.\n     |- Try 181 - 12 = 169. Evaluate 169 != 19, drop this branch.\n     |- Try 181 * 12 = 2172. 2172 exceeds the maximum intermediate result, drop this branch.\n     |- Try 181 \/ 12 = 15.1. 15.1 is a decimal, drop this branch.\n    |- Try 160 - 21 = 139. Add 139 to the number set. Current number set: [139, 12], target: 19, just two numbers left.\n     |- Try 139 + 12 = 151. Evaluate 151 != 19, drop this branch.\n     |- Try 139 - 12 = 127. Evaluate 127 != 19, drop this branch.\n     |- Try 139 * 12 = 1668. Evaluate 1668 != 19, drop this branch.\n     |- Try 139 \/ 12 = 11.6. 11.6 is a decimal, drop this branch.\n    |- Try 160 * 21 = 3360. 3360 exceeds the maximum intermediate result, drop this branch.\n    |- Try 160 \/ 21 = 7.6. 7.6 is a decimal, drop this branch.\n   |- Pick two numbers (160, 12) (numbers left: [21]). Try possible operations.\n    |- Try 160 + 12 = 172. Add 172 to the number set. Current number set: [172, 21], target: 19, just two numbers left.\n     |- Try 172 + 21 = 193. Evaluate 193 != 19, drop this branch.\n     |- Try 172 - 21 = 151. Evaluate 151 != 19, drop this branch.\n     |- Try 172 * 21 = 3612. 3612 exceeds the maximum intermediate result, drop this branch.\n     |- Try 172 \/ 21 = 8.2. 8.2 is a decimal, drop this branch.\n    |- Try 160 - 12 = 148. Add 148 to the number set. Current number set: [148, 21], target: 19, just two numbers left.\n     |- Try 148 + 21 = 169. Evaluate 169 != 19, drop this branch.\n     |- Try 148 - 21 = 127. Evaluate 127 != 19, drop this branch.\n     |- Try 148 * 21 = 3108. 3108 exceeds the maximum intermediate result, drop this branch.\n     |- Try 148 \/ 21 = 7.0. 7.0 is a decimal, drop this branch.\n    |- Try 160 * 12 = 1920. Add 1920 to the number set. Current number set: [1920, 21], target: 19, just two numbers left.\n     |- Try 1920 + 21 = 1941. Evaluate 1941 != 19, drop this branch.\n     |- Try 1920 - 21 = 1899. Evaluate 1899 != 19, drop this branch.\n     |- Try 1920 * 21 = 40320. 40320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1920 \/ 21 = 91.4. 91.4 is a decimal, drop this branch.\n    |- Try 160 \/ 12 = 13.3. 13.3 is a decimal, drop this branch.\n   |- Pick two numbers (21, 12) (numbers left: [160]). Try possible operations.\n    |- Try 21 + 12 = 33. Add 33 to the number set. Current number set: [33, 160], target: 19, just two numbers left.\n     |- Try 160 + 33 = 193. Evaluate 193 != 19, drop this branch.\n     |- Try 160 - 33 = 127. Evaluate 127 != 19, drop this branch.\n     |- Try 160 * 33 = 5280. 5280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 160 \/ 33 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 21 - 12 = 9. Add 9 to the number set. Current number set: [9, 160], target: 19, just two numbers left.\n     |- Try 160 + 9 = 169. Evaluate 169 != 19, drop this branch.\n     |- Try 160 - 9 = 151. Evaluate 151 != 19, drop this branch.\n     |- Try 160 * 9 = 1440. Evaluate 1440 != 19, drop this branch.\n     |- Try 160 \/ 9 = 17.8. 17.8 is a decimal, drop this branch.\n    |- Try 21 * 12 = 252. Add 252 to the number set. Current number set: [252, 160], target: 19, just two numbers left.\n     |- Try 252 + 160 = 412. Evaluate 412 != 19, drop this branch.\n     |- Try 252 - 160 = 92. Evaluate 92 != 19, drop this branch.\n     |- Try 252 * 160 = 40320. 40320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 252 \/ 160 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 21 \/ 12 = 1.8. 1.8 is a decimal, drop this branch.\n  |- Try 40 \/ 4 = 10. Add 10 to the number set. Current number set: [10, 21, 12], target: 19. Options for choosing two numbers: [(10, 21), (10, 12), (21, 12)].\n   |- Pick two numbers (10, 21) (numbers left: [12]). Try possible operations.\n    |- Try 21 + 10 = 31. Add 31 to the number set. Current number set: [31, 12], target: 19, just two numbers left.\n     |- Try 31 + 12 = 43. Evaluate 43 != 19, drop this branch.\n     |- Try 31 - 12 = 19. Evaluate 19 == 19, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 31 - 12 = 19\nThe step before: 21 + 10 = 31\nThe first step: 40 \/ 4 = 10\n\nOutput the solution in the required format:\n<Solution>\n40 \/ 4 = 10\n21 + 10 = 31\n31 - 12 = 19\n<\/Solution>\n","item":{"nums":[4,40,21,12],"solution":["40 \/ 4 = 10","21 + 10 = 31","31 - 12 = 19"],"target":19}}
+{"instance_id":"countdown_8k_125","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [27, 5, 31, 2]\nTarget: 22","reference_output":"# Search Procedure\nInitial number set: [27, 5, 31, 2], target: 22. Options for choosing two numbers: [(27, 5), (27, 31), (27, 2), (5, 31), (5, 2), (31, 2)].\n |- Pick two numbers (27, 5) (numbers left: [31, 2]). Try possible operations.\n  |- Try 27 + 5 = 32. Add 32 to the number set. Current number set: [32, 31, 2], target: 22. Options for choosing two numbers: [(32, 31), (32, 2), (31, 2)].\n   |- Pick two numbers (32, 31) (numbers left: [2]). Try possible operations.\n    |- Try 32 + 31 = 63. Add 63 to the number set. Current number set: [63, 2], target: 22, just two numbers left.\n     |- Try 63 + 2 = 65. Evaluate 65 != 22, drop this branch.\n     |- Try 63 - 2 = 61. Evaluate 61 != 22, drop this branch.\n     |- Try 63 * 2 = 126. Evaluate 126 != 22, drop this branch.\n     |- Try 63 \/ 2 = 31.5. 31.5 is a decimal, drop this branch.\n    |- Try 32 - 31 = 1. Add 1 to the number set. Current number set: [1, 2], target: 22, just two numbers left.\n     |- Try 2 + 1 = 3. Evaluate 3 != 22, drop this branch.\n     |- Try 2 - 1 = 1. Evaluate 1 != 22, drop this branch.\n     |- Try 2 * 1 = 2. Evaluate 2 != 22, drop this branch.\n     |- Try 2 \/ 1 = 2. Evaluate 2 != 22, drop this branch.\n    |- Try 32 * 31 = 992. Add 992 to the number set. Current number set: [992, 2], target: 22, just two numbers left.\n     |- Try 992 + 2 = 994. Evaluate 994 != 22, drop this branch.\n     |- Try 992 - 2 = 990. Evaluate 990 != 22, drop this branch.\n     |- Try 992 * 2 = 1984. Evaluate 1984 != 22, drop this branch.\n     |- Try 992 \/ 2 = 496. Evaluate 496 != 22, drop this branch.\n    |- Try 32 \/ 31 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (32, 2) (numbers left: [31]). Try possible operations.\n    |- Try 32 + 2 = 34. Add 34 to the number set. Current number set: [34, 31], target: 22, just two numbers left.\n     |- Try 34 + 31 = 65. Evaluate 65 != 22, drop this branch.\n     |- Try 34 - 31 = 3. Evaluate 3 != 22, drop this branch.\n     |- Try 34 * 31 = 1054. Evaluate 1054 != 22, drop this branch.\n     |- Try 34 \/ 31 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 32 - 2 = 30. Add 30 to the number set. Current number set: [30, 31], target: 22, just two numbers left.\n     |- Try 31 + 30 = 61. Evaluate 61 != 22, drop this branch.\n     |- Try 31 - 30 = 1. Evaluate 1 != 22, drop this branch.\n     |- Try 31 * 30 = 930. Evaluate 930 != 22, drop this branch.\n     |- Try 31 \/ 30 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 32 * 2 = 64. Add 64 to the number set. Current number set: [64, 31], target: 22, just two numbers left.\n     |- Try 64 + 31 = 95. Evaluate 95 != 22, drop this branch.\n     |- Try 64 - 31 = 33. Evaluate 33 != 22, drop this branch.\n     |- Try 64 * 31 = 1984. Evaluate 1984 != 22, drop this branch.\n     |- Try 64 \/ 31 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 32 \/ 2 = 16. Add 16 to the number set. Current number set: [16, 31], target: 22, just two numbers left.\n     |- Try 31 + 16 = 47. Evaluate 47 != 22, drop this branch.\n     |- Try 31 - 16 = 15. Evaluate 15 != 22, drop this branch.\n     |- Try 31 * 16 = 496. Evaluate 496 != 22, drop this branch.\n     |- Try 31 \/ 16 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (31, 2) (numbers left: [32]). Try possible operations.\n    |- Try 31 + 2 = 33. Add 33 to the number set. Current number set: [33, 32], target: 22, just two numbers left.\n     |- Try 33 + 32 = 65. Evaluate 65 != 22, drop this branch.\n     |- Try 33 - 32 = 1. Evaluate 1 != 22, drop this branch.\n     |- Try 33 * 32 = 1056. Evaluate 1056 != 22, drop this branch.\n     |- Try 33 \/ 32 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 31 - 2 = 29. Add 29 to the number set. Current number set: [29, 32], target: 22, just two numbers left.\n     |- Try 32 + 29 = 61. Evaluate 61 != 22, drop this branch.\n     |- Try 32 - 29 = 3. Evaluate 3 != 22, drop this branch.\n     |- Try 32 * 29 = 928. Evaluate 928 != 22, drop this branch.\n     |- Try 32 \/ 29 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 31 * 2 = 62. Add 62 to the number set. Current number set: [62, 32], target: 22, just two numbers left.\n     |- Try 62 + 32 = 94. Evaluate 94 != 22, drop this branch.\n     |- Try 62 - 32 = 30. Evaluate 30 != 22, drop this branch.\n     |- Try 62 * 32 = 1984. Evaluate 1984 != 22, drop this branch.\n     |- Try 62 \/ 32 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 31 \/ 2 = 15.5. 15.5 is a decimal, drop this branch.\n  |- Try 27 - 5 = 22. Add 22 to the number set. Current number set: [22, 31, 2], target: 22. Options for choosing two numbers: [(22, 31), (22, 2), (31, 2)].\n   |- Pick two numbers (22, 31) (numbers left: [2]). Try possible operations.\n    |- Try 31 + 22 = 53. Add 53 to the number set. Current number set: [53, 2], target: 22, just two numbers left.\n     |- Try 53 + 2 = 55. Evaluate 55 != 22, drop this branch.\n     |- Try 53 - 2 = 51. Evaluate 51 != 22, drop this branch.\n     |- Try 53 * 2 = 106. Evaluate 106 != 22, drop this branch.\n     |- Try 53 \/ 2 = 26.5. 26.5 is a decimal, drop this branch.\n    |- Try 31 - 22 = 9. Add 9 to the number set. Current number set: [9, 2], target: 22, just two numbers left.\n     |- Try 9 + 2 = 11. Evaluate 11 != 22, drop this branch.\n     |- Try 9 - 2 = 7. Evaluate 7 != 22, drop this branch.\n     |- Try 9 * 2 = 18. Evaluate 18 != 22, drop this branch.\n     |- Try 9 \/ 2 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 31 * 22 = 682. Add 682 to the number set. Current number set: [682, 2], target: 22, just two numbers left.\n     |- Try 682 + 2 = 684. Evaluate 684 != 22, drop this branch.\n     |- Try 682 - 2 = 680. Evaluate 680 != 22, drop this branch.\n     |- Try 682 * 2 = 1364. Evaluate 1364 != 22, drop this branch.\n     |- Try 682 \/ 2 = 341. Evaluate 341 != 22, drop this branch.\n    |- Try 31 \/ 22 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (22, 2) (numbers left: [31]). Try possible operations.\n    |- Try 22 + 2 = 24. Add 24 to the number set. Current number set: [24, 31], target: 22, just two numbers left.\n     |- Try 31 + 24 = 55. Evaluate 55 != 22, drop this branch.\n     |- Try 31 - 24 = 7. Evaluate 7 != 22, drop this branch.\n     |- Try 31 * 24 = 744. Evaluate 744 != 22, drop this branch.\n     |- Try 31 \/ 24 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 22 - 2 = 20. Add 20 to the number set. Current number set: [20, 31], target: 22, just two numbers left.\n     |- Try 31 + 20 = 51. Evaluate 51 != 22, drop this branch.\n     |- Try 31 - 20 = 11. Evaluate 11 != 22, drop this branch.\n     |- Try 31 * 20 = 620. Evaluate 620 != 22, drop this branch.\n     |- Try 31 \/ 20 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 22 * 2 = 44. Add 44 to the number set. Current number set: [44, 31], target: 22, just two numbers left.\n     |- Try 44 + 31 = 75. Evaluate 75 != 22, drop this branch.\n     |- Try 44 - 31 = 13. Evaluate 13 != 22, drop this branch.\n     |- Try 44 * 31 = 1364. Evaluate 1364 != 22, drop this branch.\n     |- Try 44 \/ 31 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 22 \/ 2 = 11. Add 11 to the number set. Current number set: [11, 31], target: 22, just two numbers left.\n     |- Try 31 + 11 = 42. Evaluate 42 != 22, drop this branch.\n     |- Try 31 - 11 = 20. Evaluate 20 != 22, drop this branch.\n     |- Try 31 * 11 = 341. Evaluate 341 != 22, drop this branch.\n     |- Try 31 \/ 11 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (31, 2) (numbers left: [22]). Try possible operations.\n    |- Try 31 + 2 = 33. Add 33 to the number set. Current number set: [33, 22], target: 22, just two numbers left.\n     |- Try 33 + 22 = 55. Evaluate 55 != 22, drop this branch.\n     |- Try 33 - 22 = 11. Evaluate 11 != 22, drop this branch.\n     |- Try 33 * 22 = 726. Evaluate 726 != 22, drop this branch.\n     |- Try 33 \/ 22 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 31 - 2 = 29. Add 29 to the number set. Current number set: [29, 22], target: 22, just two numbers left.\n     |- Try 29 + 22 = 51. Evaluate 51 != 22, drop this branch.\n     |- Try 29 - 22 = 7. Evaluate 7 != 22, drop this branch.\n     |- Try 29 * 22 = 638. Evaluate 638 != 22, drop this branch.\n     |- Try 29 \/ 22 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 31 * 2 = 62. Add 62 to the number set. Current number set: [62, 22], target: 22, just two numbers left.\n     |- Try 62 + 22 = 84. Evaluate 84 != 22, drop this branch.\n     |- Try 62 - 22 = 40. Evaluate 40 != 22, drop this branch.\n     |- Try 62 * 22 = 1364. Evaluate 1364 != 22, drop this branch.\n     |- Try 62 \/ 22 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 31 \/ 2 = 15.5. 15.5 is a decimal, drop this branch.\n  |- Try 27 * 5 = 135. Add 135 to the number set. Current number set: [135, 31, 2], target: 22. Options for choosing two numbers: [(135, 31), (135, 2), (31, 2)].\n   |- Pick two numbers (135, 31) (numbers left: [2]). Try possible operations.\n    |- Try 135 + 31 = 166. Add 166 to the number set. Current number set: [166, 2], target: 22, just two numbers left.\n     |- Try 166 + 2 = 168. Evaluate 168 != 22, drop this branch.\n     |- Try 166 - 2 = 164. Evaluate 164 != 22, drop this branch.\n     |- Try 166 * 2 = 332. Evaluate 332 != 22, drop this branch.\n     |- Try 166 \/ 2 = 83. Evaluate 83 != 22, drop this branch.\n    |- Try 135 - 31 = 104. Add 104 to the number set. Current number set: [104, 2], target: 22, just two numbers left.\n     |- Try 104 + 2 = 106. Evaluate 106 != 22, drop this branch.\n     |- Try 104 - 2 = 102. Evaluate 102 != 22, drop this branch.\n     |- Try 104 * 2 = 208. Evaluate 208 != 22, drop this branch.\n     |- Try 104 \/ 2 = 52. Evaluate 52 != 22, drop this branch.\n    |- Try 135 * 31 = 4185. 4185 exceeds the maximum intermediate result, drop this branch.\n    |- Try 135 \/ 31 = 4.4. 4.4 is a decimal, drop this branch.\n   |- Pick two numbers (135, 2) (numbers left: [31]). Try possible operations.\n    |- Try 135 + 2 = 137. Add 137 to the number set. Current number set: [137, 31], target: 22, just two numbers left.\n     |- Try 137 + 31 = 168. Evaluate 168 != 22, drop this branch.\n     |- Try 137 - 31 = 106. Evaluate 106 != 22, drop this branch.\n     |- Try 137 * 31 = 4247. 4247 exceeds the maximum intermediate result, drop this branch.\n     |- Try 137 \/ 31 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 135 - 2 = 133. Add 133 to the number set. Current number set: [133, 31], target: 22, just two numbers left.\n     |- Try 133 + 31 = 164. Evaluate 164 != 22, drop this branch.\n     |- Try 133 - 31 = 102. Evaluate 102 != 22, drop this branch.\n     |- Try 133 * 31 = 4123. 4123 exceeds the maximum intermediate result, drop this branch.\n     |- Try 133 \/ 31 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 135 * 2 = 270. Add 270 to the number set. Current number set: [270, 31], target: 22, just two numbers left.\n     |- Try 270 + 31 = 301. Evaluate 301 != 22, drop this branch.\n     |- Try 270 - 31 = 239. Evaluate 239 != 22, drop this branch.\n     |- Try 270 * 31 = 8370. 8370 exceeds the maximum intermediate result, drop this branch.\n     |- Try 270 \/ 31 = 8.7. 8.7 is a decimal, drop this branch.\n    |- Try 135 \/ 2 = 67.5. 67.5 is a decimal, drop this branch.\n   |- Pick two numbers (31, 2) (numbers left: [135]). Try possible operations.\n    |- Try 31 + 2 = 33. Add 33 to the number set. Current number set: [33, 135], target: 22, just two numbers left.\n     |- Try 135 + 33 = 168. Evaluate 168 != 22, drop this branch.\n     |- Try 135 - 33 = 102. Evaluate 102 != 22, drop this branch.\n     |- Try 135 * 33 = 4455. 4455 exceeds the maximum intermediate result, drop this branch.\n     |- Try 135 \/ 33 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 31 - 2 = 29. Add 29 to the number set. Current number set: [29, 135], target: 22, just two numbers left.\n     |- Try 135 + 29 = 164. Evaluate 164 != 22, drop this branch.\n     |- Try 135 - 29 = 106. Evaluate 106 != 22, drop this branch.\n     |- Try 135 * 29 = 3915. 3915 exceeds the maximum intermediate result, drop this branch.\n     |- Try 135 \/ 29 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 31 * 2 = 62. Add 62 to the number set. Current number set: [62, 135], target: 22, just two numbers left.\n     |- Try 135 + 62 = 197. Evaluate 197 != 22, drop this branch.\n     |- Try 135 - 62 = 73. Evaluate 73 != 22, drop this branch.\n     |- Try 135 * 62 = 8370. 8370 exceeds the maximum intermediate result, drop this branch.\n     |- Try 135 \/ 62 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 31 \/ 2 = 15.5. 15.5 is a decimal, drop this branch.\n  |- Try 27 \/ 5 = 5.4. 5.4 is a decimal, drop this branch.\n |- Pick two numbers (27, 31) (numbers left: [5, 2]). Try possible operations.\n  |- Try 31 + 27 = 58. Add 58 to the number set. Current number set: [58, 5, 2], target: 22. Options for choosing two numbers: [(58, 5), (58, 2), (5, 2)].\n   |- Pick two numbers (58, 5) (numbers left: [2]). Try possible operations.\n    |- Try 58 + 5 = 63. Add 63 to the number set. Current number set: [63, 2], target: 22, just two numbers left.\n     |- Try 63 + 2 = 65. Evaluate 65 != 22, drop this branch.\n     |- Try 63 - 2 = 61. Evaluate 61 != 22, drop this branch.\n     |- Try 63 * 2 = 126. Evaluate 126 != 22, drop this branch.\n     |- Try 63 \/ 2 = 31.5. 31.5 is a decimal, drop this branch.\n    |- Try 58 - 5 = 53. Add 53 to the number set. Current number set: [53, 2], target: 22, just two numbers left.\n     |- Try 53 + 2 = 55. Evaluate 55 != 22, drop this branch.\n     |- Try 53 - 2 = 51. Evaluate 51 != 22, drop this branch.\n     |- Try 53 * 2 = 106. Evaluate 106 != 22, drop this branch.\n     |- Try 53 \/ 2 = 26.5. 26.5 is a decimal, drop this branch.\n    |- Try 58 * 5 = 290. Add 290 to the number set. Current number set: [290, 2], target: 22, just two numbers left.\n     |- Try 290 + 2 = 292. Evaluate 292 != 22, drop this branch.\n     |- Try 290 - 2 = 288. Evaluate 288 != 22, drop this branch.\n     |- Try 290 * 2 = 580. Evaluate 580 != 22, drop this branch.\n     |- Try 290 \/ 2 = 145. Evaluate 145 != 22, drop this branch.\n    |- Try 58 \/ 5 = 11.6. 11.6 is a decimal, drop this branch.\n   |- Pick two numbers (58, 2) (numbers left: [5]). Try possible operations.\n    |- Try 58 + 2 = 60. Add 60 to the number set. Current number set: [60, 5], target: 22, just two numbers left.\n     |- Try 60 + 5 = 65. Evaluate 65 != 22, drop this branch.\n     |- Try 60 - 5 = 55. Evaluate 55 != 22, drop this branch.\n     |- Try 60 * 5 = 300. Evaluate 300 != 22, drop this branch.\n     |- Try 60 \/ 5 = 12. Evaluate 12 != 22, drop this branch.\n    |- Try 58 - 2 = 56. Add 56 to the number set. Current number set: [56, 5], target: 22, just two numbers left.\n     |- Try 56 + 5 = 61. Evaluate 61 != 22, drop this branch.\n     |- Try 56 - 5 = 51. Evaluate 51 != 22, drop this branch.\n     |- Try 56 * 5 = 280. Evaluate 280 != 22, drop this branch.\n     |- Try 56 \/ 5 = 11.2. 11.2 is a decimal, drop this branch.\n    |- Try 58 * 2 = 116. Add 116 to the number set. Current number set: [116, 5], target: 22, just two numbers left.\n     |- Try 116 + 5 = 121. Evaluate 121 != 22, drop this branch.\n     |- Try 116 - 5 = 111. Evaluate 111 != 22, drop this branch.\n     |- Try 116 * 5 = 580. Evaluate 580 != 22, drop this branch.\n     |- Try 116 \/ 5 = 23.2. 23.2 is a decimal, drop this branch.\n    |- Try 58 \/ 2 = 29. Add 29 to the number set. Current number set: [29, 5], target: 22, just two numbers left.\n     |- Try 29 + 5 = 34. Evaluate 34 != 22, drop this branch.\n     |- Try 29 - 5 = 24. Evaluate 24 != 22, drop this branch.\n     |- Try 29 * 5 = 145. Evaluate 145 != 22, drop this branch.\n     |- Try 29 \/ 5 = 5.8. 5.8 is a decimal, drop this branch.\n   |- Pick two numbers (5, 2) (numbers left: [58]). Try possible operations.\n    |- Try 5 + 2 = 7. Add 7 to the number set. Current number set: [7, 58], target: 22, just two numbers left.\n     |- Try 58 + 7 = 65. Evaluate 65 != 22, drop this branch.\n     |- Try 58 - 7 = 51. Evaluate 51 != 22, drop this branch.\n     |- Try 58 * 7 = 406. Evaluate 406 != 22, drop this branch.\n     |- Try 58 \/ 7 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 5 - 2 = 3. Add 3 to the number set. Current number set: [3, 58], target: 22, just two numbers left.\n     |- Try 58 + 3 = 61. Evaluate 61 != 22, drop this branch.\n     |- Try 58 - 3 = 55. Evaluate 55 != 22, drop this branch.\n     |- Try 58 * 3 = 174. Evaluate 174 != 22, drop this branch.\n     |- Try 58 \/ 3 = 19.3. 19.3 is a decimal, drop this branch.\n    |- Try 5 * 2 = 10. Add 10 to the number set. Current number set: [10, 58], target: 22, just two numbers left.\n     |- Try 58 + 10 = 68. Evaluate 68 != 22, drop this branch.\n     |- Try 58 - 10 = 48. Evaluate 48 != 22, drop this branch.\n     |- Try 58 * 10 = 580. Evaluate 580 != 22, drop this branch.\n     |- Try 58 \/ 10 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 5 \/ 2 = 2.5. 2.5 is a decimal, drop this branch.\n  |- Try 31 - 27 = 4. Add 4 to the number set. Current number set: [4, 5, 2], target: 22. Options for choosing two numbers: [(4, 5), (4, 2), (5, 2)].\n   |- Pick two numbers (4, 5) (numbers left: [2]). Try possible operations.\n    |- Try 5 + 4 = 9. Add 9 to the number set. Current number set: [9, 2], target: 22, just two numbers left.\n     |- Try 9 + 2 = 11. Evaluate 11 != 22, drop this branch.\n     |- Try 9 - 2 = 7. Evaluate 7 != 22, drop this branch.\n     |- Try 9 * 2 = 18. Evaluate 18 != 22, drop this branch.\n     |- Try 9 \/ 2 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 5 - 4 = 1. Add 1 to the number set. Current number set: [1, 2], target: 22, just two numbers left.\n     |- Try 2 + 1 = 3. Evaluate 3 != 22, drop this branch.\n     |- Try 2 - 1 = 1. Evaluate 1 != 22, drop this branch.\n     |- Try 2 * 1 = 2. Evaluate 2 != 22, drop this branch.\n     |- Try 2 \/ 1 = 2. Evaluate 2 != 22, drop this branch.\n    |- Try 5 * 4 = 20. Add 20 to the number set. Current number set: [20, 2], target: 22, just two numbers left.\n     |- Try 20 + 2 = 22. Evaluate 22 == 22, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 20 + 2 = 22\nThe step before: 5 * 4 = 20\nThe first step: 31 - 27 = 4\n\nOutput the solution in the required format:\n<Solution>\n31 - 27 = 4\n5 * 4 = 20\n20 + 2 = 22\n<\/Solution>\n","item":{"nums":[27,5,31,2],"solution":["31 - 27 = 4","5 * 4 = 20","20 + 2 = 22"],"target":22}}
+{"instance_id":"countdown_8k_126","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [19, 3, 11, 48]\nTarget: 38","reference_output":"# Search Procedure\nInitial number set: [19, 3, 11, 48], target: 38. Options for choosing two numbers: [(19, 3), (19, 11), (19, 48), (3, 11), (3, 48), (11, 48)].\n |- Pick two numbers (19, 3) (numbers left: [11, 48]). Try possible operations.\n  |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 11, 48], target: 38. Options for choosing two numbers: [(22, 11), (22, 48), (11, 48)].\n   |- Pick two numbers (22, 11) (numbers left: [48]). Try possible operations.\n    |- Try 22 + 11 = 33. Add 33 to the number set. Current number set: [33, 48], target: 38, just two numbers left.\n     |- Try 48 + 33 = 81. Evaluate 81 != 38, drop this branch.\n     |- Try 48 - 33 = 15. Evaluate 15 != 38, drop this branch.\n     |- Try 48 * 33 = 1584. Evaluate 1584 != 38, drop this branch.\n     |- Try 48 \/ 33 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 22 - 11 = 11. Add 11 to the number set. Current number set: [11, 48], target: 38, just two numbers left.\n     |- Try 48 + 11 = 59. Evaluate 59 != 38, drop this branch.\n     |- Try 48 - 11 = 37. Evaluate 37 != 38, drop this branch.\n     |- Try 48 * 11 = 528. Evaluate 528 != 38, drop this branch.\n     |- Try 48 \/ 11 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 22 * 11 = 242. Add 242 to the number set. Current number set: [242, 48], target: 38, just two numbers left.\n     |- Try 242 + 48 = 290. Evaluate 290 != 38, drop this branch.\n     |- Try 242 - 48 = 194. Evaluate 194 != 38, drop this branch.\n     |- Try 242 * 48 = 11616. 11616 exceeds the maximum intermediate result, drop this branch.\n     |- Try 242 \/ 48 = 5.0. 5.0 is a decimal, drop this branch.\n    |- Try 22 \/ 11 = 2. Add 2 to the number set. Current number set: [2, 48], target: 38, just two numbers left.\n     |- Try 48 + 2 = 50. Evaluate 50 != 38, drop this branch.\n     |- Try 48 - 2 = 46. Evaluate 46 != 38, drop this branch.\n     |- Try 48 * 2 = 96. Evaluate 96 != 38, drop this branch.\n     |- Try 48 \/ 2 = 24. Evaluate 24 != 38, drop this branch.\n   |- Pick two numbers (22, 48) (numbers left: [11]). Try possible operations.\n    |- Try 48 + 22 = 70. Add 70 to the number set. Current number set: [70, 11], target: 38, just two numbers left.\n     |- Try 70 + 11 = 81. Evaluate 81 != 38, drop this branch.\n     |- Try 70 - 11 = 59. Evaluate 59 != 38, drop this branch.\n     |- Try 70 * 11 = 770. Evaluate 770 != 38, drop this branch.\n     |- Try 70 \/ 11 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 48 - 22 = 26. Add 26 to the number set. Current number set: [26, 11], target: 38, just two numbers left.\n     |- Try 26 + 11 = 37. Evaluate 37 != 38, drop this branch.\n     |- Try 26 - 11 = 15. Evaluate 15 != 38, drop this branch.\n     |- Try 26 * 11 = 286. Evaluate 286 != 38, drop this branch.\n     |- Try 26 \/ 11 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 48 * 22 = 1056. Add 1056 to the number set. Current number set: [1056, 11], target: 38, just two numbers left.\n     |- Try 1056 + 11 = 1067. Evaluate 1067 != 38, drop this branch.\n     |- Try 1056 - 11 = 1045. Evaluate 1045 != 38, drop this branch.\n     |- Try 1056 * 11 = 11616. 11616 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1056 \/ 11 = 96. Evaluate 96 != 38, drop this branch.\n    |- Try 48 \/ 22 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (11, 48) (numbers left: [22]). Try possible operations.\n    |- Try 48 + 11 = 59. Add 59 to the number set. Current number set: [59, 22], target: 38, just two numbers left.\n     |- Try 59 + 22 = 81. Evaluate 81 != 38, drop this branch.\n     |- Try 59 - 22 = 37. Evaluate 37 != 38, drop this branch.\n     |- Try 59 * 22 = 1298. Evaluate 1298 != 38, drop this branch.\n     |- Try 59 \/ 22 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 48 - 11 = 37. Add 37 to the number set. Current number set: [37, 22], target: 38, just two numbers left.\n     |- Try 37 + 22 = 59. Evaluate 59 != 38, drop this branch.\n     |- Try 37 - 22 = 15. Evaluate 15 != 38, drop this branch.\n     |- Try 37 * 22 = 814. Evaluate 814 != 38, drop this branch.\n     |- Try 37 \/ 22 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 48 * 11 = 528. Add 528 to the number set. Current number set: [528, 22], target: 38, just two numbers left.\n     |- Try 528 + 22 = 550. Evaluate 550 != 38, drop this branch.\n     |- Try 528 - 22 = 506. Evaluate 506 != 38, drop this branch.\n     |- Try 528 * 22 = 11616. 11616 exceeds the maximum intermediate result, drop this branch.\n     |- Try 528 \/ 22 = 24. Evaluate 24 != 38, drop this branch.\n    |- Try 48 \/ 11 = 4.4. 4.4 is a decimal, drop this branch.\n  |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 11, 48], target: 38. Options for choosing two numbers: [(16, 11), (16, 48), (11, 48)].\n   |- Pick two numbers (16, 11) (numbers left: [48]). Try possible operations.\n    |- Try 16 + 11 = 27. Add 27 to the number set. Current number set: [27, 48], target: 38, just two numbers left.\n     |- Try 48 + 27 = 75. Evaluate 75 != 38, drop this branch.\n     |- Try 48 - 27 = 21. Evaluate 21 != 38, drop this branch.\n     |- Try 48 * 27 = 1296. Evaluate 1296 != 38, drop this branch.\n     |- Try 48 \/ 27 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 16 - 11 = 5. Add 5 to the number set. Current number set: [5, 48], target: 38, just two numbers left.\n     |- Try 48 + 5 = 53. Evaluate 53 != 38, drop this branch.\n     |- Try 48 - 5 = 43. Evaluate 43 != 38, drop this branch.\n     |- Try 48 * 5 = 240. Evaluate 240 != 38, drop this branch.\n     |- Try 48 \/ 5 = 9.6. 9.6 is a decimal, drop this branch.\n    |- Try 16 * 11 = 176. Add 176 to the number set. Current number set: [176, 48], target: 38, just two numbers left.\n     |- Try 176 + 48 = 224. Evaluate 224 != 38, drop this branch.\n     |- Try 176 - 48 = 128. Evaluate 128 != 38, drop this branch.\n     |- Try 176 * 48 = 8448. 8448 exceeds the maximum intermediate result, drop this branch.\n     |- Try 176 \/ 48 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 16 \/ 11 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (16, 48) (numbers left: [11]). Try possible operations.\n    |- Try 48 + 16 = 64. Add 64 to the number set. Current number set: [64, 11], target: 38, just two numbers left.\n     |- Try 64 + 11 = 75. Evaluate 75 != 38, drop this branch.\n     |- Try 64 - 11 = 53. Evaluate 53 != 38, drop this branch.\n     |- Try 64 * 11 = 704. Evaluate 704 != 38, drop this branch.\n     |- Try 64 \/ 11 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 48 - 16 = 32. Add 32 to the number set. Current number set: [32, 11], target: 38, just two numbers left.\n     |- Try 32 + 11 = 43. Evaluate 43 != 38, drop this branch.\n     |- Try 32 - 11 = 21. Evaluate 21 != 38, drop this branch.\n     |- Try 32 * 11 = 352. Evaluate 352 != 38, drop this branch.\n     |- Try 32 \/ 11 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 48 * 16 = 768. Add 768 to the number set. Current number set: [768, 11], target: 38, just two numbers left.\n     |- Try 768 + 11 = 779. Evaluate 779 != 38, drop this branch.\n     |- Try 768 - 11 = 757. Evaluate 757 != 38, drop this branch.\n     |- Try 768 * 11 = 8448. 8448 exceeds the maximum intermediate result, drop this branch.\n     |- Try 768 \/ 11 = 69.8. 69.8 is a decimal, drop this branch.\n    |- Try 48 \/ 16 = 3. Add 3 to the number set. Current number set: [3, 11], target: 38, just two numbers left.\n     |- Try 11 + 3 = 14. Evaluate 14 != 38, drop this branch.\n     |- Try 11 - 3 = 8. Evaluate 8 != 38, drop this branch.\n     |- Try 11 * 3 = 33. Evaluate 33 != 38, drop this branch.\n     |- Try 11 \/ 3 = 3.7. 3.7 is a decimal, drop this branch.\n   |- Pick two numbers (11, 48) (numbers left: [16]). Try possible operations.\n    |- Try 48 + 11 = 59. Add 59 to the number set. Current number set: [59, 16], target: 38, just two numbers left.\n     |- Try 59 + 16 = 75. Evaluate 75 != 38, drop this branch.\n     |- Try 59 - 16 = 43. Evaluate 43 != 38, drop this branch.\n     |- Try 59 * 16 = 944. Evaluate 944 != 38, drop this branch.\n     |- Try 59 \/ 16 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 48 - 11 = 37. Add 37 to the number set. Current number set: [37, 16], target: 38, just two numbers left.\n     |- Try 37 + 16 = 53. Evaluate 53 != 38, drop this branch.\n     |- Try 37 - 16 = 21. Evaluate 21 != 38, drop this branch.\n     |- Try 37 * 16 = 592. Evaluate 592 != 38, drop this branch.\n     |- Try 37 \/ 16 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 48 * 11 = 528. Add 528 to the number set. Current number set: [528, 16], target: 38, just two numbers left.\n     |- Try 528 + 16 = 544. Evaluate 544 != 38, drop this branch.\n     |- Try 528 - 16 = 512. Evaluate 512 != 38, drop this branch.\n     |- Try 528 * 16 = 8448. 8448 exceeds the maximum intermediate result, drop this branch.\n     |- Try 528 \/ 16 = 33. Evaluate 33 != 38, drop this branch.\n    |- Try 48 \/ 11 = 4.4. 4.4 is a decimal, drop this branch.\n  |- Try 19 * 3 = 57. Add 57 to the number set. Current number set: [57, 11, 48], target: 38. Options for choosing two numbers: [(57, 11), (57, 48), (11, 48)].\n   |- Pick two numbers (57, 11) (numbers left: [48]). Try possible operations.\n    |- Try 57 + 11 = 68. Add 68 to the number set. Current number set: [68, 48], target: 38, just two numbers left.\n     |- Try 68 + 48 = 116. Evaluate 116 != 38, drop this branch.\n     |- Try 68 - 48 = 20. Evaluate 20 != 38, drop this branch.\n     |- Try 68 * 48 = 3264. 3264 exceeds the maximum intermediate result, drop this branch.\n     |- Try 68 \/ 48 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 57 - 11 = 46. Add 46 to the number set. Current number set: [46, 48], target: 38, just two numbers left.\n     |- Try 48 + 46 = 94. Evaluate 94 != 38, drop this branch.\n     |- Try 48 - 46 = 2. Evaluate 2 != 38, drop this branch.\n     |- Try 48 * 46 = 2208. 2208 exceeds the maximum intermediate result, drop this branch.\n     |- Try 48 \/ 46 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 57 * 11 = 627. Add 627 to the number set. Current number set: [627, 48], target: 38, just two numbers left.\n     |- Try 627 + 48 = 675. Evaluate 675 != 38, drop this branch.\n     |- Try 627 - 48 = 579. Evaluate 579 != 38, drop this branch.\n     |- Try 627 * 48 = 30096. 30096 exceeds the maximum intermediate result, drop this branch.\n     |- Try 627 \/ 48 = 13.1. 13.1 is a decimal, drop this branch.\n    |- Try 57 \/ 11 = 5.2. 5.2 is a decimal, drop this branch.\n   |- Pick two numbers (57, 48) (numbers left: [11]). Try possible operations.\n    |- Try 57 + 48 = 105. Add 105 to the number set. Current number set: [105, 11], target: 38, just two numbers left.\n     |- Try 105 + 11 = 116. Evaluate 116 != 38, drop this branch.\n     |- Try 105 - 11 = 94. Evaluate 94 != 38, drop this branch.\n     |- Try 105 * 11 = 1155. Evaluate 1155 != 38, drop this branch.\n     |- Try 105 \/ 11 = 9.5. 9.5 is a decimal, drop this branch.\n    |- Try 57 - 48 = 9. Add 9 to the number set. Current number set: [9, 11], target: 38, just two numbers left.\n     |- Try 11 + 9 = 20. Evaluate 20 != 38, drop this branch.\n     |- Try 11 - 9 = 2. Evaluate 2 != 38, drop this branch.\n     |- Try 11 * 9 = 99. Evaluate 99 != 38, drop this branch.\n     |- Try 11 \/ 9 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 57 * 48 = 2736. 2736 exceeds the maximum intermediate result, drop this branch.\n    |- Try 57 \/ 48 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (11, 48) (numbers left: [57]). Try possible operations.\n    |- Try 48 + 11 = 59. Add 59 to the number set. Current number set: [59, 57], target: 38, just two numbers left.\n     |- Try 59 + 57 = 116. Evaluate 116 != 38, drop this branch.\n     |- Try 59 - 57 = 2. Evaluate 2 != 38, drop this branch.\n     |- Try 59 * 57 = 3363. 3363 exceeds the maximum intermediate result, drop this branch.\n     |- Try 59 \/ 57 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 48 - 11 = 37. Add 37 to the number set. Current number set: [37, 57], target: 38, just two numbers left.\n     |- Try 57 + 37 = 94. Evaluate 94 != 38, drop this branch.\n     |- Try 57 - 37 = 20. Evaluate 20 != 38, drop this branch.\n     |- Try 57 * 37 = 2109. 2109 exceeds the maximum intermediate result, drop this branch.\n     |- Try 57 \/ 37 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 48 * 11 = 528. Add 528 to the number set. Current number set: [528, 57], target: 38, just two numbers left.\n     |- Try 528 + 57 = 585. Evaluate 585 != 38, drop this branch.\n     |- Try 528 - 57 = 471. Evaluate 471 != 38, drop this branch.\n     |- Try 528 * 57 = 30096. 30096 exceeds the maximum intermediate result, drop this branch.\n     |- Try 528 \/ 57 = 9.3. 9.3 is a decimal, drop this branch.\n    |- Try 48 \/ 11 = 4.4. 4.4 is a decimal, drop this branch.\n  |- Try 19 \/ 3 = 6.3. 6.3 is a decimal, drop this branch.\n |- Pick two numbers (19, 11) (numbers left: [3, 48]). Try possible operations.\n  |- Try 19 + 11 = 30. Add 30 to the number set. Current number set: [30, 3, 48], target: 38. Options for choosing two numbers: [(30, 3), (30, 48), (3, 48)].\n   |- Pick two numbers (30, 3) (numbers left: [48]). Try possible operations.\n    |- Try 30 + 3 = 33. Add 33 to the number set. Current number set: [33, 48], target: 38, just two numbers left.\n     |- Try 48 + 33 = 81. Evaluate 81 != 38, drop this branch.\n     |- Try 48 - 33 = 15. Evaluate 15 != 38, drop this branch.\n     |- Try 48 * 33 = 1584. Evaluate 1584 != 38, drop this branch.\n     |- Try 48 \/ 33 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 30 - 3 = 27. Add 27 to the number set. Current number set: [27, 48], target: 38, just two numbers left.\n     |- Try 48 + 27 = 75. Evaluate 75 != 38, drop this branch.\n     |- Try 48 - 27 = 21. Evaluate 21 != 38, drop this branch.\n     |- Try 48 * 27 = 1296. Evaluate 1296 != 38, drop this branch.\n     |- Try 48 \/ 27 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 30 * 3 = 90. Add 90 to the number set. Current number set: [90, 48], target: 38, just two numbers left.\n     |- Try 90 + 48 = 138. Evaluate 138 != 38, drop this branch.\n     |- Try 90 - 48 = 42. Evaluate 42 != 38, drop this branch.\n     |- Try 90 * 48 = 4320. 4320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 90 \/ 48 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 30 \/ 3 = 10. Add 10 to the number set. Current number set: [10, 48], target: 38, just two numbers left.\n     |- Try 48 + 10 = 58. Evaluate 58 != 38, drop this branch.\n     |- Try 48 - 10 = 38. Evaluate 38 == 38, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 48 - 10 = 38\nThe step before: 30 \/ 3 = 10\nThe first step: 19 + 11 = 30\n\nOutput the solution in the required format:\n<Solution>\n19 + 11 = 30\n30 \/ 3 = 10\n48 - 10 = 38\n<\/Solution>\n","item":{"nums":[19,3,11,48],"solution":["19 + 11 = 30","30 \/ 3 = 10","48 - 10 = 38"],"target":38}}
+{"instance_id":"countdown_8k_127","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [26, 8, 18, 37]\nTarget: 27","reference_output":"# Search Procedure\nInitial number set: [26, 8, 18, 37], target: 27. Options for choosing two numbers: [(26, 8), (26, 18), (26, 37), (8, 18), (8, 37), (18, 37)].\n |- Pick two numbers (26, 8) (numbers left: [18, 37]). Try possible operations.\n  |- Try 26 + 8 = 34. Add 34 to the number set. Current number set: [34, 18, 37], target: 27. Options for choosing two numbers: [(34, 18), (34, 37), (18, 37)].\n   |- Pick two numbers (34, 18) (numbers left: [37]). Try possible operations.\n    |- Try 34 + 18 = 52. Add 52 to the number set. Current number set: [52, 37], target: 27, just two numbers left.\n     |- Try 52 + 37 = 89. Evaluate 89 != 27, drop this branch.\n     |- Try 52 - 37 = 15. Evaluate 15 != 27, drop this branch.\n     |- Try 52 * 37 = 1924. Evaluate 1924 != 27, drop this branch.\n     |- Try 52 \/ 37 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 34 - 18 = 16. Add 16 to the number set. Current number set: [16, 37], target: 27, just two numbers left.\n     |- Try 37 + 16 = 53. Evaluate 53 != 27, drop this branch.\n     |- Try 37 - 16 = 21. Evaluate 21 != 27, drop this branch.\n     |- Try 37 * 16 = 592. Evaluate 592 != 27, drop this branch.\n     |- Try 37 \/ 16 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 34 * 18 = 612. Add 612 to the number set. Current number set: [612, 37], target: 27, just two numbers left.\n     |- Try 612 + 37 = 649. Evaluate 649 != 27, drop this branch.\n     |- Try 612 - 37 = 575. Evaluate 575 != 27, drop this branch.\n     |- Try 612 * 37 = 22644. 22644 exceeds the maximum intermediate result, drop this branch.\n     |- Try 612 \/ 37 = 16.5. 16.5 is a decimal, drop this branch.\n    |- Try 34 \/ 18 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (34, 37) (numbers left: [18]). Try possible operations.\n    |- Try 37 + 34 = 71. Add 71 to the number set. Current number set: [71, 18], target: 27, just two numbers left.\n     |- Try 71 + 18 = 89. Evaluate 89 != 27, drop this branch.\n     |- Try 71 - 18 = 53. Evaluate 53 != 27, drop this branch.\n     |- Try 71 * 18 = 1278. Evaluate 1278 != 27, drop this branch.\n     |- Try 71 \/ 18 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 37 - 34 = 3. Add 3 to the number set. Current number set: [3, 18], target: 27, just two numbers left.\n     |- Try 18 + 3 = 21. Evaluate 21 != 27, drop this branch.\n     |- Try 18 - 3 = 15. Evaluate 15 != 27, drop this branch.\n     |- Try 18 * 3 = 54. Evaluate 54 != 27, drop this branch.\n     |- Try 18 \/ 3 = 6. Evaluate 6 != 27, drop this branch.\n    |- Try 37 * 34 = 1258. Add 1258 to the number set. Current number set: [1258, 18], target: 27, just two numbers left.\n     |- Try 1258 + 18 = 1276. Evaluate 1276 != 27, drop this branch.\n     |- Try 1258 - 18 = 1240. Evaluate 1240 != 27, drop this branch.\n     |- Try 1258 * 18 = 22644. 22644 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1258 \/ 18 = 69.9. 69.9 is a decimal, drop this branch.\n    |- Try 37 \/ 34 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (18, 37) (numbers left: [34]). Try possible operations.\n    |- Try 37 + 18 = 55. Add 55 to the number set. Current number set: [55, 34], target: 27, just two numbers left.\n     |- Try 55 + 34 = 89. Evaluate 89 != 27, drop this branch.\n     |- Try 55 - 34 = 21. Evaluate 21 != 27, drop this branch.\n     |- Try 55 * 34 = 1870. Evaluate 1870 != 27, drop this branch.\n     |- Try 55 \/ 34 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 37 - 18 = 19. Add 19 to the number set. Current number set: [19, 34], target: 27, just two numbers left.\n     |- Try 34 + 19 = 53. Evaluate 53 != 27, drop this branch.\n     |- Try 34 - 19 = 15. Evaluate 15 != 27, drop this branch.\n     |- Try 34 * 19 = 646. Evaluate 646 != 27, drop this branch.\n     |- Try 34 \/ 19 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 37 * 18 = 666. Add 666 to the number set. Current number set: [666, 34], target: 27, just two numbers left.\n     |- Try 666 + 34 = 700. Evaluate 700 != 27, drop this branch.\n     |- Try 666 - 34 = 632. Evaluate 632 != 27, drop this branch.\n     |- Try 666 * 34 = 22644. 22644 exceeds the maximum intermediate result, drop this branch.\n     |- Try 666 \/ 34 = 19.6. 19.6 is a decimal, drop this branch.\n    |- Try 37 \/ 18 = 2.1. 2.1 is a decimal, drop this branch.\n  |- Try 26 - 8 = 18. Add 18 to the number set. Current number set: [18, 18, 37], target: 27. Options for choosing two numbers: [(18, 18), (18, 37), (18, 37)].\n   |- Pick two numbers (18, 18) (numbers left: [37]). Try possible operations.\n    |- Try 18 + 18 = 36. Add 36 to the number set. Current number set: [36, 37], target: 27, just two numbers left.\n     |- Try 37 + 36 = 73. Evaluate 73 != 27, drop this branch.\n     |- Try 37 - 36 = 1. Evaluate 1 != 27, drop this branch.\n     |- Try 37 * 36 = 1332. Evaluate 1332 != 27, drop this branch.\n     |- Try 37 \/ 36 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 18 = 0. Add 0 to the number set. Current number set: [0, 37], target: 27, just two numbers left.\n     |- Try 37 + 0 = 37. Evaluate 37 != 27, drop this branch.\n     |- Try 37 - 0 = 37. Evaluate 37 != 27, drop this branch.\n     |- Try 37 * 0 = 0. Evaluate 0 != 27, drop this branch.\n     |- Try 37 \/ 0 (invalid operation). drop this branch.\n    |- Try 18 * 18 = 324. Add 324 to the number set. Current number set: [324, 37], target: 27, just two numbers left.\n     |- Try 324 + 37 = 361. Evaluate 361 != 27, drop this branch.\n     |- Try 324 - 37 = 287. Evaluate 287 != 27, drop this branch.\n     |- Try 324 * 37 = 11988. 11988 exceeds the maximum intermediate result, drop this branch.\n     |- Try 324 \/ 37 = 8.8. 8.8 is a decimal, drop this branch.\n    |- Try 18 \/ 18 = 1. Add 1 to the number set. Current number set: [1, 37], target: 27, just two numbers left.\n     |- Try 37 + 1 = 38. Evaluate 38 != 27, drop this branch.\n     |- Try 37 - 1 = 36. Evaluate 36 != 27, drop this branch.\n     |- Try 37 * 1 = 37. Evaluate 37 != 27, drop this branch.\n     |- Try 37 \/ 1 = 37. Evaluate 37 != 27, drop this branch.\n   |- Pick two numbers (18, 37) (numbers left: [18]). Try possible operations.\n    |- Try 37 + 18 = 55. Add 55 to the number set. Current number set: [55, 18], target: 27, just two numbers left.\n     |- Try 55 + 18 = 73. Evaluate 73 != 27, drop this branch.\n     |- Try 55 - 18 = 37. Evaluate 37 != 27, drop this branch.\n     |- Try 55 * 18 = 990. Evaluate 990 != 27, drop this branch.\n     |- Try 55 \/ 18 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 37 - 18 = 19. Add 19 to the number set. Current number set: [19, 18], target: 27, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 27, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 27, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 27, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 37 * 18 = 666. Add 666 to the number set. Current number set: [666, 18], target: 27, just two numbers left.\n     |- Try 666 + 18 = 684. Evaluate 684 != 27, drop this branch.\n     |- Try 666 - 18 = 648. Evaluate 648 != 27, drop this branch.\n     |- Try 666 * 18 = 11988. 11988 exceeds the maximum intermediate result, drop this branch.\n     |- Try 666 \/ 18 = 37. Evaluate 37 != 27, drop this branch.\n    |- Try 37 \/ 18 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (18, 37) (numbers left: [18]). Try possible operations.\n    |- Try 37 + 18 = 55. Add 55 to the number set. Current number set: [55, 18], target: 27, just two numbers left.\n     |- Try 55 + 18 = 73. Evaluate 73 != 27, drop this branch.\n     |- Try 55 - 18 = 37. Evaluate 37 != 27, drop this branch.\n     |- Try 55 * 18 = 990. Evaluate 990 != 27, drop this branch.\n     |- Try 55 \/ 18 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 37 - 18 = 19. Add 19 to the number set. Current number set: [19, 18], target: 27, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 27, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 27, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 27, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 37 * 18 = 666. Add 666 to the number set. Current number set: [666, 18], target: 27, just two numbers left.\n     |- Try 666 + 18 = 684. Evaluate 684 != 27, drop this branch.\n     |- Try 666 - 18 = 648. Evaluate 648 != 27, drop this branch.\n     |- Try 666 * 18 = 11988. 11988 exceeds the maximum intermediate result, drop this branch.\n     |- Try 666 \/ 18 = 37. Evaluate 37 != 27, drop this branch.\n    |- Try 37 \/ 18 = 2.1. 2.1 is a decimal, drop this branch.\n  |- Try 26 * 8 = 208. Add 208 to the number set. Current number set: [208, 18, 37], target: 27. Options for choosing two numbers: [(208, 18), (208, 37), (18, 37)].\n   |- Pick two numbers (208, 18) (numbers left: [37]). Try possible operations.\n    |- Try 208 + 18 = 226. Add 226 to the number set. Current number set: [226, 37], target: 27, just two numbers left.\n     |- Try 226 + 37 = 263. Evaluate 263 != 27, drop this branch.\n     |- Try 226 - 37 = 189. Evaluate 189 != 27, drop this branch.\n     |- Try 226 * 37 = 8362. 8362 exceeds the maximum intermediate result, drop this branch.\n     |- Try 226 \/ 37 = 6.1. 6.1 is a decimal, drop this branch.\n    |- Try 208 - 18 = 190. Add 190 to the number set. Current number set: [190, 37], target: 27, just two numbers left.\n     |- Try 190 + 37 = 227. Evaluate 227 != 27, drop this branch.\n     |- Try 190 - 37 = 153. Evaluate 153 != 27, drop this branch.\n     |- Try 190 * 37 = 7030. 7030 exceeds the maximum intermediate result, drop this branch.\n     |- Try 190 \/ 37 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 208 * 18 = 3744. 3744 exceeds the maximum intermediate result, drop this branch.\n    |- Try 208 \/ 18 = 11.6. 11.6 is a decimal, drop this branch.\n   |- Pick two numbers (208, 37) (numbers left: [18]). Try possible operations.\n    |- Try 208 + 37 = 245. Add 245 to the number set. Current number set: [245, 18], target: 27, just two numbers left.\n     |- Try 245 + 18 = 263. Evaluate 263 != 27, drop this branch.\n     |- Try 245 - 18 = 227. Evaluate 227 != 27, drop this branch.\n     |- Try 245 * 18 = 4410. 4410 exceeds the maximum intermediate result, drop this branch.\n     |- Try 245 \/ 18 = 13.6. 13.6 is a decimal, drop this branch.\n    |- Try 208 - 37 = 171. Add 171 to the number set. Current number set: [171, 18], target: 27, just two numbers left.\n     |- Try 171 + 18 = 189. Evaluate 189 != 27, drop this branch.\n     |- Try 171 - 18 = 153. Evaluate 153 != 27, drop this branch.\n     |- Try 171 * 18 = 3078. 3078 exceeds the maximum intermediate result, drop this branch.\n     |- Try 171 \/ 18 = 9.5. 9.5 is a decimal, drop this branch.\n    |- Try 208 * 37 = 7696. 7696 exceeds the maximum intermediate result, drop this branch.\n    |- Try 208 \/ 37 = 5.6. 5.6 is a decimal, drop this branch.\n   |- Pick two numbers (18, 37) (numbers left: [208]). Try possible operations.\n    |- Try 37 + 18 = 55. Add 55 to the number set. Current number set: [55, 208], target: 27, just two numbers left.\n     |- Try 208 + 55 = 263. Evaluate 263 != 27, drop this branch.\n     |- Try 208 - 55 = 153. Evaluate 153 != 27, drop this branch.\n     |- Try 208 * 55 = 11440. 11440 exceeds the maximum intermediate result, drop this branch.\n     |- Try 208 \/ 55 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 37 - 18 = 19. Add 19 to the number set. Current number set: [19, 208], target: 27, just two numbers left.\n     |- Try 208 + 19 = 227. Evaluate 227 != 27, drop this branch.\n     |- Try 208 - 19 = 189. Evaluate 189 != 27, drop this branch.\n     |- Try 208 * 19 = 3952. 3952 exceeds the maximum intermediate result, drop this branch.\n     |- Try 208 \/ 19 = 10.9. 10.9 is a decimal, drop this branch.\n    |- Try 37 * 18 = 666. Add 666 to the number set. Current number set: [666, 208], target: 27, just two numbers left.\n     |- Try 666 + 208 = 874. Evaluate 874 != 27, drop this branch.\n     |- Try 666 - 208 = 458. Evaluate 458 != 27, drop this branch.\n     |- Try 666 * 208 = 138528. 138528 exceeds the maximum intermediate result, drop this branch.\n     |- Try 666 \/ 208 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 37 \/ 18 = 2.1. 2.1 is a decimal, drop this branch.\n  |- Try 26 \/ 8 = 3.2. 3.2 is a decimal, drop this branch.\n |- Pick two numbers (26, 18) (numbers left: [8, 37]). Try possible operations.\n  |- Try 26 + 18 = 44. Add 44 to the number set. Current number set: [44, 8, 37], target: 27. Options for choosing two numbers: [(44, 8), (44, 37), (8, 37)].\n   |- Pick two numbers (44, 8) (numbers left: [37]). Try possible operations.\n    |- Try 44 + 8 = 52. Add 52 to the number set. Current number set: [52, 37], target: 27, just two numbers left.\n     |- Try 52 + 37 = 89. Evaluate 89 != 27, drop this branch.\n     |- Try 52 - 37 = 15. Evaluate 15 != 27, drop this branch.\n     |- Try 52 * 37 = 1924. Evaluate 1924 != 27, drop this branch.\n     |- Try 52 \/ 37 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 44 - 8 = 36. Add 36 to the number set. Current number set: [36, 37], target: 27, just two numbers left.\n     |- Try 37 + 36 = 73. Evaluate 73 != 27, drop this branch.\n     |- Try 37 - 36 = 1. Evaluate 1 != 27, drop this branch.\n     |- Try 37 * 36 = 1332. Evaluate 1332 != 27, drop this branch.\n     |- Try 37 \/ 36 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 44 * 8 = 352. Add 352 to the number set. Current number set: [352, 37], target: 27, just two numbers left.\n     |- Try 352 + 37 = 389. Evaluate 389 != 27, drop this branch.\n     |- Try 352 - 37 = 315. Evaluate 315 != 27, drop this branch.\n     |- Try 352 * 37 = 13024. 13024 exceeds the maximum intermediate result, drop this branch.\n     |- Try 352 \/ 37 = 9.5. 9.5 is a decimal, drop this branch.\n    |- Try 44 \/ 8 = 5.5. 5.5 is a decimal, drop this branch.\n   |- Pick two numbers (44, 37) (numbers left: [8]). Try possible operations.\n    |- Try 44 + 37 = 81. Add 81 to the number set. Current number set: [81, 8], target: 27, just two numbers left.\n     |- Try 81 + 8 = 89. Evaluate 89 != 27, drop this branch.\n     |- Try 81 - 8 = 73. Evaluate 73 != 27, drop this branch.\n     |- Try 81 * 8 = 648. Evaluate 648 != 27, drop this branch.\n     |- Try 81 \/ 8 = 10.1. 10.1 is a decimal, drop this branch.\n    |- Try 44 - 37 = 7. Add 7 to the number set. Current number set: [7, 8], target: 27, just two numbers left.\n     |- Try 8 + 7 = 15. Evaluate 15 != 27, drop this branch.\n     |- Try 8 - 7 = 1. Evaluate 1 != 27, drop this branch.\n     |- Try 8 * 7 = 56. Evaluate 56 != 27, drop this branch.\n     |- Try 8 \/ 7 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 44 * 37 = 1628. Add 1628 to the number set. Current number set: [1628, 8], target: 27, just two numbers left.\n     |- Try 1628 + 8 = 1636. Evaluate 1636 != 27, drop this branch.\n     |- Try 1628 - 8 = 1620. Evaluate 1620 != 27, drop this branch.\n     |- Try 1628 * 8 = 13024. 13024 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1628 \/ 8 = 203.5. 203.5 is a decimal, drop this branch.\n    |- Try 44 \/ 37 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (8, 37) (numbers left: [44]). Try possible operations.\n    |- Try 37 + 8 = 45. Add 45 to the number set. Current number set: [45, 44], target: 27, just two numbers left.\n     |- Try 45 + 44 = 89. Evaluate 89 != 27, drop this branch.\n     |- Try 45 - 44 = 1. Evaluate 1 != 27, drop this branch.\n     |- Try 45 * 44 = 1980. Evaluate 1980 != 27, drop this branch.\n     |- Try 45 \/ 44 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 37 - 8 = 29. Add 29 to the number set. Current number set: [29, 44], target: 27, just two numbers left.\n     |- Try 44 + 29 = 73. Evaluate 73 != 27, drop this branch.\n     |- Try 44 - 29 = 15. Evaluate 15 != 27, drop this branch.\n     |- Try 44 * 29 = 1276. Evaluate 1276 != 27, drop this branch.\n     |- Try 44 \/ 29 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 37 * 8 = 296. Add 296 to the number set. Current number set: [296, 44], target: 27, just two numbers left.\n     |- Try 296 + 44 = 340. Evaluate 340 != 27, drop this branch.\n     |- Try 296 - 44 = 252. Evaluate 252 != 27, drop this branch.\n     |- Try 296 * 44 = 13024. 13024 exceeds the maximum intermediate result, drop this branch.\n     |- Try 296 \/ 44 = 6.7. 6.7 is a decimal, drop this branch.\n    |- Try 37 \/ 8 = 4.6. 4.6 is a decimal, drop this branch.\n  |- Try 26 - 18 = 8. Add 8 to the number set. Current number set: [8, 8, 37], target: 27. Options for choosing two numbers: [(8, 8), (8, 37), (8, 37)].\n   |- Pick two numbers (8, 8) (numbers left: [37]). Try possible operations.\n    |- Try 8 + 8 = 16. Add 16 to the number set. Current number set: [16, 37], target: 27, just two numbers left.\n     |- Try 37 + 16 = 53. Evaluate 53 != 27, drop this branch.\n     |- Try 37 - 16 = 21. Evaluate 21 != 27, drop this branch.\n     |- Try 37 * 16 = 592. Evaluate 592 != 27, drop this branch.\n     |- Try 37 \/ 16 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 8 - 8 = 0. Add 0 to the number set. Current number set: [0, 37], target: 27, just two numbers left.\n     |- Try 37 + 0 = 37. Evaluate 37 != 27, drop this branch.\n     |- Try 37 - 0 = 37. Evaluate 37 != 27, drop this branch.\n     |- Try 37 * 0 = 0. Evaluate 0 != 27, drop this branch.\n     |- Try 37 \/ 0 (invalid operation). drop this branch.\n    |- Try 8 * 8 = 64. Add 64 to the number set. Current number set: [64, 37], target: 27, just two numbers left.\n     |- Try 64 + 37 = 101. Evaluate 101 != 27, drop this branch.\n     |- Try 64 - 37 = 27. Evaluate 27 == 27, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 64 - 37 = 27\nThe step before: 8 * 8 = 64\nThe first step: 26 - 18 = 8\n\nOutput the solution in the required format:\n<Solution>\n26 - 18 = 8\n8 * 8 = 64\n64 - 37 = 27\n<\/Solution>\n","item":{"nums":[26,8,18,37],"solution":["26 - 18 = 8","8 * 8 = 64","64 - 37 = 27"],"target":27}}
+{"instance_id":"countdown_8k_128","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [26, 13, 22, 6]\nTarget: 10","reference_output":"# Search Procedure\nInitial number set: [26, 13, 22, 6], target: 10. Options for choosing two numbers: [(26, 13), (26, 22), (26, 6), (13, 22), (13, 6), (22, 6)].\n |- Pick two numbers (26, 13) (numbers left: [22, 6]). Try possible operations.\n  |- Try 26 + 13 = 39. Add 39 to the number set. Current number set: [39, 22, 6], target: 10. Options for choosing two numbers: [(39, 22), (39, 6), (22, 6)].\n   |- Pick two numbers (39, 22) (numbers left: [6]). Try possible operations.\n    |- Try 39 + 22 = 61. Add 61 to the number set. Current number set: [61, 6], target: 10, just two numbers left.\n     |- Try 61 + 6 = 67. Evaluate 67 != 10, drop this branch.\n     |- Try 61 - 6 = 55. Evaluate 55 != 10, drop this branch.\n     |- Try 61 * 6 = 366. Evaluate 366 != 10, drop this branch.\n     |- Try 61 \/ 6 = 10.2. 10.2 is a decimal, drop this branch.\n    |- Try 39 - 22 = 17. Add 17 to the number set. Current number set: [17, 6], target: 10, just two numbers left.\n     |- Try 17 + 6 = 23. Evaluate 23 != 10, drop this branch.\n     |- Try 17 - 6 = 11. Evaluate 11 != 10, drop this branch.\n     |- Try 17 * 6 = 102. Evaluate 102 != 10, drop this branch.\n     |- Try 17 \/ 6 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 39 * 22 = 858. Add 858 to the number set. Current number set: [858, 6], target: 10, just two numbers left.\n     |- Try 858 + 6 = 864. Evaluate 864 != 10, drop this branch.\n     |- Try 858 - 6 = 852. Evaluate 852 != 10, drop this branch.\n     |- Try 858 * 6 = 5148. 5148 exceeds the maximum intermediate result, drop this branch.\n     |- Try 858 \/ 6 = 143. Evaluate 143 != 10, drop this branch.\n    |- Try 39 \/ 22 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (39, 6) (numbers left: [22]). Try possible operations.\n    |- Try 39 + 6 = 45. Add 45 to the number set. Current number set: [45, 22], target: 10, just two numbers left.\n     |- Try 45 + 22 = 67. Evaluate 67 != 10, drop this branch.\n     |- Try 45 - 22 = 23. Evaluate 23 != 10, drop this branch.\n     |- Try 45 * 22 = 990. Evaluate 990 != 10, drop this branch.\n     |- Try 45 \/ 22 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 39 - 6 = 33. Add 33 to the number set. Current number set: [33, 22], target: 10, just two numbers left.\n     |- Try 33 + 22 = 55. Evaluate 55 != 10, drop this branch.\n     |- Try 33 - 22 = 11. Evaluate 11 != 10, drop this branch.\n     |- Try 33 * 22 = 726. Evaluate 726 != 10, drop this branch.\n     |- Try 33 \/ 22 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 39 * 6 = 234. Add 234 to the number set. Current number set: [234, 22], target: 10, just two numbers left.\n     |- Try 234 + 22 = 256. Evaluate 256 != 10, drop this branch.\n     |- Try 234 - 22 = 212. Evaluate 212 != 10, drop this branch.\n     |- Try 234 * 22 = 5148. 5148 exceeds the maximum intermediate result, drop this branch.\n     |- Try 234 \/ 22 = 10.6. 10.6 is a decimal, drop this branch.\n    |- Try 39 \/ 6 = 6.5. 6.5 is a decimal, drop this branch.\n   |- Pick two numbers (22, 6) (numbers left: [39]). Try possible operations.\n    |- Try 22 + 6 = 28. Add 28 to the number set. Current number set: [28, 39], target: 10, just two numbers left.\n     |- Try 39 + 28 = 67. Evaluate 67 != 10, drop this branch.\n     |- Try 39 - 28 = 11. Evaluate 11 != 10, drop this branch.\n     |- Try 39 * 28 = 1092. Evaluate 1092 != 10, drop this branch.\n     |- Try 39 \/ 28 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 22 - 6 = 16. Add 16 to the number set. Current number set: [16, 39], target: 10, just two numbers left.\n     |- Try 39 + 16 = 55. Evaluate 55 != 10, drop this branch.\n     |- Try 39 - 16 = 23. Evaluate 23 != 10, drop this branch.\n     |- Try 39 * 16 = 624. Evaluate 624 != 10, drop this branch.\n     |- Try 39 \/ 16 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 22 * 6 = 132. Add 132 to the number set. Current number set: [132, 39], target: 10, just two numbers left.\n     |- Try 132 + 39 = 171. Evaluate 171 != 10, drop this branch.\n     |- Try 132 - 39 = 93. Evaluate 93 != 10, drop this branch.\n     |- Try 132 * 39 = 5148. 5148 exceeds the maximum intermediate result, drop this branch.\n     |- Try 132 \/ 39 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 22 \/ 6 = 3.7. 3.7 is a decimal, drop this branch.\n  |- Try 26 - 13 = 13. Add 13 to the number set. Current number set: [13, 22, 6], target: 10. Options for choosing two numbers: [(13, 22), (13, 6), (22, 6)].\n   |- Pick two numbers (13, 22) (numbers left: [6]). Try possible operations.\n    |- Try 22 + 13 = 35. Add 35 to the number set. Current number set: [35, 6], target: 10, just two numbers left.\n     |- Try 35 + 6 = 41. Evaluate 41 != 10, drop this branch.\n     |- Try 35 - 6 = 29. Evaluate 29 != 10, drop this branch.\n     |- Try 35 * 6 = 210. Evaluate 210 != 10, drop this branch.\n     |- Try 35 \/ 6 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 22 - 13 = 9. Add 9 to the number set. Current number set: [9, 6], target: 10, just two numbers left.\n     |- Try 9 + 6 = 15. Evaluate 15 != 10, drop this branch.\n     |- Try 9 - 6 = 3. Evaluate 3 != 10, drop this branch.\n     |- Try 9 * 6 = 54. Evaluate 54 != 10, drop this branch.\n     |- Try 9 \/ 6 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 22 * 13 = 286. Add 286 to the number set. Current number set: [286, 6], target: 10, just two numbers left.\n     |- Try 286 + 6 = 292. Evaluate 292 != 10, drop this branch.\n     |- Try 286 - 6 = 280. Evaluate 280 != 10, drop this branch.\n     |- Try 286 * 6 = 1716. Evaluate 1716 != 10, drop this branch.\n     |- Try 286 \/ 6 = 47.7. 47.7 is a decimal, drop this branch.\n    |- Try 22 \/ 13 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (13, 6) (numbers left: [22]). Try possible operations.\n    |- Try 13 + 6 = 19. Add 19 to the number set. Current number set: [19, 22], target: 10, just two numbers left.\n     |- Try 22 + 19 = 41. Evaluate 41 != 10, drop this branch.\n     |- Try 22 - 19 = 3. Evaluate 3 != 10, drop this branch.\n     |- Try 22 * 19 = 418. Evaluate 418 != 10, drop this branch.\n     |- Try 22 \/ 19 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 13 - 6 = 7. Add 7 to the number set. Current number set: [7, 22], target: 10, just two numbers left.\n     |- Try 22 + 7 = 29. Evaluate 29 != 10, drop this branch.\n     |- Try 22 - 7 = 15. Evaluate 15 != 10, drop this branch.\n     |- Try 22 * 7 = 154. Evaluate 154 != 10, drop this branch.\n     |- Try 22 \/ 7 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 13 * 6 = 78. Add 78 to the number set. Current number set: [78, 22], target: 10, just two numbers left.\n     |- Try 78 + 22 = 100. Evaluate 100 != 10, drop this branch.\n     |- Try 78 - 22 = 56. Evaluate 56 != 10, drop this branch.\n     |- Try 78 * 22 = 1716. Evaluate 1716 != 10, drop this branch.\n     |- Try 78 \/ 22 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 13 \/ 6 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (22, 6) (numbers left: [13]). Try possible operations.\n    |- Try 22 + 6 = 28. Add 28 to the number set. Current number set: [28, 13], target: 10, just two numbers left.\n     |- Try 28 + 13 = 41. Evaluate 41 != 10, drop this branch.\n     |- Try 28 - 13 = 15. Evaluate 15 != 10, drop this branch.\n     |- Try 28 * 13 = 364. Evaluate 364 != 10, drop this branch.\n     |- Try 28 \/ 13 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 22 - 6 = 16. Add 16 to the number set. Current number set: [16, 13], target: 10, just two numbers left.\n     |- Try 16 + 13 = 29. Evaluate 29 != 10, drop this branch.\n     |- Try 16 - 13 = 3. Evaluate 3 != 10, drop this branch.\n     |- Try 16 * 13 = 208. Evaluate 208 != 10, drop this branch.\n     |- Try 16 \/ 13 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 22 * 6 = 132. Add 132 to the number set. Current number set: [132, 13], target: 10, just two numbers left.\n     |- Try 132 + 13 = 145. Evaluate 145 != 10, drop this branch.\n     |- Try 132 - 13 = 119. Evaluate 119 != 10, drop this branch.\n     |- Try 132 * 13 = 1716. Evaluate 1716 != 10, drop this branch.\n     |- Try 132 \/ 13 = 10.2. 10.2 is a decimal, drop this branch.\n    |- Try 22 \/ 6 = 3.7. 3.7 is a decimal, drop this branch.\n  |- Try 26 * 13 = 338. Add 338 to the number set. Current number set: [338, 22, 6], target: 10. Options for choosing two numbers: [(338, 22), (338, 6), (22, 6)].\n   |- Pick two numbers (338, 22) (numbers left: [6]). Try possible operations.\n    |- Try 338 + 22 = 360. Add 360 to the number set. Current number set: [360, 6], target: 10, just two numbers left.\n     |- Try 360 + 6 = 366. Evaluate 366 != 10, drop this branch.\n     |- Try 360 - 6 = 354. Evaluate 354 != 10, drop this branch.\n     |- Try 360 * 6 = 2160. 2160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 360 \/ 6 = 60. Evaluate 60 != 10, drop this branch.\n    |- Try 338 - 22 = 316. Add 316 to the number set. Current number set: [316, 6], target: 10, just two numbers left.\n     |- Try 316 + 6 = 322. Evaluate 322 != 10, drop this branch.\n     |- Try 316 - 6 = 310. Evaluate 310 != 10, drop this branch.\n     |- Try 316 * 6 = 1896. Evaluate 1896 != 10, drop this branch.\n     |- Try 316 \/ 6 = 52.7. 52.7 is a decimal, drop this branch.\n    |- Try 338 * 22 = 7436. 7436 exceeds the maximum intermediate result, drop this branch.\n    |- Try 338 \/ 22 = 15.4. 15.4 is a decimal, drop this branch.\n   |- Pick two numbers (338, 6) (numbers left: [22]). Try possible operations.\n    |- Try 338 + 6 = 344. Add 344 to the number set. Current number set: [344, 22], target: 10, just two numbers left.\n     |- Try 344 + 22 = 366. Evaluate 366 != 10, drop this branch.\n     |- Try 344 - 22 = 322. Evaluate 322 != 10, drop this branch.\n     |- Try 344 * 22 = 7568. 7568 exceeds the maximum intermediate result, drop this branch.\n     |- Try 344 \/ 22 = 15.6. 15.6 is a decimal, drop this branch.\n    |- Try 338 - 6 = 332. Add 332 to the number set. Current number set: [332, 22], target: 10, just two numbers left.\n     |- Try 332 + 22 = 354. Evaluate 354 != 10, drop this branch.\n     |- Try 332 - 22 = 310. Evaluate 310 != 10, drop this branch.\n     |- Try 332 * 22 = 7304. 7304 exceeds the maximum intermediate result, drop this branch.\n     |- Try 332 \/ 22 = 15.1. 15.1 is a decimal, drop this branch.\n    |- Try 338 * 6 = 2028. 2028 exceeds the maximum intermediate result, drop this branch.\n    |- Try 338 \/ 6 = 56.3. 56.3 is a decimal, drop this branch.\n   |- Pick two numbers (22, 6) (numbers left: [338]). Try possible operations.\n    |- Try 22 + 6 = 28. Add 28 to the number set. Current number set: [28, 338], target: 10, just two numbers left.\n     |- Try 338 + 28 = 366. Evaluate 366 != 10, drop this branch.\n     |- Try 338 - 28 = 310. Evaluate 310 != 10, drop this branch.\n     |- Try 338 * 28 = 9464. 9464 exceeds the maximum intermediate result, drop this branch.\n     |- Try 338 \/ 28 = 12.1. 12.1 is a decimal, drop this branch.\n    |- Try 22 - 6 = 16. Add 16 to the number set. Current number set: [16, 338], target: 10, just two numbers left.\n     |- Try 338 + 16 = 354. Evaluate 354 != 10, drop this branch.\n     |- Try 338 - 16 = 322. Evaluate 322 != 10, drop this branch.\n     |- Try 338 * 16 = 5408. 5408 exceeds the maximum intermediate result, drop this branch.\n     |- Try 338 \/ 16 = 21.1. 21.1 is a decimal, drop this branch.\n    |- Try 22 * 6 = 132. Add 132 to the number set. Current number set: [132, 338], target: 10, just two numbers left.\n     |- Try 338 + 132 = 470. Evaluate 470 != 10, drop this branch.\n     |- Try 338 - 132 = 206. Evaluate 206 != 10, drop this branch.\n     |- Try 338 * 132 = 44616. 44616 exceeds the maximum intermediate result, drop this branch.\n     |- Try 338 \/ 132 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 22 \/ 6 = 3.7. 3.7 is a decimal, drop this branch.\n  |- Try 26 \/ 13 = 2. Add 2 to the number set. Current number set: [2, 22, 6], target: 10. Options for choosing two numbers: [(2, 22), (2, 6), (22, 6)].\n   |- Pick two numbers (2, 22) (numbers left: [6]). Try possible operations.\n    |- Try 22 + 2 = 24. Add 24 to the number set. Current number set: [24, 6], target: 10, just two numbers left.\n     |- Try 24 + 6 = 30. Evaluate 30 != 10, drop this branch.\n     |- Try 24 - 6 = 18. Evaluate 18 != 10, drop this branch.\n     |- Try 24 * 6 = 144. Evaluate 144 != 10, drop this branch.\n     |- Try 24 \/ 6 = 4. Evaluate 4 != 10, drop this branch.\n    |- Try 22 - 2 = 20. Add 20 to the number set. Current number set: [20, 6], target: 10, just two numbers left.\n     |- Try 20 + 6 = 26. Evaluate 26 != 10, drop this branch.\n     |- Try 20 - 6 = 14. Evaluate 14 != 10, drop this branch.\n     |- Try 20 * 6 = 120. Evaluate 120 != 10, drop this branch.\n     |- Try 20 \/ 6 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 22 * 2 = 44. Add 44 to the number set. Current number set: [44, 6], target: 10, just two numbers left.\n     |- Try 44 + 6 = 50. Evaluate 50 != 10, drop this branch.\n     |- Try 44 - 6 = 38. Evaluate 38 != 10, drop this branch.\n     |- Try 44 * 6 = 264. Evaluate 264 != 10, drop this branch.\n     |- Try 44 \/ 6 = 7.3. 7.3 is a decimal, drop this branch.\n    |- Try 22 \/ 2 = 11. Add 11 to the number set. Current number set: [11, 6], target: 10, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 10, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 10, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 10, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (2, 6) (numbers left: [22]). Try possible operations.\n    |- Try 6 + 2 = 8. Add 8 to the number set. Current number set: [8, 22], target: 10, just two numbers left.\n     |- Try 22 + 8 = 30. Evaluate 30 != 10, drop this branch.\n     |- Try 22 - 8 = 14. Evaluate 14 != 10, drop this branch.\n     |- Try 22 * 8 = 176. Evaluate 176 != 10, drop this branch.\n     |- Try 22 \/ 8 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 6 - 2 = 4. Add 4 to the number set. Current number set: [4, 22], target: 10, just two numbers left.\n     |- Try 22 + 4 = 26. Evaluate 26 != 10, drop this branch.\n     |- Try 22 - 4 = 18. Evaluate 18 != 10, drop this branch.\n     |- Try 22 * 4 = 88. Evaluate 88 != 10, drop this branch.\n     |- Try 22 \/ 4 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 6 * 2 = 12. Add 12 to the number set. Current number set: [12, 22], target: 10, just two numbers left.\n     |- Try 22 + 12 = 34. Evaluate 34 != 10, drop this branch.\n     |- Try 22 - 12 = 10. Evaluate 10 == 10, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 22 - 12 = 10\nThe step before: 6 * 2 = 12\nThe first step: 26 \/ 13 = 2\n\nOutput the solution in the required format:\n<Solution>\n26 \/ 13 = 2\n6 * 2 = 12\n22 - 12 = 10\n<\/Solution>\n","item":{"nums":[26,13,22,6],"solution":["26 \/ 13 = 2","6 * 2 = 12","22 - 12 = 10"],"target":10}}
+{"instance_id":"countdown_8k_129","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [38, 8, 6, 4]\nTarget: 46","reference_output":"# Search Procedure\nInitial number set: [38, 8, 6, 4], target: 46. Options for choosing two numbers: [(38, 8), (38, 6), (38, 4), (8, 6), (8, 4), (6, 4)].\n |- Pick two numbers (38, 8) (numbers left: [6, 4]). Try possible operations.\n  |- Try 38 + 8 = 46. Add 46 to the number set. Current number set: [46, 6, 4], target: 46. Options for choosing two numbers: [(46, 6), (46, 4), (6, 4)].\n   |- Pick two numbers (46, 6) (numbers left: [4]). Try possible operations.\n    |- Try 46 + 6 = 52. Add 52 to the number set. Current number set: [52, 4], target: 46, just two numbers left.\n     |- Try 52 + 4 = 56. Evaluate 56 != 46, drop this branch.\n     |- Try 52 - 4 = 48. Evaluate 48 != 46, drop this branch.\n     |- Try 52 * 4 = 208. Evaluate 208 != 46, drop this branch.\n     |- Try 52 \/ 4 = 13. Evaluate 13 != 46, drop this branch.\n    |- Try 46 - 6 = 40. Add 40 to the number set. Current number set: [40, 4], target: 46, just two numbers left.\n     |- Try 40 + 4 = 44. Evaluate 44 != 46, drop this branch.\n     |- Try 40 - 4 = 36. Evaluate 36 != 46, drop this branch.\n     |- Try 40 * 4 = 160. Evaluate 160 != 46, drop this branch.\n     |- Try 40 \/ 4 = 10. Evaluate 10 != 46, drop this branch.\n    |- Try 46 * 6 = 276. Add 276 to the number set. Current number set: [276, 4], target: 46, just two numbers left.\n     |- Try 276 + 4 = 280. Evaluate 280 != 46, drop this branch.\n     |- Try 276 - 4 = 272. Evaluate 272 != 46, drop this branch.\n     |- Try 276 * 4 = 1104. Evaluate 1104 != 46, drop this branch.\n     |- Try 276 \/ 4 = 69. Evaluate 69 != 46, drop this branch.\n    |- Try 46 \/ 6 = 7.7. 7.7 is a decimal, drop this branch.\n   |- Pick two numbers (46, 4) (numbers left: [6]). Try possible operations.\n    |- Try 46 + 4 = 50. Add 50 to the number set. Current number set: [50, 6], target: 46, just two numbers left.\n     |- Try 50 + 6 = 56. Evaluate 56 != 46, drop this branch.\n     |- Try 50 - 6 = 44. Evaluate 44 != 46, drop this branch.\n     |- Try 50 * 6 = 300. Evaluate 300 != 46, drop this branch.\n     |- Try 50 \/ 6 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 46 - 4 = 42. Add 42 to the number set. Current number set: [42, 6], target: 46, just two numbers left.\n     |- Try 42 + 6 = 48. Evaluate 48 != 46, drop this branch.\n     |- Try 42 - 6 = 36. Evaluate 36 != 46, drop this branch.\n     |- Try 42 * 6 = 252. Evaluate 252 != 46, drop this branch.\n     |- Try 42 \/ 6 = 7. Evaluate 7 != 46, drop this branch.\n    |- Try 46 * 4 = 184. Add 184 to the number set. Current number set: [184, 6], target: 46, just two numbers left.\n     |- Try 184 + 6 = 190. Evaluate 190 != 46, drop this branch.\n     |- Try 184 - 6 = 178. Evaluate 178 != 46, drop this branch.\n     |- Try 184 * 6 = 1104. Evaluate 1104 != 46, drop this branch.\n     |- Try 184 \/ 6 = 30.7. 30.7 is a decimal, drop this branch.\n    |- Try 46 \/ 4 = 11.5. 11.5 is a decimal, drop this branch.\n   |- Pick two numbers (6, 4) (numbers left: [46]). Try possible operations.\n    |- Try 6 + 4 = 10. Add 10 to the number set. Current number set: [10, 46], target: 46, just two numbers left.\n     |- Try 46 + 10 = 56. Evaluate 56 != 46, drop this branch.\n     |- Try 46 - 10 = 36. Evaluate 36 != 46, drop this branch.\n     |- Try 46 * 10 = 460. Evaluate 460 != 46, drop this branch.\n     |- Try 46 \/ 10 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 6 - 4 = 2. Add 2 to the number set. Current number set: [2, 46], target: 46, just two numbers left.\n     |- Try 46 + 2 = 48. Evaluate 48 != 46, drop this branch.\n     |- Try 46 - 2 = 44. Evaluate 44 != 46, drop this branch.\n     |- Try 46 * 2 = 92. Evaluate 92 != 46, drop this branch.\n     |- Try 46 \/ 2 = 23. Evaluate 23 != 46, drop this branch.\n    |- Try 6 * 4 = 24. Add 24 to the number set. Current number set: [24, 46], target: 46, just two numbers left.\n     |- Try 46 + 24 = 70. Evaluate 70 != 46, drop this branch.\n     |- Try 46 - 24 = 22. Evaluate 22 != 46, drop this branch.\n     |- Try 46 * 24 = 1104. Evaluate 1104 != 46, drop this branch.\n     |- Try 46 \/ 24 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 6 \/ 4 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 38 - 8 = 30. Add 30 to the number set. Current number set: [30, 6, 4], target: 46. Options for choosing two numbers: [(30, 6), (30, 4), (6, 4)].\n   |- Pick two numbers (30, 6) (numbers left: [4]). Try possible operations.\n    |- Try 30 + 6 = 36. Add 36 to the number set. Current number set: [36, 4], target: 46, just two numbers left.\n     |- Try 36 + 4 = 40. Evaluate 40 != 46, drop this branch.\n     |- Try 36 - 4 = 32. Evaluate 32 != 46, drop this branch.\n     |- Try 36 * 4 = 144. Evaluate 144 != 46, drop this branch.\n     |- Try 36 \/ 4 = 9. Evaluate 9 != 46, drop this branch.\n    |- Try 30 - 6 = 24. Add 24 to the number set. Current number set: [24, 4], target: 46, just two numbers left.\n     |- Try 24 + 4 = 28. Evaluate 28 != 46, drop this branch.\n     |- Try 24 - 4 = 20. Evaluate 20 != 46, drop this branch.\n     |- Try 24 * 4 = 96. Evaluate 96 != 46, drop this branch.\n     |- Try 24 \/ 4 = 6. Evaluate 6 != 46, drop this branch.\n    |- Try 30 * 6 = 180. Add 180 to the number set. Current number set: [180, 4], target: 46, just two numbers left.\n     |- Try 180 + 4 = 184. Evaluate 184 != 46, drop this branch.\n     |- Try 180 - 4 = 176. Evaluate 176 != 46, drop this branch.\n     |- Try 180 * 4 = 720. Evaluate 720 != 46, drop this branch.\n     |- Try 180 \/ 4 = 45. Evaluate 45 != 46, drop this branch.\n    |- Try 30 \/ 6 = 5. Add 5 to the number set. Current number set: [5, 4], target: 46, just two numbers left.\n     |- Try 5 + 4 = 9. Evaluate 9 != 46, drop this branch.\n     |- Try 5 - 4 = 1. Evaluate 1 != 46, drop this branch.\n     |- Try 5 * 4 = 20. Evaluate 20 != 46, drop this branch.\n     |- Try 5 \/ 4 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (30, 4) (numbers left: [6]). Try possible operations.\n    |- Try 30 + 4 = 34. Add 34 to the number set. Current number set: [34, 6], target: 46, just two numbers left.\n     |- Try 34 + 6 = 40. Evaluate 40 != 46, drop this branch.\n     |- Try 34 - 6 = 28. Evaluate 28 != 46, drop this branch.\n     |- Try 34 * 6 = 204. Evaluate 204 != 46, drop this branch.\n     |- Try 34 \/ 6 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 30 - 4 = 26. Add 26 to the number set. Current number set: [26, 6], target: 46, just two numbers left.\n     |- Try 26 + 6 = 32. Evaluate 32 != 46, drop this branch.\n     |- Try 26 - 6 = 20. Evaluate 20 != 46, drop this branch.\n     |- Try 26 * 6 = 156. Evaluate 156 != 46, drop this branch.\n     |- Try 26 \/ 6 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 30 * 4 = 120. Add 120 to the number set. Current number set: [120, 6], target: 46, just two numbers left.\n     |- Try 120 + 6 = 126. Evaluate 126 != 46, drop this branch.\n     |- Try 120 - 6 = 114. Evaluate 114 != 46, drop this branch.\n     |- Try 120 * 6 = 720. Evaluate 720 != 46, drop this branch.\n     |- Try 120 \/ 6 = 20. Evaluate 20 != 46, drop this branch.\n    |- Try 30 \/ 4 = 7.5. 7.5 is a decimal, drop this branch.\n   |- Pick two numbers (6, 4) (numbers left: [30]). Try possible operations.\n    |- Try 6 + 4 = 10. Add 10 to the number set. Current number set: [10, 30], target: 46, just two numbers left.\n     |- Try 30 + 10 = 40. Evaluate 40 != 46, drop this branch.\n     |- Try 30 - 10 = 20. Evaluate 20 != 46, drop this branch.\n     |- Try 30 * 10 = 300. Evaluate 300 != 46, drop this branch.\n     |- Try 30 \/ 10 = 3. Evaluate 3 != 46, drop this branch.\n    |- Try 6 - 4 = 2. Add 2 to the number set. Current number set: [2, 30], target: 46, just two numbers left.\n     |- Try 30 + 2 = 32. Evaluate 32 != 46, drop this branch.\n     |- Try 30 - 2 = 28. Evaluate 28 != 46, drop this branch.\n     |- Try 30 * 2 = 60. Evaluate 60 != 46, drop this branch.\n     |- Try 30 \/ 2 = 15. Evaluate 15 != 46, drop this branch.\n    |- Try 6 * 4 = 24. Add 24 to the number set. Current number set: [24, 30], target: 46, just two numbers left.\n     |- Try 30 + 24 = 54. Evaluate 54 != 46, drop this branch.\n     |- Try 30 - 24 = 6. Evaluate 6 != 46, drop this branch.\n     |- Try 30 * 24 = 720. Evaluate 720 != 46, drop this branch.\n     |- Try 30 \/ 24 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 6 \/ 4 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 38 * 8 = 304. Add 304 to the number set. Current number set: [304, 6, 4], target: 46. Options for choosing two numbers: [(304, 6), (304, 4), (6, 4)].\n   |- Pick two numbers (304, 6) (numbers left: [4]). Try possible operations.\n    |- Try 304 + 6 = 310. Add 310 to the number set. Current number set: [310, 4], target: 46, just two numbers left.\n     |- Try 310 + 4 = 314. Evaluate 314 != 46, drop this branch.\n     |- Try 310 - 4 = 306. Evaluate 306 != 46, drop this branch.\n     |- Try 310 * 4 = 1240. Evaluate 1240 != 46, drop this branch.\n     |- Try 310 \/ 4 = 77.5. 77.5 is a decimal, drop this branch.\n    |- Try 304 - 6 = 298. Add 298 to the number set. Current number set: [298, 4], target: 46, just two numbers left.\n     |- Try 298 + 4 = 302. Evaluate 302 != 46, drop this branch.\n     |- Try 298 - 4 = 294. Evaluate 294 != 46, drop this branch.\n     |- Try 298 * 4 = 1192. Evaluate 1192 != 46, drop this branch.\n     |- Try 298 \/ 4 = 74.5. 74.5 is a decimal, drop this branch.\n    |- Try 304 * 6 = 1824. Add 1824 to the number set. Current number set: [1824, 4], target: 46, just two numbers left.\n     |- Try 1824 + 4 = 1828. Evaluate 1828 != 46, drop this branch.\n     |- Try 1824 - 4 = 1820. Evaluate 1820 != 46, drop this branch.\n     |- Try 1824 * 4 = 7296. 7296 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1824 \/ 4 = 456. Evaluate 456 != 46, drop this branch.\n    |- Try 304 \/ 6 = 50.7. 50.7 is a decimal, drop this branch.\n   |- Pick two numbers (304, 4) (numbers left: [6]). Try possible operations.\n    |- Try 304 + 4 = 308. Add 308 to the number set. Current number set: [308, 6], target: 46, just two numbers left.\n     |- Try 308 + 6 = 314. Evaluate 314 != 46, drop this branch.\n     |- Try 308 - 6 = 302. Evaluate 302 != 46, drop this branch.\n     |- Try 308 * 6 = 1848. Evaluate 1848 != 46, drop this branch.\n     |- Try 308 \/ 6 = 51.3. 51.3 is a decimal, drop this branch.\n    |- Try 304 - 4 = 300. Add 300 to the number set. Current number set: [300, 6], target: 46, just two numbers left.\n     |- Try 300 + 6 = 306. Evaluate 306 != 46, drop this branch.\n     |- Try 300 - 6 = 294. Evaluate 294 != 46, drop this branch.\n     |- Try 300 * 6 = 1800. Evaluate 1800 != 46, drop this branch.\n     |- Try 300 \/ 6 = 50. Evaluate 50 != 46, drop this branch.\n    |- Try 304 * 4 = 1216. Add 1216 to the number set. Current number set: [1216, 6], target: 46, just two numbers left.\n     |- Try 1216 + 6 = 1222. Evaluate 1222 != 46, drop this branch.\n     |- Try 1216 - 6 = 1210. Evaluate 1210 != 46, drop this branch.\n     |- Try 1216 * 6 = 7296. 7296 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1216 \/ 6 = 202.7. 202.7 is a decimal, drop this branch.\n    |- Try 304 \/ 4 = 76. Add 76 to the number set. Current number set: [76, 6], target: 46, just two numbers left.\n     |- Try 76 + 6 = 82. Evaluate 82 != 46, drop this branch.\n     |- Try 76 - 6 = 70. Evaluate 70 != 46, drop this branch.\n     |- Try 76 * 6 = 456. Evaluate 456 != 46, drop this branch.\n     |- Try 76 \/ 6 = 12.7. 12.7 is a decimal, drop this branch.\n   |- Pick two numbers (6, 4) (numbers left: [304]). Try possible operations.\n    |- Try 6 + 4 = 10. Add 10 to the number set. Current number set: [10, 304], target: 46, just two numbers left.\n     |- Try 304 + 10 = 314. Evaluate 314 != 46, drop this branch.\n     |- Try 304 - 10 = 294. Evaluate 294 != 46, drop this branch.\n     |- Try 304 * 10 = 3040. 3040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 304 \/ 10 = 30.4. 30.4 is a decimal, drop this branch.\n    |- Try 6 - 4 = 2. Add 2 to the number set. Current number set: [2, 304], target: 46, just two numbers left.\n     |- Try 304 + 2 = 306. Evaluate 306 != 46, drop this branch.\n     |- Try 304 - 2 = 302. Evaluate 302 != 46, drop this branch.\n     |- Try 304 * 2 = 608. Evaluate 608 != 46, drop this branch.\n     |- Try 304 \/ 2 = 152. Evaluate 152 != 46, drop this branch.\n    |- Try 6 * 4 = 24. Add 24 to the number set. Current number set: [24, 304], target: 46, just two numbers left.\n     |- Try 304 + 24 = 328. Evaluate 328 != 46, drop this branch.\n     |- Try 304 - 24 = 280. Evaluate 280 != 46, drop this branch.\n     |- Try 304 * 24 = 7296. 7296 exceeds the maximum intermediate result, drop this branch.\n     |- Try 304 \/ 24 = 12.7. 12.7 is a decimal, drop this branch.\n    |- Try 6 \/ 4 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 38 \/ 8 = 4.8. 4.8 is a decimal, drop this branch.\n |- Pick two numbers (38, 6) (numbers left: [8, 4]). Try possible operations.\n  |- Try 38 + 6 = 44. Add 44 to the number set. Current number set: [44, 8, 4], target: 46. Options for choosing two numbers: [(44, 8), (44, 4), (8, 4)].\n   |- Pick two numbers (44, 8) (numbers left: [4]). Try possible operations.\n    |- Try 44 + 8 = 52. Add 52 to the number set. Current number set: [52, 4], target: 46, just two numbers left.\n     |- Try 52 + 4 = 56. Evaluate 56 != 46, drop this branch.\n     |- Try 52 - 4 = 48. Evaluate 48 != 46, drop this branch.\n     |- Try 52 * 4 = 208. Evaluate 208 != 46, drop this branch.\n     |- Try 52 \/ 4 = 13. Evaluate 13 != 46, drop this branch.\n    |- Try 44 - 8 = 36. Add 36 to the number set. Current number set: [36, 4], target: 46, just two numbers left.\n     |- Try 36 + 4 = 40. Evaluate 40 != 46, drop this branch.\n     |- Try 36 - 4 = 32. Evaluate 32 != 46, drop this branch.\n     |- Try 36 * 4 = 144. Evaluate 144 != 46, drop this branch.\n     |- Try 36 \/ 4 = 9. Evaluate 9 != 46, drop this branch.\n    |- Try 44 * 8 = 352. Add 352 to the number set. Current number set: [352, 4], target: 46, just two numbers left.\n     |- Try 352 + 4 = 356. Evaluate 356 != 46, drop this branch.\n     |- Try 352 - 4 = 348. Evaluate 348 != 46, drop this branch.\n     |- Try 352 * 4 = 1408. Evaluate 1408 != 46, drop this branch.\n     |- Try 352 \/ 4 = 88. Evaluate 88 != 46, drop this branch.\n    |- Try 44 \/ 8 = 5.5. 5.5 is a decimal, drop this branch.\n   |- Pick two numbers (44, 4) (numbers left: [8]). Try possible operations.\n    |- Try 44 + 4 = 48. Add 48 to the number set. Current number set: [48, 8], target: 46, just two numbers left.\n     |- Try 48 + 8 = 56. Evaluate 56 != 46, drop this branch.\n     |- Try 48 - 8 = 40. Evaluate 40 != 46, drop this branch.\n     |- Try 48 * 8 = 384. Evaluate 384 != 46, drop this branch.\n     |- Try 48 \/ 8 = 6. Evaluate 6 != 46, drop this branch.\n    |- Try 44 - 4 = 40. Add 40 to the number set. Current number set: [40, 8], target: 46, just two numbers left.\n     |- Try 40 + 8 = 48. Evaluate 48 != 46, drop this branch.\n     |- Try 40 - 8 = 32. Evaluate 32 != 46, drop this branch.\n     |- Try 40 * 8 = 320. Evaluate 320 != 46, drop this branch.\n     |- Try 40 \/ 8 = 5. Evaluate 5 != 46, drop this branch.\n    |- Try 44 * 4 = 176. Add 176 to the number set. Current number set: [176, 8], target: 46, just two numbers left.\n     |- Try 176 + 8 = 184. Evaluate 184 != 46, drop this branch.\n     |- Try 176 - 8 = 168. Evaluate 168 != 46, drop this branch.\n     |- Try 176 * 8 = 1408. Evaluate 1408 != 46, drop this branch.\n     |- Try 176 \/ 8 = 22. Evaluate 22 != 46, drop this branch.\n    |- Try 44 \/ 4 = 11. Add 11 to the number set. Current number set: [11, 8], target: 46, just two numbers left.\n     |- Try 11 + 8 = 19. Evaluate 19 != 46, drop this branch.\n     |- Try 11 - 8 = 3. Evaluate 3 != 46, drop this branch.\n     |- Try 11 * 8 = 88. Evaluate 88 != 46, drop this branch.\n     |- Try 11 \/ 8 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (8, 4) (numbers left: [44]). Try possible operations.\n    |- Try 8 + 4 = 12. Add 12 to the number set. Current number set: [12, 44], target: 46, just two numbers left.\n     |- Try 44 + 12 = 56. Evaluate 56 != 46, drop this branch.\n     |- Try 44 - 12 = 32. Evaluate 32 != 46, drop this branch.\n     |- Try 44 * 12 = 528. Evaluate 528 != 46, drop this branch.\n     |- Try 44 \/ 12 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 8 - 4 = 4. Add 4 to the number set. Current number set: [4, 44], target: 46, just two numbers left.\n     |- Try 44 + 4 = 48. Evaluate 48 != 46, drop this branch.\n     |- Try 44 - 4 = 40. Evaluate 40 != 46, drop this branch.\n     |- Try 44 * 4 = 176. Evaluate 176 != 46, drop this branch.\n     |- Try 44 \/ 4 = 11. Evaluate 11 != 46, drop this branch.\n    |- Try 8 * 4 = 32. Add 32 to the number set. Current number set: [32, 44], target: 46, just two numbers left.\n     |- Try 44 + 32 = 76. Evaluate 76 != 46, drop this branch.\n     |- Try 44 - 32 = 12. Evaluate 12 != 46, drop this branch.\n     |- Try 44 * 32 = 1408. Evaluate 1408 != 46, drop this branch.\n     |- Try 44 \/ 32 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 8 \/ 4 = 2. Add 2 to the number set. Current number set: [2, 44], target: 46, just two numbers left.\n     |- Try 44 + 2 = 46. Evaluate 46 == 46, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 44 + 2 = 46\nThe step before: 8 \/ 4 = 2\nThe first step: 38 + 6 = 44\n\nOutput the solution in the required format:\n<Solution>\n38 + 6 = 44\n8 \/ 4 = 2\n44 + 2 = 46\n<\/Solution>\n","item":{"nums":[38,8,6,4],"solution":["38 + 6 = 44","8 \/ 4 = 2","44 + 2 = 46"],"target":46}}
+{"instance_id":"countdown_8k_130","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [7, 1, 39, 46]\nTarget: 49","reference_output":"# Search Procedure\nInitial number set: [7, 1, 39, 46], target: 49. Options for choosing two numbers: [(7, 1), (7, 39), (7, 46), (1, 39), (1, 46), (39, 46)].\n |- Pick two numbers (7, 1) (numbers left: [39, 46]). Try possible operations.\n  |- Try 7 + 1 = 8. Add 8 to the number set. Current number set: [8, 39, 46], target: 49. Options for choosing two numbers: [(8, 39), (8, 46), (39, 46)].\n   |- Pick two numbers (8, 39) (numbers left: [46]). Try possible operations.\n    |- Try 39 + 8 = 47. Add 47 to the number set. Current number set: [47, 46], target: 49, just two numbers left.\n     |- Try 47 + 46 = 93. Evaluate 93 != 49, drop this branch.\n     |- Try 47 - 46 = 1. Evaluate 1 != 49, drop this branch.\n     |- Try 47 * 46 = 2162. 2162 exceeds the maximum intermediate result, drop this branch.\n     |- Try 47 \/ 46 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 39 - 8 = 31. Add 31 to the number set. Current number set: [31, 46], target: 49, just two numbers left.\n     |- Try 46 + 31 = 77. Evaluate 77 != 49, drop this branch.\n     |- Try 46 - 31 = 15. Evaluate 15 != 49, drop this branch.\n     |- Try 46 * 31 = 1426. Evaluate 1426 != 49, drop this branch.\n     |- Try 46 \/ 31 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 39 * 8 = 312. Add 312 to the number set. Current number set: [312, 46], target: 49, just two numbers left.\n     |- Try 312 + 46 = 358. Evaluate 358 != 49, drop this branch.\n     |- Try 312 - 46 = 266. Evaluate 266 != 49, drop this branch.\n     |- Try 312 * 46 = 14352. 14352 exceeds the maximum intermediate result, drop this branch.\n     |- Try 312 \/ 46 = 6.8. 6.8 is a decimal, drop this branch.\n    |- Try 39 \/ 8 = 4.9. 4.9 is a decimal, drop this branch.\n   |- Pick two numbers (8, 46) (numbers left: [39]). Try possible operations.\n    |- Try 46 + 8 = 54. Add 54 to the number set. Current number set: [54, 39], target: 49, just two numbers left.\n     |- Try 54 + 39 = 93. Evaluate 93 != 49, drop this branch.\n     |- Try 54 - 39 = 15. Evaluate 15 != 49, drop this branch.\n     |- Try 54 * 39 = 2106. 2106 exceeds the maximum intermediate result, drop this branch.\n     |- Try 54 \/ 39 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 46 - 8 = 38. Add 38 to the number set. Current number set: [38, 39], target: 49, just two numbers left.\n     |- Try 39 + 38 = 77. Evaluate 77 != 49, drop this branch.\n     |- Try 39 - 38 = 1. Evaluate 1 != 49, drop this branch.\n     |- Try 39 * 38 = 1482. Evaluate 1482 != 49, drop this branch.\n     |- Try 39 \/ 38 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 46 * 8 = 368. Add 368 to the number set. Current number set: [368, 39], target: 49, just two numbers left.\n     |- Try 368 + 39 = 407. Evaluate 407 != 49, drop this branch.\n     |- Try 368 - 39 = 329. Evaluate 329 != 49, drop this branch.\n     |- Try 368 * 39 = 14352. 14352 exceeds the maximum intermediate result, drop this branch.\n     |- Try 368 \/ 39 = 9.4. 9.4 is a decimal, drop this branch.\n    |- Try 46 \/ 8 = 5.8. 5.8 is a decimal, drop this branch.\n   |- Pick two numbers (39, 46) (numbers left: [8]). Try possible operations.\n    |- Try 46 + 39 = 85. Add 85 to the number set. Current number set: [85, 8], target: 49, just two numbers left.\n     |- Try 85 + 8 = 93. Evaluate 93 != 49, drop this branch.\n     |- Try 85 - 8 = 77. Evaluate 77 != 49, drop this branch.\n     |- Try 85 * 8 = 680. Evaluate 680 != 49, drop this branch.\n     |- Try 85 \/ 8 = 10.6. 10.6 is a decimal, drop this branch.\n    |- Try 46 - 39 = 7. Add 7 to the number set. Current number set: [7, 8], target: 49, just two numbers left.\n     |- Try 8 + 7 = 15. Evaluate 15 != 49, drop this branch.\n     |- Try 8 - 7 = 1. Evaluate 1 != 49, drop this branch.\n     |- Try 8 * 7 = 56. Evaluate 56 != 49, drop this branch.\n     |- Try 8 \/ 7 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 46 * 39 = 1794. Add 1794 to the number set. Current number set: [1794, 8], target: 49, just two numbers left.\n     |- Try 1794 + 8 = 1802. Evaluate 1802 != 49, drop this branch.\n     |- Try 1794 - 8 = 1786. Evaluate 1786 != 49, drop this branch.\n     |- Try 1794 * 8 = 14352. 14352 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1794 \/ 8 = 224.2. 224.2 is a decimal, drop this branch.\n    |- Try 46 \/ 39 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 7 - 1 = 6. Add 6 to the number set. Current number set: [6, 39, 46], target: 49. Options for choosing two numbers: [(6, 39), (6, 46), (39, 46)].\n   |- Pick two numbers (6, 39) (numbers left: [46]). Try possible operations.\n    |- Try 39 + 6 = 45. Add 45 to the number set. Current number set: [45, 46], target: 49, just two numbers left.\n     |- Try 46 + 45 = 91. Evaluate 91 != 49, drop this branch.\n     |- Try 46 - 45 = 1. Evaluate 1 != 49, drop this branch.\n     |- Try 46 * 45 = 2070. 2070 exceeds the maximum intermediate result, drop this branch.\n     |- Try 46 \/ 45 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 39 - 6 = 33. Add 33 to the number set. Current number set: [33, 46], target: 49, just two numbers left.\n     |- Try 46 + 33 = 79. Evaluate 79 != 49, drop this branch.\n     |- Try 46 - 33 = 13. Evaluate 13 != 49, drop this branch.\n     |- Try 46 * 33 = 1518. Evaluate 1518 != 49, drop this branch.\n     |- Try 46 \/ 33 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 39 * 6 = 234. Add 234 to the number set. Current number set: [234, 46], target: 49, just two numbers left.\n     |- Try 234 + 46 = 280. Evaluate 280 != 49, drop this branch.\n     |- Try 234 - 46 = 188. Evaluate 188 != 49, drop this branch.\n     |- Try 234 * 46 = 10764. 10764 exceeds the maximum intermediate result, drop this branch.\n     |- Try 234 \/ 46 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 39 \/ 6 = 6.5. 6.5 is a decimal, drop this branch.\n   |- Pick two numbers (6, 46) (numbers left: [39]). Try possible operations.\n    |- Try 46 + 6 = 52. Add 52 to the number set. Current number set: [52, 39], target: 49, just two numbers left.\n     |- Try 52 + 39 = 91. Evaluate 91 != 49, drop this branch.\n     |- Try 52 - 39 = 13. Evaluate 13 != 49, drop this branch.\n     |- Try 52 * 39 = 2028. 2028 exceeds the maximum intermediate result, drop this branch.\n     |- Try 52 \/ 39 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 46 - 6 = 40. Add 40 to the number set. Current number set: [40, 39], target: 49, just two numbers left.\n     |- Try 40 + 39 = 79. Evaluate 79 != 49, drop this branch.\n     |- Try 40 - 39 = 1. Evaluate 1 != 49, drop this branch.\n     |- Try 40 * 39 = 1560. Evaluate 1560 != 49, drop this branch.\n     |- Try 40 \/ 39 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 46 * 6 = 276. Add 276 to the number set. Current number set: [276, 39], target: 49, just two numbers left.\n     |- Try 276 + 39 = 315. Evaluate 315 != 49, drop this branch.\n     |- Try 276 - 39 = 237. Evaluate 237 != 49, drop this branch.\n     |- Try 276 * 39 = 10764. 10764 exceeds the maximum intermediate result, drop this branch.\n     |- Try 276 \/ 39 = 7.1. 7.1 is a decimal, drop this branch.\n    |- Try 46 \/ 6 = 7.7. 7.7 is a decimal, drop this branch.\n   |- Pick two numbers (39, 46) (numbers left: [6]). Try possible operations.\n    |- Try 46 + 39 = 85. Add 85 to the number set. Current number set: [85, 6], target: 49, just two numbers left.\n     |- Try 85 + 6 = 91. Evaluate 91 != 49, drop this branch.\n     |- Try 85 - 6 = 79. Evaluate 79 != 49, drop this branch.\n     |- Try 85 * 6 = 510. Evaluate 510 != 49, drop this branch.\n     |- Try 85 \/ 6 = 14.2. 14.2 is a decimal, drop this branch.\n    |- Try 46 - 39 = 7. Add 7 to the number set. Current number set: [7, 6], target: 49, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 49, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 49, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 49, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 46 * 39 = 1794. Add 1794 to the number set. Current number set: [1794, 6], target: 49, just two numbers left.\n     |- Try 1794 + 6 = 1800. Evaluate 1800 != 49, drop this branch.\n     |- Try 1794 - 6 = 1788. Evaluate 1788 != 49, drop this branch.\n     |- Try 1794 * 6 = 10764. 10764 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1794 \/ 6 = 299. Evaluate 299 != 49, drop this branch.\n    |- Try 46 \/ 39 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 7 * 1 = 7. Add 7 to the number set. Current number set: [7, 39, 46], target: 49. Options for choosing two numbers: [(7, 39), (7, 46), (39, 46)].\n   |- Pick two numbers (7, 39) (numbers left: [46]). Try possible operations.\n    |- Try 39 + 7 = 46. Add 46 to the number set. Current number set: [46, 46], target: 49, just two numbers left.\n     |- Try 46 + 46 = 92. Evaluate 92 != 49, drop this branch.\n     |- Try 46 - 46 = 0. Evaluate 0 != 49, drop this branch.\n     |- Try 46 * 46 = 2116. 2116 exceeds the maximum intermediate result, drop this branch.\n     |- Try 46 \/ 46 = 1. Evaluate 1 != 49, drop this branch.\n    |- Try 39 - 7 = 32. Add 32 to the number set. Current number set: [32, 46], target: 49, just two numbers left.\n     |- Try 46 + 32 = 78. Evaluate 78 != 49, drop this branch.\n     |- Try 46 - 32 = 14. Evaluate 14 != 49, drop this branch.\n     |- Try 46 * 32 = 1472. Evaluate 1472 != 49, drop this branch.\n     |- Try 46 \/ 32 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 39 * 7 = 273. Add 273 to the number set. Current number set: [273, 46], target: 49, just two numbers left.\n     |- Try 273 + 46 = 319. Evaluate 319 != 49, drop this branch.\n     |- Try 273 - 46 = 227. Evaluate 227 != 49, drop this branch.\n     |- Try 273 * 46 = 12558. 12558 exceeds the maximum intermediate result, drop this branch.\n     |- Try 273 \/ 46 = 5.9. 5.9 is a decimal, drop this branch.\n    |- Try 39 \/ 7 = 5.6. 5.6 is a decimal, drop this branch.\n   |- Pick two numbers (7, 46) (numbers left: [39]). Try possible operations.\n    |- Try 46 + 7 = 53. Add 53 to the number set. Current number set: [53, 39], target: 49, just two numbers left.\n     |- Try 53 + 39 = 92. Evaluate 92 != 49, drop this branch.\n     |- Try 53 - 39 = 14. Evaluate 14 != 49, drop this branch.\n     |- Try 53 * 39 = 2067. 2067 exceeds the maximum intermediate result, drop this branch.\n     |- Try 53 \/ 39 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 46 - 7 = 39. Add 39 to the number set. Current number set: [39, 39], target: 49, just two numbers left.\n     |- Try 39 + 39 = 78. Evaluate 78 != 49, drop this branch.\n     |- Try 39 - 39 = 0. Evaluate 0 != 49, drop this branch.\n     |- Try 39 * 39 = 1521. Evaluate 1521 != 49, drop this branch.\n     |- Try 39 \/ 39 = 1. Evaluate 1 != 49, drop this branch.\n    |- Try 46 * 7 = 322. Add 322 to the number set. Current number set: [322, 39], target: 49, just two numbers left.\n     |- Try 322 + 39 = 361. Evaluate 361 != 49, drop this branch.\n     |- Try 322 - 39 = 283. Evaluate 283 != 49, drop this branch.\n     |- Try 322 * 39 = 12558. 12558 exceeds the maximum intermediate result, drop this branch.\n     |- Try 322 \/ 39 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 46 \/ 7 = 6.6. 6.6 is a decimal, drop this branch.\n   |- Pick two numbers (39, 46) (numbers left: [7]). Try possible operations.\n    |- Try 46 + 39 = 85. Add 85 to the number set. Current number set: [85, 7], target: 49, just two numbers left.\n     |- Try 85 + 7 = 92. Evaluate 92 != 49, drop this branch.\n     |- Try 85 - 7 = 78. Evaluate 78 != 49, drop this branch.\n     |- Try 85 * 7 = 595. Evaluate 595 != 49, drop this branch.\n     |- Try 85 \/ 7 = 12.1. 12.1 is a decimal, drop this branch.\n    |- Try 46 - 39 = 7. Add 7 to the number set. Current number set: [7, 7], target: 49, just two numbers left.\n     |- Try 7 + 7 = 14. Evaluate 14 != 49, drop this branch.\n     |- Try 7 - 7 = 0. Evaluate 0 != 49, drop this branch.\n     |- Try 7 * 7 = 49. Evaluate 49 == 49, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 7 * 7 = 49\nThe step before: 46 - 39 = 7\nThe first step: 7 * 1 = 7\n\nOutput the solution in the required format:\n<Solution>\n7 * 1 = 7\n46 - 39 = 7\n7 * 7 = 49\n<\/Solution>\n","item":{"nums":[7,1,39,46],"solution":["7 * 1 = 7","46 - 39 = 7","7 * 7 = 49"],"target":49}}
+{"instance_id":"countdown_8k_131","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [13, 43, 31, 45]\nTarget: 22","reference_output":"# Search Procedure\nInitial number set: [13, 43, 31, 45], target: 22. Options for choosing two numbers: [(13, 43), (13, 31), (13, 45), (43, 31), (43, 45), (31, 45)].\n |- Pick two numbers (13, 43) (numbers left: [31, 45]). Try possible operations.\n  |- Try 43 + 13 = 56. Add 56 to the number set. Current number set: [56, 31, 45], target: 22. Options for choosing two numbers: [(56, 31), (56, 45), (31, 45)].\n   |- Pick two numbers (56, 31) (numbers left: [45]). Try possible operations.\n    |- Try 56 + 31 = 87. Add 87 to the number set. Current number set: [87, 45], target: 22, just two numbers left.\n     |- Try 87 + 45 = 132. Evaluate 132 != 22, drop this branch.\n     |- Try 87 - 45 = 42. Evaluate 42 != 22, drop this branch.\n     |- Try 87 * 45 = 3915. 3915 exceeds the maximum intermediate result, drop this branch.\n     |- Try 87 \/ 45 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 56 - 31 = 25. Add 25 to the number set. Current number set: [25, 45], target: 22, just two numbers left.\n     |- Try 45 + 25 = 70. Evaluate 70 != 22, drop this branch.\n     |- Try 45 - 25 = 20. Evaluate 20 != 22, drop this branch.\n     |- Try 45 * 25 = 1125. Evaluate 1125 != 22, drop this branch.\n     |- Try 45 \/ 25 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 56 * 31 = 1736. Add 1736 to the number set. Current number set: [1736, 45], target: 22, just two numbers left.\n     |- Try 1736 + 45 = 1781. Evaluate 1781 != 22, drop this branch.\n     |- Try 1736 - 45 = 1691. Evaluate 1691 != 22, drop this branch.\n     |- Try 1736 * 45 = 78120. 78120 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1736 \/ 45 = 38.6. 38.6 is a decimal, drop this branch.\n    |- Try 56 \/ 31 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (56, 45) (numbers left: [31]). Try possible operations.\n    |- Try 56 + 45 = 101. Add 101 to the number set. Current number set: [101, 31], target: 22, just two numbers left.\n     |- Try 101 + 31 = 132. Evaluate 132 != 22, drop this branch.\n     |- Try 101 - 31 = 70. Evaluate 70 != 22, drop this branch.\n     |- Try 101 * 31 = 3131. 3131 exceeds the maximum intermediate result, drop this branch.\n     |- Try 101 \/ 31 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 56 - 45 = 11. Add 11 to the number set. Current number set: [11, 31], target: 22, just two numbers left.\n     |- Try 31 + 11 = 42. Evaluate 42 != 22, drop this branch.\n     |- Try 31 - 11 = 20. Evaluate 20 != 22, drop this branch.\n     |- Try 31 * 11 = 341. Evaluate 341 != 22, drop this branch.\n     |- Try 31 \/ 11 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 56 * 45 = 2520. 2520 exceeds the maximum intermediate result, drop this branch.\n    |- Try 56 \/ 45 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (31, 45) (numbers left: [56]). Try possible operations.\n    |- Try 45 + 31 = 76. Add 76 to the number set. Current number set: [76, 56], target: 22, just two numbers left.\n     |- Try 76 + 56 = 132. Evaluate 132 != 22, drop this branch.\n     |- Try 76 - 56 = 20. Evaluate 20 != 22, drop this branch.\n     |- Try 76 * 56 = 4256. 4256 exceeds the maximum intermediate result, drop this branch.\n     |- Try 76 \/ 56 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 45 - 31 = 14. Add 14 to the number set. Current number set: [14, 56], target: 22, just two numbers left.\n     |- Try 56 + 14 = 70. Evaluate 70 != 22, drop this branch.\n     |- Try 56 - 14 = 42. Evaluate 42 != 22, drop this branch.\n     |- Try 56 * 14 = 784. Evaluate 784 != 22, drop this branch.\n     |- Try 56 \/ 14 = 4. Evaluate 4 != 22, drop this branch.\n    |- Try 45 * 31 = 1395. Add 1395 to the number set. Current number set: [1395, 56], target: 22, just two numbers left.\n     |- Try 1395 + 56 = 1451. Evaluate 1451 != 22, drop this branch.\n     |- Try 1395 - 56 = 1339. Evaluate 1339 != 22, drop this branch.\n     |- Try 1395 * 56 = 78120. 78120 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1395 \/ 56 = 24.9. 24.9 is a decimal, drop this branch.\n    |- Try 45 \/ 31 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 43 - 13 = 30. Add 30 to the number set. Current number set: [30, 31, 45], target: 22. Options for choosing two numbers: [(30, 31), (30, 45), (31, 45)].\n   |- Pick two numbers (30, 31) (numbers left: [45]). Try possible operations.\n    |- Try 31 + 30 = 61. Add 61 to the number set. Current number set: [61, 45], target: 22, just two numbers left.\n     |- Try 61 + 45 = 106. Evaluate 106 != 22, drop this branch.\n     |- Try 61 - 45 = 16. Evaluate 16 != 22, drop this branch.\n     |- Try 61 * 45 = 2745. 2745 exceeds the maximum intermediate result, drop this branch.\n     |- Try 61 \/ 45 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 31 - 30 = 1. Add 1 to the number set. Current number set: [1, 45], target: 22, just two numbers left.\n     |- Try 45 + 1 = 46. Evaluate 46 != 22, drop this branch.\n     |- Try 45 - 1 = 44. Evaluate 44 != 22, drop this branch.\n     |- Try 45 * 1 = 45. Evaluate 45 != 22, drop this branch.\n     |- Try 45 \/ 1 = 45. Evaluate 45 != 22, drop this branch.\n    |- Try 31 * 30 = 930. Add 930 to the number set. Current number set: [930, 45], target: 22, just two numbers left.\n     |- Try 930 + 45 = 975. Evaluate 975 != 22, drop this branch.\n     |- Try 930 - 45 = 885. Evaluate 885 != 22, drop this branch.\n     |- Try 930 * 45 = 41850. 41850 exceeds the maximum intermediate result, drop this branch.\n     |- Try 930 \/ 45 = 20.7. 20.7 is a decimal, drop this branch.\n    |- Try 31 \/ 30 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (30, 45) (numbers left: [31]). Try possible operations.\n    |- Try 45 + 30 = 75. Add 75 to the number set. Current number set: [75, 31], target: 22, just two numbers left.\n     |- Try 75 + 31 = 106. Evaluate 106 != 22, drop this branch.\n     |- Try 75 - 31 = 44. Evaluate 44 != 22, drop this branch.\n     |- Try 75 * 31 = 2325. 2325 exceeds the maximum intermediate result, drop this branch.\n     |- Try 75 \/ 31 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 45 - 30 = 15. Add 15 to the number set. Current number set: [15, 31], target: 22, just two numbers left.\n     |- Try 31 + 15 = 46. Evaluate 46 != 22, drop this branch.\n     |- Try 31 - 15 = 16. Evaluate 16 != 22, drop this branch.\n     |- Try 31 * 15 = 465. Evaluate 465 != 22, drop this branch.\n     |- Try 31 \/ 15 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 45 * 30 = 1350. Add 1350 to the number set. Current number set: [1350, 31], target: 22, just two numbers left.\n     |- Try 1350 + 31 = 1381. Evaluate 1381 != 22, drop this branch.\n     |- Try 1350 - 31 = 1319. Evaluate 1319 != 22, drop this branch.\n     |- Try 1350 * 31 = 41850. 41850 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1350 \/ 31 = 43.5. 43.5 is a decimal, drop this branch.\n    |- Try 45 \/ 30 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (31, 45) (numbers left: [30]). Try possible operations.\n    |- Try 45 + 31 = 76. Add 76 to the number set. Current number set: [76, 30], target: 22, just two numbers left.\n     |- Try 76 + 30 = 106. Evaluate 106 != 22, drop this branch.\n     |- Try 76 - 30 = 46. Evaluate 46 != 22, drop this branch.\n     |- Try 76 * 30 = 2280. 2280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 76 \/ 30 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 45 - 31 = 14. Add 14 to the number set. Current number set: [14, 30], target: 22, just two numbers left.\n     |- Try 30 + 14 = 44. Evaluate 44 != 22, drop this branch.\n     |- Try 30 - 14 = 16. Evaluate 16 != 22, drop this branch.\n     |- Try 30 * 14 = 420. Evaluate 420 != 22, drop this branch.\n     |- Try 30 \/ 14 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 45 * 31 = 1395. Add 1395 to the number set. Current number set: [1395, 30], target: 22, just two numbers left.\n     |- Try 1395 + 30 = 1425. Evaluate 1425 != 22, drop this branch.\n     |- Try 1395 - 30 = 1365. Evaluate 1365 != 22, drop this branch.\n     |- Try 1395 * 30 = 41850. 41850 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1395 \/ 30 = 46.5. 46.5 is a decimal, drop this branch.\n    |- Try 45 \/ 31 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 43 * 13 = 559. Add 559 to the number set. Current number set: [559, 31, 45], target: 22. Options for choosing two numbers: [(559, 31), (559, 45), (31, 45)].\n   |- Pick two numbers (559, 31) (numbers left: [45]). Try possible operations.\n    |- Try 559 + 31 = 590. Add 590 to the number set. Current number set: [590, 45], target: 22, just two numbers left.\n     |- Try 590 + 45 = 635. Evaluate 635 != 22, drop this branch.\n     |- Try 590 - 45 = 545. Evaluate 545 != 22, drop this branch.\n     |- Try 590 * 45 = 26550. 26550 exceeds the maximum intermediate result, drop this branch.\n     |- Try 590 \/ 45 = 13.1. 13.1 is a decimal, drop this branch.\n    |- Try 559 - 31 = 528. Add 528 to the number set. Current number set: [528, 45], target: 22, just two numbers left.\n     |- Try 528 + 45 = 573. Evaluate 573 != 22, drop this branch.\n     |- Try 528 - 45 = 483. Evaluate 483 != 22, drop this branch.\n     |- Try 528 * 45 = 23760. 23760 exceeds the maximum intermediate result, drop this branch.\n     |- Try 528 \/ 45 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 559 * 31 = 17329. 17329 exceeds the maximum intermediate result, drop this branch.\n    |- Try 559 \/ 31 = 18.0. 18.0 is a decimal, drop this branch.\n   |- Pick two numbers (559, 45) (numbers left: [31]). Try possible operations.\n    |- Try 559 + 45 = 604. Add 604 to the number set. Current number set: [604, 31], target: 22, just two numbers left.\n     |- Try 604 + 31 = 635. Evaluate 635 != 22, drop this branch.\n     |- Try 604 - 31 = 573. Evaluate 573 != 22, drop this branch.\n     |- Try 604 * 31 = 18724. 18724 exceeds the maximum intermediate result, drop this branch.\n     |- Try 604 \/ 31 = 19.5. 19.5 is a decimal, drop this branch.\n    |- Try 559 - 45 = 514. Add 514 to the number set. Current number set: [514, 31], target: 22, just two numbers left.\n     |- Try 514 + 31 = 545. Evaluate 545 != 22, drop this branch.\n     |- Try 514 - 31 = 483. Evaluate 483 != 22, drop this branch.\n     |- Try 514 * 31 = 15934. 15934 exceeds the maximum intermediate result, drop this branch.\n     |- Try 514 \/ 31 = 16.6. 16.6 is a decimal, drop this branch.\n    |- Try 559 * 45 = 25155. 25155 exceeds the maximum intermediate result, drop this branch.\n    |- Try 559 \/ 45 = 12.4. 12.4 is a decimal, drop this branch.\n   |- Pick two numbers (31, 45) (numbers left: [559]). Try possible operations.\n    |- Try 45 + 31 = 76. Add 76 to the number set. Current number set: [76, 559], target: 22, just two numbers left.\n     |- Try 559 + 76 = 635. Evaluate 635 != 22, drop this branch.\n     |- Try 559 - 76 = 483. Evaluate 483 != 22, drop this branch.\n     |- Try 559 * 76 = 42484. 42484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 559 \/ 76 = 7.4. 7.4 is a decimal, drop this branch.\n    |- Try 45 - 31 = 14. Add 14 to the number set. Current number set: [14, 559], target: 22, just two numbers left.\n     |- Try 559 + 14 = 573. Evaluate 573 != 22, drop this branch.\n     |- Try 559 - 14 = 545. Evaluate 545 != 22, drop this branch.\n     |- Try 559 * 14 = 7826. 7826 exceeds the maximum intermediate result, drop this branch.\n     |- Try 559 \/ 14 = 39.9. 39.9 is a decimal, drop this branch.\n    |- Try 45 * 31 = 1395. Add 1395 to the number set. Current number set: [1395, 559], target: 22, just two numbers left.\n     |- Try 1395 + 559 = 1954. Evaluate 1954 != 22, drop this branch.\n     |- Try 1395 - 559 = 836. Evaluate 836 != 22, drop this branch.\n     |- Try 1395 * 559 = 779805. 779805 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1395 \/ 559 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 45 \/ 31 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 43 \/ 13 = 3.3. 3.3 is a decimal, drop this branch.\n |- Pick two numbers (13, 31) (numbers left: [43, 45]). Try possible operations.\n  |- Try 31 + 13 = 44. Add 44 to the number set. Current number set: [44, 43, 45], target: 22. Options for choosing two numbers: [(44, 43), (44, 45), (43, 45)].\n   |- Pick two numbers (44, 43) (numbers left: [45]). Try possible operations.\n    |- Try 44 + 43 = 87. Add 87 to the number set. Current number set: [87, 45], target: 22, just two numbers left.\n     |- Try 87 + 45 = 132. Evaluate 132 != 22, drop this branch.\n     |- Try 87 - 45 = 42. Evaluate 42 != 22, drop this branch.\n     |- Try 87 * 45 = 3915. 3915 exceeds the maximum intermediate result, drop this branch.\n     |- Try 87 \/ 45 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 44 - 43 = 1. Add 1 to the number set. Current number set: [1, 45], target: 22, just two numbers left.\n     |- Try 45 + 1 = 46. Evaluate 46 != 22, drop this branch.\n     |- Try 45 - 1 = 44. Evaluate 44 != 22, drop this branch.\n     |- Try 45 * 1 = 45. Evaluate 45 != 22, drop this branch.\n     |- Try 45 \/ 1 = 45. Evaluate 45 != 22, drop this branch.\n    |- Try 44 * 43 = 1892. Add 1892 to the number set. Current number set: [1892, 45], target: 22, just two numbers left.\n     |- Try 1892 + 45 = 1937. Evaluate 1937 != 22, drop this branch.\n     |- Try 1892 - 45 = 1847. Evaluate 1847 != 22, drop this branch.\n     |- Try 1892 * 45 = 85140. 85140 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1892 \/ 45 = 42.0. 42.0 is a decimal, drop this branch.\n    |- Try 44 \/ 43 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (44, 45) (numbers left: [43]). Try possible operations.\n    |- Try 45 + 44 = 89. Add 89 to the number set. Current number set: [89, 43], target: 22, just two numbers left.\n     |- Try 89 + 43 = 132. Evaluate 132 != 22, drop this branch.\n     |- Try 89 - 43 = 46. Evaluate 46 != 22, drop this branch.\n     |- Try 89 * 43 = 3827. 3827 exceeds the maximum intermediate result, drop this branch.\n     |- Try 89 \/ 43 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 45 - 44 = 1. Add 1 to the number set. Current number set: [1, 43], target: 22, just two numbers left.\n     |- Try 43 + 1 = 44. Evaluate 44 != 22, drop this branch.\n     |- Try 43 - 1 = 42. Evaluate 42 != 22, drop this branch.\n     |- Try 43 * 1 = 43. Evaluate 43 != 22, drop this branch.\n     |- Try 43 \/ 1 = 43. Evaluate 43 != 22, drop this branch.\n    |- Try 45 * 44 = 1980. Add 1980 to the number set. Current number set: [1980, 43], target: 22, just two numbers left.\n     |- Try 1980 + 43 = 2023. 2023 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1980 - 43 = 1937. Evaluate 1937 != 22, drop this branch.\n     |- Try 1980 * 43 = 85140. 85140 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1980 \/ 43 = 46.0. 46.0 is a decimal, drop this branch.\n    |- Try 45 \/ 44 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (43, 45) (numbers left: [44]). Try possible operations.\n    |- Try 45 + 43 = 88. Add 88 to the number set. Current number set: [88, 44], target: 22, just two numbers left.\n     |- Try 88 + 44 = 132. Evaluate 132 != 22, drop this branch.\n     |- Try 88 - 44 = 44. Evaluate 44 != 22, drop this branch.\n     |- Try 88 * 44 = 3872. 3872 exceeds the maximum intermediate result, drop this branch.\n     |- Try 88 \/ 44 = 2. Evaluate 2 != 22, drop this branch.\n    |- Try 45 - 43 = 2. Add 2 to the number set. Current number set: [2, 44], target: 22, just two numbers left.\n     |- Try 44 + 2 = 46. Evaluate 46 != 22, drop this branch.\n     |- Try 44 - 2 = 42. Evaluate 42 != 22, drop this branch.\n     |- Try 44 * 2 = 88. Evaluate 88 != 22, drop this branch.\n     |- Try 44 \/ 2 = 22. Evaluate 22 == 22, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 44 \/ 2 = 22\nThe step before: 45 - 43 = 2\nThe first step: 31 + 13 = 44\n\nOutput the solution in the required format:\n<Solution>\n31 + 13 = 44\n45 - 43 = 2\n44 \/ 2 = 22\n<\/Solution>\n","item":{"nums":[13,43,31,45],"solution":["31 + 13 = 44","45 - 43 = 2","44 \/ 2 = 22"],"target":22}}
+{"instance_id":"countdown_8k_132","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [1, 5, 23, 2]\nTarget: 33","reference_output":"# Search Procedure\nInitial number set: [1, 5, 23, 2], target: 33. Options for choosing two numbers: [(1, 5), (1, 23), (1, 2), (5, 23), (5, 2), (23, 2)].\n |- Pick two numbers (1, 5) (numbers left: [23, 2]). Try possible operations.\n  |- Try 5 + 1 = 6. Add 6 to the number set. Current number set: [6, 23, 2], target: 33. Options for choosing two numbers: [(6, 23), (6, 2), (23, 2)].\n   |- Pick two numbers (6, 23) (numbers left: [2]). Try possible operations.\n    |- Try 23 + 6 = 29. Add 29 to the number set. Current number set: [29, 2], target: 33, just two numbers left.\n     |- Try 29 + 2 = 31. Evaluate 31 != 33, drop this branch.\n     |- Try 29 - 2 = 27. Evaluate 27 != 33, drop this branch.\n     |- Try 29 * 2 = 58. Evaluate 58 != 33, drop this branch.\n     |- Try 29 \/ 2 = 14.5. 14.5 is a decimal, drop this branch.\n    |- Try 23 - 6 = 17. Add 17 to the number set. Current number set: [17, 2], target: 33, just two numbers left.\n     |- Try 17 + 2 = 19. Evaluate 19 != 33, drop this branch.\n     |- Try 17 - 2 = 15. Evaluate 15 != 33, drop this branch.\n     |- Try 17 * 2 = 34. Evaluate 34 != 33, drop this branch.\n     |- Try 17 \/ 2 = 8.5. 8.5 is a decimal, drop this branch.\n    |- Try 23 * 6 = 138. Add 138 to the number set. Current number set: [138, 2], target: 33, just two numbers left.\n     |- Try 138 + 2 = 140. Evaluate 140 != 33, drop this branch.\n     |- Try 138 - 2 = 136. Evaluate 136 != 33, drop this branch.\n     |- Try 138 * 2 = 276. Evaluate 276 != 33, drop this branch.\n     |- Try 138 \/ 2 = 69. Evaluate 69 != 33, drop this branch.\n    |- Try 23 \/ 6 = 3.8. 3.8 is a decimal, drop this branch.\n   |- Pick two numbers (6, 2) (numbers left: [23]). Try possible operations.\n    |- Try 6 + 2 = 8. Add 8 to the number set. Current number set: [8, 23], target: 33, just two numbers left.\n     |- Try 23 + 8 = 31. Evaluate 31 != 33, drop this branch.\n     |- Try 23 - 8 = 15. Evaluate 15 != 33, drop this branch.\n     |- Try 23 * 8 = 184. Evaluate 184 != 33, drop this branch.\n     |- Try 23 \/ 8 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 6 - 2 = 4. Add 4 to the number set. Current number set: [4, 23], target: 33, just two numbers left.\n     |- Try 23 + 4 = 27. Evaluate 27 != 33, drop this branch.\n     |- Try 23 - 4 = 19. Evaluate 19 != 33, drop this branch.\n     |- Try 23 * 4 = 92. Evaluate 92 != 33, drop this branch.\n     |- Try 23 \/ 4 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 6 * 2 = 12. Add 12 to the number set. Current number set: [12, 23], target: 33, just two numbers left.\n     |- Try 23 + 12 = 35. Evaluate 35 != 33, drop this branch.\n     |- Try 23 - 12 = 11. Evaluate 11 != 33, drop this branch.\n     |- Try 23 * 12 = 276. Evaluate 276 != 33, drop this branch.\n     |- Try 23 \/ 12 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 6 \/ 2 = 3. Add 3 to the number set. Current number set: [3, 23], target: 33, just two numbers left.\n     |- Try 23 + 3 = 26. Evaluate 26 != 33, drop this branch.\n     |- Try 23 - 3 = 20. Evaluate 20 != 33, drop this branch.\n     |- Try 23 * 3 = 69. Evaluate 69 != 33, drop this branch.\n     |- Try 23 \/ 3 = 7.7. 7.7 is a decimal, drop this branch.\n   |- Pick two numbers (23, 2) (numbers left: [6]). Try possible operations.\n    |- Try 23 + 2 = 25. Add 25 to the number set. Current number set: [25, 6], target: 33, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 33, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 33, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 33, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 23 - 2 = 21. Add 21 to the number set. Current number set: [21, 6], target: 33, just two numbers left.\n     |- Try 21 + 6 = 27. Evaluate 27 != 33, drop this branch.\n     |- Try 21 - 6 = 15. Evaluate 15 != 33, drop this branch.\n     |- Try 21 * 6 = 126. Evaluate 126 != 33, drop this branch.\n     |- Try 21 \/ 6 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 23 * 2 = 46. Add 46 to the number set. Current number set: [46, 6], target: 33, just two numbers left.\n     |- Try 46 + 6 = 52. Evaluate 52 != 33, drop this branch.\n     |- Try 46 - 6 = 40. Evaluate 40 != 33, drop this branch.\n     |- Try 46 * 6 = 276. Evaluate 276 != 33, drop this branch.\n     |- Try 46 \/ 6 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 23 \/ 2 = 11.5. 11.5 is a decimal, drop this branch.\n  |- Try 5 - 1 = 4. Add 4 to the number set. Current number set: [4, 23, 2], target: 33. Options for choosing two numbers: [(4, 23), (4, 2), (23, 2)].\n   |- Pick two numbers (4, 23) (numbers left: [2]). Try possible operations.\n    |- Try 23 + 4 = 27. Add 27 to the number set. Current number set: [27, 2], target: 33, just two numbers left.\n     |- Try 27 + 2 = 29. Evaluate 29 != 33, drop this branch.\n     |- Try 27 - 2 = 25. Evaluate 25 != 33, drop this branch.\n     |- Try 27 * 2 = 54. Evaluate 54 != 33, drop this branch.\n     |- Try 27 \/ 2 = 13.5. 13.5 is a decimal, drop this branch.\n    |- Try 23 - 4 = 19. Add 19 to the number set. Current number set: [19, 2], target: 33, just two numbers left.\n     |- Try 19 + 2 = 21. Evaluate 21 != 33, drop this branch.\n     |- Try 19 - 2 = 17. Evaluate 17 != 33, drop this branch.\n     |- Try 19 * 2 = 38. Evaluate 38 != 33, drop this branch.\n     |- Try 19 \/ 2 = 9.5. 9.5 is a decimal, drop this branch.\n    |- Try 23 * 4 = 92. Add 92 to the number set. Current number set: [92, 2], target: 33, just two numbers left.\n     |- Try 92 + 2 = 94. Evaluate 94 != 33, drop this branch.\n     |- Try 92 - 2 = 90. Evaluate 90 != 33, drop this branch.\n     |- Try 92 * 2 = 184. Evaluate 184 != 33, drop this branch.\n     |- Try 92 \/ 2 = 46. Evaluate 46 != 33, drop this branch.\n    |- Try 23 \/ 4 = 5.8. 5.8 is a decimal, drop this branch.\n   |- Pick two numbers (4, 2) (numbers left: [23]). Try possible operations.\n    |- Try 4 + 2 = 6. Add 6 to the number set. Current number set: [6, 23], target: 33, just two numbers left.\n     |- Try 23 + 6 = 29. Evaluate 29 != 33, drop this branch.\n     |- Try 23 - 6 = 17. Evaluate 17 != 33, drop this branch.\n     |- Try 23 * 6 = 138. Evaluate 138 != 33, drop this branch.\n     |- Try 23 \/ 6 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 4 - 2 = 2. Add 2 to the number set. Current number set: [2, 23], target: 33, just two numbers left.\n     |- Try 23 + 2 = 25. Evaluate 25 != 33, drop this branch.\n     |- Try 23 - 2 = 21. Evaluate 21 != 33, drop this branch.\n     |- Try 23 * 2 = 46. Evaluate 46 != 33, drop this branch.\n     |- Try 23 \/ 2 = 11.5. 11.5 is a decimal, drop this branch.\n    |- Try 4 * 2 = 8. Add 8 to the number set. Current number set: [8, 23], target: 33, just two numbers left.\n     |- Try 23 + 8 = 31. Evaluate 31 != 33, drop this branch.\n     |- Try 23 - 8 = 15. Evaluate 15 != 33, drop this branch.\n     |- Try 23 * 8 = 184. Evaluate 184 != 33, drop this branch.\n     |- Try 23 \/ 8 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 4 \/ 2 = 2. Add 2 to the number set. Current number set: [2, 23], target: 33, just two numbers left.\n     |- Try 23 + 2 = 25. Evaluate 25 != 33, drop this branch.\n     |- Try 23 - 2 = 21. Evaluate 21 != 33, drop this branch.\n     |- Try 23 * 2 = 46. Evaluate 46 != 33, drop this branch.\n     |- Try 23 \/ 2 = 11.5. 11.5 is a decimal, drop this branch.\n   |- Pick two numbers (23, 2) (numbers left: [4]). Try possible operations.\n    |- Try 23 + 2 = 25. Add 25 to the number set. Current number set: [25, 4], target: 33, just two numbers left.\n     |- Try 25 + 4 = 29. Evaluate 29 != 33, drop this branch.\n     |- Try 25 - 4 = 21. Evaluate 21 != 33, drop this branch.\n     |- Try 25 * 4 = 100. Evaluate 100 != 33, drop this branch.\n     |- Try 25 \/ 4 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 23 - 2 = 21. Add 21 to the number set. Current number set: [21, 4], target: 33, just two numbers left.\n     |- Try 21 + 4 = 25. Evaluate 25 != 33, drop this branch.\n     |- Try 21 - 4 = 17. Evaluate 17 != 33, drop this branch.\n     |- Try 21 * 4 = 84. Evaluate 84 != 33, drop this branch.\n     |- Try 21 \/ 4 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 23 * 2 = 46. Add 46 to the number set. Current number set: [46, 4], target: 33, just two numbers left.\n     |- Try 46 + 4 = 50. Evaluate 50 != 33, drop this branch.\n     |- Try 46 - 4 = 42. Evaluate 42 != 33, drop this branch.\n     |- Try 46 * 4 = 184. Evaluate 184 != 33, drop this branch.\n     |- Try 46 \/ 4 = 11.5. 11.5 is a decimal, drop this branch.\n    |- Try 23 \/ 2 = 11.5. 11.5 is a decimal, drop this branch.\n  |- Try 5 * 1 = 5. Add 5 to the number set. Current number set: [5, 23, 2], target: 33. Options for choosing two numbers: [(5, 23), (5, 2), (23, 2)].\n   |- Pick two numbers (5, 23) (numbers left: [2]). Try possible operations.\n    |- Try 23 + 5 = 28. Add 28 to the number set. Current number set: [28, 2], target: 33, just two numbers left.\n     |- Try 28 + 2 = 30. Evaluate 30 != 33, drop this branch.\n     |- Try 28 - 2 = 26. Evaluate 26 != 33, drop this branch.\n     |- Try 28 * 2 = 56. Evaluate 56 != 33, drop this branch.\n     |- Try 28 \/ 2 = 14. Evaluate 14 != 33, drop this branch.\n    |- Try 23 - 5 = 18. Add 18 to the number set. Current number set: [18, 2], target: 33, just two numbers left.\n     |- Try 18 + 2 = 20. Evaluate 20 != 33, drop this branch.\n     |- Try 18 - 2 = 16. Evaluate 16 != 33, drop this branch.\n     |- Try 18 * 2 = 36. Evaluate 36 != 33, drop this branch.\n     |- Try 18 \/ 2 = 9. Evaluate 9 != 33, drop this branch.\n    |- Try 23 * 5 = 115. Add 115 to the number set. Current number set: [115, 2], target: 33, just two numbers left.\n     |- Try 115 + 2 = 117. Evaluate 117 != 33, drop this branch.\n     |- Try 115 - 2 = 113. Evaluate 113 != 33, drop this branch.\n     |- Try 115 * 2 = 230. Evaluate 230 != 33, drop this branch.\n     |- Try 115 \/ 2 = 57.5. 57.5 is a decimal, drop this branch.\n    |- Try 23 \/ 5 = 4.6. 4.6 is a decimal, drop this branch.\n   |- Pick two numbers (5, 2) (numbers left: [23]). Try possible operations.\n    |- Try 5 + 2 = 7. Add 7 to the number set. Current number set: [7, 23], target: 33, just two numbers left.\n     |- Try 23 + 7 = 30. Evaluate 30 != 33, drop this branch.\n     |- Try 23 - 7 = 16. Evaluate 16 != 33, drop this branch.\n     |- Try 23 * 7 = 161. Evaluate 161 != 33, drop this branch.\n     |- Try 23 \/ 7 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 5 - 2 = 3. Add 3 to the number set. Current number set: [3, 23], target: 33, just two numbers left.\n     |- Try 23 + 3 = 26. Evaluate 26 != 33, drop this branch.\n     |- Try 23 - 3 = 20. Evaluate 20 != 33, drop this branch.\n     |- Try 23 * 3 = 69. Evaluate 69 != 33, drop this branch.\n     |- Try 23 \/ 3 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 5 * 2 = 10. Add 10 to the number set. Current number set: [10, 23], target: 33, just two numbers left.\n     |- Try 23 + 10 = 33. Evaluate 33 == 33, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 23 + 10 = 33\nThe step before: 5 * 2 = 10\nThe first step: 5 * 1 = 5\n\nOutput the solution in the required format:\n<Solution>\n5 * 1 = 5\n5 * 2 = 10\n23 + 10 = 33\n<\/Solution>\n","item":{"nums":[1,5,23,2],"solution":["5 * 1 = 5","5 * 2 = 10","23 + 10 = 33"],"target":33}}
+{"instance_id":"countdown_8k_133","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [8, 10, 9, 13]\nTarget: 23","reference_output":"# Search Procedure\nInitial number set: [8, 10, 9, 13], target: 23. Options for choosing two numbers: [(8, 10), (8, 9), (8, 13), (10, 9), (10, 13), (9, 13)].\n |- Pick two numbers (8, 10) (numbers left: [9, 13]). Try possible operations.\n  |- Try 10 + 8 = 18. Add 18 to the number set. Current number set: [18, 9, 13], target: 23. Options for choosing two numbers: [(18, 9), (18, 13), (9, 13)].\n   |- Pick two numbers (18, 9) (numbers left: [13]). Try possible operations.\n    |- Try 18 + 9 = 27. Add 27 to the number set. Current number set: [27, 13], target: 23, just two numbers left.\n     |- Try 27 + 13 = 40. Evaluate 40 != 23, drop this branch.\n     |- Try 27 - 13 = 14. Evaluate 14 != 23, drop this branch.\n     |- Try 27 * 13 = 351. Evaluate 351 != 23, drop this branch.\n     |- Try 27 \/ 13 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 - 9 = 9. Add 9 to the number set. Current number set: [9, 13], target: 23, just two numbers left.\n     |- Try 13 + 9 = 22. Evaluate 22 != 23, drop this branch.\n     |- Try 13 - 9 = 4. Evaluate 4 != 23, drop this branch.\n     |- Try 13 * 9 = 117. Evaluate 117 != 23, drop this branch.\n     |- Try 13 \/ 9 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 18 * 9 = 162. Add 162 to the number set. Current number set: [162, 13], target: 23, just two numbers left.\n     |- Try 162 + 13 = 175. Evaluate 175 != 23, drop this branch.\n     |- Try 162 - 13 = 149. Evaluate 149 != 23, drop this branch.\n     |- Try 162 * 13 = 2106. 2106 exceeds the maximum intermediate result, drop this branch.\n     |- Try 162 \/ 13 = 12.5. 12.5 is a decimal, drop this branch.\n    |- Try 18 \/ 9 = 2. Add 2 to the number set. Current number set: [2, 13], target: 23, just two numbers left.\n     |- Try 13 + 2 = 15. Evaluate 15 != 23, drop this branch.\n     |- Try 13 - 2 = 11. Evaluate 11 != 23, drop this branch.\n     |- Try 13 * 2 = 26. Evaluate 26 != 23, drop this branch.\n     |- Try 13 \/ 2 = 6.5. 6.5 is a decimal, drop this branch.\n   |- Pick two numbers (18, 13) (numbers left: [9]). Try possible operations.\n    |- Try 18 + 13 = 31. Add 31 to the number set. Current number set: [31, 9], target: 23, just two numbers left.\n     |- Try 31 + 9 = 40. Evaluate 40 != 23, drop this branch.\n     |- Try 31 - 9 = 22. Evaluate 22 != 23, drop this branch.\n     |- Try 31 * 9 = 279. Evaluate 279 != 23, drop this branch.\n     |- Try 31 \/ 9 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 13 = 5. Add 5 to the number set. Current number set: [5, 9], target: 23, just two numbers left.\n     |- Try 9 + 5 = 14. Evaluate 14 != 23, drop this branch.\n     |- Try 9 - 5 = 4. Evaluate 4 != 23, drop this branch.\n     |- Try 9 * 5 = 45. Evaluate 45 != 23, drop this branch.\n     |- Try 9 \/ 5 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 13 = 234. Add 234 to the number set. Current number set: [234, 9], target: 23, just two numbers left.\n     |- Try 234 + 9 = 243. Evaluate 243 != 23, drop this branch.\n     |- Try 234 - 9 = 225. Evaluate 225 != 23, drop this branch.\n     |- Try 234 * 9 = 2106. 2106 exceeds the maximum intermediate result, drop this branch.\n     |- Try 234 \/ 9 = 26. Evaluate 26 != 23, drop this branch.\n    |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (9, 13) (numbers left: [18]). Try possible operations.\n    |- Try 13 + 9 = 22. Add 22 to the number set. Current number set: [22, 18], target: 23, just two numbers left.\n     |- Try 22 + 18 = 40. Evaluate 40 != 23, drop this branch.\n     |- Try 22 - 18 = 4. Evaluate 4 != 23, drop this branch.\n     |- Try 22 * 18 = 396. Evaluate 396 != 23, drop this branch.\n     |- Try 22 \/ 18 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 13 - 9 = 4. Add 4 to the number set. Current number set: [4, 18], target: 23, just two numbers left.\n     |- Try 18 + 4 = 22. Evaluate 22 != 23, drop this branch.\n     |- Try 18 - 4 = 14. Evaluate 14 != 23, drop this branch.\n     |- Try 18 * 4 = 72. Evaluate 72 != 23, drop this branch.\n     |- Try 18 \/ 4 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 13 * 9 = 117. Add 117 to the number set. Current number set: [117, 18], target: 23, just two numbers left.\n     |- Try 117 + 18 = 135. Evaluate 135 != 23, drop this branch.\n     |- Try 117 - 18 = 99. Evaluate 99 != 23, drop this branch.\n     |- Try 117 * 18 = 2106. 2106 exceeds the maximum intermediate result, drop this branch.\n     |- Try 117 \/ 18 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 13 \/ 9 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 10 - 8 = 2. Add 2 to the number set. Current number set: [2, 9, 13], target: 23. Options for choosing two numbers: [(2, 9), (2, 13), (9, 13)].\n   |- Pick two numbers (2, 9) (numbers left: [13]). Try possible operations.\n    |- Try 9 + 2 = 11. Add 11 to the number set. Current number set: [11, 13], target: 23, just two numbers left.\n     |- Try 13 + 11 = 24. Evaluate 24 != 23, drop this branch.\n     |- Try 13 - 11 = 2. Evaluate 2 != 23, drop this branch.\n     |- Try 13 * 11 = 143. Evaluate 143 != 23, drop this branch.\n     |- Try 13 \/ 11 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 9 - 2 = 7. Add 7 to the number set. Current number set: [7, 13], target: 23, just two numbers left.\n     |- Try 13 + 7 = 20. Evaluate 20 != 23, drop this branch.\n     |- Try 13 - 7 = 6. Evaluate 6 != 23, drop this branch.\n     |- Try 13 * 7 = 91. Evaluate 91 != 23, drop this branch.\n     |- Try 13 \/ 7 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 9 * 2 = 18. Add 18 to the number set. Current number set: [18, 13], target: 23, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 23, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 23, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 23, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 9 \/ 2 = 4.5. 4.5 is a decimal, drop this branch.\n   |- Pick two numbers (2, 13) (numbers left: [9]). Try possible operations.\n    |- Try 13 + 2 = 15. Add 15 to the number set. Current number set: [15, 9], target: 23, just two numbers left.\n     |- Try 15 + 9 = 24. Evaluate 24 != 23, drop this branch.\n     |- Try 15 - 9 = 6. Evaluate 6 != 23, drop this branch.\n     |- Try 15 * 9 = 135. Evaluate 135 != 23, drop this branch.\n     |- Try 15 \/ 9 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 13 - 2 = 11. Add 11 to the number set. Current number set: [11, 9], target: 23, just two numbers left.\n     |- Try 11 + 9 = 20. Evaluate 20 != 23, drop this branch.\n     |- Try 11 - 9 = 2. Evaluate 2 != 23, drop this branch.\n     |- Try 11 * 9 = 99. Evaluate 99 != 23, drop this branch.\n     |- Try 11 \/ 9 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 13 * 2 = 26. Add 26 to the number set. Current number set: [26, 9], target: 23, just two numbers left.\n     |- Try 26 + 9 = 35. Evaluate 35 != 23, drop this branch.\n     |- Try 26 - 9 = 17. Evaluate 17 != 23, drop this branch.\n     |- Try 26 * 9 = 234. Evaluate 234 != 23, drop this branch.\n     |- Try 26 \/ 9 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 13 \/ 2 = 6.5. 6.5 is a decimal, drop this branch.\n   |- Pick two numbers (9, 13) (numbers left: [2]). Try possible operations.\n    |- Try 13 + 9 = 22. Add 22 to the number set. Current number set: [22, 2], target: 23, just two numbers left.\n     |- Try 22 + 2 = 24. Evaluate 24 != 23, drop this branch.\n     |- Try 22 - 2 = 20. Evaluate 20 != 23, drop this branch.\n     |- Try 22 * 2 = 44. Evaluate 44 != 23, drop this branch.\n     |- Try 22 \/ 2 = 11. Evaluate 11 != 23, drop this branch.\n    |- Try 13 - 9 = 4. Add 4 to the number set. Current number set: [4, 2], target: 23, just two numbers left.\n     |- Try 4 + 2 = 6. Evaluate 6 != 23, drop this branch.\n     |- Try 4 - 2 = 2. Evaluate 2 != 23, drop this branch.\n     |- Try 4 * 2 = 8. Evaluate 8 != 23, drop this branch.\n     |- Try 4 \/ 2 = 2. Evaluate 2 != 23, drop this branch.\n    |- Try 13 * 9 = 117. Add 117 to the number set. Current number set: [117, 2], target: 23, just two numbers left.\n     |- Try 117 + 2 = 119. Evaluate 119 != 23, drop this branch.\n     |- Try 117 - 2 = 115. Evaluate 115 != 23, drop this branch.\n     |- Try 117 * 2 = 234. Evaluate 234 != 23, drop this branch.\n     |- Try 117 \/ 2 = 58.5. 58.5 is a decimal, drop this branch.\n    |- Try 13 \/ 9 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 10 * 8 = 80. Add 80 to the number set. Current number set: [80, 9, 13], target: 23. Options for choosing two numbers: [(80, 9), (80, 13), (9, 13)].\n   |- Pick two numbers (80, 9) (numbers left: [13]). Try possible operations.\n    |- Try 80 + 9 = 89. Add 89 to the number set. Current number set: [89, 13], target: 23, just two numbers left.\n     |- Try 89 + 13 = 102. Evaluate 102 != 23, drop this branch.\n     |- Try 89 - 13 = 76. Evaluate 76 != 23, drop this branch.\n     |- Try 89 * 13 = 1157. Evaluate 1157 != 23, drop this branch.\n     |- Try 89 \/ 13 = 6.8. 6.8 is a decimal, drop this branch.\n    |- Try 80 - 9 = 71. Add 71 to the number set. Current number set: [71, 13], target: 23, just two numbers left.\n     |- Try 71 + 13 = 84. Evaluate 84 != 23, drop this branch.\n     |- Try 71 - 13 = 58. Evaluate 58 != 23, drop this branch.\n     |- Try 71 * 13 = 923. Evaluate 923 != 23, drop this branch.\n     |- Try 71 \/ 13 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 80 * 9 = 720. Add 720 to the number set. Current number set: [720, 13], target: 23, just two numbers left.\n     |- Try 720 + 13 = 733. Evaluate 733 != 23, drop this branch.\n     |- Try 720 - 13 = 707. Evaluate 707 != 23, drop this branch.\n     |- Try 720 * 13 = 9360. 9360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 720 \/ 13 = 55.4. 55.4 is a decimal, drop this branch.\n    |- Try 80 \/ 9 = 8.9. 8.9 is a decimal, drop this branch.\n   |- Pick two numbers (80, 13) (numbers left: [9]). Try possible operations.\n    |- Try 80 + 13 = 93. Add 93 to the number set. Current number set: [93, 9], target: 23, just two numbers left.\n     |- Try 93 + 9 = 102. Evaluate 102 != 23, drop this branch.\n     |- Try 93 - 9 = 84. Evaluate 84 != 23, drop this branch.\n     |- Try 93 * 9 = 837. Evaluate 837 != 23, drop this branch.\n     |- Try 93 \/ 9 = 10.3. 10.3 is a decimal, drop this branch.\n    |- Try 80 - 13 = 67. Add 67 to the number set. Current number set: [67, 9], target: 23, just two numbers left.\n     |- Try 67 + 9 = 76. Evaluate 76 != 23, drop this branch.\n     |- Try 67 - 9 = 58. Evaluate 58 != 23, drop this branch.\n     |- Try 67 * 9 = 603. Evaluate 603 != 23, drop this branch.\n     |- Try 67 \/ 9 = 7.4. 7.4 is a decimal, drop this branch.\n    |- Try 80 * 13 = 1040. Add 1040 to the number set. Current number set: [1040, 9], target: 23, just two numbers left.\n     |- Try 1040 + 9 = 1049. Evaluate 1049 != 23, drop this branch.\n     |- Try 1040 - 9 = 1031. Evaluate 1031 != 23, drop this branch.\n     |- Try 1040 * 9 = 9360. 9360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1040 \/ 9 = 115.6. 115.6 is a decimal, drop this branch.\n    |- Try 80 \/ 13 = 6.2. 6.2 is a decimal, drop this branch.\n   |- Pick two numbers (9, 13) (numbers left: [80]). Try possible operations.\n    |- Try 13 + 9 = 22. Add 22 to the number set. Current number set: [22, 80], target: 23, just two numbers left.\n     |- Try 80 + 22 = 102. Evaluate 102 != 23, drop this branch.\n     |- Try 80 - 22 = 58. Evaluate 58 != 23, drop this branch.\n     |- Try 80 * 22 = 1760. Evaluate 1760 != 23, drop this branch.\n     |- Try 80 \/ 22 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 13 - 9 = 4. Add 4 to the number set. Current number set: [4, 80], target: 23, just two numbers left.\n     |- Try 80 + 4 = 84. Evaluate 84 != 23, drop this branch.\n     |- Try 80 - 4 = 76. Evaluate 76 != 23, drop this branch.\n     |- Try 80 * 4 = 320. Evaluate 320 != 23, drop this branch.\n     |- Try 80 \/ 4 = 20. Evaluate 20 != 23, drop this branch.\n    |- Try 13 * 9 = 117. Add 117 to the number set. Current number set: [117, 80], target: 23, just two numbers left.\n     |- Try 117 + 80 = 197. Evaluate 197 != 23, drop this branch.\n     |- Try 117 - 80 = 37. Evaluate 37 != 23, drop this branch.\n     |- Try 117 * 80 = 9360. 9360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 117 \/ 80 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 13 \/ 9 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 10 \/ 8 = 1.2. 1.2 is a decimal, drop this branch.\n |- Pick two numbers (8, 9) (numbers left: [10, 13]). Try possible operations.\n  |- Try 9 + 8 = 17. Add 17 to the number set. Current number set: [17, 10, 13], target: 23. Options for choosing two numbers: [(17, 10), (17, 13), (10, 13)].\n   |- Pick two numbers (17, 10) (numbers left: [13]). Try possible operations.\n    |- Try 17 + 10 = 27. Add 27 to the number set. Current number set: [27, 13], target: 23, just two numbers left.\n     |- Try 27 + 13 = 40. Evaluate 40 != 23, drop this branch.\n     |- Try 27 - 13 = 14. Evaluate 14 != 23, drop this branch.\n     |- Try 27 * 13 = 351. Evaluate 351 != 23, drop this branch.\n     |- Try 27 \/ 13 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 17 - 10 = 7. Add 7 to the number set. Current number set: [7, 13], target: 23, just two numbers left.\n     |- Try 13 + 7 = 20. Evaluate 20 != 23, drop this branch.\n     |- Try 13 - 7 = 6. Evaluate 6 != 23, drop this branch.\n     |- Try 13 * 7 = 91. Evaluate 91 != 23, drop this branch.\n     |- Try 13 \/ 7 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 17 * 10 = 170. Add 170 to the number set. Current number set: [170, 13], target: 23, just two numbers left.\n     |- Try 170 + 13 = 183. Evaluate 183 != 23, drop this branch.\n     |- Try 170 - 13 = 157. Evaluate 157 != 23, drop this branch.\n     |- Try 170 * 13 = 2210. 2210 exceeds the maximum intermediate result, drop this branch.\n     |- Try 170 \/ 13 = 13.1. 13.1 is a decimal, drop this branch.\n    |- Try 17 \/ 10 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (17, 13) (numbers left: [10]). Try possible operations.\n    |- Try 17 + 13 = 30. Add 30 to the number set. Current number set: [30, 10], target: 23, just two numbers left.\n     |- Try 30 + 10 = 40. Evaluate 40 != 23, drop this branch.\n     |- Try 30 - 10 = 20. Evaluate 20 != 23, drop this branch.\n     |- Try 30 * 10 = 300. Evaluate 300 != 23, drop this branch.\n     |- Try 30 \/ 10 = 3. Evaluate 3 != 23, drop this branch.\n    |- Try 17 - 13 = 4. Add 4 to the number set. Current number set: [4, 10], target: 23, just two numbers left.\n     |- Try 10 + 4 = 14. Evaluate 14 != 23, drop this branch.\n     |- Try 10 - 4 = 6. Evaluate 6 != 23, drop this branch.\n     |- Try 10 * 4 = 40. Evaluate 40 != 23, drop this branch.\n     |- Try 10 \/ 4 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 17 * 13 = 221. Add 221 to the number set. Current number set: [221, 10], target: 23, just two numbers left.\n     |- Try 221 + 10 = 231. Evaluate 231 != 23, drop this branch.\n     |- Try 221 - 10 = 211. Evaluate 211 != 23, drop this branch.\n     |- Try 221 * 10 = 2210. 2210 exceeds the maximum intermediate result, drop this branch.\n     |- Try 221 \/ 10 = 22.1. 22.1 is a decimal, drop this branch.\n    |- Try 17 \/ 13 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (10, 13) (numbers left: [17]). Try possible operations.\n    |- Try 13 + 10 = 23. Add 23 to the number set. Current number set: [23, 17], target: 23, just two numbers left.\n     |- Try 23 + 17 = 40. Evaluate 40 != 23, drop this branch.\n     |- Try 23 - 17 = 6. Evaluate 6 != 23, drop this branch.\n     |- Try 23 * 17 = 391. Evaluate 391 != 23, drop this branch.\n     |- Try 23 \/ 17 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 13 - 10 = 3. Add 3 to the number set. Current number set: [3, 17], target: 23, just two numbers left.\n     |- Try 17 + 3 = 20. Evaluate 20 != 23, drop this branch.\n     |- Try 17 - 3 = 14. Evaluate 14 != 23, drop this branch.\n     |- Try 17 * 3 = 51. Evaluate 51 != 23, drop this branch.\n     |- Try 17 \/ 3 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 13 * 10 = 130. Add 130 to the number set. Current number set: [130, 17], target: 23, just two numbers left.\n     |- Try 130 + 17 = 147. Evaluate 147 != 23, drop this branch.\n     |- Try 130 - 17 = 113. Evaluate 113 != 23, drop this branch.\n     |- Try 130 * 17 = 2210. 2210 exceeds the maximum intermediate result, drop this branch.\n     |- Try 130 \/ 17 = 7.6. 7.6 is a decimal, drop this branch.\n    |- Try 13 \/ 10 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 9 - 8 = 1. Add 1 to the number set. Current number set: [1, 10, 13], target: 23. Options for choosing two numbers: [(1, 10), (1, 13), (10, 13)].\n   |- Pick two numbers (1, 10) (numbers left: [13]). Try possible operations.\n    |- Try 10 + 1 = 11. Add 11 to the number set. Current number set: [11, 13], target: 23, just two numbers left.\n     |- Try 13 + 11 = 24. Evaluate 24 != 23, drop this branch.\n     |- Try 13 - 11 = 2. Evaluate 2 != 23, drop this branch.\n     |- Try 13 * 11 = 143. Evaluate 143 != 23, drop this branch.\n     |- Try 13 \/ 11 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 10 - 1 = 9. Add 9 to the number set. Current number set: [9, 13], target: 23, just two numbers left.\n     |- Try 13 + 9 = 22. Evaluate 22 != 23, drop this branch.\n     |- Try 13 - 9 = 4. Evaluate 4 != 23, drop this branch.\n     |- Try 13 * 9 = 117. Evaluate 117 != 23, drop this branch.\n     |- Try 13 \/ 9 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 10 * 1 = 10. Add 10 to the number set. Current number set: [10, 13], target: 23, just two numbers left.\n     |- Try 13 + 10 = 23. Evaluate 23 == 23, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 13 + 10 = 23\nThe step before: 10 * 1 = 10\nThe first step: 9 - 8 = 1\n\nOutput the solution in the required format:\n<Solution>\n9 - 8 = 1\n10 * 1 = 10\n13 + 10 = 23\n<\/Solution>\n","item":{"nums":[8,10,9,13],"solution":["9 - 8 = 1","10 * 1 = 10","13 + 10 = 23"],"target":23}}
+{"instance_id":"countdown_8k_134","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [39, 28, 41, 16]\nTarget: 30","reference_output":"# Search Procedure\nInitial number set: [39, 28, 41, 16], target: 30. Options for choosing two numbers: [(39, 28), (39, 41), (39, 16), (28, 41), (28, 16), (41, 16)].\n |- Pick two numbers (39, 28) (numbers left: [41, 16]). Try possible operations.\n  |- Try 39 + 28 = 67. Add 67 to the number set. Current number set: [67, 41, 16], target: 30. Options for choosing two numbers: [(67, 41), (67, 16), (41, 16)].\n   |- Pick two numbers (67, 41) (numbers left: [16]). Try possible operations.\n    |- Try 67 + 41 = 108. Add 108 to the number set. Current number set: [108, 16], target: 30, just two numbers left.\n     |- Try 108 + 16 = 124. Evaluate 124 != 30, drop this branch.\n     |- Try 108 - 16 = 92. Evaluate 92 != 30, drop this branch.\n     |- Try 108 * 16 = 1728. Evaluate 1728 != 30, drop this branch.\n     |- Try 108 \/ 16 = 6.8. 6.8 is a decimal, drop this branch.\n    |- Try 67 - 41 = 26. Add 26 to the number set. Current number set: [26, 16], target: 30, just two numbers left.\n     |- Try 26 + 16 = 42. Evaluate 42 != 30, drop this branch.\n     |- Try 26 - 16 = 10. Evaluate 10 != 30, drop this branch.\n     |- Try 26 * 16 = 416. Evaluate 416 != 30, drop this branch.\n     |- Try 26 \/ 16 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 67 * 41 = 2747. 2747 exceeds the maximum intermediate result, drop this branch.\n    |- Try 67 \/ 41 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (67, 16) (numbers left: [41]). Try possible operations.\n    |- Try 67 + 16 = 83. Add 83 to the number set. Current number set: [83, 41], target: 30, just two numbers left.\n     |- Try 83 + 41 = 124. Evaluate 124 != 30, drop this branch.\n     |- Try 83 - 41 = 42. Evaluate 42 != 30, drop this branch.\n     |- Try 83 * 41 = 3403. 3403 exceeds the maximum intermediate result, drop this branch.\n     |- Try 83 \/ 41 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 67 - 16 = 51. Add 51 to the number set. Current number set: [51, 41], target: 30, just two numbers left.\n     |- Try 51 + 41 = 92. Evaluate 92 != 30, drop this branch.\n     |- Try 51 - 41 = 10. Evaluate 10 != 30, drop this branch.\n     |- Try 51 * 41 = 2091. 2091 exceeds the maximum intermediate result, drop this branch.\n     |- Try 51 \/ 41 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 67 * 16 = 1072. Add 1072 to the number set. Current number set: [1072, 41], target: 30, just two numbers left.\n     |- Try 1072 + 41 = 1113. Evaluate 1113 != 30, drop this branch.\n     |- Try 1072 - 41 = 1031. Evaluate 1031 != 30, drop this branch.\n     |- Try 1072 * 41 = 43952. 43952 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1072 \/ 41 = 26.1. 26.1 is a decimal, drop this branch.\n    |- Try 67 \/ 16 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (41, 16) (numbers left: [67]). Try possible operations.\n    |- Try 41 + 16 = 57. Add 57 to the number set. Current number set: [57, 67], target: 30, just two numbers left.\n     |- Try 67 + 57 = 124. Evaluate 124 != 30, drop this branch.\n     |- Try 67 - 57 = 10. Evaluate 10 != 30, drop this branch.\n     |- Try 67 * 57 = 3819. 3819 exceeds the maximum intermediate result, drop this branch.\n     |- Try 67 \/ 57 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 41 - 16 = 25. Add 25 to the number set. Current number set: [25, 67], target: 30, just two numbers left.\n     |- Try 67 + 25 = 92. Evaluate 92 != 30, drop this branch.\n     |- Try 67 - 25 = 42. Evaluate 42 != 30, drop this branch.\n     |- Try 67 * 25 = 1675. Evaluate 1675 != 30, drop this branch.\n     |- Try 67 \/ 25 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 41 * 16 = 656. Add 656 to the number set. Current number set: [656, 67], target: 30, just two numbers left.\n     |- Try 656 + 67 = 723. Evaluate 723 != 30, drop this branch.\n     |- Try 656 - 67 = 589. Evaluate 589 != 30, drop this branch.\n     |- Try 656 * 67 = 43952. 43952 exceeds the maximum intermediate result, drop this branch.\n     |- Try 656 \/ 67 = 9.8. 9.8 is a decimal, drop this branch.\n    |- Try 41 \/ 16 = 2.6. 2.6 is a decimal, drop this branch.\n  |- Try 39 - 28 = 11. Add 11 to the number set. Current number set: [11, 41, 16], target: 30. Options for choosing two numbers: [(11, 41), (11, 16), (41, 16)].\n   |- Pick two numbers (11, 41) (numbers left: [16]). Try possible operations.\n    |- Try 41 + 11 = 52. Add 52 to the number set. Current number set: [52, 16], target: 30, just two numbers left.\n     |- Try 52 + 16 = 68. Evaluate 68 != 30, drop this branch.\n     |- Try 52 - 16 = 36. Evaluate 36 != 30, drop this branch.\n     |- Try 52 * 16 = 832. Evaluate 832 != 30, drop this branch.\n     |- Try 52 \/ 16 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 41 - 11 = 30. Add 30 to the number set. Current number set: [30, 16], target: 30, just two numbers left.\n     |- Try 30 + 16 = 46. Evaluate 46 != 30, drop this branch.\n     |- Try 30 - 16 = 14. Evaluate 14 != 30, drop this branch.\n     |- Try 30 * 16 = 480. Evaluate 480 != 30, drop this branch.\n     |- Try 30 \/ 16 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 41 * 11 = 451. Add 451 to the number set. Current number set: [451, 16], target: 30, just two numbers left.\n     |- Try 451 + 16 = 467. Evaluate 467 != 30, drop this branch.\n     |- Try 451 - 16 = 435. Evaluate 435 != 30, drop this branch.\n     |- Try 451 * 16 = 7216. 7216 exceeds the maximum intermediate result, drop this branch.\n     |- Try 451 \/ 16 = 28.2. 28.2 is a decimal, drop this branch.\n    |- Try 41 \/ 11 = 3.7. 3.7 is a decimal, drop this branch.\n   |- Pick two numbers (11, 16) (numbers left: [41]). Try possible operations.\n    |- Try 16 + 11 = 27. Add 27 to the number set. Current number set: [27, 41], target: 30, just two numbers left.\n     |- Try 41 + 27 = 68. Evaluate 68 != 30, drop this branch.\n     |- Try 41 - 27 = 14. Evaluate 14 != 30, drop this branch.\n     |- Try 41 * 27 = 1107. Evaluate 1107 != 30, drop this branch.\n     |- Try 41 \/ 27 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 16 - 11 = 5. Add 5 to the number set. Current number set: [5, 41], target: 30, just two numbers left.\n     |- Try 41 + 5 = 46. Evaluate 46 != 30, drop this branch.\n     |- Try 41 - 5 = 36. Evaluate 36 != 30, drop this branch.\n     |- Try 41 * 5 = 205. Evaluate 205 != 30, drop this branch.\n     |- Try 41 \/ 5 = 8.2. 8.2 is a decimal, drop this branch.\n    |- Try 16 * 11 = 176. Add 176 to the number set. Current number set: [176, 41], target: 30, just two numbers left.\n     |- Try 176 + 41 = 217. Evaluate 217 != 30, drop this branch.\n     |- Try 176 - 41 = 135. Evaluate 135 != 30, drop this branch.\n     |- Try 176 * 41 = 7216. 7216 exceeds the maximum intermediate result, drop this branch.\n     |- Try 176 \/ 41 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 16 \/ 11 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (41, 16) (numbers left: [11]). Try possible operations.\n    |- Try 41 + 16 = 57. Add 57 to the number set. Current number set: [57, 11], target: 30, just two numbers left.\n     |- Try 57 + 11 = 68. Evaluate 68 != 30, drop this branch.\n     |- Try 57 - 11 = 46. Evaluate 46 != 30, drop this branch.\n     |- Try 57 * 11 = 627. Evaluate 627 != 30, drop this branch.\n     |- Try 57 \/ 11 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 41 - 16 = 25. Add 25 to the number set. Current number set: [25, 11], target: 30, just two numbers left.\n     |- Try 25 + 11 = 36. Evaluate 36 != 30, drop this branch.\n     |- Try 25 - 11 = 14. Evaluate 14 != 30, drop this branch.\n     |- Try 25 * 11 = 275. Evaluate 275 != 30, drop this branch.\n     |- Try 25 \/ 11 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 41 * 16 = 656. Add 656 to the number set. Current number set: [656, 11], target: 30, just two numbers left.\n     |- Try 656 + 11 = 667. Evaluate 667 != 30, drop this branch.\n     |- Try 656 - 11 = 645. Evaluate 645 != 30, drop this branch.\n     |- Try 656 * 11 = 7216. 7216 exceeds the maximum intermediate result, drop this branch.\n     |- Try 656 \/ 11 = 59.6. 59.6 is a decimal, drop this branch.\n    |- Try 41 \/ 16 = 2.6. 2.6 is a decimal, drop this branch.\n  |- Try 39 * 28 = 1092. Add 1092 to the number set. Current number set: [1092, 41, 16], target: 30. Options for choosing two numbers: [(1092, 41), (1092, 16), (41, 16)].\n   |- Pick two numbers (1092, 41) (numbers left: [16]). Try possible operations.\n    |- Try 1092 + 41 = 1133. Add 1133 to the number set. Current number set: [1133, 16], target: 30, just two numbers left.\n     |- Try 1133 + 16 = 1149. Evaluate 1149 != 30, drop this branch.\n     |- Try 1133 - 16 = 1117. Evaluate 1117 != 30, drop this branch.\n     |- Try 1133 * 16 = 18128. 18128 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1133 \/ 16 = 70.8. 70.8 is a decimal, drop this branch.\n    |- Try 1092 - 41 = 1051. Add 1051 to the number set. Current number set: [1051, 16], target: 30, just two numbers left.\n     |- Try 1051 + 16 = 1067. Evaluate 1067 != 30, drop this branch.\n     |- Try 1051 - 16 = 1035. Evaluate 1035 != 30, drop this branch.\n     |- Try 1051 * 16 = 16816. 16816 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1051 \/ 16 = 65.7. 65.7 is a decimal, drop this branch.\n    |- Try 1092 * 41 = 44772. 44772 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1092 \/ 41 = 26.6. 26.6 is a decimal, drop this branch.\n   |- Pick two numbers (1092, 16) (numbers left: [41]). Try possible operations.\n    |- Try 1092 + 16 = 1108. Add 1108 to the number set. Current number set: [1108, 41], target: 30, just two numbers left.\n     |- Try 1108 + 41 = 1149. Evaluate 1149 != 30, drop this branch.\n     |- Try 1108 - 41 = 1067. Evaluate 1067 != 30, drop this branch.\n     |- Try 1108 * 41 = 45428. 45428 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1108 \/ 41 = 27.0. 27.0 is a decimal, drop this branch.\n    |- Try 1092 - 16 = 1076. Add 1076 to the number set. Current number set: [1076, 41], target: 30, just two numbers left.\n     |- Try 1076 + 41 = 1117. Evaluate 1117 != 30, drop this branch.\n     |- Try 1076 - 41 = 1035. Evaluate 1035 != 30, drop this branch.\n     |- Try 1076 * 41 = 44116. 44116 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1076 \/ 41 = 26.2. 26.2 is a decimal, drop this branch.\n    |- Try 1092 * 16 = 17472. 17472 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1092 \/ 16 = 68.2. 68.2 is a decimal, drop this branch.\n   |- Pick two numbers (41, 16) (numbers left: [1092]). Try possible operations.\n    |- Try 41 + 16 = 57. Add 57 to the number set. Current number set: [57, 1092], target: 30, just two numbers left.\n     |- Try 1092 + 57 = 1149. Evaluate 1149 != 30, drop this branch.\n     |- Try 1092 - 57 = 1035. Evaluate 1035 != 30, drop this branch.\n     |- Try 1092 * 57 = 62244. 62244 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1092 \/ 57 = 19.2. 19.2 is a decimal, drop this branch.\n    |- Try 41 - 16 = 25. Add 25 to the number set. Current number set: [25, 1092], target: 30, just two numbers left.\n     |- Try 1092 + 25 = 1117. Evaluate 1117 != 30, drop this branch.\n     |- Try 1092 - 25 = 1067. Evaluate 1067 != 30, drop this branch.\n     |- Try 1092 * 25 = 27300. 27300 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1092 \/ 25 = 43.7. 43.7 is a decimal, drop this branch.\n    |- Try 41 * 16 = 656. Add 656 to the number set. Current number set: [656, 1092], target: 30, just two numbers left.\n     |- Try 1092 + 656 = 1748. Evaluate 1748 != 30, drop this branch.\n     |- Try 1092 - 656 = 436. Evaluate 436 != 30, drop this branch.\n     |- Try 1092 * 656 = 716352. 716352 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1092 \/ 656 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 41 \/ 16 = 2.6. 2.6 is a decimal, drop this branch.\n  |- Try 39 \/ 28 = 1.4. 1.4 is a decimal, drop this branch.\n |- Pick two numbers (39, 41) (numbers left: [28, 16]). Try possible operations.\n  |- Try 41 + 39 = 80. Add 80 to the number set. Current number set: [80, 28, 16], target: 30. Options for choosing two numbers: [(80, 28), (80, 16), (28, 16)].\n   |- Pick two numbers (80, 28) (numbers left: [16]). Try possible operations.\n    |- Try 80 + 28 = 108. Add 108 to the number set. Current number set: [108, 16], target: 30, just two numbers left.\n     |- Try 108 + 16 = 124. Evaluate 124 != 30, drop this branch.\n     |- Try 108 - 16 = 92. Evaluate 92 != 30, drop this branch.\n     |- Try 108 * 16 = 1728. Evaluate 1728 != 30, drop this branch.\n     |- Try 108 \/ 16 = 6.8. 6.8 is a decimal, drop this branch.\n    |- Try 80 - 28 = 52. Add 52 to the number set. Current number set: [52, 16], target: 30, just two numbers left.\n     |- Try 52 + 16 = 68. Evaluate 68 != 30, drop this branch.\n     |- Try 52 - 16 = 36. Evaluate 36 != 30, drop this branch.\n     |- Try 52 * 16 = 832. Evaluate 832 != 30, drop this branch.\n     |- Try 52 \/ 16 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 80 * 28 = 2240. 2240 exceeds the maximum intermediate result, drop this branch.\n    |- Try 80 \/ 28 = 2.9. 2.9 is a decimal, drop this branch.\n   |- Pick two numbers (80, 16) (numbers left: [28]). Try possible operations.\n    |- Try 80 + 16 = 96. Add 96 to the number set. Current number set: [96, 28], target: 30, just two numbers left.\n     |- Try 96 + 28 = 124. Evaluate 124 != 30, drop this branch.\n     |- Try 96 - 28 = 68. Evaluate 68 != 30, drop this branch.\n     |- Try 96 * 28 = 2688. 2688 exceeds the maximum intermediate result, drop this branch.\n     |- Try 96 \/ 28 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 80 - 16 = 64. Add 64 to the number set. Current number set: [64, 28], target: 30, just two numbers left.\n     |- Try 64 + 28 = 92. Evaluate 92 != 30, drop this branch.\n     |- Try 64 - 28 = 36. Evaluate 36 != 30, drop this branch.\n     |- Try 64 * 28 = 1792. Evaluate 1792 != 30, drop this branch.\n     |- Try 64 \/ 28 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 80 * 16 = 1280. Add 1280 to the number set. Current number set: [1280, 28], target: 30, just two numbers left.\n     |- Try 1280 + 28 = 1308. Evaluate 1308 != 30, drop this branch.\n     |- Try 1280 - 28 = 1252. Evaluate 1252 != 30, drop this branch.\n     |- Try 1280 * 28 = 35840. 35840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1280 \/ 28 = 45.7. 45.7 is a decimal, drop this branch.\n    |- Try 80 \/ 16 = 5. Add 5 to the number set. Current number set: [5, 28], target: 30, just two numbers left.\n     |- Try 28 + 5 = 33. Evaluate 33 != 30, drop this branch.\n     |- Try 28 - 5 = 23. Evaluate 23 != 30, drop this branch.\n     |- Try 28 * 5 = 140. Evaluate 140 != 30, drop this branch.\n     |- Try 28 \/ 5 = 5.6. 5.6 is a decimal, drop this branch.\n   |- Pick two numbers (28, 16) (numbers left: [80]). Try possible operations.\n    |- Try 28 + 16 = 44. Add 44 to the number set. Current number set: [44, 80], target: 30, just two numbers left.\n     |- Try 80 + 44 = 124. Evaluate 124 != 30, drop this branch.\n     |- Try 80 - 44 = 36. Evaluate 36 != 30, drop this branch.\n     |- Try 80 * 44 = 3520. 3520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 80 \/ 44 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 28 - 16 = 12. Add 12 to the number set. Current number set: [12, 80], target: 30, just two numbers left.\n     |- Try 80 + 12 = 92. Evaluate 92 != 30, drop this branch.\n     |- Try 80 - 12 = 68. Evaluate 68 != 30, drop this branch.\n     |- Try 80 * 12 = 960. Evaluate 960 != 30, drop this branch.\n     |- Try 80 \/ 12 = 6.7. 6.7 is a decimal, drop this branch.\n    |- Try 28 * 16 = 448. Add 448 to the number set. Current number set: [448, 80], target: 30, just two numbers left.\n     |- Try 448 + 80 = 528. Evaluate 528 != 30, drop this branch.\n     |- Try 448 - 80 = 368. Evaluate 368 != 30, drop this branch.\n     |- Try 448 * 80 = 35840. 35840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 448 \/ 80 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 28 \/ 16 = 1.8. 1.8 is a decimal, drop this branch.\n  |- Try 41 - 39 = 2. Add 2 to the number set. Current number set: [2, 28, 16], target: 30. Options for choosing two numbers: [(2, 28), (2, 16), (28, 16)].\n   |- Pick two numbers (2, 28) (numbers left: [16]). Try possible operations.\n    |- Try 28 + 2 = 30. Add 30 to the number set. Current number set: [30, 16], target: 30, just two numbers left.\n     |- Try 30 + 16 = 46. Evaluate 46 != 30, drop this branch.\n     |- Try 30 - 16 = 14. Evaluate 14 != 30, drop this branch.\n     |- Try 30 * 16 = 480. Evaluate 480 != 30, drop this branch.\n     |- Try 30 \/ 16 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 28 - 2 = 26. Add 26 to the number set. Current number set: [26, 16], target: 30, just two numbers left.\n     |- Try 26 + 16 = 42. Evaluate 42 != 30, drop this branch.\n     |- Try 26 - 16 = 10. Evaluate 10 != 30, drop this branch.\n     |- Try 26 * 16 = 416. Evaluate 416 != 30, drop this branch.\n     |- Try 26 \/ 16 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 28 * 2 = 56. Add 56 to the number set. Current number set: [56, 16], target: 30, just two numbers left.\n     |- Try 56 + 16 = 72. Evaluate 72 != 30, drop this branch.\n     |- Try 56 - 16 = 40. Evaluate 40 != 30, drop this branch.\n     |- Try 56 * 16 = 896. Evaluate 896 != 30, drop this branch.\n     |- Try 56 \/ 16 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 28 \/ 2 = 14. Add 14 to the number set. Current number set: [14, 16], target: 30, just two numbers left.\n     |- Try 16 + 14 = 30. Evaluate 30 == 30, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 16 + 14 = 30\nThe step before: 28 \/ 2 = 14\nThe first step: 41 - 39 = 2\n\nOutput the solution in the required format:\n<Solution>\n41 - 39 = 2\n28 \/ 2 = 14\n16 + 14 = 30\n<\/Solution>\n","item":{"nums":[39,28,41,16],"solution":["41 - 39 = 2","28 \/ 2 = 14","16 + 14 = 30"],"target":30}}
+{"instance_id":"countdown_8k_135","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [20, 48, 44, 18]\nTarget: 24","reference_output":"# Search Procedure\nInitial number set: [20, 48, 44, 18], target: 24. Options for choosing two numbers: [(20, 48), (20, 44), (20, 18), (48, 44), (48, 18), (44, 18)].\n |- Pick two numbers (20, 48) (numbers left: [44, 18]). Try possible operations.\n  |- Try 48 + 20 = 68. Add 68 to the number set. Current number set: [68, 44, 18], target: 24. Options for choosing two numbers: [(68, 44), (68, 18), (44, 18)].\n   |- Pick two numbers (68, 44) (numbers left: [18]). Try possible operations.\n    |- Try 68 + 44 = 112. Add 112 to the number set. Current number set: [112, 18], target: 24, just two numbers left.\n     |- Try 112 + 18 = 130. Evaluate 130 != 24, drop this branch.\n     |- Try 112 - 18 = 94. Evaluate 94 != 24, drop this branch.\n     |- Try 112 * 18 = 2016. 2016 exceeds the maximum intermediate result, drop this branch.\n     |- Try 112 \/ 18 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 68 - 44 = 24. Add 24 to the number set. Current number set: [24, 18], target: 24, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 24, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 24, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 24, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 68 * 44 = 2992. 2992 exceeds the maximum intermediate result, drop this branch.\n    |- Try 68 \/ 44 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (68, 18) (numbers left: [44]). Try possible operations.\n    |- Try 68 + 18 = 86. Add 86 to the number set. Current number set: [86, 44], target: 24, just two numbers left.\n     |- Try 86 + 44 = 130. Evaluate 130 != 24, drop this branch.\n     |- Try 86 - 44 = 42. Evaluate 42 != 24, drop this branch.\n     |- Try 86 * 44 = 3784. 3784 exceeds the maximum intermediate result, drop this branch.\n     |- Try 86 \/ 44 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 68 - 18 = 50. Add 50 to the number set. Current number set: [50, 44], target: 24, just two numbers left.\n     |- Try 50 + 44 = 94. Evaluate 94 != 24, drop this branch.\n     |- Try 50 - 44 = 6. Evaluate 6 != 24, drop this branch.\n     |- Try 50 * 44 = 2200. 2200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 50 \/ 44 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 68 * 18 = 1224. Add 1224 to the number set. Current number set: [1224, 44], target: 24, just two numbers left.\n     |- Try 1224 + 44 = 1268. Evaluate 1268 != 24, drop this branch.\n     |- Try 1224 - 44 = 1180. Evaluate 1180 != 24, drop this branch.\n     |- Try 1224 * 44 = 53856. 53856 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1224 \/ 44 = 27.8. 27.8 is a decimal, drop this branch.\n    |- Try 68 \/ 18 = 3.8. 3.8 is a decimal, drop this branch.\n   |- Pick two numbers (44, 18) (numbers left: [68]). Try possible operations.\n    |- Try 44 + 18 = 62. Add 62 to the number set. Current number set: [62, 68], target: 24, just two numbers left.\n     |- Try 68 + 62 = 130. Evaluate 130 != 24, drop this branch.\n     |- Try 68 - 62 = 6. Evaluate 6 != 24, drop this branch.\n     |- Try 68 * 62 = 4216. 4216 exceeds the maximum intermediate result, drop this branch.\n     |- Try 68 \/ 62 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 44 - 18 = 26. Add 26 to the number set. Current number set: [26, 68], target: 24, just two numbers left.\n     |- Try 68 + 26 = 94. Evaluate 94 != 24, drop this branch.\n     |- Try 68 - 26 = 42. Evaluate 42 != 24, drop this branch.\n     |- Try 68 * 26 = 1768. Evaluate 1768 != 24, drop this branch.\n     |- Try 68 \/ 26 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 44 * 18 = 792. Add 792 to the number set. Current number set: [792, 68], target: 24, just two numbers left.\n     |- Try 792 + 68 = 860. Evaluate 860 != 24, drop this branch.\n     |- Try 792 - 68 = 724. Evaluate 724 != 24, drop this branch.\n     |- Try 792 * 68 = 53856. 53856 exceeds the maximum intermediate result, drop this branch.\n     |- Try 792 \/ 68 = 11.6. 11.6 is a decimal, drop this branch.\n    |- Try 44 \/ 18 = 2.4. 2.4 is a decimal, drop this branch.\n  |- Try 48 - 20 = 28. Add 28 to the number set. Current number set: [28, 44, 18], target: 24. Options for choosing two numbers: [(28, 44), (28, 18), (44, 18)].\n   |- Pick two numbers (28, 44) (numbers left: [18]). Try possible operations.\n    |- Try 44 + 28 = 72. Add 72 to the number set. Current number set: [72, 18], target: 24, just two numbers left.\n     |- Try 72 + 18 = 90. Evaluate 90 != 24, drop this branch.\n     |- Try 72 - 18 = 54. Evaluate 54 != 24, drop this branch.\n     |- Try 72 * 18 = 1296. Evaluate 1296 != 24, drop this branch.\n     |- Try 72 \/ 18 = 4. Evaluate 4 != 24, drop this branch.\n    |- Try 44 - 28 = 16. Add 16 to the number set. Current number set: [16, 18], target: 24, just two numbers left.\n     |- Try 18 + 16 = 34. Evaluate 34 != 24, drop this branch.\n     |- Try 18 - 16 = 2. Evaluate 2 != 24, drop this branch.\n     |- Try 18 * 16 = 288. Evaluate 288 != 24, drop this branch.\n     |- Try 18 \/ 16 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 44 * 28 = 1232. Add 1232 to the number set. Current number set: [1232, 18], target: 24, just two numbers left.\n     |- Try 1232 + 18 = 1250. Evaluate 1250 != 24, drop this branch.\n     |- Try 1232 - 18 = 1214. Evaluate 1214 != 24, drop this branch.\n     |- Try 1232 * 18 = 22176. 22176 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1232 \/ 18 = 68.4. 68.4 is a decimal, drop this branch.\n    |- Try 44 \/ 28 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (28, 18) (numbers left: [44]). Try possible operations.\n    |- Try 28 + 18 = 46. Add 46 to the number set. Current number set: [46, 44], target: 24, just two numbers left.\n     |- Try 46 + 44 = 90. Evaluate 90 != 24, drop this branch.\n     |- Try 46 - 44 = 2. Evaluate 2 != 24, drop this branch.\n     |- Try 46 * 44 = 2024. 2024 exceeds the maximum intermediate result, drop this branch.\n     |- Try 46 \/ 44 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 28 - 18 = 10. Add 10 to the number set. Current number set: [10, 44], target: 24, just two numbers left.\n     |- Try 44 + 10 = 54. Evaluate 54 != 24, drop this branch.\n     |- Try 44 - 10 = 34. Evaluate 34 != 24, drop this branch.\n     |- Try 44 * 10 = 440. Evaluate 440 != 24, drop this branch.\n     |- Try 44 \/ 10 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 28 * 18 = 504. Add 504 to the number set. Current number set: [504, 44], target: 24, just two numbers left.\n     |- Try 504 + 44 = 548. Evaluate 548 != 24, drop this branch.\n     |- Try 504 - 44 = 460. Evaluate 460 != 24, drop this branch.\n     |- Try 504 * 44 = 22176. 22176 exceeds the maximum intermediate result, drop this branch.\n     |- Try 504 \/ 44 = 11.5. 11.5 is a decimal, drop this branch.\n    |- Try 28 \/ 18 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (44, 18) (numbers left: [28]). Try possible operations.\n    |- Try 44 + 18 = 62. Add 62 to the number set. Current number set: [62, 28], target: 24, just two numbers left.\n     |- Try 62 + 28 = 90. Evaluate 90 != 24, drop this branch.\n     |- Try 62 - 28 = 34. Evaluate 34 != 24, drop this branch.\n     |- Try 62 * 28 = 1736. Evaluate 1736 != 24, drop this branch.\n     |- Try 62 \/ 28 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 44 - 18 = 26. Add 26 to the number set. Current number set: [26, 28], target: 24, just two numbers left.\n     |- Try 28 + 26 = 54. Evaluate 54 != 24, drop this branch.\n     |- Try 28 - 26 = 2. Evaluate 2 != 24, drop this branch.\n     |- Try 28 * 26 = 728. Evaluate 728 != 24, drop this branch.\n     |- Try 28 \/ 26 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 44 * 18 = 792. Add 792 to the number set. Current number set: [792, 28], target: 24, just two numbers left.\n     |- Try 792 + 28 = 820. Evaluate 820 != 24, drop this branch.\n     |- Try 792 - 28 = 764. Evaluate 764 != 24, drop this branch.\n     |- Try 792 * 28 = 22176. 22176 exceeds the maximum intermediate result, drop this branch.\n     |- Try 792 \/ 28 = 28.3. 28.3 is a decimal, drop this branch.\n    |- Try 44 \/ 18 = 2.4. 2.4 is a decimal, drop this branch.\n  |- Try 48 * 20 = 960. Add 960 to the number set. Current number set: [960, 44, 18], target: 24. Options for choosing two numbers: [(960, 44), (960, 18), (44, 18)].\n   |- Pick two numbers (960, 44) (numbers left: [18]). Try possible operations.\n    |- Try 960 + 44 = 1004. Add 1004 to the number set. Current number set: [1004, 18], target: 24, just two numbers left.\n     |- Try 1004 + 18 = 1022. Evaluate 1022 != 24, drop this branch.\n     |- Try 1004 - 18 = 986. Evaluate 986 != 24, drop this branch.\n     |- Try 1004 * 18 = 18072. 18072 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1004 \/ 18 = 55.8. 55.8 is a decimal, drop this branch.\n    |- Try 960 - 44 = 916. Add 916 to the number set. Current number set: [916, 18], target: 24, just two numbers left.\n     |- Try 916 + 18 = 934. Evaluate 934 != 24, drop this branch.\n     |- Try 916 - 18 = 898. Evaluate 898 != 24, drop this branch.\n     |- Try 916 * 18 = 16488. 16488 exceeds the maximum intermediate result, drop this branch.\n     |- Try 916 \/ 18 = 50.9. 50.9 is a decimal, drop this branch.\n    |- Try 960 * 44 = 42240. 42240 exceeds the maximum intermediate result, drop this branch.\n    |- Try 960 \/ 44 = 21.8. 21.8 is a decimal, drop this branch.\n   |- Pick two numbers (960, 18) (numbers left: [44]). Try possible operations.\n    |- Try 960 + 18 = 978. Add 978 to the number set. Current number set: [978, 44], target: 24, just two numbers left.\n     |- Try 978 + 44 = 1022. Evaluate 1022 != 24, drop this branch.\n     |- Try 978 - 44 = 934. Evaluate 934 != 24, drop this branch.\n     |- Try 978 * 44 = 43032. 43032 exceeds the maximum intermediate result, drop this branch.\n     |- Try 978 \/ 44 = 22.2. 22.2 is a decimal, drop this branch.\n    |- Try 960 - 18 = 942. Add 942 to the number set. Current number set: [942, 44], target: 24, just two numbers left.\n     |- Try 942 + 44 = 986. Evaluate 986 != 24, drop this branch.\n     |- Try 942 - 44 = 898. Evaluate 898 != 24, drop this branch.\n     |- Try 942 * 44 = 41448. 41448 exceeds the maximum intermediate result, drop this branch.\n     |- Try 942 \/ 44 = 21.4. 21.4 is a decimal, drop this branch.\n    |- Try 960 * 18 = 17280. 17280 exceeds the maximum intermediate result, drop this branch.\n    |- Try 960 \/ 18 = 53.3. 53.3 is a decimal, drop this branch.\n   |- Pick two numbers (44, 18) (numbers left: [960]). Try possible operations.\n    |- Try 44 + 18 = 62. Add 62 to the number set. Current number set: [62, 960], target: 24, just two numbers left.\n     |- Try 960 + 62 = 1022. Evaluate 1022 != 24, drop this branch.\n     |- Try 960 - 62 = 898. Evaluate 898 != 24, drop this branch.\n     |- Try 960 * 62 = 59520. 59520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 960 \/ 62 = 15.5. 15.5 is a decimal, drop this branch.\n    |- Try 44 - 18 = 26. Add 26 to the number set. Current number set: [26, 960], target: 24, just two numbers left.\n     |- Try 960 + 26 = 986. Evaluate 986 != 24, drop this branch.\n     |- Try 960 - 26 = 934. Evaluate 934 != 24, drop this branch.\n     |- Try 960 * 26 = 24960. 24960 exceeds the maximum intermediate result, drop this branch.\n     |- Try 960 \/ 26 = 36.9. 36.9 is a decimal, drop this branch.\n    |- Try 44 * 18 = 792. Add 792 to the number set. Current number set: [792, 960], target: 24, just two numbers left.\n     |- Try 960 + 792 = 1752. Evaluate 1752 != 24, drop this branch.\n     |- Try 960 - 792 = 168. Evaluate 168 != 24, drop this branch.\n     |- Try 960 * 792 = 760320. 760320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 960 \/ 792 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 44 \/ 18 = 2.4. 2.4 is a decimal, drop this branch.\n  |- Try 48 \/ 20 = 2.4. 2.4 is a decimal, drop this branch.\n |- Pick two numbers (20, 44) (numbers left: [48, 18]). Try possible operations.\n  |- Try 44 + 20 = 64. Add 64 to the number set. Current number set: [64, 48, 18], target: 24. Options for choosing two numbers: [(64, 48), (64, 18), (48, 18)].\n   |- Pick two numbers (64, 48) (numbers left: [18]). Try possible operations.\n    |- Try 64 + 48 = 112. Add 112 to the number set. Current number set: [112, 18], target: 24, just two numbers left.\n     |- Try 112 + 18 = 130. Evaluate 130 != 24, drop this branch.\n     |- Try 112 - 18 = 94. Evaluate 94 != 24, drop this branch.\n     |- Try 112 * 18 = 2016. 2016 exceeds the maximum intermediate result, drop this branch.\n     |- Try 112 \/ 18 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 64 - 48 = 16. Add 16 to the number set. Current number set: [16, 18], target: 24, just two numbers left.\n     |- Try 18 + 16 = 34. Evaluate 34 != 24, drop this branch.\n     |- Try 18 - 16 = 2. Evaluate 2 != 24, drop this branch.\n     |- Try 18 * 16 = 288. Evaluate 288 != 24, drop this branch.\n     |- Try 18 \/ 16 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 64 * 48 = 3072. 3072 exceeds the maximum intermediate result, drop this branch.\n    |- Try 64 \/ 48 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (64, 18) (numbers left: [48]). Try possible operations.\n    |- Try 64 + 18 = 82. Add 82 to the number set. Current number set: [82, 48], target: 24, just two numbers left.\n     |- Try 82 + 48 = 130. Evaluate 130 != 24, drop this branch.\n     |- Try 82 - 48 = 34. Evaluate 34 != 24, drop this branch.\n     |- Try 82 * 48 = 3936. 3936 exceeds the maximum intermediate result, drop this branch.\n     |- Try 82 \/ 48 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 64 - 18 = 46. Add 46 to the number set. Current number set: [46, 48], target: 24, just two numbers left.\n     |- Try 48 + 46 = 94. Evaluate 94 != 24, drop this branch.\n     |- Try 48 - 46 = 2. Evaluate 2 != 24, drop this branch.\n     |- Try 48 * 46 = 2208. 2208 exceeds the maximum intermediate result, drop this branch.\n     |- Try 48 \/ 46 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 64 * 18 = 1152. Add 1152 to the number set. Current number set: [1152, 48], target: 24, just two numbers left.\n     |- Try 1152 + 48 = 1200. Evaluate 1200 != 24, drop this branch.\n     |- Try 1152 - 48 = 1104. Evaluate 1104 != 24, drop this branch.\n     |- Try 1152 * 48 = 55296. 55296 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1152 \/ 48 = 24. Evaluate 24 == 24, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 1152 \/ 48 = 24\nThe step before: 64 * 18 = 1152\nThe first step: 44 + 20 = 64\n\nOutput the solution in the required format:\n<Solution>\n44 + 20 = 64\n64 * 18 = 1152\n1152 \/ 48 = 24\n<\/Solution>\n","item":{"nums":[20,48,44,18],"solution":["44 + 20 = 64","64 * 18 = 1152","1152 \/ 48 = 24"],"target":24}}
+{"instance_id":"countdown_8k_136","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [14, 9, 14, 20]\nTarget: 20","reference_output":"# Search Procedure\nInitial number set: [14, 9, 14, 20], target: 20. Options for choosing two numbers: [(14, 9), (14, 14), (14, 20), (9, 14), (9, 20), (14, 20)].\n |- Pick two numbers (14, 9) (numbers left: [14, 20]). Try possible operations.\n  |- Try 14 + 9 = 23. Add 23 to the number set. Current number set: [23, 14, 20], target: 20. Options for choosing two numbers: [(23, 14), (23, 20), (14, 20)].\n   |- Pick two numbers (23, 14) (numbers left: [20]). Try possible operations.\n    |- Try 23 + 14 = 37. Add 37 to the number set. Current number set: [37, 20], target: 20, just two numbers left.\n     |- Try 37 + 20 = 57. Evaluate 57 != 20, drop this branch.\n     |- Try 37 - 20 = 17. Evaluate 17 != 20, drop this branch.\n     |- Try 37 * 20 = 740. Evaluate 740 != 20, drop this branch.\n     |- Try 37 \/ 20 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 23 - 14 = 9. Add 9 to the number set. Current number set: [9, 20], target: 20, just two numbers left.\n     |- Try 20 + 9 = 29. Evaluate 29 != 20, drop this branch.\n     |- Try 20 - 9 = 11. Evaluate 11 != 20, drop this branch.\n     |- Try 20 * 9 = 180. Evaluate 180 != 20, drop this branch.\n     |- Try 20 \/ 9 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 23 * 14 = 322. Add 322 to the number set. Current number set: [322, 20], target: 20, just two numbers left.\n     |- Try 322 + 20 = 342. Evaluate 342 != 20, drop this branch.\n     |- Try 322 - 20 = 302. Evaluate 302 != 20, drop this branch.\n     |- Try 322 * 20 = 6440. 6440 exceeds the maximum intermediate result, drop this branch.\n     |- Try 322 \/ 20 = 16.1. 16.1 is a decimal, drop this branch.\n    |- Try 23 \/ 14 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (23, 20) (numbers left: [14]). Try possible operations.\n    |- Try 23 + 20 = 43. Add 43 to the number set. Current number set: [43, 14], target: 20, just two numbers left.\n     |- Try 43 + 14 = 57. Evaluate 57 != 20, drop this branch.\n     |- Try 43 - 14 = 29. Evaluate 29 != 20, drop this branch.\n     |- Try 43 * 14 = 602. Evaluate 602 != 20, drop this branch.\n     |- Try 43 \/ 14 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 23 - 20 = 3. Add 3 to the number set. Current number set: [3, 14], target: 20, just two numbers left.\n     |- Try 14 + 3 = 17. Evaluate 17 != 20, drop this branch.\n     |- Try 14 - 3 = 11. Evaluate 11 != 20, drop this branch.\n     |- Try 14 * 3 = 42. Evaluate 42 != 20, drop this branch.\n     |- Try 14 \/ 3 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 23 * 20 = 460. Add 460 to the number set. Current number set: [460, 14], target: 20, just two numbers left.\n     |- Try 460 + 14 = 474. Evaluate 474 != 20, drop this branch.\n     |- Try 460 - 14 = 446. Evaluate 446 != 20, drop this branch.\n     |- Try 460 * 14 = 6440. 6440 exceeds the maximum intermediate result, drop this branch.\n     |- Try 460 \/ 14 = 32.9. 32.9 is a decimal, drop this branch.\n    |- Try 23 \/ 20 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (14, 20) (numbers left: [23]). Try possible operations.\n    |- Try 20 + 14 = 34. Add 34 to the number set. Current number set: [34, 23], target: 20, just two numbers left.\n     |- Try 34 + 23 = 57. Evaluate 57 != 20, drop this branch.\n     |- Try 34 - 23 = 11. Evaluate 11 != 20, drop this branch.\n     |- Try 34 * 23 = 782. Evaluate 782 != 20, drop this branch.\n     |- Try 34 \/ 23 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 20 - 14 = 6. Add 6 to the number set. Current number set: [6, 23], target: 20, just two numbers left.\n     |- Try 23 + 6 = 29. Evaluate 29 != 20, drop this branch.\n     |- Try 23 - 6 = 17. Evaluate 17 != 20, drop this branch.\n     |- Try 23 * 6 = 138. Evaluate 138 != 20, drop this branch.\n     |- Try 23 \/ 6 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 20 * 14 = 280. Add 280 to the number set. Current number set: [280, 23], target: 20, just two numbers left.\n     |- Try 280 + 23 = 303. Evaluate 303 != 20, drop this branch.\n     |- Try 280 - 23 = 257. Evaluate 257 != 20, drop this branch.\n     |- Try 280 * 23 = 6440. 6440 exceeds the maximum intermediate result, drop this branch.\n     |- Try 280 \/ 23 = 12.2. 12.2 is a decimal, drop this branch.\n    |- Try 20 \/ 14 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 14 - 9 = 5. Add 5 to the number set. Current number set: [5, 14, 20], target: 20. Options for choosing two numbers: [(5, 14), (5, 20), (14, 20)].\n   |- Pick two numbers (5, 14) (numbers left: [20]). Try possible operations.\n    |- Try 14 + 5 = 19. Add 19 to the number set. Current number set: [19, 20], target: 20, just two numbers left.\n     |- Try 20 + 19 = 39. Evaluate 39 != 20, drop this branch.\n     |- Try 20 - 19 = 1. Evaluate 1 != 20, drop this branch.\n     |- Try 20 * 19 = 380. Evaluate 380 != 20, drop this branch.\n     |- Try 20 \/ 19 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 14 - 5 = 9. Add 9 to the number set. Current number set: [9, 20], target: 20, just two numbers left.\n     |- Try 20 + 9 = 29. Evaluate 29 != 20, drop this branch.\n     |- Try 20 - 9 = 11. Evaluate 11 != 20, drop this branch.\n     |- Try 20 * 9 = 180. Evaluate 180 != 20, drop this branch.\n     |- Try 20 \/ 9 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 14 * 5 = 70. Add 70 to the number set. Current number set: [70, 20], target: 20, just two numbers left.\n     |- Try 70 + 20 = 90. Evaluate 90 != 20, drop this branch.\n     |- Try 70 - 20 = 50. Evaluate 50 != 20, drop this branch.\n     |- Try 70 * 20 = 1400. Evaluate 1400 != 20, drop this branch.\n     |- Try 70 \/ 20 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 14 \/ 5 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (5, 20) (numbers left: [14]). Try possible operations.\n    |- Try 20 + 5 = 25. Add 25 to the number set. Current number set: [25, 14], target: 20, just two numbers left.\n     |- Try 25 + 14 = 39. Evaluate 39 != 20, drop this branch.\n     |- Try 25 - 14 = 11. Evaluate 11 != 20, drop this branch.\n     |- Try 25 * 14 = 350. Evaluate 350 != 20, drop this branch.\n     |- Try 25 \/ 14 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 20 - 5 = 15. Add 15 to the number set. Current number set: [15, 14], target: 20, just two numbers left.\n     |- Try 15 + 14 = 29. Evaluate 29 != 20, drop this branch.\n     |- Try 15 - 14 = 1. Evaluate 1 != 20, drop this branch.\n     |- Try 15 * 14 = 210. Evaluate 210 != 20, drop this branch.\n     |- Try 15 \/ 14 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 20 * 5 = 100. Add 100 to the number set. Current number set: [100, 14], target: 20, just two numbers left.\n     |- Try 100 + 14 = 114. Evaluate 114 != 20, drop this branch.\n     |- Try 100 - 14 = 86. Evaluate 86 != 20, drop this branch.\n     |- Try 100 * 14 = 1400. Evaluate 1400 != 20, drop this branch.\n     |- Try 100 \/ 14 = 7.1. 7.1 is a decimal, drop this branch.\n    |- Try 20 \/ 5 = 4. Add 4 to the number set. Current number set: [4, 14], target: 20, just two numbers left.\n     |- Try 14 + 4 = 18. Evaluate 18 != 20, drop this branch.\n     |- Try 14 - 4 = 10. Evaluate 10 != 20, drop this branch.\n     |- Try 14 * 4 = 56. Evaluate 56 != 20, drop this branch.\n     |- Try 14 \/ 4 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (14, 20) (numbers left: [5]). Try possible operations.\n    |- Try 20 + 14 = 34. Add 34 to the number set. Current number set: [34, 5], target: 20, just two numbers left.\n     |- Try 34 + 5 = 39. Evaluate 39 != 20, drop this branch.\n     |- Try 34 - 5 = 29. Evaluate 29 != 20, drop this branch.\n     |- Try 34 * 5 = 170. Evaluate 170 != 20, drop this branch.\n     |- Try 34 \/ 5 = 6.8. 6.8 is a decimal, drop this branch.\n    |- Try 20 - 14 = 6. Add 6 to the number set. Current number set: [6, 5], target: 20, just two numbers left.\n     |- Try 6 + 5 = 11. Evaluate 11 != 20, drop this branch.\n     |- Try 6 - 5 = 1. Evaluate 1 != 20, drop this branch.\n     |- Try 6 * 5 = 30. Evaluate 30 != 20, drop this branch.\n     |- Try 6 \/ 5 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 20 * 14 = 280. Add 280 to the number set. Current number set: [280, 5], target: 20, just two numbers left.\n     |- Try 280 + 5 = 285. Evaluate 285 != 20, drop this branch.\n     |- Try 280 - 5 = 275. Evaluate 275 != 20, drop this branch.\n     |- Try 280 * 5 = 1400. Evaluate 1400 != 20, drop this branch.\n     |- Try 280 \/ 5 = 56. Evaluate 56 != 20, drop this branch.\n    |- Try 20 \/ 14 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 14 * 9 = 126. Add 126 to the number set. Current number set: [126, 14, 20], target: 20. Options for choosing two numbers: [(126, 14), (126, 20), (14, 20)].\n   |- Pick two numbers (126, 14) (numbers left: [20]). Try possible operations.\n    |- Try 126 + 14 = 140. Add 140 to the number set. Current number set: [140, 20], target: 20, just two numbers left.\n     |- Try 140 + 20 = 160. Evaluate 160 != 20, drop this branch.\n     |- Try 140 - 20 = 120. Evaluate 120 != 20, drop this branch.\n     |- Try 140 * 20 = 2800. 2800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 140 \/ 20 = 7. Evaluate 7 != 20, drop this branch.\n    |- Try 126 - 14 = 112. Add 112 to the number set. Current number set: [112, 20], target: 20, just two numbers left.\n     |- Try 112 + 20 = 132. Evaluate 132 != 20, drop this branch.\n     |- Try 112 - 20 = 92. Evaluate 92 != 20, drop this branch.\n     |- Try 112 * 20 = 2240. 2240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 112 \/ 20 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 126 * 14 = 1764. Add 1764 to the number set. Current number set: [1764, 20], target: 20, just two numbers left.\n     |- Try 1764 + 20 = 1784. Evaluate 1784 != 20, drop this branch.\n     |- Try 1764 - 20 = 1744. Evaluate 1744 != 20, drop this branch.\n     |- Try 1764 * 20 = 35280. 35280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1764 \/ 20 = 88.2. 88.2 is a decimal, drop this branch.\n    |- Try 126 \/ 14 = 9. Add 9 to the number set. Current number set: [9, 20], target: 20, just two numbers left.\n     |- Try 20 + 9 = 29. Evaluate 29 != 20, drop this branch.\n     |- Try 20 - 9 = 11. Evaluate 11 != 20, drop this branch.\n     |- Try 20 * 9 = 180. Evaluate 180 != 20, drop this branch.\n     |- Try 20 \/ 9 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (126, 20) (numbers left: [14]). Try possible operations.\n    |- Try 126 + 20 = 146. Add 146 to the number set. Current number set: [146, 14], target: 20, just two numbers left.\n     |- Try 146 + 14 = 160. Evaluate 160 != 20, drop this branch.\n     |- Try 146 - 14 = 132. Evaluate 132 != 20, drop this branch.\n     |- Try 146 * 14 = 2044. 2044 exceeds the maximum intermediate result, drop this branch.\n     |- Try 146 \/ 14 = 10.4. 10.4 is a decimal, drop this branch.\n    |- Try 126 - 20 = 106. Add 106 to the number set. Current number set: [106, 14], target: 20, just two numbers left.\n     |- Try 106 + 14 = 120. Evaluate 120 != 20, drop this branch.\n     |- Try 106 - 14 = 92. Evaluate 92 != 20, drop this branch.\n     |- Try 106 * 14 = 1484. Evaluate 1484 != 20, drop this branch.\n     |- Try 106 \/ 14 = 7.6. 7.6 is a decimal, drop this branch.\n    |- Try 126 * 20 = 2520. 2520 exceeds the maximum intermediate result, drop this branch.\n    |- Try 126 \/ 20 = 6.3. 6.3 is a decimal, drop this branch.\n   |- Pick two numbers (14, 20) (numbers left: [126]). Try possible operations.\n    |- Try 20 + 14 = 34. Add 34 to the number set. Current number set: [34, 126], target: 20, just two numbers left.\n     |- Try 126 + 34 = 160. Evaluate 160 != 20, drop this branch.\n     |- Try 126 - 34 = 92. Evaluate 92 != 20, drop this branch.\n     |- Try 126 * 34 = 4284. 4284 exceeds the maximum intermediate result, drop this branch.\n     |- Try 126 \/ 34 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 20 - 14 = 6. Add 6 to the number set. Current number set: [6, 126], target: 20, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 20, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 20, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 20, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 20, drop this branch.\n    |- Try 20 * 14 = 280. Add 280 to the number set. Current number set: [280, 126], target: 20, just two numbers left.\n     |- Try 280 + 126 = 406. Evaluate 406 != 20, drop this branch.\n     |- Try 280 - 126 = 154. Evaluate 154 != 20, drop this branch.\n     |- Try 280 * 126 = 35280. 35280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 280 \/ 126 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 20 \/ 14 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 14 \/ 9 = 1.6. 1.6 is a decimal, drop this branch.\n |- Pick two numbers (14, 14) (numbers left: [9, 20]). Try possible operations.\n  |- Try 14 + 14 = 28. Add 28 to the number set. Current number set: [28, 9, 20], target: 20. Options for choosing two numbers: [(28, 9), (28, 20), (9, 20)].\n   |- Pick two numbers (28, 9) (numbers left: [20]). Try possible operations.\n    |- Try 28 + 9 = 37. Add 37 to the number set. Current number set: [37, 20], target: 20, just two numbers left.\n     |- Try 37 + 20 = 57. Evaluate 57 != 20, drop this branch.\n     |- Try 37 - 20 = 17. Evaluate 17 != 20, drop this branch.\n     |- Try 37 * 20 = 740. Evaluate 740 != 20, drop this branch.\n     |- Try 37 \/ 20 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 28 - 9 = 19. Add 19 to the number set. Current number set: [19, 20], target: 20, just two numbers left.\n     |- Try 20 + 19 = 39. Evaluate 39 != 20, drop this branch.\n     |- Try 20 - 19 = 1. Evaluate 1 != 20, drop this branch.\n     |- Try 20 * 19 = 380. Evaluate 380 != 20, drop this branch.\n     |- Try 20 \/ 19 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 28 * 9 = 252. Add 252 to the number set. Current number set: [252, 20], target: 20, just two numbers left.\n     |- Try 252 + 20 = 272. Evaluate 272 != 20, drop this branch.\n     |- Try 252 - 20 = 232. Evaluate 232 != 20, drop this branch.\n     |- Try 252 * 20 = 5040. 5040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 252 \/ 20 = 12.6. 12.6 is a decimal, drop this branch.\n    |- Try 28 \/ 9 = 3.1. 3.1 is a decimal, drop this branch.\n   |- Pick two numbers (28, 20) (numbers left: [9]). Try possible operations.\n    |- Try 28 + 20 = 48. Add 48 to the number set. Current number set: [48, 9], target: 20, just two numbers left.\n     |- Try 48 + 9 = 57. Evaluate 57 != 20, drop this branch.\n     |- Try 48 - 9 = 39. Evaluate 39 != 20, drop this branch.\n     |- Try 48 * 9 = 432. Evaluate 432 != 20, drop this branch.\n     |- Try 48 \/ 9 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 28 - 20 = 8. Add 8 to the number set. Current number set: [8, 9], target: 20, just two numbers left.\n     |- Try 9 + 8 = 17. Evaluate 17 != 20, drop this branch.\n     |- Try 9 - 8 = 1. Evaluate 1 != 20, drop this branch.\n     |- Try 9 * 8 = 72. Evaluate 72 != 20, drop this branch.\n     |- Try 9 \/ 8 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 28 * 20 = 560. Add 560 to the number set. Current number set: [560, 9], target: 20, just two numbers left.\n     |- Try 560 + 9 = 569. Evaluate 569 != 20, drop this branch.\n     |- Try 560 - 9 = 551. Evaluate 551 != 20, drop this branch.\n     |- Try 560 * 9 = 5040. 5040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 560 \/ 9 = 62.2. 62.2 is a decimal, drop this branch.\n    |- Try 28 \/ 20 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (9, 20) (numbers left: [28]). Try possible operations.\n    |- Try 20 + 9 = 29. Add 29 to the number set. Current number set: [29, 28], target: 20, just two numbers left.\n     |- Try 29 + 28 = 57. Evaluate 57 != 20, drop this branch.\n     |- Try 29 - 28 = 1. Evaluate 1 != 20, drop this branch.\n     |- Try 29 * 28 = 812. Evaluate 812 != 20, drop this branch.\n     |- Try 29 \/ 28 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 20 - 9 = 11. Add 11 to the number set. Current number set: [11, 28], target: 20, just two numbers left.\n     |- Try 28 + 11 = 39. Evaluate 39 != 20, drop this branch.\n     |- Try 28 - 11 = 17. Evaluate 17 != 20, drop this branch.\n     |- Try 28 * 11 = 308. Evaluate 308 != 20, drop this branch.\n     |- Try 28 \/ 11 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 20 * 9 = 180. Add 180 to the number set. Current number set: [180, 28], target: 20, just two numbers left.\n     |- Try 180 + 28 = 208. Evaluate 208 != 20, drop this branch.\n     |- Try 180 - 28 = 152. Evaluate 152 != 20, drop this branch.\n     |- Try 180 * 28 = 5040. 5040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 180 \/ 28 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 20 \/ 9 = 2.2. 2.2 is a decimal, drop this branch.\n  |- Try 14 - 14 = 0. Add 0 to the number set. Current number set: [0, 9, 20], target: 20. Options for choosing two numbers: [(0, 9), (0, 20), (9, 20)].\n   |- Pick two numbers (0, 9) (numbers left: [20]). Try possible operations.\n    |- Try 9 + 0 = 9. Add 9 to the number set. Current number set: [9, 20], target: 20, just two numbers left.\n     |- Try 20 + 9 = 29. Evaluate 29 != 20, drop this branch.\n     |- Try 20 - 9 = 11. Evaluate 11 != 20, drop this branch.\n     |- Try 20 * 9 = 180. Evaluate 180 != 20, drop this branch.\n     |- Try 20 \/ 9 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 9 - 0 = 9. Add 9 to the number set. Current number set: [9, 20], target: 20, just two numbers left.\n     |- Try 20 + 9 = 29. Evaluate 29 != 20, drop this branch.\n     |- Try 20 - 9 = 11. Evaluate 11 != 20, drop this branch.\n     |- Try 20 * 9 = 180. Evaluate 180 != 20, drop this branch.\n     |- Try 20 \/ 9 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 9 * 0 = 0. Add 0 to the number set. Current number set: [0, 20], target: 20, just two numbers left.\n     |- Try 20 + 0 = 20. Evaluate 20 == 20, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 20 + 0 = 20\nThe step before: 9 * 0 = 0\nThe first step: 14 - 14 = 0\n\nOutput the solution in the required format:\n<Solution>\n14 - 14 = 0\n9 * 0 = 0\n20 + 0 = 20\n<\/Solution>\n","item":{"nums":[14,9,14,20],"solution":["14 - 14 = 0","9 * 0 = 0","20 + 0 = 20"],"target":20}}
+{"instance_id":"countdown_8k_137","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [39, 21, 41, 45]\nTarget: 48","reference_output":"# Search Procedure\nInitial number set: [39, 21, 41, 45], target: 48. Options for choosing two numbers: [(39, 21), (39, 41), (39, 45), (21, 41), (21, 45), (41, 45)].\n |- Pick two numbers (39, 21) (numbers left: [41, 45]). Try possible operations.\n  |- Try 39 + 21 = 60. Add 60 to the number set. Current number set: [60, 41, 45], target: 48. Options for choosing two numbers: [(60, 41), (60, 45), (41, 45)].\n   |- Pick two numbers (60, 41) (numbers left: [45]). Try possible operations.\n    |- Try 60 + 41 = 101. Add 101 to the number set. Current number set: [101, 45], target: 48, just two numbers left.\n     |- Try 101 + 45 = 146. Evaluate 146 != 48, drop this branch.\n     |- Try 101 - 45 = 56. Evaluate 56 != 48, drop this branch.\n     |- Try 101 * 45 = 4545. 4545 exceeds the maximum intermediate result, drop this branch.\n     |- Try 101 \/ 45 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 60 - 41 = 19. Add 19 to the number set. Current number set: [19, 45], target: 48, just two numbers left.\n     |- Try 45 + 19 = 64. Evaluate 64 != 48, drop this branch.\n     |- Try 45 - 19 = 26. Evaluate 26 != 48, drop this branch.\n     |- Try 45 * 19 = 855. Evaluate 855 != 48, drop this branch.\n     |- Try 45 \/ 19 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 60 * 41 = 2460. 2460 exceeds the maximum intermediate result, drop this branch.\n    |- Try 60 \/ 41 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (60, 45) (numbers left: [41]). Try possible operations.\n    |- Try 60 + 45 = 105. Add 105 to the number set. Current number set: [105, 41], target: 48, just two numbers left.\n     |- Try 105 + 41 = 146. Evaluate 146 != 48, drop this branch.\n     |- Try 105 - 41 = 64. Evaluate 64 != 48, drop this branch.\n     |- Try 105 * 41 = 4305. 4305 exceeds the maximum intermediate result, drop this branch.\n     |- Try 105 \/ 41 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 60 - 45 = 15. Add 15 to the number set. Current number set: [15, 41], target: 48, just two numbers left.\n     |- Try 41 + 15 = 56. Evaluate 56 != 48, drop this branch.\n     |- Try 41 - 15 = 26. Evaluate 26 != 48, drop this branch.\n     |- Try 41 * 15 = 615. Evaluate 615 != 48, drop this branch.\n     |- Try 41 \/ 15 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 60 * 45 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n    |- Try 60 \/ 45 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (41, 45) (numbers left: [60]). Try possible operations.\n    |- Try 45 + 41 = 86. Add 86 to the number set. Current number set: [86, 60], target: 48, just two numbers left.\n     |- Try 86 + 60 = 146. Evaluate 146 != 48, drop this branch.\n     |- Try 86 - 60 = 26. Evaluate 26 != 48, drop this branch.\n     |- Try 86 * 60 = 5160. 5160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 86 \/ 60 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 45 - 41 = 4. Add 4 to the number set. Current number set: [4, 60], target: 48, just two numbers left.\n     |- Try 60 + 4 = 64. Evaluate 64 != 48, drop this branch.\n     |- Try 60 - 4 = 56. Evaluate 56 != 48, drop this branch.\n     |- Try 60 * 4 = 240. Evaluate 240 != 48, drop this branch.\n     |- Try 60 \/ 4 = 15. Evaluate 15 != 48, drop this branch.\n    |- Try 45 * 41 = 1845. Add 1845 to the number set. Current number set: [1845, 60], target: 48, just two numbers left.\n     |- Try 1845 + 60 = 1905. Evaluate 1905 != 48, drop this branch.\n     |- Try 1845 - 60 = 1785. Evaluate 1785 != 48, drop this branch.\n     |- Try 1845 * 60 = 110700. 110700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1845 \/ 60 = 30.8. 30.8 is a decimal, drop this branch.\n    |- Try 45 \/ 41 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 39 - 21 = 18. Add 18 to the number set. Current number set: [18, 41, 45], target: 48. Options for choosing two numbers: [(18, 41), (18, 45), (41, 45)].\n   |- Pick two numbers (18, 41) (numbers left: [45]). Try possible operations.\n    |- Try 41 + 18 = 59. Add 59 to the number set. Current number set: [59, 45], target: 48, just two numbers left.\n     |- Try 59 + 45 = 104. Evaluate 104 != 48, drop this branch.\n     |- Try 59 - 45 = 14. Evaluate 14 != 48, drop this branch.\n     |- Try 59 * 45 = 2655. 2655 exceeds the maximum intermediate result, drop this branch.\n     |- Try 59 \/ 45 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 41 - 18 = 23. Add 23 to the number set. Current number set: [23, 45], target: 48, just two numbers left.\n     |- Try 45 + 23 = 68. Evaluate 68 != 48, drop this branch.\n     |- Try 45 - 23 = 22. Evaluate 22 != 48, drop this branch.\n     |- Try 45 * 23 = 1035. Evaluate 1035 != 48, drop this branch.\n     |- Try 45 \/ 23 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 41 * 18 = 738. Add 738 to the number set. Current number set: [738, 45], target: 48, just two numbers left.\n     |- Try 738 + 45 = 783. Evaluate 783 != 48, drop this branch.\n     |- Try 738 - 45 = 693. Evaluate 693 != 48, drop this branch.\n     |- Try 738 * 45 = 33210. 33210 exceeds the maximum intermediate result, drop this branch.\n     |- Try 738 \/ 45 = 16.4. 16.4 is a decimal, drop this branch.\n    |- Try 41 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (18, 45) (numbers left: [41]). Try possible operations.\n    |- Try 45 + 18 = 63. Add 63 to the number set. Current number set: [63, 41], target: 48, just two numbers left.\n     |- Try 63 + 41 = 104. Evaluate 104 != 48, drop this branch.\n     |- Try 63 - 41 = 22. Evaluate 22 != 48, drop this branch.\n     |- Try 63 * 41 = 2583. 2583 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 41 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 45 - 18 = 27. Add 27 to the number set. Current number set: [27, 41], target: 48, just two numbers left.\n     |- Try 41 + 27 = 68. Evaluate 68 != 48, drop this branch.\n     |- Try 41 - 27 = 14. Evaluate 14 != 48, drop this branch.\n     |- Try 41 * 27 = 1107. Evaluate 1107 != 48, drop this branch.\n     |- Try 41 \/ 27 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 45 * 18 = 810. Add 810 to the number set. Current number set: [810, 41], target: 48, just two numbers left.\n     |- Try 810 + 41 = 851. Evaluate 851 != 48, drop this branch.\n     |- Try 810 - 41 = 769. Evaluate 769 != 48, drop this branch.\n     |- Try 810 * 41 = 33210. 33210 exceeds the maximum intermediate result, drop this branch.\n     |- Try 810 \/ 41 = 19.8. 19.8 is a decimal, drop this branch.\n    |- Try 45 \/ 18 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (41, 45) (numbers left: [18]). Try possible operations.\n    |- Try 45 + 41 = 86. Add 86 to the number set. Current number set: [86, 18], target: 48, just two numbers left.\n     |- Try 86 + 18 = 104. Evaluate 104 != 48, drop this branch.\n     |- Try 86 - 18 = 68. Evaluate 68 != 48, drop this branch.\n     |- Try 86 * 18 = 1548. Evaluate 1548 != 48, drop this branch.\n     |- Try 86 \/ 18 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 45 - 41 = 4. Add 4 to the number set. Current number set: [4, 18], target: 48, just two numbers left.\n     |- Try 18 + 4 = 22. Evaluate 22 != 48, drop this branch.\n     |- Try 18 - 4 = 14. Evaluate 14 != 48, drop this branch.\n     |- Try 18 * 4 = 72. Evaluate 72 != 48, drop this branch.\n     |- Try 18 \/ 4 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 45 * 41 = 1845. Add 1845 to the number set. Current number set: [1845, 18], target: 48, just two numbers left.\n     |- Try 1845 + 18 = 1863. Evaluate 1863 != 48, drop this branch.\n     |- Try 1845 - 18 = 1827. Evaluate 1827 != 48, drop this branch.\n     |- Try 1845 * 18 = 33210. 33210 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1845 \/ 18 = 102.5. 102.5 is a decimal, drop this branch.\n    |- Try 45 \/ 41 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 39 * 21 = 819. Add 819 to the number set. Current number set: [819, 41, 45], target: 48. Options for choosing two numbers: [(819, 41), (819, 45), (41, 45)].\n   |- Pick two numbers (819, 41) (numbers left: [45]). Try possible operations.\n    |- Try 819 + 41 = 860. Add 860 to the number set. Current number set: [860, 45], target: 48, just two numbers left.\n     |- Try 860 + 45 = 905. Evaluate 905 != 48, drop this branch.\n     |- Try 860 - 45 = 815. Evaluate 815 != 48, drop this branch.\n     |- Try 860 * 45 = 38700. 38700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 860 \/ 45 = 19.1. 19.1 is a decimal, drop this branch.\n    |- Try 819 - 41 = 778. Add 778 to the number set. Current number set: [778, 45], target: 48, just two numbers left.\n     |- Try 778 + 45 = 823. Evaluate 823 != 48, drop this branch.\n     |- Try 778 - 45 = 733. Evaluate 733 != 48, drop this branch.\n     |- Try 778 * 45 = 35010. 35010 exceeds the maximum intermediate result, drop this branch.\n     |- Try 778 \/ 45 = 17.3. 17.3 is a decimal, drop this branch.\n    |- Try 819 * 41 = 33579. 33579 exceeds the maximum intermediate result, drop this branch.\n    |- Try 819 \/ 41 = 20.0. 20.0 is a decimal, drop this branch.\n   |- Pick two numbers (819, 45) (numbers left: [41]). Try possible operations.\n    |- Try 819 + 45 = 864. Add 864 to the number set. Current number set: [864, 41], target: 48, just two numbers left.\n     |- Try 864 + 41 = 905. Evaluate 905 != 48, drop this branch.\n     |- Try 864 - 41 = 823. Evaluate 823 != 48, drop this branch.\n     |- Try 864 * 41 = 35424. 35424 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 41 = 21.1. 21.1 is a decimal, drop this branch.\n    |- Try 819 - 45 = 774. Add 774 to the number set. Current number set: [774, 41], target: 48, just two numbers left.\n     |- Try 774 + 41 = 815. Evaluate 815 != 48, drop this branch.\n     |- Try 774 - 41 = 733. Evaluate 733 != 48, drop this branch.\n     |- Try 774 * 41 = 31734. 31734 exceeds the maximum intermediate result, drop this branch.\n     |- Try 774 \/ 41 = 18.9. 18.9 is a decimal, drop this branch.\n    |- Try 819 * 45 = 36855. 36855 exceeds the maximum intermediate result, drop this branch.\n    |- Try 819 \/ 45 = 18.2. 18.2 is a decimal, drop this branch.\n   |- Pick two numbers (41, 45) (numbers left: [819]). Try possible operations.\n    |- Try 45 + 41 = 86. Add 86 to the number set. Current number set: [86, 819], target: 48, just two numbers left.\n     |- Try 819 + 86 = 905. Evaluate 905 != 48, drop this branch.\n     |- Try 819 - 86 = 733. Evaluate 733 != 48, drop this branch.\n     |- Try 819 * 86 = 70434. 70434 exceeds the maximum intermediate result, drop this branch.\n     |- Try 819 \/ 86 = 9.5. 9.5 is a decimal, drop this branch.\n    |- Try 45 - 41 = 4. Add 4 to the number set. Current number set: [4, 819], target: 48, just two numbers left.\n     |- Try 819 + 4 = 823. Evaluate 823 != 48, drop this branch.\n     |- Try 819 - 4 = 815. Evaluate 815 != 48, drop this branch.\n     |- Try 819 * 4 = 3276. 3276 exceeds the maximum intermediate result, drop this branch.\n     |- Try 819 \/ 4 = 204.8. 204.8 is a decimal, drop this branch.\n    |- Try 45 * 41 = 1845. Add 1845 to the number set. Current number set: [1845, 819], target: 48, just two numbers left.\n     |- Try 1845 + 819 = 2664. 2664 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1845 - 819 = 1026. Evaluate 1026 != 48, drop this branch.\n     |- Try 1845 * 819 = 1511055. 1511055 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1845 \/ 819 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 45 \/ 41 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 39 \/ 21 = 1.9. 1.9 is a decimal, drop this branch.\n |- Pick two numbers (39, 41) (numbers left: [21, 45]). Try possible operations.\n  |- Try 41 + 39 = 80. Add 80 to the number set. Current number set: [80, 21, 45], target: 48. Options for choosing two numbers: [(80, 21), (80, 45), (21, 45)].\n   |- Pick two numbers (80, 21) (numbers left: [45]). Try possible operations.\n    |- Try 80 + 21 = 101. Add 101 to the number set. Current number set: [101, 45], target: 48, just two numbers left.\n     |- Try 101 + 45 = 146. Evaluate 146 != 48, drop this branch.\n     |- Try 101 - 45 = 56. Evaluate 56 != 48, drop this branch.\n     |- Try 101 * 45 = 4545. 4545 exceeds the maximum intermediate result, drop this branch.\n     |- Try 101 \/ 45 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 80 - 21 = 59. Add 59 to the number set. Current number set: [59, 45], target: 48, just two numbers left.\n     |- Try 59 + 45 = 104. Evaluate 104 != 48, drop this branch.\n     |- Try 59 - 45 = 14. Evaluate 14 != 48, drop this branch.\n     |- Try 59 * 45 = 2655. 2655 exceeds the maximum intermediate result, drop this branch.\n     |- Try 59 \/ 45 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 80 * 21 = 1680. Add 1680 to the number set. Current number set: [1680, 45], target: 48, just two numbers left.\n     |- Try 1680 + 45 = 1725. Evaluate 1725 != 48, drop this branch.\n     |- Try 1680 - 45 = 1635. Evaluate 1635 != 48, drop this branch.\n     |- Try 1680 * 45 = 75600. 75600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1680 \/ 45 = 37.3. 37.3 is a decimal, drop this branch.\n    |- Try 80 \/ 21 = 3.8. 3.8 is a decimal, drop this branch.\n   |- Pick two numbers (80, 45) (numbers left: [21]). Try possible operations.\n    |- Try 80 + 45 = 125. Add 125 to the number set. Current number set: [125, 21], target: 48, just two numbers left.\n     |- Try 125 + 21 = 146. Evaluate 146 != 48, drop this branch.\n     |- Try 125 - 21 = 104. Evaluate 104 != 48, drop this branch.\n     |- Try 125 * 21 = 2625. 2625 exceeds the maximum intermediate result, drop this branch.\n     |- Try 125 \/ 21 = 6.0. 6.0 is a decimal, drop this branch.\n    |- Try 80 - 45 = 35. Add 35 to the number set. Current number set: [35, 21], target: 48, just two numbers left.\n     |- Try 35 + 21 = 56. Evaluate 56 != 48, drop this branch.\n     |- Try 35 - 21 = 14. Evaluate 14 != 48, drop this branch.\n     |- Try 35 * 21 = 735. Evaluate 735 != 48, drop this branch.\n     |- Try 35 \/ 21 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 80 * 45 = 3600. 3600 exceeds the maximum intermediate result, drop this branch.\n    |- Try 80 \/ 45 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (21, 45) (numbers left: [80]). Try possible operations.\n    |- Try 45 + 21 = 66. Add 66 to the number set. Current number set: [66, 80], target: 48, just two numbers left.\n     |- Try 80 + 66 = 146. Evaluate 146 != 48, drop this branch.\n     |- Try 80 - 66 = 14. Evaluate 14 != 48, drop this branch.\n     |- Try 80 * 66 = 5280. 5280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 80 \/ 66 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 45 - 21 = 24. Add 24 to the number set. Current number set: [24, 80], target: 48, just two numbers left.\n     |- Try 80 + 24 = 104. Evaluate 104 != 48, drop this branch.\n     |- Try 80 - 24 = 56. Evaluate 56 != 48, drop this branch.\n     |- Try 80 * 24 = 1920. Evaluate 1920 != 48, drop this branch.\n     |- Try 80 \/ 24 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 45 * 21 = 945. Add 945 to the number set. Current number set: [945, 80], target: 48, just two numbers left.\n     |- Try 945 + 80 = 1025. Evaluate 1025 != 48, drop this branch.\n     |- Try 945 - 80 = 865. Evaluate 865 != 48, drop this branch.\n     |- Try 945 * 80 = 75600. 75600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 945 \/ 80 = 11.8. 11.8 is a decimal, drop this branch.\n    |- Try 45 \/ 21 = 2.1. 2.1 is a decimal, drop this branch.\n  |- Try 41 - 39 = 2. Add 2 to the number set. Current number set: [2, 21, 45], target: 48. Options for choosing two numbers: [(2, 21), (2, 45), (21, 45)].\n   |- Pick two numbers (2, 21) (numbers left: [45]). Try possible operations.\n    |- Try 21 + 2 = 23. Add 23 to the number set. Current number set: [23, 45], target: 48, just two numbers left.\n     |- Try 45 + 23 = 68. Evaluate 68 != 48, drop this branch.\n     |- Try 45 - 23 = 22. Evaluate 22 != 48, drop this branch.\n     |- Try 45 * 23 = 1035. Evaluate 1035 != 48, drop this branch.\n     |- Try 45 \/ 23 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 21 - 2 = 19. Add 19 to the number set. Current number set: [19, 45], target: 48, just two numbers left.\n     |- Try 45 + 19 = 64. Evaluate 64 != 48, drop this branch.\n     |- Try 45 - 19 = 26. Evaluate 26 != 48, drop this branch.\n     |- Try 45 * 19 = 855. Evaluate 855 != 48, drop this branch.\n     |- Try 45 \/ 19 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 21 * 2 = 42. Add 42 to the number set. Current number set: [42, 45], target: 48, just two numbers left.\n     |- Try 45 + 42 = 87. Evaluate 87 != 48, drop this branch.\n     |- Try 45 - 42 = 3. Evaluate 3 != 48, drop this branch.\n     |- Try 45 * 42 = 1890. Evaluate 1890 != 48, drop this branch.\n     |- Try 45 \/ 42 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 21 \/ 2 = 10.5. 10.5 is a decimal, drop this branch.\n   |- Pick two numbers (2, 45) (numbers left: [21]). Try possible operations.\n    |- Try 45 + 2 = 47. Add 47 to the number set. Current number set: [47, 21], target: 48, just two numbers left.\n     |- Try 47 + 21 = 68. Evaluate 68 != 48, drop this branch.\n     |- Try 47 - 21 = 26. Evaluate 26 != 48, drop this branch.\n     |- Try 47 * 21 = 987. Evaluate 987 != 48, drop this branch.\n     |- Try 47 \/ 21 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 45 - 2 = 43. Add 43 to the number set. Current number set: [43, 21], target: 48, just two numbers left.\n     |- Try 43 + 21 = 64. Evaluate 64 != 48, drop this branch.\n     |- Try 43 - 21 = 22. Evaluate 22 != 48, drop this branch.\n     |- Try 43 * 21 = 903. Evaluate 903 != 48, drop this branch.\n     |- Try 43 \/ 21 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 45 * 2 = 90. Add 90 to the number set. Current number set: [90, 21], target: 48, just two numbers left.\n     |- Try 90 + 21 = 111. Evaluate 111 != 48, drop this branch.\n     |- Try 90 - 21 = 69. Evaluate 69 != 48, drop this branch.\n     |- Try 90 * 21 = 1890. Evaluate 1890 != 48, drop this branch.\n     |- Try 90 \/ 21 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 45 \/ 2 = 22.5. 22.5 is a decimal, drop this branch.\n   |- Pick two numbers (21, 45) (numbers left: [2]). Try possible operations.\n    |- Try 45 + 21 = 66. Add 66 to the number set. Current number set: [66, 2], target: 48, just two numbers left.\n     |- Try 66 + 2 = 68. Evaluate 68 != 48, drop this branch.\n     |- Try 66 - 2 = 64. Evaluate 64 != 48, drop this branch.\n     |- Try 66 * 2 = 132. Evaluate 132 != 48, drop this branch.\n     |- Try 66 \/ 2 = 33. Evaluate 33 != 48, drop this branch.\n    |- Try 45 - 21 = 24. Add 24 to the number set. Current number set: [24, 2], target: 48, just two numbers left.\n     |- Try 24 + 2 = 26. Evaluate 26 != 48, drop this branch.\n     |- Try 24 - 2 = 22. Evaluate 22 != 48, drop this branch.\n     |- Try 24 * 2 = 48. Evaluate 48 == 48, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 24 * 2 = 48\nThe step before: 45 - 21 = 24\nThe first step: 41 - 39 = 2\n\nOutput the solution in the required format:\n<Solution>\n41 - 39 = 2\n45 - 21 = 24\n24 * 2 = 48\n<\/Solution>\n","item":{"nums":[39,21,41,45],"solution":["41 - 39 = 2","45 - 21 = 24","24 * 2 = 48"],"target":48}}
+{"instance_id":"countdown_8k_138","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [23, 10, 18, 48]\nTarget: 46","reference_output":"# Search Procedure\nInitial number set: [23, 10, 18, 48], target: 46. Options for choosing two numbers: [(23, 10), (23, 18), (23, 48), (10, 18), (10, 48), (18, 48)].\n |- Pick two numbers (23, 10) (numbers left: [18, 48]). Try possible operations.\n  |- Try 23 + 10 = 33. Add 33 to the number set. Current number set: [33, 18, 48], target: 46. Options for choosing two numbers: [(33, 18), (33, 48), (18, 48)].\n   |- Pick two numbers (33, 18) (numbers left: [48]). Try possible operations.\n    |- Try 33 + 18 = 51. Add 51 to the number set. Current number set: [51, 48], target: 46, just two numbers left.\n     |- Try 51 + 48 = 99. Evaluate 99 != 46, drop this branch.\n     |- Try 51 - 48 = 3. Evaluate 3 != 46, drop this branch.\n     |- Try 51 * 48 = 2448. 2448 exceeds the maximum intermediate result, drop this branch.\n     |- Try 51 \/ 48 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 33 - 18 = 15. Add 15 to the number set. Current number set: [15, 48], target: 46, just two numbers left.\n     |- Try 48 + 15 = 63. Evaluate 63 != 46, drop this branch.\n     |- Try 48 - 15 = 33. Evaluate 33 != 46, drop this branch.\n     |- Try 48 * 15 = 720. Evaluate 720 != 46, drop this branch.\n     |- Try 48 \/ 15 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 33 * 18 = 594. Add 594 to the number set. Current number set: [594, 48], target: 46, just two numbers left.\n     |- Try 594 + 48 = 642. Evaluate 642 != 46, drop this branch.\n     |- Try 594 - 48 = 546. Evaluate 546 != 46, drop this branch.\n     |- Try 594 * 48 = 28512. 28512 exceeds the maximum intermediate result, drop this branch.\n     |- Try 594 \/ 48 = 12.4. 12.4 is a decimal, drop this branch.\n    |- Try 33 \/ 18 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (33, 48) (numbers left: [18]). Try possible operations.\n    |- Try 48 + 33 = 81. Add 81 to the number set. Current number set: [81, 18], target: 46, just two numbers left.\n     |- Try 81 + 18 = 99. Evaluate 99 != 46, drop this branch.\n     |- Try 81 - 18 = 63. Evaluate 63 != 46, drop this branch.\n     |- Try 81 * 18 = 1458. Evaluate 1458 != 46, drop this branch.\n     |- Try 81 \/ 18 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 48 - 33 = 15. Add 15 to the number set. Current number set: [15, 18], target: 46, just two numbers left.\n     |- Try 18 + 15 = 33. Evaluate 33 != 46, drop this branch.\n     |- Try 18 - 15 = 3. Evaluate 3 != 46, drop this branch.\n     |- Try 18 * 15 = 270. Evaluate 270 != 46, drop this branch.\n     |- Try 18 \/ 15 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 48 * 33 = 1584. Add 1584 to the number set. Current number set: [1584, 18], target: 46, just two numbers left.\n     |- Try 1584 + 18 = 1602. Evaluate 1602 != 46, drop this branch.\n     |- Try 1584 - 18 = 1566. Evaluate 1566 != 46, drop this branch.\n     |- Try 1584 * 18 = 28512. 28512 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1584 \/ 18 = 88. Evaluate 88 != 46, drop this branch.\n    |- Try 48 \/ 33 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (18, 48) (numbers left: [33]). Try possible operations.\n    |- Try 48 + 18 = 66. Add 66 to the number set. Current number set: [66, 33], target: 46, just two numbers left.\n     |- Try 66 + 33 = 99. Evaluate 99 != 46, drop this branch.\n     |- Try 66 - 33 = 33. Evaluate 33 != 46, drop this branch.\n     |- Try 66 * 33 = 2178. 2178 exceeds the maximum intermediate result, drop this branch.\n     |- Try 66 \/ 33 = 2. Evaluate 2 != 46, drop this branch.\n    |- Try 48 - 18 = 30. Add 30 to the number set. Current number set: [30, 33], target: 46, just two numbers left.\n     |- Try 33 + 30 = 63. Evaluate 63 != 46, drop this branch.\n     |- Try 33 - 30 = 3. Evaluate 3 != 46, drop this branch.\n     |- Try 33 * 30 = 990. Evaluate 990 != 46, drop this branch.\n     |- Try 33 \/ 30 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 48 * 18 = 864. Add 864 to the number set. Current number set: [864, 33], target: 46, just two numbers left.\n     |- Try 864 + 33 = 897. Evaluate 897 != 46, drop this branch.\n     |- Try 864 - 33 = 831. Evaluate 831 != 46, drop this branch.\n     |- Try 864 * 33 = 28512. 28512 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 33 = 26.2. 26.2 is a decimal, drop this branch.\n    |- Try 48 \/ 18 = 2.7. 2.7 is a decimal, drop this branch.\n  |- Try 23 - 10 = 13. Add 13 to the number set. Current number set: [13, 18, 48], target: 46. Options for choosing two numbers: [(13, 18), (13, 48), (18, 48)].\n   |- Pick two numbers (13, 18) (numbers left: [48]). Try possible operations.\n    |- Try 18 + 13 = 31. Add 31 to the number set. Current number set: [31, 48], target: 46, just two numbers left.\n     |- Try 48 + 31 = 79. Evaluate 79 != 46, drop this branch.\n     |- Try 48 - 31 = 17. Evaluate 17 != 46, drop this branch.\n     |- Try 48 * 31 = 1488. Evaluate 1488 != 46, drop this branch.\n     |- Try 48 \/ 31 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 18 - 13 = 5. Add 5 to the number set. Current number set: [5, 48], target: 46, just two numbers left.\n     |- Try 48 + 5 = 53. Evaluate 53 != 46, drop this branch.\n     |- Try 48 - 5 = 43. Evaluate 43 != 46, drop this branch.\n     |- Try 48 * 5 = 240. Evaluate 240 != 46, drop this branch.\n     |- Try 48 \/ 5 = 9.6. 9.6 is a decimal, drop this branch.\n    |- Try 18 * 13 = 234. Add 234 to the number set. Current number set: [234, 48], target: 46, just two numbers left.\n     |- Try 234 + 48 = 282. Evaluate 282 != 46, drop this branch.\n     |- Try 234 - 48 = 186. Evaluate 186 != 46, drop this branch.\n     |- Try 234 * 48 = 11232. 11232 exceeds the maximum intermediate result, drop this branch.\n     |- Try 234 \/ 48 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (13, 48) (numbers left: [18]). Try possible operations.\n    |- Try 48 + 13 = 61. Add 61 to the number set. Current number set: [61, 18], target: 46, just two numbers left.\n     |- Try 61 + 18 = 79. Evaluate 79 != 46, drop this branch.\n     |- Try 61 - 18 = 43. Evaluate 43 != 46, drop this branch.\n     |- Try 61 * 18 = 1098. Evaluate 1098 != 46, drop this branch.\n     |- Try 61 \/ 18 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 48 - 13 = 35. Add 35 to the number set. Current number set: [35, 18], target: 46, just two numbers left.\n     |- Try 35 + 18 = 53. Evaluate 53 != 46, drop this branch.\n     |- Try 35 - 18 = 17. Evaluate 17 != 46, drop this branch.\n     |- Try 35 * 18 = 630. Evaluate 630 != 46, drop this branch.\n     |- Try 35 \/ 18 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 48 * 13 = 624. Add 624 to the number set. Current number set: [624, 18], target: 46, just two numbers left.\n     |- Try 624 + 18 = 642. Evaluate 642 != 46, drop this branch.\n     |- Try 624 - 18 = 606. Evaluate 606 != 46, drop this branch.\n     |- Try 624 * 18 = 11232. 11232 exceeds the maximum intermediate result, drop this branch.\n     |- Try 624 \/ 18 = 34.7. 34.7 is a decimal, drop this branch.\n    |- Try 48 \/ 13 = 3.7. 3.7 is a decimal, drop this branch.\n   |- Pick two numbers (18, 48) (numbers left: [13]). Try possible operations.\n    |- Try 48 + 18 = 66. Add 66 to the number set. Current number set: [66, 13], target: 46, just two numbers left.\n     |- Try 66 + 13 = 79. Evaluate 79 != 46, drop this branch.\n     |- Try 66 - 13 = 53. Evaluate 53 != 46, drop this branch.\n     |- Try 66 * 13 = 858. Evaluate 858 != 46, drop this branch.\n     |- Try 66 \/ 13 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 48 - 18 = 30. Add 30 to the number set. Current number set: [30, 13], target: 46, just two numbers left.\n     |- Try 30 + 13 = 43. Evaluate 43 != 46, drop this branch.\n     |- Try 30 - 13 = 17. Evaluate 17 != 46, drop this branch.\n     |- Try 30 * 13 = 390. Evaluate 390 != 46, drop this branch.\n     |- Try 30 \/ 13 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 48 * 18 = 864. Add 864 to the number set. Current number set: [864, 13], target: 46, just two numbers left.\n     |- Try 864 + 13 = 877. Evaluate 877 != 46, drop this branch.\n     |- Try 864 - 13 = 851. Evaluate 851 != 46, drop this branch.\n     |- Try 864 * 13 = 11232. 11232 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 13 = 66.5. 66.5 is a decimal, drop this branch.\n    |- Try 48 \/ 18 = 2.7. 2.7 is a decimal, drop this branch.\n  |- Try 23 * 10 = 230. Add 230 to the number set. Current number set: [230, 18, 48], target: 46. Options for choosing two numbers: [(230, 18), (230, 48), (18, 48)].\n   |- Pick two numbers (230, 18) (numbers left: [48]). Try possible operations.\n    |- Try 230 + 18 = 248. Add 248 to the number set. Current number set: [248, 48], target: 46, just two numbers left.\n     |- Try 248 + 48 = 296. Evaluate 296 != 46, drop this branch.\n     |- Try 248 - 48 = 200. Evaluate 200 != 46, drop this branch.\n     |- Try 248 * 48 = 11904. 11904 exceeds the maximum intermediate result, drop this branch.\n     |- Try 248 \/ 48 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 230 - 18 = 212. Add 212 to the number set. Current number set: [212, 48], target: 46, just two numbers left.\n     |- Try 212 + 48 = 260. Evaluate 260 != 46, drop this branch.\n     |- Try 212 - 48 = 164. Evaluate 164 != 46, drop this branch.\n     |- Try 212 * 48 = 10176. 10176 exceeds the maximum intermediate result, drop this branch.\n     |- Try 212 \/ 48 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 230 * 18 = 4140. 4140 exceeds the maximum intermediate result, drop this branch.\n    |- Try 230 \/ 18 = 12.8. 12.8 is a decimal, drop this branch.\n   |- Pick two numbers (230, 48) (numbers left: [18]). Try possible operations.\n    |- Try 230 + 48 = 278. Add 278 to the number set. Current number set: [278, 18], target: 46, just two numbers left.\n     |- Try 278 + 18 = 296. Evaluate 296 != 46, drop this branch.\n     |- Try 278 - 18 = 260. Evaluate 260 != 46, drop this branch.\n     |- Try 278 * 18 = 5004. 5004 exceeds the maximum intermediate result, drop this branch.\n     |- Try 278 \/ 18 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 230 - 48 = 182. Add 182 to the number set. Current number set: [182, 18], target: 46, just two numbers left.\n     |- Try 182 + 18 = 200. Evaluate 200 != 46, drop this branch.\n     |- Try 182 - 18 = 164. Evaluate 164 != 46, drop this branch.\n     |- Try 182 * 18 = 3276. 3276 exceeds the maximum intermediate result, drop this branch.\n     |- Try 182 \/ 18 = 10.1. 10.1 is a decimal, drop this branch.\n    |- Try 230 * 48 = 11040. 11040 exceeds the maximum intermediate result, drop this branch.\n    |- Try 230 \/ 48 = 4.8. 4.8 is a decimal, drop this branch.\n   |- Pick two numbers (18, 48) (numbers left: [230]). Try possible operations.\n    |- Try 48 + 18 = 66. Add 66 to the number set. Current number set: [66, 230], target: 46, just two numbers left.\n     |- Try 230 + 66 = 296. Evaluate 296 != 46, drop this branch.\n     |- Try 230 - 66 = 164. Evaluate 164 != 46, drop this branch.\n     |- Try 230 * 66 = 15180. 15180 exceeds the maximum intermediate result, drop this branch.\n     |- Try 230 \/ 66 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 48 - 18 = 30. Add 30 to the number set. Current number set: [30, 230], target: 46, just two numbers left.\n     |- Try 230 + 30 = 260. Evaluate 260 != 46, drop this branch.\n     |- Try 230 - 30 = 200. Evaluate 200 != 46, drop this branch.\n     |- Try 230 * 30 = 6900. 6900 exceeds the maximum intermediate result, drop this branch.\n     |- Try 230 \/ 30 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 48 * 18 = 864. Add 864 to the number set. Current number set: [864, 230], target: 46, just two numbers left.\n     |- Try 864 + 230 = 1094. Evaluate 1094 != 46, drop this branch.\n     |- Try 864 - 230 = 634. Evaluate 634 != 46, drop this branch.\n     |- Try 864 * 230 = 198720. 198720 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 230 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 48 \/ 18 = 2.7. 2.7 is a decimal, drop this branch.\n  |- Try 23 \/ 10 = 2.3. 2.3 is a decimal, drop this branch.\n |- Pick two numbers (23, 18) (numbers left: [10, 48]). Try possible operations.\n  |- Try 23 + 18 = 41. Add 41 to the number set. Current number set: [41, 10, 48], target: 46. Options for choosing two numbers: [(41, 10), (41, 48), (10, 48)].\n   |- Pick two numbers (41, 10) (numbers left: [48]). Try possible operations.\n    |- Try 41 + 10 = 51. Add 51 to the number set. Current number set: [51, 48], target: 46, just two numbers left.\n     |- Try 51 + 48 = 99. Evaluate 99 != 46, drop this branch.\n     |- Try 51 - 48 = 3. Evaluate 3 != 46, drop this branch.\n     |- Try 51 * 48 = 2448. 2448 exceeds the maximum intermediate result, drop this branch.\n     |- Try 51 \/ 48 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 41 - 10 = 31. Add 31 to the number set. Current number set: [31, 48], target: 46, just two numbers left.\n     |- Try 48 + 31 = 79. Evaluate 79 != 46, drop this branch.\n     |- Try 48 - 31 = 17. Evaluate 17 != 46, drop this branch.\n     |- Try 48 * 31 = 1488. Evaluate 1488 != 46, drop this branch.\n     |- Try 48 \/ 31 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 41 * 10 = 410. Add 410 to the number set. Current number set: [410, 48], target: 46, just two numbers left.\n     |- Try 410 + 48 = 458. Evaluate 458 != 46, drop this branch.\n     |- Try 410 - 48 = 362. Evaluate 362 != 46, drop this branch.\n     |- Try 410 * 48 = 19680. 19680 exceeds the maximum intermediate result, drop this branch.\n     |- Try 410 \/ 48 = 8.5. 8.5 is a decimal, drop this branch.\n    |- Try 41 \/ 10 = 4.1. 4.1 is a decimal, drop this branch.\n   |- Pick two numbers (41, 48) (numbers left: [10]). Try possible operations.\n    |- Try 48 + 41 = 89. Add 89 to the number set. Current number set: [89, 10], target: 46, just two numbers left.\n     |- Try 89 + 10 = 99. Evaluate 99 != 46, drop this branch.\n     |- Try 89 - 10 = 79. Evaluate 79 != 46, drop this branch.\n     |- Try 89 * 10 = 890. Evaluate 890 != 46, drop this branch.\n     |- Try 89 \/ 10 = 8.9. 8.9 is a decimal, drop this branch.\n    |- Try 48 - 41 = 7. Add 7 to the number set. Current number set: [7, 10], target: 46, just two numbers left.\n     |- Try 10 + 7 = 17. Evaluate 17 != 46, drop this branch.\n     |- Try 10 - 7 = 3. Evaluate 3 != 46, drop this branch.\n     |- Try 10 * 7 = 70. Evaluate 70 != 46, drop this branch.\n     |- Try 10 \/ 7 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 48 * 41 = 1968. Add 1968 to the number set. Current number set: [1968, 10], target: 46, just two numbers left.\n     |- Try 1968 + 10 = 1978. Evaluate 1978 != 46, drop this branch.\n     |- Try 1968 - 10 = 1958. Evaluate 1958 != 46, drop this branch.\n     |- Try 1968 * 10 = 19680. 19680 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1968 \/ 10 = 196.8. 196.8 is a decimal, drop this branch.\n    |- Try 48 \/ 41 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (10, 48) (numbers left: [41]). Try possible operations.\n    |- Try 48 + 10 = 58. Add 58 to the number set. Current number set: [58, 41], target: 46, just two numbers left.\n     |- Try 58 + 41 = 99. Evaluate 99 != 46, drop this branch.\n     |- Try 58 - 41 = 17. Evaluate 17 != 46, drop this branch.\n     |- Try 58 * 41 = 2378. 2378 exceeds the maximum intermediate result, drop this branch.\n     |- Try 58 \/ 41 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 48 - 10 = 38. Add 38 to the number set. Current number set: [38, 41], target: 46, just two numbers left.\n     |- Try 41 + 38 = 79. Evaluate 79 != 46, drop this branch.\n     |- Try 41 - 38 = 3. Evaluate 3 != 46, drop this branch.\n     |- Try 41 * 38 = 1558. Evaluate 1558 != 46, drop this branch.\n     |- Try 41 \/ 38 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 48 * 10 = 480. Add 480 to the number set. Current number set: [480, 41], target: 46, just two numbers left.\n     |- Try 480 + 41 = 521. Evaluate 521 != 46, drop this branch.\n     |- Try 480 - 41 = 439. Evaluate 439 != 46, drop this branch.\n     |- Try 480 * 41 = 19680. 19680 exceeds the maximum intermediate result, drop this branch.\n     |- Try 480 \/ 41 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 48 \/ 10 = 4.8. 4.8 is a decimal, drop this branch.\n  |- Try 23 - 18 = 5. Add 5 to the number set. Current number set: [5, 10, 48], target: 46. Options for choosing two numbers: [(5, 10), (5, 48), (10, 48)].\n   |- Pick two numbers (5, 10) (numbers left: [48]). Try possible operations.\n    |- Try 10 + 5 = 15. Add 15 to the number set. Current number set: [15, 48], target: 46, just two numbers left.\n     |- Try 48 + 15 = 63. Evaluate 63 != 46, drop this branch.\n     |- Try 48 - 15 = 33. Evaluate 33 != 46, drop this branch.\n     |- Try 48 * 15 = 720. Evaluate 720 != 46, drop this branch.\n     |- Try 48 \/ 15 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 10 - 5 = 5. Add 5 to the number set. Current number set: [5, 48], target: 46, just two numbers left.\n     |- Try 48 + 5 = 53. Evaluate 53 != 46, drop this branch.\n     |- Try 48 - 5 = 43. Evaluate 43 != 46, drop this branch.\n     |- Try 48 * 5 = 240. Evaluate 240 != 46, drop this branch.\n     |- Try 48 \/ 5 = 9.6. 9.6 is a decimal, drop this branch.\n    |- Try 10 * 5 = 50. Add 50 to the number set. Current number set: [50, 48], target: 46, just two numbers left.\n     |- Try 50 + 48 = 98. Evaluate 98 != 46, drop this branch.\n     |- Try 50 - 48 = 2. Evaluate 2 != 46, drop this branch.\n     |- Try 50 * 48 = 2400. 2400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 50 \/ 48 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 10 \/ 5 = 2. Add 2 to the number set. Current number set: [2, 48], target: 46, just two numbers left.\n     |- Try 48 + 2 = 50. Evaluate 50 != 46, drop this branch.\n     |- Try 48 - 2 = 46. Evaluate 46 == 46, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 48 - 2 = 46\nThe step before: 10 \/ 5 = 2\nThe first step: 23 - 18 = 5\n\nOutput the solution in the required format:\n<Solution>\n23 - 18 = 5\n10 \/ 5 = 2\n48 - 2 = 46\n<\/Solution>\n","item":{"nums":[23,10,18,48],"solution":["23 - 18 = 5","10 \/ 5 = 2","48 - 2 = 46"],"target":46}}
+{"instance_id":"countdown_8k_139","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [5, 45, 27, 34]\nTarget: 16","reference_output":"# Search Procedure\nInitial number set: [5, 45, 27, 34], target: 16. Options for choosing two numbers: [(5, 45), (5, 27), (5, 34), (45, 27), (45, 34), (27, 34)].\n |- Pick two numbers (5, 45) (numbers left: [27, 34]). Try possible operations.\n  |- Try 45 + 5 = 50. Add 50 to the number set. Current number set: [50, 27, 34], target: 16. Options for choosing two numbers: [(50, 27), (50, 34), (27, 34)].\n   |- Pick two numbers (50, 27) (numbers left: [34]). Try possible operations.\n    |- Try 50 + 27 = 77. Add 77 to the number set. Current number set: [77, 34], target: 16, just two numbers left.\n     |- Try 77 + 34 = 111. Evaluate 111 != 16, drop this branch.\n     |- Try 77 - 34 = 43. Evaluate 43 != 16, drop this branch.\n     |- Try 77 * 34 = 2618. 2618 exceeds the maximum intermediate result, drop this branch.\n     |- Try 77 \/ 34 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 50 - 27 = 23. Add 23 to the number set. Current number set: [23, 34], target: 16, just two numbers left.\n     |- Try 34 + 23 = 57. Evaluate 57 != 16, drop this branch.\n     |- Try 34 - 23 = 11. Evaluate 11 != 16, drop this branch.\n     |- Try 34 * 23 = 782. Evaluate 782 != 16, drop this branch.\n     |- Try 34 \/ 23 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 50 * 27 = 1350. Add 1350 to the number set. Current number set: [1350, 34], target: 16, just two numbers left.\n     |- Try 1350 + 34 = 1384. Evaluate 1384 != 16, drop this branch.\n     |- Try 1350 - 34 = 1316. Evaluate 1316 != 16, drop this branch.\n     |- Try 1350 * 34 = 45900. 45900 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1350 \/ 34 = 39.7. 39.7 is a decimal, drop this branch.\n    |- Try 50 \/ 27 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (50, 34) (numbers left: [27]). Try possible operations.\n    |- Try 50 + 34 = 84. Add 84 to the number set. Current number set: [84, 27], target: 16, just two numbers left.\n     |- Try 84 + 27 = 111. Evaluate 111 != 16, drop this branch.\n     |- Try 84 - 27 = 57. Evaluate 57 != 16, drop this branch.\n     |- Try 84 * 27 = 2268. 2268 exceeds the maximum intermediate result, drop this branch.\n     |- Try 84 \/ 27 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 50 - 34 = 16. Add 16 to the number set. Current number set: [16, 27], target: 16, just two numbers left.\n     |- Try 27 + 16 = 43. Evaluate 43 != 16, drop this branch.\n     |- Try 27 - 16 = 11. Evaluate 11 != 16, drop this branch.\n     |- Try 27 * 16 = 432. Evaluate 432 != 16, drop this branch.\n     |- Try 27 \/ 16 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 50 * 34 = 1700. Add 1700 to the number set. Current number set: [1700, 27], target: 16, just two numbers left.\n     |- Try 1700 + 27 = 1727. Evaluate 1727 != 16, drop this branch.\n     |- Try 1700 - 27 = 1673. Evaluate 1673 != 16, drop this branch.\n     |- Try 1700 * 27 = 45900. 45900 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1700 \/ 27 = 63.0. 63.0 is a decimal, drop this branch.\n    |- Try 50 \/ 34 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (27, 34) (numbers left: [50]). Try possible operations.\n    |- Try 34 + 27 = 61. Add 61 to the number set. Current number set: [61, 50], target: 16, just two numbers left.\n     |- Try 61 + 50 = 111. Evaluate 111 != 16, drop this branch.\n     |- Try 61 - 50 = 11. Evaluate 11 != 16, drop this branch.\n     |- Try 61 * 50 = 3050. 3050 exceeds the maximum intermediate result, drop this branch.\n     |- Try 61 \/ 50 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 34 - 27 = 7. Add 7 to the number set. Current number set: [7, 50], target: 16, just two numbers left.\n     |- Try 50 + 7 = 57. Evaluate 57 != 16, drop this branch.\n     |- Try 50 - 7 = 43. Evaluate 43 != 16, drop this branch.\n     |- Try 50 * 7 = 350. Evaluate 350 != 16, drop this branch.\n     |- Try 50 \/ 7 = 7.1. 7.1 is a decimal, drop this branch.\n    |- Try 34 * 27 = 918. Add 918 to the number set. Current number set: [918, 50], target: 16, just two numbers left.\n     |- Try 918 + 50 = 968. Evaluate 968 != 16, drop this branch.\n     |- Try 918 - 50 = 868. Evaluate 868 != 16, drop this branch.\n     |- Try 918 * 50 = 45900. 45900 exceeds the maximum intermediate result, drop this branch.\n     |- Try 918 \/ 50 = 18.4. 18.4 is a decimal, drop this branch.\n    |- Try 34 \/ 27 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 45 - 5 = 40. Add 40 to the number set. Current number set: [40, 27, 34], target: 16. Options for choosing two numbers: [(40, 27), (40, 34), (27, 34)].\n   |- Pick two numbers (40, 27) (numbers left: [34]). Try possible operations.\n    |- Try 40 + 27 = 67. Add 67 to the number set. Current number set: [67, 34], target: 16, just two numbers left.\n     |- Try 67 + 34 = 101. Evaluate 101 != 16, drop this branch.\n     |- Try 67 - 34 = 33. Evaluate 33 != 16, drop this branch.\n     |- Try 67 * 34 = 2278. 2278 exceeds the maximum intermediate result, drop this branch.\n     |- Try 67 \/ 34 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 40 - 27 = 13. Add 13 to the number set. Current number set: [13, 34], target: 16, just two numbers left.\n     |- Try 34 + 13 = 47. Evaluate 47 != 16, drop this branch.\n     |- Try 34 - 13 = 21. Evaluate 21 != 16, drop this branch.\n     |- Try 34 * 13 = 442. Evaluate 442 != 16, drop this branch.\n     |- Try 34 \/ 13 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 40 * 27 = 1080. Add 1080 to the number set. Current number set: [1080, 34], target: 16, just two numbers left.\n     |- Try 1080 + 34 = 1114. Evaluate 1114 != 16, drop this branch.\n     |- Try 1080 - 34 = 1046. Evaluate 1046 != 16, drop this branch.\n     |- Try 1080 * 34 = 36720. 36720 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1080 \/ 34 = 31.8. 31.8 is a decimal, drop this branch.\n    |- Try 40 \/ 27 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (40, 34) (numbers left: [27]). Try possible operations.\n    |- Try 40 + 34 = 74. Add 74 to the number set. Current number set: [74, 27], target: 16, just two numbers left.\n     |- Try 74 + 27 = 101. Evaluate 101 != 16, drop this branch.\n     |- Try 74 - 27 = 47. Evaluate 47 != 16, drop this branch.\n     |- Try 74 * 27 = 1998. Evaluate 1998 != 16, drop this branch.\n     |- Try 74 \/ 27 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 40 - 34 = 6. Add 6 to the number set. Current number set: [6, 27], target: 16, just two numbers left.\n     |- Try 27 + 6 = 33. Evaluate 33 != 16, drop this branch.\n     |- Try 27 - 6 = 21. Evaluate 21 != 16, drop this branch.\n     |- Try 27 * 6 = 162. Evaluate 162 != 16, drop this branch.\n     |- Try 27 \/ 6 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 40 * 34 = 1360. Add 1360 to the number set. Current number set: [1360, 27], target: 16, just two numbers left.\n     |- Try 1360 + 27 = 1387. Evaluate 1387 != 16, drop this branch.\n     |- Try 1360 - 27 = 1333. Evaluate 1333 != 16, drop this branch.\n     |- Try 1360 * 27 = 36720. 36720 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1360 \/ 27 = 50.4. 50.4 is a decimal, drop this branch.\n    |- Try 40 \/ 34 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (27, 34) (numbers left: [40]). Try possible operations.\n    |- Try 34 + 27 = 61. Add 61 to the number set. Current number set: [61, 40], target: 16, just two numbers left.\n     |- Try 61 + 40 = 101. Evaluate 101 != 16, drop this branch.\n     |- Try 61 - 40 = 21. Evaluate 21 != 16, drop this branch.\n     |- Try 61 * 40 = 2440. 2440 exceeds the maximum intermediate result, drop this branch.\n     |- Try 61 \/ 40 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 34 - 27 = 7. Add 7 to the number set. Current number set: [7, 40], target: 16, just two numbers left.\n     |- Try 40 + 7 = 47. Evaluate 47 != 16, drop this branch.\n     |- Try 40 - 7 = 33. Evaluate 33 != 16, drop this branch.\n     |- Try 40 * 7 = 280. Evaluate 280 != 16, drop this branch.\n     |- Try 40 \/ 7 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 34 * 27 = 918. Add 918 to the number set. Current number set: [918, 40], target: 16, just two numbers left.\n     |- Try 918 + 40 = 958. Evaluate 958 != 16, drop this branch.\n     |- Try 918 - 40 = 878. Evaluate 878 != 16, drop this branch.\n     |- Try 918 * 40 = 36720. 36720 exceeds the maximum intermediate result, drop this branch.\n     |- Try 918 \/ 40 = 22.9. 22.9 is a decimal, drop this branch.\n    |- Try 34 \/ 27 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 45 * 5 = 225. Add 225 to the number set. Current number set: [225, 27, 34], target: 16. Options for choosing two numbers: [(225, 27), (225, 34), (27, 34)].\n   |- Pick two numbers (225, 27) (numbers left: [34]). Try possible operations.\n    |- Try 225 + 27 = 252. Add 252 to the number set. Current number set: [252, 34], target: 16, just two numbers left.\n     |- Try 252 + 34 = 286. Evaluate 286 != 16, drop this branch.\n     |- Try 252 - 34 = 218. Evaluate 218 != 16, drop this branch.\n     |- Try 252 * 34 = 8568. 8568 exceeds the maximum intermediate result, drop this branch.\n     |- Try 252 \/ 34 = 7.4. 7.4 is a decimal, drop this branch.\n    |- Try 225 - 27 = 198. Add 198 to the number set. Current number set: [198, 34], target: 16, just two numbers left.\n     |- Try 198 + 34 = 232. Evaluate 232 != 16, drop this branch.\n     |- Try 198 - 34 = 164. Evaluate 164 != 16, drop this branch.\n     |- Try 198 * 34 = 6732. 6732 exceeds the maximum intermediate result, drop this branch.\n     |- Try 198 \/ 34 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 225 * 27 = 6075. 6075 exceeds the maximum intermediate result, drop this branch.\n    |- Try 225 \/ 27 = 8.3. 8.3 is a decimal, drop this branch.\n   |- Pick two numbers (225, 34) (numbers left: [27]). Try possible operations.\n    |- Try 225 + 34 = 259. Add 259 to the number set. Current number set: [259, 27], target: 16, just two numbers left.\n     |- Try 259 + 27 = 286. Evaluate 286 != 16, drop this branch.\n     |- Try 259 - 27 = 232. Evaluate 232 != 16, drop this branch.\n     |- Try 259 * 27 = 6993. 6993 exceeds the maximum intermediate result, drop this branch.\n     |- Try 259 \/ 27 = 9.6. 9.6 is a decimal, drop this branch.\n    |- Try 225 - 34 = 191. Add 191 to the number set. Current number set: [191, 27], target: 16, just two numbers left.\n     |- Try 191 + 27 = 218. Evaluate 218 != 16, drop this branch.\n     |- Try 191 - 27 = 164. Evaluate 164 != 16, drop this branch.\n     |- Try 191 * 27 = 5157. 5157 exceeds the maximum intermediate result, drop this branch.\n     |- Try 191 \/ 27 = 7.1. 7.1 is a decimal, drop this branch.\n    |- Try 225 * 34 = 7650. 7650 exceeds the maximum intermediate result, drop this branch.\n    |- Try 225 \/ 34 = 6.6. 6.6 is a decimal, drop this branch.\n   |- Pick two numbers (27, 34) (numbers left: [225]). Try possible operations.\n    |- Try 34 + 27 = 61. Add 61 to the number set. Current number set: [61, 225], target: 16, just two numbers left.\n     |- Try 225 + 61 = 286. Evaluate 286 != 16, drop this branch.\n     |- Try 225 - 61 = 164. Evaluate 164 != 16, drop this branch.\n     |- Try 225 * 61 = 13725. 13725 exceeds the maximum intermediate result, drop this branch.\n     |- Try 225 \/ 61 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 34 - 27 = 7. Add 7 to the number set. Current number set: [7, 225], target: 16, just two numbers left.\n     |- Try 225 + 7 = 232. Evaluate 232 != 16, drop this branch.\n     |- Try 225 - 7 = 218. Evaluate 218 != 16, drop this branch.\n     |- Try 225 * 7 = 1575. Evaluate 1575 != 16, drop this branch.\n     |- Try 225 \/ 7 = 32.1. 32.1 is a decimal, drop this branch.\n    |- Try 34 * 27 = 918. Add 918 to the number set. Current number set: [918, 225], target: 16, just two numbers left.\n     |- Try 918 + 225 = 1143. Evaluate 1143 != 16, drop this branch.\n     |- Try 918 - 225 = 693. Evaluate 693 != 16, drop this branch.\n     |- Try 918 * 225 = 206550. 206550 exceeds the maximum intermediate result, drop this branch.\n     |- Try 918 \/ 225 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 34 \/ 27 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 45 \/ 5 = 9. Add 9 to the number set. Current number set: [9, 27, 34], target: 16. Options for choosing two numbers: [(9, 27), (9, 34), (27, 34)].\n   |- Pick two numbers (9, 27) (numbers left: [34]). Try possible operations.\n    |- Try 27 + 9 = 36. Add 36 to the number set. Current number set: [36, 34], target: 16, just two numbers left.\n     |- Try 36 + 34 = 70. Evaluate 70 != 16, drop this branch.\n     |- Try 36 - 34 = 2. Evaluate 2 != 16, drop this branch.\n     |- Try 36 * 34 = 1224. Evaluate 1224 != 16, drop this branch.\n     |- Try 36 \/ 34 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 27 - 9 = 18. Add 18 to the number set. Current number set: [18, 34], target: 16, just two numbers left.\n     |- Try 34 + 18 = 52. Evaluate 52 != 16, drop this branch.\n     |- Try 34 - 18 = 16. Evaluate 16 == 16, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 34 - 18 = 16\nThe step before: 27 - 9 = 18\nThe first step: 45 \/ 5 = 9\n\nOutput the solution in the required format:\n<Solution>\n45 \/ 5 = 9\n27 - 9 = 18\n34 - 18 = 16\n<\/Solution>\n","item":{"nums":[5,45,27,34],"solution":["45 \/ 5 = 9","27 - 9 = 18","34 - 18 = 16"],"target":16}}
+{"instance_id":"countdown_8k_140","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [22, 2, 38, 16]\nTarget: 14","reference_output":"# Search Procedure\nInitial number set: [22, 2, 38, 16], target: 14. Options for choosing two numbers: [(22, 2), (22, 38), (22, 16), (2, 38), (2, 16), (38, 16)].\n |- Pick two numbers (22, 2) (numbers left: [38, 16]). Try possible operations.\n  |- Try 22 + 2 = 24. Add 24 to the number set. Current number set: [24, 38, 16], target: 14. Options for choosing two numbers: [(24, 38), (24, 16), (38, 16)].\n   |- Pick two numbers (24, 38) (numbers left: [16]). Try possible operations.\n    |- Try 38 + 24 = 62. Add 62 to the number set. Current number set: [62, 16], target: 14, just two numbers left.\n     |- Try 62 + 16 = 78. Evaluate 78 != 14, drop this branch.\n     |- Try 62 - 16 = 46. Evaluate 46 != 14, drop this branch.\n     |- Try 62 * 16 = 992. Evaluate 992 != 14, drop this branch.\n     |- Try 62 \/ 16 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 38 - 24 = 14. Add 14 to the number set. Current number set: [14, 16], target: 14, just two numbers left.\n     |- Try 16 + 14 = 30. Evaluate 30 != 14, drop this branch.\n     |- Try 16 - 14 = 2. Evaluate 2 != 14, drop this branch.\n     |- Try 16 * 14 = 224. Evaluate 224 != 14, drop this branch.\n     |- Try 16 \/ 14 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 38 * 24 = 912. Add 912 to the number set. Current number set: [912, 16], target: 14, just two numbers left.\n     |- Try 912 + 16 = 928. Evaluate 928 != 14, drop this branch.\n     |- Try 912 - 16 = 896. Evaluate 896 != 14, drop this branch.\n     |- Try 912 * 16 = 14592. 14592 exceeds the maximum intermediate result, drop this branch.\n     |- Try 912 \/ 16 = 57. Evaluate 57 != 14, drop this branch.\n    |- Try 38 \/ 24 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (24, 16) (numbers left: [38]). Try possible operations.\n    |- Try 24 + 16 = 40. Add 40 to the number set. Current number set: [40, 38], target: 14, just two numbers left.\n     |- Try 40 + 38 = 78. Evaluate 78 != 14, drop this branch.\n     |- Try 40 - 38 = 2. Evaluate 2 != 14, drop this branch.\n     |- Try 40 * 38 = 1520. Evaluate 1520 != 14, drop this branch.\n     |- Try 40 \/ 38 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 24 - 16 = 8. Add 8 to the number set. Current number set: [8, 38], target: 14, just two numbers left.\n     |- Try 38 + 8 = 46. Evaluate 46 != 14, drop this branch.\n     |- Try 38 - 8 = 30. Evaluate 30 != 14, drop this branch.\n     |- Try 38 * 8 = 304. Evaluate 304 != 14, drop this branch.\n     |- Try 38 \/ 8 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 24 * 16 = 384. Add 384 to the number set. Current number set: [384, 38], target: 14, just two numbers left.\n     |- Try 384 + 38 = 422. Evaluate 422 != 14, drop this branch.\n     |- Try 384 - 38 = 346. Evaluate 346 != 14, drop this branch.\n     |- Try 384 * 38 = 14592. 14592 exceeds the maximum intermediate result, drop this branch.\n     |- Try 384 \/ 38 = 10.1. 10.1 is a decimal, drop this branch.\n    |- Try 24 \/ 16 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (38, 16) (numbers left: [24]). Try possible operations.\n    |- Try 38 + 16 = 54. Add 54 to the number set. Current number set: [54, 24], target: 14, just two numbers left.\n     |- Try 54 + 24 = 78. Evaluate 78 != 14, drop this branch.\n     |- Try 54 - 24 = 30. Evaluate 30 != 14, drop this branch.\n     |- Try 54 * 24 = 1296. Evaluate 1296 != 14, drop this branch.\n     |- Try 54 \/ 24 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 38 - 16 = 22. Add 22 to the number set. Current number set: [22, 24], target: 14, just two numbers left.\n     |- Try 24 + 22 = 46. Evaluate 46 != 14, drop this branch.\n     |- Try 24 - 22 = 2. Evaluate 2 != 14, drop this branch.\n     |- Try 24 * 22 = 528. Evaluate 528 != 14, drop this branch.\n     |- Try 24 \/ 22 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 38 * 16 = 608. Add 608 to the number set. Current number set: [608, 24], target: 14, just two numbers left.\n     |- Try 608 + 24 = 632. Evaluate 632 != 14, drop this branch.\n     |- Try 608 - 24 = 584. Evaluate 584 != 14, drop this branch.\n     |- Try 608 * 24 = 14592. 14592 exceeds the maximum intermediate result, drop this branch.\n     |- Try 608 \/ 24 = 25.3. 25.3 is a decimal, drop this branch.\n    |- Try 38 \/ 16 = 2.4. 2.4 is a decimal, drop this branch.\n  |- Try 22 - 2 = 20. Add 20 to the number set. Current number set: [20, 38, 16], target: 14. Options for choosing two numbers: [(20, 38), (20, 16), (38, 16)].\n   |- Pick two numbers (20, 38) (numbers left: [16]). Try possible operations.\n    |- Try 38 + 20 = 58. Add 58 to the number set. Current number set: [58, 16], target: 14, just two numbers left.\n     |- Try 58 + 16 = 74. Evaluate 74 != 14, drop this branch.\n     |- Try 58 - 16 = 42. Evaluate 42 != 14, drop this branch.\n     |- Try 58 * 16 = 928. Evaluate 928 != 14, drop this branch.\n     |- Try 58 \/ 16 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 38 - 20 = 18. Add 18 to the number set. Current number set: [18, 16], target: 14, just two numbers left.\n     |- Try 18 + 16 = 34. Evaluate 34 != 14, drop this branch.\n     |- Try 18 - 16 = 2. Evaluate 2 != 14, drop this branch.\n     |- Try 18 * 16 = 288. Evaluate 288 != 14, drop this branch.\n     |- Try 18 \/ 16 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 38 * 20 = 760. Add 760 to the number set. Current number set: [760, 16], target: 14, just two numbers left.\n     |- Try 760 + 16 = 776. Evaluate 776 != 14, drop this branch.\n     |- Try 760 - 16 = 744. Evaluate 744 != 14, drop this branch.\n     |- Try 760 * 16 = 12160. 12160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 760 \/ 16 = 47.5. 47.5 is a decimal, drop this branch.\n    |- Try 38 \/ 20 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (20, 16) (numbers left: [38]). Try possible operations.\n    |- Try 20 + 16 = 36. Add 36 to the number set. Current number set: [36, 38], target: 14, just two numbers left.\n     |- Try 38 + 36 = 74. Evaluate 74 != 14, drop this branch.\n     |- Try 38 - 36 = 2. Evaluate 2 != 14, drop this branch.\n     |- Try 38 * 36 = 1368. Evaluate 1368 != 14, drop this branch.\n     |- Try 38 \/ 36 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 20 - 16 = 4. Add 4 to the number set. Current number set: [4, 38], target: 14, just two numbers left.\n     |- Try 38 + 4 = 42. Evaluate 42 != 14, drop this branch.\n     |- Try 38 - 4 = 34. Evaluate 34 != 14, drop this branch.\n     |- Try 38 * 4 = 152. Evaluate 152 != 14, drop this branch.\n     |- Try 38 \/ 4 = 9.5. 9.5 is a decimal, drop this branch.\n    |- Try 20 * 16 = 320. Add 320 to the number set. Current number set: [320, 38], target: 14, just two numbers left.\n     |- Try 320 + 38 = 358. Evaluate 358 != 14, drop this branch.\n     |- Try 320 - 38 = 282. Evaluate 282 != 14, drop this branch.\n     |- Try 320 * 38 = 12160. 12160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 320 \/ 38 = 8.4. 8.4 is a decimal, drop this branch.\n    |- Try 20 \/ 16 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (38, 16) (numbers left: [20]). Try possible operations.\n    |- Try 38 + 16 = 54. Add 54 to the number set. Current number set: [54, 20], target: 14, just two numbers left.\n     |- Try 54 + 20 = 74. Evaluate 74 != 14, drop this branch.\n     |- Try 54 - 20 = 34. Evaluate 34 != 14, drop this branch.\n     |- Try 54 * 20 = 1080. Evaluate 1080 != 14, drop this branch.\n     |- Try 54 \/ 20 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 38 - 16 = 22. Add 22 to the number set. Current number set: [22, 20], target: 14, just two numbers left.\n     |- Try 22 + 20 = 42. Evaluate 42 != 14, drop this branch.\n     |- Try 22 - 20 = 2. Evaluate 2 != 14, drop this branch.\n     |- Try 22 * 20 = 440. Evaluate 440 != 14, drop this branch.\n     |- Try 22 \/ 20 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 38 * 16 = 608. Add 608 to the number set. Current number set: [608, 20], target: 14, just two numbers left.\n     |- Try 608 + 20 = 628. Evaluate 628 != 14, drop this branch.\n     |- Try 608 - 20 = 588. Evaluate 588 != 14, drop this branch.\n     |- Try 608 * 20 = 12160. 12160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 608 \/ 20 = 30.4. 30.4 is a decimal, drop this branch.\n    |- Try 38 \/ 16 = 2.4. 2.4 is a decimal, drop this branch.\n  |- Try 22 * 2 = 44. Add 44 to the number set. Current number set: [44, 38, 16], target: 14. Options for choosing two numbers: [(44, 38), (44, 16), (38, 16)].\n   |- Pick two numbers (44, 38) (numbers left: [16]). Try possible operations.\n    |- Try 44 + 38 = 82. Add 82 to the number set. Current number set: [82, 16], target: 14, just two numbers left.\n     |- Try 82 + 16 = 98. Evaluate 98 != 14, drop this branch.\n     |- Try 82 - 16 = 66. Evaluate 66 != 14, drop this branch.\n     |- Try 82 * 16 = 1312. Evaluate 1312 != 14, drop this branch.\n     |- Try 82 \/ 16 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 44 - 38 = 6. Add 6 to the number set. Current number set: [6, 16], target: 14, just two numbers left.\n     |- Try 16 + 6 = 22. Evaluate 22 != 14, drop this branch.\n     |- Try 16 - 6 = 10. Evaluate 10 != 14, drop this branch.\n     |- Try 16 * 6 = 96. Evaluate 96 != 14, drop this branch.\n     |- Try 16 \/ 6 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 44 * 38 = 1672. Add 1672 to the number set. Current number set: [1672, 16], target: 14, just two numbers left.\n     |- Try 1672 + 16 = 1688. Evaluate 1688 != 14, drop this branch.\n     |- Try 1672 - 16 = 1656. Evaluate 1656 != 14, drop this branch.\n     |- Try 1672 * 16 = 26752. 26752 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1672 \/ 16 = 104.5. 104.5 is a decimal, drop this branch.\n    |- Try 44 \/ 38 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (44, 16) (numbers left: [38]). Try possible operations.\n    |- Try 44 + 16 = 60. Add 60 to the number set. Current number set: [60, 38], target: 14, just two numbers left.\n     |- Try 60 + 38 = 98. Evaluate 98 != 14, drop this branch.\n     |- Try 60 - 38 = 22. Evaluate 22 != 14, drop this branch.\n     |- Try 60 * 38 = 2280. 2280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 60 \/ 38 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 44 - 16 = 28. Add 28 to the number set. Current number set: [28, 38], target: 14, just two numbers left.\n     |- Try 38 + 28 = 66. Evaluate 66 != 14, drop this branch.\n     |- Try 38 - 28 = 10. Evaluate 10 != 14, drop this branch.\n     |- Try 38 * 28 = 1064. Evaluate 1064 != 14, drop this branch.\n     |- Try 38 \/ 28 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 44 * 16 = 704. Add 704 to the number set. Current number set: [704, 38], target: 14, just two numbers left.\n     |- Try 704 + 38 = 742. Evaluate 742 != 14, drop this branch.\n     |- Try 704 - 38 = 666. Evaluate 666 != 14, drop this branch.\n     |- Try 704 * 38 = 26752. 26752 exceeds the maximum intermediate result, drop this branch.\n     |- Try 704 \/ 38 = 18.5. 18.5 is a decimal, drop this branch.\n    |- Try 44 \/ 16 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (38, 16) (numbers left: [44]). Try possible operations.\n    |- Try 38 + 16 = 54. Add 54 to the number set. Current number set: [54, 44], target: 14, just two numbers left.\n     |- Try 54 + 44 = 98. Evaluate 98 != 14, drop this branch.\n     |- Try 54 - 44 = 10. Evaluate 10 != 14, drop this branch.\n     |- Try 54 * 44 = 2376. 2376 exceeds the maximum intermediate result, drop this branch.\n     |- Try 54 \/ 44 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 38 - 16 = 22. Add 22 to the number set. Current number set: [22, 44], target: 14, just two numbers left.\n     |- Try 44 + 22 = 66. Evaluate 66 != 14, drop this branch.\n     |- Try 44 - 22 = 22. Evaluate 22 != 14, drop this branch.\n     |- Try 44 * 22 = 968. Evaluate 968 != 14, drop this branch.\n     |- Try 44 \/ 22 = 2. Evaluate 2 != 14, drop this branch.\n    |- Try 38 * 16 = 608. Add 608 to the number set. Current number set: [608, 44], target: 14, just two numbers left.\n     |- Try 608 + 44 = 652. Evaluate 652 != 14, drop this branch.\n     |- Try 608 - 44 = 564. Evaluate 564 != 14, drop this branch.\n     |- Try 608 * 44 = 26752. 26752 exceeds the maximum intermediate result, drop this branch.\n     |- Try 608 \/ 44 = 13.8. 13.8 is a decimal, drop this branch.\n    |- Try 38 \/ 16 = 2.4. 2.4 is a decimal, drop this branch.\n  |- Try 22 \/ 2 = 11. Add 11 to the number set. Current number set: [11, 38, 16], target: 14. Options for choosing two numbers: [(11, 38), (11, 16), (38, 16)].\n   |- Pick two numbers (11, 38) (numbers left: [16]). Try possible operations.\n    |- Try 38 + 11 = 49. Add 49 to the number set. Current number set: [49, 16], target: 14, just two numbers left.\n     |- Try 49 + 16 = 65. Evaluate 65 != 14, drop this branch.\n     |- Try 49 - 16 = 33. Evaluate 33 != 14, drop this branch.\n     |- Try 49 * 16 = 784. Evaluate 784 != 14, drop this branch.\n     |- Try 49 \/ 16 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 38 - 11 = 27. Add 27 to the number set. Current number set: [27, 16], target: 14, just two numbers left.\n     |- Try 27 + 16 = 43. Evaluate 43 != 14, drop this branch.\n     |- Try 27 - 16 = 11. Evaluate 11 != 14, drop this branch.\n     |- Try 27 * 16 = 432. Evaluate 432 != 14, drop this branch.\n     |- Try 27 \/ 16 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 38 * 11 = 418. Add 418 to the number set. Current number set: [418, 16], target: 14, just two numbers left.\n     |- Try 418 + 16 = 434. Evaluate 434 != 14, drop this branch.\n     |- Try 418 - 16 = 402. Evaluate 402 != 14, drop this branch.\n     |- Try 418 * 16 = 6688. 6688 exceeds the maximum intermediate result, drop this branch.\n     |- Try 418 \/ 16 = 26.1. 26.1 is a decimal, drop this branch.\n    |- Try 38 \/ 11 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (11, 16) (numbers left: [38]). Try possible operations.\n    |- Try 16 + 11 = 27. Add 27 to the number set. Current number set: [27, 38], target: 14, just two numbers left.\n     |- Try 38 + 27 = 65. Evaluate 65 != 14, drop this branch.\n     |- Try 38 - 27 = 11. Evaluate 11 != 14, drop this branch.\n     |- Try 38 * 27 = 1026. Evaluate 1026 != 14, drop this branch.\n     |- Try 38 \/ 27 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 16 - 11 = 5. Add 5 to the number set. Current number set: [5, 38], target: 14, just two numbers left.\n     |- Try 38 + 5 = 43. Evaluate 43 != 14, drop this branch.\n     |- Try 38 - 5 = 33. Evaluate 33 != 14, drop this branch.\n     |- Try 38 * 5 = 190. Evaluate 190 != 14, drop this branch.\n     |- Try 38 \/ 5 = 7.6. 7.6 is a decimal, drop this branch.\n    |- Try 16 * 11 = 176. Add 176 to the number set. Current number set: [176, 38], target: 14, just two numbers left.\n     |- Try 176 + 38 = 214. Evaluate 214 != 14, drop this branch.\n     |- Try 176 - 38 = 138. Evaluate 138 != 14, drop this branch.\n     |- Try 176 * 38 = 6688. 6688 exceeds the maximum intermediate result, drop this branch.\n     |- Try 176 \/ 38 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 16 \/ 11 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (38, 16) (numbers left: [11]). Try possible operations.\n    |- Try 38 + 16 = 54. Add 54 to the number set. Current number set: [54, 11], target: 14, just two numbers left.\n     |- Try 54 + 11 = 65. Evaluate 65 != 14, drop this branch.\n     |- Try 54 - 11 = 43. Evaluate 43 != 14, drop this branch.\n     |- Try 54 * 11 = 594. Evaluate 594 != 14, drop this branch.\n     |- Try 54 \/ 11 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 38 - 16 = 22. Add 22 to the number set. Current number set: [22, 11], target: 14, just two numbers left.\n     |- Try 22 + 11 = 33. Evaluate 33 != 14, drop this branch.\n     |- Try 22 - 11 = 11. Evaluate 11 != 14, drop this branch.\n     |- Try 22 * 11 = 242. Evaluate 242 != 14, drop this branch.\n     |- Try 22 \/ 11 = 2. Evaluate 2 != 14, drop this branch.\n    |- Try 38 * 16 = 608. Add 608 to the number set. Current number set: [608, 11], target: 14, just two numbers left.\n     |- Try 608 + 11 = 619. Evaluate 619 != 14, drop this branch.\n     |- Try 608 - 11 = 597. Evaluate 597 != 14, drop this branch.\n     |- Try 608 * 11 = 6688. 6688 exceeds the maximum intermediate result, drop this branch.\n     |- Try 608 \/ 11 = 55.3. 55.3 is a decimal, drop this branch.\n    |- Try 38 \/ 16 = 2.4. 2.4 is a decimal, drop this branch.\n |- Pick two numbers (22, 38) (numbers left: [2, 16]). Try possible operations.\n  |- Try 38 + 22 = 60. Add 60 to the number set. Current number set: [60, 2, 16], target: 14. Options for choosing two numbers: [(60, 2), (60, 16), (2, 16)].\n   |- Pick two numbers (60, 2) (numbers left: [16]). Try possible operations.\n    |- Try 60 + 2 = 62. Add 62 to the number set. Current number set: [62, 16], target: 14, just two numbers left.\n     |- Try 62 + 16 = 78. Evaluate 78 != 14, drop this branch.\n     |- Try 62 - 16 = 46. Evaluate 46 != 14, drop this branch.\n     |- Try 62 * 16 = 992. Evaluate 992 != 14, drop this branch.\n     |- Try 62 \/ 16 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 60 - 2 = 58. Add 58 to the number set. Current number set: [58, 16], target: 14, just two numbers left.\n     |- Try 58 + 16 = 74. Evaluate 74 != 14, drop this branch.\n     |- Try 58 - 16 = 42. Evaluate 42 != 14, drop this branch.\n     |- Try 58 * 16 = 928. Evaluate 928 != 14, drop this branch.\n     |- Try 58 \/ 16 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 60 * 2 = 120. Add 120 to the number set. Current number set: [120, 16], target: 14, just two numbers left.\n     |- Try 120 + 16 = 136. Evaluate 136 != 14, drop this branch.\n     |- Try 120 - 16 = 104. Evaluate 104 != 14, drop this branch.\n     |- Try 120 * 16 = 1920. Evaluate 1920 != 14, drop this branch.\n     |- Try 120 \/ 16 = 7.5. 7.5 is a decimal, drop this branch.\n    |- Try 60 \/ 2 = 30. Add 30 to the number set. Current number set: [30, 16], target: 14, just two numbers left.\n     |- Try 30 + 16 = 46. Evaluate 46 != 14, drop this branch.\n     |- Try 30 - 16 = 14. Evaluate 14 == 14, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 30 - 16 = 14\nThe step before: 60 \/ 2 = 30\nThe first step: 38 + 22 = 60\n\nOutput the solution in the required format:\n<Solution>\n38 + 22 = 60\n60 \/ 2 = 30\n30 - 16 = 14\n<\/Solution>\n","item":{"nums":[22,2,38,16],"solution":["38 + 22 = 60","60 \/ 2 = 30","30 - 16 = 14"],"target":14}}
+{"instance_id":"countdown_8k_141","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [24, 43, 26, 25]\nTarget: 34","reference_output":"# Search Procedure\nInitial number set: [24, 43, 26, 25], target: 34. Options for choosing two numbers: [(24, 43), (24, 26), (24, 25), (43, 26), (43, 25), (26, 25)].\n |- Pick two numbers (24, 43) (numbers left: [26, 25]). Try possible operations.\n  |- Try 43 + 24 = 67. Add 67 to the number set. Current number set: [67, 26, 25], target: 34. Options for choosing two numbers: [(67, 26), (67, 25), (26, 25)].\n   |- Pick two numbers (67, 26) (numbers left: [25]). Try possible operations.\n    |- Try 67 + 26 = 93. Add 93 to the number set. Current number set: [93, 25], target: 34, just two numbers left.\n     |- Try 93 + 25 = 118. Evaluate 118 != 34, drop this branch.\n     |- Try 93 - 25 = 68. Evaluate 68 != 34, drop this branch.\n     |- Try 93 * 25 = 2325. 2325 exceeds the maximum intermediate result, drop this branch.\n     |- Try 93 \/ 25 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 67 - 26 = 41. Add 41 to the number set. Current number set: [41, 25], target: 34, just two numbers left.\n     |- Try 41 + 25 = 66. Evaluate 66 != 34, drop this branch.\n     |- Try 41 - 25 = 16. Evaluate 16 != 34, drop this branch.\n     |- Try 41 * 25 = 1025. Evaluate 1025 != 34, drop this branch.\n     |- Try 41 \/ 25 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 67 * 26 = 1742. Add 1742 to the number set. Current number set: [1742, 25], target: 34, just two numbers left.\n     |- Try 1742 + 25 = 1767. Evaluate 1767 != 34, drop this branch.\n     |- Try 1742 - 25 = 1717. Evaluate 1717 != 34, drop this branch.\n     |- Try 1742 * 25 = 43550. 43550 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1742 \/ 25 = 69.7. 69.7 is a decimal, drop this branch.\n    |- Try 67 \/ 26 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (67, 25) (numbers left: [26]). Try possible operations.\n    |- Try 67 + 25 = 92. Add 92 to the number set. Current number set: [92, 26], target: 34, just two numbers left.\n     |- Try 92 + 26 = 118. Evaluate 118 != 34, drop this branch.\n     |- Try 92 - 26 = 66. Evaluate 66 != 34, drop this branch.\n     |- Try 92 * 26 = 2392. 2392 exceeds the maximum intermediate result, drop this branch.\n     |- Try 92 \/ 26 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 67 - 25 = 42. Add 42 to the number set. Current number set: [42, 26], target: 34, just two numbers left.\n     |- Try 42 + 26 = 68. Evaluate 68 != 34, drop this branch.\n     |- Try 42 - 26 = 16. Evaluate 16 != 34, drop this branch.\n     |- Try 42 * 26 = 1092. Evaluate 1092 != 34, drop this branch.\n     |- Try 42 \/ 26 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 67 * 25 = 1675. Add 1675 to the number set. Current number set: [1675, 26], target: 34, just two numbers left.\n     |- Try 1675 + 26 = 1701. Evaluate 1701 != 34, drop this branch.\n     |- Try 1675 - 26 = 1649. Evaluate 1649 != 34, drop this branch.\n     |- Try 1675 * 26 = 43550. 43550 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1675 \/ 26 = 64.4. 64.4 is a decimal, drop this branch.\n    |- Try 67 \/ 25 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (26, 25) (numbers left: [67]). Try possible operations.\n    |- Try 26 + 25 = 51. Add 51 to the number set. Current number set: [51, 67], target: 34, just two numbers left.\n     |- Try 67 + 51 = 118. Evaluate 118 != 34, drop this branch.\n     |- Try 67 - 51 = 16. Evaluate 16 != 34, drop this branch.\n     |- Try 67 * 51 = 3417. 3417 exceeds the maximum intermediate result, drop this branch.\n     |- Try 67 \/ 51 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 26 - 25 = 1. Add 1 to the number set. Current number set: [1, 67], target: 34, just two numbers left.\n     |- Try 67 + 1 = 68. Evaluate 68 != 34, drop this branch.\n     |- Try 67 - 1 = 66. Evaluate 66 != 34, drop this branch.\n     |- Try 67 * 1 = 67. Evaluate 67 != 34, drop this branch.\n     |- Try 67 \/ 1 = 67. Evaluate 67 != 34, drop this branch.\n    |- Try 26 * 25 = 650. Add 650 to the number set. Current number set: [650, 67], target: 34, just two numbers left.\n     |- Try 650 + 67 = 717. Evaluate 717 != 34, drop this branch.\n     |- Try 650 - 67 = 583. Evaluate 583 != 34, drop this branch.\n     |- Try 650 * 67 = 43550. 43550 exceeds the maximum intermediate result, drop this branch.\n     |- Try 650 \/ 67 = 9.7. 9.7 is a decimal, drop this branch.\n    |- Try 26 \/ 25 = 1.0. 1.0 is a decimal, drop this branch.\n  |- Try 43 - 24 = 19. Add 19 to the number set. Current number set: [19, 26, 25], target: 34. Options for choosing two numbers: [(19, 26), (19, 25), (26, 25)].\n   |- Pick two numbers (19, 26) (numbers left: [25]). Try possible operations.\n    |- Try 26 + 19 = 45. Add 45 to the number set. Current number set: [45, 25], target: 34, just two numbers left.\n     |- Try 45 + 25 = 70. Evaluate 70 != 34, drop this branch.\n     |- Try 45 - 25 = 20. Evaluate 20 != 34, drop this branch.\n     |- Try 45 * 25 = 1125. Evaluate 1125 != 34, drop this branch.\n     |- Try 45 \/ 25 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 26 - 19 = 7. Add 7 to the number set. Current number set: [7, 25], target: 34, just two numbers left.\n     |- Try 25 + 7 = 32. Evaluate 32 != 34, drop this branch.\n     |- Try 25 - 7 = 18. Evaluate 18 != 34, drop this branch.\n     |- Try 25 * 7 = 175. Evaluate 175 != 34, drop this branch.\n     |- Try 25 \/ 7 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 26 * 19 = 494. Add 494 to the number set. Current number set: [494, 25], target: 34, just two numbers left.\n     |- Try 494 + 25 = 519. Evaluate 519 != 34, drop this branch.\n     |- Try 494 - 25 = 469. Evaluate 469 != 34, drop this branch.\n     |- Try 494 * 25 = 12350. 12350 exceeds the maximum intermediate result, drop this branch.\n     |- Try 494 \/ 25 = 19.8. 19.8 is a decimal, drop this branch.\n    |- Try 26 \/ 19 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (19, 25) (numbers left: [26]). Try possible operations.\n    |- Try 25 + 19 = 44. Add 44 to the number set. Current number set: [44, 26], target: 34, just two numbers left.\n     |- Try 44 + 26 = 70. Evaluate 70 != 34, drop this branch.\n     |- Try 44 - 26 = 18. Evaluate 18 != 34, drop this branch.\n     |- Try 44 * 26 = 1144. Evaluate 1144 != 34, drop this branch.\n     |- Try 44 \/ 26 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 19 = 6. Add 6 to the number set. Current number set: [6, 26], target: 34, just two numbers left.\n     |- Try 26 + 6 = 32. Evaluate 32 != 34, drop this branch.\n     |- Try 26 - 6 = 20. Evaluate 20 != 34, drop this branch.\n     |- Try 26 * 6 = 156. Evaluate 156 != 34, drop this branch.\n     |- Try 26 \/ 6 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 25 * 19 = 475. Add 475 to the number set. Current number set: [475, 26], target: 34, just two numbers left.\n     |- Try 475 + 26 = 501. Evaluate 501 != 34, drop this branch.\n     |- Try 475 - 26 = 449. Evaluate 449 != 34, drop this branch.\n     |- Try 475 * 26 = 12350. 12350 exceeds the maximum intermediate result, drop this branch.\n     |- Try 475 \/ 26 = 18.3. 18.3 is a decimal, drop this branch.\n    |- Try 25 \/ 19 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (26, 25) (numbers left: [19]). Try possible operations.\n    |- Try 26 + 25 = 51. Add 51 to the number set. Current number set: [51, 19], target: 34, just two numbers left.\n     |- Try 51 + 19 = 70. Evaluate 70 != 34, drop this branch.\n     |- Try 51 - 19 = 32. Evaluate 32 != 34, drop this branch.\n     |- Try 51 * 19 = 969. Evaluate 969 != 34, drop this branch.\n     |- Try 51 \/ 19 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 26 - 25 = 1. Add 1 to the number set. Current number set: [1, 19], target: 34, just two numbers left.\n     |- Try 19 + 1 = 20. Evaluate 20 != 34, drop this branch.\n     |- Try 19 - 1 = 18. Evaluate 18 != 34, drop this branch.\n     |- Try 19 * 1 = 19. Evaluate 19 != 34, drop this branch.\n     |- Try 19 \/ 1 = 19. Evaluate 19 != 34, drop this branch.\n    |- Try 26 * 25 = 650. Add 650 to the number set. Current number set: [650, 19], target: 34, just two numbers left.\n     |- Try 650 + 19 = 669. Evaluate 669 != 34, drop this branch.\n     |- Try 650 - 19 = 631. Evaluate 631 != 34, drop this branch.\n     |- Try 650 * 19 = 12350. 12350 exceeds the maximum intermediate result, drop this branch.\n     |- Try 650 \/ 19 = 34.2. 34.2 is a decimal, drop this branch.\n    |- Try 26 \/ 25 = 1.0. 1.0 is a decimal, drop this branch.\n  |- Try 43 * 24 = 1032. Add 1032 to the number set. Current number set: [1032, 26, 25], target: 34. Options for choosing two numbers: [(1032, 26), (1032, 25), (26, 25)].\n   |- Pick two numbers (1032, 26) (numbers left: [25]). Try possible operations.\n    |- Try 1032 + 26 = 1058. Add 1058 to the number set. Current number set: [1058, 25], target: 34, just two numbers left.\n     |- Try 1058 + 25 = 1083. Evaluate 1083 != 34, drop this branch.\n     |- Try 1058 - 25 = 1033. Evaluate 1033 != 34, drop this branch.\n     |- Try 1058 * 25 = 26450. 26450 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1058 \/ 25 = 42.3. 42.3 is a decimal, drop this branch.\n    |- Try 1032 - 26 = 1006. Add 1006 to the number set. Current number set: [1006, 25], target: 34, just two numbers left.\n     |- Try 1006 + 25 = 1031. Evaluate 1031 != 34, drop this branch.\n     |- Try 1006 - 25 = 981. Evaluate 981 != 34, drop this branch.\n     |- Try 1006 * 25 = 25150. 25150 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1006 \/ 25 = 40.2. 40.2 is a decimal, drop this branch.\n    |- Try 1032 * 26 = 26832. 26832 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1032 \/ 26 = 39.7. 39.7 is a decimal, drop this branch.\n   |- Pick two numbers (1032, 25) (numbers left: [26]). Try possible operations.\n    |- Try 1032 + 25 = 1057. Add 1057 to the number set. Current number set: [1057, 26], target: 34, just two numbers left.\n     |- Try 1057 + 26 = 1083. Evaluate 1083 != 34, drop this branch.\n     |- Try 1057 - 26 = 1031. Evaluate 1031 != 34, drop this branch.\n     |- Try 1057 * 26 = 27482. 27482 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1057 \/ 26 = 40.7. 40.7 is a decimal, drop this branch.\n    |- Try 1032 - 25 = 1007. Add 1007 to the number set. Current number set: [1007, 26], target: 34, just two numbers left.\n     |- Try 1007 + 26 = 1033. Evaluate 1033 != 34, drop this branch.\n     |- Try 1007 - 26 = 981. Evaluate 981 != 34, drop this branch.\n     |- Try 1007 * 26 = 26182. 26182 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1007 \/ 26 = 38.7. 38.7 is a decimal, drop this branch.\n    |- Try 1032 * 25 = 25800. 25800 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1032 \/ 25 = 41.3. 41.3 is a decimal, drop this branch.\n   |- Pick two numbers (26, 25) (numbers left: [1032]). Try possible operations.\n    |- Try 26 + 25 = 51. Add 51 to the number set. Current number set: [51, 1032], target: 34, just two numbers left.\n     |- Try 1032 + 51 = 1083. Evaluate 1083 != 34, drop this branch.\n     |- Try 1032 - 51 = 981. Evaluate 981 != 34, drop this branch.\n     |- Try 1032 * 51 = 52632. 52632 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1032 \/ 51 = 20.2. 20.2 is a decimal, drop this branch.\n    |- Try 26 - 25 = 1. Add 1 to the number set. Current number set: [1, 1032], target: 34, just two numbers left.\n     |- Try 1032 + 1 = 1033. Evaluate 1033 != 34, drop this branch.\n     |- Try 1032 - 1 = 1031. Evaluate 1031 != 34, drop this branch.\n     |- Try 1032 * 1 = 1032. Evaluate 1032 != 34, drop this branch.\n     |- Try 1032 \/ 1 = 1032. Evaluate 1032 != 34, drop this branch.\n    |- Try 26 * 25 = 650. Add 650 to the number set. Current number set: [650, 1032], target: 34, just two numbers left.\n     |- Try 1032 + 650 = 1682. Evaluate 1682 != 34, drop this branch.\n     |- Try 1032 - 650 = 382. Evaluate 382 != 34, drop this branch.\n     |- Try 1032 * 650 = 670800. 670800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1032 \/ 650 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 26 \/ 25 = 1.0. 1.0 is a decimal, drop this branch.\n  |- Try 43 \/ 24 = 1.8. 1.8 is a decimal, drop this branch.\n |- Pick two numbers (24, 26) (numbers left: [43, 25]). Try possible operations.\n  |- Try 26 + 24 = 50. Add 50 to the number set. Current number set: [50, 43, 25], target: 34. Options for choosing two numbers: [(50, 43), (50, 25), (43, 25)].\n   |- Pick two numbers (50, 43) (numbers left: [25]). Try possible operations.\n    |- Try 50 + 43 = 93. Add 93 to the number set. Current number set: [93, 25], target: 34, just two numbers left.\n     |- Try 93 + 25 = 118. Evaluate 118 != 34, drop this branch.\n     |- Try 93 - 25 = 68. Evaluate 68 != 34, drop this branch.\n     |- Try 93 * 25 = 2325. 2325 exceeds the maximum intermediate result, drop this branch.\n     |- Try 93 \/ 25 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 50 - 43 = 7. Add 7 to the number set. Current number set: [7, 25], target: 34, just two numbers left.\n     |- Try 25 + 7 = 32. Evaluate 32 != 34, drop this branch.\n     |- Try 25 - 7 = 18. Evaluate 18 != 34, drop this branch.\n     |- Try 25 * 7 = 175. Evaluate 175 != 34, drop this branch.\n     |- Try 25 \/ 7 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 50 * 43 = 2150. 2150 exceeds the maximum intermediate result, drop this branch.\n    |- Try 50 \/ 43 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (50, 25) (numbers left: [43]). Try possible operations.\n    |- Try 50 + 25 = 75. Add 75 to the number set. Current number set: [75, 43], target: 34, just two numbers left.\n     |- Try 75 + 43 = 118. Evaluate 118 != 34, drop this branch.\n     |- Try 75 - 43 = 32. Evaluate 32 != 34, drop this branch.\n     |- Try 75 * 43 = 3225. 3225 exceeds the maximum intermediate result, drop this branch.\n     |- Try 75 \/ 43 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 50 - 25 = 25. Add 25 to the number set. Current number set: [25, 43], target: 34, just two numbers left.\n     |- Try 43 + 25 = 68. Evaluate 68 != 34, drop this branch.\n     |- Try 43 - 25 = 18. Evaluate 18 != 34, drop this branch.\n     |- Try 43 * 25 = 1075. Evaluate 1075 != 34, drop this branch.\n     |- Try 43 \/ 25 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 50 * 25 = 1250. Add 1250 to the number set. Current number set: [1250, 43], target: 34, just two numbers left.\n     |- Try 1250 + 43 = 1293. Evaluate 1293 != 34, drop this branch.\n     |- Try 1250 - 43 = 1207. Evaluate 1207 != 34, drop this branch.\n     |- Try 1250 * 43 = 53750. 53750 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1250 \/ 43 = 29.1. 29.1 is a decimal, drop this branch.\n    |- Try 50 \/ 25 = 2. Add 2 to the number set. Current number set: [2, 43], target: 34, just two numbers left.\n     |- Try 43 + 2 = 45. Evaluate 45 != 34, drop this branch.\n     |- Try 43 - 2 = 41. Evaluate 41 != 34, drop this branch.\n     |- Try 43 * 2 = 86. Evaluate 86 != 34, drop this branch.\n     |- Try 43 \/ 2 = 21.5. 21.5 is a decimal, drop this branch.\n   |- Pick two numbers (43, 25) (numbers left: [50]). Try possible operations.\n    |- Try 43 + 25 = 68. Add 68 to the number set. Current number set: [68, 50], target: 34, just two numbers left.\n     |- Try 68 + 50 = 118. Evaluate 118 != 34, drop this branch.\n     |- Try 68 - 50 = 18. Evaluate 18 != 34, drop this branch.\n     |- Try 68 * 50 = 3400. 3400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 68 \/ 50 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 43 - 25 = 18. Add 18 to the number set. Current number set: [18, 50], target: 34, just two numbers left.\n     |- Try 50 + 18 = 68. Evaluate 68 != 34, drop this branch.\n     |- Try 50 - 18 = 32. Evaluate 32 != 34, drop this branch.\n     |- Try 50 * 18 = 900. Evaluate 900 != 34, drop this branch.\n     |- Try 50 \/ 18 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 43 * 25 = 1075. Add 1075 to the number set. Current number set: [1075, 50], target: 34, just two numbers left.\n     |- Try 1075 + 50 = 1125. Evaluate 1125 != 34, drop this branch.\n     |- Try 1075 - 50 = 1025. Evaluate 1025 != 34, drop this branch.\n     |- Try 1075 * 50 = 53750. 53750 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1075 \/ 50 = 21.5. 21.5 is a decimal, drop this branch.\n    |- Try 43 \/ 25 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 26 - 24 = 2. Add 2 to the number set. Current number set: [2, 43, 25], target: 34. Options for choosing two numbers: [(2, 43), (2, 25), (43, 25)].\n   |- Pick two numbers (2, 43) (numbers left: [25]). Try possible operations.\n    |- Try 43 + 2 = 45. Add 45 to the number set. Current number set: [45, 25], target: 34, just two numbers left.\n     |- Try 45 + 25 = 70. Evaluate 70 != 34, drop this branch.\n     |- Try 45 - 25 = 20. Evaluate 20 != 34, drop this branch.\n     |- Try 45 * 25 = 1125. Evaluate 1125 != 34, drop this branch.\n     |- Try 45 \/ 25 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 43 - 2 = 41. Add 41 to the number set. Current number set: [41, 25], target: 34, just two numbers left.\n     |- Try 41 + 25 = 66. Evaluate 66 != 34, drop this branch.\n     |- Try 41 - 25 = 16. Evaluate 16 != 34, drop this branch.\n     |- Try 41 * 25 = 1025. Evaluate 1025 != 34, drop this branch.\n     |- Try 41 \/ 25 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 43 * 2 = 86. Add 86 to the number set. Current number set: [86, 25], target: 34, just two numbers left.\n     |- Try 86 + 25 = 111. Evaluate 111 != 34, drop this branch.\n     |- Try 86 - 25 = 61. Evaluate 61 != 34, drop this branch.\n     |- Try 86 * 25 = 2150. 2150 exceeds the maximum intermediate result, drop this branch.\n     |- Try 86 \/ 25 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 43 \/ 2 = 21.5. 21.5 is a decimal, drop this branch.\n   |- Pick two numbers (2, 25) (numbers left: [43]). Try possible operations.\n    |- Try 25 + 2 = 27. Add 27 to the number set. Current number set: [27, 43], target: 34, just two numbers left.\n     |- Try 43 + 27 = 70. Evaluate 70 != 34, drop this branch.\n     |- Try 43 - 27 = 16. Evaluate 16 != 34, drop this branch.\n     |- Try 43 * 27 = 1161. Evaluate 1161 != 34, drop this branch.\n     |- Try 43 \/ 27 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 25 - 2 = 23. Add 23 to the number set. Current number set: [23, 43], target: 34, just two numbers left.\n     |- Try 43 + 23 = 66. Evaluate 66 != 34, drop this branch.\n     |- Try 43 - 23 = 20. Evaluate 20 != 34, drop this branch.\n     |- Try 43 * 23 = 989. Evaluate 989 != 34, drop this branch.\n     |- Try 43 \/ 23 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 25 * 2 = 50. Add 50 to the number set. Current number set: [50, 43], target: 34, just two numbers left.\n     |- Try 50 + 43 = 93. Evaluate 93 != 34, drop this branch.\n     |- Try 50 - 43 = 7. Evaluate 7 != 34, drop this branch.\n     |- Try 50 * 43 = 2150. 2150 exceeds the maximum intermediate result, drop this branch.\n     |- Try 50 \/ 43 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 \/ 2 = 12.5. 12.5 is a decimal, drop this branch.\n   |- Pick two numbers (43, 25) (numbers left: [2]). Try possible operations.\n    |- Try 43 + 25 = 68. Add 68 to the number set. Current number set: [68, 2], target: 34, just two numbers left.\n     |- Try 68 + 2 = 70. Evaluate 70 != 34, drop this branch.\n     |- Try 68 - 2 = 66. Evaluate 66 != 34, drop this branch.\n     |- Try 68 * 2 = 136. Evaluate 136 != 34, drop this branch.\n     |- Try 68 \/ 2 = 34. Evaluate 34 == 34, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 68 \/ 2 = 34\nThe step before: 43 + 25 = 68\nThe first step: 26 - 24 = 2\n\nOutput the solution in the required format:\n<Solution>\n26 - 24 = 2\n43 + 25 = 68\n68 \/ 2 = 34\n<\/Solution>\n","item":{"nums":[24,43,26,25],"solution":["26 - 24 = 2","43 + 25 = 68","68 \/ 2 = 34"],"target":34}}
+{"instance_id":"countdown_8k_142","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [21, 25, 37, 48]\nTarget: 28","reference_output":"# Search Procedure\nInitial number set: [21, 25, 37, 48], target: 28. Options for choosing two numbers: [(21, 25), (21, 37), (21, 48), (25, 37), (25, 48), (37, 48)].\n |- Pick two numbers (21, 25) (numbers left: [37, 48]). Try possible operations.\n  |- Try 25 + 21 = 46. Add 46 to the number set. Current number set: [46, 37, 48], target: 28. Options for choosing two numbers: [(46, 37), (46, 48), (37, 48)].\n   |- Pick two numbers (46, 37) (numbers left: [48]). Try possible operations.\n    |- Try 46 + 37 = 83. Add 83 to the number set. Current number set: [83, 48], target: 28, just two numbers left.\n     |- Try 83 + 48 = 131. Evaluate 131 != 28, drop this branch.\n     |- Try 83 - 48 = 35. Evaluate 35 != 28, drop this branch.\n     |- Try 83 * 48 = 3984. 3984 exceeds the maximum intermediate result, drop this branch.\n     |- Try 83 \/ 48 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 46 - 37 = 9. Add 9 to the number set. Current number set: [9, 48], target: 28, just two numbers left.\n     |- Try 48 + 9 = 57. Evaluate 57 != 28, drop this branch.\n     |- Try 48 - 9 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 48 * 9 = 432. Evaluate 432 != 28, drop this branch.\n     |- Try 48 \/ 9 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 46 * 37 = 1702. Add 1702 to the number set. Current number set: [1702, 48], target: 28, just two numbers left.\n     |- Try 1702 + 48 = 1750. Evaluate 1750 != 28, drop this branch.\n     |- Try 1702 - 48 = 1654. Evaluate 1654 != 28, drop this branch.\n     |- Try 1702 * 48 = 81696. 81696 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1702 \/ 48 = 35.5. 35.5 is a decimal, drop this branch.\n    |- Try 46 \/ 37 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (46, 48) (numbers left: [37]). Try possible operations.\n    |- Try 48 + 46 = 94. Add 94 to the number set. Current number set: [94, 37], target: 28, just two numbers left.\n     |- Try 94 + 37 = 131. Evaluate 131 != 28, drop this branch.\n     |- Try 94 - 37 = 57. Evaluate 57 != 28, drop this branch.\n     |- Try 94 * 37 = 3478. 3478 exceeds the maximum intermediate result, drop this branch.\n     |- Try 94 \/ 37 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 48 - 46 = 2. Add 2 to the number set. Current number set: [2, 37], target: 28, just two numbers left.\n     |- Try 37 + 2 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 37 - 2 = 35. Evaluate 35 != 28, drop this branch.\n     |- Try 37 * 2 = 74. Evaluate 74 != 28, drop this branch.\n     |- Try 37 \/ 2 = 18.5. 18.5 is a decimal, drop this branch.\n    |- Try 48 * 46 = 2208. 2208 exceeds the maximum intermediate result, drop this branch.\n    |- Try 48 \/ 46 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (37, 48) (numbers left: [46]). Try possible operations.\n    |- Try 48 + 37 = 85. Add 85 to the number set. Current number set: [85, 46], target: 28, just two numbers left.\n     |- Try 85 + 46 = 131. Evaluate 131 != 28, drop this branch.\n     |- Try 85 - 46 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 85 * 46 = 3910. 3910 exceeds the maximum intermediate result, drop this branch.\n     |- Try 85 \/ 46 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 48 - 37 = 11. Add 11 to the number set. Current number set: [11, 46], target: 28, just two numbers left.\n     |- Try 46 + 11 = 57. Evaluate 57 != 28, drop this branch.\n     |- Try 46 - 11 = 35. Evaluate 35 != 28, drop this branch.\n     |- Try 46 * 11 = 506. Evaluate 506 != 28, drop this branch.\n     |- Try 46 \/ 11 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 48 * 37 = 1776. Add 1776 to the number set. Current number set: [1776, 46], target: 28, just two numbers left.\n     |- Try 1776 + 46 = 1822. Evaluate 1822 != 28, drop this branch.\n     |- Try 1776 - 46 = 1730. Evaluate 1730 != 28, drop this branch.\n     |- Try 1776 * 46 = 81696. 81696 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1776 \/ 46 = 38.6. 38.6 is a decimal, drop this branch.\n    |- Try 48 \/ 37 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 25 - 21 = 4. Add 4 to the number set. Current number set: [4, 37, 48], target: 28. Options for choosing two numbers: [(4, 37), (4, 48), (37, 48)].\n   |- Pick two numbers (4, 37) (numbers left: [48]). Try possible operations.\n    |- Try 37 + 4 = 41. Add 41 to the number set. Current number set: [41, 48], target: 28, just two numbers left.\n     |- Try 48 + 41 = 89. Evaluate 89 != 28, drop this branch.\n     |- Try 48 - 41 = 7. Evaluate 7 != 28, drop this branch.\n     |- Try 48 * 41 = 1968. Evaluate 1968 != 28, drop this branch.\n     |- Try 48 \/ 41 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 37 - 4 = 33. Add 33 to the number set. Current number set: [33, 48], target: 28, just two numbers left.\n     |- Try 48 + 33 = 81. Evaluate 81 != 28, drop this branch.\n     |- Try 48 - 33 = 15. Evaluate 15 != 28, drop this branch.\n     |- Try 48 * 33 = 1584. Evaluate 1584 != 28, drop this branch.\n     |- Try 48 \/ 33 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 37 * 4 = 148. Add 148 to the number set. Current number set: [148, 48], target: 28, just two numbers left.\n     |- Try 148 + 48 = 196. Evaluate 196 != 28, drop this branch.\n     |- Try 148 - 48 = 100. Evaluate 100 != 28, drop this branch.\n     |- Try 148 * 48 = 7104. 7104 exceeds the maximum intermediate result, drop this branch.\n     |- Try 148 \/ 48 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 37 \/ 4 = 9.2. 9.2 is a decimal, drop this branch.\n   |- Pick two numbers (4, 48) (numbers left: [37]). Try possible operations.\n    |- Try 48 + 4 = 52. Add 52 to the number set. Current number set: [52, 37], target: 28, just two numbers left.\n     |- Try 52 + 37 = 89. Evaluate 89 != 28, drop this branch.\n     |- Try 52 - 37 = 15. Evaluate 15 != 28, drop this branch.\n     |- Try 52 * 37 = 1924. Evaluate 1924 != 28, drop this branch.\n     |- Try 52 \/ 37 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 48 - 4 = 44. Add 44 to the number set. Current number set: [44, 37], target: 28, just two numbers left.\n     |- Try 44 + 37 = 81. Evaluate 81 != 28, drop this branch.\n     |- Try 44 - 37 = 7. Evaluate 7 != 28, drop this branch.\n     |- Try 44 * 37 = 1628. Evaluate 1628 != 28, drop this branch.\n     |- Try 44 \/ 37 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 48 * 4 = 192. Add 192 to the number set. Current number set: [192, 37], target: 28, just two numbers left.\n     |- Try 192 + 37 = 229. Evaluate 229 != 28, drop this branch.\n     |- Try 192 - 37 = 155. Evaluate 155 != 28, drop this branch.\n     |- Try 192 * 37 = 7104. 7104 exceeds the maximum intermediate result, drop this branch.\n     |- Try 192 \/ 37 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 48 \/ 4 = 12. Add 12 to the number set. Current number set: [12, 37], target: 28, just two numbers left.\n     |- Try 37 + 12 = 49. Evaluate 49 != 28, drop this branch.\n     |- Try 37 - 12 = 25. Evaluate 25 != 28, drop this branch.\n     |- Try 37 * 12 = 444. Evaluate 444 != 28, drop this branch.\n     |- Try 37 \/ 12 = 3.1. 3.1 is a decimal, drop this branch.\n   |- Pick two numbers (37, 48) (numbers left: [4]). Try possible operations.\n    |- Try 48 + 37 = 85. Add 85 to the number set. Current number set: [85, 4], target: 28, just two numbers left.\n     |- Try 85 + 4 = 89. Evaluate 89 != 28, drop this branch.\n     |- Try 85 - 4 = 81. Evaluate 81 != 28, drop this branch.\n     |- Try 85 * 4 = 340. Evaluate 340 != 28, drop this branch.\n     |- Try 85 \/ 4 = 21.2. 21.2 is a decimal, drop this branch.\n    |- Try 48 - 37 = 11. Add 11 to the number set. Current number set: [11, 4], target: 28, just two numbers left.\n     |- Try 11 + 4 = 15. Evaluate 15 != 28, drop this branch.\n     |- Try 11 - 4 = 7. Evaluate 7 != 28, drop this branch.\n     |- Try 11 * 4 = 44. Evaluate 44 != 28, drop this branch.\n     |- Try 11 \/ 4 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 48 * 37 = 1776. Add 1776 to the number set. Current number set: [1776, 4], target: 28, just two numbers left.\n     |- Try 1776 + 4 = 1780. Evaluate 1780 != 28, drop this branch.\n     |- Try 1776 - 4 = 1772. Evaluate 1772 != 28, drop this branch.\n     |- Try 1776 * 4 = 7104. 7104 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1776 \/ 4 = 444. Evaluate 444 != 28, drop this branch.\n    |- Try 48 \/ 37 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 25 * 21 = 525. Add 525 to the number set. Current number set: [525, 37, 48], target: 28. Options for choosing two numbers: [(525, 37), (525, 48), (37, 48)].\n   |- Pick two numbers (525, 37) (numbers left: [48]). Try possible operations.\n    |- Try 525 + 37 = 562. Add 562 to the number set. Current number set: [562, 48], target: 28, just two numbers left.\n     |- Try 562 + 48 = 610. Evaluate 610 != 28, drop this branch.\n     |- Try 562 - 48 = 514. Evaluate 514 != 28, drop this branch.\n     |- Try 562 * 48 = 26976. 26976 exceeds the maximum intermediate result, drop this branch.\n     |- Try 562 \/ 48 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 525 - 37 = 488. Add 488 to the number set. Current number set: [488, 48], target: 28, just two numbers left.\n     |- Try 488 + 48 = 536. Evaluate 536 != 28, drop this branch.\n     |- Try 488 - 48 = 440. Evaluate 440 != 28, drop this branch.\n     |- Try 488 * 48 = 23424. 23424 exceeds the maximum intermediate result, drop this branch.\n     |- Try 488 \/ 48 = 10.2. 10.2 is a decimal, drop this branch.\n    |- Try 525 * 37 = 19425. 19425 exceeds the maximum intermediate result, drop this branch.\n    |- Try 525 \/ 37 = 14.2. 14.2 is a decimal, drop this branch.\n   |- Pick two numbers (525, 48) (numbers left: [37]). Try possible operations.\n    |- Try 525 + 48 = 573. Add 573 to the number set. Current number set: [573, 37], target: 28, just two numbers left.\n     |- Try 573 + 37 = 610. Evaluate 610 != 28, drop this branch.\n     |- Try 573 - 37 = 536. Evaluate 536 != 28, drop this branch.\n     |- Try 573 * 37 = 21201. 21201 exceeds the maximum intermediate result, drop this branch.\n     |- Try 573 \/ 37 = 15.5. 15.5 is a decimal, drop this branch.\n    |- Try 525 - 48 = 477. Add 477 to the number set. Current number set: [477, 37], target: 28, just two numbers left.\n     |- Try 477 + 37 = 514. Evaluate 514 != 28, drop this branch.\n     |- Try 477 - 37 = 440. Evaluate 440 != 28, drop this branch.\n     |- Try 477 * 37 = 17649. 17649 exceeds the maximum intermediate result, drop this branch.\n     |- Try 477 \/ 37 = 12.9. 12.9 is a decimal, drop this branch.\n    |- Try 525 * 48 = 25200. 25200 exceeds the maximum intermediate result, drop this branch.\n    |- Try 525 \/ 48 = 10.9. 10.9 is a decimal, drop this branch.\n   |- Pick two numbers (37, 48) (numbers left: [525]). Try possible operations.\n    |- Try 48 + 37 = 85. Add 85 to the number set. Current number set: [85, 525], target: 28, just two numbers left.\n     |- Try 525 + 85 = 610. Evaluate 610 != 28, drop this branch.\n     |- Try 525 - 85 = 440. Evaluate 440 != 28, drop this branch.\n     |- Try 525 * 85 = 44625. 44625 exceeds the maximum intermediate result, drop this branch.\n     |- Try 525 \/ 85 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 48 - 37 = 11. Add 11 to the number set. Current number set: [11, 525], target: 28, just two numbers left.\n     |- Try 525 + 11 = 536. Evaluate 536 != 28, drop this branch.\n     |- Try 525 - 11 = 514. Evaluate 514 != 28, drop this branch.\n     |- Try 525 * 11 = 5775. 5775 exceeds the maximum intermediate result, drop this branch.\n     |- Try 525 \/ 11 = 47.7. 47.7 is a decimal, drop this branch.\n    |- Try 48 * 37 = 1776. Add 1776 to the number set. Current number set: [1776, 525], target: 28, just two numbers left.\n     |- Try 1776 + 525 = 2301. 2301 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1776 - 525 = 1251. Evaluate 1251 != 28, drop this branch.\n     |- Try 1776 * 525 = 932400. 932400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1776 \/ 525 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 48 \/ 37 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 25 \/ 21 = 1.2. 1.2 is a decimal, drop this branch.\n |- Pick two numbers (21, 37) (numbers left: [25, 48]). Try possible operations.\n  |- Try 37 + 21 = 58. Add 58 to the number set. Current number set: [58, 25, 48], target: 28. Options for choosing two numbers: [(58, 25), (58, 48), (25, 48)].\n   |- Pick two numbers (58, 25) (numbers left: [48]). Try possible operations.\n    |- Try 58 + 25 = 83. Add 83 to the number set. Current number set: [83, 48], target: 28, just two numbers left.\n     |- Try 83 + 48 = 131. Evaluate 131 != 28, drop this branch.\n     |- Try 83 - 48 = 35. Evaluate 35 != 28, drop this branch.\n     |- Try 83 * 48 = 3984. 3984 exceeds the maximum intermediate result, drop this branch.\n     |- Try 83 \/ 48 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 58 - 25 = 33. Add 33 to the number set. Current number set: [33, 48], target: 28, just two numbers left.\n     |- Try 48 + 33 = 81. Evaluate 81 != 28, drop this branch.\n     |- Try 48 - 33 = 15. Evaluate 15 != 28, drop this branch.\n     |- Try 48 * 33 = 1584. Evaluate 1584 != 28, drop this branch.\n     |- Try 48 \/ 33 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 58 * 25 = 1450. Add 1450 to the number set. Current number set: [1450, 48], target: 28, just two numbers left.\n     |- Try 1450 + 48 = 1498. Evaluate 1498 != 28, drop this branch.\n     |- Try 1450 - 48 = 1402. Evaluate 1402 != 28, drop this branch.\n     |- Try 1450 * 48 = 69600. 69600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1450 \/ 48 = 30.2. 30.2 is a decimal, drop this branch.\n    |- Try 58 \/ 25 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (58, 48) (numbers left: [25]). Try possible operations.\n    |- Try 58 + 48 = 106. Add 106 to the number set. Current number set: [106, 25], target: 28, just two numbers left.\n     |- Try 106 + 25 = 131. Evaluate 131 != 28, drop this branch.\n     |- Try 106 - 25 = 81. Evaluate 81 != 28, drop this branch.\n     |- Try 106 * 25 = 2650. 2650 exceeds the maximum intermediate result, drop this branch.\n     |- Try 106 \/ 25 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 58 - 48 = 10. Add 10 to the number set. Current number set: [10, 25], target: 28, just two numbers left.\n     |- Try 25 + 10 = 35. Evaluate 35 != 28, drop this branch.\n     |- Try 25 - 10 = 15. Evaluate 15 != 28, drop this branch.\n     |- Try 25 * 10 = 250. Evaluate 250 != 28, drop this branch.\n     |- Try 25 \/ 10 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 58 * 48 = 2784. 2784 exceeds the maximum intermediate result, drop this branch.\n    |- Try 58 \/ 48 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 48) (numbers left: [58]). Try possible operations.\n    |- Try 48 + 25 = 73. Add 73 to the number set. Current number set: [73, 58], target: 28, just two numbers left.\n     |- Try 73 + 58 = 131. Evaluate 131 != 28, drop this branch.\n     |- Try 73 - 58 = 15. Evaluate 15 != 28, drop this branch.\n     |- Try 73 * 58 = 4234. 4234 exceeds the maximum intermediate result, drop this branch.\n     |- Try 73 \/ 58 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 48 - 25 = 23. Add 23 to the number set. Current number set: [23, 58], target: 28, just two numbers left.\n     |- Try 58 + 23 = 81. Evaluate 81 != 28, drop this branch.\n     |- Try 58 - 23 = 35. Evaluate 35 != 28, drop this branch.\n     |- Try 58 * 23 = 1334. Evaluate 1334 != 28, drop this branch.\n     |- Try 58 \/ 23 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 48 * 25 = 1200. Add 1200 to the number set. Current number set: [1200, 58], target: 28, just two numbers left.\n     |- Try 1200 + 58 = 1258. Evaluate 1258 != 28, drop this branch.\n     |- Try 1200 - 58 = 1142. Evaluate 1142 != 28, drop this branch.\n     |- Try 1200 * 58 = 69600. 69600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1200 \/ 58 = 20.7. 20.7 is a decimal, drop this branch.\n    |- Try 48 \/ 25 = 1.9. 1.9 is a decimal, drop this branch.\n  |- Try 37 - 21 = 16. Add 16 to the number set. Current number set: [16, 25, 48], target: 28. Options for choosing two numbers: [(16, 25), (16, 48), (25, 48)].\n   |- Pick two numbers (16, 25) (numbers left: [48]). Try possible operations.\n    |- Try 25 + 16 = 41. Add 41 to the number set. Current number set: [41, 48], target: 28, just two numbers left.\n     |- Try 48 + 41 = 89. Evaluate 89 != 28, drop this branch.\n     |- Try 48 - 41 = 7. Evaluate 7 != 28, drop this branch.\n     |- Try 48 * 41 = 1968. Evaluate 1968 != 28, drop this branch.\n     |- Try 48 \/ 41 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 - 16 = 9. Add 9 to the number set. Current number set: [9, 48], target: 28, just two numbers left.\n     |- Try 48 + 9 = 57. Evaluate 57 != 28, drop this branch.\n     |- Try 48 - 9 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 48 * 9 = 432. Evaluate 432 != 28, drop this branch.\n     |- Try 48 \/ 9 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 25 * 16 = 400. Add 400 to the number set. Current number set: [400, 48], target: 28, just two numbers left.\n     |- Try 400 + 48 = 448. Evaluate 448 != 28, drop this branch.\n     |- Try 400 - 48 = 352. Evaluate 352 != 28, drop this branch.\n     |- Try 400 * 48 = 19200. 19200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 400 \/ 48 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 16 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (16, 48) (numbers left: [25]). Try possible operations.\n    |- Try 48 + 16 = 64. Add 64 to the number set. Current number set: [64, 25], target: 28, just two numbers left.\n     |- Try 64 + 25 = 89. Evaluate 89 != 28, drop this branch.\n     |- Try 64 - 25 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 64 * 25 = 1600. Evaluate 1600 != 28, drop this branch.\n     |- Try 64 \/ 25 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 48 - 16 = 32. Add 32 to the number set. Current number set: [32, 25], target: 28, just two numbers left.\n     |- Try 32 + 25 = 57. Evaluate 57 != 28, drop this branch.\n     |- Try 32 - 25 = 7. Evaluate 7 != 28, drop this branch.\n     |- Try 32 * 25 = 800. Evaluate 800 != 28, drop this branch.\n     |- Try 32 \/ 25 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 48 * 16 = 768. Add 768 to the number set. Current number set: [768, 25], target: 28, just two numbers left.\n     |- Try 768 + 25 = 793. Evaluate 793 != 28, drop this branch.\n     |- Try 768 - 25 = 743. Evaluate 743 != 28, drop this branch.\n     |- Try 768 * 25 = 19200. 19200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 768 \/ 25 = 30.7. 30.7 is a decimal, drop this branch.\n    |- Try 48 \/ 16 = 3. Add 3 to the number set. Current number set: [3, 25], target: 28, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 == 28, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 25 + 3 = 28\nThe step before: 48 \/ 16 = 3\nThe first step: 37 - 21 = 16\n\nOutput the solution in the required format:\n<Solution>\n37 - 21 = 16\n48 \/ 16 = 3\n25 + 3 = 28\n<\/Solution>\n","item":{"nums":[21,25,37,48],"solution":["37 - 21 = 16","48 \/ 16 = 3","25 + 3 = 28"],"target":28}}
+{"instance_id":"countdown_8k_143","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [30, 21, 10, 19]\nTarget: 10","reference_output":"# Search Procedure\nInitial number set: [30, 21, 10, 19], target: 10. Options for choosing two numbers: [(30, 21), (30, 10), (30, 19), (21, 10), (21, 19), (10, 19)].\n |- Pick two numbers (30, 21) (numbers left: [10, 19]). Try possible operations.\n  |- Try 30 + 21 = 51. Add 51 to the number set. Current number set: [51, 10, 19], target: 10. Options for choosing two numbers: [(51, 10), (51, 19), (10, 19)].\n   |- Pick two numbers (51, 10) (numbers left: [19]). Try possible operations.\n    |- Try 51 + 10 = 61. Add 61 to the number set. Current number set: [61, 19], target: 10, just two numbers left.\n     |- Try 61 + 19 = 80. Evaluate 80 != 10, drop this branch.\n     |- Try 61 - 19 = 42. Evaluate 42 != 10, drop this branch.\n     |- Try 61 * 19 = 1159. Evaluate 1159 != 10, drop this branch.\n     |- Try 61 \/ 19 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 51 - 10 = 41. Add 41 to the number set. Current number set: [41, 19], target: 10, just two numbers left.\n     |- Try 41 + 19 = 60. Evaluate 60 != 10, drop this branch.\n     |- Try 41 - 19 = 22. Evaluate 22 != 10, drop this branch.\n     |- Try 41 * 19 = 779. Evaluate 779 != 10, drop this branch.\n     |- Try 41 \/ 19 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 51 * 10 = 510. Add 510 to the number set. Current number set: [510, 19], target: 10, just two numbers left.\n     |- Try 510 + 19 = 529. Evaluate 529 != 10, drop this branch.\n     |- Try 510 - 19 = 491. Evaluate 491 != 10, drop this branch.\n     |- Try 510 * 19 = 9690. 9690 exceeds the maximum intermediate result, drop this branch.\n     |- Try 510 \/ 19 = 26.8. 26.8 is a decimal, drop this branch.\n    |- Try 51 \/ 10 = 5.1. 5.1 is a decimal, drop this branch.\n   |- Pick two numbers (51, 19) (numbers left: [10]). Try possible operations.\n    |- Try 51 + 19 = 70. Add 70 to the number set. Current number set: [70, 10], target: 10, just two numbers left.\n     |- Try 70 + 10 = 80. Evaluate 80 != 10, drop this branch.\n     |- Try 70 - 10 = 60. Evaluate 60 != 10, drop this branch.\n     |- Try 70 * 10 = 700. Evaluate 700 != 10, drop this branch.\n     |- Try 70 \/ 10 = 7. Evaluate 7 != 10, drop this branch.\n    |- Try 51 - 19 = 32. Add 32 to the number set. Current number set: [32, 10], target: 10, just two numbers left.\n     |- Try 32 + 10 = 42. Evaluate 42 != 10, drop this branch.\n     |- Try 32 - 10 = 22. Evaluate 22 != 10, drop this branch.\n     |- Try 32 * 10 = 320. Evaluate 320 != 10, drop this branch.\n     |- Try 32 \/ 10 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 51 * 19 = 969. Add 969 to the number set. Current number set: [969, 10], target: 10, just two numbers left.\n     |- Try 969 + 10 = 979. Evaluate 979 != 10, drop this branch.\n     |- Try 969 - 10 = 959. Evaluate 959 != 10, drop this branch.\n     |- Try 969 * 10 = 9690. 9690 exceeds the maximum intermediate result, drop this branch.\n     |- Try 969 \/ 10 = 96.9. 96.9 is a decimal, drop this branch.\n    |- Try 51 \/ 19 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (10, 19) (numbers left: [51]). Try possible operations.\n    |- Try 19 + 10 = 29. Add 29 to the number set. Current number set: [29, 51], target: 10, just two numbers left.\n     |- Try 51 + 29 = 80. Evaluate 80 != 10, drop this branch.\n     |- Try 51 - 29 = 22. Evaluate 22 != 10, drop this branch.\n     |- Try 51 * 29 = 1479. Evaluate 1479 != 10, drop this branch.\n     |- Try 51 \/ 29 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 19 - 10 = 9. Add 9 to the number set. Current number set: [9, 51], target: 10, just two numbers left.\n     |- Try 51 + 9 = 60. Evaluate 60 != 10, drop this branch.\n     |- Try 51 - 9 = 42. Evaluate 42 != 10, drop this branch.\n     |- Try 51 * 9 = 459. Evaluate 459 != 10, drop this branch.\n     |- Try 51 \/ 9 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 19 * 10 = 190. Add 190 to the number set. Current number set: [190, 51], target: 10, just two numbers left.\n     |- Try 190 + 51 = 241. Evaluate 241 != 10, drop this branch.\n     |- Try 190 - 51 = 139. Evaluate 139 != 10, drop this branch.\n     |- Try 190 * 51 = 9690. 9690 exceeds the maximum intermediate result, drop this branch.\n     |- Try 190 \/ 51 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 19 \/ 10 = 1.9. 1.9 is a decimal, drop this branch.\n  |- Try 30 - 21 = 9. Add 9 to the number set. Current number set: [9, 10, 19], target: 10. Options for choosing two numbers: [(9, 10), (9, 19), (10, 19)].\n   |- Pick two numbers (9, 10) (numbers left: [19]). Try possible operations.\n    |- Try 10 + 9 = 19. Add 19 to the number set. Current number set: [19, 19], target: 10, just two numbers left.\n     |- Try 19 + 19 = 38. Evaluate 38 != 10, drop this branch.\n     |- Try 19 - 19 = 0. Evaluate 0 != 10, drop this branch.\n     |- Try 19 * 19 = 361. Evaluate 361 != 10, drop this branch.\n     |- Try 19 \/ 19 = 1. Evaluate 1 != 10, drop this branch.\n    |- Try 10 - 9 = 1. Add 1 to the number set. Current number set: [1, 19], target: 10, just two numbers left.\n     |- Try 19 + 1 = 20. Evaluate 20 != 10, drop this branch.\n     |- Try 19 - 1 = 18. Evaluate 18 != 10, drop this branch.\n     |- Try 19 * 1 = 19. Evaluate 19 != 10, drop this branch.\n     |- Try 19 \/ 1 = 19. Evaluate 19 != 10, drop this branch.\n    |- Try 10 * 9 = 90. Add 90 to the number set. Current number set: [90, 19], target: 10, just two numbers left.\n     |- Try 90 + 19 = 109. Evaluate 109 != 10, drop this branch.\n     |- Try 90 - 19 = 71. Evaluate 71 != 10, drop this branch.\n     |- Try 90 * 19 = 1710. Evaluate 1710 != 10, drop this branch.\n     |- Try 90 \/ 19 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 10 \/ 9 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (9, 19) (numbers left: [10]). Try possible operations.\n    |- Try 19 + 9 = 28. Add 28 to the number set. Current number set: [28, 10], target: 10, just two numbers left.\n     |- Try 28 + 10 = 38. Evaluate 38 != 10, drop this branch.\n     |- Try 28 - 10 = 18. Evaluate 18 != 10, drop this branch.\n     |- Try 28 * 10 = 280. Evaluate 280 != 10, drop this branch.\n     |- Try 28 \/ 10 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 19 - 9 = 10. Add 10 to the number set. Current number set: [10, 10], target: 10, just two numbers left.\n     |- Try 10 + 10 = 20. Evaluate 20 != 10, drop this branch.\n     |- Try 10 - 10 = 0. Evaluate 0 != 10, drop this branch.\n     |- Try 10 * 10 = 100. Evaluate 100 != 10, drop this branch.\n     |- Try 10 \/ 10 = 1. Evaluate 1 != 10, drop this branch.\n    |- Try 19 * 9 = 171. Add 171 to the number set. Current number set: [171, 10], target: 10, just two numbers left.\n     |- Try 171 + 10 = 181. Evaluate 181 != 10, drop this branch.\n     |- Try 171 - 10 = 161. Evaluate 161 != 10, drop this branch.\n     |- Try 171 * 10 = 1710. Evaluate 1710 != 10, drop this branch.\n     |- Try 171 \/ 10 = 17.1. 17.1 is a decimal, drop this branch.\n    |- Try 19 \/ 9 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (10, 19) (numbers left: [9]). Try possible operations.\n    |- Try 19 + 10 = 29. Add 29 to the number set. Current number set: [29, 9], target: 10, just two numbers left.\n     |- Try 29 + 9 = 38. Evaluate 38 != 10, drop this branch.\n     |- Try 29 - 9 = 20. Evaluate 20 != 10, drop this branch.\n     |- Try 29 * 9 = 261. Evaluate 261 != 10, drop this branch.\n     |- Try 29 \/ 9 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 19 - 10 = 9. Add 9 to the number set. Current number set: [9, 9], target: 10, just two numbers left.\n     |- Try 9 + 9 = 18. Evaluate 18 != 10, drop this branch.\n     |- Try 9 - 9 = 0. Evaluate 0 != 10, drop this branch.\n     |- Try 9 * 9 = 81. Evaluate 81 != 10, drop this branch.\n     |- Try 9 \/ 9 = 1. Evaluate 1 != 10, drop this branch.\n    |- Try 19 * 10 = 190. Add 190 to the number set. Current number set: [190, 9], target: 10, just two numbers left.\n     |- Try 190 + 9 = 199. Evaluate 199 != 10, drop this branch.\n     |- Try 190 - 9 = 181. Evaluate 181 != 10, drop this branch.\n     |- Try 190 * 9 = 1710. Evaluate 1710 != 10, drop this branch.\n     |- Try 190 \/ 9 = 21.1. 21.1 is a decimal, drop this branch.\n    |- Try 19 \/ 10 = 1.9. 1.9 is a decimal, drop this branch.\n  |- Try 30 * 21 = 630. Add 630 to the number set. Current number set: [630, 10, 19], target: 10. Options for choosing two numbers: [(630, 10), (630, 19), (10, 19)].\n   |- Pick two numbers (630, 10) (numbers left: [19]). Try possible operations.\n    |- Try 630 + 10 = 640. Add 640 to the number set. Current number set: [640, 19], target: 10, just two numbers left.\n     |- Try 640 + 19 = 659. Evaluate 659 != 10, drop this branch.\n     |- Try 640 - 19 = 621. Evaluate 621 != 10, drop this branch.\n     |- Try 640 * 19 = 12160. 12160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 640 \/ 19 = 33.7. 33.7 is a decimal, drop this branch.\n    |- Try 630 - 10 = 620. Add 620 to the number set. Current number set: [620, 19], target: 10, just two numbers left.\n     |- Try 620 + 19 = 639. Evaluate 639 != 10, drop this branch.\n     |- Try 620 - 19 = 601. Evaluate 601 != 10, drop this branch.\n     |- Try 620 * 19 = 11780. 11780 exceeds the maximum intermediate result, drop this branch.\n     |- Try 620 \/ 19 = 32.6. 32.6 is a decimal, drop this branch.\n    |- Try 630 * 10 = 6300. 6300 exceeds the maximum intermediate result, drop this branch.\n    |- Try 630 \/ 10 = 63. Add 63 to the number set. Current number set: [63, 19], target: 10, just two numbers left.\n     |- Try 63 + 19 = 82. Evaluate 82 != 10, drop this branch.\n     |- Try 63 - 19 = 44. Evaluate 44 != 10, drop this branch.\n     |- Try 63 * 19 = 1197. Evaluate 1197 != 10, drop this branch.\n     |- Try 63 \/ 19 = 3.3. 3.3 is a decimal, drop this branch.\n   |- Pick two numbers (630, 19) (numbers left: [10]). Try possible operations.\n    |- Try 630 + 19 = 649. Add 649 to the number set. Current number set: [649, 10], target: 10, just two numbers left.\n     |- Try 649 + 10 = 659. Evaluate 659 != 10, drop this branch.\n     |- Try 649 - 10 = 639. Evaluate 639 != 10, drop this branch.\n     |- Try 649 * 10 = 6490. 6490 exceeds the maximum intermediate result, drop this branch.\n     |- Try 649 \/ 10 = 64.9. 64.9 is a decimal, drop this branch.\n    |- Try 630 - 19 = 611. Add 611 to the number set. Current number set: [611, 10], target: 10, just two numbers left.\n     |- Try 611 + 10 = 621. Evaluate 621 != 10, drop this branch.\n     |- Try 611 - 10 = 601. Evaluate 601 != 10, drop this branch.\n     |- Try 611 * 10 = 6110. 6110 exceeds the maximum intermediate result, drop this branch.\n     |- Try 611 \/ 10 = 61.1. 61.1 is a decimal, drop this branch.\n    |- Try 630 * 19 = 11970. 11970 exceeds the maximum intermediate result, drop this branch.\n    |- Try 630 \/ 19 = 33.2. 33.2 is a decimal, drop this branch.\n   |- Pick two numbers (10, 19) (numbers left: [630]). Try possible operations.\n    |- Try 19 + 10 = 29. Add 29 to the number set. Current number set: [29, 630], target: 10, just two numbers left.\n     |- Try 630 + 29 = 659. Evaluate 659 != 10, drop this branch.\n     |- Try 630 - 29 = 601. Evaluate 601 != 10, drop this branch.\n     |- Try 630 * 29 = 18270. 18270 exceeds the maximum intermediate result, drop this branch.\n     |- Try 630 \/ 29 = 21.7. 21.7 is a decimal, drop this branch.\n    |- Try 19 - 10 = 9. Add 9 to the number set. Current number set: [9, 630], target: 10, just two numbers left.\n     |- Try 630 + 9 = 639. Evaluate 639 != 10, drop this branch.\n     |- Try 630 - 9 = 621. Evaluate 621 != 10, drop this branch.\n     |- Try 630 * 9 = 5670. 5670 exceeds the maximum intermediate result, drop this branch.\n     |- Try 630 \/ 9 = 70. Evaluate 70 != 10, drop this branch.\n    |- Try 19 * 10 = 190. Add 190 to the number set. Current number set: [190, 630], target: 10, just two numbers left.\n     |- Try 630 + 190 = 820. Evaluate 820 != 10, drop this branch.\n     |- Try 630 - 190 = 440. Evaluate 440 != 10, drop this branch.\n     |- Try 630 * 190 = 119700. 119700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 630 \/ 190 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 19 \/ 10 = 1.9. 1.9 is a decimal, drop this branch.\n  |- Try 30 \/ 21 = 1.4. 1.4 is a decimal, drop this branch.\n |- Pick two numbers (30, 10) (numbers left: [21, 19]). Try possible operations.\n  |- Try 30 + 10 = 40. Add 40 to the number set. Current number set: [40, 21, 19], target: 10. Options for choosing two numbers: [(40, 21), (40, 19), (21, 19)].\n   |- Pick two numbers (40, 21) (numbers left: [19]). Try possible operations.\n    |- Try 40 + 21 = 61. Add 61 to the number set. Current number set: [61, 19], target: 10, just two numbers left.\n     |- Try 61 + 19 = 80. Evaluate 80 != 10, drop this branch.\n     |- Try 61 - 19 = 42. Evaluate 42 != 10, drop this branch.\n     |- Try 61 * 19 = 1159. Evaluate 1159 != 10, drop this branch.\n     |- Try 61 \/ 19 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 40 - 21 = 19. Add 19 to the number set. Current number set: [19, 19], target: 10, just two numbers left.\n     |- Try 19 + 19 = 38. Evaluate 38 != 10, drop this branch.\n     |- Try 19 - 19 = 0. Evaluate 0 != 10, drop this branch.\n     |- Try 19 * 19 = 361. Evaluate 361 != 10, drop this branch.\n     |- Try 19 \/ 19 = 1. Evaluate 1 != 10, drop this branch.\n    |- Try 40 * 21 = 840. Add 840 to the number set. Current number set: [840, 19], target: 10, just two numbers left.\n     |- Try 840 + 19 = 859. Evaluate 859 != 10, drop this branch.\n     |- Try 840 - 19 = 821. Evaluate 821 != 10, drop this branch.\n     |- Try 840 * 19 = 15960. 15960 exceeds the maximum intermediate result, drop this branch.\n     |- Try 840 \/ 19 = 44.2. 44.2 is a decimal, drop this branch.\n    |- Try 40 \/ 21 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (40, 19) (numbers left: [21]). Try possible operations.\n    |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 21], target: 10, just two numbers left.\n     |- Try 59 + 21 = 80. Evaluate 80 != 10, drop this branch.\n     |- Try 59 - 21 = 38. Evaluate 38 != 10, drop this branch.\n     |- Try 59 * 21 = 1239. Evaluate 1239 != 10, drop this branch.\n     |- Try 59 \/ 21 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 40 - 19 = 21. Add 21 to the number set. Current number set: [21, 21], target: 10, just two numbers left.\n     |- Try 21 + 21 = 42. Evaluate 42 != 10, drop this branch.\n     |- Try 21 - 21 = 0. Evaluate 0 != 10, drop this branch.\n     |- Try 21 * 21 = 441. Evaluate 441 != 10, drop this branch.\n     |- Try 21 \/ 21 = 1. Evaluate 1 != 10, drop this branch.\n    |- Try 40 * 19 = 760. Add 760 to the number set. Current number set: [760, 21], target: 10, just two numbers left.\n     |- Try 760 + 21 = 781. Evaluate 781 != 10, drop this branch.\n     |- Try 760 - 21 = 739. Evaluate 739 != 10, drop this branch.\n     |- Try 760 * 21 = 15960. 15960 exceeds the maximum intermediate result, drop this branch.\n     |- Try 760 \/ 21 = 36.2. 36.2 is a decimal, drop this branch.\n    |- Try 40 \/ 19 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (21, 19) (numbers left: [40]). Try possible operations.\n    |- Try 21 + 19 = 40. Add 40 to the number set. Current number set: [40, 40], target: 10, just two numbers left.\n     |- Try 40 + 40 = 80. Evaluate 80 != 10, drop this branch.\n     |- Try 40 - 40 = 0. Evaluate 0 != 10, drop this branch.\n     |- Try 40 * 40 = 1600. Evaluate 1600 != 10, drop this branch.\n     |- Try 40 \/ 40 = 1. Evaluate 1 != 10, drop this branch.\n    |- Try 21 - 19 = 2. Add 2 to the number set. Current number set: [2, 40], target: 10, just two numbers left.\n     |- Try 40 + 2 = 42. Evaluate 42 != 10, drop this branch.\n     |- Try 40 - 2 = 38. Evaluate 38 != 10, drop this branch.\n     |- Try 40 * 2 = 80. Evaluate 80 != 10, drop this branch.\n     |- Try 40 \/ 2 = 20. Evaluate 20 != 10, drop this branch.\n    |- Try 21 * 19 = 399. Add 399 to the number set. Current number set: [399, 40], target: 10, just two numbers left.\n     |- Try 399 + 40 = 439. Evaluate 439 != 10, drop this branch.\n     |- Try 399 - 40 = 359. Evaluate 359 != 10, drop this branch.\n     |- Try 399 * 40 = 15960. 15960 exceeds the maximum intermediate result, drop this branch.\n     |- Try 399 \/ 40 = 10.0. 10.0 is a decimal, drop this branch.\n    |- Try 21 \/ 19 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 30 - 10 = 20. Add 20 to the number set. Current number set: [20, 21, 19], target: 10. Options for choosing two numbers: [(20, 21), (20, 19), (21, 19)].\n   |- Pick two numbers (20, 21) (numbers left: [19]). Try possible operations.\n    |- Try 21 + 20 = 41. Add 41 to the number set. Current number set: [41, 19], target: 10, just two numbers left.\n     |- Try 41 + 19 = 60. Evaluate 60 != 10, drop this branch.\n     |- Try 41 - 19 = 22. Evaluate 22 != 10, drop this branch.\n     |- Try 41 * 19 = 779. Evaluate 779 != 10, drop this branch.\n     |- Try 41 \/ 19 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 21 - 20 = 1. Add 1 to the number set. Current number set: [1, 19], target: 10, just two numbers left.\n     |- Try 19 + 1 = 20. Evaluate 20 != 10, drop this branch.\n     |- Try 19 - 1 = 18. Evaluate 18 != 10, drop this branch.\n     |- Try 19 * 1 = 19. Evaluate 19 != 10, drop this branch.\n     |- Try 19 \/ 1 = 19. Evaluate 19 != 10, drop this branch.\n    |- Try 21 * 20 = 420. Add 420 to the number set. Current number set: [420, 19], target: 10, just two numbers left.\n     |- Try 420 + 19 = 439. Evaluate 439 != 10, drop this branch.\n     |- Try 420 - 19 = 401. Evaluate 401 != 10, drop this branch.\n     |- Try 420 * 19 = 7980. 7980 exceeds the maximum intermediate result, drop this branch.\n     |- Try 420 \/ 19 = 22.1. 22.1 is a decimal, drop this branch.\n    |- Try 21 \/ 20 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (20, 19) (numbers left: [21]). Try possible operations.\n    |- Try 20 + 19 = 39. Add 39 to the number set. Current number set: [39, 21], target: 10, just two numbers left.\n     |- Try 39 + 21 = 60. Evaluate 60 != 10, drop this branch.\n     |- Try 39 - 21 = 18. Evaluate 18 != 10, drop this branch.\n     |- Try 39 * 21 = 819. Evaluate 819 != 10, drop this branch.\n     |- Try 39 \/ 21 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 20 - 19 = 1. Add 1 to the number set. Current number set: [1, 21], target: 10, just two numbers left.\n     |- Try 21 + 1 = 22. Evaluate 22 != 10, drop this branch.\n     |- Try 21 - 1 = 20. Evaluate 20 != 10, drop this branch.\n     |- Try 21 * 1 = 21. Evaluate 21 != 10, drop this branch.\n     |- Try 21 \/ 1 = 21. Evaluate 21 != 10, drop this branch.\n    |- Try 20 * 19 = 380. Add 380 to the number set. Current number set: [380, 21], target: 10, just two numbers left.\n     |- Try 380 + 21 = 401. Evaluate 401 != 10, drop this branch.\n     |- Try 380 - 21 = 359. Evaluate 359 != 10, drop this branch.\n     |- Try 380 * 21 = 7980. 7980 exceeds the maximum intermediate result, drop this branch.\n     |- Try 380 \/ 21 = 18.1. 18.1 is a decimal, drop this branch.\n    |- Try 20 \/ 19 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (21, 19) (numbers left: [20]). Try possible operations.\n    |- Try 21 + 19 = 40. Add 40 to the number set. Current number set: [40, 20], target: 10, just two numbers left.\n     |- Try 40 + 20 = 60. Evaluate 60 != 10, drop this branch.\n     |- Try 40 - 20 = 20. Evaluate 20 != 10, drop this branch.\n     |- Try 40 * 20 = 800. Evaluate 800 != 10, drop this branch.\n     |- Try 40 \/ 20 = 2. Evaluate 2 != 10, drop this branch.\n    |- Try 21 - 19 = 2. Add 2 to the number set. Current number set: [2, 20], target: 10, just two numbers left.\n     |- Try 20 + 2 = 22. Evaluate 22 != 10, drop this branch.\n     |- Try 20 - 2 = 18. Evaluate 18 != 10, drop this branch.\n     |- Try 20 * 2 = 40. Evaluate 40 != 10, drop this branch.\n     |- Try 20 \/ 2 = 10. Evaluate 10 == 10, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 20 \/ 2 = 10\nThe step before: 21 - 19 = 2\nThe first step: 30 - 10 = 20\n\nOutput the solution in the required format:\n<Solution>\n30 - 10 = 20\n21 - 19 = 2\n20 \/ 2 = 10\n<\/Solution>\n","item":{"nums":[30,21,10,19],"solution":["30 - 10 = 20","21 - 19 = 2","20 \/ 2 = 10"],"target":10}}
+{"instance_id":"countdown_8k_144","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [32, 44, 30, 10]\nTarget: 24","reference_output":"# Search Procedure\nInitial number set: [32, 44, 30, 10], target: 24. Options for choosing two numbers: [(32, 44), (32, 30), (32, 10), (44, 30), (44, 10), (30, 10)].\n |- Pick two numbers (32, 44) (numbers left: [30, 10]). Try possible operations.\n  |- Try 44 + 32 = 76. Add 76 to the number set. Current number set: [76, 30, 10], target: 24. Options for choosing two numbers: [(76, 30), (76, 10), (30, 10)].\n   |- Pick two numbers (76, 30) (numbers left: [10]). Try possible operations.\n    |- Try 76 + 30 = 106. Add 106 to the number set. Current number set: [106, 10], target: 24, just two numbers left.\n     |- Try 106 + 10 = 116. Evaluate 116 != 24, drop this branch.\n     |- Try 106 - 10 = 96. Evaluate 96 != 24, drop this branch.\n     |- Try 106 * 10 = 1060. Evaluate 1060 != 24, drop this branch.\n     |- Try 106 \/ 10 = 10.6. 10.6 is a decimal, drop this branch.\n    |- Try 76 - 30 = 46. Add 46 to the number set. Current number set: [46, 10], target: 24, just two numbers left.\n     |- Try 46 + 10 = 56. Evaluate 56 != 24, drop this branch.\n     |- Try 46 - 10 = 36. Evaluate 36 != 24, drop this branch.\n     |- Try 46 * 10 = 460. Evaluate 460 != 24, drop this branch.\n     |- Try 46 \/ 10 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 76 * 30 = 2280. 2280 exceeds the maximum intermediate result, drop this branch.\n    |- Try 76 \/ 30 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (76, 10) (numbers left: [30]). Try possible operations.\n    |- Try 76 + 10 = 86. Add 86 to the number set. Current number set: [86, 30], target: 24, just two numbers left.\n     |- Try 86 + 30 = 116. Evaluate 116 != 24, drop this branch.\n     |- Try 86 - 30 = 56. Evaluate 56 != 24, drop this branch.\n     |- Try 86 * 30 = 2580. 2580 exceeds the maximum intermediate result, drop this branch.\n     |- Try 86 \/ 30 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 76 - 10 = 66. Add 66 to the number set. Current number set: [66, 30], target: 24, just two numbers left.\n     |- Try 66 + 30 = 96. Evaluate 96 != 24, drop this branch.\n     |- Try 66 - 30 = 36. Evaluate 36 != 24, drop this branch.\n     |- Try 66 * 30 = 1980. Evaluate 1980 != 24, drop this branch.\n     |- Try 66 \/ 30 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 76 * 10 = 760. Add 760 to the number set. Current number set: [760, 30], target: 24, just two numbers left.\n     |- Try 760 + 30 = 790. Evaluate 790 != 24, drop this branch.\n     |- Try 760 - 30 = 730. Evaluate 730 != 24, drop this branch.\n     |- Try 760 * 30 = 22800. 22800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 760 \/ 30 = 25.3. 25.3 is a decimal, drop this branch.\n    |- Try 76 \/ 10 = 7.6. 7.6 is a decimal, drop this branch.\n   |- Pick two numbers (30, 10) (numbers left: [76]). Try possible operations.\n    |- Try 30 + 10 = 40. Add 40 to the number set. Current number set: [40, 76], target: 24, just two numbers left.\n     |- Try 76 + 40 = 116. Evaluate 116 != 24, drop this branch.\n     |- Try 76 - 40 = 36. Evaluate 36 != 24, drop this branch.\n     |- Try 76 * 40 = 3040. 3040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 76 \/ 40 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 30 - 10 = 20. Add 20 to the number set. Current number set: [20, 76], target: 24, just two numbers left.\n     |- Try 76 + 20 = 96. Evaluate 96 != 24, drop this branch.\n     |- Try 76 - 20 = 56. Evaluate 56 != 24, drop this branch.\n     |- Try 76 * 20 = 1520. Evaluate 1520 != 24, drop this branch.\n     |- Try 76 \/ 20 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 30 * 10 = 300. Add 300 to the number set. Current number set: [300, 76], target: 24, just two numbers left.\n     |- Try 300 + 76 = 376. Evaluate 376 != 24, drop this branch.\n     |- Try 300 - 76 = 224. Evaluate 224 != 24, drop this branch.\n     |- Try 300 * 76 = 22800. 22800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 300 \/ 76 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 30 \/ 10 = 3. Add 3 to the number set. Current number set: [3, 76], target: 24, just two numbers left.\n     |- Try 76 + 3 = 79. Evaluate 79 != 24, drop this branch.\n     |- Try 76 - 3 = 73. Evaluate 73 != 24, drop this branch.\n     |- Try 76 * 3 = 228. Evaluate 228 != 24, drop this branch.\n     |- Try 76 \/ 3 = 25.3. 25.3 is a decimal, drop this branch.\n  |- Try 44 - 32 = 12. Add 12 to the number set. Current number set: [12, 30, 10], target: 24. Options for choosing two numbers: [(12, 30), (12, 10), (30, 10)].\n   |- Pick two numbers (12, 30) (numbers left: [10]). Try possible operations.\n    |- Try 30 + 12 = 42. Add 42 to the number set. Current number set: [42, 10], target: 24, just two numbers left.\n     |- Try 42 + 10 = 52. Evaluate 52 != 24, drop this branch.\n     |- Try 42 - 10 = 32. Evaluate 32 != 24, drop this branch.\n     |- Try 42 * 10 = 420. Evaluate 420 != 24, drop this branch.\n     |- Try 42 \/ 10 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 30 - 12 = 18. Add 18 to the number set. Current number set: [18, 10], target: 24, just two numbers left.\n     |- Try 18 + 10 = 28. Evaluate 28 != 24, drop this branch.\n     |- Try 18 - 10 = 8. Evaluate 8 != 24, drop this branch.\n     |- Try 18 * 10 = 180. Evaluate 180 != 24, drop this branch.\n     |- Try 18 \/ 10 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 30 * 12 = 360. Add 360 to the number set. Current number set: [360, 10], target: 24, just two numbers left.\n     |- Try 360 + 10 = 370. Evaluate 370 != 24, drop this branch.\n     |- Try 360 - 10 = 350. Evaluate 350 != 24, drop this branch.\n     |- Try 360 * 10 = 3600. 3600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 360 \/ 10 = 36. Evaluate 36 != 24, drop this branch.\n    |- Try 30 \/ 12 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (12, 10) (numbers left: [30]). Try possible operations.\n    |- Try 12 + 10 = 22. Add 22 to the number set. Current number set: [22, 30], target: 24, just two numbers left.\n     |- Try 30 + 22 = 52. Evaluate 52 != 24, drop this branch.\n     |- Try 30 - 22 = 8. Evaluate 8 != 24, drop this branch.\n     |- Try 30 * 22 = 660. Evaluate 660 != 24, drop this branch.\n     |- Try 30 \/ 22 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 12 - 10 = 2. Add 2 to the number set. Current number set: [2, 30], target: 24, just two numbers left.\n     |- Try 30 + 2 = 32. Evaluate 32 != 24, drop this branch.\n     |- Try 30 - 2 = 28. Evaluate 28 != 24, drop this branch.\n     |- Try 30 * 2 = 60. Evaluate 60 != 24, drop this branch.\n     |- Try 30 \/ 2 = 15. Evaluate 15 != 24, drop this branch.\n    |- Try 12 * 10 = 120. Add 120 to the number set. Current number set: [120, 30], target: 24, just two numbers left.\n     |- Try 120 + 30 = 150. Evaluate 150 != 24, drop this branch.\n     |- Try 120 - 30 = 90. Evaluate 90 != 24, drop this branch.\n     |- Try 120 * 30 = 3600. 3600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 120 \/ 30 = 4. Evaluate 4 != 24, drop this branch.\n    |- Try 12 \/ 10 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (30, 10) (numbers left: [12]). Try possible operations.\n    |- Try 30 + 10 = 40. Add 40 to the number set. Current number set: [40, 12], target: 24, just two numbers left.\n     |- Try 40 + 12 = 52. Evaluate 52 != 24, drop this branch.\n     |- Try 40 - 12 = 28. Evaluate 28 != 24, drop this branch.\n     |- Try 40 * 12 = 480. Evaluate 480 != 24, drop this branch.\n     |- Try 40 \/ 12 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 30 - 10 = 20. Add 20 to the number set. Current number set: [20, 12], target: 24, just two numbers left.\n     |- Try 20 + 12 = 32. Evaluate 32 != 24, drop this branch.\n     |- Try 20 - 12 = 8. Evaluate 8 != 24, drop this branch.\n     |- Try 20 * 12 = 240. Evaluate 240 != 24, drop this branch.\n     |- Try 20 \/ 12 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 30 * 10 = 300. Add 300 to the number set. Current number set: [300, 12], target: 24, just two numbers left.\n     |- Try 300 + 12 = 312. Evaluate 312 != 24, drop this branch.\n     |- Try 300 - 12 = 288. Evaluate 288 != 24, drop this branch.\n     |- Try 300 * 12 = 3600. 3600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 300 \/ 12 = 25. Evaluate 25 != 24, drop this branch.\n    |- Try 30 \/ 10 = 3. Add 3 to the number set. Current number set: [3, 12], target: 24, just two numbers left.\n     |- Try 12 + 3 = 15. Evaluate 15 != 24, drop this branch.\n     |- Try 12 - 3 = 9. Evaluate 9 != 24, drop this branch.\n     |- Try 12 * 3 = 36. Evaluate 36 != 24, drop this branch.\n     |- Try 12 \/ 3 = 4. Evaluate 4 != 24, drop this branch.\n  |- Try 44 * 32 = 1408. Add 1408 to the number set. Current number set: [1408, 30, 10], target: 24. Options for choosing two numbers: [(1408, 30), (1408, 10), (30, 10)].\n   |- Pick two numbers (1408, 30) (numbers left: [10]). Try possible operations.\n    |- Try 1408 + 30 = 1438. Add 1438 to the number set. Current number set: [1438, 10], target: 24, just two numbers left.\n     |- Try 1438 + 10 = 1448. Evaluate 1448 != 24, drop this branch.\n     |- Try 1438 - 10 = 1428. Evaluate 1428 != 24, drop this branch.\n     |- Try 1438 * 10 = 14380. 14380 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1438 \/ 10 = 143.8. 143.8 is a decimal, drop this branch.\n    |- Try 1408 - 30 = 1378. Add 1378 to the number set. Current number set: [1378, 10], target: 24, just two numbers left.\n     |- Try 1378 + 10 = 1388. Evaluate 1388 != 24, drop this branch.\n     |- Try 1378 - 10 = 1368. Evaluate 1368 != 24, drop this branch.\n     |- Try 1378 * 10 = 13780. 13780 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1378 \/ 10 = 137.8. 137.8 is a decimal, drop this branch.\n    |- Try 1408 * 30 = 42240. 42240 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1408 \/ 30 = 46.9. 46.9 is a decimal, drop this branch.\n   |- Pick two numbers (1408, 10) (numbers left: [30]). Try possible operations.\n    |- Try 1408 + 10 = 1418. Add 1418 to the number set. Current number set: [1418, 30], target: 24, just two numbers left.\n     |- Try 1418 + 30 = 1448. Evaluate 1448 != 24, drop this branch.\n     |- Try 1418 - 30 = 1388. Evaluate 1388 != 24, drop this branch.\n     |- Try 1418 * 30 = 42540. 42540 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1418 \/ 30 = 47.3. 47.3 is a decimal, drop this branch.\n    |- Try 1408 - 10 = 1398. Add 1398 to the number set. Current number set: [1398, 30], target: 24, just two numbers left.\n     |- Try 1398 + 30 = 1428. Evaluate 1428 != 24, drop this branch.\n     |- Try 1398 - 30 = 1368. Evaluate 1368 != 24, drop this branch.\n     |- Try 1398 * 30 = 41940. 41940 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1398 \/ 30 = 46.6. 46.6 is a decimal, drop this branch.\n    |- Try 1408 * 10 = 14080. 14080 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1408 \/ 10 = 140.8. 140.8 is a decimal, drop this branch.\n   |- Pick two numbers (30, 10) (numbers left: [1408]). Try possible operations.\n    |- Try 30 + 10 = 40. Add 40 to the number set. Current number set: [40, 1408], target: 24, just two numbers left.\n     |- Try 1408 + 40 = 1448. Evaluate 1448 != 24, drop this branch.\n     |- Try 1408 - 40 = 1368. Evaluate 1368 != 24, drop this branch.\n     |- Try 1408 * 40 = 56320. 56320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1408 \/ 40 = 35.2. 35.2 is a decimal, drop this branch.\n    |- Try 30 - 10 = 20. Add 20 to the number set. Current number set: [20, 1408], target: 24, just two numbers left.\n     |- Try 1408 + 20 = 1428. Evaluate 1428 != 24, drop this branch.\n     |- Try 1408 - 20 = 1388. Evaluate 1388 != 24, drop this branch.\n     |- Try 1408 * 20 = 28160. 28160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1408 \/ 20 = 70.4. 70.4 is a decimal, drop this branch.\n    |- Try 30 * 10 = 300. Add 300 to the number set. Current number set: [300, 1408], target: 24, just two numbers left.\n     |- Try 1408 + 300 = 1708. Evaluate 1708 != 24, drop this branch.\n     |- Try 1408 - 300 = 1108. Evaluate 1108 != 24, drop this branch.\n     |- Try 1408 * 300 = 422400. 422400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1408 \/ 300 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 30 \/ 10 = 3. Add 3 to the number set. Current number set: [3, 1408], target: 24, just two numbers left.\n     |- Try 1408 + 3 = 1411. Evaluate 1411 != 24, drop this branch.\n     |- Try 1408 - 3 = 1405. Evaluate 1405 != 24, drop this branch.\n     |- Try 1408 * 3 = 4224. 4224 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1408 \/ 3 = 469.3. 469.3 is a decimal, drop this branch.\n  |- Try 44 \/ 32 = 1.4. 1.4 is a decimal, drop this branch.\n |- Pick two numbers (32, 30) (numbers left: [44, 10]). Try possible operations.\n  |- Try 32 + 30 = 62. Add 62 to the number set. Current number set: [62, 44, 10], target: 24. Options for choosing two numbers: [(62, 44), (62, 10), (44, 10)].\n   |- Pick two numbers (62, 44) (numbers left: [10]). Try possible operations.\n    |- Try 62 + 44 = 106. Add 106 to the number set. Current number set: [106, 10], target: 24, just two numbers left.\n     |- Try 106 + 10 = 116. Evaluate 116 != 24, drop this branch.\n     |- Try 106 - 10 = 96. Evaluate 96 != 24, drop this branch.\n     |- Try 106 * 10 = 1060. Evaluate 1060 != 24, drop this branch.\n     |- Try 106 \/ 10 = 10.6. 10.6 is a decimal, drop this branch.\n    |- Try 62 - 44 = 18. Add 18 to the number set. Current number set: [18, 10], target: 24, just two numbers left.\n     |- Try 18 + 10 = 28. Evaluate 28 != 24, drop this branch.\n     |- Try 18 - 10 = 8. Evaluate 8 != 24, drop this branch.\n     |- Try 18 * 10 = 180. Evaluate 180 != 24, drop this branch.\n     |- Try 18 \/ 10 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 62 * 44 = 2728. 2728 exceeds the maximum intermediate result, drop this branch.\n    |- Try 62 \/ 44 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (62, 10) (numbers left: [44]). Try possible operations.\n    |- Try 62 + 10 = 72. Add 72 to the number set. Current number set: [72, 44], target: 24, just two numbers left.\n     |- Try 72 + 44 = 116. Evaluate 116 != 24, drop this branch.\n     |- Try 72 - 44 = 28. Evaluate 28 != 24, drop this branch.\n     |- Try 72 * 44 = 3168. 3168 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 44 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 62 - 10 = 52. Add 52 to the number set. Current number set: [52, 44], target: 24, just two numbers left.\n     |- Try 52 + 44 = 96. Evaluate 96 != 24, drop this branch.\n     |- Try 52 - 44 = 8. Evaluate 8 != 24, drop this branch.\n     |- Try 52 * 44 = 2288. 2288 exceeds the maximum intermediate result, drop this branch.\n     |- Try 52 \/ 44 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 62 * 10 = 620. Add 620 to the number set. Current number set: [620, 44], target: 24, just two numbers left.\n     |- Try 620 + 44 = 664. Evaluate 664 != 24, drop this branch.\n     |- Try 620 - 44 = 576. Evaluate 576 != 24, drop this branch.\n     |- Try 620 * 44 = 27280. 27280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 620 \/ 44 = 14.1. 14.1 is a decimal, drop this branch.\n    |- Try 62 \/ 10 = 6.2. 6.2 is a decimal, drop this branch.\n   |- Pick two numbers (44, 10) (numbers left: [62]). Try possible operations.\n    |- Try 44 + 10 = 54. Add 54 to the number set. Current number set: [54, 62], target: 24, just two numbers left.\n     |- Try 62 + 54 = 116. Evaluate 116 != 24, drop this branch.\n     |- Try 62 - 54 = 8. Evaluate 8 != 24, drop this branch.\n     |- Try 62 * 54 = 3348. 3348 exceeds the maximum intermediate result, drop this branch.\n     |- Try 62 \/ 54 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 44 - 10 = 34. Add 34 to the number set. Current number set: [34, 62], target: 24, just two numbers left.\n     |- Try 62 + 34 = 96. Evaluate 96 != 24, drop this branch.\n     |- Try 62 - 34 = 28. Evaluate 28 != 24, drop this branch.\n     |- Try 62 * 34 = 2108. 2108 exceeds the maximum intermediate result, drop this branch.\n     |- Try 62 \/ 34 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 44 * 10 = 440. Add 440 to the number set. Current number set: [440, 62], target: 24, just two numbers left.\n     |- Try 440 + 62 = 502. Evaluate 502 != 24, drop this branch.\n     |- Try 440 - 62 = 378. Evaluate 378 != 24, drop this branch.\n     |- Try 440 * 62 = 27280. 27280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 440 \/ 62 = 7.1. 7.1 is a decimal, drop this branch.\n    |- Try 44 \/ 10 = 4.4. 4.4 is a decimal, drop this branch.\n  |- Try 32 - 30 = 2. Add 2 to the number set. Current number set: [2, 44, 10], target: 24. Options for choosing two numbers: [(2, 44), (2, 10), (44, 10)].\n   |- Pick two numbers (2, 44) (numbers left: [10]). Try possible operations.\n    |- Try 44 + 2 = 46. Add 46 to the number set. Current number set: [46, 10], target: 24, just two numbers left.\n     |- Try 46 + 10 = 56. Evaluate 56 != 24, drop this branch.\n     |- Try 46 - 10 = 36. Evaluate 36 != 24, drop this branch.\n     |- Try 46 * 10 = 460. Evaluate 460 != 24, drop this branch.\n     |- Try 46 \/ 10 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 44 - 2 = 42. Add 42 to the number set. Current number set: [42, 10], target: 24, just two numbers left.\n     |- Try 42 + 10 = 52. Evaluate 52 != 24, drop this branch.\n     |- Try 42 - 10 = 32. Evaluate 32 != 24, drop this branch.\n     |- Try 42 * 10 = 420. Evaluate 420 != 24, drop this branch.\n     |- Try 42 \/ 10 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 44 * 2 = 88. Add 88 to the number set. Current number set: [88, 10], target: 24, just two numbers left.\n     |- Try 88 + 10 = 98. Evaluate 98 != 24, drop this branch.\n     |- Try 88 - 10 = 78. Evaluate 78 != 24, drop this branch.\n     |- Try 88 * 10 = 880. Evaluate 880 != 24, drop this branch.\n     |- Try 88 \/ 10 = 8.8. 8.8 is a decimal, drop this branch.\n    |- Try 44 \/ 2 = 22. Add 22 to the number set. Current number set: [22, 10], target: 24, just two numbers left.\n     |- Try 22 + 10 = 32. Evaluate 32 != 24, drop this branch.\n     |- Try 22 - 10 = 12. Evaluate 12 != 24, drop this branch.\n     |- Try 22 * 10 = 220. Evaluate 220 != 24, drop this branch.\n     |- Try 22 \/ 10 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (2, 10) (numbers left: [44]). Try possible operations.\n    |- Try 10 + 2 = 12. Add 12 to the number set. Current number set: [12, 44], target: 24, just two numbers left.\n     |- Try 44 + 12 = 56. Evaluate 56 != 24, drop this branch.\n     |- Try 44 - 12 = 32. Evaluate 32 != 24, drop this branch.\n     |- Try 44 * 12 = 528. Evaluate 528 != 24, drop this branch.\n     |- Try 44 \/ 12 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 10 - 2 = 8. Add 8 to the number set. Current number set: [8, 44], target: 24, just two numbers left.\n     |- Try 44 + 8 = 52. Evaluate 52 != 24, drop this branch.\n     |- Try 44 - 8 = 36. Evaluate 36 != 24, drop this branch.\n     |- Try 44 * 8 = 352. Evaluate 352 != 24, drop this branch.\n     |- Try 44 \/ 8 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 10 * 2 = 20. Add 20 to the number set. Current number set: [20, 44], target: 24, just two numbers left.\n     |- Try 44 + 20 = 64. Evaluate 64 != 24, drop this branch.\n     |- Try 44 - 20 = 24. Evaluate 24 == 24, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 44 - 20 = 24\nThe step before: 10 * 2 = 20\nThe first step: 32 - 30 = 2\n\nOutput the solution in the required format:\n<Solution>\n32 - 30 = 2\n10 * 2 = 20\n44 - 20 = 24\n<\/Solution>\n","item":{"nums":[32,44,30,10],"solution":["32 - 30 = 2","10 * 2 = 20","44 - 20 = 24"],"target":24}}
+{"instance_id":"countdown_8k_145","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [4, 28, 32, 25]\nTarget: 14","reference_output":"# Search Procedure\nInitial number set: [4, 28, 32, 25], target: 14. Options for choosing two numbers: [(4, 28), (4, 32), (4, 25), (28, 32), (28, 25), (32, 25)].\n |- Pick two numbers (4, 28) (numbers left: [32, 25]). Try possible operations.\n  |- Try 28 + 4 = 32. Add 32 to the number set. Current number set: [32, 32, 25], target: 14. Options for choosing two numbers: [(32, 32), (32, 25), (32, 25)].\n   |- Pick two numbers (32, 32) (numbers left: [25]). Try possible operations.\n    |- Try 32 + 32 = 64. Add 64 to the number set. Current number set: [64, 25], target: 14, just two numbers left.\n     |- Try 64 + 25 = 89. Evaluate 89 != 14, drop this branch.\n     |- Try 64 - 25 = 39. Evaluate 39 != 14, drop this branch.\n     |- Try 64 * 25 = 1600. Evaluate 1600 != 14, drop this branch.\n     |- Try 64 \/ 25 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 32 - 32 = 0. Add 0 to the number set. Current number set: [0, 25], target: 14, just two numbers left.\n     |- Try 25 + 0 = 25. Evaluate 25 != 14, drop this branch.\n     |- Try 25 - 0 = 25. Evaluate 25 != 14, drop this branch.\n     |- Try 25 * 0 = 0. Evaluate 0 != 14, drop this branch.\n     |- Try 25 \/ 0 (invalid operation). drop this branch.\n    |- Try 32 * 32 = 1024. Add 1024 to the number set. Current number set: [1024, 25], target: 14, just two numbers left.\n     |- Try 1024 + 25 = 1049. Evaluate 1049 != 14, drop this branch.\n     |- Try 1024 - 25 = 999. Evaluate 999 != 14, drop this branch.\n     |- Try 1024 * 25 = 25600. 25600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1024 \/ 25 = 41.0. 41.0 is a decimal, drop this branch.\n    |- Try 32 \/ 32 = 1. Add 1 to the number set. Current number set: [1, 25], target: 14, just two numbers left.\n     |- Try 25 + 1 = 26. Evaluate 26 != 14, drop this branch.\n     |- Try 25 - 1 = 24. Evaluate 24 != 14, drop this branch.\n     |- Try 25 * 1 = 25. Evaluate 25 != 14, drop this branch.\n     |- Try 25 \/ 1 = 25. Evaluate 25 != 14, drop this branch.\n   |- Pick two numbers (32, 25) (numbers left: [32]). Try possible operations.\n    |- Try 32 + 25 = 57. Add 57 to the number set. Current number set: [57, 32], target: 14, just two numbers left.\n     |- Try 57 + 32 = 89. Evaluate 89 != 14, drop this branch.\n     |- Try 57 - 32 = 25. Evaluate 25 != 14, drop this branch.\n     |- Try 57 * 32 = 1824. Evaluate 1824 != 14, drop this branch.\n     |- Try 57 \/ 32 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 32 - 25 = 7. Add 7 to the number set. Current number set: [7, 32], target: 14, just two numbers left.\n     |- Try 32 + 7 = 39. Evaluate 39 != 14, drop this branch.\n     |- Try 32 - 7 = 25. Evaluate 25 != 14, drop this branch.\n     |- Try 32 * 7 = 224. Evaluate 224 != 14, drop this branch.\n     |- Try 32 \/ 7 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 32 * 25 = 800. Add 800 to the number set. Current number set: [800, 32], target: 14, just two numbers left.\n     |- Try 800 + 32 = 832. Evaluate 832 != 14, drop this branch.\n     |- Try 800 - 32 = 768. Evaluate 768 != 14, drop this branch.\n     |- Try 800 * 32 = 25600. 25600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 800 \/ 32 = 25. Evaluate 25 != 14, drop this branch.\n    |- Try 32 \/ 25 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (32, 25) (numbers left: [32]). Try possible operations.\n    |- Try 32 + 25 = 57. Add 57 to the number set. Current number set: [57, 32], target: 14, just two numbers left.\n     |- Try 57 + 32 = 89. Evaluate 89 != 14, drop this branch.\n     |- Try 57 - 32 = 25. Evaluate 25 != 14, drop this branch.\n     |- Try 57 * 32 = 1824. Evaluate 1824 != 14, drop this branch.\n     |- Try 57 \/ 32 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 32 - 25 = 7. Add 7 to the number set. Current number set: [7, 32], target: 14, just two numbers left.\n     |- Try 32 + 7 = 39. Evaluate 39 != 14, drop this branch.\n     |- Try 32 - 7 = 25. Evaluate 25 != 14, drop this branch.\n     |- Try 32 * 7 = 224. Evaluate 224 != 14, drop this branch.\n     |- Try 32 \/ 7 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 32 * 25 = 800. Add 800 to the number set. Current number set: [800, 32], target: 14, just two numbers left.\n     |- Try 800 + 32 = 832. Evaluate 832 != 14, drop this branch.\n     |- Try 800 - 32 = 768. Evaluate 768 != 14, drop this branch.\n     |- Try 800 * 32 = 25600. 25600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 800 \/ 32 = 25. Evaluate 25 != 14, drop this branch.\n    |- Try 32 \/ 25 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 28 - 4 = 24. Add 24 to the number set. Current number set: [24, 32, 25], target: 14. Options for choosing two numbers: [(24, 32), (24, 25), (32, 25)].\n   |- Pick two numbers (24, 32) (numbers left: [25]). Try possible operations.\n    |- Try 32 + 24 = 56. Add 56 to the number set. Current number set: [56, 25], target: 14, just two numbers left.\n     |- Try 56 + 25 = 81. Evaluate 81 != 14, drop this branch.\n     |- Try 56 - 25 = 31. Evaluate 31 != 14, drop this branch.\n     |- Try 56 * 25 = 1400. Evaluate 1400 != 14, drop this branch.\n     |- Try 56 \/ 25 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 32 - 24 = 8. Add 8 to the number set. Current number set: [8, 25], target: 14, just two numbers left.\n     |- Try 25 + 8 = 33. Evaluate 33 != 14, drop this branch.\n     |- Try 25 - 8 = 17. Evaluate 17 != 14, drop this branch.\n     |- Try 25 * 8 = 200. Evaluate 200 != 14, drop this branch.\n     |- Try 25 \/ 8 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 32 * 24 = 768. Add 768 to the number set. Current number set: [768, 25], target: 14, just two numbers left.\n     |- Try 768 + 25 = 793. Evaluate 793 != 14, drop this branch.\n     |- Try 768 - 25 = 743. Evaluate 743 != 14, drop this branch.\n     |- Try 768 * 25 = 19200. 19200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 768 \/ 25 = 30.7. 30.7 is a decimal, drop this branch.\n    |- Try 32 \/ 24 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (24, 25) (numbers left: [32]). Try possible operations.\n    |- Try 25 + 24 = 49. Add 49 to the number set. Current number set: [49, 32], target: 14, just two numbers left.\n     |- Try 49 + 32 = 81. Evaluate 81 != 14, drop this branch.\n     |- Try 49 - 32 = 17. Evaluate 17 != 14, drop this branch.\n     |- Try 49 * 32 = 1568. Evaluate 1568 != 14, drop this branch.\n     |- Try 49 \/ 32 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 25 - 24 = 1. Add 1 to the number set. Current number set: [1, 32], target: 14, just two numbers left.\n     |- Try 32 + 1 = 33. Evaluate 33 != 14, drop this branch.\n     |- Try 32 - 1 = 31. Evaluate 31 != 14, drop this branch.\n     |- Try 32 * 1 = 32. Evaluate 32 != 14, drop this branch.\n     |- Try 32 \/ 1 = 32. Evaluate 32 != 14, drop this branch.\n    |- Try 25 * 24 = 600. Add 600 to the number set. Current number set: [600, 32], target: 14, just two numbers left.\n     |- Try 600 + 32 = 632. Evaluate 632 != 14, drop this branch.\n     |- Try 600 - 32 = 568. Evaluate 568 != 14, drop this branch.\n     |- Try 600 * 32 = 19200. 19200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 600 \/ 32 = 18.8. 18.8 is a decimal, drop this branch.\n    |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n   |- Pick two numbers (32, 25) (numbers left: [24]). Try possible operations.\n    |- Try 32 + 25 = 57. Add 57 to the number set. Current number set: [57, 24], target: 14, just two numbers left.\n     |- Try 57 + 24 = 81. Evaluate 81 != 14, drop this branch.\n     |- Try 57 - 24 = 33. Evaluate 33 != 14, drop this branch.\n     |- Try 57 * 24 = 1368. Evaluate 1368 != 14, drop this branch.\n     |- Try 57 \/ 24 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 32 - 25 = 7. Add 7 to the number set. Current number set: [7, 24], target: 14, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 14, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 14, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 14, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 32 * 25 = 800. Add 800 to the number set. Current number set: [800, 24], target: 14, just two numbers left.\n     |- Try 800 + 24 = 824. Evaluate 824 != 14, drop this branch.\n     |- Try 800 - 24 = 776. Evaluate 776 != 14, drop this branch.\n     |- Try 800 * 24 = 19200. 19200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 800 \/ 24 = 33.3. 33.3 is a decimal, drop this branch.\n    |- Try 32 \/ 25 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 28 * 4 = 112. Add 112 to the number set. Current number set: [112, 32, 25], target: 14. Options for choosing two numbers: [(112, 32), (112, 25), (32, 25)].\n   |- Pick two numbers (112, 32) (numbers left: [25]). Try possible operations.\n    |- Try 112 + 32 = 144. Add 144 to the number set. Current number set: [144, 25], target: 14, just two numbers left.\n     |- Try 144 + 25 = 169. Evaluate 169 != 14, drop this branch.\n     |- Try 144 - 25 = 119. Evaluate 119 != 14, drop this branch.\n     |- Try 144 * 25 = 3600. 3600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 25 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 112 - 32 = 80. Add 80 to the number set. Current number set: [80, 25], target: 14, just two numbers left.\n     |- Try 80 + 25 = 105. Evaluate 105 != 14, drop this branch.\n     |- Try 80 - 25 = 55. Evaluate 55 != 14, drop this branch.\n     |- Try 80 * 25 = 2000. 2000 exceeds the maximum intermediate result, drop this branch.\n     |- Try 80 \/ 25 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 112 * 32 = 3584. 3584 exceeds the maximum intermediate result, drop this branch.\n    |- Try 112 \/ 32 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (112, 25) (numbers left: [32]). Try possible operations.\n    |- Try 112 + 25 = 137. Add 137 to the number set. Current number set: [137, 32], target: 14, just two numbers left.\n     |- Try 137 + 32 = 169. Evaluate 169 != 14, drop this branch.\n     |- Try 137 - 32 = 105. Evaluate 105 != 14, drop this branch.\n     |- Try 137 * 32 = 4384. 4384 exceeds the maximum intermediate result, drop this branch.\n     |- Try 137 \/ 32 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 112 - 25 = 87. Add 87 to the number set. Current number set: [87, 32], target: 14, just two numbers left.\n     |- Try 87 + 32 = 119. Evaluate 119 != 14, drop this branch.\n     |- Try 87 - 32 = 55. Evaluate 55 != 14, drop this branch.\n     |- Try 87 * 32 = 2784. 2784 exceeds the maximum intermediate result, drop this branch.\n     |- Try 87 \/ 32 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 112 * 25 = 2800. 2800 exceeds the maximum intermediate result, drop this branch.\n    |- Try 112 \/ 25 = 4.5. 4.5 is a decimal, drop this branch.\n   |- Pick two numbers (32, 25) (numbers left: [112]). Try possible operations.\n    |- Try 32 + 25 = 57. Add 57 to the number set. Current number set: [57, 112], target: 14, just two numbers left.\n     |- Try 112 + 57 = 169. Evaluate 169 != 14, drop this branch.\n     |- Try 112 - 57 = 55. Evaluate 55 != 14, drop this branch.\n     |- Try 112 * 57 = 6384. 6384 exceeds the maximum intermediate result, drop this branch.\n     |- Try 112 \/ 57 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 32 - 25 = 7. Add 7 to the number set. Current number set: [7, 112], target: 14, just two numbers left.\n     |- Try 112 + 7 = 119. Evaluate 119 != 14, drop this branch.\n     |- Try 112 - 7 = 105. Evaluate 105 != 14, drop this branch.\n     |- Try 112 * 7 = 784. Evaluate 784 != 14, drop this branch.\n     |- Try 112 \/ 7 = 16. Evaluate 16 != 14, drop this branch.\n    |- Try 32 * 25 = 800. Add 800 to the number set. Current number set: [800, 112], target: 14, just two numbers left.\n     |- Try 800 + 112 = 912. Evaluate 912 != 14, drop this branch.\n     |- Try 800 - 112 = 688. Evaluate 688 != 14, drop this branch.\n     |- Try 800 * 112 = 89600. 89600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 800 \/ 112 = 7.1. 7.1 is a decimal, drop this branch.\n    |- Try 32 \/ 25 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 28 \/ 4 = 7. Add 7 to the number set. Current number set: [7, 32, 25], target: 14. Options for choosing two numbers: [(7, 32), (7, 25), (32, 25)].\n   |- Pick two numbers (7, 32) (numbers left: [25]). Try possible operations.\n    |- Try 32 + 7 = 39. Add 39 to the number set. Current number set: [39, 25], target: 14, just two numbers left.\n     |- Try 39 + 25 = 64. Evaluate 64 != 14, drop this branch.\n     |- Try 39 - 25 = 14. Evaluate 14 == 14, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 39 - 25 = 14\nThe step before: 32 + 7 = 39\nThe first step: 28 \/ 4 = 7\n\nOutput the solution in the required format:\n<Solution>\n28 \/ 4 = 7\n32 + 7 = 39\n39 - 25 = 14\n<\/Solution>\n","item":{"nums":[4,28,32,25],"solution":["28 \/ 4 = 7","32 + 7 = 39","39 - 25 = 14"],"target":14}}
+{"instance_id":"countdown_8k_146","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [8, 13, 19, 3]\nTarget: 22","reference_output":"# Search Procedure\nInitial number set: [8, 13, 19, 3], target: 22. Options for choosing two numbers: [(8, 13), (8, 19), (8, 3), (13, 19), (13, 3), (19, 3)].\n |- Pick two numbers (8, 13) (numbers left: [19, 3]). Try possible operations.\n  |- Try 13 + 8 = 21. Add 21 to the number set. Current number set: [21, 19, 3], target: 22. Options for choosing two numbers: [(21, 19), (21, 3), (19, 3)].\n   |- Pick two numbers (21, 19) (numbers left: [3]). Try possible operations.\n    |- Try 21 + 19 = 40. Add 40 to the number set. Current number set: [40, 3], target: 22, just two numbers left.\n     |- Try 40 + 3 = 43. Evaluate 43 != 22, drop this branch.\n     |- Try 40 - 3 = 37. Evaluate 37 != 22, drop this branch.\n     |- Try 40 * 3 = 120. Evaluate 120 != 22, drop this branch.\n     |- Try 40 \/ 3 = 13.3. 13.3 is a decimal, drop this branch.\n    |- Try 21 - 19 = 2. Add 2 to the number set. Current number set: [2, 3], target: 22, just two numbers left.\n     |- Try 3 + 2 = 5. Evaluate 5 != 22, drop this branch.\n     |- Try 3 - 2 = 1. Evaluate 1 != 22, drop this branch.\n     |- Try 3 * 2 = 6. Evaluate 6 != 22, drop this branch.\n     |- Try 3 \/ 2 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 21 * 19 = 399. Add 399 to the number set. Current number set: [399, 3], target: 22, just two numbers left.\n     |- Try 399 + 3 = 402. Evaluate 402 != 22, drop this branch.\n     |- Try 399 - 3 = 396. Evaluate 396 != 22, drop this branch.\n     |- Try 399 * 3 = 1197. Evaluate 1197 != 22, drop this branch.\n     |- Try 399 \/ 3 = 133. Evaluate 133 != 22, drop this branch.\n    |- Try 21 \/ 19 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (21, 3) (numbers left: [19]). Try possible operations.\n    |- Try 21 + 3 = 24. Add 24 to the number set. Current number set: [24, 19], target: 22, just two numbers left.\n     |- Try 24 + 19 = 43. Evaluate 43 != 22, drop this branch.\n     |- Try 24 - 19 = 5. Evaluate 5 != 22, drop this branch.\n     |- Try 24 * 19 = 456. Evaluate 456 != 22, drop this branch.\n     |- Try 24 \/ 19 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 21 - 3 = 18. Add 18 to the number set. Current number set: [18, 19], target: 22, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 22, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 22, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 22, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 21 * 3 = 63. Add 63 to the number set. Current number set: [63, 19], target: 22, just two numbers left.\n     |- Try 63 + 19 = 82. Evaluate 82 != 22, drop this branch.\n     |- Try 63 - 19 = 44. Evaluate 44 != 22, drop this branch.\n     |- Try 63 * 19 = 1197. Evaluate 1197 != 22, drop this branch.\n     |- Try 63 \/ 19 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 21 \/ 3 = 7. Add 7 to the number set. Current number set: [7, 19], target: 22, just two numbers left.\n     |- Try 19 + 7 = 26. Evaluate 26 != 22, drop this branch.\n     |- Try 19 - 7 = 12. Evaluate 12 != 22, drop this branch.\n     |- Try 19 * 7 = 133. Evaluate 133 != 22, drop this branch.\n     |- Try 19 \/ 7 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (19, 3) (numbers left: [21]). Try possible operations.\n    |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 21], target: 22, just two numbers left.\n     |- Try 22 + 21 = 43. Evaluate 43 != 22, drop this branch.\n     |- Try 22 - 21 = 1. Evaluate 1 != 22, drop this branch.\n     |- Try 22 * 21 = 462. Evaluate 462 != 22, drop this branch.\n     |- Try 22 \/ 21 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 21], target: 22, just two numbers left.\n     |- Try 21 + 16 = 37. Evaluate 37 != 22, drop this branch.\n     |- Try 21 - 16 = 5. Evaluate 5 != 22, drop this branch.\n     |- Try 21 * 16 = 336. Evaluate 336 != 22, drop this branch.\n     |- Try 21 \/ 16 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 19 * 3 = 57. Add 57 to the number set. Current number set: [57, 21], target: 22, just two numbers left.\n     |- Try 57 + 21 = 78. Evaluate 78 != 22, drop this branch.\n     |- Try 57 - 21 = 36. Evaluate 36 != 22, drop this branch.\n     |- Try 57 * 21 = 1197. Evaluate 1197 != 22, drop this branch.\n     |- Try 57 \/ 21 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 19 \/ 3 = 6.3. 6.3 is a decimal, drop this branch.\n  |- Try 13 - 8 = 5. Add 5 to the number set. Current number set: [5, 19, 3], target: 22. Options for choosing two numbers: [(5, 19), (5, 3), (19, 3)].\n   |- Pick two numbers (5, 19) (numbers left: [3]). Try possible operations.\n    |- Try 19 + 5 = 24. Add 24 to the number set. Current number set: [24, 3], target: 22, just two numbers left.\n     |- Try 24 + 3 = 27. Evaluate 27 != 22, drop this branch.\n     |- Try 24 - 3 = 21. Evaluate 21 != 22, drop this branch.\n     |- Try 24 * 3 = 72. Evaluate 72 != 22, drop this branch.\n     |- Try 24 \/ 3 = 8. Evaluate 8 != 22, drop this branch.\n    |- Try 19 - 5 = 14. Add 14 to the number set. Current number set: [14, 3], target: 22, just two numbers left.\n     |- Try 14 + 3 = 17. Evaluate 17 != 22, drop this branch.\n     |- Try 14 - 3 = 11. Evaluate 11 != 22, drop this branch.\n     |- Try 14 * 3 = 42. Evaluate 42 != 22, drop this branch.\n     |- Try 14 \/ 3 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 19 * 5 = 95. Add 95 to the number set. Current number set: [95, 3], target: 22, just two numbers left.\n     |- Try 95 + 3 = 98. Evaluate 98 != 22, drop this branch.\n     |- Try 95 - 3 = 92. Evaluate 92 != 22, drop this branch.\n     |- Try 95 * 3 = 285. Evaluate 285 != 22, drop this branch.\n     |- Try 95 \/ 3 = 31.7. 31.7 is a decimal, drop this branch.\n    |- Try 19 \/ 5 = 3.8. 3.8 is a decimal, drop this branch.\n   |- Pick two numbers (5, 3) (numbers left: [19]). Try possible operations.\n    |- Try 5 + 3 = 8. Add 8 to the number set. Current number set: [8, 19], target: 22, just two numbers left.\n     |- Try 19 + 8 = 27. Evaluate 27 != 22, drop this branch.\n     |- Try 19 - 8 = 11. Evaluate 11 != 22, drop this branch.\n     |- Try 19 * 8 = 152. Evaluate 152 != 22, drop this branch.\n     |- Try 19 \/ 8 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 5 - 3 = 2. Add 2 to the number set. Current number set: [2, 19], target: 22, just two numbers left.\n     |- Try 19 + 2 = 21. Evaluate 21 != 22, drop this branch.\n     |- Try 19 - 2 = 17. Evaluate 17 != 22, drop this branch.\n     |- Try 19 * 2 = 38. Evaluate 38 != 22, drop this branch.\n     |- Try 19 \/ 2 = 9.5. 9.5 is a decimal, drop this branch.\n    |- Try 5 * 3 = 15. Add 15 to the number set. Current number set: [15, 19], target: 22, just two numbers left.\n     |- Try 19 + 15 = 34. Evaluate 34 != 22, drop this branch.\n     |- Try 19 - 15 = 4. Evaluate 4 != 22, drop this branch.\n     |- Try 19 * 15 = 285. Evaluate 285 != 22, drop this branch.\n     |- Try 19 \/ 15 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 5 \/ 3 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (19, 3) (numbers left: [5]). Try possible operations.\n    |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 5], target: 22, just two numbers left.\n     |- Try 22 + 5 = 27. Evaluate 27 != 22, drop this branch.\n     |- Try 22 - 5 = 17. Evaluate 17 != 22, drop this branch.\n     |- Try 22 * 5 = 110. Evaluate 110 != 22, drop this branch.\n     |- Try 22 \/ 5 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 5], target: 22, just two numbers left.\n     |- Try 16 + 5 = 21. Evaluate 21 != 22, drop this branch.\n     |- Try 16 - 5 = 11. Evaluate 11 != 22, drop this branch.\n     |- Try 16 * 5 = 80. Evaluate 80 != 22, drop this branch.\n     |- Try 16 \/ 5 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 19 * 3 = 57. Add 57 to the number set. Current number set: [57, 5], target: 22, just two numbers left.\n     |- Try 57 + 5 = 62. Evaluate 62 != 22, drop this branch.\n     |- Try 57 - 5 = 52. Evaluate 52 != 22, drop this branch.\n     |- Try 57 * 5 = 285. Evaluate 285 != 22, drop this branch.\n     |- Try 57 \/ 5 = 11.4. 11.4 is a decimal, drop this branch.\n    |- Try 19 \/ 3 = 6.3. 6.3 is a decimal, drop this branch.\n  |- Try 13 * 8 = 104. Add 104 to the number set. Current number set: [104, 19, 3], target: 22. Options for choosing two numbers: [(104, 19), (104, 3), (19, 3)].\n   |- Pick two numbers (104, 19) (numbers left: [3]). Try possible operations.\n    |- Try 104 + 19 = 123. Add 123 to the number set. Current number set: [123, 3], target: 22, just two numbers left.\n     |- Try 123 + 3 = 126. Evaluate 126 != 22, drop this branch.\n     |- Try 123 - 3 = 120. Evaluate 120 != 22, drop this branch.\n     |- Try 123 * 3 = 369. Evaluate 369 != 22, drop this branch.\n     |- Try 123 \/ 3 = 41. Evaluate 41 != 22, drop this branch.\n    |- Try 104 - 19 = 85. Add 85 to the number set. Current number set: [85, 3], target: 22, just two numbers left.\n     |- Try 85 + 3 = 88. Evaluate 88 != 22, drop this branch.\n     |- Try 85 - 3 = 82. Evaluate 82 != 22, drop this branch.\n     |- Try 85 * 3 = 255. Evaluate 255 != 22, drop this branch.\n     |- Try 85 \/ 3 = 28.3. 28.3 is a decimal, drop this branch.\n    |- Try 104 * 19 = 1976. Add 1976 to the number set. Current number set: [1976, 3], target: 22, just two numbers left.\n     |- Try 1976 + 3 = 1979. Evaluate 1979 != 22, drop this branch.\n     |- Try 1976 - 3 = 1973. Evaluate 1973 != 22, drop this branch.\n     |- Try 1976 * 3 = 5928. 5928 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1976 \/ 3 = 658.7. 658.7 is a decimal, drop this branch.\n    |- Try 104 \/ 19 = 5.5. 5.5 is a decimal, drop this branch.\n   |- Pick two numbers (104, 3) (numbers left: [19]). Try possible operations.\n    |- Try 104 + 3 = 107. Add 107 to the number set. Current number set: [107, 19], target: 22, just two numbers left.\n     |- Try 107 + 19 = 126. Evaluate 126 != 22, drop this branch.\n     |- Try 107 - 19 = 88. Evaluate 88 != 22, drop this branch.\n     |- Try 107 * 19 = 2033. 2033 exceeds the maximum intermediate result, drop this branch.\n     |- Try 107 \/ 19 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 104 - 3 = 101. Add 101 to the number set. Current number set: [101, 19], target: 22, just two numbers left.\n     |- Try 101 + 19 = 120. Evaluate 120 != 22, drop this branch.\n     |- Try 101 - 19 = 82. Evaluate 82 != 22, drop this branch.\n     |- Try 101 * 19 = 1919. Evaluate 1919 != 22, drop this branch.\n     |- Try 101 \/ 19 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 104 * 3 = 312. Add 312 to the number set. Current number set: [312, 19], target: 22, just two numbers left.\n     |- Try 312 + 19 = 331. Evaluate 331 != 22, drop this branch.\n     |- Try 312 - 19 = 293. Evaluate 293 != 22, drop this branch.\n     |- Try 312 * 19 = 5928. 5928 exceeds the maximum intermediate result, drop this branch.\n     |- Try 312 \/ 19 = 16.4. 16.4 is a decimal, drop this branch.\n    |- Try 104 \/ 3 = 34.7. 34.7 is a decimal, drop this branch.\n   |- Pick two numbers (19, 3) (numbers left: [104]). Try possible operations.\n    |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 104], target: 22, just two numbers left.\n     |- Try 104 + 22 = 126. Evaluate 126 != 22, drop this branch.\n     |- Try 104 - 22 = 82. Evaluate 82 != 22, drop this branch.\n     |- Try 104 * 22 = 2288. 2288 exceeds the maximum intermediate result, drop this branch.\n     |- Try 104 \/ 22 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 104], target: 22, just two numbers left.\n     |- Try 104 + 16 = 120. Evaluate 120 != 22, drop this branch.\n     |- Try 104 - 16 = 88. Evaluate 88 != 22, drop this branch.\n     |- Try 104 * 16 = 1664. Evaluate 1664 != 22, drop this branch.\n     |- Try 104 \/ 16 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 19 * 3 = 57. Add 57 to the number set. Current number set: [57, 104], target: 22, just two numbers left.\n     |- Try 104 + 57 = 161. Evaluate 161 != 22, drop this branch.\n     |- Try 104 - 57 = 47. Evaluate 47 != 22, drop this branch.\n     |- Try 104 * 57 = 5928. 5928 exceeds the maximum intermediate result, drop this branch.\n     |- Try 104 \/ 57 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 19 \/ 3 = 6.3. 6.3 is a decimal, drop this branch.\n  |- Try 13 \/ 8 = 1.6. 1.6 is a decimal, drop this branch.\n |- Pick two numbers (8, 19) (numbers left: [13, 3]). Try possible operations.\n  |- Try 19 + 8 = 27. Add 27 to the number set. Current number set: [27, 13, 3], target: 22. Options for choosing two numbers: [(27, 13), (27, 3), (13, 3)].\n   |- Pick two numbers (27, 13) (numbers left: [3]). Try possible operations.\n    |- Try 27 + 13 = 40. Add 40 to the number set. Current number set: [40, 3], target: 22, just two numbers left.\n     |- Try 40 + 3 = 43. Evaluate 43 != 22, drop this branch.\n     |- Try 40 - 3 = 37. Evaluate 37 != 22, drop this branch.\n     |- Try 40 * 3 = 120. Evaluate 120 != 22, drop this branch.\n     |- Try 40 \/ 3 = 13.3. 13.3 is a decimal, drop this branch.\n    |- Try 27 - 13 = 14. Add 14 to the number set. Current number set: [14, 3], target: 22, just two numbers left.\n     |- Try 14 + 3 = 17. Evaluate 17 != 22, drop this branch.\n     |- Try 14 - 3 = 11. Evaluate 11 != 22, drop this branch.\n     |- Try 14 * 3 = 42. Evaluate 42 != 22, drop this branch.\n     |- Try 14 \/ 3 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 27 * 13 = 351. Add 351 to the number set. Current number set: [351, 3], target: 22, just two numbers left.\n     |- Try 351 + 3 = 354. Evaluate 354 != 22, drop this branch.\n     |- Try 351 - 3 = 348. Evaluate 348 != 22, drop this branch.\n     |- Try 351 * 3 = 1053. Evaluate 1053 != 22, drop this branch.\n     |- Try 351 \/ 3 = 117. Evaluate 117 != 22, drop this branch.\n    |- Try 27 \/ 13 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (27, 3) (numbers left: [13]). Try possible operations.\n    |- Try 27 + 3 = 30. Add 30 to the number set. Current number set: [30, 13], target: 22, just two numbers left.\n     |- Try 30 + 13 = 43. Evaluate 43 != 22, drop this branch.\n     |- Try 30 - 13 = 17. Evaluate 17 != 22, drop this branch.\n     |- Try 30 * 13 = 390. Evaluate 390 != 22, drop this branch.\n     |- Try 30 \/ 13 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 27 - 3 = 24. Add 24 to the number set. Current number set: [24, 13], target: 22, just two numbers left.\n     |- Try 24 + 13 = 37. Evaluate 37 != 22, drop this branch.\n     |- Try 24 - 13 = 11. Evaluate 11 != 22, drop this branch.\n     |- Try 24 * 13 = 312. Evaluate 312 != 22, drop this branch.\n     |- Try 24 \/ 13 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 27 * 3 = 81. Add 81 to the number set. Current number set: [81, 13], target: 22, just two numbers left.\n     |- Try 81 + 13 = 94. Evaluate 94 != 22, drop this branch.\n     |- Try 81 - 13 = 68. Evaluate 68 != 22, drop this branch.\n     |- Try 81 * 13 = 1053. Evaluate 1053 != 22, drop this branch.\n     |- Try 81 \/ 13 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 27 \/ 3 = 9. Add 9 to the number set. Current number set: [9, 13], target: 22, just two numbers left.\n     |- Try 13 + 9 = 22. Evaluate 22 == 22, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 13 + 9 = 22\nThe step before: 27 \/ 3 = 9\nThe first step: 19 + 8 = 27\n\nOutput the solution in the required format:\n<Solution>\n19 + 8 = 27\n27 \/ 3 = 9\n13 + 9 = 22\n<\/Solution>\n","item":{"nums":[8,13,19,3],"solution":["19 + 8 = 27","27 \/ 3 = 9","13 + 9 = 22"],"target":22}}
+{"instance_id":"countdown_8k_147","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [32, 24, 22, 20]\nTarget: 26","reference_output":"# Search Procedure\nInitial number set: [32, 24, 22, 20], target: 26. Options for choosing two numbers: [(32, 24), (32, 22), (32, 20), (24, 22), (24, 20), (22, 20)].\n |- Pick two numbers (32, 24) (numbers left: [22, 20]). Try possible operations.\n  |- Try 32 + 24 = 56. Add 56 to the number set. Current number set: [56, 22, 20], target: 26. Options for choosing two numbers: [(56, 22), (56, 20), (22, 20)].\n   |- Pick two numbers (56, 22) (numbers left: [20]). Try possible operations.\n    |- Try 56 + 22 = 78. Add 78 to the number set. Current number set: [78, 20], target: 26, just two numbers left.\n     |- Try 78 + 20 = 98. Evaluate 98 != 26, drop this branch.\n     |- Try 78 - 20 = 58. Evaluate 58 != 26, drop this branch.\n     |- Try 78 * 20 = 1560. Evaluate 1560 != 26, drop this branch.\n     |- Try 78 \/ 20 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 56 - 22 = 34. Add 34 to the number set. Current number set: [34, 20], target: 26, just two numbers left.\n     |- Try 34 + 20 = 54. Evaluate 54 != 26, drop this branch.\n     |- Try 34 - 20 = 14. Evaluate 14 != 26, drop this branch.\n     |- Try 34 * 20 = 680. Evaluate 680 != 26, drop this branch.\n     |- Try 34 \/ 20 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 56 * 22 = 1232. Add 1232 to the number set. Current number set: [1232, 20], target: 26, just two numbers left.\n     |- Try 1232 + 20 = 1252. Evaluate 1252 != 26, drop this branch.\n     |- Try 1232 - 20 = 1212. Evaluate 1212 != 26, drop this branch.\n     |- Try 1232 * 20 = 24640. 24640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1232 \/ 20 = 61.6. 61.6 is a decimal, drop this branch.\n    |- Try 56 \/ 22 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (56, 20) (numbers left: [22]). Try possible operations.\n    |- Try 56 + 20 = 76. Add 76 to the number set. Current number set: [76, 22], target: 26, just two numbers left.\n     |- Try 76 + 22 = 98. Evaluate 98 != 26, drop this branch.\n     |- Try 76 - 22 = 54. Evaluate 54 != 26, drop this branch.\n     |- Try 76 * 22 = 1672. Evaluate 1672 != 26, drop this branch.\n     |- Try 76 \/ 22 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 56 - 20 = 36. Add 36 to the number set. Current number set: [36, 22], target: 26, just two numbers left.\n     |- Try 36 + 22 = 58. Evaluate 58 != 26, drop this branch.\n     |- Try 36 - 22 = 14. Evaluate 14 != 26, drop this branch.\n     |- Try 36 * 22 = 792. Evaluate 792 != 26, drop this branch.\n     |- Try 36 \/ 22 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 56 * 20 = 1120. Add 1120 to the number set. Current number set: [1120, 22], target: 26, just two numbers left.\n     |- Try 1120 + 22 = 1142. Evaluate 1142 != 26, drop this branch.\n     |- Try 1120 - 22 = 1098. Evaluate 1098 != 26, drop this branch.\n     |- Try 1120 * 22 = 24640. 24640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1120 \/ 22 = 50.9. 50.9 is a decimal, drop this branch.\n    |- Try 56 \/ 20 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (22, 20) (numbers left: [56]). Try possible operations.\n    |- Try 22 + 20 = 42. Add 42 to the number set. Current number set: [42, 56], target: 26, just two numbers left.\n     |- Try 56 + 42 = 98. Evaluate 98 != 26, drop this branch.\n     |- Try 56 - 42 = 14. Evaluate 14 != 26, drop this branch.\n     |- Try 56 * 42 = 2352. 2352 exceeds the maximum intermediate result, drop this branch.\n     |- Try 56 \/ 42 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 22 - 20 = 2. Add 2 to the number set. Current number set: [2, 56], target: 26, just two numbers left.\n     |- Try 56 + 2 = 58. Evaluate 58 != 26, drop this branch.\n     |- Try 56 - 2 = 54. Evaluate 54 != 26, drop this branch.\n     |- Try 56 * 2 = 112. Evaluate 112 != 26, drop this branch.\n     |- Try 56 \/ 2 = 28. Evaluate 28 != 26, drop this branch.\n    |- Try 22 * 20 = 440. Add 440 to the number set. Current number set: [440, 56], target: 26, just two numbers left.\n     |- Try 440 + 56 = 496. Evaluate 496 != 26, drop this branch.\n     |- Try 440 - 56 = 384. Evaluate 384 != 26, drop this branch.\n     |- Try 440 * 56 = 24640. 24640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 440 \/ 56 = 7.9. 7.9 is a decimal, drop this branch.\n    |- Try 22 \/ 20 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 32 - 24 = 8. Add 8 to the number set. Current number set: [8, 22, 20], target: 26. Options for choosing two numbers: [(8, 22), (8, 20), (22, 20)].\n   |- Pick two numbers (8, 22) (numbers left: [20]). Try possible operations.\n    |- Try 22 + 8 = 30. Add 30 to the number set. Current number set: [30, 20], target: 26, just two numbers left.\n     |- Try 30 + 20 = 50. Evaluate 50 != 26, drop this branch.\n     |- Try 30 - 20 = 10. Evaluate 10 != 26, drop this branch.\n     |- Try 30 * 20 = 600. Evaluate 600 != 26, drop this branch.\n     |- Try 30 \/ 20 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 22 - 8 = 14. Add 14 to the number set. Current number set: [14, 20], target: 26, just two numbers left.\n     |- Try 20 + 14 = 34. Evaluate 34 != 26, drop this branch.\n     |- Try 20 - 14 = 6. Evaluate 6 != 26, drop this branch.\n     |- Try 20 * 14 = 280. Evaluate 280 != 26, drop this branch.\n     |- Try 20 \/ 14 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 22 * 8 = 176. Add 176 to the number set. Current number set: [176, 20], target: 26, just two numbers left.\n     |- Try 176 + 20 = 196. Evaluate 196 != 26, drop this branch.\n     |- Try 176 - 20 = 156. Evaluate 156 != 26, drop this branch.\n     |- Try 176 * 20 = 3520. 3520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 176 \/ 20 = 8.8. 8.8 is a decimal, drop this branch.\n    |- Try 22 \/ 8 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (8, 20) (numbers left: [22]). Try possible operations.\n    |- Try 20 + 8 = 28. Add 28 to the number set. Current number set: [28, 22], target: 26, just two numbers left.\n     |- Try 28 + 22 = 50. Evaluate 50 != 26, drop this branch.\n     |- Try 28 - 22 = 6. Evaluate 6 != 26, drop this branch.\n     |- Try 28 * 22 = 616. Evaluate 616 != 26, drop this branch.\n     |- Try 28 \/ 22 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 20 - 8 = 12. Add 12 to the number set. Current number set: [12, 22], target: 26, just two numbers left.\n     |- Try 22 + 12 = 34. Evaluate 34 != 26, drop this branch.\n     |- Try 22 - 12 = 10. Evaluate 10 != 26, drop this branch.\n     |- Try 22 * 12 = 264. Evaluate 264 != 26, drop this branch.\n     |- Try 22 \/ 12 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 20 * 8 = 160. Add 160 to the number set. Current number set: [160, 22], target: 26, just two numbers left.\n     |- Try 160 + 22 = 182. Evaluate 182 != 26, drop this branch.\n     |- Try 160 - 22 = 138. Evaluate 138 != 26, drop this branch.\n     |- Try 160 * 22 = 3520. 3520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 160 \/ 22 = 7.3. 7.3 is a decimal, drop this branch.\n    |- Try 20 \/ 8 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (22, 20) (numbers left: [8]). Try possible operations.\n    |- Try 22 + 20 = 42. Add 42 to the number set. Current number set: [42, 8], target: 26, just two numbers left.\n     |- Try 42 + 8 = 50. Evaluate 50 != 26, drop this branch.\n     |- Try 42 - 8 = 34. Evaluate 34 != 26, drop this branch.\n     |- Try 42 * 8 = 336. Evaluate 336 != 26, drop this branch.\n     |- Try 42 \/ 8 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 22 - 20 = 2. Add 2 to the number set. Current number set: [2, 8], target: 26, just two numbers left.\n     |- Try 8 + 2 = 10. Evaluate 10 != 26, drop this branch.\n     |- Try 8 - 2 = 6. Evaluate 6 != 26, drop this branch.\n     |- Try 8 * 2 = 16. Evaluate 16 != 26, drop this branch.\n     |- Try 8 \/ 2 = 4. Evaluate 4 != 26, drop this branch.\n    |- Try 22 * 20 = 440. Add 440 to the number set. Current number set: [440, 8], target: 26, just two numbers left.\n     |- Try 440 + 8 = 448. Evaluate 448 != 26, drop this branch.\n     |- Try 440 - 8 = 432. Evaluate 432 != 26, drop this branch.\n     |- Try 440 * 8 = 3520. 3520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 440 \/ 8 = 55. Evaluate 55 != 26, drop this branch.\n    |- Try 22 \/ 20 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 32 * 24 = 768. Add 768 to the number set. Current number set: [768, 22, 20], target: 26. Options for choosing two numbers: [(768, 22), (768, 20), (22, 20)].\n   |- Pick two numbers (768, 22) (numbers left: [20]). Try possible operations.\n    |- Try 768 + 22 = 790. Add 790 to the number set. Current number set: [790, 20], target: 26, just two numbers left.\n     |- Try 790 + 20 = 810. Evaluate 810 != 26, drop this branch.\n     |- Try 790 - 20 = 770. Evaluate 770 != 26, drop this branch.\n     |- Try 790 * 20 = 15800. 15800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 790 \/ 20 = 39.5. 39.5 is a decimal, drop this branch.\n    |- Try 768 - 22 = 746. Add 746 to the number set. Current number set: [746, 20], target: 26, just two numbers left.\n     |- Try 746 + 20 = 766. Evaluate 766 != 26, drop this branch.\n     |- Try 746 - 20 = 726. Evaluate 726 != 26, drop this branch.\n     |- Try 746 * 20 = 14920. 14920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 746 \/ 20 = 37.3. 37.3 is a decimal, drop this branch.\n    |- Try 768 * 22 = 16896. 16896 exceeds the maximum intermediate result, drop this branch.\n    |- Try 768 \/ 22 = 34.9. 34.9 is a decimal, drop this branch.\n   |- Pick two numbers (768, 20) (numbers left: [22]). Try possible operations.\n    |- Try 768 + 20 = 788. Add 788 to the number set. Current number set: [788, 22], target: 26, just two numbers left.\n     |- Try 788 + 22 = 810. Evaluate 810 != 26, drop this branch.\n     |- Try 788 - 22 = 766. Evaluate 766 != 26, drop this branch.\n     |- Try 788 * 22 = 17336. 17336 exceeds the maximum intermediate result, drop this branch.\n     |- Try 788 \/ 22 = 35.8. 35.8 is a decimal, drop this branch.\n    |- Try 768 - 20 = 748. Add 748 to the number set. Current number set: [748, 22], target: 26, just two numbers left.\n     |- Try 748 + 22 = 770. Evaluate 770 != 26, drop this branch.\n     |- Try 748 - 22 = 726. Evaluate 726 != 26, drop this branch.\n     |- Try 748 * 22 = 16456. 16456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 748 \/ 22 = 34. Evaluate 34 != 26, drop this branch.\n    |- Try 768 * 20 = 15360. 15360 exceeds the maximum intermediate result, drop this branch.\n    |- Try 768 \/ 20 = 38.4. 38.4 is a decimal, drop this branch.\n   |- Pick two numbers (22, 20) (numbers left: [768]). Try possible operations.\n    |- Try 22 + 20 = 42. Add 42 to the number set. Current number set: [42, 768], target: 26, just two numbers left.\n     |- Try 768 + 42 = 810. Evaluate 810 != 26, drop this branch.\n     |- Try 768 - 42 = 726. Evaluate 726 != 26, drop this branch.\n     |- Try 768 * 42 = 32256. 32256 exceeds the maximum intermediate result, drop this branch.\n     |- Try 768 \/ 42 = 18.3. 18.3 is a decimal, drop this branch.\n    |- Try 22 - 20 = 2. Add 2 to the number set. Current number set: [2, 768], target: 26, just two numbers left.\n     |- Try 768 + 2 = 770. Evaluate 770 != 26, drop this branch.\n     |- Try 768 - 2 = 766. Evaluate 766 != 26, drop this branch.\n     |- Try 768 * 2 = 1536. Evaluate 1536 != 26, drop this branch.\n     |- Try 768 \/ 2 = 384. Evaluate 384 != 26, drop this branch.\n    |- Try 22 * 20 = 440. Add 440 to the number set. Current number set: [440, 768], target: 26, just two numbers left.\n     |- Try 768 + 440 = 1208. Evaluate 1208 != 26, drop this branch.\n     |- Try 768 - 440 = 328. Evaluate 328 != 26, drop this branch.\n     |- Try 768 * 440 = 337920. 337920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 768 \/ 440 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 22 \/ 20 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 32 \/ 24 = 1.3. 1.3 is a decimal, drop this branch.\n |- Pick two numbers (32, 22) (numbers left: [24, 20]). Try possible operations.\n  |- Try 32 + 22 = 54. Add 54 to the number set. Current number set: [54, 24, 20], target: 26. Options for choosing two numbers: [(54, 24), (54, 20), (24, 20)].\n   |- Pick two numbers (54, 24) (numbers left: [20]). Try possible operations.\n    |- Try 54 + 24 = 78. Add 78 to the number set. Current number set: [78, 20], target: 26, just two numbers left.\n     |- Try 78 + 20 = 98. Evaluate 98 != 26, drop this branch.\n     |- Try 78 - 20 = 58. Evaluate 58 != 26, drop this branch.\n     |- Try 78 * 20 = 1560. Evaluate 1560 != 26, drop this branch.\n     |- Try 78 \/ 20 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 54 - 24 = 30. Add 30 to the number set. Current number set: [30, 20], target: 26, just two numbers left.\n     |- Try 30 + 20 = 50. Evaluate 50 != 26, drop this branch.\n     |- Try 30 - 20 = 10. Evaluate 10 != 26, drop this branch.\n     |- Try 30 * 20 = 600. Evaluate 600 != 26, drop this branch.\n     |- Try 30 \/ 20 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 54 * 24 = 1296. Add 1296 to the number set. Current number set: [1296, 20], target: 26, just two numbers left.\n     |- Try 1296 + 20 = 1316. Evaluate 1316 != 26, drop this branch.\n     |- Try 1296 - 20 = 1276. Evaluate 1276 != 26, drop this branch.\n     |- Try 1296 * 20 = 25920. 25920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1296 \/ 20 = 64.8. 64.8 is a decimal, drop this branch.\n    |- Try 54 \/ 24 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (54, 20) (numbers left: [24]). Try possible operations.\n    |- Try 54 + 20 = 74. Add 74 to the number set. Current number set: [74, 24], target: 26, just two numbers left.\n     |- Try 74 + 24 = 98. Evaluate 98 != 26, drop this branch.\n     |- Try 74 - 24 = 50. Evaluate 50 != 26, drop this branch.\n     |- Try 74 * 24 = 1776. Evaluate 1776 != 26, drop this branch.\n     |- Try 74 \/ 24 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 54 - 20 = 34. Add 34 to the number set. Current number set: [34, 24], target: 26, just two numbers left.\n     |- Try 34 + 24 = 58. Evaluate 58 != 26, drop this branch.\n     |- Try 34 - 24 = 10. Evaluate 10 != 26, drop this branch.\n     |- Try 34 * 24 = 816. Evaluate 816 != 26, drop this branch.\n     |- Try 34 \/ 24 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 54 * 20 = 1080. Add 1080 to the number set. Current number set: [1080, 24], target: 26, just two numbers left.\n     |- Try 1080 + 24 = 1104. Evaluate 1104 != 26, drop this branch.\n     |- Try 1080 - 24 = 1056. Evaluate 1056 != 26, drop this branch.\n     |- Try 1080 * 24 = 25920. 25920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1080 \/ 24 = 45. Evaluate 45 != 26, drop this branch.\n    |- Try 54 \/ 20 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (24, 20) (numbers left: [54]). Try possible operations.\n    |- Try 24 + 20 = 44. Add 44 to the number set. Current number set: [44, 54], target: 26, just two numbers left.\n     |- Try 54 + 44 = 98. Evaluate 98 != 26, drop this branch.\n     |- Try 54 - 44 = 10. Evaluate 10 != 26, drop this branch.\n     |- Try 54 * 44 = 2376. 2376 exceeds the maximum intermediate result, drop this branch.\n     |- Try 54 \/ 44 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 24 - 20 = 4. Add 4 to the number set. Current number set: [4, 54], target: 26, just two numbers left.\n     |- Try 54 + 4 = 58. Evaluate 58 != 26, drop this branch.\n     |- Try 54 - 4 = 50. Evaluate 50 != 26, drop this branch.\n     |- Try 54 * 4 = 216. Evaluate 216 != 26, drop this branch.\n     |- Try 54 \/ 4 = 13.5. 13.5 is a decimal, drop this branch.\n    |- Try 24 * 20 = 480. Add 480 to the number set. Current number set: [480, 54], target: 26, just two numbers left.\n     |- Try 480 + 54 = 534. Evaluate 534 != 26, drop this branch.\n     |- Try 480 - 54 = 426. Evaluate 426 != 26, drop this branch.\n     |- Try 480 * 54 = 25920. 25920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 480 \/ 54 = 8.9. 8.9 is a decimal, drop this branch.\n    |- Try 24 \/ 20 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 32 - 22 = 10. Add 10 to the number set. Current number set: [10, 24, 20], target: 26. Options for choosing two numbers: [(10, 24), (10, 20), (24, 20)].\n   |- Pick two numbers (10, 24) (numbers left: [20]). Try possible operations.\n    |- Try 24 + 10 = 34. Add 34 to the number set. Current number set: [34, 20], target: 26, just two numbers left.\n     |- Try 34 + 20 = 54. Evaluate 54 != 26, drop this branch.\n     |- Try 34 - 20 = 14. Evaluate 14 != 26, drop this branch.\n     |- Try 34 * 20 = 680. Evaluate 680 != 26, drop this branch.\n     |- Try 34 \/ 20 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 24 - 10 = 14. Add 14 to the number set. Current number set: [14, 20], target: 26, just two numbers left.\n     |- Try 20 + 14 = 34. Evaluate 34 != 26, drop this branch.\n     |- Try 20 - 14 = 6. Evaluate 6 != 26, drop this branch.\n     |- Try 20 * 14 = 280. Evaluate 280 != 26, drop this branch.\n     |- Try 20 \/ 14 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 24 * 10 = 240. Add 240 to the number set. Current number set: [240, 20], target: 26, just two numbers left.\n     |- Try 240 + 20 = 260. Evaluate 260 != 26, drop this branch.\n     |- Try 240 - 20 = 220. Evaluate 220 != 26, drop this branch.\n     |- Try 240 * 20 = 4800. 4800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 240 \/ 20 = 12. Evaluate 12 != 26, drop this branch.\n    |- Try 24 \/ 10 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (10, 20) (numbers left: [24]). Try possible operations.\n    |- Try 20 + 10 = 30. Add 30 to the number set. Current number set: [30, 24], target: 26, just two numbers left.\n     |- Try 30 + 24 = 54. Evaluate 54 != 26, drop this branch.\n     |- Try 30 - 24 = 6. Evaluate 6 != 26, drop this branch.\n     |- Try 30 * 24 = 720. Evaluate 720 != 26, drop this branch.\n     |- Try 30 \/ 24 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 20 - 10 = 10. Add 10 to the number set. Current number set: [10, 24], target: 26, just two numbers left.\n     |- Try 24 + 10 = 34. Evaluate 34 != 26, drop this branch.\n     |- Try 24 - 10 = 14. Evaluate 14 != 26, drop this branch.\n     |- Try 24 * 10 = 240. Evaluate 240 != 26, drop this branch.\n     |- Try 24 \/ 10 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 20 * 10 = 200. Add 200 to the number set. Current number set: [200, 24], target: 26, just two numbers left.\n     |- Try 200 + 24 = 224. Evaluate 224 != 26, drop this branch.\n     |- Try 200 - 24 = 176. Evaluate 176 != 26, drop this branch.\n     |- Try 200 * 24 = 4800. 4800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 200 \/ 24 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 20 \/ 10 = 2. Add 2 to the number set. Current number set: [2, 24], target: 26, just two numbers left.\n     |- Try 24 + 2 = 26. Evaluate 26 == 26, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 24 + 2 = 26\nThe step before: 20 \/ 10 = 2\nThe first step: 32 - 22 = 10\n\nOutput the solution in the required format:\n<Solution>\n32 - 22 = 10\n20 \/ 10 = 2\n24 + 2 = 26\n<\/Solution>\n","item":{"nums":[32,24,22,20],"solution":["32 - 22 = 10","20 \/ 10 = 2","24 + 2 = 26"],"target":26}}
+{"instance_id":"countdown_8k_148","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [47, 10, 3, 9]\nTarget: 44","reference_output":"# Search Procedure\nInitial number set: [47, 10, 3, 9], target: 44. Options for choosing two numbers: [(47, 10), (47, 3), (47, 9), (10, 3), (10, 9), (3, 9)].\n |- Pick two numbers (47, 10) (numbers left: [3, 9]). Try possible operations.\n  |- Try 47 + 10 = 57. Add 57 to the number set. Current number set: [57, 3, 9], target: 44. Options for choosing two numbers: [(57, 3), (57, 9), (3, 9)].\n   |- Pick two numbers (57, 3) (numbers left: [9]). Try possible operations.\n    |- Try 57 + 3 = 60. Add 60 to the number set. Current number set: [60, 9], target: 44, just two numbers left.\n     |- Try 60 + 9 = 69. Evaluate 69 != 44, drop this branch.\n     |- Try 60 - 9 = 51. Evaluate 51 != 44, drop this branch.\n     |- Try 60 * 9 = 540. Evaluate 540 != 44, drop this branch.\n     |- Try 60 \/ 9 = 6.7. 6.7 is a decimal, drop this branch.\n    |- Try 57 - 3 = 54. Add 54 to the number set. Current number set: [54, 9], target: 44, just two numbers left.\n     |- Try 54 + 9 = 63. Evaluate 63 != 44, drop this branch.\n     |- Try 54 - 9 = 45. Evaluate 45 != 44, drop this branch.\n     |- Try 54 * 9 = 486. Evaluate 486 != 44, drop this branch.\n     |- Try 54 \/ 9 = 6. Evaluate 6 != 44, drop this branch.\n    |- Try 57 * 3 = 171. Add 171 to the number set. Current number set: [171, 9], target: 44, just two numbers left.\n     |- Try 171 + 9 = 180. Evaluate 180 != 44, drop this branch.\n     |- Try 171 - 9 = 162. Evaluate 162 != 44, drop this branch.\n     |- Try 171 * 9 = 1539. Evaluate 1539 != 44, drop this branch.\n     |- Try 171 \/ 9 = 19. Evaluate 19 != 44, drop this branch.\n    |- Try 57 \/ 3 = 19. Add 19 to the number set. Current number set: [19, 9], target: 44, just two numbers left.\n     |- Try 19 + 9 = 28. Evaluate 28 != 44, drop this branch.\n     |- Try 19 - 9 = 10. Evaluate 10 != 44, drop this branch.\n     |- Try 19 * 9 = 171. Evaluate 171 != 44, drop this branch.\n     |- Try 19 \/ 9 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (57, 9) (numbers left: [3]). Try possible operations.\n    |- Try 57 + 9 = 66. Add 66 to the number set. Current number set: [66, 3], target: 44, just two numbers left.\n     |- Try 66 + 3 = 69. Evaluate 69 != 44, drop this branch.\n     |- Try 66 - 3 = 63. Evaluate 63 != 44, drop this branch.\n     |- Try 66 * 3 = 198. Evaluate 198 != 44, drop this branch.\n     |- Try 66 \/ 3 = 22. Evaluate 22 != 44, drop this branch.\n    |- Try 57 - 9 = 48. Add 48 to the number set. Current number set: [48, 3], target: 44, just two numbers left.\n     |- Try 48 + 3 = 51. Evaluate 51 != 44, drop this branch.\n     |- Try 48 - 3 = 45. Evaluate 45 != 44, drop this branch.\n     |- Try 48 * 3 = 144. Evaluate 144 != 44, drop this branch.\n     |- Try 48 \/ 3 = 16. Evaluate 16 != 44, drop this branch.\n    |- Try 57 * 9 = 513. Add 513 to the number set. Current number set: [513, 3], target: 44, just two numbers left.\n     |- Try 513 + 3 = 516. Evaluate 516 != 44, drop this branch.\n     |- Try 513 - 3 = 510. Evaluate 510 != 44, drop this branch.\n     |- Try 513 * 3 = 1539. Evaluate 1539 != 44, drop this branch.\n     |- Try 513 \/ 3 = 171. Evaluate 171 != 44, drop this branch.\n    |- Try 57 \/ 9 = 6.3. 6.3 is a decimal, drop this branch.\n   |- Pick two numbers (3, 9) (numbers left: [57]). Try possible operations.\n    |- Try 9 + 3 = 12. Add 12 to the number set. Current number set: [12, 57], target: 44, just two numbers left.\n     |- Try 57 + 12 = 69. Evaluate 69 != 44, drop this branch.\n     |- Try 57 - 12 = 45. Evaluate 45 != 44, drop this branch.\n     |- Try 57 * 12 = 684. Evaluate 684 != 44, drop this branch.\n     |- Try 57 \/ 12 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 9 - 3 = 6. Add 6 to the number set. Current number set: [6, 57], target: 44, just two numbers left.\n     |- Try 57 + 6 = 63. Evaluate 63 != 44, drop this branch.\n     |- Try 57 - 6 = 51. Evaluate 51 != 44, drop this branch.\n     |- Try 57 * 6 = 342. Evaluate 342 != 44, drop this branch.\n     |- Try 57 \/ 6 = 9.5. 9.5 is a decimal, drop this branch.\n    |- Try 9 * 3 = 27. Add 27 to the number set. Current number set: [27, 57], target: 44, just two numbers left.\n     |- Try 57 + 27 = 84. Evaluate 84 != 44, drop this branch.\n     |- Try 57 - 27 = 30. Evaluate 30 != 44, drop this branch.\n     |- Try 57 * 27 = 1539. Evaluate 1539 != 44, drop this branch.\n     |- Try 57 \/ 27 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 9 \/ 3 = 3. Add 3 to the number set. Current number set: [3, 57], target: 44, just two numbers left.\n     |- Try 57 + 3 = 60. Evaluate 60 != 44, drop this branch.\n     |- Try 57 - 3 = 54. Evaluate 54 != 44, drop this branch.\n     |- Try 57 * 3 = 171. Evaluate 171 != 44, drop this branch.\n     |- Try 57 \/ 3 = 19. Evaluate 19 != 44, drop this branch.\n  |- Try 47 - 10 = 37. Add 37 to the number set. Current number set: [37, 3, 9], target: 44. Options for choosing two numbers: [(37, 3), (37, 9), (3, 9)].\n   |- Pick two numbers (37, 3) (numbers left: [9]). Try possible operations.\n    |- Try 37 + 3 = 40. Add 40 to the number set. Current number set: [40, 9], target: 44, just two numbers left.\n     |- Try 40 + 9 = 49. Evaluate 49 != 44, drop this branch.\n     |- Try 40 - 9 = 31. Evaluate 31 != 44, drop this branch.\n     |- Try 40 * 9 = 360. Evaluate 360 != 44, drop this branch.\n     |- Try 40 \/ 9 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 37 - 3 = 34. Add 34 to the number set. Current number set: [34, 9], target: 44, just two numbers left.\n     |- Try 34 + 9 = 43. Evaluate 43 != 44, drop this branch.\n     |- Try 34 - 9 = 25. Evaluate 25 != 44, drop this branch.\n     |- Try 34 * 9 = 306. Evaluate 306 != 44, drop this branch.\n     |- Try 34 \/ 9 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 37 * 3 = 111. Add 111 to the number set. Current number set: [111, 9], target: 44, just two numbers left.\n     |- Try 111 + 9 = 120. Evaluate 120 != 44, drop this branch.\n     |- Try 111 - 9 = 102. Evaluate 102 != 44, drop this branch.\n     |- Try 111 * 9 = 999. Evaluate 999 != 44, drop this branch.\n     |- Try 111 \/ 9 = 12.3. 12.3 is a decimal, drop this branch.\n    |- Try 37 \/ 3 = 12.3. 12.3 is a decimal, drop this branch.\n   |- Pick two numbers (37, 9) (numbers left: [3]). Try possible operations.\n    |- Try 37 + 9 = 46. Add 46 to the number set. Current number set: [46, 3], target: 44, just two numbers left.\n     |- Try 46 + 3 = 49. Evaluate 49 != 44, drop this branch.\n     |- Try 46 - 3 = 43. Evaluate 43 != 44, drop this branch.\n     |- Try 46 * 3 = 138. Evaluate 138 != 44, drop this branch.\n     |- Try 46 \/ 3 = 15.3. 15.3 is a decimal, drop this branch.\n    |- Try 37 - 9 = 28. Add 28 to the number set. Current number set: [28, 3], target: 44, just two numbers left.\n     |- Try 28 + 3 = 31. Evaluate 31 != 44, drop this branch.\n     |- Try 28 - 3 = 25. Evaluate 25 != 44, drop this branch.\n     |- Try 28 * 3 = 84. Evaluate 84 != 44, drop this branch.\n     |- Try 28 \/ 3 = 9.3. 9.3 is a decimal, drop this branch.\n    |- Try 37 * 9 = 333. Add 333 to the number set. Current number set: [333, 3], target: 44, just two numbers left.\n     |- Try 333 + 3 = 336. Evaluate 336 != 44, drop this branch.\n     |- Try 333 - 3 = 330. Evaluate 330 != 44, drop this branch.\n     |- Try 333 * 3 = 999. Evaluate 999 != 44, drop this branch.\n     |- Try 333 \/ 3 = 111. Evaluate 111 != 44, drop this branch.\n    |- Try 37 \/ 9 = 4.1. 4.1 is a decimal, drop this branch.\n   |- Pick two numbers (3, 9) (numbers left: [37]). Try possible operations.\n    |- Try 9 + 3 = 12. Add 12 to the number set. Current number set: [12, 37], target: 44, just two numbers left.\n     |- Try 37 + 12 = 49. Evaluate 49 != 44, drop this branch.\n     |- Try 37 - 12 = 25. Evaluate 25 != 44, drop this branch.\n     |- Try 37 * 12 = 444. Evaluate 444 != 44, drop this branch.\n     |- Try 37 \/ 12 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 9 - 3 = 6. Add 6 to the number set. Current number set: [6, 37], target: 44, just two numbers left.\n     |- Try 37 + 6 = 43. Evaluate 43 != 44, drop this branch.\n     |- Try 37 - 6 = 31. Evaluate 31 != 44, drop this branch.\n     |- Try 37 * 6 = 222. Evaluate 222 != 44, drop this branch.\n     |- Try 37 \/ 6 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 9 * 3 = 27. Add 27 to the number set. Current number set: [27, 37], target: 44, just two numbers left.\n     |- Try 37 + 27 = 64. Evaluate 64 != 44, drop this branch.\n     |- Try 37 - 27 = 10. Evaluate 10 != 44, drop this branch.\n     |- Try 37 * 27 = 999. Evaluate 999 != 44, drop this branch.\n     |- Try 37 \/ 27 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 9 \/ 3 = 3. Add 3 to the number set. Current number set: [3, 37], target: 44, just two numbers left.\n     |- Try 37 + 3 = 40. Evaluate 40 != 44, drop this branch.\n     |- Try 37 - 3 = 34. Evaluate 34 != 44, drop this branch.\n     |- Try 37 * 3 = 111. Evaluate 111 != 44, drop this branch.\n     |- Try 37 \/ 3 = 12.3. 12.3 is a decimal, drop this branch.\n  |- Try 47 * 10 = 470. Add 470 to the number set. Current number set: [470, 3, 9], target: 44. Options for choosing two numbers: [(470, 3), (470, 9), (3, 9)].\n   |- Pick two numbers (470, 3) (numbers left: [9]). Try possible operations.\n    |- Try 470 + 3 = 473. Add 473 to the number set. Current number set: [473, 9], target: 44, just two numbers left.\n     |- Try 473 + 9 = 482. Evaluate 482 != 44, drop this branch.\n     |- Try 473 - 9 = 464. Evaluate 464 != 44, drop this branch.\n     |- Try 473 * 9 = 4257. 4257 exceeds the maximum intermediate result, drop this branch.\n     |- Try 473 \/ 9 = 52.6. 52.6 is a decimal, drop this branch.\n    |- Try 470 - 3 = 467. Add 467 to the number set. Current number set: [467, 9], target: 44, just two numbers left.\n     |- Try 467 + 9 = 476. Evaluate 476 != 44, drop this branch.\n     |- Try 467 - 9 = 458. Evaluate 458 != 44, drop this branch.\n     |- Try 467 * 9 = 4203. 4203 exceeds the maximum intermediate result, drop this branch.\n     |- Try 467 \/ 9 = 51.9. 51.9 is a decimal, drop this branch.\n    |- Try 470 * 3 = 1410. Add 1410 to the number set. Current number set: [1410, 9], target: 44, just two numbers left.\n     |- Try 1410 + 9 = 1419. Evaluate 1419 != 44, drop this branch.\n     |- Try 1410 - 9 = 1401. Evaluate 1401 != 44, drop this branch.\n     |- Try 1410 * 9 = 12690. 12690 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1410 \/ 9 = 156.7. 156.7 is a decimal, drop this branch.\n    |- Try 470 \/ 3 = 156.7. 156.7 is a decimal, drop this branch.\n   |- Pick two numbers (470, 9) (numbers left: [3]). Try possible operations.\n    |- Try 470 + 9 = 479. Add 479 to the number set. Current number set: [479, 3], target: 44, just two numbers left.\n     |- Try 479 + 3 = 482. Evaluate 482 != 44, drop this branch.\n     |- Try 479 - 3 = 476. Evaluate 476 != 44, drop this branch.\n     |- Try 479 * 3 = 1437. Evaluate 1437 != 44, drop this branch.\n     |- Try 479 \/ 3 = 159.7. 159.7 is a decimal, drop this branch.\n    |- Try 470 - 9 = 461. Add 461 to the number set. Current number set: [461, 3], target: 44, just two numbers left.\n     |- Try 461 + 3 = 464. Evaluate 464 != 44, drop this branch.\n     |- Try 461 - 3 = 458. Evaluate 458 != 44, drop this branch.\n     |- Try 461 * 3 = 1383. Evaluate 1383 != 44, drop this branch.\n     |- Try 461 \/ 3 = 153.7. 153.7 is a decimal, drop this branch.\n    |- Try 470 * 9 = 4230. 4230 exceeds the maximum intermediate result, drop this branch.\n    |- Try 470 \/ 9 = 52.2. 52.2 is a decimal, drop this branch.\n   |- Pick two numbers (3, 9) (numbers left: [470]). Try possible operations.\n    |- Try 9 + 3 = 12. Add 12 to the number set. Current number set: [12, 470], target: 44, just two numbers left.\n     |- Try 470 + 12 = 482. Evaluate 482 != 44, drop this branch.\n     |- Try 470 - 12 = 458. Evaluate 458 != 44, drop this branch.\n     |- Try 470 * 12 = 5640. 5640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 470 \/ 12 = 39.2. 39.2 is a decimal, drop this branch.\n    |- Try 9 - 3 = 6. Add 6 to the number set. Current number set: [6, 470], target: 44, just two numbers left.\n     |- Try 470 + 6 = 476. Evaluate 476 != 44, drop this branch.\n     |- Try 470 - 6 = 464. Evaluate 464 != 44, drop this branch.\n     |- Try 470 * 6 = 2820. 2820 exceeds the maximum intermediate result, drop this branch.\n     |- Try 470 \/ 6 = 78.3. 78.3 is a decimal, drop this branch.\n    |- Try 9 * 3 = 27. Add 27 to the number set. Current number set: [27, 470], target: 44, just two numbers left.\n     |- Try 470 + 27 = 497. Evaluate 497 != 44, drop this branch.\n     |- Try 470 - 27 = 443. Evaluate 443 != 44, drop this branch.\n     |- Try 470 * 27 = 12690. 12690 exceeds the maximum intermediate result, drop this branch.\n     |- Try 470 \/ 27 = 17.4. 17.4 is a decimal, drop this branch.\n    |- Try 9 \/ 3 = 3. Add 3 to the number set. Current number set: [3, 470], target: 44, just two numbers left.\n     |- Try 470 + 3 = 473. Evaluate 473 != 44, drop this branch.\n     |- Try 470 - 3 = 467. Evaluate 467 != 44, drop this branch.\n     |- Try 470 * 3 = 1410. Evaluate 1410 != 44, drop this branch.\n     |- Try 470 \/ 3 = 156.7. 156.7 is a decimal, drop this branch.\n  |- Try 47 \/ 10 = 4.7. 4.7 is a decimal, drop this branch.\n |- Pick two numbers (47, 3) (numbers left: [10, 9]). Try possible operations.\n  |- Try 47 + 3 = 50. Add 50 to the number set. Current number set: [50, 10, 9], target: 44. Options for choosing two numbers: [(50, 10), (50, 9), (10, 9)].\n   |- Pick two numbers (50, 10) (numbers left: [9]). Try possible operations.\n    |- Try 50 + 10 = 60. Add 60 to the number set. Current number set: [60, 9], target: 44, just two numbers left.\n     |- Try 60 + 9 = 69. Evaluate 69 != 44, drop this branch.\n     |- Try 60 - 9 = 51. Evaluate 51 != 44, drop this branch.\n     |- Try 60 * 9 = 540. Evaluate 540 != 44, drop this branch.\n     |- Try 60 \/ 9 = 6.7. 6.7 is a decimal, drop this branch.\n    |- Try 50 - 10 = 40. Add 40 to the number set. Current number set: [40, 9], target: 44, just two numbers left.\n     |- Try 40 + 9 = 49. Evaluate 49 != 44, drop this branch.\n     |- Try 40 - 9 = 31. Evaluate 31 != 44, drop this branch.\n     |- Try 40 * 9 = 360. Evaluate 360 != 44, drop this branch.\n     |- Try 40 \/ 9 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 50 * 10 = 500. Add 500 to the number set. Current number set: [500, 9], target: 44, just two numbers left.\n     |- Try 500 + 9 = 509. Evaluate 509 != 44, drop this branch.\n     |- Try 500 - 9 = 491. Evaluate 491 != 44, drop this branch.\n     |- Try 500 * 9 = 4500. 4500 exceeds the maximum intermediate result, drop this branch.\n     |- Try 500 \/ 9 = 55.6. 55.6 is a decimal, drop this branch.\n    |- Try 50 \/ 10 = 5. Add 5 to the number set. Current number set: [5, 9], target: 44, just two numbers left.\n     |- Try 9 + 5 = 14. Evaluate 14 != 44, drop this branch.\n     |- Try 9 - 5 = 4. Evaluate 4 != 44, drop this branch.\n     |- Try 9 * 5 = 45. Evaluate 45 != 44, drop this branch.\n     |- Try 9 \/ 5 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (50, 9) (numbers left: [10]). Try possible operations.\n    |- Try 50 + 9 = 59. Add 59 to the number set. Current number set: [59, 10], target: 44, just two numbers left.\n     |- Try 59 + 10 = 69. Evaluate 69 != 44, drop this branch.\n     |- Try 59 - 10 = 49. Evaluate 49 != 44, drop this branch.\n     |- Try 59 * 10 = 590. Evaluate 590 != 44, drop this branch.\n     |- Try 59 \/ 10 = 5.9. 5.9 is a decimal, drop this branch.\n    |- Try 50 - 9 = 41. Add 41 to the number set. Current number set: [41, 10], target: 44, just two numbers left.\n     |- Try 41 + 10 = 51. Evaluate 51 != 44, drop this branch.\n     |- Try 41 - 10 = 31. Evaluate 31 != 44, drop this branch.\n     |- Try 41 * 10 = 410. Evaluate 410 != 44, drop this branch.\n     |- Try 41 \/ 10 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 50 * 9 = 450. Add 450 to the number set. Current number set: [450, 10], target: 44, just two numbers left.\n     |- Try 450 + 10 = 460. Evaluate 460 != 44, drop this branch.\n     |- Try 450 - 10 = 440. Evaluate 440 != 44, drop this branch.\n     |- Try 450 * 10 = 4500. 4500 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 10 = 45. Evaluate 45 != 44, drop this branch.\n    |- Try 50 \/ 9 = 5.6. 5.6 is a decimal, drop this branch.\n   |- Pick two numbers (10, 9) (numbers left: [50]). Try possible operations.\n    |- Try 10 + 9 = 19. Add 19 to the number set. Current number set: [19, 50], target: 44, just two numbers left.\n     |- Try 50 + 19 = 69. Evaluate 69 != 44, drop this branch.\n     |- Try 50 - 19 = 31. Evaluate 31 != 44, drop this branch.\n     |- Try 50 * 19 = 950. Evaluate 950 != 44, drop this branch.\n     |- Try 50 \/ 19 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 10 - 9 = 1. Add 1 to the number set. Current number set: [1, 50], target: 44, just two numbers left.\n     |- Try 50 + 1 = 51. Evaluate 51 != 44, drop this branch.\n     |- Try 50 - 1 = 49. Evaluate 49 != 44, drop this branch.\n     |- Try 50 * 1 = 50. Evaluate 50 != 44, drop this branch.\n     |- Try 50 \/ 1 = 50. Evaluate 50 != 44, drop this branch.\n    |- Try 10 * 9 = 90. Add 90 to the number set. Current number set: [90, 50], target: 44, just two numbers left.\n     |- Try 90 + 50 = 140. Evaluate 140 != 44, drop this branch.\n     |- Try 90 - 50 = 40. Evaluate 40 != 44, drop this branch.\n     |- Try 90 * 50 = 4500. 4500 exceeds the maximum intermediate result, drop this branch.\n     |- Try 90 \/ 50 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 10 \/ 9 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 47 - 3 = 44. Add 44 to the number set. Current number set: [44, 10, 9], target: 44. Options for choosing two numbers: [(44, 10), (44, 9), (10, 9)].\n   |- Pick two numbers (44, 10) (numbers left: [9]). Try possible operations.\n    |- Try 44 + 10 = 54. Add 54 to the number set. Current number set: [54, 9], target: 44, just two numbers left.\n     |- Try 54 + 9 = 63. Evaluate 63 != 44, drop this branch.\n     |- Try 54 - 9 = 45. Evaluate 45 != 44, drop this branch.\n     |- Try 54 * 9 = 486. Evaluate 486 != 44, drop this branch.\n     |- Try 54 \/ 9 = 6. Evaluate 6 != 44, drop this branch.\n    |- Try 44 - 10 = 34. Add 34 to the number set. Current number set: [34, 9], target: 44, just two numbers left.\n     |- Try 34 + 9 = 43. Evaluate 43 != 44, drop this branch.\n     |- Try 34 - 9 = 25. Evaluate 25 != 44, drop this branch.\n     |- Try 34 * 9 = 306. Evaluate 306 != 44, drop this branch.\n     |- Try 34 \/ 9 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 44 * 10 = 440. Add 440 to the number set. Current number set: [440, 9], target: 44, just two numbers left.\n     |- Try 440 + 9 = 449. Evaluate 449 != 44, drop this branch.\n     |- Try 440 - 9 = 431. Evaluate 431 != 44, drop this branch.\n     |- Try 440 * 9 = 3960. 3960 exceeds the maximum intermediate result, drop this branch.\n     |- Try 440 \/ 9 = 48.9. 48.9 is a decimal, drop this branch.\n    |- Try 44 \/ 10 = 4.4. 4.4 is a decimal, drop this branch.\n   |- Pick two numbers (44, 9) (numbers left: [10]). Try possible operations.\n    |- Try 44 + 9 = 53. Add 53 to the number set. Current number set: [53, 10], target: 44, just two numbers left.\n     |- Try 53 + 10 = 63. Evaluate 63 != 44, drop this branch.\n     |- Try 53 - 10 = 43. Evaluate 43 != 44, drop this branch.\n     |- Try 53 * 10 = 530. Evaluate 530 != 44, drop this branch.\n     |- Try 53 \/ 10 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 44 - 9 = 35. Add 35 to the number set. Current number set: [35, 10], target: 44, just two numbers left.\n     |- Try 35 + 10 = 45. Evaluate 45 != 44, drop this branch.\n     |- Try 35 - 10 = 25. Evaluate 25 != 44, drop this branch.\n     |- Try 35 * 10 = 350. Evaluate 350 != 44, drop this branch.\n     |- Try 35 \/ 10 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 44 * 9 = 396. Add 396 to the number set. Current number set: [396, 10], target: 44, just two numbers left.\n     |- Try 396 + 10 = 406. Evaluate 406 != 44, drop this branch.\n     |- Try 396 - 10 = 386. Evaluate 386 != 44, drop this branch.\n     |- Try 396 * 10 = 3960. 3960 exceeds the maximum intermediate result, drop this branch.\n     |- Try 396 \/ 10 = 39.6. 39.6 is a decimal, drop this branch.\n    |- Try 44 \/ 9 = 4.9. 4.9 is a decimal, drop this branch.\n   |- Pick two numbers (10, 9) (numbers left: [44]). Try possible operations.\n    |- Try 10 + 9 = 19. Add 19 to the number set. Current number set: [19, 44], target: 44, just two numbers left.\n     |- Try 44 + 19 = 63. Evaluate 63 != 44, drop this branch.\n     |- Try 44 - 19 = 25. Evaluate 25 != 44, drop this branch.\n     |- Try 44 * 19 = 836. Evaluate 836 != 44, drop this branch.\n     |- Try 44 \/ 19 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 10 - 9 = 1. Add 1 to the number set. Current number set: [1, 44], target: 44, just two numbers left.\n     |- Try 44 + 1 = 45. Evaluate 45 != 44, drop this branch.\n     |- Try 44 - 1 = 43. Evaluate 43 != 44, drop this branch.\n     |- Try 44 * 1 = 44. Evaluate 44 == 44, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 44 * 1 = 44\nThe step before: 10 - 9 = 1\nThe first step: 47 - 3 = 44\n\nOutput the solution in the required format:\n<Solution>\n47 - 3 = 44\n10 - 9 = 1\n44 * 1 = 44\n<\/Solution>\n","item":{"nums":[47,10,3,9],"solution":["47 - 3 = 44","10 - 9 = 1","44 * 1 = 44"],"target":44}}
+{"instance_id":"countdown_8k_149","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [49, 36, 23, 24]\nTarget: 22","reference_output":"# Search Procedure\nInitial number set: [49, 36, 23, 24], target: 22. Options for choosing two numbers: [(49, 36), (49, 23), (49, 24), (36, 23), (36, 24), (23, 24)].\n |- Pick two numbers (49, 36) (numbers left: [23, 24]). Try possible operations.\n  |- Try 49 + 36 = 85. Add 85 to the number set. Current number set: [85, 23, 24], target: 22. Options for choosing two numbers: [(85, 23), (85, 24), (23, 24)].\n   |- Pick two numbers (85, 23) (numbers left: [24]). Try possible operations.\n    |- Try 85 + 23 = 108. Add 108 to the number set. Current number set: [108, 24], target: 22, just two numbers left.\n     |- Try 108 + 24 = 132. Evaluate 132 != 22, drop this branch.\n     |- Try 108 - 24 = 84. Evaluate 84 != 22, drop this branch.\n     |- Try 108 * 24 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 24 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 85 - 23 = 62. Add 62 to the number set. Current number set: [62, 24], target: 22, just two numbers left.\n     |- Try 62 + 24 = 86. Evaluate 86 != 22, drop this branch.\n     |- Try 62 - 24 = 38. Evaluate 38 != 22, drop this branch.\n     |- Try 62 * 24 = 1488. Evaluate 1488 != 22, drop this branch.\n     |- Try 62 \/ 24 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 85 * 23 = 1955. Add 1955 to the number set. Current number set: [1955, 24], target: 22, just two numbers left.\n     |- Try 1955 + 24 = 1979. Evaluate 1979 != 22, drop this branch.\n     |- Try 1955 - 24 = 1931. Evaluate 1931 != 22, drop this branch.\n     |- Try 1955 * 24 = 46920. 46920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1955 \/ 24 = 81.5. 81.5 is a decimal, drop this branch.\n    |- Try 85 \/ 23 = 3.7. 3.7 is a decimal, drop this branch.\n   |- Pick two numbers (85, 24) (numbers left: [23]). Try possible operations.\n    |- Try 85 + 24 = 109. Add 109 to the number set. Current number set: [109, 23], target: 22, just two numbers left.\n     |- Try 109 + 23 = 132. Evaluate 132 != 22, drop this branch.\n     |- Try 109 - 23 = 86. Evaluate 86 != 22, drop this branch.\n     |- Try 109 * 23 = 2507. 2507 exceeds the maximum intermediate result, drop this branch.\n     |- Try 109 \/ 23 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 85 - 24 = 61. Add 61 to the number set. Current number set: [61, 23], target: 22, just two numbers left.\n     |- Try 61 + 23 = 84. Evaluate 84 != 22, drop this branch.\n     |- Try 61 - 23 = 38. Evaluate 38 != 22, drop this branch.\n     |- Try 61 * 23 = 1403. Evaluate 1403 != 22, drop this branch.\n     |- Try 61 \/ 23 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 85 * 24 = 2040. 2040 exceeds the maximum intermediate result, drop this branch.\n    |- Try 85 \/ 24 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (23, 24) (numbers left: [85]). Try possible operations.\n    |- Try 24 + 23 = 47. Add 47 to the number set. Current number set: [47, 85], target: 22, just two numbers left.\n     |- Try 85 + 47 = 132. Evaluate 132 != 22, drop this branch.\n     |- Try 85 - 47 = 38. Evaluate 38 != 22, drop this branch.\n     |- Try 85 * 47 = 3995. 3995 exceeds the maximum intermediate result, drop this branch.\n     |- Try 85 \/ 47 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 24 - 23 = 1. Add 1 to the number set. Current number set: [1, 85], target: 22, just two numbers left.\n     |- Try 85 + 1 = 86. Evaluate 86 != 22, drop this branch.\n     |- Try 85 - 1 = 84. Evaluate 84 != 22, drop this branch.\n     |- Try 85 * 1 = 85. Evaluate 85 != 22, drop this branch.\n     |- Try 85 \/ 1 = 85. Evaluate 85 != 22, drop this branch.\n    |- Try 24 * 23 = 552. Add 552 to the number set. Current number set: [552, 85], target: 22, just two numbers left.\n     |- Try 552 + 85 = 637. Evaluate 637 != 22, drop this branch.\n     |- Try 552 - 85 = 467. Evaluate 467 != 22, drop this branch.\n     |- Try 552 * 85 = 46920. 46920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 552 \/ 85 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 24 \/ 23 = 1.0. 1.0 is a decimal, drop this branch.\n  |- Try 49 - 36 = 13. Add 13 to the number set. Current number set: [13, 23, 24], target: 22. Options for choosing two numbers: [(13, 23), (13, 24), (23, 24)].\n   |- Pick two numbers (13, 23) (numbers left: [24]). Try possible operations.\n    |- Try 23 + 13 = 36. Add 36 to the number set. Current number set: [36, 24], target: 22, just two numbers left.\n     |- Try 36 + 24 = 60. Evaluate 60 != 22, drop this branch.\n     |- Try 36 - 24 = 12. Evaluate 12 != 22, drop this branch.\n     |- Try 36 * 24 = 864. Evaluate 864 != 22, drop this branch.\n     |- Try 36 \/ 24 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 23 - 13 = 10. Add 10 to the number set. Current number set: [10, 24], target: 22, just two numbers left.\n     |- Try 24 + 10 = 34. Evaluate 34 != 22, drop this branch.\n     |- Try 24 - 10 = 14. Evaluate 14 != 22, drop this branch.\n     |- Try 24 * 10 = 240. Evaluate 240 != 22, drop this branch.\n     |- Try 24 \/ 10 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 23 * 13 = 299. Add 299 to the number set. Current number set: [299, 24], target: 22, just two numbers left.\n     |- Try 299 + 24 = 323. Evaluate 323 != 22, drop this branch.\n     |- Try 299 - 24 = 275. Evaluate 275 != 22, drop this branch.\n     |- Try 299 * 24 = 7176. 7176 exceeds the maximum intermediate result, drop this branch.\n     |- Try 299 \/ 24 = 12.5. 12.5 is a decimal, drop this branch.\n    |- Try 23 \/ 13 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (13, 24) (numbers left: [23]). Try possible operations.\n    |- Try 24 + 13 = 37. Add 37 to the number set. Current number set: [37, 23], target: 22, just two numbers left.\n     |- Try 37 + 23 = 60. Evaluate 60 != 22, drop this branch.\n     |- Try 37 - 23 = 14. Evaluate 14 != 22, drop this branch.\n     |- Try 37 * 23 = 851. Evaluate 851 != 22, drop this branch.\n     |- Try 37 \/ 23 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 24 - 13 = 11. Add 11 to the number set. Current number set: [11, 23], target: 22, just two numbers left.\n     |- Try 23 + 11 = 34. Evaluate 34 != 22, drop this branch.\n     |- Try 23 - 11 = 12. Evaluate 12 != 22, drop this branch.\n     |- Try 23 * 11 = 253. Evaluate 253 != 22, drop this branch.\n     |- Try 23 \/ 11 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 24 * 13 = 312. Add 312 to the number set. Current number set: [312, 23], target: 22, just two numbers left.\n     |- Try 312 + 23 = 335. Evaluate 335 != 22, drop this branch.\n     |- Try 312 - 23 = 289. Evaluate 289 != 22, drop this branch.\n     |- Try 312 * 23 = 7176. 7176 exceeds the maximum intermediate result, drop this branch.\n     |- Try 312 \/ 23 = 13.6. 13.6 is a decimal, drop this branch.\n    |- Try 24 \/ 13 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (23, 24) (numbers left: [13]). Try possible operations.\n    |- Try 24 + 23 = 47. Add 47 to the number set. Current number set: [47, 13], target: 22, just two numbers left.\n     |- Try 47 + 13 = 60. Evaluate 60 != 22, drop this branch.\n     |- Try 47 - 13 = 34. Evaluate 34 != 22, drop this branch.\n     |- Try 47 * 13 = 611. Evaluate 611 != 22, drop this branch.\n     |- Try 47 \/ 13 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 24 - 23 = 1. Add 1 to the number set. Current number set: [1, 13], target: 22, just two numbers left.\n     |- Try 13 + 1 = 14. Evaluate 14 != 22, drop this branch.\n     |- Try 13 - 1 = 12. Evaluate 12 != 22, drop this branch.\n     |- Try 13 * 1 = 13. Evaluate 13 != 22, drop this branch.\n     |- Try 13 \/ 1 = 13. Evaluate 13 != 22, drop this branch.\n    |- Try 24 * 23 = 552. Add 552 to the number set. Current number set: [552, 13], target: 22, just two numbers left.\n     |- Try 552 + 13 = 565. Evaluate 565 != 22, drop this branch.\n     |- Try 552 - 13 = 539. Evaluate 539 != 22, drop this branch.\n     |- Try 552 * 13 = 7176. 7176 exceeds the maximum intermediate result, drop this branch.\n     |- Try 552 \/ 13 = 42.5. 42.5 is a decimal, drop this branch.\n    |- Try 24 \/ 23 = 1.0. 1.0 is a decimal, drop this branch.\n  |- Try 49 * 36 = 1764. Add 1764 to the number set. Current number set: [1764, 23, 24], target: 22. Options for choosing two numbers: [(1764, 23), (1764, 24), (23, 24)].\n   |- Pick two numbers (1764, 23) (numbers left: [24]). Try possible operations.\n    |- Try 1764 + 23 = 1787. Add 1787 to the number set. Current number set: [1787, 24], target: 22, just two numbers left.\n     |- Try 1787 + 24 = 1811. Evaluate 1811 != 22, drop this branch.\n     |- Try 1787 - 24 = 1763. Evaluate 1763 != 22, drop this branch.\n     |- Try 1787 * 24 = 42888. 42888 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1787 \/ 24 = 74.5. 74.5 is a decimal, drop this branch.\n    |- Try 1764 - 23 = 1741. Add 1741 to the number set. Current number set: [1741, 24], target: 22, just two numbers left.\n     |- Try 1741 + 24 = 1765. Evaluate 1765 != 22, drop this branch.\n     |- Try 1741 - 24 = 1717. Evaluate 1717 != 22, drop this branch.\n     |- Try 1741 * 24 = 41784. 41784 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1741 \/ 24 = 72.5. 72.5 is a decimal, drop this branch.\n    |- Try 1764 * 23 = 40572. 40572 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1764 \/ 23 = 76.7. 76.7 is a decimal, drop this branch.\n   |- Pick two numbers (1764, 24) (numbers left: [23]). Try possible operations.\n    |- Try 1764 + 24 = 1788. Add 1788 to the number set. Current number set: [1788, 23], target: 22, just two numbers left.\n     |- Try 1788 + 23 = 1811. Evaluate 1811 != 22, drop this branch.\n     |- Try 1788 - 23 = 1765. Evaluate 1765 != 22, drop this branch.\n     |- Try 1788 * 23 = 41124. 41124 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1788 \/ 23 = 77.7. 77.7 is a decimal, drop this branch.\n    |- Try 1764 - 24 = 1740. Add 1740 to the number set. Current number set: [1740, 23], target: 22, just two numbers left.\n     |- Try 1740 + 23 = 1763. Evaluate 1763 != 22, drop this branch.\n     |- Try 1740 - 23 = 1717. Evaluate 1717 != 22, drop this branch.\n     |- Try 1740 * 23 = 40020. 40020 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1740 \/ 23 = 75.7. 75.7 is a decimal, drop this branch.\n    |- Try 1764 * 24 = 42336. 42336 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1764 \/ 24 = 73.5. 73.5 is a decimal, drop this branch.\n   |- Pick two numbers (23, 24) (numbers left: [1764]). Try possible operations.\n    |- Try 24 + 23 = 47. Add 47 to the number set. Current number set: [47, 1764], target: 22, just two numbers left.\n     |- Try 1764 + 47 = 1811. Evaluate 1811 != 22, drop this branch.\n     |- Try 1764 - 47 = 1717. Evaluate 1717 != 22, drop this branch.\n     |- Try 1764 * 47 = 82908. 82908 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1764 \/ 47 = 37.5. 37.5 is a decimal, drop this branch.\n    |- Try 24 - 23 = 1. Add 1 to the number set. Current number set: [1, 1764], target: 22, just two numbers left.\n     |- Try 1764 + 1 = 1765. Evaluate 1765 != 22, drop this branch.\n     |- Try 1764 - 1 = 1763. Evaluate 1763 != 22, drop this branch.\n     |- Try 1764 * 1 = 1764. Evaluate 1764 != 22, drop this branch.\n     |- Try 1764 \/ 1 = 1764. Evaluate 1764 != 22, drop this branch.\n    |- Try 24 * 23 = 552. Add 552 to the number set. Current number set: [552, 1764], target: 22, just two numbers left.\n     |- Try 1764 + 552 = 2316. 2316 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1764 - 552 = 1212. Evaluate 1212 != 22, drop this branch.\n     |- Try 1764 * 552 = 973728. 973728 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1764 \/ 552 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 24 \/ 23 = 1.0. 1.0 is a decimal, drop this branch.\n  |- Try 49 \/ 36 = 1.4. 1.4 is a decimal, drop this branch.\n |- Pick two numbers (49, 23) (numbers left: [36, 24]). Try possible operations.\n  |- Try 49 + 23 = 72. Add 72 to the number set. Current number set: [72, 36, 24], target: 22. Options for choosing two numbers: [(72, 36), (72, 24), (36, 24)].\n   |- Pick two numbers (72, 36) (numbers left: [24]). Try possible operations.\n    |- Try 72 + 36 = 108. Add 108 to the number set. Current number set: [108, 24], target: 22, just two numbers left.\n     |- Try 108 + 24 = 132. Evaluate 132 != 22, drop this branch.\n     |- Try 108 - 24 = 84. Evaluate 84 != 22, drop this branch.\n     |- Try 108 * 24 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 24 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 72 - 36 = 36. Add 36 to the number set. Current number set: [36, 24], target: 22, just two numbers left.\n     |- Try 36 + 24 = 60. Evaluate 60 != 22, drop this branch.\n     |- Try 36 - 24 = 12. Evaluate 12 != 22, drop this branch.\n     |- Try 36 * 24 = 864. Evaluate 864 != 22, drop this branch.\n     |- Try 36 \/ 24 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 72 * 36 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 72 \/ 36 = 2. Add 2 to the number set. Current number set: [2, 24], target: 22, just two numbers left.\n     |- Try 24 + 2 = 26. Evaluate 26 != 22, drop this branch.\n     |- Try 24 - 2 = 22. Evaluate 22 == 22, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 24 - 2 = 22\nThe step before: 72 \/ 36 = 2\nThe first step: 49 + 23 = 72\n\nOutput the solution in the required format:\n<Solution>\n49 + 23 = 72\n72 \/ 36 = 2\n24 - 2 = 22\n<\/Solution>\n","item":{"nums":[49,36,23,24],"solution":["49 + 23 = 72","72 \/ 36 = 2","24 - 2 = 22"],"target":22}}
+{"instance_id":"countdown_8k_150","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [45, 9, 19, 3]\nTarget: 27","reference_output":"# Search Procedure\nInitial number set: [45, 9, 19, 3], target: 27. Options for choosing two numbers: [(45, 9), (45, 19), (45, 3), (9, 19), (9, 3), (19, 3)].\n |- Pick two numbers (45, 9) (numbers left: [19, 3]). Try possible operations.\n  |- Try 45 + 9 = 54. Add 54 to the number set. Current number set: [54, 19, 3], target: 27. Options for choosing two numbers: [(54, 19), (54, 3), (19, 3)].\n   |- Pick two numbers (54, 19) (numbers left: [3]). Try possible operations.\n    |- Try 54 + 19 = 73. Add 73 to the number set. Current number set: [73, 3], target: 27, just two numbers left.\n     |- Try 73 + 3 = 76. Evaluate 76 != 27, drop this branch.\n     |- Try 73 - 3 = 70. Evaluate 70 != 27, drop this branch.\n     |- Try 73 * 3 = 219. Evaluate 219 != 27, drop this branch.\n     |- Try 73 \/ 3 = 24.3. 24.3 is a decimal, drop this branch.\n    |- Try 54 - 19 = 35. Add 35 to the number set. Current number set: [35, 3], target: 27, just two numbers left.\n     |- Try 35 + 3 = 38. Evaluate 38 != 27, drop this branch.\n     |- Try 35 - 3 = 32. Evaluate 32 != 27, drop this branch.\n     |- Try 35 * 3 = 105. Evaluate 105 != 27, drop this branch.\n     |- Try 35 \/ 3 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 54 * 19 = 1026. Add 1026 to the number set. Current number set: [1026, 3], target: 27, just two numbers left.\n     |- Try 1026 + 3 = 1029. Evaluate 1029 != 27, drop this branch.\n     |- Try 1026 - 3 = 1023. Evaluate 1023 != 27, drop this branch.\n     |- Try 1026 * 3 = 3078. 3078 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1026 \/ 3 = 342. Evaluate 342 != 27, drop this branch.\n    |- Try 54 \/ 19 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (54, 3) (numbers left: [19]). Try possible operations.\n    |- Try 54 + 3 = 57. Add 57 to the number set. Current number set: [57, 19], target: 27, just two numbers left.\n     |- Try 57 + 19 = 76. Evaluate 76 != 27, drop this branch.\n     |- Try 57 - 19 = 38. Evaluate 38 != 27, drop this branch.\n     |- Try 57 * 19 = 1083. Evaluate 1083 != 27, drop this branch.\n     |- Try 57 \/ 19 = 3. Evaluate 3 != 27, drop this branch.\n    |- Try 54 - 3 = 51. Add 51 to the number set. Current number set: [51, 19], target: 27, just two numbers left.\n     |- Try 51 + 19 = 70. Evaluate 70 != 27, drop this branch.\n     |- Try 51 - 19 = 32. Evaluate 32 != 27, drop this branch.\n     |- Try 51 * 19 = 969. Evaluate 969 != 27, drop this branch.\n     |- Try 51 \/ 19 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 54 * 3 = 162. Add 162 to the number set. Current number set: [162, 19], target: 27, just two numbers left.\n     |- Try 162 + 19 = 181. Evaluate 181 != 27, drop this branch.\n     |- Try 162 - 19 = 143. Evaluate 143 != 27, drop this branch.\n     |- Try 162 * 19 = 3078. 3078 exceeds the maximum intermediate result, drop this branch.\n     |- Try 162 \/ 19 = 8.5. 8.5 is a decimal, drop this branch.\n    |- Try 54 \/ 3 = 18. Add 18 to the number set. Current number set: [18, 19], target: 27, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 27, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 27, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 27, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (19, 3) (numbers left: [54]). Try possible operations.\n    |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 54], target: 27, just two numbers left.\n     |- Try 54 + 22 = 76. Evaluate 76 != 27, drop this branch.\n     |- Try 54 - 22 = 32. Evaluate 32 != 27, drop this branch.\n     |- Try 54 * 22 = 1188. Evaluate 1188 != 27, drop this branch.\n     |- Try 54 \/ 22 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 54], target: 27, just two numbers left.\n     |- Try 54 + 16 = 70. Evaluate 70 != 27, drop this branch.\n     |- Try 54 - 16 = 38. Evaluate 38 != 27, drop this branch.\n     |- Try 54 * 16 = 864. Evaluate 864 != 27, drop this branch.\n     |- Try 54 \/ 16 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 19 * 3 = 57. Add 57 to the number set. Current number set: [57, 54], target: 27, just two numbers left.\n     |- Try 57 + 54 = 111. Evaluate 111 != 27, drop this branch.\n     |- Try 57 - 54 = 3. Evaluate 3 != 27, drop this branch.\n     |- Try 57 * 54 = 3078. 3078 exceeds the maximum intermediate result, drop this branch.\n     |- Try 57 \/ 54 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 19 \/ 3 = 6.3. 6.3 is a decimal, drop this branch.\n  |- Try 45 - 9 = 36. Add 36 to the number set. Current number set: [36, 19, 3], target: 27. Options for choosing two numbers: [(36, 19), (36, 3), (19, 3)].\n   |- Pick two numbers (36, 19) (numbers left: [3]). Try possible operations.\n    |- Try 36 + 19 = 55. Add 55 to the number set. Current number set: [55, 3], target: 27, just two numbers left.\n     |- Try 55 + 3 = 58. Evaluate 58 != 27, drop this branch.\n     |- Try 55 - 3 = 52. Evaluate 52 != 27, drop this branch.\n     |- Try 55 * 3 = 165. Evaluate 165 != 27, drop this branch.\n     |- Try 55 \/ 3 = 18.3. 18.3 is a decimal, drop this branch.\n    |- Try 36 - 19 = 17. Add 17 to the number set. Current number set: [17, 3], target: 27, just two numbers left.\n     |- Try 17 + 3 = 20. Evaluate 20 != 27, drop this branch.\n     |- Try 17 - 3 = 14. Evaluate 14 != 27, drop this branch.\n     |- Try 17 * 3 = 51. Evaluate 51 != 27, drop this branch.\n     |- Try 17 \/ 3 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 36 * 19 = 684. Add 684 to the number set. Current number set: [684, 3], target: 27, just two numbers left.\n     |- Try 684 + 3 = 687. Evaluate 687 != 27, drop this branch.\n     |- Try 684 - 3 = 681. Evaluate 681 != 27, drop this branch.\n     |- Try 684 * 3 = 2052. 2052 exceeds the maximum intermediate result, drop this branch.\n     |- Try 684 \/ 3 = 228. Evaluate 228 != 27, drop this branch.\n    |- Try 36 \/ 19 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (36, 3) (numbers left: [19]). Try possible operations.\n    |- Try 36 + 3 = 39. Add 39 to the number set. Current number set: [39, 19], target: 27, just two numbers left.\n     |- Try 39 + 19 = 58. Evaluate 58 != 27, drop this branch.\n     |- Try 39 - 19 = 20. Evaluate 20 != 27, drop this branch.\n     |- Try 39 * 19 = 741. Evaluate 741 != 27, drop this branch.\n     |- Try 39 \/ 19 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 36 - 3 = 33. Add 33 to the number set. Current number set: [33, 19], target: 27, just two numbers left.\n     |- Try 33 + 19 = 52. Evaluate 52 != 27, drop this branch.\n     |- Try 33 - 19 = 14. Evaluate 14 != 27, drop this branch.\n     |- Try 33 * 19 = 627. Evaluate 627 != 27, drop this branch.\n     |- Try 33 \/ 19 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 36 * 3 = 108. Add 108 to the number set. Current number set: [108, 19], target: 27, just two numbers left.\n     |- Try 108 + 19 = 127. Evaluate 127 != 27, drop this branch.\n     |- Try 108 - 19 = 89. Evaluate 89 != 27, drop this branch.\n     |- Try 108 * 19 = 2052. 2052 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 19 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 36 \/ 3 = 12. Add 12 to the number set. Current number set: [12, 19], target: 27, just two numbers left.\n     |- Try 19 + 12 = 31. Evaluate 31 != 27, drop this branch.\n     |- Try 19 - 12 = 7. Evaluate 7 != 27, drop this branch.\n     |- Try 19 * 12 = 228. Evaluate 228 != 27, drop this branch.\n     |- Try 19 \/ 12 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (19, 3) (numbers left: [36]). Try possible operations.\n    |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 36], target: 27, just two numbers left.\n     |- Try 36 + 22 = 58. Evaluate 58 != 27, drop this branch.\n     |- Try 36 - 22 = 14. Evaluate 14 != 27, drop this branch.\n     |- Try 36 * 22 = 792. Evaluate 792 != 27, drop this branch.\n     |- Try 36 \/ 22 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 36], target: 27, just two numbers left.\n     |- Try 36 + 16 = 52. Evaluate 52 != 27, drop this branch.\n     |- Try 36 - 16 = 20. Evaluate 20 != 27, drop this branch.\n     |- Try 36 * 16 = 576. Evaluate 576 != 27, drop this branch.\n     |- Try 36 \/ 16 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 19 * 3 = 57. Add 57 to the number set. Current number set: [57, 36], target: 27, just two numbers left.\n     |- Try 57 + 36 = 93. Evaluate 93 != 27, drop this branch.\n     |- Try 57 - 36 = 21. Evaluate 21 != 27, drop this branch.\n     |- Try 57 * 36 = 2052. 2052 exceeds the maximum intermediate result, drop this branch.\n     |- Try 57 \/ 36 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 19 \/ 3 = 6.3. 6.3 is a decimal, drop this branch.\n  |- Try 45 * 9 = 405. Add 405 to the number set. Current number set: [405, 19, 3], target: 27. Options for choosing two numbers: [(405, 19), (405, 3), (19, 3)].\n   |- Pick two numbers (405, 19) (numbers left: [3]). Try possible operations.\n    |- Try 405 + 19 = 424. Add 424 to the number set. Current number set: [424, 3], target: 27, just two numbers left.\n     |- Try 424 + 3 = 427. Evaluate 427 != 27, drop this branch.\n     |- Try 424 - 3 = 421. Evaluate 421 != 27, drop this branch.\n     |- Try 424 * 3 = 1272. Evaluate 1272 != 27, drop this branch.\n     |- Try 424 \/ 3 = 141.3. 141.3 is a decimal, drop this branch.\n    |- Try 405 - 19 = 386. Add 386 to the number set. Current number set: [386, 3], target: 27, just two numbers left.\n     |- Try 386 + 3 = 389. Evaluate 389 != 27, drop this branch.\n     |- Try 386 - 3 = 383. Evaluate 383 != 27, drop this branch.\n     |- Try 386 * 3 = 1158. Evaluate 1158 != 27, drop this branch.\n     |- Try 386 \/ 3 = 128.7. 128.7 is a decimal, drop this branch.\n    |- Try 405 * 19 = 7695. 7695 exceeds the maximum intermediate result, drop this branch.\n    |- Try 405 \/ 19 = 21.3. 21.3 is a decimal, drop this branch.\n   |- Pick two numbers (405, 3) (numbers left: [19]). Try possible operations.\n    |- Try 405 + 3 = 408. Add 408 to the number set. Current number set: [408, 19], target: 27, just two numbers left.\n     |- Try 408 + 19 = 427. Evaluate 427 != 27, drop this branch.\n     |- Try 408 - 19 = 389. Evaluate 389 != 27, drop this branch.\n     |- Try 408 * 19 = 7752. 7752 exceeds the maximum intermediate result, drop this branch.\n     |- Try 408 \/ 19 = 21.5. 21.5 is a decimal, drop this branch.\n    |- Try 405 - 3 = 402. Add 402 to the number set. Current number set: [402, 19], target: 27, just two numbers left.\n     |- Try 402 + 19 = 421. Evaluate 421 != 27, drop this branch.\n     |- Try 402 - 19 = 383. Evaluate 383 != 27, drop this branch.\n     |- Try 402 * 19 = 7638. 7638 exceeds the maximum intermediate result, drop this branch.\n     |- Try 402 \/ 19 = 21.2. 21.2 is a decimal, drop this branch.\n    |- Try 405 * 3 = 1215. Add 1215 to the number set. Current number set: [1215, 19], target: 27, just two numbers left.\n     |- Try 1215 + 19 = 1234. Evaluate 1234 != 27, drop this branch.\n     |- Try 1215 - 19 = 1196. Evaluate 1196 != 27, drop this branch.\n     |- Try 1215 * 19 = 23085. 23085 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1215 \/ 19 = 63.9. 63.9 is a decimal, drop this branch.\n    |- Try 405 \/ 3 = 135. Add 135 to the number set. Current number set: [135, 19], target: 27, just two numbers left.\n     |- Try 135 + 19 = 154. Evaluate 154 != 27, drop this branch.\n     |- Try 135 - 19 = 116. Evaluate 116 != 27, drop this branch.\n     |- Try 135 * 19 = 2565. 2565 exceeds the maximum intermediate result, drop this branch.\n     |- Try 135 \/ 19 = 7.1. 7.1 is a decimal, drop this branch.\n   |- Pick two numbers (19, 3) (numbers left: [405]). Try possible operations.\n    |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 405], target: 27, just two numbers left.\n     |- Try 405 + 22 = 427. Evaluate 427 != 27, drop this branch.\n     |- Try 405 - 22 = 383. Evaluate 383 != 27, drop this branch.\n     |- Try 405 * 22 = 8910. 8910 exceeds the maximum intermediate result, drop this branch.\n     |- Try 405 \/ 22 = 18.4. 18.4 is a decimal, drop this branch.\n    |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 405], target: 27, just two numbers left.\n     |- Try 405 + 16 = 421. Evaluate 421 != 27, drop this branch.\n     |- Try 405 - 16 = 389. Evaluate 389 != 27, drop this branch.\n     |- Try 405 * 16 = 6480. 6480 exceeds the maximum intermediate result, drop this branch.\n     |- Try 405 \/ 16 = 25.3. 25.3 is a decimal, drop this branch.\n    |- Try 19 * 3 = 57. Add 57 to the number set. Current number set: [57, 405], target: 27, just two numbers left.\n     |- Try 405 + 57 = 462. Evaluate 462 != 27, drop this branch.\n     |- Try 405 - 57 = 348. Evaluate 348 != 27, drop this branch.\n     |- Try 405 * 57 = 23085. 23085 exceeds the maximum intermediate result, drop this branch.\n     |- Try 405 \/ 57 = 7.1. 7.1 is a decimal, drop this branch.\n    |- Try 19 \/ 3 = 6.3. 6.3 is a decimal, drop this branch.\n  |- Try 45 \/ 9 = 5. Add 5 to the number set. Current number set: [5, 19, 3], target: 27. Options for choosing two numbers: [(5, 19), (5, 3), (19, 3)].\n   |- Pick two numbers (5, 19) (numbers left: [3]). Try possible operations.\n    |- Try 19 + 5 = 24. Add 24 to the number set. Current number set: [24, 3], target: 27, just two numbers left.\n     |- Try 24 + 3 = 27. Evaluate 27 == 27, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 24 + 3 = 27\nThe step before: 19 + 5 = 24\nThe first step: 45 \/ 9 = 5\n\nOutput the solution in the required format:\n<Solution>\n45 \/ 9 = 5\n19 + 5 = 24\n24 + 3 = 27\n<\/Solution>\n","item":{"nums":[45,9,19,3],"solution":["45 \/ 9 = 5","19 + 5 = 24","24 + 3 = 27"],"target":27}}
+{"instance_id":"countdown_8k_151","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [9, 16, 6, 18]\nTarget: 12","reference_output":"# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n","item":{"nums":[9,16,6,18],"solution":["16 * 9 = 144","18 - 6 = 12","144 \/ 12 = 12"],"target":12}}
+{"instance_id":"countdown_8k_152","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [3, 39, 10, 12]\nTarget: 15","reference_output":"# Search Procedure\nInitial number set: [3, 39, 10, 12], target: 15. Options for choosing two numbers: [(3, 39), (3, 10), (3, 12), (39, 10), (39, 12), (10, 12)].\n |- Pick two numbers (3, 39) (numbers left: [10, 12]). Try possible operations.\n  |- Try 39 + 3 = 42. Add 42 to the number set. Current number set: [42, 10, 12], target: 15. Options for choosing two numbers: [(42, 10), (42, 12), (10, 12)].\n   |- Pick two numbers (42, 10) (numbers left: [12]). Try possible operations.\n    |- Try 42 + 10 = 52. Add 52 to the number set. Current number set: [52, 12], target: 15, just two numbers left.\n     |- Try 52 + 12 = 64. Evaluate 64 != 15, drop this branch.\n     |- Try 52 - 12 = 40. Evaluate 40 != 15, drop this branch.\n     |- Try 52 * 12 = 624. Evaluate 624 != 15, drop this branch.\n     |- Try 52 \/ 12 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 42 - 10 = 32. Add 32 to the number set. Current number set: [32, 12], target: 15, just two numbers left.\n     |- Try 32 + 12 = 44. Evaluate 44 != 15, drop this branch.\n     |- Try 32 - 12 = 20. Evaluate 20 != 15, drop this branch.\n     |- Try 32 * 12 = 384. Evaluate 384 != 15, drop this branch.\n     |- Try 32 \/ 12 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 42 * 10 = 420. Add 420 to the number set. Current number set: [420, 12], target: 15, just two numbers left.\n     |- Try 420 + 12 = 432. Evaluate 432 != 15, drop this branch.\n     |- Try 420 - 12 = 408. Evaluate 408 != 15, drop this branch.\n     |- Try 420 * 12 = 5040. 5040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 420 \/ 12 = 35. Evaluate 35 != 15, drop this branch.\n    |- Try 42 \/ 10 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (42, 12) (numbers left: [10]). Try possible operations.\n    |- Try 42 + 12 = 54. Add 54 to the number set. Current number set: [54, 10], target: 15, just two numbers left.\n     |- Try 54 + 10 = 64. Evaluate 64 != 15, drop this branch.\n     |- Try 54 - 10 = 44. Evaluate 44 != 15, drop this branch.\n     |- Try 54 * 10 = 540. Evaluate 540 != 15, drop this branch.\n     |- Try 54 \/ 10 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 42 - 12 = 30. Add 30 to the number set. Current number set: [30, 10], target: 15, just two numbers left.\n     |- Try 30 + 10 = 40. Evaluate 40 != 15, drop this branch.\n     |- Try 30 - 10 = 20. Evaluate 20 != 15, drop this branch.\n     |- Try 30 * 10 = 300. Evaluate 300 != 15, drop this branch.\n     |- Try 30 \/ 10 = 3. Evaluate 3 != 15, drop this branch.\n    |- Try 42 * 12 = 504. Add 504 to the number set. Current number set: [504, 10], target: 15, just two numbers left.\n     |- Try 504 + 10 = 514. Evaluate 514 != 15, drop this branch.\n     |- Try 504 - 10 = 494. Evaluate 494 != 15, drop this branch.\n     |- Try 504 * 10 = 5040. 5040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 504 \/ 10 = 50.4. 50.4 is a decimal, drop this branch.\n    |- Try 42 \/ 12 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (10, 12) (numbers left: [42]). Try possible operations.\n    |- Try 12 + 10 = 22. Add 22 to the number set. Current number set: [22, 42], target: 15, just two numbers left.\n     |- Try 42 + 22 = 64. Evaluate 64 != 15, drop this branch.\n     |- Try 42 - 22 = 20. Evaluate 20 != 15, drop this branch.\n     |- Try 42 * 22 = 924. Evaluate 924 != 15, drop this branch.\n     |- Try 42 \/ 22 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 12 - 10 = 2. Add 2 to the number set. Current number set: [2, 42], target: 15, just two numbers left.\n     |- Try 42 + 2 = 44. Evaluate 44 != 15, drop this branch.\n     |- Try 42 - 2 = 40. Evaluate 40 != 15, drop this branch.\n     |- Try 42 * 2 = 84. Evaluate 84 != 15, drop this branch.\n     |- Try 42 \/ 2 = 21. Evaluate 21 != 15, drop this branch.\n    |- Try 12 * 10 = 120. Add 120 to the number set. Current number set: [120, 42], target: 15, just two numbers left.\n     |- Try 120 + 42 = 162. Evaluate 162 != 15, drop this branch.\n     |- Try 120 - 42 = 78. Evaluate 78 != 15, drop this branch.\n     |- Try 120 * 42 = 5040. 5040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 120 \/ 42 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 12 \/ 10 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 39 - 3 = 36. Add 36 to the number set. Current number set: [36, 10, 12], target: 15. Options for choosing two numbers: [(36, 10), (36, 12), (10, 12)].\n   |- Pick two numbers (36, 10) (numbers left: [12]). Try possible operations.\n    |- Try 36 + 10 = 46. Add 46 to the number set. Current number set: [46, 12], target: 15, just two numbers left.\n     |- Try 46 + 12 = 58. Evaluate 58 != 15, drop this branch.\n     |- Try 46 - 12 = 34. Evaluate 34 != 15, drop this branch.\n     |- Try 46 * 12 = 552. Evaluate 552 != 15, drop this branch.\n     |- Try 46 \/ 12 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 36 - 10 = 26. Add 26 to the number set. Current number set: [26, 12], target: 15, just two numbers left.\n     |- Try 26 + 12 = 38. Evaluate 38 != 15, drop this branch.\n     |- Try 26 - 12 = 14. Evaluate 14 != 15, drop this branch.\n     |- Try 26 * 12 = 312. Evaluate 312 != 15, drop this branch.\n     |- Try 26 \/ 12 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 36 * 10 = 360. Add 360 to the number set. Current number set: [360, 12], target: 15, just two numbers left.\n     |- Try 360 + 12 = 372. Evaluate 372 != 15, drop this branch.\n     |- Try 360 - 12 = 348. Evaluate 348 != 15, drop this branch.\n     |- Try 360 * 12 = 4320. 4320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 360 \/ 12 = 30. Evaluate 30 != 15, drop this branch.\n    |- Try 36 \/ 10 = 3.6. 3.6 is a decimal, drop this branch.\n   |- Pick two numbers (36, 12) (numbers left: [10]). Try possible operations.\n    |- Try 36 + 12 = 48. Add 48 to the number set. Current number set: [48, 10], target: 15, just two numbers left.\n     |- Try 48 + 10 = 58. Evaluate 58 != 15, drop this branch.\n     |- Try 48 - 10 = 38. Evaluate 38 != 15, drop this branch.\n     |- Try 48 * 10 = 480. Evaluate 480 != 15, drop this branch.\n     |- Try 48 \/ 10 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 36 - 12 = 24. Add 24 to the number set. Current number set: [24, 10], target: 15, just two numbers left.\n     |- Try 24 + 10 = 34. Evaluate 34 != 15, drop this branch.\n     |- Try 24 - 10 = 14. Evaluate 14 != 15, drop this branch.\n     |- Try 24 * 10 = 240. Evaluate 240 != 15, drop this branch.\n     |- Try 24 \/ 10 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 36 * 12 = 432. Add 432 to the number set. Current number set: [432, 10], target: 15, just two numbers left.\n     |- Try 432 + 10 = 442. Evaluate 442 != 15, drop this branch.\n     |- Try 432 - 10 = 422. Evaluate 422 != 15, drop this branch.\n     |- Try 432 * 10 = 4320. 4320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 432 \/ 10 = 43.2. 43.2 is a decimal, drop this branch.\n    |- Try 36 \/ 12 = 3. Add 3 to the number set. Current number set: [3, 10], target: 15, just two numbers left.\n     |- Try 10 + 3 = 13. Evaluate 13 != 15, drop this branch.\n     |- Try 10 - 3 = 7. Evaluate 7 != 15, drop this branch.\n     |- Try 10 * 3 = 30. Evaluate 30 != 15, drop this branch.\n     |- Try 10 \/ 3 = 3.3. 3.3 is a decimal, drop this branch.\n   |- Pick two numbers (10, 12) (numbers left: [36]). Try possible operations.\n    |- Try 12 + 10 = 22. Add 22 to the number set. Current number set: [22, 36], target: 15, just two numbers left.\n     |- Try 36 + 22 = 58. Evaluate 58 != 15, drop this branch.\n     |- Try 36 - 22 = 14. Evaluate 14 != 15, drop this branch.\n     |- Try 36 * 22 = 792. Evaluate 792 != 15, drop this branch.\n     |- Try 36 \/ 22 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 12 - 10 = 2. Add 2 to the number set. Current number set: [2, 36], target: 15, just two numbers left.\n     |- Try 36 + 2 = 38. Evaluate 38 != 15, drop this branch.\n     |- Try 36 - 2 = 34. Evaluate 34 != 15, drop this branch.\n     |- Try 36 * 2 = 72. Evaluate 72 != 15, drop this branch.\n     |- Try 36 \/ 2 = 18. Evaluate 18 != 15, drop this branch.\n    |- Try 12 * 10 = 120. Add 120 to the number set. Current number set: [120, 36], target: 15, just two numbers left.\n     |- Try 120 + 36 = 156. Evaluate 156 != 15, drop this branch.\n     |- Try 120 - 36 = 84. Evaluate 84 != 15, drop this branch.\n     |- Try 120 * 36 = 4320. 4320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 120 \/ 36 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 12 \/ 10 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 39 * 3 = 117. Add 117 to the number set. Current number set: [117, 10, 12], target: 15. Options for choosing two numbers: [(117, 10), (117, 12), (10, 12)].\n   |- Pick two numbers (117, 10) (numbers left: [12]). Try possible operations.\n    |- Try 117 + 10 = 127. Add 127 to the number set. Current number set: [127, 12], target: 15, just two numbers left.\n     |- Try 127 + 12 = 139. Evaluate 139 != 15, drop this branch.\n     |- Try 127 - 12 = 115. Evaluate 115 != 15, drop this branch.\n     |- Try 127 * 12 = 1524. Evaluate 1524 != 15, drop this branch.\n     |- Try 127 \/ 12 = 10.6. 10.6 is a decimal, drop this branch.\n    |- Try 117 - 10 = 107. Add 107 to the number set. Current number set: [107, 12], target: 15, just two numbers left.\n     |- Try 107 + 12 = 119. Evaluate 119 != 15, drop this branch.\n     |- Try 107 - 12 = 95. Evaluate 95 != 15, drop this branch.\n     |- Try 107 * 12 = 1284. Evaluate 1284 != 15, drop this branch.\n     |- Try 107 \/ 12 = 8.9. 8.9 is a decimal, drop this branch.\n    |- Try 117 * 10 = 1170. Add 1170 to the number set. Current number set: [1170, 12], target: 15, just two numbers left.\n     |- Try 1170 + 12 = 1182. Evaluate 1182 != 15, drop this branch.\n     |- Try 1170 - 12 = 1158. Evaluate 1158 != 15, drop this branch.\n     |- Try 1170 * 12 = 14040. 14040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1170 \/ 12 = 97.5. 97.5 is a decimal, drop this branch.\n    |- Try 117 \/ 10 = 11.7. 11.7 is a decimal, drop this branch.\n   |- Pick two numbers (117, 12) (numbers left: [10]). Try possible operations.\n    |- Try 117 + 12 = 129. Add 129 to the number set. Current number set: [129, 10], target: 15, just two numbers left.\n     |- Try 129 + 10 = 139. Evaluate 139 != 15, drop this branch.\n     |- Try 129 - 10 = 119. Evaluate 119 != 15, drop this branch.\n     |- Try 129 * 10 = 1290. Evaluate 1290 != 15, drop this branch.\n     |- Try 129 \/ 10 = 12.9. 12.9 is a decimal, drop this branch.\n    |- Try 117 - 12 = 105. Add 105 to the number set. Current number set: [105, 10], target: 15, just two numbers left.\n     |- Try 105 + 10 = 115. Evaluate 115 != 15, drop this branch.\n     |- Try 105 - 10 = 95. Evaluate 95 != 15, drop this branch.\n     |- Try 105 * 10 = 1050. Evaluate 1050 != 15, drop this branch.\n     |- Try 105 \/ 10 = 10.5. 10.5 is a decimal, drop this branch.\n    |- Try 117 * 12 = 1404. Add 1404 to the number set. Current number set: [1404, 10], target: 15, just two numbers left.\n     |- Try 1404 + 10 = 1414. Evaluate 1414 != 15, drop this branch.\n     |- Try 1404 - 10 = 1394. Evaluate 1394 != 15, drop this branch.\n     |- Try 1404 * 10 = 14040. 14040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1404 \/ 10 = 140.4. 140.4 is a decimal, drop this branch.\n    |- Try 117 \/ 12 = 9.8. 9.8 is a decimal, drop this branch.\n   |- Pick two numbers (10, 12) (numbers left: [117]). Try possible operations.\n    |- Try 12 + 10 = 22. Add 22 to the number set. Current number set: [22, 117], target: 15, just two numbers left.\n     |- Try 117 + 22 = 139. Evaluate 139 != 15, drop this branch.\n     |- Try 117 - 22 = 95. Evaluate 95 != 15, drop this branch.\n     |- Try 117 * 22 = 2574. 2574 exceeds the maximum intermediate result, drop this branch.\n     |- Try 117 \/ 22 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 12 - 10 = 2. Add 2 to the number set. Current number set: [2, 117], target: 15, just two numbers left.\n     |- Try 117 + 2 = 119. Evaluate 119 != 15, drop this branch.\n     |- Try 117 - 2 = 115. Evaluate 115 != 15, drop this branch.\n     |- Try 117 * 2 = 234. Evaluate 234 != 15, drop this branch.\n     |- Try 117 \/ 2 = 58.5. 58.5 is a decimal, drop this branch.\n    |- Try 12 * 10 = 120. Add 120 to the number set. Current number set: [120, 117], target: 15, just two numbers left.\n     |- Try 120 + 117 = 237. Evaluate 237 != 15, drop this branch.\n     |- Try 120 - 117 = 3. Evaluate 3 != 15, drop this branch.\n     |- Try 120 * 117 = 14040. 14040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 120 \/ 117 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 12 \/ 10 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 39 \/ 3 = 13. Add 13 to the number set. Current number set: [13, 10, 12], target: 15. Options for choosing two numbers: [(13, 10), (13, 12), (10, 12)].\n   |- Pick two numbers (13, 10) (numbers left: [12]). Try possible operations.\n    |- Try 13 + 10 = 23. Add 23 to the number set. Current number set: [23, 12], target: 15, just two numbers left.\n     |- Try 23 + 12 = 35. Evaluate 35 != 15, drop this branch.\n     |- Try 23 - 12 = 11. Evaluate 11 != 15, drop this branch.\n     |- Try 23 * 12 = 276. Evaluate 276 != 15, drop this branch.\n     |- Try 23 \/ 12 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 13 - 10 = 3. Add 3 to the number set. Current number set: [3, 12], target: 15, just two numbers left.\n     |- Try 12 + 3 = 15. Evaluate 15 == 15, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 12 + 3 = 15\nThe step before: 13 - 10 = 3\nThe first step: 39 \/ 3 = 13\n\nOutput the solution in the required format:\n<Solution>\n39 \/ 3 = 13\n13 - 10 = 3\n12 + 3 = 15\n<\/Solution>\n","item":{"nums":[3,39,10,12],"solution":["39 \/ 3 = 13","13 - 10 = 3","12 + 3 = 15"],"target":15}}
+{"instance_id":"countdown_8k_153","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [15, 45, 6, 16]\nTarget: 48","reference_output":"# Search Procedure\nInitial number set: [15, 45, 6, 16], target: 48. Options for choosing two numbers: [(15, 45), (15, 6), (15, 16), (45, 6), (45, 16), (6, 16)].\n |- Pick two numbers (15, 45) (numbers left: [6, 16]). Try possible operations.\n  |- Try 45 + 15 = 60. Add 60 to the number set. Current number set: [60, 6, 16], target: 48. Options for choosing two numbers: [(60, 6), (60, 16), (6, 16)].\n   |- Pick two numbers (60, 6) (numbers left: [16]). Try possible operations.\n    |- Try 60 + 6 = 66. Add 66 to the number set. Current number set: [66, 16], target: 48, just two numbers left.\n     |- Try 66 + 16 = 82. Evaluate 82 != 48, drop this branch.\n     |- Try 66 - 16 = 50. Evaluate 50 != 48, drop this branch.\n     |- Try 66 * 16 = 1056. Evaluate 1056 != 48, drop this branch.\n     |- Try 66 \/ 16 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 60 - 6 = 54. Add 54 to the number set. Current number set: [54, 16], target: 48, just two numbers left.\n     |- Try 54 + 16 = 70. Evaluate 70 != 48, drop this branch.\n     |- Try 54 - 16 = 38. Evaluate 38 != 48, drop this branch.\n     |- Try 54 * 16 = 864. Evaluate 864 != 48, drop this branch.\n     |- Try 54 \/ 16 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 60 * 6 = 360. Add 360 to the number set. Current number set: [360, 16], target: 48, just two numbers left.\n     |- Try 360 + 16 = 376. Evaluate 376 != 48, drop this branch.\n     |- Try 360 - 16 = 344. Evaluate 344 != 48, drop this branch.\n     |- Try 360 * 16 = 5760. 5760 exceeds the maximum intermediate result, drop this branch.\n     |- Try 360 \/ 16 = 22.5. 22.5 is a decimal, drop this branch.\n    |- Try 60 \/ 6 = 10. Add 10 to the number set. Current number set: [10, 16], target: 48, just two numbers left.\n     |- Try 16 + 10 = 26. Evaluate 26 != 48, drop this branch.\n     |- Try 16 - 10 = 6. Evaluate 6 != 48, drop this branch.\n     |- Try 16 * 10 = 160. Evaluate 160 != 48, drop this branch.\n     |- Try 16 \/ 10 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (60, 16) (numbers left: [6]). Try possible operations.\n    |- Try 60 + 16 = 76. Add 76 to the number set. Current number set: [76, 6], target: 48, just two numbers left.\n     |- Try 76 + 6 = 82. Evaluate 82 != 48, drop this branch.\n     |- Try 76 - 6 = 70. Evaluate 70 != 48, drop this branch.\n     |- Try 76 * 6 = 456. Evaluate 456 != 48, drop this branch.\n     |- Try 76 \/ 6 = 12.7. 12.7 is a decimal, drop this branch.\n    |- Try 60 - 16 = 44. Add 44 to the number set. Current number set: [44, 6], target: 48, just two numbers left.\n     |- Try 44 + 6 = 50. Evaluate 50 != 48, drop this branch.\n     |- Try 44 - 6 = 38. Evaluate 38 != 48, drop this branch.\n     |- Try 44 * 6 = 264. Evaluate 264 != 48, drop this branch.\n     |- Try 44 \/ 6 = 7.3. 7.3 is a decimal, drop this branch.\n    |- Try 60 * 16 = 960. Add 960 to the number set. Current number set: [960, 6], target: 48, just two numbers left.\n     |- Try 960 + 6 = 966. Evaluate 966 != 48, drop this branch.\n     |- Try 960 - 6 = 954. Evaluate 954 != 48, drop this branch.\n     |- Try 960 * 6 = 5760. 5760 exceeds the maximum intermediate result, drop this branch.\n     |- Try 960 \/ 6 = 160. Evaluate 160 != 48, drop this branch.\n    |- Try 60 \/ 16 = 3.8. 3.8 is a decimal, drop this branch.\n   |- Pick two numbers (6, 16) (numbers left: [60]). Try possible operations.\n    |- Try 16 + 6 = 22. Add 22 to the number set. Current number set: [22, 60], target: 48, just two numbers left.\n     |- Try 60 + 22 = 82. Evaluate 82 != 48, drop this branch.\n     |- Try 60 - 22 = 38. Evaluate 38 != 48, drop this branch.\n     |- Try 60 * 22 = 1320. Evaluate 1320 != 48, drop this branch.\n     |- Try 60 \/ 22 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 16 - 6 = 10. Add 10 to the number set. Current number set: [10, 60], target: 48, just two numbers left.\n     |- Try 60 + 10 = 70. Evaluate 70 != 48, drop this branch.\n     |- Try 60 - 10 = 50. Evaluate 50 != 48, drop this branch.\n     |- Try 60 * 10 = 600. Evaluate 600 != 48, drop this branch.\n     |- Try 60 \/ 10 = 6. Evaluate 6 != 48, drop this branch.\n    |- Try 16 * 6 = 96. Add 96 to the number set. Current number set: [96, 60], target: 48, just two numbers left.\n     |- Try 96 + 60 = 156. Evaluate 156 != 48, drop this branch.\n     |- Try 96 - 60 = 36. Evaluate 36 != 48, drop this branch.\n     |- Try 96 * 60 = 5760. 5760 exceeds the maximum intermediate result, drop this branch.\n     |- Try 96 \/ 60 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 16 \/ 6 = 2.7. 2.7 is a decimal, drop this branch.\n  |- Try 45 - 15 = 30. Add 30 to the number set. Current number set: [30, 6, 16], target: 48. Options for choosing two numbers: [(30, 6), (30, 16), (6, 16)].\n   |- Pick two numbers (30, 6) (numbers left: [16]). Try possible operations.\n    |- Try 30 + 6 = 36. Add 36 to the number set. Current number set: [36, 16], target: 48, just two numbers left.\n     |- Try 36 + 16 = 52. Evaluate 52 != 48, drop this branch.\n     |- Try 36 - 16 = 20. Evaluate 20 != 48, drop this branch.\n     |- Try 36 * 16 = 576. Evaluate 576 != 48, drop this branch.\n     |- Try 36 \/ 16 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 30 - 6 = 24. Add 24 to the number set. Current number set: [24, 16], target: 48, just two numbers left.\n     |- Try 24 + 16 = 40. Evaluate 40 != 48, drop this branch.\n     |- Try 24 - 16 = 8. Evaluate 8 != 48, drop this branch.\n     |- Try 24 * 16 = 384. Evaluate 384 != 48, drop this branch.\n     |- Try 24 \/ 16 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 30 * 6 = 180. Add 180 to the number set. Current number set: [180, 16], target: 48, just two numbers left.\n     |- Try 180 + 16 = 196. Evaluate 196 != 48, drop this branch.\n     |- Try 180 - 16 = 164. Evaluate 164 != 48, drop this branch.\n     |- Try 180 * 16 = 2880. 2880 exceeds the maximum intermediate result, drop this branch.\n     |- Try 180 \/ 16 = 11.2. 11.2 is a decimal, drop this branch.\n    |- Try 30 \/ 6 = 5. Add 5 to the number set. Current number set: [5, 16], target: 48, just two numbers left.\n     |- Try 16 + 5 = 21. Evaluate 21 != 48, drop this branch.\n     |- Try 16 - 5 = 11. Evaluate 11 != 48, drop this branch.\n     |- Try 16 * 5 = 80. Evaluate 80 != 48, drop this branch.\n     |- Try 16 \/ 5 = 3.2. 3.2 is a decimal, drop this branch.\n   |- Pick two numbers (30, 16) (numbers left: [6]). Try possible operations.\n    |- Try 30 + 16 = 46. Add 46 to the number set. Current number set: [46, 6], target: 48, just two numbers left.\n     |- Try 46 + 6 = 52. Evaluate 52 != 48, drop this branch.\n     |- Try 46 - 6 = 40. Evaluate 40 != 48, drop this branch.\n     |- Try 46 * 6 = 276. Evaluate 276 != 48, drop this branch.\n     |- Try 46 \/ 6 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 30 - 16 = 14. Add 14 to the number set. Current number set: [14, 6], target: 48, just two numbers left.\n     |- Try 14 + 6 = 20. Evaluate 20 != 48, drop this branch.\n     |- Try 14 - 6 = 8. Evaluate 8 != 48, drop this branch.\n     |- Try 14 * 6 = 84. Evaluate 84 != 48, drop this branch.\n     |- Try 14 \/ 6 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 30 * 16 = 480. Add 480 to the number set. Current number set: [480, 6], target: 48, just two numbers left.\n     |- Try 480 + 6 = 486. Evaluate 486 != 48, drop this branch.\n     |- Try 480 - 6 = 474. Evaluate 474 != 48, drop this branch.\n     |- Try 480 * 6 = 2880. 2880 exceeds the maximum intermediate result, drop this branch.\n     |- Try 480 \/ 6 = 80. Evaluate 80 != 48, drop this branch.\n    |- Try 30 \/ 16 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (6, 16) (numbers left: [30]). Try possible operations.\n    |- Try 16 + 6 = 22. Add 22 to the number set. Current number set: [22, 30], target: 48, just two numbers left.\n     |- Try 30 + 22 = 52. Evaluate 52 != 48, drop this branch.\n     |- Try 30 - 22 = 8. Evaluate 8 != 48, drop this branch.\n     |- Try 30 * 22 = 660. Evaluate 660 != 48, drop this branch.\n     |- Try 30 \/ 22 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 16 - 6 = 10. Add 10 to the number set. Current number set: [10, 30], target: 48, just two numbers left.\n     |- Try 30 + 10 = 40. Evaluate 40 != 48, drop this branch.\n     |- Try 30 - 10 = 20. Evaluate 20 != 48, drop this branch.\n     |- Try 30 * 10 = 300. Evaluate 300 != 48, drop this branch.\n     |- Try 30 \/ 10 = 3. Evaluate 3 != 48, drop this branch.\n    |- Try 16 * 6 = 96. Add 96 to the number set. Current number set: [96, 30], target: 48, just two numbers left.\n     |- Try 96 + 30 = 126. Evaluate 126 != 48, drop this branch.\n     |- Try 96 - 30 = 66. Evaluate 66 != 48, drop this branch.\n     |- Try 96 * 30 = 2880. 2880 exceeds the maximum intermediate result, drop this branch.\n     |- Try 96 \/ 30 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 16 \/ 6 = 2.7. 2.7 is a decimal, drop this branch.\n  |- Try 45 * 15 = 675. Add 675 to the number set. Current number set: [675, 6, 16], target: 48. Options for choosing two numbers: [(675, 6), (675, 16), (6, 16)].\n   |- Pick two numbers (675, 6) (numbers left: [16]). Try possible operations.\n    |- Try 675 + 6 = 681. Add 681 to the number set. Current number set: [681, 16], target: 48, just two numbers left.\n     |- Try 681 + 16 = 697. Evaluate 697 != 48, drop this branch.\n     |- Try 681 - 16 = 665. Evaluate 665 != 48, drop this branch.\n     |- Try 681 * 16 = 10896. 10896 exceeds the maximum intermediate result, drop this branch.\n     |- Try 681 \/ 16 = 42.6. 42.6 is a decimal, drop this branch.\n    |- Try 675 - 6 = 669. Add 669 to the number set. Current number set: [669, 16], target: 48, just two numbers left.\n     |- Try 669 + 16 = 685. Evaluate 685 != 48, drop this branch.\n     |- Try 669 - 16 = 653. Evaluate 653 != 48, drop this branch.\n     |- Try 669 * 16 = 10704. 10704 exceeds the maximum intermediate result, drop this branch.\n     |- Try 669 \/ 16 = 41.8. 41.8 is a decimal, drop this branch.\n    |- Try 675 * 6 = 4050. 4050 exceeds the maximum intermediate result, drop this branch.\n    |- Try 675 \/ 6 = 112.5. 112.5 is a decimal, drop this branch.\n   |- Pick two numbers (675, 16) (numbers left: [6]). Try possible operations.\n    |- Try 675 + 16 = 691. Add 691 to the number set. Current number set: [691, 6], target: 48, just two numbers left.\n     |- Try 691 + 6 = 697. Evaluate 697 != 48, drop this branch.\n     |- Try 691 - 6 = 685. Evaluate 685 != 48, drop this branch.\n     |- Try 691 * 6 = 4146. 4146 exceeds the maximum intermediate result, drop this branch.\n     |- Try 691 \/ 6 = 115.2. 115.2 is a decimal, drop this branch.\n    |- Try 675 - 16 = 659. Add 659 to the number set. Current number set: [659, 6], target: 48, just two numbers left.\n     |- Try 659 + 6 = 665. Evaluate 665 != 48, drop this branch.\n     |- Try 659 - 6 = 653. Evaluate 653 != 48, drop this branch.\n     |- Try 659 * 6 = 3954. 3954 exceeds the maximum intermediate result, drop this branch.\n     |- Try 659 \/ 6 = 109.8. 109.8 is a decimal, drop this branch.\n    |- Try 675 * 16 = 10800. 10800 exceeds the maximum intermediate result, drop this branch.\n    |- Try 675 \/ 16 = 42.2. 42.2 is a decimal, drop this branch.\n   |- Pick two numbers (6, 16) (numbers left: [675]). Try possible operations.\n    |- Try 16 + 6 = 22. Add 22 to the number set. Current number set: [22, 675], target: 48, just two numbers left.\n     |- Try 675 + 22 = 697. Evaluate 697 != 48, drop this branch.\n     |- Try 675 - 22 = 653. Evaluate 653 != 48, drop this branch.\n     |- Try 675 * 22 = 14850. 14850 exceeds the maximum intermediate result, drop this branch.\n     |- Try 675 \/ 22 = 30.7. 30.7 is a decimal, drop this branch.\n    |- Try 16 - 6 = 10. Add 10 to the number set. Current number set: [10, 675], target: 48, just two numbers left.\n     |- Try 675 + 10 = 685. Evaluate 685 != 48, drop this branch.\n     |- Try 675 - 10 = 665. Evaluate 665 != 48, drop this branch.\n     |- Try 675 * 10 = 6750. 6750 exceeds the maximum intermediate result, drop this branch.\n     |- Try 675 \/ 10 = 67.5. 67.5 is a decimal, drop this branch.\n    |- Try 16 * 6 = 96. Add 96 to the number set. Current number set: [96, 675], target: 48, just two numbers left.\n     |- Try 675 + 96 = 771. Evaluate 771 != 48, drop this branch.\n     |- Try 675 - 96 = 579. Evaluate 579 != 48, drop this branch.\n     |- Try 675 * 96 = 64800. 64800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 675 \/ 96 = 7.0. 7.0 is a decimal, drop this branch.\n    |- Try 16 \/ 6 = 2.7. 2.7 is a decimal, drop this branch.\n  |- Try 45 \/ 15 = 3. Add 3 to the number set. Current number set: [3, 6, 16], target: 48. Options for choosing two numbers: [(3, 6), (3, 16), (6, 16)].\n   |- Pick two numbers (3, 6) (numbers left: [16]). Try possible operations.\n    |- Try 6 + 3 = 9. Add 9 to the number set. Current number set: [9, 16], target: 48, just two numbers left.\n     |- Try 16 + 9 = 25. Evaluate 25 != 48, drop this branch.\n     |- Try 16 - 9 = 7. Evaluate 7 != 48, drop this branch.\n     |- Try 16 * 9 = 144. Evaluate 144 != 48, drop this branch.\n     |- Try 16 \/ 9 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 6 - 3 = 3. Add 3 to the number set. Current number set: [3, 16], target: 48, just two numbers left.\n     |- Try 16 + 3 = 19. Evaluate 19 != 48, drop this branch.\n     |- Try 16 - 3 = 13. Evaluate 13 != 48, drop this branch.\n     |- Try 16 * 3 = 48. Evaluate 48 == 48, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 16 * 3 = 48\nThe step before: 6 - 3 = 3\nThe first step: 45 \/ 15 = 3\n\nOutput the solution in the required format:\n<Solution>\n45 \/ 15 = 3\n6 - 3 = 3\n16 * 3 = 48\n<\/Solution>\n","item":{"nums":[15,45,6,16],"solution":["45 \/ 15 = 3","6 - 3 = 3","16 * 3 = 48"],"target":48}}
+{"instance_id":"countdown_8k_154","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [14, 15, 4, 48]\nTarget: 32","reference_output":"# Search Procedure\nInitial number set: [14, 15, 4, 48], target: 32. Options for choosing two numbers: [(14, 15), (14, 4), (14, 48), (15, 4), (15, 48), (4, 48)].\n |- Pick two numbers (14, 15) (numbers left: [4, 48]). Try possible operations.\n  |- Try 15 + 14 = 29. Add 29 to the number set. Current number set: [29, 4, 48], target: 32. Options for choosing two numbers: [(29, 4), (29, 48), (4, 48)].\n   |- Pick two numbers (29, 4) (numbers left: [48]). Try possible operations.\n    |- Try 29 + 4 = 33. Add 33 to the number set. Current number set: [33, 48], target: 32, just two numbers left.\n     |- Try 48 + 33 = 81. Evaluate 81 != 32, drop this branch.\n     |- Try 48 - 33 = 15. Evaluate 15 != 32, drop this branch.\n     |- Try 48 * 33 = 1584. Evaluate 1584 != 32, drop this branch.\n     |- Try 48 \/ 33 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 29 - 4 = 25. Add 25 to the number set. Current number set: [25, 48], target: 32, just two numbers left.\n     |- Try 48 + 25 = 73. Evaluate 73 != 32, drop this branch.\n     |- Try 48 - 25 = 23. Evaluate 23 != 32, drop this branch.\n     |- Try 48 * 25 = 1200. Evaluate 1200 != 32, drop this branch.\n     |- Try 48 \/ 25 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 29 * 4 = 116. Add 116 to the number set. Current number set: [116, 48], target: 32, just two numbers left.\n     |- Try 116 + 48 = 164. Evaluate 164 != 32, drop this branch.\n     |- Try 116 - 48 = 68. Evaluate 68 != 32, drop this branch.\n     |- Try 116 * 48 = 5568. 5568 exceeds the maximum intermediate result, drop this branch.\n     |- Try 116 \/ 48 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 29 \/ 4 = 7.2. 7.2 is a decimal, drop this branch.\n   |- Pick two numbers (29, 48) (numbers left: [4]). Try possible operations.\n    |- Try 48 + 29 = 77. Add 77 to the number set. Current number set: [77, 4], target: 32, just two numbers left.\n     |- Try 77 + 4 = 81. Evaluate 81 != 32, drop this branch.\n     |- Try 77 - 4 = 73. Evaluate 73 != 32, drop this branch.\n     |- Try 77 * 4 = 308. Evaluate 308 != 32, drop this branch.\n     |- Try 77 \/ 4 = 19.2. 19.2 is a decimal, drop this branch.\n    |- Try 48 - 29 = 19. Add 19 to the number set. Current number set: [19, 4], target: 32, just two numbers left.\n     |- Try 19 + 4 = 23. Evaluate 23 != 32, drop this branch.\n     |- Try 19 - 4 = 15. Evaluate 15 != 32, drop this branch.\n     |- Try 19 * 4 = 76. Evaluate 76 != 32, drop this branch.\n     |- Try 19 \/ 4 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 48 * 29 = 1392. Add 1392 to the number set. Current number set: [1392, 4], target: 32, just two numbers left.\n     |- Try 1392 + 4 = 1396. Evaluate 1396 != 32, drop this branch.\n     |- Try 1392 - 4 = 1388. Evaluate 1388 != 32, drop this branch.\n     |- Try 1392 * 4 = 5568. 5568 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1392 \/ 4 = 348. Evaluate 348 != 32, drop this branch.\n    |- Try 48 \/ 29 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (4, 48) (numbers left: [29]). Try possible operations.\n    |- Try 48 + 4 = 52. Add 52 to the number set. Current number set: [52, 29], target: 32, just two numbers left.\n     |- Try 52 + 29 = 81. Evaluate 81 != 32, drop this branch.\n     |- Try 52 - 29 = 23. Evaluate 23 != 32, drop this branch.\n     |- Try 52 * 29 = 1508. Evaluate 1508 != 32, drop this branch.\n     |- Try 52 \/ 29 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 48 - 4 = 44. Add 44 to the number set. Current number set: [44, 29], target: 32, just two numbers left.\n     |- Try 44 + 29 = 73. Evaluate 73 != 32, drop this branch.\n     |- Try 44 - 29 = 15. Evaluate 15 != 32, drop this branch.\n     |- Try 44 * 29 = 1276. Evaluate 1276 != 32, drop this branch.\n     |- Try 44 \/ 29 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 48 * 4 = 192. Add 192 to the number set. Current number set: [192, 29], target: 32, just two numbers left.\n     |- Try 192 + 29 = 221. Evaluate 221 != 32, drop this branch.\n     |- Try 192 - 29 = 163. Evaluate 163 != 32, drop this branch.\n     |- Try 192 * 29 = 5568. 5568 exceeds the maximum intermediate result, drop this branch.\n     |- Try 192 \/ 29 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 48 \/ 4 = 12. Add 12 to the number set. Current number set: [12, 29], target: 32, just two numbers left.\n     |- Try 29 + 12 = 41. Evaluate 41 != 32, drop this branch.\n     |- Try 29 - 12 = 17. Evaluate 17 != 32, drop this branch.\n     |- Try 29 * 12 = 348. Evaluate 348 != 32, drop this branch.\n     |- Try 29 \/ 12 = 2.4. 2.4 is a decimal, drop this branch.\n  |- Try 15 - 14 = 1. Add 1 to the number set. Current number set: [1, 4, 48], target: 32. Options for choosing two numbers: [(1, 4), (1, 48), (4, 48)].\n   |- Pick two numbers (1, 4) (numbers left: [48]). Try possible operations.\n    |- Try 4 + 1 = 5. Add 5 to the number set. Current number set: [5, 48], target: 32, just two numbers left.\n     |- Try 48 + 5 = 53. Evaluate 53 != 32, drop this branch.\n     |- Try 48 - 5 = 43. Evaluate 43 != 32, drop this branch.\n     |- Try 48 * 5 = 240. Evaluate 240 != 32, drop this branch.\n     |- Try 48 \/ 5 = 9.6. 9.6 is a decimal, drop this branch.\n    |- Try 4 - 1 = 3. Add 3 to the number set. Current number set: [3, 48], target: 32, just two numbers left.\n     |- Try 48 + 3 = 51. Evaluate 51 != 32, drop this branch.\n     |- Try 48 - 3 = 45. Evaluate 45 != 32, drop this branch.\n     |- Try 48 * 3 = 144. Evaluate 144 != 32, drop this branch.\n     |- Try 48 \/ 3 = 16. Evaluate 16 != 32, drop this branch.\n    |- Try 4 * 1 = 4. Add 4 to the number set. Current number set: [4, 48], target: 32, just two numbers left.\n     |- Try 48 + 4 = 52. Evaluate 52 != 32, drop this branch.\n     |- Try 48 - 4 = 44. Evaluate 44 != 32, drop this branch.\n     |- Try 48 * 4 = 192. Evaluate 192 != 32, drop this branch.\n     |- Try 48 \/ 4 = 12. Evaluate 12 != 32, drop this branch.\n    |- Try 4 \/ 1 = 4. Add 4 to the number set. Current number set: [4, 48], target: 32, just two numbers left.\n     |- Try 48 + 4 = 52. Evaluate 52 != 32, drop this branch.\n     |- Try 48 - 4 = 44. Evaluate 44 != 32, drop this branch.\n     |- Try 48 * 4 = 192. Evaluate 192 != 32, drop this branch.\n     |- Try 48 \/ 4 = 12. Evaluate 12 != 32, drop this branch.\n   |- Pick two numbers (1, 48) (numbers left: [4]). Try possible operations.\n    |- Try 48 + 1 = 49. Add 49 to the number set. Current number set: [49, 4], target: 32, just two numbers left.\n     |- Try 49 + 4 = 53. Evaluate 53 != 32, drop this branch.\n     |- Try 49 - 4 = 45. Evaluate 45 != 32, drop this branch.\n     |- Try 49 * 4 = 196. Evaluate 196 != 32, drop this branch.\n     |- Try 49 \/ 4 = 12.2. 12.2 is a decimal, drop this branch.\n    |- Try 48 - 1 = 47. Add 47 to the number set. Current number set: [47, 4], target: 32, just two numbers left.\n     |- Try 47 + 4 = 51. Evaluate 51 != 32, drop this branch.\n     |- Try 47 - 4 = 43. Evaluate 43 != 32, drop this branch.\n     |- Try 47 * 4 = 188. Evaluate 188 != 32, drop this branch.\n     |- Try 47 \/ 4 = 11.8. 11.8 is a decimal, drop this branch.\n    |- Try 48 * 1 = 48. Add 48 to the number set. Current number set: [48, 4], target: 32, just two numbers left.\n     |- Try 48 + 4 = 52. Evaluate 52 != 32, drop this branch.\n     |- Try 48 - 4 = 44. Evaluate 44 != 32, drop this branch.\n     |- Try 48 * 4 = 192. Evaluate 192 != 32, drop this branch.\n     |- Try 48 \/ 4 = 12. Evaluate 12 != 32, drop this branch.\n    |- Try 48 \/ 1 = 48. Add 48 to the number set. Current number set: [48, 4], target: 32, just two numbers left.\n     |- Try 48 + 4 = 52. Evaluate 52 != 32, drop this branch.\n     |- Try 48 - 4 = 44. Evaluate 44 != 32, drop this branch.\n     |- Try 48 * 4 = 192. Evaluate 192 != 32, drop this branch.\n     |- Try 48 \/ 4 = 12. Evaluate 12 != 32, drop this branch.\n   |- Pick two numbers (4, 48) (numbers left: [1]). Try possible operations.\n    |- Try 48 + 4 = 52. Add 52 to the number set. Current number set: [52, 1], target: 32, just two numbers left.\n     |- Try 52 + 1 = 53. Evaluate 53 != 32, drop this branch.\n     |- Try 52 - 1 = 51. Evaluate 51 != 32, drop this branch.\n     |- Try 52 * 1 = 52. Evaluate 52 != 32, drop this branch.\n     |- Try 52 \/ 1 = 52. Evaluate 52 != 32, drop this branch.\n    |- Try 48 - 4 = 44. Add 44 to the number set. Current number set: [44, 1], target: 32, just two numbers left.\n     |- Try 44 + 1 = 45. Evaluate 45 != 32, drop this branch.\n     |- Try 44 - 1 = 43. Evaluate 43 != 32, drop this branch.\n     |- Try 44 * 1 = 44. Evaluate 44 != 32, drop this branch.\n     |- Try 44 \/ 1 = 44. Evaluate 44 != 32, drop this branch.\n    |- Try 48 * 4 = 192. Add 192 to the number set. Current number set: [192, 1], target: 32, just two numbers left.\n     |- Try 192 + 1 = 193. Evaluate 193 != 32, drop this branch.\n     |- Try 192 - 1 = 191. Evaluate 191 != 32, drop this branch.\n     |- Try 192 * 1 = 192. Evaluate 192 != 32, drop this branch.\n     |- Try 192 \/ 1 = 192. Evaluate 192 != 32, drop this branch.\n    |- Try 48 \/ 4 = 12. Add 12 to the number set. Current number set: [12, 1], target: 32, just two numbers left.\n     |- Try 12 + 1 = 13. Evaluate 13 != 32, drop this branch.\n     |- Try 12 - 1 = 11. Evaluate 11 != 32, drop this branch.\n     |- Try 12 * 1 = 12. Evaluate 12 != 32, drop this branch.\n     |- Try 12 \/ 1 = 12. Evaluate 12 != 32, drop this branch.\n  |- Try 15 * 14 = 210. Add 210 to the number set. Current number set: [210, 4, 48], target: 32. Options for choosing two numbers: [(210, 4), (210, 48), (4, 48)].\n   |- Pick two numbers (210, 4) (numbers left: [48]). Try possible operations.\n    |- Try 210 + 4 = 214. Add 214 to the number set. Current number set: [214, 48], target: 32, just two numbers left.\n     |- Try 214 + 48 = 262. Evaluate 262 != 32, drop this branch.\n     |- Try 214 - 48 = 166. Evaluate 166 != 32, drop this branch.\n     |- Try 214 * 48 = 10272. 10272 exceeds the maximum intermediate result, drop this branch.\n     |- Try 214 \/ 48 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 210 - 4 = 206. Add 206 to the number set. Current number set: [206, 48], target: 32, just two numbers left.\n     |- Try 206 + 48 = 254. Evaluate 254 != 32, drop this branch.\n     |- Try 206 - 48 = 158. Evaluate 158 != 32, drop this branch.\n     |- Try 206 * 48 = 9888. 9888 exceeds the maximum intermediate result, drop this branch.\n     |- Try 206 \/ 48 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 210 * 4 = 840. Add 840 to the number set. Current number set: [840, 48], target: 32, just two numbers left.\n     |- Try 840 + 48 = 888. Evaluate 888 != 32, drop this branch.\n     |- Try 840 - 48 = 792. Evaluate 792 != 32, drop this branch.\n     |- Try 840 * 48 = 40320. 40320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 840 \/ 48 = 17.5. 17.5 is a decimal, drop this branch.\n    |- Try 210 \/ 4 = 52.5. 52.5 is a decimal, drop this branch.\n   |- Pick two numbers (210, 48) (numbers left: [4]). Try possible operations.\n    |- Try 210 + 48 = 258. Add 258 to the number set. Current number set: [258, 4], target: 32, just two numbers left.\n     |- Try 258 + 4 = 262. Evaluate 262 != 32, drop this branch.\n     |- Try 258 - 4 = 254. Evaluate 254 != 32, drop this branch.\n     |- Try 258 * 4 = 1032. Evaluate 1032 != 32, drop this branch.\n     |- Try 258 \/ 4 = 64.5. 64.5 is a decimal, drop this branch.\n    |- Try 210 - 48 = 162. Add 162 to the number set. Current number set: [162, 4], target: 32, just two numbers left.\n     |- Try 162 + 4 = 166. Evaluate 166 != 32, drop this branch.\n     |- Try 162 - 4 = 158. Evaluate 158 != 32, drop this branch.\n     |- Try 162 * 4 = 648. Evaluate 648 != 32, drop this branch.\n     |- Try 162 \/ 4 = 40.5. 40.5 is a decimal, drop this branch.\n    |- Try 210 * 48 = 10080. 10080 exceeds the maximum intermediate result, drop this branch.\n    |- Try 210 \/ 48 = 4.4. 4.4 is a decimal, drop this branch.\n   |- Pick two numbers (4, 48) (numbers left: [210]). Try possible operations.\n    |- Try 48 + 4 = 52. Add 52 to the number set. Current number set: [52, 210], target: 32, just two numbers left.\n     |- Try 210 + 52 = 262. Evaluate 262 != 32, drop this branch.\n     |- Try 210 - 52 = 158. Evaluate 158 != 32, drop this branch.\n     |- Try 210 * 52 = 10920. 10920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 210 \/ 52 = 4.0. 4.0 is a decimal, drop this branch.\n    |- Try 48 - 4 = 44. Add 44 to the number set. Current number set: [44, 210], target: 32, just two numbers left.\n     |- Try 210 + 44 = 254. Evaluate 254 != 32, drop this branch.\n     |- Try 210 - 44 = 166. Evaluate 166 != 32, drop this branch.\n     |- Try 210 * 44 = 9240. 9240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 210 \/ 44 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 48 * 4 = 192. Add 192 to the number set. Current number set: [192, 210], target: 32, just two numbers left.\n     |- Try 210 + 192 = 402. Evaluate 402 != 32, drop this branch.\n     |- Try 210 - 192 = 18. Evaluate 18 != 32, drop this branch.\n     |- Try 210 * 192 = 40320. 40320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 210 \/ 192 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 48 \/ 4 = 12. Add 12 to the number set. Current number set: [12, 210], target: 32, just two numbers left.\n     |- Try 210 + 12 = 222. Evaluate 222 != 32, drop this branch.\n     |- Try 210 - 12 = 198. Evaluate 198 != 32, drop this branch.\n     |- Try 210 * 12 = 2520. 2520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 210 \/ 12 = 17.5. 17.5 is a decimal, drop this branch.\n  |- Try 15 \/ 14 = 1.1. 1.1 is a decimal, drop this branch.\n |- Pick two numbers (14, 4) (numbers left: [15, 48]). Try possible operations.\n  |- Try 14 + 4 = 18. Add 18 to the number set. Current number set: [18, 15, 48], target: 32. Options for choosing two numbers: [(18, 15), (18, 48), (15, 48)].\n   |- Pick two numbers (18, 15) (numbers left: [48]). Try possible operations.\n    |- Try 18 + 15 = 33. Add 33 to the number set. Current number set: [33, 48], target: 32, just two numbers left.\n     |- Try 48 + 33 = 81. Evaluate 81 != 32, drop this branch.\n     |- Try 48 - 33 = 15. Evaluate 15 != 32, drop this branch.\n     |- Try 48 * 33 = 1584. Evaluate 1584 != 32, drop this branch.\n     |- Try 48 \/ 33 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 18 - 15 = 3. Add 3 to the number set. Current number set: [3, 48], target: 32, just two numbers left.\n     |- Try 48 + 3 = 51. Evaluate 51 != 32, drop this branch.\n     |- Try 48 - 3 = 45. Evaluate 45 != 32, drop this branch.\n     |- Try 48 * 3 = 144. Evaluate 144 != 32, drop this branch.\n     |- Try 48 \/ 3 = 16. Evaluate 16 != 32, drop this branch.\n    |- Try 18 * 15 = 270. Add 270 to the number set. Current number set: [270, 48], target: 32, just two numbers left.\n     |- Try 270 + 48 = 318. Evaluate 318 != 32, drop this branch.\n     |- Try 270 - 48 = 222. Evaluate 222 != 32, drop this branch.\n     |- Try 270 * 48 = 12960. 12960 exceeds the maximum intermediate result, drop this branch.\n     |- Try 270 \/ 48 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 18 \/ 15 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (18, 48) (numbers left: [15]). Try possible operations.\n    |- Try 48 + 18 = 66. Add 66 to the number set. Current number set: [66, 15], target: 32, just two numbers left.\n     |- Try 66 + 15 = 81. Evaluate 81 != 32, drop this branch.\n     |- Try 66 - 15 = 51. Evaluate 51 != 32, drop this branch.\n     |- Try 66 * 15 = 990. Evaluate 990 != 32, drop this branch.\n     |- Try 66 \/ 15 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 48 - 18 = 30. Add 30 to the number set. Current number set: [30, 15], target: 32, just two numbers left.\n     |- Try 30 + 15 = 45. Evaluate 45 != 32, drop this branch.\n     |- Try 30 - 15 = 15. Evaluate 15 != 32, drop this branch.\n     |- Try 30 * 15 = 450. Evaluate 450 != 32, drop this branch.\n     |- Try 30 \/ 15 = 2. Evaluate 2 != 32, drop this branch.\n    |- Try 48 * 18 = 864. Add 864 to the number set. Current number set: [864, 15], target: 32, just two numbers left.\n     |- Try 864 + 15 = 879. Evaluate 879 != 32, drop this branch.\n     |- Try 864 - 15 = 849. Evaluate 849 != 32, drop this branch.\n     |- Try 864 * 15 = 12960. 12960 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 15 = 57.6. 57.6 is a decimal, drop this branch.\n    |- Try 48 \/ 18 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (15, 48) (numbers left: [18]). Try possible operations.\n    |- Try 48 + 15 = 63. Add 63 to the number set. Current number set: [63, 18], target: 32, just two numbers left.\n     |- Try 63 + 18 = 81. Evaluate 81 != 32, drop this branch.\n     |- Try 63 - 18 = 45. Evaluate 45 != 32, drop this branch.\n     |- Try 63 * 18 = 1134. Evaluate 1134 != 32, drop this branch.\n     |- Try 63 \/ 18 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 48 - 15 = 33. Add 33 to the number set. Current number set: [33, 18], target: 32, just two numbers left.\n     |- Try 33 + 18 = 51. Evaluate 51 != 32, drop this branch.\n     |- Try 33 - 18 = 15. Evaluate 15 != 32, drop this branch.\n     |- Try 33 * 18 = 594. Evaluate 594 != 32, drop this branch.\n     |- Try 33 \/ 18 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 48 * 15 = 720. Add 720 to the number set. Current number set: [720, 18], target: 32, just two numbers left.\n     |- Try 720 + 18 = 738. Evaluate 738 != 32, drop this branch.\n     |- Try 720 - 18 = 702. Evaluate 702 != 32, drop this branch.\n     |- Try 720 * 18 = 12960. 12960 exceeds the maximum intermediate result, drop this branch.\n     |- Try 720 \/ 18 = 40. Evaluate 40 != 32, drop this branch.\n    |- Try 48 \/ 15 = 3.2. 3.2 is a decimal, drop this branch.\n  |- Try 14 - 4 = 10. Add 10 to the number set. Current number set: [10, 15, 48], target: 32. Options for choosing two numbers: [(10, 15), (10, 48), (15, 48)].\n   |- Pick two numbers (10, 15) (numbers left: [48]). Try possible operations.\n    |- Try 15 + 10 = 25. Add 25 to the number set. Current number set: [25, 48], target: 32, just two numbers left.\n     |- Try 48 + 25 = 73. Evaluate 73 != 32, drop this branch.\n     |- Try 48 - 25 = 23. Evaluate 23 != 32, drop this branch.\n     |- Try 48 * 25 = 1200. Evaluate 1200 != 32, drop this branch.\n     |- Try 48 \/ 25 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 15 - 10 = 5. Add 5 to the number set. Current number set: [5, 48], target: 32, just two numbers left.\n     |- Try 48 + 5 = 53. Evaluate 53 != 32, drop this branch.\n     |- Try 48 - 5 = 43. Evaluate 43 != 32, drop this branch.\n     |- Try 48 * 5 = 240. Evaluate 240 != 32, drop this branch.\n     |- Try 48 \/ 5 = 9.6. 9.6 is a decimal, drop this branch.\n    |- Try 15 * 10 = 150. Add 150 to the number set. Current number set: [150, 48], target: 32, just two numbers left.\n     |- Try 150 + 48 = 198. Evaluate 198 != 32, drop this branch.\n     |- Try 150 - 48 = 102. Evaluate 102 != 32, drop this branch.\n     |- Try 150 * 48 = 7200. 7200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 48 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 15 \/ 10 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (10, 48) (numbers left: [15]). Try possible operations.\n    |- Try 48 + 10 = 58. Add 58 to the number set. Current number set: [58, 15], target: 32, just two numbers left.\n     |- Try 58 + 15 = 73. Evaluate 73 != 32, drop this branch.\n     |- Try 58 - 15 = 43. Evaluate 43 != 32, drop this branch.\n     |- Try 58 * 15 = 870. Evaluate 870 != 32, drop this branch.\n     |- Try 58 \/ 15 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 48 - 10 = 38. Add 38 to the number set. Current number set: [38, 15], target: 32, just two numbers left.\n     |- Try 38 + 15 = 53. Evaluate 53 != 32, drop this branch.\n     |- Try 38 - 15 = 23. Evaluate 23 != 32, drop this branch.\n     |- Try 38 * 15 = 570. Evaluate 570 != 32, drop this branch.\n     |- Try 38 \/ 15 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 48 * 10 = 480. Add 480 to the number set. Current number set: [480, 15], target: 32, just two numbers left.\n     |- Try 480 + 15 = 495. Evaluate 495 != 32, drop this branch.\n     |- Try 480 - 15 = 465. Evaluate 465 != 32, drop this branch.\n     |- Try 480 * 15 = 7200. 7200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 480 \/ 15 = 32. Evaluate 32 == 32, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 480 \/ 15 = 32\nThe step before: 48 * 10 = 480\nThe first step: 14 - 4 = 10\n\nOutput the solution in the required format:\n<Solution>\n14 - 4 = 10\n48 * 10 = 480\n480 \/ 15 = 32\n<\/Solution>\n","item":{"nums":[14,15,4,48],"solution":["14 - 4 = 10","48 * 10 = 480","480 \/ 15 = 32"],"target":32}}
+{"instance_id":"countdown_8k_155","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [48, 9, 48, 34]\nTarget: 34","reference_output":"# Search Procedure\nInitial number set: [48, 9, 48, 34], target: 34. Options for choosing two numbers: [(48, 9), (48, 48), (48, 34), (9, 48), (9, 34), (48, 34)].\n |- Pick two numbers (48, 9) (numbers left: [48, 34]). Try possible operations.\n  |- Try 48 + 9 = 57. Add 57 to the number set. Current number set: [57, 48, 34], target: 34. Options for choosing two numbers: [(57, 48), (57, 34), (48, 34)].\n   |- Pick two numbers (57, 48) (numbers left: [34]). Try possible operations.\n    |- Try 57 + 48 = 105. Add 105 to the number set. Current number set: [105, 34], target: 34, just two numbers left.\n     |- Try 105 + 34 = 139. Evaluate 139 != 34, drop this branch.\n     |- Try 105 - 34 = 71. Evaluate 71 != 34, drop this branch.\n     |- Try 105 * 34 = 3570. 3570 exceeds the maximum intermediate result, drop this branch.\n     |- Try 105 \/ 34 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 57 - 48 = 9. Add 9 to the number set. Current number set: [9, 34], target: 34, just two numbers left.\n     |- Try 34 + 9 = 43. Evaluate 43 != 34, drop this branch.\n     |- Try 34 - 9 = 25. Evaluate 25 != 34, drop this branch.\n     |- Try 34 * 9 = 306. Evaluate 306 != 34, drop this branch.\n     |- Try 34 \/ 9 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 57 * 48 = 2736. 2736 exceeds the maximum intermediate result, drop this branch.\n    |- Try 57 \/ 48 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (57, 34) (numbers left: [48]). Try possible operations.\n    |- Try 57 + 34 = 91. Add 91 to the number set. Current number set: [91, 48], target: 34, just two numbers left.\n     |- Try 91 + 48 = 139. Evaluate 139 != 34, drop this branch.\n     |- Try 91 - 48 = 43. Evaluate 43 != 34, drop this branch.\n     |- Try 91 * 48 = 4368. 4368 exceeds the maximum intermediate result, drop this branch.\n     |- Try 91 \/ 48 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 57 - 34 = 23. Add 23 to the number set. Current number set: [23, 48], target: 34, just two numbers left.\n     |- Try 48 + 23 = 71. Evaluate 71 != 34, drop this branch.\n     |- Try 48 - 23 = 25. Evaluate 25 != 34, drop this branch.\n     |- Try 48 * 23 = 1104. Evaluate 1104 != 34, drop this branch.\n     |- Try 48 \/ 23 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 57 * 34 = 1938. Add 1938 to the number set. Current number set: [1938, 48], target: 34, just two numbers left.\n     |- Try 1938 + 48 = 1986. Evaluate 1986 != 34, drop this branch.\n     |- Try 1938 - 48 = 1890. Evaluate 1890 != 34, drop this branch.\n     |- Try 1938 * 48 = 93024. 93024 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1938 \/ 48 = 40.4. 40.4 is a decimal, drop this branch.\n    |- Try 57 \/ 34 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (48, 34) (numbers left: [57]). Try possible operations.\n    |- Try 48 + 34 = 82. Add 82 to the number set. Current number set: [82, 57], target: 34, just two numbers left.\n     |- Try 82 + 57 = 139. Evaluate 139 != 34, drop this branch.\n     |- Try 82 - 57 = 25. Evaluate 25 != 34, drop this branch.\n     |- Try 82 * 57 = 4674. 4674 exceeds the maximum intermediate result, drop this branch.\n     |- Try 82 \/ 57 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 48 - 34 = 14. Add 14 to the number set. Current number set: [14, 57], target: 34, just two numbers left.\n     |- Try 57 + 14 = 71. Evaluate 71 != 34, drop this branch.\n     |- Try 57 - 14 = 43. Evaluate 43 != 34, drop this branch.\n     |- Try 57 * 14 = 798. Evaluate 798 != 34, drop this branch.\n     |- Try 57 \/ 14 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 48 * 34 = 1632. Add 1632 to the number set. Current number set: [1632, 57], target: 34, just two numbers left.\n     |- Try 1632 + 57 = 1689. Evaluate 1689 != 34, drop this branch.\n     |- Try 1632 - 57 = 1575. Evaluate 1575 != 34, drop this branch.\n     |- Try 1632 * 57 = 93024. 93024 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1632 \/ 57 = 28.6. 28.6 is a decimal, drop this branch.\n    |- Try 48 \/ 34 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 48 - 9 = 39. Add 39 to the number set. Current number set: [39, 48, 34], target: 34. Options for choosing two numbers: [(39, 48), (39, 34), (48, 34)].\n   |- Pick two numbers (39, 48) (numbers left: [34]). Try possible operations.\n    |- Try 48 + 39 = 87. Add 87 to the number set. Current number set: [87, 34], target: 34, just two numbers left.\n     |- Try 87 + 34 = 121. Evaluate 121 != 34, drop this branch.\n     |- Try 87 - 34 = 53. Evaluate 53 != 34, drop this branch.\n     |- Try 87 * 34 = 2958. 2958 exceeds the maximum intermediate result, drop this branch.\n     |- Try 87 \/ 34 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 48 - 39 = 9. Add 9 to the number set. Current number set: [9, 34], target: 34, just two numbers left.\n     |- Try 34 + 9 = 43. Evaluate 43 != 34, drop this branch.\n     |- Try 34 - 9 = 25. Evaluate 25 != 34, drop this branch.\n     |- Try 34 * 9 = 306. Evaluate 306 != 34, drop this branch.\n     |- Try 34 \/ 9 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 48 * 39 = 1872. Add 1872 to the number set. Current number set: [1872, 34], target: 34, just two numbers left.\n     |- Try 1872 + 34 = 1906. Evaluate 1906 != 34, drop this branch.\n     |- Try 1872 - 34 = 1838. Evaluate 1838 != 34, drop this branch.\n     |- Try 1872 * 34 = 63648. 63648 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1872 \/ 34 = 55.1. 55.1 is a decimal, drop this branch.\n    |- Try 48 \/ 39 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (39, 34) (numbers left: [48]). Try possible operations.\n    |- Try 39 + 34 = 73. Add 73 to the number set. Current number set: [73, 48], target: 34, just two numbers left.\n     |- Try 73 + 48 = 121. Evaluate 121 != 34, drop this branch.\n     |- Try 73 - 48 = 25. Evaluate 25 != 34, drop this branch.\n     |- Try 73 * 48 = 3504. 3504 exceeds the maximum intermediate result, drop this branch.\n     |- Try 73 \/ 48 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 39 - 34 = 5. Add 5 to the number set. Current number set: [5, 48], target: 34, just two numbers left.\n     |- Try 48 + 5 = 53. Evaluate 53 != 34, drop this branch.\n     |- Try 48 - 5 = 43. Evaluate 43 != 34, drop this branch.\n     |- Try 48 * 5 = 240. Evaluate 240 != 34, drop this branch.\n     |- Try 48 \/ 5 = 9.6. 9.6 is a decimal, drop this branch.\n    |- Try 39 * 34 = 1326. Add 1326 to the number set. Current number set: [1326, 48], target: 34, just two numbers left.\n     |- Try 1326 + 48 = 1374. Evaluate 1374 != 34, drop this branch.\n     |- Try 1326 - 48 = 1278. Evaluate 1278 != 34, drop this branch.\n     |- Try 1326 * 48 = 63648. 63648 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1326 \/ 48 = 27.6. 27.6 is a decimal, drop this branch.\n    |- Try 39 \/ 34 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (48, 34) (numbers left: [39]). Try possible operations.\n    |- Try 48 + 34 = 82. Add 82 to the number set. Current number set: [82, 39], target: 34, just two numbers left.\n     |- Try 82 + 39 = 121. Evaluate 121 != 34, drop this branch.\n     |- Try 82 - 39 = 43. Evaluate 43 != 34, drop this branch.\n     |- Try 82 * 39 = 3198. 3198 exceeds the maximum intermediate result, drop this branch.\n     |- Try 82 \/ 39 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 48 - 34 = 14. Add 14 to the number set. Current number set: [14, 39], target: 34, just two numbers left.\n     |- Try 39 + 14 = 53. Evaluate 53 != 34, drop this branch.\n     |- Try 39 - 14 = 25. Evaluate 25 != 34, drop this branch.\n     |- Try 39 * 14 = 546. Evaluate 546 != 34, drop this branch.\n     |- Try 39 \/ 14 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 48 * 34 = 1632. Add 1632 to the number set. Current number set: [1632, 39], target: 34, just two numbers left.\n     |- Try 1632 + 39 = 1671. Evaluate 1671 != 34, drop this branch.\n     |- Try 1632 - 39 = 1593. Evaluate 1593 != 34, drop this branch.\n     |- Try 1632 * 39 = 63648. 63648 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1632 \/ 39 = 41.8. 41.8 is a decimal, drop this branch.\n    |- Try 48 \/ 34 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 48 * 9 = 432. Add 432 to the number set. Current number set: [432, 48, 34], target: 34. Options for choosing two numbers: [(432, 48), (432, 34), (48, 34)].\n   |- Pick two numbers (432, 48) (numbers left: [34]). Try possible operations.\n    |- Try 432 + 48 = 480. Add 480 to the number set. Current number set: [480, 34], target: 34, just two numbers left.\n     |- Try 480 + 34 = 514. Evaluate 514 != 34, drop this branch.\n     |- Try 480 - 34 = 446. Evaluate 446 != 34, drop this branch.\n     |- Try 480 * 34 = 16320. 16320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 480 \/ 34 = 14.1. 14.1 is a decimal, drop this branch.\n    |- Try 432 - 48 = 384. Add 384 to the number set. Current number set: [384, 34], target: 34, just two numbers left.\n     |- Try 384 + 34 = 418. Evaluate 418 != 34, drop this branch.\n     |- Try 384 - 34 = 350. Evaluate 350 != 34, drop this branch.\n     |- Try 384 * 34 = 13056. 13056 exceeds the maximum intermediate result, drop this branch.\n     |- Try 384 \/ 34 = 11.3. 11.3 is a decimal, drop this branch.\n    |- Try 432 * 48 = 20736. 20736 exceeds the maximum intermediate result, drop this branch.\n    |- Try 432 \/ 48 = 9. Add 9 to the number set. Current number set: [9, 34], target: 34, just two numbers left.\n     |- Try 34 + 9 = 43. Evaluate 43 != 34, drop this branch.\n     |- Try 34 - 9 = 25. Evaluate 25 != 34, drop this branch.\n     |- Try 34 * 9 = 306. Evaluate 306 != 34, drop this branch.\n     |- Try 34 \/ 9 = 3.8. 3.8 is a decimal, drop this branch.\n   |- Pick two numbers (432, 34) (numbers left: [48]). Try possible operations.\n    |- Try 432 + 34 = 466. Add 466 to the number set. Current number set: [466, 48], target: 34, just two numbers left.\n     |- Try 466 + 48 = 514. Evaluate 514 != 34, drop this branch.\n     |- Try 466 - 48 = 418. Evaluate 418 != 34, drop this branch.\n     |- Try 466 * 48 = 22368. 22368 exceeds the maximum intermediate result, drop this branch.\n     |- Try 466 \/ 48 = 9.7. 9.7 is a decimal, drop this branch.\n    |- Try 432 - 34 = 398. Add 398 to the number set. Current number set: [398, 48], target: 34, just two numbers left.\n     |- Try 398 + 48 = 446. Evaluate 446 != 34, drop this branch.\n     |- Try 398 - 48 = 350. Evaluate 350 != 34, drop this branch.\n     |- Try 398 * 48 = 19104. 19104 exceeds the maximum intermediate result, drop this branch.\n     |- Try 398 \/ 48 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 432 * 34 = 14688. 14688 exceeds the maximum intermediate result, drop this branch.\n    |- Try 432 \/ 34 = 12.7. 12.7 is a decimal, drop this branch.\n   |- Pick two numbers (48, 34) (numbers left: [432]). Try possible operations.\n    |- Try 48 + 34 = 82. Add 82 to the number set. Current number set: [82, 432], target: 34, just two numbers left.\n     |- Try 432 + 82 = 514. Evaluate 514 != 34, drop this branch.\n     |- Try 432 - 82 = 350. Evaluate 350 != 34, drop this branch.\n     |- Try 432 * 82 = 35424. 35424 exceeds the maximum intermediate result, drop this branch.\n     |- Try 432 \/ 82 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 48 - 34 = 14. Add 14 to the number set. Current number set: [14, 432], target: 34, just two numbers left.\n     |- Try 432 + 14 = 446. Evaluate 446 != 34, drop this branch.\n     |- Try 432 - 14 = 418. Evaluate 418 != 34, drop this branch.\n     |- Try 432 * 14 = 6048. 6048 exceeds the maximum intermediate result, drop this branch.\n     |- Try 432 \/ 14 = 30.9. 30.9 is a decimal, drop this branch.\n    |- Try 48 * 34 = 1632. Add 1632 to the number set. Current number set: [1632, 432], target: 34, just two numbers left.\n     |- Try 1632 + 432 = 2064. 2064 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1632 - 432 = 1200. Evaluate 1200 != 34, drop this branch.\n     |- Try 1632 * 432 = 705024. 705024 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1632 \/ 432 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 48 \/ 34 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 48 \/ 9 = 5.3. 5.3 is a decimal, drop this branch.\n |- Pick two numbers (48, 48) (numbers left: [9, 34]). Try possible operations.\n  |- Try 48 + 48 = 96. Add 96 to the number set. Current number set: [96, 9, 34], target: 34. Options for choosing two numbers: [(96, 9), (96, 34), (9, 34)].\n   |- Pick two numbers (96, 9) (numbers left: [34]). Try possible operations.\n    |- Try 96 + 9 = 105. Add 105 to the number set. Current number set: [105, 34], target: 34, just two numbers left.\n     |- Try 105 + 34 = 139. Evaluate 139 != 34, drop this branch.\n     |- Try 105 - 34 = 71. Evaluate 71 != 34, drop this branch.\n     |- Try 105 * 34 = 3570. 3570 exceeds the maximum intermediate result, drop this branch.\n     |- Try 105 \/ 34 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 96 - 9 = 87. Add 87 to the number set. Current number set: [87, 34], target: 34, just two numbers left.\n     |- Try 87 + 34 = 121. Evaluate 121 != 34, drop this branch.\n     |- Try 87 - 34 = 53. Evaluate 53 != 34, drop this branch.\n     |- Try 87 * 34 = 2958. 2958 exceeds the maximum intermediate result, drop this branch.\n     |- Try 87 \/ 34 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 96 * 9 = 864. Add 864 to the number set. Current number set: [864, 34], target: 34, just two numbers left.\n     |- Try 864 + 34 = 898. Evaluate 898 != 34, drop this branch.\n     |- Try 864 - 34 = 830. Evaluate 830 != 34, drop this branch.\n     |- Try 864 * 34 = 29376. 29376 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 34 = 25.4. 25.4 is a decimal, drop this branch.\n    |- Try 96 \/ 9 = 10.7. 10.7 is a decimal, drop this branch.\n   |- Pick two numbers (96, 34) (numbers left: [9]). Try possible operations.\n    |- Try 96 + 34 = 130. Add 130 to the number set. Current number set: [130, 9], target: 34, just two numbers left.\n     |- Try 130 + 9 = 139. Evaluate 139 != 34, drop this branch.\n     |- Try 130 - 9 = 121. Evaluate 121 != 34, drop this branch.\n     |- Try 130 * 9 = 1170. Evaluate 1170 != 34, drop this branch.\n     |- Try 130 \/ 9 = 14.4. 14.4 is a decimal, drop this branch.\n    |- Try 96 - 34 = 62. Add 62 to the number set. Current number set: [62, 9], target: 34, just two numbers left.\n     |- Try 62 + 9 = 71. Evaluate 71 != 34, drop this branch.\n     |- Try 62 - 9 = 53. Evaluate 53 != 34, drop this branch.\n     |- Try 62 * 9 = 558. Evaluate 558 != 34, drop this branch.\n     |- Try 62 \/ 9 = 6.9. 6.9 is a decimal, drop this branch.\n    |- Try 96 * 34 = 3264. 3264 exceeds the maximum intermediate result, drop this branch.\n    |- Try 96 \/ 34 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (9, 34) (numbers left: [96]). Try possible operations.\n    |- Try 34 + 9 = 43. Add 43 to the number set. Current number set: [43, 96], target: 34, just two numbers left.\n     |- Try 96 + 43 = 139. Evaluate 139 != 34, drop this branch.\n     |- Try 96 - 43 = 53. Evaluate 53 != 34, drop this branch.\n     |- Try 96 * 43 = 4128. 4128 exceeds the maximum intermediate result, drop this branch.\n     |- Try 96 \/ 43 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 34 - 9 = 25. Add 25 to the number set. Current number set: [25, 96], target: 34, just two numbers left.\n     |- Try 96 + 25 = 121. Evaluate 121 != 34, drop this branch.\n     |- Try 96 - 25 = 71. Evaluate 71 != 34, drop this branch.\n     |- Try 96 * 25 = 2400. 2400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 96 \/ 25 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 34 * 9 = 306. Add 306 to the number set. Current number set: [306, 96], target: 34, just two numbers left.\n     |- Try 306 + 96 = 402. Evaluate 402 != 34, drop this branch.\n     |- Try 306 - 96 = 210. Evaluate 210 != 34, drop this branch.\n     |- Try 306 * 96 = 29376. 29376 exceeds the maximum intermediate result, drop this branch.\n     |- Try 306 \/ 96 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 34 \/ 9 = 3.8. 3.8 is a decimal, drop this branch.\n  |- Try 48 - 48 = 0. Add 0 to the number set. Current number set: [0, 9, 34], target: 34. Options for choosing two numbers: [(0, 9), (0, 34), (9, 34)].\n   |- Pick two numbers (0, 9) (numbers left: [34]). Try possible operations.\n    |- Try 9 + 0 = 9. Add 9 to the number set. Current number set: [9, 34], target: 34, just two numbers left.\n     |- Try 34 + 9 = 43. Evaluate 43 != 34, drop this branch.\n     |- Try 34 - 9 = 25. Evaluate 25 != 34, drop this branch.\n     |- Try 34 * 9 = 306. Evaluate 306 != 34, drop this branch.\n     |- Try 34 \/ 9 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 9 - 0 = 9. Add 9 to the number set. Current number set: [9, 34], target: 34, just two numbers left.\n     |- Try 34 + 9 = 43. Evaluate 43 != 34, drop this branch.\n     |- Try 34 - 9 = 25. Evaluate 25 != 34, drop this branch.\n     |- Try 34 * 9 = 306. Evaluate 306 != 34, drop this branch.\n     |- Try 34 \/ 9 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 9 * 0 = 0. Add 0 to the number set. Current number set: [0, 34], target: 34, just two numbers left.\n     |- Try 34 + 0 = 34. Evaluate 34 == 34, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 34 + 0 = 34\nThe step before: 9 * 0 = 0\nThe first step: 48 - 48 = 0\n\nOutput the solution in the required format:\n<Solution>\n48 - 48 = 0\n9 * 0 = 0\n34 + 0 = 34\n<\/Solution>\n","item":{"nums":[48,9,48,34],"solution":["48 - 48 = 0","9 * 0 = 0","34 + 0 = 34"],"target":34}}
+{"instance_id":"countdown_8k_156","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [35, 7, 5, 14]\nTarget: 20","reference_output":"# Search Procedure\nInitial number set: [35, 7, 5, 14], target: 20. Options for choosing two numbers: [(35, 7), (35, 5), (35, 14), (7, 5), (7, 14), (5, 14)].\n |- Pick two numbers (35, 7) (numbers left: [5, 14]). Try possible operations.\n  |- Try 35 + 7 = 42. Add 42 to the number set. Current number set: [42, 5, 14], target: 20. Options for choosing two numbers: [(42, 5), (42, 14), (5, 14)].\n   |- Pick two numbers (42, 5) (numbers left: [14]). Try possible operations.\n    |- Try 42 + 5 = 47. Add 47 to the number set. Current number set: [47, 14], target: 20, just two numbers left.\n     |- Try 47 + 14 = 61. Evaluate 61 != 20, drop this branch.\n     |- Try 47 - 14 = 33. Evaluate 33 != 20, drop this branch.\n     |- Try 47 * 14 = 658. Evaluate 658 != 20, drop this branch.\n     |- Try 47 \/ 14 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 42 - 5 = 37. Add 37 to the number set. Current number set: [37, 14], target: 20, just two numbers left.\n     |- Try 37 + 14 = 51. Evaluate 51 != 20, drop this branch.\n     |- Try 37 - 14 = 23. Evaluate 23 != 20, drop this branch.\n     |- Try 37 * 14 = 518. Evaluate 518 != 20, drop this branch.\n     |- Try 37 \/ 14 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 42 * 5 = 210. Add 210 to the number set. Current number set: [210, 14], target: 20, just two numbers left.\n     |- Try 210 + 14 = 224. Evaluate 224 != 20, drop this branch.\n     |- Try 210 - 14 = 196. Evaluate 196 != 20, drop this branch.\n     |- Try 210 * 14 = 2940. 2940 exceeds the maximum intermediate result, drop this branch.\n     |- Try 210 \/ 14 = 15. Evaluate 15 != 20, drop this branch.\n    |- Try 42 \/ 5 = 8.4. 8.4 is a decimal, drop this branch.\n   |- Pick two numbers (42, 14) (numbers left: [5]). Try possible operations.\n    |- Try 42 + 14 = 56. Add 56 to the number set. Current number set: [56, 5], target: 20, just two numbers left.\n     |- Try 56 + 5 = 61. Evaluate 61 != 20, drop this branch.\n     |- Try 56 - 5 = 51. Evaluate 51 != 20, drop this branch.\n     |- Try 56 * 5 = 280. Evaluate 280 != 20, drop this branch.\n     |- Try 56 \/ 5 = 11.2. 11.2 is a decimal, drop this branch.\n    |- Try 42 - 14 = 28. Add 28 to the number set. Current number set: [28, 5], target: 20, just two numbers left.\n     |- Try 28 + 5 = 33. Evaluate 33 != 20, drop this branch.\n     |- Try 28 - 5 = 23. Evaluate 23 != 20, drop this branch.\n     |- Try 28 * 5 = 140. Evaluate 140 != 20, drop this branch.\n     |- Try 28 \/ 5 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 42 * 14 = 588. Add 588 to the number set. Current number set: [588, 5], target: 20, just two numbers left.\n     |- Try 588 + 5 = 593. Evaluate 593 != 20, drop this branch.\n     |- Try 588 - 5 = 583. Evaluate 583 != 20, drop this branch.\n     |- Try 588 * 5 = 2940. 2940 exceeds the maximum intermediate result, drop this branch.\n     |- Try 588 \/ 5 = 117.6. 117.6 is a decimal, drop this branch.\n    |- Try 42 \/ 14 = 3. Add 3 to the number set. Current number set: [3, 5], target: 20, just two numbers left.\n     |- Try 5 + 3 = 8. Evaluate 8 != 20, drop this branch.\n     |- Try 5 - 3 = 2. Evaluate 2 != 20, drop this branch.\n     |- Try 5 * 3 = 15. Evaluate 15 != 20, drop this branch.\n     |- Try 5 \/ 3 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (5, 14) (numbers left: [42]). Try possible operations.\n    |- Try 14 + 5 = 19. Add 19 to the number set. Current number set: [19, 42], target: 20, just two numbers left.\n     |- Try 42 + 19 = 61. Evaluate 61 != 20, drop this branch.\n     |- Try 42 - 19 = 23. Evaluate 23 != 20, drop this branch.\n     |- Try 42 * 19 = 798. Evaluate 798 != 20, drop this branch.\n     |- Try 42 \/ 19 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 14 - 5 = 9. Add 9 to the number set. Current number set: [9, 42], target: 20, just two numbers left.\n     |- Try 42 + 9 = 51. Evaluate 51 != 20, drop this branch.\n     |- Try 42 - 9 = 33. Evaluate 33 != 20, drop this branch.\n     |- Try 42 * 9 = 378. Evaluate 378 != 20, drop this branch.\n     |- Try 42 \/ 9 = 4.7. 4.7 is a decimal, drop this branch.\n    |- Try 14 * 5 = 70. Add 70 to the number set. Current number set: [70, 42], target: 20, just two numbers left.\n     |- Try 70 + 42 = 112. Evaluate 112 != 20, drop this branch.\n     |- Try 70 - 42 = 28. Evaluate 28 != 20, drop this branch.\n     |- Try 70 * 42 = 2940. 2940 exceeds the maximum intermediate result, drop this branch.\n     |- Try 70 \/ 42 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 14 \/ 5 = 2.8. 2.8 is a decimal, drop this branch.\n  |- Try 35 - 7 = 28. Add 28 to the number set. Current number set: [28, 5, 14], target: 20. Options for choosing two numbers: [(28, 5), (28, 14), (5, 14)].\n   |- Pick two numbers (28, 5) (numbers left: [14]). Try possible operations.\n    |- Try 28 + 5 = 33. Add 33 to the number set. Current number set: [33, 14], target: 20, just two numbers left.\n     |- Try 33 + 14 = 47. Evaluate 47 != 20, drop this branch.\n     |- Try 33 - 14 = 19. Evaluate 19 != 20, drop this branch.\n     |- Try 33 * 14 = 462. Evaluate 462 != 20, drop this branch.\n     |- Try 33 \/ 14 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 28 - 5 = 23. Add 23 to the number set. Current number set: [23, 14], target: 20, just two numbers left.\n     |- Try 23 + 14 = 37. Evaluate 37 != 20, drop this branch.\n     |- Try 23 - 14 = 9. Evaluate 9 != 20, drop this branch.\n     |- Try 23 * 14 = 322. Evaluate 322 != 20, drop this branch.\n     |- Try 23 \/ 14 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 28 * 5 = 140. Add 140 to the number set. Current number set: [140, 14], target: 20, just two numbers left.\n     |- Try 140 + 14 = 154. Evaluate 154 != 20, drop this branch.\n     |- Try 140 - 14 = 126. Evaluate 126 != 20, drop this branch.\n     |- Try 140 * 14 = 1960. Evaluate 1960 != 20, drop this branch.\n     |- Try 140 \/ 14 = 10. Evaluate 10 != 20, drop this branch.\n    |- Try 28 \/ 5 = 5.6. 5.6 is a decimal, drop this branch.\n   |- Pick two numbers (28, 14) (numbers left: [5]). Try possible operations.\n    |- Try 28 + 14 = 42. Add 42 to the number set. Current number set: [42, 5], target: 20, just two numbers left.\n     |- Try 42 + 5 = 47. Evaluate 47 != 20, drop this branch.\n     |- Try 42 - 5 = 37. Evaluate 37 != 20, drop this branch.\n     |- Try 42 * 5 = 210. Evaluate 210 != 20, drop this branch.\n     |- Try 42 \/ 5 = 8.4. 8.4 is a decimal, drop this branch.\n    |- Try 28 - 14 = 14. Add 14 to the number set. Current number set: [14, 5], target: 20, just two numbers left.\n     |- Try 14 + 5 = 19. Evaluate 19 != 20, drop this branch.\n     |- Try 14 - 5 = 9. Evaluate 9 != 20, drop this branch.\n     |- Try 14 * 5 = 70. Evaluate 70 != 20, drop this branch.\n     |- Try 14 \/ 5 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 28 * 14 = 392. Add 392 to the number set. Current number set: [392, 5], target: 20, just two numbers left.\n     |- Try 392 + 5 = 397. Evaluate 397 != 20, drop this branch.\n     |- Try 392 - 5 = 387. Evaluate 387 != 20, drop this branch.\n     |- Try 392 * 5 = 1960. Evaluate 1960 != 20, drop this branch.\n     |- Try 392 \/ 5 = 78.4. 78.4 is a decimal, drop this branch.\n    |- Try 28 \/ 14 = 2. Add 2 to the number set. Current number set: [2, 5], target: 20, just two numbers left.\n     |- Try 5 + 2 = 7. Evaluate 7 != 20, drop this branch.\n     |- Try 5 - 2 = 3. Evaluate 3 != 20, drop this branch.\n     |- Try 5 * 2 = 10. Evaluate 10 != 20, drop this branch.\n     |- Try 5 \/ 2 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (5, 14) (numbers left: [28]). Try possible operations.\n    |- Try 14 + 5 = 19. Add 19 to the number set. Current number set: [19, 28], target: 20, just two numbers left.\n     |- Try 28 + 19 = 47. Evaluate 47 != 20, drop this branch.\n     |- Try 28 - 19 = 9. Evaluate 9 != 20, drop this branch.\n     |- Try 28 * 19 = 532. Evaluate 532 != 20, drop this branch.\n     |- Try 28 \/ 19 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 14 - 5 = 9. Add 9 to the number set. Current number set: [9, 28], target: 20, just two numbers left.\n     |- Try 28 + 9 = 37. Evaluate 37 != 20, drop this branch.\n     |- Try 28 - 9 = 19. Evaluate 19 != 20, drop this branch.\n     |- Try 28 * 9 = 252. Evaluate 252 != 20, drop this branch.\n     |- Try 28 \/ 9 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 14 * 5 = 70. Add 70 to the number set. Current number set: [70, 28], target: 20, just two numbers left.\n     |- Try 70 + 28 = 98. Evaluate 98 != 20, drop this branch.\n     |- Try 70 - 28 = 42. Evaluate 42 != 20, drop this branch.\n     |- Try 70 * 28 = 1960. Evaluate 1960 != 20, drop this branch.\n     |- Try 70 \/ 28 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 14 \/ 5 = 2.8. 2.8 is a decimal, drop this branch.\n  |- Try 35 * 7 = 245. Add 245 to the number set. Current number set: [245, 5, 14], target: 20. Options for choosing two numbers: [(245, 5), (245, 14), (5, 14)].\n   |- Pick two numbers (245, 5) (numbers left: [14]). Try possible operations.\n    |- Try 245 + 5 = 250. Add 250 to the number set. Current number set: [250, 14], target: 20, just two numbers left.\n     |- Try 250 + 14 = 264. Evaluate 264 != 20, drop this branch.\n     |- Try 250 - 14 = 236. Evaluate 236 != 20, drop this branch.\n     |- Try 250 * 14 = 3500. 3500 exceeds the maximum intermediate result, drop this branch.\n     |- Try 250 \/ 14 = 17.9. 17.9 is a decimal, drop this branch.\n    |- Try 245 - 5 = 240. Add 240 to the number set. Current number set: [240, 14], target: 20, just two numbers left.\n     |- Try 240 + 14 = 254. Evaluate 254 != 20, drop this branch.\n     |- Try 240 - 14 = 226. Evaluate 226 != 20, drop this branch.\n     |- Try 240 * 14 = 3360. 3360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 240 \/ 14 = 17.1. 17.1 is a decimal, drop this branch.\n    |- Try 245 * 5 = 1225. Add 1225 to the number set. Current number set: [1225, 14], target: 20, just two numbers left.\n     |- Try 1225 + 14 = 1239. Evaluate 1239 != 20, drop this branch.\n     |- Try 1225 - 14 = 1211. Evaluate 1211 != 20, drop this branch.\n     |- Try 1225 * 14 = 17150. 17150 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1225 \/ 14 = 87.5. 87.5 is a decimal, drop this branch.\n    |- Try 245 \/ 5 = 49. Add 49 to the number set. Current number set: [49, 14], target: 20, just two numbers left.\n     |- Try 49 + 14 = 63. Evaluate 63 != 20, drop this branch.\n     |- Try 49 - 14 = 35. Evaluate 35 != 20, drop this branch.\n     |- Try 49 * 14 = 686. Evaluate 686 != 20, drop this branch.\n     |- Try 49 \/ 14 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (245, 14) (numbers left: [5]). Try possible operations.\n    |- Try 245 + 14 = 259. Add 259 to the number set. Current number set: [259, 5], target: 20, just two numbers left.\n     |- Try 259 + 5 = 264. Evaluate 264 != 20, drop this branch.\n     |- Try 259 - 5 = 254. Evaluate 254 != 20, drop this branch.\n     |- Try 259 * 5 = 1295. Evaluate 1295 != 20, drop this branch.\n     |- Try 259 \/ 5 = 51.8. 51.8 is a decimal, drop this branch.\n    |- Try 245 - 14 = 231. Add 231 to the number set. Current number set: [231, 5], target: 20, just two numbers left.\n     |- Try 231 + 5 = 236. Evaluate 236 != 20, drop this branch.\n     |- Try 231 - 5 = 226. Evaluate 226 != 20, drop this branch.\n     |- Try 231 * 5 = 1155. Evaluate 1155 != 20, drop this branch.\n     |- Try 231 \/ 5 = 46.2. 46.2 is a decimal, drop this branch.\n    |- Try 245 * 14 = 3430. 3430 exceeds the maximum intermediate result, drop this branch.\n    |- Try 245 \/ 14 = 17.5. 17.5 is a decimal, drop this branch.\n   |- Pick two numbers (5, 14) (numbers left: [245]). Try possible operations.\n    |- Try 14 + 5 = 19. Add 19 to the number set. Current number set: [19, 245], target: 20, just two numbers left.\n     |- Try 245 + 19 = 264. Evaluate 264 != 20, drop this branch.\n     |- Try 245 - 19 = 226. Evaluate 226 != 20, drop this branch.\n     |- Try 245 * 19 = 4655. 4655 exceeds the maximum intermediate result, drop this branch.\n     |- Try 245 \/ 19 = 12.9. 12.9 is a decimal, drop this branch.\n    |- Try 14 - 5 = 9. Add 9 to the number set. Current number set: [9, 245], target: 20, just two numbers left.\n     |- Try 245 + 9 = 254. Evaluate 254 != 20, drop this branch.\n     |- Try 245 - 9 = 236. Evaluate 236 != 20, drop this branch.\n     |- Try 245 * 9 = 2205. 2205 exceeds the maximum intermediate result, drop this branch.\n     |- Try 245 \/ 9 = 27.2. 27.2 is a decimal, drop this branch.\n    |- Try 14 * 5 = 70. Add 70 to the number set. Current number set: [70, 245], target: 20, just two numbers left.\n     |- Try 245 + 70 = 315. Evaluate 315 != 20, drop this branch.\n     |- Try 245 - 70 = 175. Evaluate 175 != 20, drop this branch.\n     |- Try 245 * 70 = 17150. 17150 exceeds the maximum intermediate result, drop this branch.\n     |- Try 245 \/ 70 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 14 \/ 5 = 2.8. 2.8 is a decimal, drop this branch.\n  |- Try 35 \/ 7 = 5. Add 5 to the number set. Current number set: [5, 5, 14], target: 20. Options for choosing two numbers: [(5, 5), (5, 14), (5, 14)].\n   |- Pick two numbers (5, 5) (numbers left: [14]). Try possible operations.\n    |- Try 5 + 5 = 10. Add 10 to the number set. Current number set: [10, 14], target: 20, just two numbers left.\n     |- Try 14 + 10 = 24. Evaluate 24 != 20, drop this branch.\n     |- Try 14 - 10 = 4. Evaluate 4 != 20, drop this branch.\n     |- Try 14 * 10 = 140. Evaluate 140 != 20, drop this branch.\n     |- Try 14 \/ 10 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 5 - 5 = 0. Add 0 to the number set. Current number set: [0, 14], target: 20, just two numbers left.\n     |- Try 14 + 0 = 14. Evaluate 14 != 20, drop this branch.\n     |- Try 14 - 0 = 14. Evaluate 14 != 20, drop this branch.\n     |- Try 14 * 0 = 0. Evaluate 0 != 20, drop this branch.\n     |- Try 14 \/ 0 (invalid operation). drop this branch.\n    |- Try 5 * 5 = 25. Add 25 to the number set. Current number set: [25, 14], target: 20, just two numbers left.\n     |- Try 25 + 14 = 39. Evaluate 39 != 20, drop this branch.\n     |- Try 25 - 14 = 11. Evaluate 11 != 20, drop this branch.\n     |- Try 25 * 14 = 350. Evaluate 350 != 20, drop this branch.\n     |- Try 25 \/ 14 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 5 \/ 5 = 1. Add 1 to the number set. Current number set: [1, 14], target: 20, just two numbers left.\n     |- Try 14 + 1 = 15. Evaluate 15 != 20, drop this branch.\n     |- Try 14 - 1 = 13. Evaluate 13 != 20, drop this branch.\n     |- Try 14 * 1 = 14. Evaluate 14 != 20, drop this branch.\n     |- Try 14 \/ 1 = 14. Evaluate 14 != 20, drop this branch.\n   |- Pick two numbers (5, 14) (numbers left: [5]). Try possible operations.\n    |- Try 14 + 5 = 19. Add 19 to the number set. Current number set: [19, 5], target: 20, just two numbers left.\n     |- Try 19 + 5 = 24. Evaluate 24 != 20, drop this branch.\n     |- Try 19 - 5 = 14. Evaluate 14 != 20, drop this branch.\n     |- Try 19 * 5 = 95. Evaluate 95 != 20, drop this branch.\n     |- Try 19 \/ 5 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 14 - 5 = 9. Add 9 to the number set. Current number set: [9, 5], target: 20, just two numbers left.\n     |- Try 9 + 5 = 14. Evaluate 14 != 20, drop this branch.\n     |- Try 9 - 5 = 4. Evaluate 4 != 20, drop this branch.\n     |- Try 9 * 5 = 45. Evaluate 45 != 20, drop this branch.\n     |- Try 9 \/ 5 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 14 * 5 = 70. Add 70 to the number set. Current number set: [70, 5], target: 20, just two numbers left.\n     |- Try 70 + 5 = 75. Evaluate 75 != 20, drop this branch.\n     |- Try 70 - 5 = 65. Evaluate 65 != 20, drop this branch.\n     |- Try 70 * 5 = 350. Evaluate 350 != 20, drop this branch.\n     |- Try 70 \/ 5 = 14. Evaluate 14 != 20, drop this branch.\n    |- Try 14 \/ 5 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (5, 14) (numbers left: [5]). Try possible operations.\n    |- Try 14 + 5 = 19. Add 19 to the number set. Current number set: [19, 5], target: 20, just two numbers left.\n     |- Try 19 + 5 = 24. Evaluate 24 != 20, drop this branch.\n     |- Try 19 - 5 = 14. Evaluate 14 != 20, drop this branch.\n     |- Try 19 * 5 = 95. Evaluate 95 != 20, drop this branch.\n     |- Try 19 \/ 5 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 14 - 5 = 9. Add 9 to the number set. Current number set: [9, 5], target: 20, just two numbers left.\n     |- Try 9 + 5 = 14. Evaluate 14 != 20, drop this branch.\n     |- Try 9 - 5 = 4. Evaluate 4 != 20, drop this branch.\n     |- Try 9 * 5 = 45. Evaluate 45 != 20, drop this branch.\n     |- Try 9 \/ 5 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 14 * 5 = 70. Add 70 to the number set. Current number set: [70, 5], target: 20, just two numbers left.\n     |- Try 70 + 5 = 75. Evaluate 75 != 20, drop this branch.\n     |- Try 70 - 5 = 65. Evaluate 65 != 20, drop this branch.\n     |- Try 70 * 5 = 350. Evaluate 350 != 20, drop this branch.\n     |- Try 70 \/ 5 = 14. Evaluate 14 != 20, drop this branch.\n    |- Try 14 \/ 5 = 2.8. 2.8 is a decimal, drop this branch.\n |- Pick two numbers (35, 5) (numbers left: [7, 14]). Try possible operations.\n  |- Try 35 + 5 = 40. Add 40 to the number set. Current number set: [40, 7, 14], target: 20. Options for choosing two numbers: [(40, 7), (40, 14), (7, 14)].\n   |- Pick two numbers (40, 7) (numbers left: [14]). Try possible operations.\n    |- Try 40 + 7 = 47. Add 47 to the number set. Current number set: [47, 14], target: 20, just two numbers left.\n     |- Try 47 + 14 = 61. Evaluate 61 != 20, drop this branch.\n     |- Try 47 - 14 = 33. Evaluate 33 != 20, drop this branch.\n     |- Try 47 * 14 = 658. Evaluate 658 != 20, drop this branch.\n     |- Try 47 \/ 14 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 40 - 7 = 33. Add 33 to the number set. Current number set: [33, 14], target: 20, just two numbers left.\n     |- Try 33 + 14 = 47. Evaluate 47 != 20, drop this branch.\n     |- Try 33 - 14 = 19. Evaluate 19 != 20, drop this branch.\n     |- Try 33 * 14 = 462. Evaluate 462 != 20, drop this branch.\n     |- Try 33 \/ 14 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 40 * 7 = 280. Add 280 to the number set. Current number set: [280, 14], target: 20, just two numbers left.\n     |- Try 280 + 14 = 294. Evaluate 294 != 20, drop this branch.\n     |- Try 280 - 14 = 266. Evaluate 266 != 20, drop this branch.\n     |- Try 280 * 14 = 3920. 3920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 280 \/ 14 = 20. Evaluate 20 == 20, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 280 \/ 14 = 20\nThe step before: 40 * 7 = 280\nThe first step: 35 + 5 = 40\n\nOutput the solution in the required format:\n<Solution>\n35 + 5 = 40\n40 * 7 = 280\n280 \/ 14 = 20\n<\/Solution>\n","item":{"nums":[35,7,5,14],"solution":["35 + 5 = 40","40 * 7 = 280","280 \/ 14 = 20"],"target":20}}
+{"instance_id":"countdown_8k_157","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [9, 45, 44, 7]\nTarget: 32","reference_output":"# Search Procedure\nInitial number set: [9, 45, 44, 7], target: 32. Options for choosing two numbers: [(9, 45), (9, 44), (9, 7), (45, 44), (45, 7), (44, 7)].\n |- Pick two numbers (9, 45) (numbers left: [44, 7]). Try possible operations.\n  |- Try 45 + 9 = 54. Add 54 to the number set. Current number set: [54, 44, 7], target: 32. Options for choosing two numbers: [(54, 44), (54, 7), (44, 7)].\n   |- Pick two numbers (54, 44) (numbers left: [7]). Try possible operations.\n    |- Try 54 + 44 = 98. Add 98 to the number set. Current number set: [98, 7], target: 32, just two numbers left.\n     |- Try 98 + 7 = 105. Evaluate 105 != 32, drop this branch.\n     |- Try 98 - 7 = 91. Evaluate 91 != 32, drop this branch.\n     |- Try 98 * 7 = 686. Evaluate 686 != 32, drop this branch.\n     |- Try 98 \/ 7 = 14. Evaluate 14 != 32, drop this branch.\n    |- Try 54 - 44 = 10. Add 10 to the number set. Current number set: [10, 7], target: 32, just two numbers left.\n     |- Try 10 + 7 = 17. Evaluate 17 != 32, drop this branch.\n     |- Try 10 - 7 = 3. Evaluate 3 != 32, drop this branch.\n     |- Try 10 * 7 = 70. Evaluate 70 != 32, drop this branch.\n     |- Try 10 \/ 7 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 54 * 44 = 2376. 2376 exceeds the maximum intermediate result, drop this branch.\n    |- Try 54 \/ 44 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (54, 7) (numbers left: [44]). Try possible operations.\n    |- Try 54 + 7 = 61. Add 61 to the number set. Current number set: [61, 44], target: 32, just two numbers left.\n     |- Try 61 + 44 = 105. Evaluate 105 != 32, drop this branch.\n     |- Try 61 - 44 = 17. Evaluate 17 != 32, drop this branch.\n     |- Try 61 * 44 = 2684. 2684 exceeds the maximum intermediate result, drop this branch.\n     |- Try 61 \/ 44 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 54 - 7 = 47. Add 47 to the number set. Current number set: [47, 44], target: 32, just two numbers left.\n     |- Try 47 + 44 = 91. Evaluate 91 != 32, drop this branch.\n     |- Try 47 - 44 = 3. Evaluate 3 != 32, drop this branch.\n     |- Try 47 * 44 = 2068. 2068 exceeds the maximum intermediate result, drop this branch.\n     |- Try 47 \/ 44 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 54 * 7 = 378. Add 378 to the number set. Current number set: [378, 44], target: 32, just two numbers left.\n     |- Try 378 + 44 = 422. Evaluate 422 != 32, drop this branch.\n     |- Try 378 - 44 = 334. Evaluate 334 != 32, drop this branch.\n     |- Try 378 * 44 = 16632. 16632 exceeds the maximum intermediate result, drop this branch.\n     |- Try 378 \/ 44 = 8.6. 8.6 is a decimal, drop this branch.\n    |- Try 54 \/ 7 = 7.7. 7.7 is a decimal, drop this branch.\n   |- Pick two numbers (44, 7) (numbers left: [54]). Try possible operations.\n    |- Try 44 + 7 = 51. Add 51 to the number set. Current number set: [51, 54], target: 32, just two numbers left.\n     |- Try 54 + 51 = 105. Evaluate 105 != 32, drop this branch.\n     |- Try 54 - 51 = 3. Evaluate 3 != 32, drop this branch.\n     |- Try 54 * 51 = 2754. 2754 exceeds the maximum intermediate result, drop this branch.\n     |- Try 54 \/ 51 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 44 - 7 = 37. Add 37 to the number set. Current number set: [37, 54], target: 32, just two numbers left.\n     |- Try 54 + 37 = 91. Evaluate 91 != 32, drop this branch.\n     |- Try 54 - 37 = 17. Evaluate 17 != 32, drop this branch.\n     |- Try 54 * 37 = 1998. Evaluate 1998 != 32, drop this branch.\n     |- Try 54 \/ 37 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 44 * 7 = 308. Add 308 to the number set. Current number set: [308, 54], target: 32, just two numbers left.\n     |- Try 308 + 54 = 362. Evaluate 362 != 32, drop this branch.\n     |- Try 308 - 54 = 254. Evaluate 254 != 32, drop this branch.\n     |- Try 308 * 54 = 16632. 16632 exceeds the maximum intermediate result, drop this branch.\n     |- Try 308 \/ 54 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 44 \/ 7 = 6.3. 6.3 is a decimal, drop this branch.\n  |- Try 45 - 9 = 36. Add 36 to the number set. Current number set: [36, 44, 7], target: 32. Options for choosing two numbers: [(36, 44), (36, 7), (44, 7)].\n   |- Pick two numbers (36, 44) (numbers left: [7]). Try possible operations.\n    |- Try 44 + 36 = 80. Add 80 to the number set. Current number set: [80, 7], target: 32, just two numbers left.\n     |- Try 80 + 7 = 87. Evaluate 87 != 32, drop this branch.\n     |- Try 80 - 7 = 73. Evaluate 73 != 32, drop this branch.\n     |- Try 80 * 7 = 560. Evaluate 560 != 32, drop this branch.\n     |- Try 80 \/ 7 = 11.4. 11.4 is a decimal, drop this branch.\n    |- Try 44 - 36 = 8. Add 8 to the number set. Current number set: [8, 7], target: 32, just two numbers left.\n     |- Try 8 + 7 = 15. Evaluate 15 != 32, drop this branch.\n     |- Try 8 - 7 = 1. Evaluate 1 != 32, drop this branch.\n     |- Try 8 * 7 = 56. Evaluate 56 != 32, drop this branch.\n     |- Try 8 \/ 7 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 44 * 36 = 1584. Add 1584 to the number set. Current number set: [1584, 7], target: 32, just two numbers left.\n     |- Try 1584 + 7 = 1591. Evaluate 1591 != 32, drop this branch.\n     |- Try 1584 - 7 = 1577. Evaluate 1577 != 32, drop this branch.\n     |- Try 1584 * 7 = 11088. 11088 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1584 \/ 7 = 226.3. 226.3 is a decimal, drop this branch.\n    |- Try 44 \/ 36 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (36, 7) (numbers left: [44]). Try possible operations.\n    |- Try 36 + 7 = 43. Add 43 to the number set. Current number set: [43, 44], target: 32, just two numbers left.\n     |- Try 44 + 43 = 87. Evaluate 87 != 32, drop this branch.\n     |- Try 44 - 43 = 1. Evaluate 1 != 32, drop this branch.\n     |- Try 44 * 43 = 1892. Evaluate 1892 != 32, drop this branch.\n     |- Try 44 \/ 43 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 36 - 7 = 29. Add 29 to the number set. Current number set: [29, 44], target: 32, just two numbers left.\n     |- Try 44 + 29 = 73. Evaluate 73 != 32, drop this branch.\n     |- Try 44 - 29 = 15. Evaluate 15 != 32, drop this branch.\n     |- Try 44 * 29 = 1276. Evaluate 1276 != 32, drop this branch.\n     |- Try 44 \/ 29 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 36 * 7 = 252. Add 252 to the number set. Current number set: [252, 44], target: 32, just two numbers left.\n     |- Try 252 + 44 = 296. Evaluate 296 != 32, drop this branch.\n     |- Try 252 - 44 = 208. Evaluate 208 != 32, drop this branch.\n     |- Try 252 * 44 = 11088. 11088 exceeds the maximum intermediate result, drop this branch.\n     |- Try 252 \/ 44 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 36 \/ 7 = 5.1. 5.1 is a decimal, drop this branch.\n   |- Pick two numbers (44, 7) (numbers left: [36]). Try possible operations.\n    |- Try 44 + 7 = 51. Add 51 to the number set. Current number set: [51, 36], target: 32, just two numbers left.\n     |- Try 51 + 36 = 87. Evaluate 87 != 32, drop this branch.\n     |- Try 51 - 36 = 15. Evaluate 15 != 32, drop this branch.\n     |- Try 51 * 36 = 1836. Evaluate 1836 != 32, drop this branch.\n     |- Try 51 \/ 36 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 44 - 7 = 37. Add 37 to the number set. Current number set: [37, 36], target: 32, just two numbers left.\n     |- Try 37 + 36 = 73. Evaluate 73 != 32, drop this branch.\n     |- Try 37 - 36 = 1. Evaluate 1 != 32, drop this branch.\n     |- Try 37 * 36 = 1332. Evaluate 1332 != 32, drop this branch.\n     |- Try 37 \/ 36 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 44 * 7 = 308. Add 308 to the number set. Current number set: [308, 36], target: 32, just two numbers left.\n     |- Try 308 + 36 = 344. Evaluate 344 != 32, drop this branch.\n     |- Try 308 - 36 = 272. Evaluate 272 != 32, drop this branch.\n     |- Try 308 * 36 = 11088. 11088 exceeds the maximum intermediate result, drop this branch.\n     |- Try 308 \/ 36 = 8.6. 8.6 is a decimal, drop this branch.\n    |- Try 44 \/ 7 = 6.3. 6.3 is a decimal, drop this branch.\n  |- Try 45 * 9 = 405. Add 405 to the number set. Current number set: [405, 44, 7], target: 32. Options for choosing two numbers: [(405, 44), (405, 7), (44, 7)].\n   |- Pick two numbers (405, 44) (numbers left: [7]). Try possible operations.\n    |- Try 405 + 44 = 449. Add 449 to the number set. Current number set: [449, 7], target: 32, just two numbers left.\n     |- Try 449 + 7 = 456. Evaluate 456 != 32, drop this branch.\n     |- Try 449 - 7 = 442. Evaluate 442 != 32, drop this branch.\n     |- Try 449 * 7 = 3143. 3143 exceeds the maximum intermediate result, drop this branch.\n     |- Try 449 \/ 7 = 64.1. 64.1 is a decimal, drop this branch.\n    |- Try 405 - 44 = 361. Add 361 to the number set. Current number set: [361, 7], target: 32, just two numbers left.\n     |- Try 361 + 7 = 368. Evaluate 368 != 32, drop this branch.\n     |- Try 361 - 7 = 354. Evaluate 354 != 32, drop this branch.\n     |- Try 361 * 7 = 2527. 2527 exceeds the maximum intermediate result, drop this branch.\n     |- Try 361 \/ 7 = 51.6. 51.6 is a decimal, drop this branch.\n    |- Try 405 * 44 = 17820. 17820 exceeds the maximum intermediate result, drop this branch.\n    |- Try 405 \/ 44 = 9.2. 9.2 is a decimal, drop this branch.\n   |- Pick two numbers (405, 7) (numbers left: [44]). Try possible operations.\n    |- Try 405 + 7 = 412. Add 412 to the number set. Current number set: [412, 44], target: 32, just two numbers left.\n     |- Try 412 + 44 = 456. Evaluate 456 != 32, drop this branch.\n     |- Try 412 - 44 = 368. Evaluate 368 != 32, drop this branch.\n     |- Try 412 * 44 = 18128. 18128 exceeds the maximum intermediate result, drop this branch.\n     |- Try 412 \/ 44 = 9.4. 9.4 is a decimal, drop this branch.\n    |- Try 405 - 7 = 398. Add 398 to the number set. Current number set: [398, 44], target: 32, just two numbers left.\n     |- Try 398 + 44 = 442. Evaluate 442 != 32, drop this branch.\n     |- Try 398 - 44 = 354. Evaluate 354 != 32, drop this branch.\n     |- Try 398 * 44 = 17512. 17512 exceeds the maximum intermediate result, drop this branch.\n     |- Try 398 \/ 44 = 9.0. 9.0 is a decimal, drop this branch.\n    |- Try 405 * 7 = 2835. 2835 exceeds the maximum intermediate result, drop this branch.\n    |- Try 405 \/ 7 = 57.9. 57.9 is a decimal, drop this branch.\n   |- Pick two numbers (44, 7) (numbers left: [405]). Try possible operations.\n    |- Try 44 + 7 = 51. Add 51 to the number set. Current number set: [51, 405], target: 32, just two numbers left.\n     |- Try 405 + 51 = 456. Evaluate 456 != 32, drop this branch.\n     |- Try 405 - 51 = 354. Evaluate 354 != 32, drop this branch.\n     |- Try 405 * 51 = 20655. 20655 exceeds the maximum intermediate result, drop this branch.\n     |- Try 405 \/ 51 = 7.9. 7.9 is a decimal, drop this branch.\n    |- Try 44 - 7 = 37. Add 37 to the number set. Current number set: [37, 405], target: 32, just two numbers left.\n     |- Try 405 + 37 = 442. Evaluate 442 != 32, drop this branch.\n     |- Try 405 - 37 = 368. Evaluate 368 != 32, drop this branch.\n     |- Try 405 * 37 = 14985. 14985 exceeds the maximum intermediate result, drop this branch.\n     |- Try 405 \/ 37 = 10.9. 10.9 is a decimal, drop this branch.\n    |- Try 44 * 7 = 308. Add 308 to the number set. Current number set: [308, 405], target: 32, just two numbers left.\n     |- Try 405 + 308 = 713. Evaluate 713 != 32, drop this branch.\n     |- Try 405 - 308 = 97. Evaluate 97 != 32, drop this branch.\n     |- Try 405 * 308 = 124740. 124740 exceeds the maximum intermediate result, drop this branch.\n     |- Try 405 \/ 308 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 44 \/ 7 = 6.3. 6.3 is a decimal, drop this branch.\n  |- Try 45 \/ 9 = 5. Add 5 to the number set. Current number set: [5, 44, 7], target: 32. Options for choosing two numbers: [(5, 44), (5, 7), (44, 7)].\n   |- Pick two numbers (5, 44) (numbers left: [7]). Try possible operations.\n    |- Try 44 + 5 = 49. Add 49 to the number set. Current number set: [49, 7], target: 32, just two numbers left.\n     |- Try 49 + 7 = 56. Evaluate 56 != 32, drop this branch.\n     |- Try 49 - 7 = 42. Evaluate 42 != 32, drop this branch.\n     |- Try 49 * 7 = 343. Evaluate 343 != 32, drop this branch.\n     |- Try 49 \/ 7 = 7. Evaluate 7 != 32, drop this branch.\n    |- Try 44 - 5 = 39. Add 39 to the number set. Current number set: [39, 7], target: 32, just two numbers left.\n     |- Try 39 + 7 = 46. Evaluate 46 != 32, drop this branch.\n     |- Try 39 - 7 = 32. Evaluate 32 == 32, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 39 - 7 = 32\nThe step before: 44 - 5 = 39\nThe first step: 45 \/ 9 = 5\n\nOutput the solution in the required format:\n<Solution>\n45 \/ 9 = 5\n44 - 5 = 39\n39 - 7 = 32\n<\/Solution>\n","item":{"nums":[9,45,44,7],"solution":["45 \/ 9 = 5","44 - 5 = 39","39 - 7 = 32"],"target":32}}
+{"instance_id":"countdown_8k_158","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [24, 40, 28, 3]\nTarget: 28","reference_output":"# Search Procedure\nInitial number set: [24, 40, 28, 3], target: 28. Options for choosing two numbers: [(24, 40), (24, 28), (24, 3), (40, 28), (40, 3), (28, 3)].\n |- Pick two numbers (24, 40) (numbers left: [28, 3]). Try possible operations.\n  |- Try 40 + 24 = 64. Add 64 to the number set. Current number set: [64, 28, 3], target: 28. Options for choosing two numbers: [(64, 28), (64, 3), (28, 3)].\n   |- Pick two numbers (64, 28) (numbers left: [3]). Try possible operations.\n    |- Try 64 + 28 = 92. Add 92 to the number set. Current number set: [92, 3], target: 28, just two numbers left.\n     |- Try 92 + 3 = 95. Evaluate 95 != 28, drop this branch.\n     |- Try 92 - 3 = 89. Evaluate 89 != 28, drop this branch.\n     |- Try 92 * 3 = 276. Evaluate 276 != 28, drop this branch.\n     |- Try 92 \/ 3 = 30.7. 30.7 is a decimal, drop this branch.\n    |- Try 64 - 28 = 36. Add 36 to the number set. Current number set: [36, 3], target: 28, just two numbers left.\n     |- Try 36 + 3 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 36 - 3 = 33. Evaluate 33 != 28, drop this branch.\n     |- Try 36 * 3 = 108. Evaluate 108 != 28, drop this branch.\n     |- Try 36 \/ 3 = 12. Evaluate 12 != 28, drop this branch.\n    |- Try 64 * 28 = 1792. Add 1792 to the number set. Current number set: [1792, 3], target: 28, just two numbers left.\n     |- Try 1792 + 3 = 1795. Evaluate 1795 != 28, drop this branch.\n     |- Try 1792 - 3 = 1789. Evaluate 1789 != 28, drop this branch.\n     |- Try 1792 * 3 = 5376. 5376 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1792 \/ 3 = 597.3. 597.3 is a decimal, drop this branch.\n    |- Try 64 \/ 28 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (64, 3) (numbers left: [28]). Try possible operations.\n    |- Try 64 + 3 = 67. Add 67 to the number set. Current number set: [67, 28], target: 28, just two numbers left.\n     |- Try 67 + 28 = 95. Evaluate 95 != 28, drop this branch.\n     |- Try 67 - 28 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 67 * 28 = 1876. Evaluate 1876 != 28, drop this branch.\n     |- Try 67 \/ 28 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 64 - 3 = 61. Add 61 to the number set. Current number set: [61, 28], target: 28, just two numbers left.\n     |- Try 61 + 28 = 89. Evaluate 89 != 28, drop this branch.\n     |- Try 61 - 28 = 33. Evaluate 33 != 28, drop this branch.\n     |- Try 61 * 28 = 1708. Evaluate 1708 != 28, drop this branch.\n     |- Try 61 \/ 28 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 64 * 3 = 192. Add 192 to the number set. Current number set: [192, 28], target: 28, just two numbers left.\n     |- Try 192 + 28 = 220. Evaluate 220 != 28, drop this branch.\n     |- Try 192 - 28 = 164. Evaluate 164 != 28, drop this branch.\n     |- Try 192 * 28 = 5376. 5376 exceeds the maximum intermediate result, drop this branch.\n     |- Try 192 \/ 28 = 6.9. 6.9 is a decimal, drop this branch.\n    |- Try 64 \/ 3 = 21.3. 21.3 is a decimal, drop this branch.\n   |- Pick two numbers (28, 3) (numbers left: [64]). Try possible operations.\n    |- Try 28 + 3 = 31. Add 31 to the number set. Current number set: [31, 64], target: 28, just two numbers left.\n     |- Try 64 + 31 = 95. Evaluate 95 != 28, drop this branch.\n     |- Try 64 - 31 = 33. Evaluate 33 != 28, drop this branch.\n     |- Try 64 * 31 = 1984. Evaluate 1984 != 28, drop this branch.\n     |- Try 64 \/ 31 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 28 - 3 = 25. Add 25 to the number set. Current number set: [25, 64], target: 28, just two numbers left.\n     |- Try 64 + 25 = 89. Evaluate 89 != 28, drop this branch.\n     |- Try 64 - 25 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 64 * 25 = 1600. Evaluate 1600 != 28, drop this branch.\n     |- Try 64 \/ 25 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 28 * 3 = 84. Add 84 to the number set. Current number set: [84, 64], target: 28, just two numbers left.\n     |- Try 84 + 64 = 148. Evaluate 148 != 28, drop this branch.\n     |- Try 84 - 64 = 20. Evaluate 20 != 28, drop this branch.\n     |- Try 84 * 64 = 5376. 5376 exceeds the maximum intermediate result, drop this branch.\n     |- Try 84 \/ 64 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 28 \/ 3 = 9.3. 9.3 is a decimal, drop this branch.\n  |- Try 40 - 24 = 16. Add 16 to the number set. Current number set: [16, 28, 3], target: 28. Options for choosing two numbers: [(16, 28), (16, 3), (28, 3)].\n   |- Pick two numbers (16, 28) (numbers left: [3]). Try possible operations.\n    |- Try 28 + 16 = 44. Add 44 to the number set. Current number set: [44, 3], target: 28, just two numbers left.\n     |- Try 44 + 3 = 47. Evaluate 47 != 28, drop this branch.\n     |- Try 44 - 3 = 41. Evaluate 41 != 28, drop this branch.\n     |- Try 44 * 3 = 132. Evaluate 132 != 28, drop this branch.\n     |- Try 44 \/ 3 = 14.7. 14.7 is a decimal, drop this branch.\n    |- Try 28 - 16 = 12. Add 12 to the number set. Current number set: [12, 3], target: 28, just two numbers left.\n     |- Try 12 + 3 = 15. Evaluate 15 != 28, drop this branch.\n     |- Try 12 - 3 = 9. Evaluate 9 != 28, drop this branch.\n     |- Try 12 * 3 = 36. Evaluate 36 != 28, drop this branch.\n     |- Try 12 \/ 3 = 4. Evaluate 4 != 28, drop this branch.\n    |- Try 28 * 16 = 448. Add 448 to the number set. Current number set: [448, 3], target: 28, just two numbers left.\n     |- Try 448 + 3 = 451. Evaluate 451 != 28, drop this branch.\n     |- Try 448 - 3 = 445. Evaluate 445 != 28, drop this branch.\n     |- Try 448 * 3 = 1344. Evaluate 1344 != 28, drop this branch.\n     |- Try 448 \/ 3 = 149.3. 149.3 is a decimal, drop this branch.\n    |- Try 28 \/ 16 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (16, 3) (numbers left: [28]). Try possible operations.\n    |- Try 16 + 3 = 19. Add 19 to the number set. Current number set: [19, 28], target: 28, just two numbers left.\n     |- Try 28 + 19 = 47. Evaluate 47 != 28, drop this branch.\n     |- Try 28 - 19 = 9. Evaluate 9 != 28, drop this branch.\n     |- Try 28 * 19 = 532. Evaluate 532 != 28, drop this branch.\n     |- Try 28 \/ 19 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 16 - 3 = 13. Add 13 to the number set. Current number set: [13, 28], target: 28, just two numbers left.\n     |- Try 28 + 13 = 41. Evaluate 41 != 28, drop this branch.\n     |- Try 28 - 13 = 15. Evaluate 15 != 28, drop this branch.\n     |- Try 28 * 13 = 364. Evaluate 364 != 28, drop this branch.\n     |- Try 28 \/ 13 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 16 * 3 = 48. Add 48 to the number set. Current number set: [48, 28], target: 28, just two numbers left.\n     |- Try 48 + 28 = 76. Evaluate 76 != 28, drop this branch.\n     |- Try 48 - 28 = 20. Evaluate 20 != 28, drop this branch.\n     |- Try 48 * 28 = 1344. Evaluate 1344 != 28, drop this branch.\n     |- Try 48 \/ 28 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 16 \/ 3 = 5.3. 5.3 is a decimal, drop this branch.\n   |- Pick two numbers (28, 3) (numbers left: [16]). Try possible operations.\n    |- Try 28 + 3 = 31. Add 31 to the number set. Current number set: [31, 16], target: 28, just two numbers left.\n     |- Try 31 + 16 = 47. Evaluate 47 != 28, drop this branch.\n     |- Try 31 - 16 = 15. Evaluate 15 != 28, drop this branch.\n     |- Try 31 * 16 = 496. Evaluate 496 != 28, drop this branch.\n     |- Try 31 \/ 16 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 28 - 3 = 25. Add 25 to the number set. Current number set: [25, 16], target: 28, just two numbers left.\n     |- Try 25 + 16 = 41. Evaluate 41 != 28, drop this branch.\n     |- Try 25 - 16 = 9. Evaluate 9 != 28, drop this branch.\n     |- Try 25 * 16 = 400. Evaluate 400 != 28, drop this branch.\n     |- Try 25 \/ 16 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 28 * 3 = 84. Add 84 to the number set. Current number set: [84, 16], target: 28, just two numbers left.\n     |- Try 84 + 16 = 100. Evaluate 100 != 28, drop this branch.\n     |- Try 84 - 16 = 68. Evaluate 68 != 28, drop this branch.\n     |- Try 84 * 16 = 1344. Evaluate 1344 != 28, drop this branch.\n     |- Try 84 \/ 16 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 28 \/ 3 = 9.3. 9.3 is a decimal, drop this branch.\n  |- Try 40 * 24 = 960. Add 960 to the number set. Current number set: [960, 28, 3], target: 28. Options for choosing two numbers: [(960, 28), (960, 3), (28, 3)].\n   |- Pick two numbers (960, 28) (numbers left: [3]). Try possible operations.\n    |- Try 960 + 28 = 988. Add 988 to the number set. Current number set: [988, 3], target: 28, just two numbers left.\n     |- Try 988 + 3 = 991. Evaluate 991 != 28, drop this branch.\n     |- Try 988 - 3 = 985. Evaluate 985 != 28, drop this branch.\n     |- Try 988 * 3 = 2964. 2964 exceeds the maximum intermediate result, drop this branch.\n     |- Try 988 \/ 3 = 329.3. 329.3 is a decimal, drop this branch.\n    |- Try 960 - 28 = 932. Add 932 to the number set. Current number set: [932, 3], target: 28, just two numbers left.\n     |- Try 932 + 3 = 935. Evaluate 935 != 28, drop this branch.\n     |- Try 932 - 3 = 929. Evaluate 929 != 28, drop this branch.\n     |- Try 932 * 3 = 2796. 2796 exceeds the maximum intermediate result, drop this branch.\n     |- Try 932 \/ 3 = 310.7. 310.7 is a decimal, drop this branch.\n    |- Try 960 * 28 = 26880. 26880 exceeds the maximum intermediate result, drop this branch.\n    |- Try 960 \/ 28 = 34.3. 34.3 is a decimal, drop this branch.\n   |- Pick two numbers (960, 3) (numbers left: [28]). Try possible operations.\n    |- Try 960 + 3 = 963. Add 963 to the number set. Current number set: [963, 28], target: 28, just two numbers left.\n     |- Try 963 + 28 = 991. Evaluate 991 != 28, drop this branch.\n     |- Try 963 - 28 = 935. Evaluate 935 != 28, drop this branch.\n     |- Try 963 * 28 = 26964. 26964 exceeds the maximum intermediate result, drop this branch.\n     |- Try 963 \/ 28 = 34.4. 34.4 is a decimal, drop this branch.\n    |- Try 960 - 3 = 957. Add 957 to the number set. Current number set: [957, 28], target: 28, just two numbers left.\n     |- Try 957 + 28 = 985. Evaluate 985 != 28, drop this branch.\n     |- Try 957 - 28 = 929. Evaluate 929 != 28, drop this branch.\n     |- Try 957 * 28 = 26796. 26796 exceeds the maximum intermediate result, drop this branch.\n     |- Try 957 \/ 28 = 34.2. 34.2 is a decimal, drop this branch.\n    |- Try 960 * 3 = 2880. 2880 exceeds the maximum intermediate result, drop this branch.\n    |- Try 960 \/ 3 = 320. Add 320 to the number set. Current number set: [320, 28], target: 28, just two numbers left.\n     |- Try 320 + 28 = 348. Evaluate 348 != 28, drop this branch.\n     |- Try 320 - 28 = 292. Evaluate 292 != 28, drop this branch.\n     |- Try 320 * 28 = 8960. 8960 exceeds the maximum intermediate result, drop this branch.\n     |- Try 320 \/ 28 = 11.4. 11.4 is a decimal, drop this branch.\n   |- Pick two numbers (28, 3) (numbers left: [960]). Try possible operations.\n    |- Try 28 + 3 = 31. Add 31 to the number set. Current number set: [31, 960], target: 28, just two numbers left.\n     |- Try 960 + 31 = 991. Evaluate 991 != 28, drop this branch.\n     |- Try 960 - 31 = 929. Evaluate 929 != 28, drop this branch.\n     |- Try 960 * 31 = 29760. 29760 exceeds the maximum intermediate result, drop this branch.\n     |- Try 960 \/ 31 = 31.0. 31.0 is a decimal, drop this branch.\n    |- Try 28 - 3 = 25. Add 25 to the number set. Current number set: [25, 960], target: 28, just two numbers left.\n     |- Try 960 + 25 = 985. Evaluate 985 != 28, drop this branch.\n     |- Try 960 - 25 = 935. Evaluate 935 != 28, drop this branch.\n     |- Try 960 * 25 = 24000. 24000 exceeds the maximum intermediate result, drop this branch.\n     |- Try 960 \/ 25 = 38.4. 38.4 is a decimal, drop this branch.\n    |- Try 28 * 3 = 84. Add 84 to the number set. Current number set: [84, 960], target: 28, just two numbers left.\n     |- Try 960 + 84 = 1044. Evaluate 1044 != 28, drop this branch.\n     |- Try 960 - 84 = 876. Evaluate 876 != 28, drop this branch.\n     |- Try 960 * 84 = 80640. 80640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 960 \/ 84 = 11.4. 11.4 is a decimal, drop this branch.\n    |- Try 28 \/ 3 = 9.3. 9.3 is a decimal, drop this branch.\n  |- Try 40 \/ 24 = 1.7. 1.7 is a decimal, drop this branch.\n |- Pick two numbers (24, 28) (numbers left: [40, 3]). Try possible operations.\n  |- Try 28 + 24 = 52. Add 52 to the number set. Current number set: [52, 40, 3], target: 28. Options for choosing two numbers: [(52, 40), (52, 3), (40, 3)].\n   |- Pick two numbers (52, 40) (numbers left: [3]). Try possible operations.\n    |- Try 52 + 40 = 92. Add 92 to the number set. Current number set: [92, 3], target: 28, just two numbers left.\n     |- Try 92 + 3 = 95. Evaluate 95 != 28, drop this branch.\n     |- Try 92 - 3 = 89. Evaluate 89 != 28, drop this branch.\n     |- Try 92 * 3 = 276. Evaluate 276 != 28, drop this branch.\n     |- Try 92 \/ 3 = 30.7. 30.7 is a decimal, drop this branch.\n    |- Try 52 - 40 = 12. Add 12 to the number set. Current number set: [12, 3], target: 28, just two numbers left.\n     |- Try 12 + 3 = 15. Evaluate 15 != 28, drop this branch.\n     |- Try 12 - 3 = 9. Evaluate 9 != 28, drop this branch.\n     |- Try 12 * 3 = 36. Evaluate 36 != 28, drop this branch.\n     |- Try 12 \/ 3 = 4. Evaluate 4 != 28, drop this branch.\n    |- Try 52 * 40 = 2080. 2080 exceeds the maximum intermediate result, drop this branch.\n    |- Try 52 \/ 40 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (52, 3) (numbers left: [40]). Try possible operations.\n    |- Try 52 + 3 = 55. Add 55 to the number set. Current number set: [55, 40], target: 28, just two numbers left.\n     |- Try 55 + 40 = 95. Evaluate 95 != 28, drop this branch.\n     |- Try 55 - 40 = 15. Evaluate 15 != 28, drop this branch.\n     |- Try 55 * 40 = 2200. 2200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 55 \/ 40 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 52 - 3 = 49. Add 49 to the number set. Current number set: [49, 40], target: 28, just two numbers left.\n     |- Try 49 + 40 = 89. Evaluate 89 != 28, drop this branch.\n     |- Try 49 - 40 = 9. Evaluate 9 != 28, drop this branch.\n     |- Try 49 * 40 = 1960. Evaluate 1960 != 28, drop this branch.\n     |- Try 49 \/ 40 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 52 * 3 = 156. Add 156 to the number set. Current number set: [156, 40], target: 28, just two numbers left.\n     |- Try 156 + 40 = 196. Evaluate 196 != 28, drop this branch.\n     |- Try 156 - 40 = 116. Evaluate 116 != 28, drop this branch.\n     |- Try 156 * 40 = 6240. 6240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 156 \/ 40 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 52 \/ 3 = 17.3. 17.3 is a decimal, drop this branch.\n   |- Pick two numbers (40, 3) (numbers left: [52]). Try possible operations.\n    |- Try 40 + 3 = 43. Add 43 to the number set. Current number set: [43, 52], target: 28, just two numbers left.\n     |- Try 52 + 43 = 95. Evaluate 95 != 28, drop this branch.\n     |- Try 52 - 43 = 9. Evaluate 9 != 28, drop this branch.\n     |- Try 52 * 43 = 2236. 2236 exceeds the maximum intermediate result, drop this branch.\n     |- Try 52 \/ 43 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 40 - 3 = 37. Add 37 to the number set. Current number set: [37, 52], target: 28, just two numbers left.\n     |- Try 52 + 37 = 89. Evaluate 89 != 28, drop this branch.\n     |- Try 52 - 37 = 15. Evaluate 15 != 28, drop this branch.\n     |- Try 52 * 37 = 1924. Evaluate 1924 != 28, drop this branch.\n     |- Try 52 \/ 37 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 40 * 3 = 120. Add 120 to the number set. Current number set: [120, 52], target: 28, just two numbers left.\n     |- Try 120 + 52 = 172. Evaluate 172 != 28, drop this branch.\n     |- Try 120 - 52 = 68. Evaluate 68 != 28, drop this branch.\n     |- Try 120 * 52 = 6240. 6240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 120 \/ 52 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 40 \/ 3 = 13.3. 13.3 is a decimal, drop this branch.\n  |- Try 28 - 24 = 4. Add 4 to the number set. Current number set: [4, 40, 3], target: 28. Options for choosing two numbers: [(4, 40), (4, 3), (40, 3)].\n   |- Pick two numbers (4, 40) (numbers left: [3]). Try possible operations.\n    |- Try 40 + 4 = 44. Add 44 to the number set. Current number set: [44, 3], target: 28, just two numbers left.\n     |- Try 44 + 3 = 47. Evaluate 47 != 28, drop this branch.\n     |- Try 44 - 3 = 41. Evaluate 41 != 28, drop this branch.\n     |- Try 44 * 3 = 132. Evaluate 132 != 28, drop this branch.\n     |- Try 44 \/ 3 = 14.7. 14.7 is a decimal, drop this branch.\n    |- Try 40 - 4 = 36. Add 36 to the number set. Current number set: [36, 3], target: 28, just two numbers left.\n     |- Try 36 + 3 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 36 - 3 = 33. Evaluate 33 != 28, drop this branch.\n     |- Try 36 * 3 = 108. Evaluate 108 != 28, drop this branch.\n     |- Try 36 \/ 3 = 12. Evaluate 12 != 28, drop this branch.\n    |- Try 40 * 4 = 160. Add 160 to the number set. Current number set: [160, 3], target: 28, just two numbers left.\n     |- Try 160 + 3 = 163. Evaluate 163 != 28, drop this branch.\n     |- Try 160 - 3 = 157. Evaluate 157 != 28, drop this branch.\n     |- Try 160 * 3 = 480. Evaluate 480 != 28, drop this branch.\n     |- Try 160 \/ 3 = 53.3. 53.3 is a decimal, drop this branch.\n    |- Try 40 \/ 4 = 10. Add 10 to the number set. Current number set: [10, 3], target: 28, just two numbers left.\n     |- Try 10 + 3 = 13. Evaluate 13 != 28, drop this branch.\n     |- Try 10 - 3 = 7. Evaluate 7 != 28, drop this branch.\n     |- Try 10 * 3 = 30. Evaluate 30 != 28, drop this branch.\n     |- Try 10 \/ 3 = 3.3. 3.3 is a decimal, drop this branch.\n   |- Pick two numbers (4, 3) (numbers left: [40]). Try possible operations.\n    |- Try 4 + 3 = 7. Add 7 to the number set. Current number set: [7, 40], target: 28, just two numbers left.\n     |- Try 40 + 7 = 47. Evaluate 47 != 28, drop this branch.\n     |- Try 40 - 7 = 33. Evaluate 33 != 28, drop this branch.\n     |- Try 40 * 7 = 280. Evaluate 280 != 28, drop this branch.\n     |- Try 40 \/ 7 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 4 - 3 = 1. Add 1 to the number set. Current number set: [1, 40], target: 28, just two numbers left.\n     |- Try 40 + 1 = 41. Evaluate 41 != 28, drop this branch.\n     |- Try 40 - 1 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 40 * 1 = 40. Evaluate 40 != 28, drop this branch.\n     |- Try 40 \/ 1 = 40. Evaluate 40 != 28, drop this branch.\n    |- Try 4 * 3 = 12. Add 12 to the number set. Current number set: [12, 40], target: 28, just two numbers left.\n     |- Try 40 + 12 = 52. Evaluate 52 != 28, drop this branch.\n     |- Try 40 - 12 = 28. Evaluate 28 == 28, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 40 - 12 = 28\nThe step before: 4 * 3 = 12\nThe first step: 28 - 24 = 4\n\nOutput the solution in the required format:\n<Solution>\n28 - 24 = 4\n4 * 3 = 12\n40 - 12 = 28\n<\/Solution>\n","item":{"nums":[24,40,28,3],"solution":["28 - 24 = 4","4 * 3 = 12","40 - 12 = 28"],"target":28}}
+{"instance_id":"countdown_8k_159","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [26, 5, 15, 25]\nTarget: 46","reference_output":"# Search Procedure\nInitial number set: [26, 5, 15, 25], target: 46. Options for choosing two numbers: [(26, 5), (26, 15), (26, 25), (5, 15), (5, 25), (15, 25)].\n |- Pick two numbers (26, 5) (numbers left: [15, 25]). Try possible operations.\n  |- Try 26 + 5 = 31. Add 31 to the number set. Current number set: [31, 15, 25], target: 46. Options for choosing two numbers: [(31, 15), (31, 25), (15, 25)].\n   |- Pick two numbers (31, 15) (numbers left: [25]). Try possible operations.\n    |- Try 31 + 15 = 46. Add 46 to the number set. Current number set: [46, 25], target: 46, just two numbers left.\n     |- Try 46 + 25 = 71. Evaluate 71 != 46, drop this branch.\n     |- Try 46 - 25 = 21. Evaluate 21 != 46, drop this branch.\n     |- Try 46 * 25 = 1150. Evaluate 1150 != 46, drop this branch.\n     |- Try 46 \/ 25 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 31 - 15 = 16. Add 16 to the number set. Current number set: [16, 25], target: 46, just two numbers left.\n     |- Try 25 + 16 = 41. Evaluate 41 != 46, drop this branch.\n     |- Try 25 - 16 = 9. Evaluate 9 != 46, drop this branch.\n     |- Try 25 * 16 = 400. Evaluate 400 != 46, drop this branch.\n     |- Try 25 \/ 16 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 31 * 15 = 465. Add 465 to the number set. Current number set: [465, 25], target: 46, just two numbers left.\n     |- Try 465 + 25 = 490. Evaluate 490 != 46, drop this branch.\n     |- Try 465 - 25 = 440. Evaluate 440 != 46, drop this branch.\n     |- Try 465 * 25 = 11625. 11625 exceeds the maximum intermediate result, drop this branch.\n     |- Try 465 \/ 25 = 18.6. 18.6 is a decimal, drop this branch.\n    |- Try 31 \/ 15 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (31, 25) (numbers left: [15]). Try possible operations.\n    |- Try 31 + 25 = 56. Add 56 to the number set. Current number set: [56, 15], target: 46, just two numbers left.\n     |- Try 56 + 15 = 71. Evaluate 71 != 46, drop this branch.\n     |- Try 56 - 15 = 41. Evaluate 41 != 46, drop this branch.\n     |- Try 56 * 15 = 840. Evaluate 840 != 46, drop this branch.\n     |- Try 56 \/ 15 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 31 - 25 = 6. Add 6 to the number set. Current number set: [6, 15], target: 46, just two numbers left.\n     |- Try 15 + 6 = 21. Evaluate 21 != 46, drop this branch.\n     |- Try 15 - 6 = 9. Evaluate 9 != 46, drop this branch.\n     |- Try 15 * 6 = 90. Evaluate 90 != 46, drop this branch.\n     |- Try 15 \/ 6 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 31 * 25 = 775. Add 775 to the number set. Current number set: [775, 15], target: 46, just two numbers left.\n     |- Try 775 + 15 = 790. Evaluate 790 != 46, drop this branch.\n     |- Try 775 - 15 = 760. Evaluate 760 != 46, drop this branch.\n     |- Try 775 * 15 = 11625. 11625 exceeds the maximum intermediate result, drop this branch.\n     |- Try 775 \/ 15 = 51.7. 51.7 is a decimal, drop this branch.\n    |- Try 31 \/ 25 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (15, 25) (numbers left: [31]). Try possible operations.\n    |- Try 25 + 15 = 40. Add 40 to the number set. Current number set: [40, 31], target: 46, just two numbers left.\n     |- Try 40 + 31 = 71. Evaluate 71 != 46, drop this branch.\n     |- Try 40 - 31 = 9. Evaluate 9 != 46, drop this branch.\n     |- Try 40 * 31 = 1240. Evaluate 1240 != 46, drop this branch.\n     |- Try 40 \/ 31 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 25 - 15 = 10. Add 10 to the number set. Current number set: [10, 31], target: 46, just two numbers left.\n     |- Try 31 + 10 = 41. Evaluate 41 != 46, drop this branch.\n     |- Try 31 - 10 = 21. Evaluate 21 != 46, drop this branch.\n     |- Try 31 * 10 = 310. Evaluate 310 != 46, drop this branch.\n     |- Try 31 \/ 10 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 25 * 15 = 375. Add 375 to the number set. Current number set: [375, 31], target: 46, just two numbers left.\n     |- Try 375 + 31 = 406. Evaluate 406 != 46, drop this branch.\n     |- Try 375 - 31 = 344. Evaluate 344 != 46, drop this branch.\n     |- Try 375 * 31 = 11625. 11625 exceeds the maximum intermediate result, drop this branch.\n     |- Try 375 \/ 31 = 12.1. 12.1 is a decimal, drop this branch.\n    |- Try 25 \/ 15 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 26 - 5 = 21. Add 21 to the number set. Current number set: [21, 15, 25], target: 46. Options for choosing two numbers: [(21, 15), (21, 25), (15, 25)].\n   |- Pick two numbers (21, 15) (numbers left: [25]). Try possible operations.\n    |- Try 21 + 15 = 36. Add 36 to the number set. Current number set: [36, 25], target: 46, just two numbers left.\n     |- Try 36 + 25 = 61. Evaluate 61 != 46, drop this branch.\n     |- Try 36 - 25 = 11. Evaluate 11 != 46, drop this branch.\n     |- Try 36 * 25 = 900. Evaluate 900 != 46, drop this branch.\n     |- Try 36 \/ 25 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 21 - 15 = 6. Add 6 to the number set. Current number set: [6, 25], target: 46, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 46, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 46, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 46, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 21 * 15 = 315. Add 315 to the number set. Current number set: [315, 25], target: 46, just two numbers left.\n     |- Try 315 + 25 = 340. Evaluate 340 != 46, drop this branch.\n     |- Try 315 - 25 = 290. Evaluate 290 != 46, drop this branch.\n     |- Try 315 * 25 = 7875. 7875 exceeds the maximum intermediate result, drop this branch.\n     |- Try 315 \/ 25 = 12.6. 12.6 is a decimal, drop this branch.\n    |- Try 21 \/ 15 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (21, 25) (numbers left: [15]). Try possible operations.\n    |- Try 25 + 21 = 46. Add 46 to the number set. Current number set: [46, 15], target: 46, just two numbers left.\n     |- Try 46 + 15 = 61. Evaluate 61 != 46, drop this branch.\n     |- Try 46 - 15 = 31. Evaluate 31 != 46, drop this branch.\n     |- Try 46 * 15 = 690. Evaluate 690 != 46, drop this branch.\n     |- Try 46 \/ 15 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 25 - 21 = 4. Add 4 to the number set. Current number set: [4, 15], target: 46, just two numbers left.\n     |- Try 15 + 4 = 19. Evaluate 19 != 46, drop this branch.\n     |- Try 15 - 4 = 11. Evaluate 11 != 46, drop this branch.\n     |- Try 15 * 4 = 60. Evaluate 60 != 46, drop this branch.\n     |- Try 15 \/ 4 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 25 * 21 = 525. Add 525 to the number set. Current number set: [525, 15], target: 46, just two numbers left.\n     |- Try 525 + 15 = 540. Evaluate 540 != 46, drop this branch.\n     |- Try 525 - 15 = 510. Evaluate 510 != 46, drop this branch.\n     |- Try 525 * 15 = 7875. 7875 exceeds the maximum intermediate result, drop this branch.\n     |- Try 525 \/ 15 = 35. Evaluate 35 != 46, drop this branch.\n    |- Try 25 \/ 21 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (15, 25) (numbers left: [21]). Try possible operations.\n    |- Try 25 + 15 = 40. Add 40 to the number set. Current number set: [40, 21], target: 46, just two numbers left.\n     |- Try 40 + 21 = 61. Evaluate 61 != 46, drop this branch.\n     |- Try 40 - 21 = 19. Evaluate 19 != 46, drop this branch.\n     |- Try 40 * 21 = 840. Evaluate 840 != 46, drop this branch.\n     |- Try 40 \/ 21 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 25 - 15 = 10. Add 10 to the number set. Current number set: [10, 21], target: 46, just two numbers left.\n     |- Try 21 + 10 = 31. Evaluate 31 != 46, drop this branch.\n     |- Try 21 - 10 = 11. Evaluate 11 != 46, drop this branch.\n     |- Try 21 * 10 = 210. Evaluate 210 != 46, drop this branch.\n     |- Try 21 \/ 10 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 25 * 15 = 375. Add 375 to the number set. Current number set: [375, 21], target: 46, just two numbers left.\n     |- Try 375 + 21 = 396. Evaluate 396 != 46, drop this branch.\n     |- Try 375 - 21 = 354. Evaluate 354 != 46, drop this branch.\n     |- Try 375 * 21 = 7875. 7875 exceeds the maximum intermediate result, drop this branch.\n     |- Try 375 \/ 21 = 17.9. 17.9 is a decimal, drop this branch.\n    |- Try 25 \/ 15 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 26 * 5 = 130. Add 130 to the number set. Current number set: [130, 15, 25], target: 46. Options for choosing two numbers: [(130, 15), (130, 25), (15, 25)].\n   |- Pick two numbers (130, 15) (numbers left: [25]). Try possible operations.\n    |- Try 130 + 15 = 145. Add 145 to the number set. Current number set: [145, 25], target: 46, just two numbers left.\n     |- Try 145 + 25 = 170. Evaluate 170 != 46, drop this branch.\n     |- Try 145 - 25 = 120. Evaluate 120 != 46, drop this branch.\n     |- Try 145 * 25 = 3625. 3625 exceeds the maximum intermediate result, drop this branch.\n     |- Try 145 \/ 25 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 130 - 15 = 115. Add 115 to the number set. Current number set: [115, 25], target: 46, just two numbers left.\n     |- Try 115 + 25 = 140. Evaluate 140 != 46, drop this branch.\n     |- Try 115 - 25 = 90. Evaluate 90 != 46, drop this branch.\n     |- Try 115 * 25 = 2875. 2875 exceeds the maximum intermediate result, drop this branch.\n     |- Try 115 \/ 25 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 130 * 15 = 1950. Add 1950 to the number set. Current number set: [1950, 25], target: 46, just two numbers left.\n     |- Try 1950 + 25 = 1975. Evaluate 1975 != 46, drop this branch.\n     |- Try 1950 - 25 = 1925. Evaluate 1925 != 46, drop this branch.\n     |- Try 1950 * 25 = 48750. 48750 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1950 \/ 25 = 78. Evaluate 78 != 46, drop this branch.\n    |- Try 130 \/ 15 = 8.7. 8.7 is a decimal, drop this branch.\n   |- Pick two numbers (130, 25) (numbers left: [15]). Try possible operations.\n    |- Try 130 + 25 = 155. Add 155 to the number set. Current number set: [155, 15], target: 46, just two numbers left.\n     |- Try 155 + 15 = 170. Evaluate 170 != 46, drop this branch.\n     |- Try 155 - 15 = 140. Evaluate 140 != 46, drop this branch.\n     |- Try 155 * 15 = 2325. 2325 exceeds the maximum intermediate result, drop this branch.\n     |- Try 155 \/ 15 = 10.3. 10.3 is a decimal, drop this branch.\n    |- Try 130 - 25 = 105. Add 105 to the number set. Current number set: [105, 15], target: 46, just two numbers left.\n     |- Try 105 + 15 = 120. Evaluate 120 != 46, drop this branch.\n     |- Try 105 - 15 = 90. Evaluate 90 != 46, drop this branch.\n     |- Try 105 * 15 = 1575. Evaluate 1575 != 46, drop this branch.\n     |- Try 105 \/ 15 = 7. Evaluate 7 != 46, drop this branch.\n    |- Try 130 * 25 = 3250. 3250 exceeds the maximum intermediate result, drop this branch.\n    |- Try 130 \/ 25 = 5.2. 5.2 is a decimal, drop this branch.\n   |- Pick two numbers (15, 25) (numbers left: [130]). Try possible operations.\n    |- Try 25 + 15 = 40. Add 40 to the number set. Current number set: [40, 130], target: 46, just two numbers left.\n     |- Try 130 + 40 = 170. Evaluate 170 != 46, drop this branch.\n     |- Try 130 - 40 = 90. Evaluate 90 != 46, drop this branch.\n     |- Try 130 * 40 = 5200. 5200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 130 \/ 40 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 25 - 15 = 10. Add 10 to the number set. Current number set: [10, 130], target: 46, just two numbers left.\n     |- Try 130 + 10 = 140. Evaluate 140 != 46, drop this branch.\n     |- Try 130 - 10 = 120. Evaluate 120 != 46, drop this branch.\n     |- Try 130 * 10 = 1300. Evaluate 1300 != 46, drop this branch.\n     |- Try 130 \/ 10 = 13. Evaluate 13 != 46, drop this branch.\n    |- Try 25 * 15 = 375. Add 375 to the number set. Current number set: [375, 130], target: 46, just two numbers left.\n     |- Try 375 + 130 = 505. Evaluate 505 != 46, drop this branch.\n     |- Try 375 - 130 = 245. Evaluate 245 != 46, drop this branch.\n     |- Try 375 * 130 = 48750. 48750 exceeds the maximum intermediate result, drop this branch.\n     |- Try 375 \/ 130 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 25 \/ 15 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 26 \/ 5 = 5.2. 5.2 is a decimal, drop this branch.\n |- Pick two numbers (26, 15) (numbers left: [5, 25]). Try possible operations.\n  |- Try 26 + 15 = 41. Add 41 to the number set. Current number set: [41, 5, 25], target: 46. Options for choosing two numbers: [(41, 5), (41, 25), (5, 25)].\n   |- Pick two numbers (41, 5) (numbers left: [25]). Try possible operations.\n    |- Try 41 + 5 = 46. Add 46 to the number set. Current number set: [46, 25], target: 46, just two numbers left.\n     |- Try 46 + 25 = 71. Evaluate 71 != 46, drop this branch.\n     |- Try 46 - 25 = 21. Evaluate 21 != 46, drop this branch.\n     |- Try 46 * 25 = 1150. Evaluate 1150 != 46, drop this branch.\n     |- Try 46 \/ 25 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 41 - 5 = 36. Add 36 to the number set. Current number set: [36, 25], target: 46, just two numbers left.\n     |- Try 36 + 25 = 61. Evaluate 61 != 46, drop this branch.\n     |- Try 36 - 25 = 11. Evaluate 11 != 46, drop this branch.\n     |- Try 36 * 25 = 900. Evaluate 900 != 46, drop this branch.\n     |- Try 36 \/ 25 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 41 * 5 = 205. Add 205 to the number set. Current number set: [205, 25], target: 46, just two numbers left.\n     |- Try 205 + 25 = 230. Evaluate 230 != 46, drop this branch.\n     |- Try 205 - 25 = 180. Evaluate 180 != 46, drop this branch.\n     |- Try 205 * 25 = 5125. 5125 exceeds the maximum intermediate result, drop this branch.\n     |- Try 205 \/ 25 = 8.2. 8.2 is a decimal, drop this branch.\n    |- Try 41 \/ 5 = 8.2. 8.2 is a decimal, drop this branch.\n   |- Pick two numbers (41, 25) (numbers left: [5]). Try possible operations.\n    |- Try 41 + 25 = 66. Add 66 to the number set. Current number set: [66, 5], target: 46, just two numbers left.\n     |- Try 66 + 5 = 71. Evaluate 71 != 46, drop this branch.\n     |- Try 66 - 5 = 61. Evaluate 61 != 46, drop this branch.\n     |- Try 66 * 5 = 330. Evaluate 330 != 46, drop this branch.\n     |- Try 66 \/ 5 = 13.2. 13.2 is a decimal, drop this branch.\n    |- Try 41 - 25 = 16. Add 16 to the number set. Current number set: [16, 5], target: 46, just two numbers left.\n     |- Try 16 + 5 = 21. Evaluate 21 != 46, drop this branch.\n     |- Try 16 - 5 = 11. Evaluate 11 != 46, drop this branch.\n     |- Try 16 * 5 = 80. Evaluate 80 != 46, drop this branch.\n     |- Try 16 \/ 5 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 41 * 25 = 1025. Add 1025 to the number set. Current number set: [1025, 5], target: 46, just two numbers left.\n     |- Try 1025 + 5 = 1030. Evaluate 1030 != 46, drop this branch.\n     |- Try 1025 - 5 = 1020. Evaluate 1020 != 46, drop this branch.\n     |- Try 1025 * 5 = 5125. 5125 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1025 \/ 5 = 205. Evaluate 205 != 46, drop this branch.\n    |- Try 41 \/ 25 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (5, 25) (numbers left: [41]). Try possible operations.\n    |- Try 25 + 5 = 30. Add 30 to the number set. Current number set: [30, 41], target: 46, just two numbers left.\n     |- Try 41 + 30 = 71. Evaluate 71 != 46, drop this branch.\n     |- Try 41 - 30 = 11. Evaluate 11 != 46, drop this branch.\n     |- Try 41 * 30 = 1230. Evaluate 1230 != 46, drop this branch.\n     |- Try 41 \/ 30 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 25 - 5 = 20. Add 20 to the number set. Current number set: [20, 41], target: 46, just two numbers left.\n     |- Try 41 + 20 = 61. Evaluate 61 != 46, drop this branch.\n     |- Try 41 - 20 = 21. Evaluate 21 != 46, drop this branch.\n     |- Try 41 * 20 = 820. Evaluate 820 != 46, drop this branch.\n     |- Try 41 \/ 20 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 25 * 5 = 125. Add 125 to the number set. Current number set: [125, 41], target: 46, just two numbers left.\n     |- Try 125 + 41 = 166. Evaluate 166 != 46, drop this branch.\n     |- Try 125 - 41 = 84. Evaluate 84 != 46, drop this branch.\n     |- Try 125 * 41 = 5125. 5125 exceeds the maximum intermediate result, drop this branch.\n     |- Try 125 \/ 41 = 3.0. 3.0 is a decimal, drop this branch.\n    |- Try 25 \/ 5 = 5. Add 5 to the number set. Current number set: [5, 41], target: 46, just two numbers left.\n     |- Try 41 + 5 = 46. Evaluate 46 == 46, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 41 + 5 = 46\nThe step before: 25 \/ 5 = 5\nThe first step: 26 + 15 = 41\n\nOutput the solution in the required format:\n<Solution>\n26 + 15 = 41\n25 \/ 5 = 5\n41 + 5 = 46\n<\/Solution>\n","item":{"nums":[26,5,15,25],"solution":["26 + 15 = 41","25 \/ 5 = 5","41 + 5 = 46"],"target":46}}
+{"instance_id":"countdown_8k_160","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [6, 20, 46, 29]\nTarget: 27","reference_output":"# Search Procedure\nInitial number set: [6, 20, 46, 29], target: 27. Options for choosing two numbers: [(6, 20), (6, 46), (6, 29), (20, 46), (20, 29), (46, 29)].\n |- Pick two numbers (6, 20) (numbers left: [46, 29]). Try possible operations.\n  |- Try 20 + 6 = 26. Add 26 to the number set. Current number set: [26, 46, 29], target: 27. Options for choosing two numbers: [(26, 46), (26, 29), (46, 29)].\n   |- Pick two numbers (26, 46) (numbers left: [29]). Try possible operations.\n    |- Try 46 + 26 = 72. Add 72 to the number set. Current number set: [72, 29], target: 27, just two numbers left.\n     |- Try 72 + 29 = 101. Evaluate 101 != 27, drop this branch.\n     |- Try 72 - 29 = 43. Evaluate 43 != 27, drop this branch.\n     |- Try 72 * 29 = 2088. 2088 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 29 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 46 - 26 = 20. Add 20 to the number set. Current number set: [20, 29], target: 27, just two numbers left.\n     |- Try 29 + 20 = 49. Evaluate 49 != 27, drop this branch.\n     |- Try 29 - 20 = 9. Evaluate 9 != 27, drop this branch.\n     |- Try 29 * 20 = 580. Evaluate 580 != 27, drop this branch.\n     |- Try 29 \/ 20 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 46 * 26 = 1196. Add 1196 to the number set. Current number set: [1196, 29], target: 27, just two numbers left.\n     |- Try 1196 + 29 = 1225. Evaluate 1225 != 27, drop this branch.\n     |- Try 1196 - 29 = 1167. Evaluate 1167 != 27, drop this branch.\n     |- Try 1196 * 29 = 34684. 34684 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1196 \/ 29 = 41.2. 41.2 is a decimal, drop this branch.\n    |- Try 46 \/ 26 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (26, 29) (numbers left: [46]). Try possible operations.\n    |- Try 29 + 26 = 55. Add 55 to the number set. Current number set: [55, 46], target: 27, just two numbers left.\n     |- Try 55 + 46 = 101. Evaluate 101 != 27, drop this branch.\n     |- Try 55 - 46 = 9. Evaluate 9 != 27, drop this branch.\n     |- Try 55 * 46 = 2530. 2530 exceeds the maximum intermediate result, drop this branch.\n     |- Try 55 \/ 46 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 29 - 26 = 3. Add 3 to the number set. Current number set: [3, 46], target: 27, just two numbers left.\n     |- Try 46 + 3 = 49. Evaluate 49 != 27, drop this branch.\n     |- Try 46 - 3 = 43. Evaluate 43 != 27, drop this branch.\n     |- Try 46 * 3 = 138. Evaluate 138 != 27, drop this branch.\n     |- Try 46 \/ 3 = 15.3. 15.3 is a decimal, drop this branch.\n    |- Try 29 * 26 = 754. Add 754 to the number set. Current number set: [754, 46], target: 27, just two numbers left.\n     |- Try 754 + 46 = 800. Evaluate 800 != 27, drop this branch.\n     |- Try 754 - 46 = 708. Evaluate 708 != 27, drop this branch.\n     |- Try 754 * 46 = 34684. 34684 exceeds the maximum intermediate result, drop this branch.\n     |- Try 754 \/ 46 = 16.4. 16.4 is a decimal, drop this branch.\n    |- Try 29 \/ 26 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (46, 29) (numbers left: [26]). Try possible operations.\n    |- Try 46 + 29 = 75. Add 75 to the number set. Current number set: [75, 26], target: 27, just two numbers left.\n     |- Try 75 + 26 = 101. Evaluate 101 != 27, drop this branch.\n     |- Try 75 - 26 = 49. Evaluate 49 != 27, drop this branch.\n     |- Try 75 * 26 = 1950. Evaluate 1950 != 27, drop this branch.\n     |- Try 75 \/ 26 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 46 - 29 = 17. Add 17 to the number set. Current number set: [17, 26], target: 27, just two numbers left.\n     |- Try 26 + 17 = 43. Evaluate 43 != 27, drop this branch.\n     |- Try 26 - 17 = 9. Evaluate 9 != 27, drop this branch.\n     |- Try 26 * 17 = 442. Evaluate 442 != 27, drop this branch.\n     |- Try 26 \/ 17 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 46 * 29 = 1334. Add 1334 to the number set. Current number set: [1334, 26], target: 27, just two numbers left.\n     |- Try 1334 + 26 = 1360. Evaluate 1360 != 27, drop this branch.\n     |- Try 1334 - 26 = 1308. Evaluate 1308 != 27, drop this branch.\n     |- Try 1334 * 26 = 34684. 34684 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1334 \/ 26 = 51.3. 51.3 is a decimal, drop this branch.\n    |- Try 46 \/ 29 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 20 - 6 = 14. Add 14 to the number set. Current number set: [14, 46, 29], target: 27. Options for choosing two numbers: [(14, 46), (14, 29), (46, 29)].\n   |- Pick two numbers (14, 46) (numbers left: [29]). Try possible operations.\n    |- Try 46 + 14 = 60. Add 60 to the number set. Current number set: [60, 29], target: 27, just two numbers left.\n     |- Try 60 + 29 = 89. Evaluate 89 != 27, drop this branch.\n     |- Try 60 - 29 = 31. Evaluate 31 != 27, drop this branch.\n     |- Try 60 * 29 = 1740. Evaluate 1740 != 27, drop this branch.\n     |- Try 60 \/ 29 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 46 - 14 = 32. Add 32 to the number set. Current number set: [32, 29], target: 27, just two numbers left.\n     |- Try 32 + 29 = 61. Evaluate 61 != 27, drop this branch.\n     |- Try 32 - 29 = 3. Evaluate 3 != 27, drop this branch.\n     |- Try 32 * 29 = 928. Evaluate 928 != 27, drop this branch.\n     |- Try 32 \/ 29 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 46 * 14 = 644. Add 644 to the number set. Current number set: [644, 29], target: 27, just two numbers left.\n     |- Try 644 + 29 = 673. Evaluate 673 != 27, drop this branch.\n     |- Try 644 - 29 = 615. Evaluate 615 != 27, drop this branch.\n     |- Try 644 * 29 = 18676. 18676 exceeds the maximum intermediate result, drop this branch.\n     |- Try 644 \/ 29 = 22.2. 22.2 is a decimal, drop this branch.\n    |- Try 46 \/ 14 = 3.3. 3.3 is a decimal, drop this branch.\n   |- Pick two numbers (14, 29) (numbers left: [46]). Try possible operations.\n    |- Try 29 + 14 = 43. Add 43 to the number set. Current number set: [43, 46], target: 27, just two numbers left.\n     |- Try 46 + 43 = 89. Evaluate 89 != 27, drop this branch.\n     |- Try 46 - 43 = 3. Evaluate 3 != 27, drop this branch.\n     |- Try 46 * 43 = 1978. Evaluate 1978 != 27, drop this branch.\n     |- Try 46 \/ 43 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 29 - 14 = 15. Add 15 to the number set. Current number set: [15, 46], target: 27, just two numbers left.\n     |- Try 46 + 15 = 61. Evaluate 61 != 27, drop this branch.\n     |- Try 46 - 15 = 31. Evaluate 31 != 27, drop this branch.\n     |- Try 46 * 15 = 690. Evaluate 690 != 27, drop this branch.\n     |- Try 46 \/ 15 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 29 * 14 = 406. Add 406 to the number set. Current number set: [406, 46], target: 27, just two numbers left.\n     |- Try 406 + 46 = 452. Evaluate 452 != 27, drop this branch.\n     |- Try 406 - 46 = 360. Evaluate 360 != 27, drop this branch.\n     |- Try 406 * 46 = 18676. 18676 exceeds the maximum intermediate result, drop this branch.\n     |- Try 406 \/ 46 = 8.8. 8.8 is a decimal, drop this branch.\n    |- Try 29 \/ 14 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (46, 29) (numbers left: [14]). Try possible operations.\n    |- Try 46 + 29 = 75. Add 75 to the number set. Current number set: [75, 14], target: 27, just two numbers left.\n     |- Try 75 + 14 = 89. Evaluate 89 != 27, drop this branch.\n     |- Try 75 - 14 = 61. Evaluate 61 != 27, drop this branch.\n     |- Try 75 * 14 = 1050. Evaluate 1050 != 27, drop this branch.\n     |- Try 75 \/ 14 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 46 - 29 = 17. Add 17 to the number set. Current number set: [17, 14], target: 27, just two numbers left.\n     |- Try 17 + 14 = 31. Evaluate 31 != 27, drop this branch.\n     |- Try 17 - 14 = 3. Evaluate 3 != 27, drop this branch.\n     |- Try 17 * 14 = 238. Evaluate 238 != 27, drop this branch.\n     |- Try 17 \/ 14 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 46 * 29 = 1334. Add 1334 to the number set. Current number set: [1334, 14], target: 27, just two numbers left.\n     |- Try 1334 + 14 = 1348. Evaluate 1348 != 27, drop this branch.\n     |- Try 1334 - 14 = 1320. Evaluate 1320 != 27, drop this branch.\n     |- Try 1334 * 14 = 18676. 18676 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1334 \/ 14 = 95.3. 95.3 is a decimal, drop this branch.\n    |- Try 46 \/ 29 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 20 * 6 = 120. Add 120 to the number set. Current number set: [120, 46, 29], target: 27. Options for choosing two numbers: [(120, 46), (120, 29), (46, 29)].\n   |- Pick two numbers (120, 46) (numbers left: [29]). Try possible operations.\n    |- Try 120 + 46 = 166. Add 166 to the number set. Current number set: [166, 29], target: 27, just two numbers left.\n     |- Try 166 + 29 = 195. Evaluate 195 != 27, drop this branch.\n     |- Try 166 - 29 = 137. Evaluate 137 != 27, drop this branch.\n     |- Try 166 * 29 = 4814. 4814 exceeds the maximum intermediate result, drop this branch.\n     |- Try 166 \/ 29 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 120 - 46 = 74. Add 74 to the number set. Current number set: [74, 29], target: 27, just two numbers left.\n     |- Try 74 + 29 = 103. Evaluate 103 != 27, drop this branch.\n     |- Try 74 - 29 = 45. Evaluate 45 != 27, drop this branch.\n     |- Try 74 * 29 = 2146. 2146 exceeds the maximum intermediate result, drop this branch.\n     |- Try 74 \/ 29 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 120 * 46 = 5520. 5520 exceeds the maximum intermediate result, drop this branch.\n    |- Try 120 \/ 46 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (120, 29) (numbers left: [46]). Try possible operations.\n    |- Try 120 + 29 = 149. Add 149 to the number set. Current number set: [149, 46], target: 27, just two numbers left.\n     |- Try 149 + 46 = 195. Evaluate 195 != 27, drop this branch.\n     |- Try 149 - 46 = 103. Evaluate 103 != 27, drop this branch.\n     |- Try 149 * 46 = 6854. 6854 exceeds the maximum intermediate result, drop this branch.\n     |- Try 149 \/ 46 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 120 - 29 = 91. Add 91 to the number set. Current number set: [91, 46], target: 27, just two numbers left.\n     |- Try 91 + 46 = 137. Evaluate 137 != 27, drop this branch.\n     |- Try 91 - 46 = 45. Evaluate 45 != 27, drop this branch.\n     |- Try 91 * 46 = 4186. 4186 exceeds the maximum intermediate result, drop this branch.\n     |- Try 91 \/ 46 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 120 * 29 = 3480. 3480 exceeds the maximum intermediate result, drop this branch.\n    |- Try 120 \/ 29 = 4.1. 4.1 is a decimal, drop this branch.\n   |- Pick two numbers (46, 29) (numbers left: [120]). Try possible operations.\n    |- Try 46 + 29 = 75. Add 75 to the number set. Current number set: [75, 120], target: 27, just two numbers left.\n     |- Try 120 + 75 = 195. Evaluate 195 != 27, drop this branch.\n     |- Try 120 - 75 = 45. Evaluate 45 != 27, drop this branch.\n     |- Try 120 * 75 = 9000. 9000 exceeds the maximum intermediate result, drop this branch.\n     |- Try 120 \/ 75 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 46 - 29 = 17. Add 17 to the number set. Current number set: [17, 120], target: 27, just two numbers left.\n     |- Try 120 + 17 = 137. Evaluate 137 != 27, drop this branch.\n     |- Try 120 - 17 = 103. Evaluate 103 != 27, drop this branch.\n     |- Try 120 * 17 = 2040. 2040 exceeds the maximum intermediate result, drop this branch.\n     |- Try 120 \/ 17 = 7.1. 7.1 is a decimal, drop this branch.\n    |- Try 46 * 29 = 1334. Add 1334 to the number set. Current number set: [1334, 120], target: 27, just two numbers left.\n     |- Try 1334 + 120 = 1454. Evaluate 1454 != 27, drop this branch.\n     |- Try 1334 - 120 = 1214. Evaluate 1214 != 27, drop this branch.\n     |- Try 1334 * 120 = 160080. 160080 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1334 \/ 120 = 11.1. 11.1 is a decimal, drop this branch.\n    |- Try 46 \/ 29 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 20 \/ 6 = 3.3. 3.3 is a decimal, drop this branch.\n |- Pick two numbers (6, 46) (numbers left: [20, 29]). Try possible operations.\n  |- Try 46 + 6 = 52. Add 52 to the number set. Current number set: [52, 20, 29], target: 27. Options for choosing two numbers: [(52, 20), (52, 29), (20, 29)].\n   |- Pick two numbers (52, 20) (numbers left: [29]). Try possible operations.\n    |- Try 52 + 20 = 72. Add 72 to the number set. Current number set: [72, 29], target: 27, just two numbers left.\n     |- Try 72 + 29 = 101. Evaluate 101 != 27, drop this branch.\n     |- Try 72 - 29 = 43. Evaluate 43 != 27, drop this branch.\n     |- Try 72 * 29 = 2088. 2088 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 29 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 52 - 20 = 32. Add 32 to the number set. Current number set: [32, 29], target: 27, just two numbers left.\n     |- Try 32 + 29 = 61. Evaluate 61 != 27, drop this branch.\n     |- Try 32 - 29 = 3. Evaluate 3 != 27, drop this branch.\n     |- Try 32 * 29 = 928. Evaluate 928 != 27, drop this branch.\n     |- Try 32 \/ 29 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 52 * 20 = 1040. Add 1040 to the number set. Current number set: [1040, 29], target: 27, just two numbers left.\n     |- Try 1040 + 29 = 1069. Evaluate 1069 != 27, drop this branch.\n     |- Try 1040 - 29 = 1011. Evaluate 1011 != 27, drop this branch.\n     |- Try 1040 * 29 = 30160. 30160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1040 \/ 29 = 35.9. 35.9 is a decimal, drop this branch.\n    |- Try 52 \/ 20 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (52, 29) (numbers left: [20]). Try possible operations.\n    |- Try 52 + 29 = 81. Add 81 to the number set. Current number set: [81, 20], target: 27, just two numbers left.\n     |- Try 81 + 20 = 101. Evaluate 101 != 27, drop this branch.\n     |- Try 81 - 20 = 61. Evaluate 61 != 27, drop this branch.\n     |- Try 81 * 20 = 1620. Evaluate 1620 != 27, drop this branch.\n     |- Try 81 \/ 20 = 4.0. 4.0 is a decimal, drop this branch.\n    |- Try 52 - 29 = 23. Add 23 to the number set. Current number set: [23, 20], target: 27, just two numbers left.\n     |- Try 23 + 20 = 43. Evaluate 43 != 27, drop this branch.\n     |- Try 23 - 20 = 3. Evaluate 3 != 27, drop this branch.\n     |- Try 23 * 20 = 460. Evaluate 460 != 27, drop this branch.\n     |- Try 23 \/ 20 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 52 * 29 = 1508. Add 1508 to the number set. Current number set: [1508, 20], target: 27, just two numbers left.\n     |- Try 1508 + 20 = 1528. Evaluate 1528 != 27, drop this branch.\n     |- Try 1508 - 20 = 1488. Evaluate 1488 != 27, drop this branch.\n     |- Try 1508 * 20 = 30160. 30160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1508 \/ 20 = 75.4. 75.4 is a decimal, drop this branch.\n    |- Try 52 \/ 29 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (20, 29) (numbers left: [52]). Try possible operations.\n    |- Try 29 + 20 = 49. Add 49 to the number set. Current number set: [49, 52], target: 27, just two numbers left.\n     |- Try 52 + 49 = 101. Evaluate 101 != 27, drop this branch.\n     |- Try 52 - 49 = 3. Evaluate 3 != 27, drop this branch.\n     |- Try 52 * 49 = 2548. 2548 exceeds the maximum intermediate result, drop this branch.\n     |- Try 52 \/ 49 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 29 - 20 = 9. Add 9 to the number set. Current number set: [9, 52], target: 27, just two numbers left.\n     |- Try 52 + 9 = 61. Evaluate 61 != 27, drop this branch.\n     |- Try 52 - 9 = 43. Evaluate 43 != 27, drop this branch.\n     |- Try 52 * 9 = 468. Evaluate 468 != 27, drop this branch.\n     |- Try 52 \/ 9 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 29 * 20 = 580. Add 580 to the number set. Current number set: [580, 52], target: 27, just two numbers left.\n     |- Try 580 + 52 = 632. Evaluate 632 != 27, drop this branch.\n     |- Try 580 - 52 = 528. Evaluate 528 != 27, drop this branch.\n     |- Try 580 * 52 = 30160. 30160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 580 \/ 52 = 11.2. 11.2 is a decimal, drop this branch.\n    |- Try 29 \/ 20 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 46 - 6 = 40. Add 40 to the number set. Current number set: [40, 20, 29], target: 27. Options for choosing two numbers: [(40, 20), (40, 29), (20, 29)].\n   |- Pick two numbers (40, 20) (numbers left: [29]). Try possible operations.\n    |- Try 40 + 20 = 60. Add 60 to the number set. Current number set: [60, 29], target: 27, just two numbers left.\n     |- Try 60 + 29 = 89. Evaluate 89 != 27, drop this branch.\n     |- Try 60 - 29 = 31. Evaluate 31 != 27, drop this branch.\n     |- Try 60 * 29 = 1740. Evaluate 1740 != 27, drop this branch.\n     |- Try 60 \/ 29 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 40 - 20 = 20. Add 20 to the number set. Current number set: [20, 29], target: 27, just two numbers left.\n     |- Try 29 + 20 = 49. Evaluate 49 != 27, drop this branch.\n     |- Try 29 - 20 = 9. Evaluate 9 != 27, drop this branch.\n     |- Try 29 * 20 = 580. Evaluate 580 != 27, drop this branch.\n     |- Try 29 \/ 20 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 40 * 20 = 800. Add 800 to the number set. Current number set: [800, 29], target: 27, just two numbers left.\n     |- Try 800 + 29 = 829. Evaluate 829 != 27, drop this branch.\n     |- Try 800 - 29 = 771. Evaluate 771 != 27, drop this branch.\n     |- Try 800 * 29 = 23200. 23200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 800 \/ 29 = 27.6. 27.6 is a decimal, drop this branch.\n    |- Try 40 \/ 20 = 2. Add 2 to the number set. Current number set: [2, 29], target: 27, just two numbers left.\n     |- Try 29 + 2 = 31. Evaluate 31 != 27, drop this branch.\n     |- Try 29 - 2 = 27. Evaluate 27 == 27, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 29 - 2 = 27\nThe step before: 40 \/ 20 = 2\nThe first step: 46 - 6 = 40\n\nOutput the solution in the required format:\n<Solution>\n46 - 6 = 40\n40 \/ 20 = 2\n29 - 2 = 27\n<\/Solution>\n","item":{"nums":[6,20,46,29],"solution":["46 - 6 = 40","40 \/ 20 = 2","29 - 2 = 27"],"target":27}}
+{"instance_id":"countdown_8k_161","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [29, 33, 38, 3]\nTarget: 20","reference_output":"# Search Procedure\nInitial number set: [29, 33, 38, 3], target: 20. Options for choosing two numbers: [(29, 33), (29, 38), (29, 3), (33, 38), (33, 3), (38, 3)].\n |- Pick two numbers (29, 33) (numbers left: [38, 3]). Try possible operations.\n  |- Try 33 + 29 = 62. Add 62 to the number set. Current number set: [62, 38, 3], target: 20. Options for choosing two numbers: [(62, 38), (62, 3), (38, 3)].\n   |- Pick two numbers (62, 38) (numbers left: [3]). Try possible operations.\n    |- Try 62 + 38 = 100. Add 100 to the number set. Current number set: [100, 3], target: 20, just two numbers left.\n     |- Try 100 + 3 = 103. Evaluate 103 != 20, drop this branch.\n     |- Try 100 - 3 = 97. Evaluate 97 != 20, drop this branch.\n     |- Try 100 * 3 = 300. Evaluate 300 != 20, drop this branch.\n     |- Try 100 \/ 3 = 33.3. 33.3 is a decimal, drop this branch.\n    |- Try 62 - 38 = 24. Add 24 to the number set. Current number set: [24, 3], target: 20, just two numbers left.\n     |- Try 24 + 3 = 27. Evaluate 27 != 20, drop this branch.\n     |- Try 24 - 3 = 21. Evaluate 21 != 20, drop this branch.\n     |- Try 24 * 3 = 72. Evaluate 72 != 20, drop this branch.\n     |- Try 24 \/ 3 = 8. Evaluate 8 != 20, drop this branch.\n    |- Try 62 * 38 = 2356. 2356 exceeds the maximum intermediate result, drop this branch.\n    |- Try 62 \/ 38 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (62, 3) (numbers left: [38]). Try possible operations.\n    |- Try 62 + 3 = 65. Add 65 to the number set. Current number set: [65, 38], target: 20, just two numbers left.\n     |- Try 65 + 38 = 103. Evaluate 103 != 20, drop this branch.\n     |- Try 65 - 38 = 27. Evaluate 27 != 20, drop this branch.\n     |- Try 65 * 38 = 2470. 2470 exceeds the maximum intermediate result, drop this branch.\n     |- Try 65 \/ 38 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 62 - 3 = 59. Add 59 to the number set. Current number set: [59, 38], target: 20, just two numbers left.\n     |- Try 59 + 38 = 97. Evaluate 97 != 20, drop this branch.\n     |- Try 59 - 38 = 21. Evaluate 21 != 20, drop this branch.\n     |- Try 59 * 38 = 2242. 2242 exceeds the maximum intermediate result, drop this branch.\n     |- Try 59 \/ 38 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 62 * 3 = 186. Add 186 to the number set. Current number set: [186, 38], target: 20, just two numbers left.\n     |- Try 186 + 38 = 224. Evaluate 224 != 20, drop this branch.\n     |- Try 186 - 38 = 148. Evaluate 148 != 20, drop this branch.\n     |- Try 186 * 38 = 7068. 7068 exceeds the maximum intermediate result, drop this branch.\n     |- Try 186 \/ 38 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 62 \/ 3 = 20.7. 20.7 is a decimal, drop this branch.\n   |- Pick two numbers (38, 3) (numbers left: [62]). Try possible operations.\n    |- Try 38 + 3 = 41. Add 41 to the number set. Current number set: [41, 62], target: 20, just two numbers left.\n     |- Try 62 + 41 = 103. Evaluate 103 != 20, drop this branch.\n     |- Try 62 - 41 = 21. Evaluate 21 != 20, drop this branch.\n     |- Try 62 * 41 = 2542. 2542 exceeds the maximum intermediate result, drop this branch.\n     |- Try 62 \/ 41 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 38 - 3 = 35. Add 35 to the number set. Current number set: [35, 62], target: 20, just two numbers left.\n     |- Try 62 + 35 = 97. Evaluate 97 != 20, drop this branch.\n     |- Try 62 - 35 = 27. Evaluate 27 != 20, drop this branch.\n     |- Try 62 * 35 = 2170. 2170 exceeds the maximum intermediate result, drop this branch.\n     |- Try 62 \/ 35 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 38 * 3 = 114. Add 114 to the number set. Current number set: [114, 62], target: 20, just two numbers left.\n     |- Try 114 + 62 = 176. Evaluate 176 != 20, drop this branch.\n     |- Try 114 - 62 = 52. Evaluate 52 != 20, drop this branch.\n     |- Try 114 * 62 = 7068. 7068 exceeds the maximum intermediate result, drop this branch.\n     |- Try 114 \/ 62 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 38 \/ 3 = 12.7. 12.7 is a decimal, drop this branch.\n  |- Try 33 - 29 = 4. Add 4 to the number set. Current number set: [4, 38, 3], target: 20. Options for choosing two numbers: [(4, 38), (4, 3), (38, 3)].\n   |- Pick two numbers (4, 38) (numbers left: [3]). Try possible operations.\n    |- Try 38 + 4 = 42. Add 42 to the number set. Current number set: [42, 3], target: 20, just two numbers left.\n     |- Try 42 + 3 = 45. Evaluate 45 != 20, drop this branch.\n     |- Try 42 - 3 = 39. Evaluate 39 != 20, drop this branch.\n     |- Try 42 * 3 = 126. Evaluate 126 != 20, drop this branch.\n     |- Try 42 \/ 3 = 14. Evaluate 14 != 20, drop this branch.\n    |- Try 38 - 4 = 34. Add 34 to the number set. Current number set: [34, 3], target: 20, just two numbers left.\n     |- Try 34 + 3 = 37. Evaluate 37 != 20, drop this branch.\n     |- Try 34 - 3 = 31. Evaluate 31 != 20, drop this branch.\n     |- Try 34 * 3 = 102. Evaluate 102 != 20, drop this branch.\n     |- Try 34 \/ 3 = 11.3. 11.3 is a decimal, drop this branch.\n    |- Try 38 * 4 = 152. Add 152 to the number set. Current number set: [152, 3], target: 20, just two numbers left.\n     |- Try 152 + 3 = 155. Evaluate 155 != 20, drop this branch.\n     |- Try 152 - 3 = 149. Evaluate 149 != 20, drop this branch.\n     |- Try 152 * 3 = 456. Evaluate 456 != 20, drop this branch.\n     |- Try 152 \/ 3 = 50.7. 50.7 is a decimal, drop this branch.\n    |- Try 38 \/ 4 = 9.5. 9.5 is a decimal, drop this branch.\n   |- Pick two numbers (4, 3) (numbers left: [38]). Try possible operations.\n    |- Try 4 + 3 = 7. Add 7 to the number set. Current number set: [7, 38], target: 20, just two numbers left.\n     |- Try 38 + 7 = 45. Evaluate 45 != 20, drop this branch.\n     |- Try 38 - 7 = 31. Evaluate 31 != 20, drop this branch.\n     |- Try 38 * 7 = 266. Evaluate 266 != 20, drop this branch.\n     |- Try 38 \/ 7 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 4 - 3 = 1. Add 1 to the number set. Current number set: [1, 38], target: 20, just two numbers left.\n     |- Try 38 + 1 = 39. Evaluate 39 != 20, drop this branch.\n     |- Try 38 - 1 = 37. Evaluate 37 != 20, drop this branch.\n     |- Try 38 * 1 = 38. Evaluate 38 != 20, drop this branch.\n     |- Try 38 \/ 1 = 38. Evaluate 38 != 20, drop this branch.\n    |- Try 4 * 3 = 12. Add 12 to the number set. Current number set: [12, 38], target: 20, just two numbers left.\n     |- Try 38 + 12 = 50. Evaluate 50 != 20, drop this branch.\n     |- Try 38 - 12 = 26. Evaluate 26 != 20, drop this branch.\n     |- Try 38 * 12 = 456. Evaluate 456 != 20, drop this branch.\n     |- Try 38 \/ 12 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 4 \/ 3 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (38, 3) (numbers left: [4]). Try possible operations.\n    |- Try 38 + 3 = 41. Add 41 to the number set. Current number set: [41, 4], target: 20, just two numbers left.\n     |- Try 41 + 4 = 45. Evaluate 45 != 20, drop this branch.\n     |- Try 41 - 4 = 37. Evaluate 37 != 20, drop this branch.\n     |- Try 41 * 4 = 164. Evaluate 164 != 20, drop this branch.\n     |- Try 41 \/ 4 = 10.2. 10.2 is a decimal, drop this branch.\n    |- Try 38 - 3 = 35. Add 35 to the number set. Current number set: [35, 4], target: 20, just two numbers left.\n     |- Try 35 + 4 = 39. Evaluate 39 != 20, drop this branch.\n     |- Try 35 - 4 = 31. Evaluate 31 != 20, drop this branch.\n     |- Try 35 * 4 = 140. Evaluate 140 != 20, drop this branch.\n     |- Try 35 \/ 4 = 8.8. 8.8 is a decimal, drop this branch.\n    |- Try 38 * 3 = 114. Add 114 to the number set. Current number set: [114, 4], target: 20, just two numbers left.\n     |- Try 114 + 4 = 118. Evaluate 118 != 20, drop this branch.\n     |- Try 114 - 4 = 110. Evaluate 110 != 20, drop this branch.\n     |- Try 114 * 4 = 456. Evaluate 456 != 20, drop this branch.\n     |- Try 114 \/ 4 = 28.5. 28.5 is a decimal, drop this branch.\n    |- Try 38 \/ 3 = 12.7. 12.7 is a decimal, drop this branch.\n  |- Try 33 * 29 = 957. Add 957 to the number set. Current number set: [957, 38, 3], target: 20. Options for choosing two numbers: [(957, 38), (957, 3), (38, 3)].\n   |- Pick two numbers (957, 38) (numbers left: [3]). Try possible operations.\n    |- Try 957 + 38 = 995. Add 995 to the number set. Current number set: [995, 3], target: 20, just two numbers left.\n     |- Try 995 + 3 = 998. Evaluate 998 != 20, drop this branch.\n     |- Try 995 - 3 = 992. Evaluate 992 != 20, drop this branch.\n     |- Try 995 * 3 = 2985. 2985 exceeds the maximum intermediate result, drop this branch.\n     |- Try 995 \/ 3 = 331.7. 331.7 is a decimal, drop this branch.\n    |- Try 957 - 38 = 919. Add 919 to the number set. Current number set: [919, 3], target: 20, just two numbers left.\n     |- Try 919 + 3 = 922. Evaluate 922 != 20, drop this branch.\n     |- Try 919 - 3 = 916. Evaluate 916 != 20, drop this branch.\n     |- Try 919 * 3 = 2757. 2757 exceeds the maximum intermediate result, drop this branch.\n     |- Try 919 \/ 3 = 306.3. 306.3 is a decimal, drop this branch.\n    |- Try 957 * 38 = 36366. 36366 exceeds the maximum intermediate result, drop this branch.\n    |- Try 957 \/ 38 = 25.2. 25.2 is a decimal, drop this branch.\n   |- Pick two numbers (957, 3) (numbers left: [38]). Try possible operations.\n    |- Try 957 + 3 = 960. Add 960 to the number set. Current number set: [960, 38], target: 20, just two numbers left.\n     |- Try 960 + 38 = 998. Evaluate 998 != 20, drop this branch.\n     |- Try 960 - 38 = 922. Evaluate 922 != 20, drop this branch.\n     |- Try 960 * 38 = 36480. 36480 exceeds the maximum intermediate result, drop this branch.\n     |- Try 960 \/ 38 = 25.3. 25.3 is a decimal, drop this branch.\n    |- Try 957 - 3 = 954. Add 954 to the number set. Current number set: [954, 38], target: 20, just two numbers left.\n     |- Try 954 + 38 = 992. Evaluate 992 != 20, drop this branch.\n     |- Try 954 - 38 = 916. Evaluate 916 != 20, drop this branch.\n     |- Try 954 * 38 = 36252. 36252 exceeds the maximum intermediate result, drop this branch.\n     |- Try 954 \/ 38 = 25.1. 25.1 is a decimal, drop this branch.\n    |- Try 957 * 3 = 2871. 2871 exceeds the maximum intermediate result, drop this branch.\n    |- Try 957 \/ 3 = 319. Add 319 to the number set. Current number set: [319, 38], target: 20, just two numbers left.\n     |- Try 319 + 38 = 357. Evaluate 357 != 20, drop this branch.\n     |- Try 319 - 38 = 281. Evaluate 281 != 20, drop this branch.\n     |- Try 319 * 38 = 12122. 12122 exceeds the maximum intermediate result, drop this branch.\n     |- Try 319 \/ 38 = 8.4. 8.4 is a decimal, drop this branch.\n   |- Pick two numbers (38, 3) (numbers left: [957]). Try possible operations.\n    |- Try 38 + 3 = 41. Add 41 to the number set. Current number set: [41, 957], target: 20, just two numbers left.\n     |- Try 957 + 41 = 998. Evaluate 998 != 20, drop this branch.\n     |- Try 957 - 41 = 916. Evaluate 916 != 20, drop this branch.\n     |- Try 957 * 41 = 39237. 39237 exceeds the maximum intermediate result, drop this branch.\n     |- Try 957 \/ 41 = 23.3. 23.3 is a decimal, drop this branch.\n    |- Try 38 - 3 = 35. Add 35 to the number set. Current number set: [35, 957], target: 20, just two numbers left.\n     |- Try 957 + 35 = 992. Evaluate 992 != 20, drop this branch.\n     |- Try 957 - 35 = 922. Evaluate 922 != 20, drop this branch.\n     |- Try 957 * 35 = 33495. 33495 exceeds the maximum intermediate result, drop this branch.\n     |- Try 957 \/ 35 = 27.3. 27.3 is a decimal, drop this branch.\n    |- Try 38 * 3 = 114. Add 114 to the number set. Current number set: [114, 957], target: 20, just two numbers left.\n     |- Try 957 + 114 = 1071. Evaluate 1071 != 20, drop this branch.\n     |- Try 957 - 114 = 843. Evaluate 843 != 20, drop this branch.\n     |- Try 957 * 114 = 109098. 109098 exceeds the maximum intermediate result, drop this branch.\n     |- Try 957 \/ 114 = 8.4. 8.4 is a decimal, drop this branch.\n    |- Try 38 \/ 3 = 12.7. 12.7 is a decimal, drop this branch.\n  |- Try 33 \/ 29 = 1.1. 1.1 is a decimal, drop this branch.\n |- Pick two numbers (29, 38) (numbers left: [33, 3]). Try possible operations.\n  |- Try 38 + 29 = 67. Add 67 to the number set. Current number set: [67, 33, 3], target: 20. Options for choosing two numbers: [(67, 33), (67, 3), (33, 3)].\n   |- Pick two numbers (67, 33) (numbers left: [3]). Try possible operations.\n    |- Try 67 + 33 = 100. Add 100 to the number set. Current number set: [100, 3], target: 20, just two numbers left.\n     |- Try 100 + 3 = 103. Evaluate 103 != 20, drop this branch.\n     |- Try 100 - 3 = 97. Evaluate 97 != 20, drop this branch.\n     |- Try 100 * 3 = 300. Evaluate 300 != 20, drop this branch.\n     |- Try 100 \/ 3 = 33.3. 33.3 is a decimal, drop this branch.\n    |- Try 67 - 33 = 34. Add 34 to the number set. Current number set: [34, 3], target: 20, just two numbers left.\n     |- Try 34 + 3 = 37. Evaluate 37 != 20, drop this branch.\n     |- Try 34 - 3 = 31. Evaluate 31 != 20, drop this branch.\n     |- Try 34 * 3 = 102. Evaluate 102 != 20, drop this branch.\n     |- Try 34 \/ 3 = 11.3. 11.3 is a decimal, drop this branch.\n    |- Try 67 * 33 = 2211. 2211 exceeds the maximum intermediate result, drop this branch.\n    |- Try 67 \/ 33 = 2.0. 2.0 is a decimal, drop this branch.\n   |- Pick two numbers (67, 3) (numbers left: [33]). Try possible operations.\n    |- Try 67 + 3 = 70. Add 70 to the number set. Current number set: [70, 33], target: 20, just two numbers left.\n     |- Try 70 + 33 = 103. Evaluate 103 != 20, drop this branch.\n     |- Try 70 - 33 = 37. Evaluate 37 != 20, drop this branch.\n     |- Try 70 * 33 = 2310. 2310 exceeds the maximum intermediate result, drop this branch.\n     |- Try 70 \/ 33 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 67 - 3 = 64. Add 64 to the number set. Current number set: [64, 33], target: 20, just two numbers left.\n     |- Try 64 + 33 = 97. Evaluate 97 != 20, drop this branch.\n     |- Try 64 - 33 = 31. Evaluate 31 != 20, drop this branch.\n     |- Try 64 * 33 = 2112. 2112 exceeds the maximum intermediate result, drop this branch.\n     |- Try 64 \/ 33 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 67 * 3 = 201. Add 201 to the number set. Current number set: [201, 33], target: 20, just two numbers left.\n     |- Try 201 + 33 = 234. Evaluate 234 != 20, drop this branch.\n     |- Try 201 - 33 = 168. Evaluate 168 != 20, drop this branch.\n     |- Try 201 * 33 = 6633. 6633 exceeds the maximum intermediate result, drop this branch.\n     |- Try 201 \/ 33 = 6.1. 6.1 is a decimal, drop this branch.\n    |- Try 67 \/ 3 = 22.3. 22.3 is a decimal, drop this branch.\n   |- Pick two numbers (33, 3) (numbers left: [67]). Try possible operations.\n    |- Try 33 + 3 = 36. Add 36 to the number set. Current number set: [36, 67], target: 20, just two numbers left.\n     |- Try 67 + 36 = 103. Evaluate 103 != 20, drop this branch.\n     |- Try 67 - 36 = 31. Evaluate 31 != 20, drop this branch.\n     |- Try 67 * 36 = 2412. 2412 exceeds the maximum intermediate result, drop this branch.\n     |- Try 67 \/ 36 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 33 - 3 = 30. Add 30 to the number set. Current number set: [30, 67], target: 20, just two numbers left.\n     |- Try 67 + 30 = 97. Evaluate 97 != 20, drop this branch.\n     |- Try 67 - 30 = 37. Evaluate 37 != 20, drop this branch.\n     |- Try 67 * 30 = 2010. 2010 exceeds the maximum intermediate result, drop this branch.\n     |- Try 67 \/ 30 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 33 * 3 = 99. Add 99 to the number set. Current number set: [99, 67], target: 20, just two numbers left.\n     |- Try 99 + 67 = 166. Evaluate 166 != 20, drop this branch.\n     |- Try 99 - 67 = 32. Evaluate 32 != 20, drop this branch.\n     |- Try 99 * 67 = 6633. 6633 exceeds the maximum intermediate result, drop this branch.\n     |- Try 99 \/ 67 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 33 \/ 3 = 11. Add 11 to the number set. Current number set: [11, 67], target: 20, just two numbers left.\n     |- Try 67 + 11 = 78. Evaluate 78 != 20, drop this branch.\n     |- Try 67 - 11 = 56. Evaluate 56 != 20, drop this branch.\n     |- Try 67 * 11 = 737. Evaluate 737 != 20, drop this branch.\n     |- Try 67 \/ 11 = 6.1. 6.1 is a decimal, drop this branch.\n  |- Try 38 - 29 = 9. Add 9 to the number set. Current number set: [9, 33, 3], target: 20. Options for choosing two numbers: [(9, 33), (9, 3), (33, 3)].\n   |- Pick two numbers (9, 33) (numbers left: [3]). Try possible operations.\n    |- Try 33 + 9 = 42. Add 42 to the number set. Current number set: [42, 3], target: 20, just two numbers left.\n     |- Try 42 + 3 = 45. Evaluate 45 != 20, drop this branch.\n     |- Try 42 - 3 = 39. Evaluate 39 != 20, drop this branch.\n     |- Try 42 * 3 = 126. Evaluate 126 != 20, drop this branch.\n     |- Try 42 \/ 3 = 14. Evaluate 14 != 20, drop this branch.\n    |- Try 33 - 9 = 24. Add 24 to the number set. Current number set: [24, 3], target: 20, just two numbers left.\n     |- Try 24 + 3 = 27. Evaluate 27 != 20, drop this branch.\n     |- Try 24 - 3 = 21. Evaluate 21 != 20, drop this branch.\n     |- Try 24 * 3 = 72. Evaluate 72 != 20, drop this branch.\n     |- Try 24 \/ 3 = 8. Evaluate 8 != 20, drop this branch.\n    |- Try 33 * 9 = 297. Add 297 to the number set. Current number set: [297, 3], target: 20, just two numbers left.\n     |- Try 297 + 3 = 300. Evaluate 300 != 20, drop this branch.\n     |- Try 297 - 3 = 294. Evaluate 294 != 20, drop this branch.\n     |- Try 297 * 3 = 891. Evaluate 891 != 20, drop this branch.\n     |- Try 297 \/ 3 = 99. Evaluate 99 != 20, drop this branch.\n    |- Try 33 \/ 9 = 3.7. 3.7 is a decimal, drop this branch.\n   |- Pick two numbers (9, 3) (numbers left: [33]). Try possible operations.\n    |- Try 9 + 3 = 12. Add 12 to the number set. Current number set: [12, 33], target: 20, just two numbers left.\n     |- Try 33 + 12 = 45. Evaluate 45 != 20, drop this branch.\n     |- Try 33 - 12 = 21. Evaluate 21 != 20, drop this branch.\n     |- Try 33 * 12 = 396. Evaluate 396 != 20, drop this branch.\n     |- Try 33 \/ 12 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 9 - 3 = 6. Add 6 to the number set. Current number set: [6, 33], target: 20, just two numbers left.\n     |- Try 33 + 6 = 39. Evaluate 39 != 20, drop this branch.\n     |- Try 33 - 6 = 27. Evaluate 27 != 20, drop this branch.\n     |- Try 33 * 6 = 198. Evaluate 198 != 20, drop this branch.\n     |- Try 33 \/ 6 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 9 * 3 = 27. Add 27 to the number set. Current number set: [27, 33], target: 20, just two numbers left.\n     |- Try 33 + 27 = 60. Evaluate 60 != 20, drop this branch.\n     |- Try 33 - 27 = 6. Evaluate 6 != 20, drop this branch.\n     |- Try 33 * 27 = 891. Evaluate 891 != 20, drop this branch.\n     |- Try 33 \/ 27 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 9 \/ 3 = 3. Add 3 to the number set. Current number set: [3, 33], target: 20, just two numbers left.\n     |- Try 33 + 3 = 36. Evaluate 36 != 20, drop this branch.\n     |- Try 33 - 3 = 30. Evaluate 30 != 20, drop this branch.\n     |- Try 33 * 3 = 99. Evaluate 99 != 20, drop this branch.\n     |- Try 33 \/ 3 = 11. Evaluate 11 != 20, drop this branch.\n   |- Pick two numbers (33, 3) (numbers left: [9]). Try possible operations.\n    |- Try 33 + 3 = 36. Add 36 to the number set. Current number set: [36, 9], target: 20, just two numbers left.\n     |- Try 36 + 9 = 45. Evaluate 45 != 20, drop this branch.\n     |- Try 36 - 9 = 27. Evaluate 27 != 20, drop this branch.\n     |- Try 36 * 9 = 324. Evaluate 324 != 20, drop this branch.\n     |- Try 36 \/ 9 = 4. Evaluate 4 != 20, drop this branch.\n    |- Try 33 - 3 = 30. Add 30 to the number set. Current number set: [30, 9], target: 20, just two numbers left.\n     |- Try 30 + 9 = 39. Evaluate 39 != 20, drop this branch.\n     |- Try 30 - 9 = 21. Evaluate 21 != 20, drop this branch.\n     |- Try 30 * 9 = 270. Evaluate 270 != 20, drop this branch.\n     |- Try 30 \/ 9 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 33 * 3 = 99. Add 99 to the number set. Current number set: [99, 9], target: 20, just two numbers left.\n     |- Try 99 + 9 = 108. Evaluate 108 != 20, drop this branch.\n     |- Try 99 - 9 = 90. Evaluate 90 != 20, drop this branch.\n     |- Try 99 * 9 = 891. Evaluate 891 != 20, drop this branch.\n     |- Try 99 \/ 9 = 11. Evaluate 11 != 20, drop this branch.\n    |- Try 33 \/ 3 = 11. Add 11 to the number set. Current number set: [11, 9], target: 20, just two numbers left.\n     |- Try 11 + 9 = 20. Evaluate 20 == 20, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 11 + 9 = 20\nThe step before: 33 \/ 3 = 11\nThe first step: 38 - 29 = 9\n\nOutput the solution in the required format:\n<Solution>\n38 - 29 = 9\n33 \/ 3 = 11\n11 + 9 = 20\n<\/Solution>\n","item":{"nums":[29,33,38,3],"solution":["38 - 29 = 9","33 \/ 3 = 11","11 + 9 = 20"],"target":20}}
+{"instance_id":"countdown_8k_162","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [13, 39, 2, 35]\nTarget: 29","reference_output":"# Search Procedure\nInitial number set: [13, 39, 2, 35], target: 29. Options for choosing two numbers: [(13, 39), (13, 2), (13, 35), (39, 2), (39, 35), (2, 35)].\n |- Pick two numbers (13, 39) (numbers left: [2, 35]). Try possible operations.\n  |- Try 39 + 13 = 52. Add 52 to the number set. Current number set: [52, 2, 35], target: 29. Options for choosing two numbers: [(52, 2), (52, 35), (2, 35)].\n   |- Pick two numbers (52, 2) (numbers left: [35]). Try possible operations.\n    |- Try 52 + 2 = 54. Add 54 to the number set. Current number set: [54, 35], target: 29, just two numbers left.\n     |- Try 54 + 35 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 54 - 35 = 19. Evaluate 19 != 29, drop this branch.\n     |- Try 54 * 35 = 1890. Evaluate 1890 != 29, drop this branch.\n     |- Try 54 \/ 35 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 52 - 2 = 50. Add 50 to the number set. Current number set: [50, 35], target: 29, just two numbers left.\n     |- Try 50 + 35 = 85. Evaluate 85 != 29, drop this branch.\n     |- Try 50 - 35 = 15. Evaluate 15 != 29, drop this branch.\n     |- Try 50 * 35 = 1750. Evaluate 1750 != 29, drop this branch.\n     |- Try 50 \/ 35 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 52 * 2 = 104. Add 104 to the number set. Current number set: [104, 35], target: 29, just two numbers left.\n     |- Try 104 + 35 = 139. Evaluate 139 != 29, drop this branch.\n     |- Try 104 - 35 = 69. Evaluate 69 != 29, drop this branch.\n     |- Try 104 * 35 = 3640. 3640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 104 \/ 35 = 3.0. 3.0 is a decimal, drop this branch.\n    |- Try 52 \/ 2 = 26. Add 26 to the number set. Current number set: [26, 35], target: 29, just two numbers left.\n     |- Try 35 + 26 = 61. Evaluate 61 != 29, drop this branch.\n     |- Try 35 - 26 = 9. Evaluate 9 != 29, drop this branch.\n     |- Try 35 * 26 = 910. Evaluate 910 != 29, drop this branch.\n     |- Try 35 \/ 26 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (52, 35) (numbers left: [2]). Try possible operations.\n    |- Try 52 + 35 = 87. Add 87 to the number set. Current number set: [87, 2], target: 29, just two numbers left.\n     |- Try 87 + 2 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 87 - 2 = 85. Evaluate 85 != 29, drop this branch.\n     |- Try 87 * 2 = 174. Evaluate 174 != 29, drop this branch.\n     |- Try 87 \/ 2 = 43.5. 43.5 is a decimal, drop this branch.\n    |- Try 52 - 35 = 17. Add 17 to the number set. Current number set: [17, 2], target: 29, just two numbers left.\n     |- Try 17 + 2 = 19. Evaluate 19 != 29, drop this branch.\n     |- Try 17 - 2 = 15. Evaluate 15 != 29, drop this branch.\n     |- Try 17 * 2 = 34. Evaluate 34 != 29, drop this branch.\n     |- Try 17 \/ 2 = 8.5. 8.5 is a decimal, drop this branch.\n    |- Try 52 * 35 = 1820. Add 1820 to the number set. Current number set: [1820, 2], target: 29, just two numbers left.\n     |- Try 1820 + 2 = 1822. Evaluate 1822 != 29, drop this branch.\n     |- Try 1820 - 2 = 1818. Evaluate 1818 != 29, drop this branch.\n     |- Try 1820 * 2 = 3640. 3640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1820 \/ 2 = 910. Evaluate 910 != 29, drop this branch.\n    |- Try 52 \/ 35 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (2, 35) (numbers left: [52]). Try possible operations.\n    |- Try 35 + 2 = 37. Add 37 to the number set. Current number set: [37, 52], target: 29, just two numbers left.\n     |- Try 52 + 37 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 52 - 37 = 15. Evaluate 15 != 29, drop this branch.\n     |- Try 52 * 37 = 1924. Evaluate 1924 != 29, drop this branch.\n     |- Try 52 \/ 37 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 35 - 2 = 33. Add 33 to the number set. Current number set: [33, 52], target: 29, just two numbers left.\n     |- Try 52 + 33 = 85. Evaluate 85 != 29, drop this branch.\n     |- Try 52 - 33 = 19. Evaluate 19 != 29, drop this branch.\n     |- Try 52 * 33 = 1716. Evaluate 1716 != 29, drop this branch.\n     |- Try 52 \/ 33 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 35 * 2 = 70. Add 70 to the number set. Current number set: [70, 52], target: 29, just two numbers left.\n     |- Try 70 + 52 = 122. Evaluate 122 != 29, drop this branch.\n     |- Try 70 - 52 = 18. Evaluate 18 != 29, drop this branch.\n     |- Try 70 * 52 = 3640. 3640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 70 \/ 52 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 35 \/ 2 = 17.5. 17.5 is a decimal, drop this branch.\n  |- Try 39 - 13 = 26. Add 26 to the number set. Current number set: [26, 2, 35], target: 29. Options for choosing two numbers: [(26, 2), (26, 35), (2, 35)].\n   |- Pick two numbers (26, 2) (numbers left: [35]). Try possible operations.\n    |- Try 26 + 2 = 28. Add 28 to the number set. Current number set: [28, 35], target: 29, just two numbers left.\n     |- Try 35 + 28 = 63. Evaluate 63 != 29, drop this branch.\n     |- Try 35 - 28 = 7. Evaluate 7 != 29, drop this branch.\n     |- Try 35 * 28 = 980. Evaluate 980 != 29, drop this branch.\n     |- Try 35 \/ 28 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 26 - 2 = 24. Add 24 to the number set. Current number set: [24, 35], target: 29, just two numbers left.\n     |- Try 35 + 24 = 59. Evaluate 59 != 29, drop this branch.\n     |- Try 35 - 24 = 11. Evaluate 11 != 29, drop this branch.\n     |- Try 35 * 24 = 840. Evaluate 840 != 29, drop this branch.\n     |- Try 35 \/ 24 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 26 * 2 = 52. Add 52 to the number set. Current number set: [52, 35], target: 29, just two numbers left.\n     |- Try 52 + 35 = 87. Evaluate 87 != 29, drop this branch.\n     |- Try 52 - 35 = 17. Evaluate 17 != 29, drop this branch.\n     |- Try 52 * 35 = 1820. Evaluate 1820 != 29, drop this branch.\n     |- Try 52 \/ 35 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 26 \/ 2 = 13. Add 13 to the number set. Current number set: [13, 35], target: 29, just two numbers left.\n     |- Try 35 + 13 = 48. Evaluate 48 != 29, drop this branch.\n     |- Try 35 - 13 = 22. Evaluate 22 != 29, drop this branch.\n     |- Try 35 * 13 = 455. Evaluate 455 != 29, drop this branch.\n     |- Try 35 \/ 13 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (26, 35) (numbers left: [2]). Try possible operations.\n    |- Try 35 + 26 = 61. Add 61 to the number set. Current number set: [61, 2], target: 29, just two numbers left.\n     |- Try 61 + 2 = 63. Evaluate 63 != 29, drop this branch.\n     |- Try 61 - 2 = 59. Evaluate 59 != 29, drop this branch.\n     |- Try 61 * 2 = 122. Evaluate 122 != 29, drop this branch.\n     |- Try 61 \/ 2 = 30.5. 30.5 is a decimal, drop this branch.\n    |- Try 35 - 26 = 9. Add 9 to the number set. Current number set: [9, 2], target: 29, just two numbers left.\n     |- Try 9 + 2 = 11. Evaluate 11 != 29, drop this branch.\n     |- Try 9 - 2 = 7. Evaluate 7 != 29, drop this branch.\n     |- Try 9 * 2 = 18. Evaluate 18 != 29, drop this branch.\n     |- Try 9 \/ 2 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 35 * 26 = 910. Add 910 to the number set. Current number set: [910, 2], target: 29, just two numbers left.\n     |- Try 910 + 2 = 912. Evaluate 912 != 29, drop this branch.\n     |- Try 910 - 2 = 908. Evaluate 908 != 29, drop this branch.\n     |- Try 910 * 2 = 1820. Evaluate 1820 != 29, drop this branch.\n     |- Try 910 \/ 2 = 455. Evaluate 455 != 29, drop this branch.\n    |- Try 35 \/ 26 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (2, 35) (numbers left: [26]). Try possible operations.\n    |- Try 35 + 2 = 37. Add 37 to the number set. Current number set: [37, 26], target: 29, just two numbers left.\n     |- Try 37 + 26 = 63. Evaluate 63 != 29, drop this branch.\n     |- Try 37 - 26 = 11. Evaluate 11 != 29, drop this branch.\n     |- Try 37 * 26 = 962. Evaluate 962 != 29, drop this branch.\n     |- Try 37 \/ 26 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 35 - 2 = 33. Add 33 to the number set. Current number set: [33, 26], target: 29, just two numbers left.\n     |- Try 33 + 26 = 59. Evaluate 59 != 29, drop this branch.\n     |- Try 33 - 26 = 7. Evaluate 7 != 29, drop this branch.\n     |- Try 33 * 26 = 858. Evaluate 858 != 29, drop this branch.\n     |- Try 33 \/ 26 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 35 * 2 = 70. Add 70 to the number set. Current number set: [70, 26], target: 29, just two numbers left.\n     |- Try 70 + 26 = 96. Evaluate 96 != 29, drop this branch.\n     |- Try 70 - 26 = 44. Evaluate 44 != 29, drop this branch.\n     |- Try 70 * 26 = 1820. Evaluate 1820 != 29, drop this branch.\n     |- Try 70 \/ 26 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 35 \/ 2 = 17.5. 17.5 is a decimal, drop this branch.\n  |- Try 39 * 13 = 507. Add 507 to the number set. Current number set: [507, 2, 35], target: 29. Options for choosing two numbers: [(507, 2), (507, 35), (2, 35)].\n   |- Pick two numbers (507, 2) (numbers left: [35]). Try possible operations.\n    |- Try 507 + 2 = 509. Add 509 to the number set. Current number set: [509, 35], target: 29, just two numbers left.\n     |- Try 509 + 35 = 544. Evaluate 544 != 29, drop this branch.\n     |- Try 509 - 35 = 474. Evaluate 474 != 29, drop this branch.\n     |- Try 509 * 35 = 17815. 17815 exceeds the maximum intermediate result, drop this branch.\n     |- Try 509 \/ 35 = 14.5. 14.5 is a decimal, drop this branch.\n    |- Try 507 - 2 = 505. Add 505 to the number set. Current number set: [505, 35], target: 29, just two numbers left.\n     |- Try 505 + 35 = 540. Evaluate 540 != 29, drop this branch.\n     |- Try 505 - 35 = 470. Evaluate 470 != 29, drop this branch.\n     |- Try 505 * 35 = 17675. 17675 exceeds the maximum intermediate result, drop this branch.\n     |- Try 505 \/ 35 = 14.4. 14.4 is a decimal, drop this branch.\n    |- Try 507 * 2 = 1014. Add 1014 to the number set. Current number set: [1014, 35], target: 29, just two numbers left.\n     |- Try 1014 + 35 = 1049. Evaluate 1049 != 29, drop this branch.\n     |- Try 1014 - 35 = 979. Evaluate 979 != 29, drop this branch.\n     |- Try 1014 * 35 = 35490. 35490 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1014 \/ 35 = 29.0. 29.0 is a decimal, drop this branch.\n    |- Try 507 \/ 2 = 253.5. 253.5 is a decimal, drop this branch.\n   |- Pick two numbers (507, 35) (numbers left: [2]). Try possible operations.\n    |- Try 507 + 35 = 542. Add 542 to the number set. Current number set: [542, 2], target: 29, just two numbers left.\n     |- Try 542 + 2 = 544. Evaluate 544 != 29, drop this branch.\n     |- Try 542 - 2 = 540. Evaluate 540 != 29, drop this branch.\n     |- Try 542 * 2 = 1084. Evaluate 1084 != 29, drop this branch.\n     |- Try 542 \/ 2 = 271. Evaluate 271 != 29, drop this branch.\n    |- Try 507 - 35 = 472. Add 472 to the number set. Current number set: [472, 2], target: 29, just two numbers left.\n     |- Try 472 + 2 = 474. Evaluate 474 != 29, drop this branch.\n     |- Try 472 - 2 = 470. Evaluate 470 != 29, drop this branch.\n     |- Try 472 * 2 = 944. Evaluate 944 != 29, drop this branch.\n     |- Try 472 \/ 2 = 236. Evaluate 236 != 29, drop this branch.\n    |- Try 507 * 35 = 17745. 17745 exceeds the maximum intermediate result, drop this branch.\n    |- Try 507 \/ 35 = 14.5. 14.5 is a decimal, drop this branch.\n   |- Pick two numbers (2, 35) (numbers left: [507]). Try possible operations.\n    |- Try 35 + 2 = 37. Add 37 to the number set. Current number set: [37, 507], target: 29, just two numbers left.\n     |- Try 507 + 37 = 544. Evaluate 544 != 29, drop this branch.\n     |- Try 507 - 37 = 470. Evaluate 470 != 29, drop this branch.\n     |- Try 507 * 37 = 18759. 18759 exceeds the maximum intermediate result, drop this branch.\n     |- Try 507 \/ 37 = 13.7. 13.7 is a decimal, drop this branch.\n    |- Try 35 - 2 = 33. Add 33 to the number set. Current number set: [33, 507], target: 29, just two numbers left.\n     |- Try 507 + 33 = 540. Evaluate 540 != 29, drop this branch.\n     |- Try 507 - 33 = 474. Evaluate 474 != 29, drop this branch.\n     |- Try 507 * 33 = 16731. 16731 exceeds the maximum intermediate result, drop this branch.\n     |- Try 507 \/ 33 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 35 * 2 = 70. Add 70 to the number set. Current number set: [70, 507], target: 29, just two numbers left.\n     |- Try 507 + 70 = 577. Evaluate 577 != 29, drop this branch.\n     |- Try 507 - 70 = 437. Evaluate 437 != 29, drop this branch.\n     |- Try 507 * 70 = 35490. 35490 exceeds the maximum intermediate result, drop this branch.\n     |- Try 507 \/ 70 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 35 \/ 2 = 17.5. 17.5 is a decimal, drop this branch.\n  |- Try 39 \/ 13 = 3. Add 3 to the number set. Current number set: [3, 2, 35], target: 29. Options for choosing two numbers: [(3, 2), (3, 35), (2, 35)].\n   |- Pick two numbers (3, 2) (numbers left: [35]). Try possible operations.\n    |- Try 3 + 2 = 5. Add 5 to the number set. Current number set: [5, 35], target: 29, just two numbers left.\n     |- Try 35 + 5 = 40. Evaluate 40 != 29, drop this branch.\n     |- Try 35 - 5 = 30. Evaluate 30 != 29, drop this branch.\n     |- Try 35 * 5 = 175. Evaluate 175 != 29, drop this branch.\n     |- Try 35 \/ 5 = 7. Evaluate 7 != 29, drop this branch.\n    |- Try 3 - 2 = 1. Add 1 to the number set. Current number set: [1, 35], target: 29, just two numbers left.\n     |- Try 35 + 1 = 36. Evaluate 36 != 29, drop this branch.\n     |- Try 35 - 1 = 34. Evaluate 34 != 29, drop this branch.\n     |- Try 35 * 1 = 35. Evaluate 35 != 29, drop this branch.\n     |- Try 35 \/ 1 = 35. Evaluate 35 != 29, drop this branch.\n    |- Try 3 * 2 = 6. Add 6 to the number set. Current number set: [6, 35], target: 29, just two numbers left.\n     |- Try 35 + 6 = 41. Evaluate 41 != 29, drop this branch.\n     |- Try 35 - 6 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 35 - 6 = 29\nThe step before: 3 * 2 = 6\nThe first step: 39 \/ 13 = 3\n\nOutput the solution in the required format:\n<Solution>\n39 \/ 13 = 3\n3 * 2 = 6\n35 - 6 = 29\n<\/Solution>\n","item":{"nums":[13,39,2,35],"solution":["39 \/ 13 = 3","3 * 2 = 6","35 - 6 = 29"],"target":29}}
+{"instance_id":"countdown_8k_163","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [17, 12, 13, 44]\nTarget: 41","reference_output":"# Search Procedure\nInitial number set: [17, 12, 13, 44], target: 41. Options for choosing two numbers: [(17, 12), (17, 13), (17, 44), (12, 13), (12, 44), (13, 44)].\n |- Pick two numbers (17, 12) (numbers left: [13, 44]). Try possible operations.\n  |- Try 17 + 12 = 29. Add 29 to the number set. Current number set: [29, 13, 44], target: 41. Options for choosing two numbers: [(29, 13), (29, 44), (13, 44)].\n   |- Pick two numbers (29, 13) (numbers left: [44]). Try possible operations.\n    |- Try 29 + 13 = 42. Add 42 to the number set. Current number set: [42, 44], target: 41, just two numbers left.\n     |- Try 44 + 42 = 86. Evaluate 86 != 41, drop this branch.\n     |- Try 44 - 42 = 2. Evaluate 2 != 41, drop this branch.\n     |- Try 44 * 42 = 1848. Evaluate 1848 != 41, drop this branch.\n     |- Try 44 \/ 42 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 29 - 13 = 16. Add 16 to the number set. Current number set: [16, 44], target: 41, just two numbers left.\n     |- Try 44 + 16 = 60. Evaluate 60 != 41, drop this branch.\n     |- Try 44 - 16 = 28. Evaluate 28 != 41, drop this branch.\n     |- Try 44 * 16 = 704. Evaluate 704 != 41, drop this branch.\n     |- Try 44 \/ 16 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 29 * 13 = 377. Add 377 to the number set. Current number set: [377, 44], target: 41, just two numbers left.\n     |- Try 377 + 44 = 421. Evaluate 421 != 41, drop this branch.\n     |- Try 377 - 44 = 333. Evaluate 333 != 41, drop this branch.\n     |- Try 377 * 44 = 16588. 16588 exceeds the maximum intermediate result, drop this branch.\n     |- Try 377 \/ 44 = 8.6. 8.6 is a decimal, drop this branch.\n    |- Try 29 \/ 13 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (29, 44) (numbers left: [13]). Try possible operations.\n    |- Try 44 + 29 = 73. Add 73 to the number set. Current number set: [73, 13], target: 41, just two numbers left.\n     |- Try 73 + 13 = 86. Evaluate 86 != 41, drop this branch.\n     |- Try 73 - 13 = 60. Evaluate 60 != 41, drop this branch.\n     |- Try 73 * 13 = 949. Evaluate 949 != 41, drop this branch.\n     |- Try 73 \/ 13 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 44 - 29 = 15. Add 15 to the number set. Current number set: [15, 13], target: 41, just two numbers left.\n     |- Try 15 + 13 = 28. Evaluate 28 != 41, drop this branch.\n     |- Try 15 - 13 = 2. Evaluate 2 != 41, drop this branch.\n     |- Try 15 * 13 = 195. Evaluate 195 != 41, drop this branch.\n     |- Try 15 \/ 13 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 44 * 29 = 1276. Add 1276 to the number set. Current number set: [1276, 13], target: 41, just two numbers left.\n     |- Try 1276 + 13 = 1289. Evaluate 1289 != 41, drop this branch.\n     |- Try 1276 - 13 = 1263. Evaluate 1263 != 41, drop this branch.\n     |- Try 1276 * 13 = 16588. 16588 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1276 \/ 13 = 98.2. 98.2 is a decimal, drop this branch.\n    |- Try 44 \/ 29 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (13, 44) (numbers left: [29]). Try possible operations.\n    |- Try 44 + 13 = 57. Add 57 to the number set. Current number set: [57, 29], target: 41, just two numbers left.\n     |- Try 57 + 29 = 86. Evaluate 86 != 41, drop this branch.\n     |- Try 57 - 29 = 28. Evaluate 28 != 41, drop this branch.\n     |- Try 57 * 29 = 1653. Evaluate 1653 != 41, drop this branch.\n     |- Try 57 \/ 29 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 44 - 13 = 31. Add 31 to the number set. Current number set: [31, 29], target: 41, just two numbers left.\n     |- Try 31 + 29 = 60. Evaluate 60 != 41, drop this branch.\n     |- Try 31 - 29 = 2. Evaluate 2 != 41, drop this branch.\n     |- Try 31 * 29 = 899. Evaluate 899 != 41, drop this branch.\n     |- Try 31 \/ 29 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 44 * 13 = 572. Add 572 to the number set. Current number set: [572, 29], target: 41, just two numbers left.\n     |- Try 572 + 29 = 601. Evaluate 601 != 41, drop this branch.\n     |- Try 572 - 29 = 543. Evaluate 543 != 41, drop this branch.\n     |- Try 572 * 29 = 16588. 16588 exceeds the maximum intermediate result, drop this branch.\n     |- Try 572 \/ 29 = 19.7. 19.7 is a decimal, drop this branch.\n    |- Try 44 \/ 13 = 3.4. 3.4 is a decimal, drop this branch.\n  |- Try 17 - 12 = 5. Add 5 to the number set. Current number set: [5, 13, 44], target: 41. Options for choosing two numbers: [(5, 13), (5, 44), (13, 44)].\n   |- Pick two numbers (5, 13) (numbers left: [44]). Try possible operations.\n    |- Try 13 + 5 = 18. Add 18 to the number set. Current number set: [18, 44], target: 41, just two numbers left.\n     |- Try 44 + 18 = 62. Evaluate 62 != 41, drop this branch.\n     |- Try 44 - 18 = 26. Evaluate 26 != 41, drop this branch.\n     |- Try 44 * 18 = 792. Evaluate 792 != 41, drop this branch.\n     |- Try 44 \/ 18 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 13 - 5 = 8. Add 8 to the number set. Current number set: [8, 44], target: 41, just two numbers left.\n     |- Try 44 + 8 = 52. Evaluate 52 != 41, drop this branch.\n     |- Try 44 - 8 = 36. Evaluate 36 != 41, drop this branch.\n     |- Try 44 * 8 = 352. Evaluate 352 != 41, drop this branch.\n     |- Try 44 \/ 8 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 13 * 5 = 65. Add 65 to the number set. Current number set: [65, 44], target: 41, just two numbers left.\n     |- Try 65 + 44 = 109. Evaluate 109 != 41, drop this branch.\n     |- Try 65 - 44 = 21. Evaluate 21 != 41, drop this branch.\n     |- Try 65 * 44 = 2860. 2860 exceeds the maximum intermediate result, drop this branch.\n     |- Try 65 \/ 44 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 13 \/ 5 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (5, 44) (numbers left: [13]). Try possible operations.\n    |- Try 44 + 5 = 49. Add 49 to the number set. Current number set: [49, 13], target: 41, just two numbers left.\n     |- Try 49 + 13 = 62. Evaluate 62 != 41, drop this branch.\n     |- Try 49 - 13 = 36. Evaluate 36 != 41, drop this branch.\n     |- Try 49 * 13 = 637. Evaluate 637 != 41, drop this branch.\n     |- Try 49 \/ 13 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 44 - 5 = 39. Add 39 to the number set. Current number set: [39, 13], target: 41, just two numbers left.\n     |- Try 39 + 13 = 52. Evaluate 52 != 41, drop this branch.\n     |- Try 39 - 13 = 26. Evaluate 26 != 41, drop this branch.\n     |- Try 39 * 13 = 507. Evaluate 507 != 41, drop this branch.\n     |- Try 39 \/ 13 = 3. Evaluate 3 != 41, drop this branch.\n    |- Try 44 * 5 = 220. Add 220 to the number set. Current number set: [220, 13], target: 41, just two numbers left.\n     |- Try 220 + 13 = 233. Evaluate 233 != 41, drop this branch.\n     |- Try 220 - 13 = 207. Evaluate 207 != 41, drop this branch.\n     |- Try 220 * 13 = 2860. 2860 exceeds the maximum intermediate result, drop this branch.\n     |- Try 220 \/ 13 = 16.9. 16.9 is a decimal, drop this branch.\n    |- Try 44 \/ 5 = 8.8. 8.8 is a decimal, drop this branch.\n   |- Pick two numbers (13, 44) (numbers left: [5]). Try possible operations.\n    |- Try 44 + 13 = 57. Add 57 to the number set. Current number set: [57, 5], target: 41, just two numbers left.\n     |- Try 57 + 5 = 62. Evaluate 62 != 41, drop this branch.\n     |- Try 57 - 5 = 52. Evaluate 52 != 41, drop this branch.\n     |- Try 57 * 5 = 285. Evaluate 285 != 41, drop this branch.\n     |- Try 57 \/ 5 = 11.4. 11.4 is a decimal, drop this branch.\n    |- Try 44 - 13 = 31. Add 31 to the number set. Current number set: [31, 5], target: 41, just two numbers left.\n     |- Try 31 + 5 = 36. Evaluate 36 != 41, drop this branch.\n     |- Try 31 - 5 = 26. Evaluate 26 != 41, drop this branch.\n     |- Try 31 * 5 = 155. Evaluate 155 != 41, drop this branch.\n     |- Try 31 \/ 5 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 44 * 13 = 572. Add 572 to the number set. Current number set: [572, 5], target: 41, just two numbers left.\n     |- Try 572 + 5 = 577. Evaluate 577 != 41, drop this branch.\n     |- Try 572 - 5 = 567. Evaluate 567 != 41, drop this branch.\n     |- Try 572 * 5 = 2860. 2860 exceeds the maximum intermediate result, drop this branch.\n     |- Try 572 \/ 5 = 114.4. 114.4 is a decimal, drop this branch.\n    |- Try 44 \/ 13 = 3.4. 3.4 is a decimal, drop this branch.\n  |- Try 17 * 12 = 204. Add 204 to the number set. Current number set: [204, 13, 44], target: 41. Options for choosing two numbers: [(204, 13), (204, 44), (13, 44)].\n   |- Pick two numbers (204, 13) (numbers left: [44]). Try possible operations.\n    |- Try 204 + 13 = 217. Add 217 to the number set. Current number set: [217, 44], target: 41, just two numbers left.\n     |- Try 217 + 44 = 261. Evaluate 261 != 41, drop this branch.\n     |- Try 217 - 44 = 173. Evaluate 173 != 41, drop this branch.\n     |- Try 217 * 44 = 9548. 9548 exceeds the maximum intermediate result, drop this branch.\n     |- Try 217 \/ 44 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 204 - 13 = 191. Add 191 to the number set. Current number set: [191, 44], target: 41, just two numbers left.\n     |- Try 191 + 44 = 235. Evaluate 235 != 41, drop this branch.\n     |- Try 191 - 44 = 147. Evaluate 147 != 41, drop this branch.\n     |- Try 191 * 44 = 8404. 8404 exceeds the maximum intermediate result, drop this branch.\n     |- Try 191 \/ 44 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 204 * 13 = 2652. 2652 exceeds the maximum intermediate result, drop this branch.\n    |- Try 204 \/ 13 = 15.7. 15.7 is a decimal, drop this branch.\n   |- Pick two numbers (204, 44) (numbers left: [13]). Try possible operations.\n    |- Try 204 + 44 = 248. Add 248 to the number set. Current number set: [248, 13], target: 41, just two numbers left.\n     |- Try 248 + 13 = 261. Evaluate 261 != 41, drop this branch.\n     |- Try 248 - 13 = 235. Evaluate 235 != 41, drop this branch.\n     |- Try 248 * 13 = 3224. 3224 exceeds the maximum intermediate result, drop this branch.\n     |- Try 248 \/ 13 = 19.1. 19.1 is a decimal, drop this branch.\n    |- Try 204 - 44 = 160. Add 160 to the number set. Current number set: [160, 13], target: 41, just two numbers left.\n     |- Try 160 + 13 = 173. Evaluate 173 != 41, drop this branch.\n     |- Try 160 - 13 = 147. Evaluate 147 != 41, drop this branch.\n     |- Try 160 * 13 = 2080. 2080 exceeds the maximum intermediate result, drop this branch.\n     |- Try 160 \/ 13 = 12.3. 12.3 is a decimal, drop this branch.\n    |- Try 204 * 44 = 8976. 8976 exceeds the maximum intermediate result, drop this branch.\n    |- Try 204 \/ 44 = 4.6. 4.6 is a decimal, drop this branch.\n   |- Pick two numbers (13, 44) (numbers left: [204]). Try possible operations.\n    |- Try 44 + 13 = 57. Add 57 to the number set. Current number set: [57, 204], target: 41, just two numbers left.\n     |- Try 204 + 57 = 261. Evaluate 261 != 41, drop this branch.\n     |- Try 204 - 57 = 147. Evaluate 147 != 41, drop this branch.\n     |- Try 204 * 57 = 11628. 11628 exceeds the maximum intermediate result, drop this branch.\n     |- Try 204 \/ 57 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 44 - 13 = 31. Add 31 to the number set. Current number set: [31, 204], target: 41, just two numbers left.\n     |- Try 204 + 31 = 235. Evaluate 235 != 41, drop this branch.\n     |- Try 204 - 31 = 173. Evaluate 173 != 41, drop this branch.\n     |- Try 204 * 31 = 6324. 6324 exceeds the maximum intermediate result, drop this branch.\n     |- Try 204 \/ 31 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 44 * 13 = 572. Add 572 to the number set. Current number set: [572, 204], target: 41, just two numbers left.\n     |- Try 572 + 204 = 776. Evaluate 776 != 41, drop this branch.\n     |- Try 572 - 204 = 368. Evaluate 368 != 41, drop this branch.\n     |- Try 572 * 204 = 116688. 116688 exceeds the maximum intermediate result, drop this branch.\n     |- Try 572 \/ 204 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 44 \/ 13 = 3.4. 3.4 is a decimal, drop this branch.\n  |- Try 17 \/ 12 = 1.4. 1.4 is a decimal, drop this branch.\n |- Pick two numbers (17, 13) (numbers left: [12, 44]). Try possible operations.\n  |- Try 17 + 13 = 30. Add 30 to the number set. Current number set: [30, 12, 44], target: 41. Options for choosing two numbers: [(30, 12), (30, 44), (12, 44)].\n   |- Pick two numbers (30, 12) (numbers left: [44]). Try possible operations.\n    |- Try 30 + 12 = 42. Add 42 to the number set. Current number set: [42, 44], target: 41, just two numbers left.\n     |- Try 44 + 42 = 86. Evaluate 86 != 41, drop this branch.\n     |- Try 44 - 42 = 2. Evaluate 2 != 41, drop this branch.\n     |- Try 44 * 42 = 1848. Evaluate 1848 != 41, drop this branch.\n     |- Try 44 \/ 42 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 30 - 12 = 18. Add 18 to the number set. Current number set: [18, 44], target: 41, just two numbers left.\n     |- Try 44 + 18 = 62. Evaluate 62 != 41, drop this branch.\n     |- Try 44 - 18 = 26. Evaluate 26 != 41, drop this branch.\n     |- Try 44 * 18 = 792. Evaluate 792 != 41, drop this branch.\n     |- Try 44 \/ 18 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 30 * 12 = 360. Add 360 to the number set. Current number set: [360, 44], target: 41, just two numbers left.\n     |- Try 360 + 44 = 404. Evaluate 404 != 41, drop this branch.\n     |- Try 360 - 44 = 316. Evaluate 316 != 41, drop this branch.\n     |- Try 360 * 44 = 15840. 15840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 360 \/ 44 = 8.2. 8.2 is a decimal, drop this branch.\n    |- Try 30 \/ 12 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (30, 44) (numbers left: [12]). Try possible operations.\n    |- Try 44 + 30 = 74. Add 74 to the number set. Current number set: [74, 12], target: 41, just two numbers left.\n     |- Try 74 + 12 = 86. Evaluate 86 != 41, drop this branch.\n     |- Try 74 - 12 = 62. Evaluate 62 != 41, drop this branch.\n     |- Try 74 * 12 = 888. Evaluate 888 != 41, drop this branch.\n     |- Try 74 \/ 12 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 44 - 30 = 14. Add 14 to the number set. Current number set: [14, 12], target: 41, just two numbers left.\n     |- Try 14 + 12 = 26. Evaluate 26 != 41, drop this branch.\n     |- Try 14 - 12 = 2. Evaluate 2 != 41, drop this branch.\n     |- Try 14 * 12 = 168. Evaluate 168 != 41, drop this branch.\n     |- Try 14 \/ 12 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 44 * 30 = 1320. Add 1320 to the number set. Current number set: [1320, 12], target: 41, just two numbers left.\n     |- Try 1320 + 12 = 1332. Evaluate 1332 != 41, drop this branch.\n     |- Try 1320 - 12 = 1308. Evaluate 1308 != 41, drop this branch.\n     |- Try 1320 * 12 = 15840. 15840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1320 \/ 12 = 110. Evaluate 110 != 41, drop this branch.\n    |- Try 44 \/ 30 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (12, 44) (numbers left: [30]). Try possible operations.\n    |- Try 44 + 12 = 56. Add 56 to the number set. Current number set: [56, 30], target: 41, just two numbers left.\n     |- Try 56 + 30 = 86. Evaluate 86 != 41, drop this branch.\n     |- Try 56 - 30 = 26. Evaluate 26 != 41, drop this branch.\n     |- Try 56 * 30 = 1680. Evaluate 1680 != 41, drop this branch.\n     |- Try 56 \/ 30 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 44 - 12 = 32. Add 32 to the number set. Current number set: [32, 30], target: 41, just two numbers left.\n     |- Try 32 + 30 = 62. Evaluate 62 != 41, drop this branch.\n     |- Try 32 - 30 = 2. Evaluate 2 != 41, drop this branch.\n     |- Try 32 * 30 = 960. Evaluate 960 != 41, drop this branch.\n     |- Try 32 \/ 30 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 44 * 12 = 528. Add 528 to the number set. Current number set: [528, 30], target: 41, just two numbers left.\n     |- Try 528 + 30 = 558. Evaluate 558 != 41, drop this branch.\n     |- Try 528 - 30 = 498. Evaluate 498 != 41, drop this branch.\n     |- Try 528 * 30 = 15840. 15840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 528 \/ 30 = 17.6. 17.6 is a decimal, drop this branch.\n    |- Try 44 \/ 12 = 3.7. 3.7 is a decimal, drop this branch.\n  |- Try 17 - 13 = 4. Add 4 to the number set. Current number set: [4, 12, 44], target: 41. Options for choosing two numbers: [(4, 12), (4, 44), (12, 44)].\n   |- Pick two numbers (4, 12) (numbers left: [44]). Try possible operations.\n    |- Try 12 + 4 = 16. Add 16 to the number set. Current number set: [16, 44], target: 41, just two numbers left.\n     |- Try 44 + 16 = 60. Evaluate 60 != 41, drop this branch.\n     |- Try 44 - 16 = 28. Evaluate 28 != 41, drop this branch.\n     |- Try 44 * 16 = 704. Evaluate 704 != 41, drop this branch.\n     |- Try 44 \/ 16 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 12 - 4 = 8. Add 8 to the number set. Current number set: [8, 44], target: 41, just two numbers left.\n     |- Try 44 + 8 = 52. Evaluate 52 != 41, drop this branch.\n     |- Try 44 - 8 = 36. Evaluate 36 != 41, drop this branch.\n     |- Try 44 * 8 = 352. Evaluate 352 != 41, drop this branch.\n     |- Try 44 \/ 8 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 12 * 4 = 48. Add 48 to the number set. Current number set: [48, 44], target: 41, just two numbers left.\n     |- Try 48 + 44 = 92. Evaluate 92 != 41, drop this branch.\n     |- Try 48 - 44 = 4. Evaluate 4 != 41, drop this branch.\n     |- Try 48 * 44 = 2112. 2112 exceeds the maximum intermediate result, drop this branch.\n     |- Try 48 \/ 44 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 12 \/ 4 = 3. Add 3 to the number set. Current number set: [3, 44], target: 41, just two numbers left.\n     |- Try 44 + 3 = 47. Evaluate 47 != 41, drop this branch.\n     |- Try 44 - 3 = 41. Evaluate 41 == 41, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 44 - 3 = 41\nThe step before: 12 \/ 4 = 3\nThe first step: 17 - 13 = 4\n\nOutput the solution in the required format:\n<Solution>\n17 - 13 = 4\n12 \/ 4 = 3\n44 - 3 = 41\n<\/Solution>\n","item":{"nums":[17,12,13,44],"solution":["17 - 13 = 4","12 \/ 4 = 3","44 - 3 = 41"],"target":41}}
+{"instance_id":"countdown_8k_164","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [17, 3, 8, 4]\nTarget: 33","reference_output":"# Search Procedure\nInitial number set: [17, 3, 8, 4], target: 33. Options for choosing two numbers: [(17, 3), (17, 8), (17, 4), (3, 8), (3, 4), (8, 4)].\n |- Pick two numbers (17, 3) (numbers left: [8, 4]). Try possible operations.\n  |- Try 17 + 3 = 20. Add 20 to the number set. Current number set: [20, 8, 4], target: 33. Options for choosing two numbers: [(20, 8), (20, 4), (8, 4)].\n   |- Pick two numbers (20, 8) (numbers left: [4]). Try possible operations.\n    |- Try 20 + 8 = 28. Add 28 to the number set. Current number set: [28, 4], target: 33, just two numbers left.\n     |- Try 28 + 4 = 32. Evaluate 32 != 33, drop this branch.\n     |- Try 28 - 4 = 24. Evaluate 24 != 33, drop this branch.\n     |- Try 28 * 4 = 112. Evaluate 112 != 33, drop this branch.\n     |- Try 28 \/ 4 = 7. Evaluate 7 != 33, drop this branch.\n    |- Try 20 - 8 = 12. Add 12 to the number set. Current number set: [12, 4], target: 33, just two numbers left.\n     |- Try 12 + 4 = 16. Evaluate 16 != 33, drop this branch.\n     |- Try 12 - 4 = 8. Evaluate 8 != 33, drop this branch.\n     |- Try 12 * 4 = 48. Evaluate 48 != 33, drop this branch.\n     |- Try 12 \/ 4 = 3. Evaluate 3 != 33, drop this branch.\n    |- Try 20 * 8 = 160. Add 160 to the number set. Current number set: [160, 4], target: 33, just two numbers left.\n     |- Try 160 + 4 = 164. Evaluate 164 != 33, drop this branch.\n     |- Try 160 - 4 = 156. Evaluate 156 != 33, drop this branch.\n     |- Try 160 * 4 = 640. Evaluate 640 != 33, drop this branch.\n     |- Try 160 \/ 4 = 40. Evaluate 40 != 33, drop this branch.\n    |- Try 20 \/ 8 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (20, 4) (numbers left: [8]). Try possible operations.\n    |- Try 20 + 4 = 24. Add 24 to the number set. Current number set: [24, 8], target: 33, just two numbers left.\n     |- Try 24 + 8 = 32. Evaluate 32 != 33, drop this branch.\n     |- Try 24 - 8 = 16. Evaluate 16 != 33, drop this branch.\n     |- Try 24 * 8 = 192. Evaluate 192 != 33, drop this branch.\n     |- Try 24 \/ 8 = 3. Evaluate 3 != 33, drop this branch.\n    |- Try 20 - 4 = 16. Add 16 to the number set. Current number set: [16, 8], target: 33, just two numbers left.\n     |- Try 16 + 8 = 24. Evaluate 24 != 33, drop this branch.\n     |- Try 16 - 8 = 8. Evaluate 8 != 33, drop this branch.\n     |- Try 16 * 8 = 128. Evaluate 128 != 33, drop this branch.\n     |- Try 16 \/ 8 = 2. Evaluate 2 != 33, drop this branch.\n    |- Try 20 * 4 = 80. Add 80 to the number set. Current number set: [80, 8], target: 33, just two numbers left.\n     |- Try 80 + 8 = 88. Evaluate 88 != 33, drop this branch.\n     |- Try 80 - 8 = 72. Evaluate 72 != 33, drop this branch.\n     |- Try 80 * 8 = 640. Evaluate 640 != 33, drop this branch.\n     |- Try 80 \/ 8 = 10. Evaluate 10 != 33, drop this branch.\n    |- Try 20 \/ 4 = 5. Add 5 to the number set. Current number set: [5, 8], target: 33, just two numbers left.\n     |- Try 8 + 5 = 13. Evaluate 13 != 33, drop this branch.\n     |- Try 8 - 5 = 3. Evaluate 3 != 33, drop this branch.\n     |- Try 8 * 5 = 40. Evaluate 40 != 33, drop this branch.\n     |- Try 8 \/ 5 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (8, 4) (numbers left: [20]). Try possible operations.\n    |- Try 8 + 4 = 12. Add 12 to the number set. Current number set: [12, 20], target: 33, just two numbers left.\n     |- Try 20 + 12 = 32. Evaluate 32 != 33, drop this branch.\n     |- Try 20 - 12 = 8. Evaluate 8 != 33, drop this branch.\n     |- Try 20 * 12 = 240. Evaluate 240 != 33, drop this branch.\n     |- Try 20 \/ 12 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 8 - 4 = 4. Add 4 to the number set. Current number set: [4, 20], target: 33, just two numbers left.\n     |- Try 20 + 4 = 24. Evaluate 24 != 33, drop this branch.\n     |- Try 20 - 4 = 16. Evaluate 16 != 33, drop this branch.\n     |- Try 20 * 4 = 80. Evaluate 80 != 33, drop this branch.\n     |- Try 20 \/ 4 = 5. Evaluate 5 != 33, drop this branch.\n    |- Try 8 * 4 = 32. Add 32 to the number set. Current number set: [32, 20], target: 33, just two numbers left.\n     |- Try 32 + 20 = 52. Evaluate 52 != 33, drop this branch.\n     |- Try 32 - 20 = 12. Evaluate 12 != 33, drop this branch.\n     |- Try 32 * 20 = 640. Evaluate 640 != 33, drop this branch.\n     |- Try 32 \/ 20 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 8 \/ 4 = 2. Add 2 to the number set. Current number set: [2, 20], target: 33, just two numbers left.\n     |- Try 20 + 2 = 22. Evaluate 22 != 33, drop this branch.\n     |- Try 20 - 2 = 18. Evaluate 18 != 33, drop this branch.\n     |- Try 20 * 2 = 40. Evaluate 40 != 33, drop this branch.\n     |- Try 20 \/ 2 = 10. Evaluate 10 != 33, drop this branch.\n  |- Try 17 - 3 = 14. Add 14 to the number set. Current number set: [14, 8, 4], target: 33. Options for choosing two numbers: [(14, 8), (14, 4), (8, 4)].\n   |- Pick two numbers (14, 8) (numbers left: [4]). Try possible operations.\n    |- Try 14 + 8 = 22. Add 22 to the number set. Current number set: [22, 4], target: 33, just two numbers left.\n     |- Try 22 + 4 = 26. Evaluate 26 != 33, drop this branch.\n     |- Try 22 - 4 = 18. Evaluate 18 != 33, drop this branch.\n     |- Try 22 * 4 = 88. Evaluate 88 != 33, drop this branch.\n     |- Try 22 \/ 4 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 14 - 8 = 6. Add 6 to the number set. Current number set: [6, 4], target: 33, just two numbers left.\n     |- Try 6 + 4 = 10. Evaluate 10 != 33, drop this branch.\n     |- Try 6 - 4 = 2. Evaluate 2 != 33, drop this branch.\n     |- Try 6 * 4 = 24. Evaluate 24 != 33, drop this branch.\n     |- Try 6 \/ 4 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 14 * 8 = 112. Add 112 to the number set. Current number set: [112, 4], target: 33, just two numbers left.\n     |- Try 112 + 4 = 116. Evaluate 116 != 33, drop this branch.\n     |- Try 112 - 4 = 108. Evaluate 108 != 33, drop this branch.\n     |- Try 112 * 4 = 448. Evaluate 448 != 33, drop this branch.\n     |- Try 112 \/ 4 = 28. Evaluate 28 != 33, drop this branch.\n    |- Try 14 \/ 8 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (14, 4) (numbers left: [8]). Try possible operations.\n    |- Try 14 + 4 = 18. Add 18 to the number set. Current number set: [18, 8], target: 33, just two numbers left.\n     |- Try 18 + 8 = 26. Evaluate 26 != 33, drop this branch.\n     |- Try 18 - 8 = 10. Evaluate 10 != 33, drop this branch.\n     |- Try 18 * 8 = 144. Evaluate 144 != 33, drop this branch.\n     |- Try 18 \/ 8 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 14 - 4 = 10. Add 10 to the number set. Current number set: [10, 8], target: 33, just two numbers left.\n     |- Try 10 + 8 = 18. Evaluate 18 != 33, drop this branch.\n     |- Try 10 - 8 = 2. Evaluate 2 != 33, drop this branch.\n     |- Try 10 * 8 = 80. Evaluate 80 != 33, drop this branch.\n     |- Try 10 \/ 8 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 14 * 4 = 56. Add 56 to the number set. Current number set: [56, 8], target: 33, just two numbers left.\n     |- Try 56 + 8 = 64. Evaluate 64 != 33, drop this branch.\n     |- Try 56 - 8 = 48. Evaluate 48 != 33, drop this branch.\n     |- Try 56 * 8 = 448. Evaluate 448 != 33, drop this branch.\n     |- Try 56 \/ 8 = 7. Evaluate 7 != 33, drop this branch.\n    |- Try 14 \/ 4 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (8, 4) (numbers left: [14]). Try possible operations.\n    |- Try 8 + 4 = 12. Add 12 to the number set. Current number set: [12, 14], target: 33, just two numbers left.\n     |- Try 14 + 12 = 26. Evaluate 26 != 33, drop this branch.\n     |- Try 14 - 12 = 2. Evaluate 2 != 33, drop this branch.\n     |- Try 14 * 12 = 168. Evaluate 168 != 33, drop this branch.\n     |- Try 14 \/ 12 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 8 - 4 = 4. Add 4 to the number set. Current number set: [4, 14], target: 33, just two numbers left.\n     |- Try 14 + 4 = 18. Evaluate 18 != 33, drop this branch.\n     |- Try 14 - 4 = 10. Evaluate 10 != 33, drop this branch.\n     |- Try 14 * 4 = 56. Evaluate 56 != 33, drop this branch.\n     |- Try 14 \/ 4 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 8 * 4 = 32. Add 32 to the number set. Current number set: [32, 14], target: 33, just two numbers left.\n     |- Try 32 + 14 = 46. Evaluate 46 != 33, drop this branch.\n     |- Try 32 - 14 = 18. Evaluate 18 != 33, drop this branch.\n     |- Try 32 * 14 = 448. Evaluate 448 != 33, drop this branch.\n     |- Try 32 \/ 14 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 8 \/ 4 = 2. Add 2 to the number set. Current number set: [2, 14], target: 33, just two numbers left.\n     |- Try 14 + 2 = 16. Evaluate 16 != 33, drop this branch.\n     |- Try 14 - 2 = 12. Evaluate 12 != 33, drop this branch.\n     |- Try 14 * 2 = 28. Evaluate 28 != 33, drop this branch.\n     |- Try 14 \/ 2 = 7. Evaluate 7 != 33, drop this branch.\n  |- Try 17 * 3 = 51. Add 51 to the number set. Current number set: [51, 8, 4], target: 33. Options for choosing two numbers: [(51, 8), (51, 4), (8, 4)].\n   |- Pick two numbers (51, 8) (numbers left: [4]). Try possible operations.\n    |- Try 51 + 8 = 59. Add 59 to the number set. Current number set: [59, 4], target: 33, just two numbers left.\n     |- Try 59 + 4 = 63. Evaluate 63 != 33, drop this branch.\n     |- Try 59 - 4 = 55. Evaluate 55 != 33, drop this branch.\n     |- Try 59 * 4 = 236. Evaluate 236 != 33, drop this branch.\n     |- Try 59 \/ 4 = 14.8. 14.8 is a decimal, drop this branch.\n    |- Try 51 - 8 = 43. Add 43 to the number set. Current number set: [43, 4], target: 33, just two numbers left.\n     |- Try 43 + 4 = 47. Evaluate 47 != 33, drop this branch.\n     |- Try 43 - 4 = 39. Evaluate 39 != 33, drop this branch.\n     |- Try 43 * 4 = 172. Evaluate 172 != 33, drop this branch.\n     |- Try 43 \/ 4 = 10.8. 10.8 is a decimal, drop this branch.\n    |- Try 51 * 8 = 408. Add 408 to the number set. Current number set: [408, 4], target: 33, just two numbers left.\n     |- Try 408 + 4 = 412. Evaluate 412 != 33, drop this branch.\n     |- Try 408 - 4 = 404. Evaluate 404 != 33, drop this branch.\n     |- Try 408 * 4 = 1632. Evaluate 1632 != 33, drop this branch.\n     |- Try 408 \/ 4 = 102. Evaluate 102 != 33, drop this branch.\n    |- Try 51 \/ 8 = 6.4. 6.4 is a decimal, drop this branch.\n   |- Pick two numbers (51, 4) (numbers left: [8]). Try possible operations.\n    |- Try 51 + 4 = 55. Add 55 to the number set. Current number set: [55, 8], target: 33, just two numbers left.\n     |- Try 55 + 8 = 63. Evaluate 63 != 33, drop this branch.\n     |- Try 55 - 8 = 47. Evaluate 47 != 33, drop this branch.\n     |- Try 55 * 8 = 440. Evaluate 440 != 33, drop this branch.\n     |- Try 55 \/ 8 = 6.9. 6.9 is a decimal, drop this branch.\n    |- Try 51 - 4 = 47. Add 47 to the number set. Current number set: [47, 8], target: 33, just two numbers left.\n     |- Try 47 + 8 = 55. Evaluate 55 != 33, drop this branch.\n     |- Try 47 - 8 = 39. Evaluate 39 != 33, drop this branch.\n     |- Try 47 * 8 = 376. Evaluate 376 != 33, drop this branch.\n     |- Try 47 \/ 8 = 5.9. 5.9 is a decimal, drop this branch.\n    |- Try 51 * 4 = 204. Add 204 to the number set. Current number set: [204, 8], target: 33, just two numbers left.\n     |- Try 204 + 8 = 212. Evaluate 212 != 33, drop this branch.\n     |- Try 204 - 8 = 196. Evaluate 196 != 33, drop this branch.\n     |- Try 204 * 8 = 1632. Evaluate 1632 != 33, drop this branch.\n     |- Try 204 \/ 8 = 25.5. 25.5 is a decimal, drop this branch.\n    |- Try 51 \/ 4 = 12.8. 12.8 is a decimal, drop this branch.\n   |- Pick two numbers (8, 4) (numbers left: [51]). Try possible operations.\n    |- Try 8 + 4 = 12. Add 12 to the number set. Current number set: [12, 51], target: 33, just two numbers left.\n     |- Try 51 + 12 = 63. Evaluate 63 != 33, drop this branch.\n     |- Try 51 - 12 = 39. Evaluate 39 != 33, drop this branch.\n     |- Try 51 * 12 = 612. Evaluate 612 != 33, drop this branch.\n     |- Try 51 \/ 12 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 8 - 4 = 4. Add 4 to the number set. Current number set: [4, 51], target: 33, just two numbers left.\n     |- Try 51 + 4 = 55. Evaluate 55 != 33, drop this branch.\n     |- Try 51 - 4 = 47. Evaluate 47 != 33, drop this branch.\n     |- Try 51 * 4 = 204. Evaluate 204 != 33, drop this branch.\n     |- Try 51 \/ 4 = 12.8. 12.8 is a decimal, drop this branch.\n    |- Try 8 * 4 = 32. Add 32 to the number set. Current number set: [32, 51], target: 33, just two numbers left.\n     |- Try 51 + 32 = 83. Evaluate 83 != 33, drop this branch.\n     |- Try 51 - 32 = 19. Evaluate 19 != 33, drop this branch.\n     |- Try 51 * 32 = 1632. Evaluate 1632 != 33, drop this branch.\n     |- Try 51 \/ 32 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 8 \/ 4 = 2. Add 2 to the number set. Current number set: [2, 51], target: 33, just two numbers left.\n     |- Try 51 + 2 = 53. Evaluate 53 != 33, drop this branch.\n     |- Try 51 - 2 = 49. Evaluate 49 != 33, drop this branch.\n     |- Try 51 * 2 = 102. Evaluate 102 != 33, drop this branch.\n     |- Try 51 \/ 2 = 25.5. 25.5 is a decimal, drop this branch.\n  |- Try 17 \/ 3 = 5.7. 5.7 is a decimal, drop this branch.\n |- Pick two numbers (17, 8) (numbers left: [3, 4]). Try possible operations.\n  |- Try 17 + 8 = 25. Add 25 to the number set. Current number set: [25, 3, 4], target: 33. Options for choosing two numbers: [(25, 3), (25, 4), (3, 4)].\n   |- Pick two numbers (25, 3) (numbers left: [4]). Try possible operations.\n    |- Try 25 + 3 = 28. Add 28 to the number set. Current number set: [28, 4], target: 33, just two numbers left.\n     |- Try 28 + 4 = 32. Evaluate 32 != 33, drop this branch.\n     |- Try 28 - 4 = 24. Evaluate 24 != 33, drop this branch.\n     |- Try 28 * 4 = 112. Evaluate 112 != 33, drop this branch.\n     |- Try 28 \/ 4 = 7. Evaluate 7 != 33, drop this branch.\n    |- Try 25 - 3 = 22. Add 22 to the number set. Current number set: [22, 4], target: 33, just two numbers left.\n     |- Try 22 + 4 = 26. Evaluate 26 != 33, drop this branch.\n     |- Try 22 - 4 = 18. Evaluate 18 != 33, drop this branch.\n     |- Try 22 * 4 = 88. Evaluate 88 != 33, drop this branch.\n     |- Try 22 \/ 4 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 25 * 3 = 75. Add 75 to the number set. Current number set: [75, 4], target: 33, just two numbers left.\n     |- Try 75 + 4 = 79. Evaluate 79 != 33, drop this branch.\n     |- Try 75 - 4 = 71. Evaluate 71 != 33, drop this branch.\n     |- Try 75 * 4 = 300. Evaluate 300 != 33, drop this branch.\n     |- Try 75 \/ 4 = 18.8. 18.8 is a decimal, drop this branch.\n    |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n   |- Pick two numbers (25, 4) (numbers left: [3]). Try possible operations.\n    |- Try 25 + 4 = 29. Add 29 to the number set. Current number set: [29, 3], target: 33, just two numbers left.\n     |- Try 29 + 3 = 32. Evaluate 32 != 33, drop this branch.\n     |- Try 29 - 3 = 26. Evaluate 26 != 33, drop this branch.\n     |- Try 29 * 3 = 87. Evaluate 87 != 33, drop this branch.\n     |- Try 29 \/ 3 = 9.7. 9.7 is a decimal, drop this branch.\n    |- Try 25 - 4 = 21. Add 21 to the number set. Current number set: [21, 3], target: 33, just two numbers left.\n     |- Try 21 + 3 = 24. Evaluate 24 != 33, drop this branch.\n     |- Try 21 - 3 = 18. Evaluate 18 != 33, drop this branch.\n     |- Try 21 * 3 = 63. Evaluate 63 != 33, drop this branch.\n     |- Try 21 \/ 3 = 7. Evaluate 7 != 33, drop this branch.\n    |- Try 25 * 4 = 100. Add 100 to the number set. Current number set: [100, 3], target: 33, just two numbers left.\n     |- Try 100 + 3 = 103. Evaluate 103 != 33, drop this branch.\n     |- Try 100 - 3 = 97. Evaluate 97 != 33, drop this branch.\n     |- Try 100 * 3 = 300. Evaluate 300 != 33, drop this branch.\n     |- Try 100 \/ 3 = 33.3. 33.3 is a decimal, drop this branch.\n    |- Try 25 \/ 4 = 6.2. 6.2 is a decimal, drop this branch.\n   |- Pick two numbers (3, 4) (numbers left: [25]). Try possible operations.\n    |- Try 4 + 3 = 7. Add 7 to the number set. Current number set: [7, 25], target: 33, just two numbers left.\n     |- Try 25 + 7 = 32. Evaluate 32 != 33, drop this branch.\n     |- Try 25 - 7 = 18. Evaluate 18 != 33, drop this branch.\n     |- Try 25 * 7 = 175. Evaluate 175 != 33, drop this branch.\n     |- Try 25 \/ 7 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 4 - 3 = 1. Add 1 to the number set. Current number set: [1, 25], target: 33, just two numbers left.\n     |- Try 25 + 1 = 26. Evaluate 26 != 33, drop this branch.\n     |- Try 25 - 1 = 24. Evaluate 24 != 33, drop this branch.\n     |- Try 25 * 1 = 25. Evaluate 25 != 33, drop this branch.\n     |- Try 25 \/ 1 = 25. Evaluate 25 != 33, drop this branch.\n    |- Try 4 * 3 = 12. Add 12 to the number set. Current number set: [12, 25], target: 33, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 33, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 33, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 33, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 4 \/ 3 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 17 - 8 = 9. Add 9 to the number set. Current number set: [9, 3, 4], target: 33. Options for choosing two numbers: [(9, 3), (9, 4), (3, 4)].\n   |- Pick two numbers (9, 3) (numbers left: [4]). Try possible operations.\n    |- Try 9 + 3 = 12. Add 12 to the number set. Current number set: [12, 4], target: 33, just two numbers left.\n     |- Try 12 + 4 = 16. Evaluate 16 != 33, drop this branch.\n     |- Try 12 - 4 = 8. Evaluate 8 != 33, drop this branch.\n     |- Try 12 * 4 = 48. Evaluate 48 != 33, drop this branch.\n     |- Try 12 \/ 4 = 3. Evaluate 3 != 33, drop this branch.\n    |- Try 9 - 3 = 6. Add 6 to the number set. Current number set: [6, 4], target: 33, just two numbers left.\n     |- Try 6 + 4 = 10. Evaluate 10 != 33, drop this branch.\n     |- Try 6 - 4 = 2. Evaluate 2 != 33, drop this branch.\n     |- Try 6 * 4 = 24. Evaluate 24 != 33, drop this branch.\n     |- Try 6 \/ 4 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 9 * 3 = 27. Add 27 to the number set. Current number set: [27, 4], target: 33, just two numbers left.\n     |- Try 27 + 4 = 31. Evaluate 31 != 33, drop this branch.\n     |- Try 27 - 4 = 23. Evaluate 23 != 33, drop this branch.\n     |- Try 27 * 4 = 108. Evaluate 108 != 33, drop this branch.\n     |- Try 27 \/ 4 = 6.8. 6.8 is a decimal, drop this branch.\n    |- Try 9 \/ 3 = 3. Add 3 to the number set. Current number set: [3, 4], target: 33, just two numbers left.\n     |- Try 4 + 3 = 7. Evaluate 7 != 33, drop this branch.\n     |- Try 4 - 3 = 1. Evaluate 1 != 33, drop this branch.\n     |- Try 4 * 3 = 12. Evaluate 12 != 33, drop this branch.\n     |- Try 4 \/ 3 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (9, 4) (numbers left: [3]). Try possible operations.\n    |- Try 9 + 4 = 13. Add 13 to the number set. Current number set: [13, 3], target: 33, just two numbers left.\n     |- Try 13 + 3 = 16. Evaluate 16 != 33, drop this branch.\n     |- Try 13 - 3 = 10. Evaluate 10 != 33, drop this branch.\n     |- Try 13 * 3 = 39. Evaluate 39 != 33, drop this branch.\n     |- Try 13 \/ 3 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 9 - 4 = 5. Add 5 to the number set. Current number set: [5, 3], target: 33, just two numbers left.\n     |- Try 5 + 3 = 8. Evaluate 8 != 33, drop this branch.\n     |- Try 5 - 3 = 2. Evaluate 2 != 33, drop this branch.\n     |- Try 5 * 3 = 15. Evaluate 15 != 33, drop this branch.\n     |- Try 5 \/ 3 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 9 * 4 = 36. Add 36 to the number set. Current number set: [36, 3], target: 33, just two numbers left.\n     |- Try 36 + 3 = 39. Evaluate 39 != 33, drop this branch.\n     |- Try 36 - 3 = 33. Evaluate 33 == 33, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 3 = 33\nThe step before: 9 * 4 = 36\nThe first step: 17 - 8 = 9\n\nOutput the solution in the required format:\n<Solution>\n17 - 8 = 9\n9 * 4 = 36\n36 - 3 = 33\n<\/Solution>\n","item":{"nums":[17,3,8,4],"solution":["17 - 8 = 9","9 * 4 = 36","36 - 3 = 33"],"target":33}}
+{"instance_id":"countdown_8k_165","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [8, 9, 21, 10]\nTarget: 29","reference_output":"# Search Procedure\nInitial number set: [8, 9, 21, 10], target: 29. Options for choosing two numbers: [(8, 9), (8, 21), (8, 10), (9, 21), (9, 10), (21, 10)].\n |- Pick two numbers (8, 9) (numbers left: [21, 10]). Try possible operations.\n  |- Try 9 + 8 = 17. Add 17 to the number set. Current number set: [17, 21, 10], target: 29. Options for choosing two numbers: [(17, 21), (17, 10), (21, 10)].\n   |- Pick two numbers (17, 21) (numbers left: [10]). Try possible operations.\n    |- Try 21 + 17 = 38. Add 38 to the number set. Current number set: [38, 10], target: 29, just two numbers left.\n     |- Try 38 + 10 = 48. Evaluate 48 != 29, drop this branch.\n     |- Try 38 - 10 = 28. Evaluate 28 != 29, drop this branch.\n     |- Try 38 * 10 = 380. Evaluate 380 != 29, drop this branch.\n     |- Try 38 \/ 10 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 21 - 17 = 4. Add 4 to the number set. Current number set: [4, 10], target: 29, just two numbers left.\n     |- Try 10 + 4 = 14. Evaluate 14 != 29, drop this branch.\n     |- Try 10 - 4 = 6. Evaluate 6 != 29, drop this branch.\n     |- Try 10 * 4 = 40. Evaluate 40 != 29, drop this branch.\n     |- Try 10 \/ 4 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 21 * 17 = 357. Add 357 to the number set. Current number set: [357, 10], target: 29, just two numbers left.\n     |- Try 357 + 10 = 367. Evaluate 367 != 29, drop this branch.\n     |- Try 357 - 10 = 347. Evaluate 347 != 29, drop this branch.\n     |- Try 357 * 10 = 3570. 3570 exceeds the maximum intermediate result, drop this branch.\n     |- Try 357 \/ 10 = 35.7. 35.7 is a decimal, drop this branch.\n    |- Try 21 \/ 17 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (17, 10) (numbers left: [21]). Try possible operations.\n    |- Try 17 + 10 = 27. Add 27 to the number set. Current number set: [27, 21], target: 29, just two numbers left.\n     |- Try 27 + 21 = 48. Evaluate 48 != 29, drop this branch.\n     |- Try 27 - 21 = 6. Evaluate 6 != 29, drop this branch.\n     |- Try 27 * 21 = 567. Evaluate 567 != 29, drop this branch.\n     |- Try 27 \/ 21 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 17 - 10 = 7. Add 7 to the number set. Current number set: [7, 21], target: 29, just two numbers left.\n     |- Try 21 + 7 = 28. Evaluate 28 != 29, drop this branch.\n     |- Try 21 - 7 = 14. Evaluate 14 != 29, drop this branch.\n     |- Try 21 * 7 = 147. Evaluate 147 != 29, drop this branch.\n     |- Try 21 \/ 7 = 3. Evaluate 3 != 29, drop this branch.\n    |- Try 17 * 10 = 170. Add 170 to the number set. Current number set: [170, 21], target: 29, just two numbers left.\n     |- Try 170 + 21 = 191. Evaluate 191 != 29, drop this branch.\n     |- Try 170 - 21 = 149. Evaluate 149 != 29, drop this branch.\n     |- Try 170 * 21 = 3570. 3570 exceeds the maximum intermediate result, drop this branch.\n     |- Try 170 \/ 21 = 8.1. 8.1 is a decimal, drop this branch.\n    |- Try 17 \/ 10 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (21, 10) (numbers left: [17]). Try possible operations.\n    |- Try 21 + 10 = 31. Add 31 to the number set. Current number set: [31, 17], target: 29, just two numbers left.\n     |- Try 31 + 17 = 48. Evaluate 48 != 29, drop this branch.\n     |- Try 31 - 17 = 14. Evaluate 14 != 29, drop this branch.\n     |- Try 31 * 17 = 527. Evaluate 527 != 29, drop this branch.\n     |- Try 31 \/ 17 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 21 - 10 = 11. Add 11 to the number set. Current number set: [11, 17], target: 29, just two numbers left.\n     |- Try 17 + 11 = 28. Evaluate 28 != 29, drop this branch.\n     |- Try 17 - 11 = 6. Evaluate 6 != 29, drop this branch.\n     |- Try 17 * 11 = 187. Evaluate 187 != 29, drop this branch.\n     |- Try 17 \/ 11 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 21 * 10 = 210. Add 210 to the number set. Current number set: [210, 17], target: 29, just two numbers left.\n     |- Try 210 + 17 = 227. Evaluate 227 != 29, drop this branch.\n     |- Try 210 - 17 = 193. Evaluate 193 != 29, drop this branch.\n     |- Try 210 * 17 = 3570. 3570 exceeds the maximum intermediate result, drop this branch.\n     |- Try 210 \/ 17 = 12.4. 12.4 is a decimal, drop this branch.\n    |- Try 21 \/ 10 = 2.1. 2.1 is a decimal, drop this branch.\n  |- Try 9 - 8 = 1. Add 1 to the number set. Current number set: [1, 21, 10], target: 29. Options for choosing two numbers: [(1, 21), (1, 10), (21, 10)].\n   |- Pick two numbers (1, 21) (numbers left: [10]). Try possible operations.\n    |- Try 21 + 1 = 22. Add 22 to the number set. Current number set: [22, 10], target: 29, just two numbers left.\n     |- Try 22 + 10 = 32. Evaluate 32 != 29, drop this branch.\n     |- Try 22 - 10 = 12. Evaluate 12 != 29, drop this branch.\n     |- Try 22 * 10 = 220. Evaluate 220 != 29, drop this branch.\n     |- Try 22 \/ 10 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 21 - 1 = 20. Add 20 to the number set. Current number set: [20, 10], target: 29, just two numbers left.\n     |- Try 20 + 10 = 30. Evaluate 30 != 29, drop this branch.\n     |- Try 20 - 10 = 10. Evaluate 10 != 29, drop this branch.\n     |- Try 20 * 10 = 200. Evaluate 200 != 29, drop this branch.\n     |- Try 20 \/ 10 = 2. Evaluate 2 != 29, drop this branch.\n    |- Try 21 * 1 = 21. Add 21 to the number set. Current number set: [21, 10], target: 29, just two numbers left.\n     |- Try 21 + 10 = 31. Evaluate 31 != 29, drop this branch.\n     |- Try 21 - 10 = 11. Evaluate 11 != 29, drop this branch.\n     |- Try 21 * 10 = 210. Evaluate 210 != 29, drop this branch.\n     |- Try 21 \/ 10 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 21 \/ 1 = 21. Add 21 to the number set. Current number set: [21, 10], target: 29, just two numbers left.\n     |- Try 21 + 10 = 31. Evaluate 31 != 29, drop this branch.\n     |- Try 21 - 10 = 11. Evaluate 11 != 29, drop this branch.\n     |- Try 21 * 10 = 210. Evaluate 210 != 29, drop this branch.\n     |- Try 21 \/ 10 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (1, 10) (numbers left: [21]). Try possible operations.\n    |- Try 10 + 1 = 11. Add 11 to the number set. Current number set: [11, 21], target: 29, just two numbers left.\n     |- Try 21 + 11 = 32. Evaluate 32 != 29, drop this branch.\n     |- Try 21 - 11 = 10. Evaluate 10 != 29, drop this branch.\n     |- Try 21 * 11 = 231. Evaluate 231 != 29, drop this branch.\n     |- Try 21 \/ 11 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 10 - 1 = 9. Add 9 to the number set. Current number set: [9, 21], target: 29, just two numbers left.\n     |- Try 21 + 9 = 30. Evaluate 30 != 29, drop this branch.\n     |- Try 21 - 9 = 12. Evaluate 12 != 29, drop this branch.\n     |- Try 21 * 9 = 189. Evaluate 189 != 29, drop this branch.\n     |- Try 21 \/ 9 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 10 * 1 = 10. Add 10 to the number set. Current number set: [10, 21], target: 29, just two numbers left.\n     |- Try 21 + 10 = 31. Evaluate 31 != 29, drop this branch.\n     |- Try 21 - 10 = 11. Evaluate 11 != 29, drop this branch.\n     |- Try 21 * 10 = 210. Evaluate 210 != 29, drop this branch.\n     |- Try 21 \/ 10 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 10 \/ 1 = 10. Add 10 to the number set. Current number set: [10, 21], target: 29, just two numbers left.\n     |- Try 21 + 10 = 31. Evaluate 31 != 29, drop this branch.\n     |- Try 21 - 10 = 11. Evaluate 11 != 29, drop this branch.\n     |- Try 21 * 10 = 210. Evaluate 210 != 29, drop this branch.\n     |- Try 21 \/ 10 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (21, 10) (numbers left: [1]). Try possible operations.\n    |- Try 21 + 10 = 31. Add 31 to the number set. Current number set: [31, 1], target: 29, just two numbers left.\n     |- Try 31 + 1 = 32. Evaluate 32 != 29, drop this branch.\n     |- Try 31 - 1 = 30. Evaluate 30 != 29, drop this branch.\n     |- Try 31 * 1 = 31. Evaluate 31 != 29, drop this branch.\n     |- Try 31 \/ 1 = 31. Evaluate 31 != 29, drop this branch.\n    |- Try 21 - 10 = 11. Add 11 to the number set. Current number set: [11, 1], target: 29, just two numbers left.\n     |- Try 11 + 1 = 12. Evaluate 12 != 29, drop this branch.\n     |- Try 11 - 1 = 10. Evaluate 10 != 29, drop this branch.\n     |- Try 11 * 1 = 11. Evaluate 11 != 29, drop this branch.\n     |- Try 11 \/ 1 = 11. Evaluate 11 != 29, drop this branch.\n    |- Try 21 * 10 = 210. Add 210 to the number set. Current number set: [210, 1], target: 29, just two numbers left.\n     |- Try 210 + 1 = 211. Evaluate 211 != 29, drop this branch.\n     |- Try 210 - 1 = 209. Evaluate 209 != 29, drop this branch.\n     |- Try 210 * 1 = 210. Evaluate 210 != 29, drop this branch.\n     |- Try 210 \/ 1 = 210. Evaluate 210 != 29, drop this branch.\n    |- Try 21 \/ 10 = 2.1. 2.1 is a decimal, drop this branch.\n  |- Try 9 * 8 = 72. Add 72 to the number set. Current number set: [72, 21, 10], target: 29. Options for choosing two numbers: [(72, 21), (72, 10), (21, 10)].\n   |- Pick two numbers (72, 21) (numbers left: [10]). Try possible operations.\n    |- Try 72 + 21 = 93. Add 93 to the number set. Current number set: [93, 10], target: 29, just two numbers left.\n     |- Try 93 + 10 = 103. Evaluate 103 != 29, drop this branch.\n     |- Try 93 - 10 = 83. Evaluate 83 != 29, drop this branch.\n     |- Try 93 * 10 = 930. Evaluate 930 != 29, drop this branch.\n     |- Try 93 \/ 10 = 9.3. 9.3 is a decimal, drop this branch.\n    |- Try 72 - 21 = 51. Add 51 to the number set. Current number set: [51, 10], target: 29, just two numbers left.\n     |- Try 51 + 10 = 61. Evaluate 61 != 29, drop this branch.\n     |- Try 51 - 10 = 41. Evaluate 41 != 29, drop this branch.\n     |- Try 51 * 10 = 510. Evaluate 510 != 29, drop this branch.\n     |- Try 51 \/ 10 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 72 * 21 = 1512. Add 1512 to the number set. Current number set: [1512, 10], target: 29, just two numbers left.\n     |- Try 1512 + 10 = 1522. Evaluate 1522 != 29, drop this branch.\n     |- Try 1512 - 10 = 1502. Evaluate 1502 != 29, drop this branch.\n     |- Try 1512 * 10 = 15120. 15120 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1512 \/ 10 = 151.2. 151.2 is a decimal, drop this branch.\n    |- Try 72 \/ 21 = 3.4. 3.4 is a decimal, drop this branch.\n   |- Pick two numbers (72, 10) (numbers left: [21]). Try possible operations.\n    |- Try 72 + 10 = 82. Add 82 to the number set. Current number set: [82, 21], target: 29, just two numbers left.\n     |- Try 82 + 21 = 103. Evaluate 103 != 29, drop this branch.\n     |- Try 82 - 21 = 61. Evaluate 61 != 29, drop this branch.\n     |- Try 82 * 21 = 1722. Evaluate 1722 != 29, drop this branch.\n     |- Try 82 \/ 21 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 72 - 10 = 62. Add 62 to the number set. Current number set: [62, 21], target: 29, just two numbers left.\n     |- Try 62 + 21 = 83. Evaluate 83 != 29, drop this branch.\n     |- Try 62 - 21 = 41. Evaluate 41 != 29, drop this branch.\n     |- Try 62 * 21 = 1302. Evaluate 1302 != 29, drop this branch.\n     |- Try 62 \/ 21 = 3.0. 3.0 is a decimal, drop this branch.\n    |- Try 72 * 10 = 720. Add 720 to the number set. Current number set: [720, 21], target: 29, just two numbers left.\n     |- Try 720 + 21 = 741. Evaluate 741 != 29, drop this branch.\n     |- Try 720 - 21 = 699. Evaluate 699 != 29, drop this branch.\n     |- Try 720 * 21 = 15120. 15120 exceeds the maximum intermediate result, drop this branch.\n     |- Try 720 \/ 21 = 34.3. 34.3 is a decimal, drop this branch.\n    |- Try 72 \/ 10 = 7.2. 7.2 is a decimal, drop this branch.\n   |- Pick two numbers (21, 10) (numbers left: [72]). Try possible operations.\n    |- Try 21 + 10 = 31. Add 31 to the number set. Current number set: [31, 72], target: 29, just two numbers left.\n     |- Try 72 + 31 = 103. Evaluate 103 != 29, drop this branch.\n     |- Try 72 - 31 = 41. Evaluate 41 != 29, drop this branch.\n     |- Try 72 * 31 = 2232. 2232 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 31 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 21 - 10 = 11. Add 11 to the number set. Current number set: [11, 72], target: 29, just two numbers left.\n     |- Try 72 + 11 = 83. Evaluate 83 != 29, drop this branch.\n     |- Try 72 - 11 = 61. Evaluate 61 != 29, drop this branch.\n     |- Try 72 * 11 = 792. Evaluate 792 != 29, drop this branch.\n     |- Try 72 \/ 11 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 21 * 10 = 210. Add 210 to the number set. Current number set: [210, 72], target: 29, just two numbers left.\n     |- Try 210 + 72 = 282. Evaluate 282 != 29, drop this branch.\n     |- Try 210 - 72 = 138. Evaluate 138 != 29, drop this branch.\n     |- Try 210 * 72 = 15120. 15120 exceeds the maximum intermediate result, drop this branch.\n     |- Try 210 \/ 72 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 21 \/ 10 = 2.1. 2.1 is a decimal, drop this branch.\n  |- Try 9 \/ 8 = 1.1. 1.1 is a decimal, drop this branch.\n |- Pick two numbers (8, 21) (numbers left: [9, 10]). Try possible operations.\n  |- Try 21 + 8 = 29. Add 29 to the number set. Current number set: [29, 9, 10], target: 29. Options for choosing two numbers: [(29, 9), (29, 10), (9, 10)].\n   |- Pick two numbers (29, 9) (numbers left: [10]). Try possible operations.\n    |- Try 29 + 9 = 38. Add 38 to the number set. Current number set: [38, 10], target: 29, just two numbers left.\n     |- Try 38 + 10 = 48. Evaluate 48 != 29, drop this branch.\n     |- Try 38 - 10 = 28. Evaluate 28 != 29, drop this branch.\n     |- Try 38 * 10 = 380. Evaluate 380 != 29, drop this branch.\n     |- Try 38 \/ 10 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 29 - 9 = 20. Add 20 to the number set. Current number set: [20, 10], target: 29, just two numbers left.\n     |- Try 20 + 10 = 30. Evaluate 30 != 29, drop this branch.\n     |- Try 20 - 10 = 10. Evaluate 10 != 29, drop this branch.\n     |- Try 20 * 10 = 200. Evaluate 200 != 29, drop this branch.\n     |- Try 20 \/ 10 = 2. Evaluate 2 != 29, drop this branch.\n    |- Try 29 * 9 = 261. Add 261 to the number set. Current number set: [261, 10], target: 29, just two numbers left.\n     |- Try 261 + 10 = 271. Evaluate 271 != 29, drop this branch.\n     |- Try 261 - 10 = 251. Evaluate 251 != 29, drop this branch.\n     |- Try 261 * 10 = 2610. 2610 exceeds the maximum intermediate result, drop this branch.\n     |- Try 261 \/ 10 = 26.1. 26.1 is a decimal, drop this branch.\n    |- Try 29 \/ 9 = 3.2. 3.2 is a decimal, drop this branch.\n   |- Pick two numbers (29, 10) (numbers left: [9]). Try possible operations.\n    |- Try 29 + 10 = 39. Add 39 to the number set. Current number set: [39, 9], target: 29, just two numbers left.\n     |- Try 39 + 9 = 48. Evaluate 48 != 29, drop this branch.\n     |- Try 39 - 9 = 30. Evaluate 30 != 29, drop this branch.\n     |- Try 39 * 9 = 351. Evaluate 351 != 29, drop this branch.\n     |- Try 39 \/ 9 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 29 - 10 = 19. Add 19 to the number set. Current number set: [19, 9], target: 29, just two numbers left.\n     |- Try 19 + 9 = 28. Evaluate 28 != 29, drop this branch.\n     |- Try 19 - 9 = 10. Evaluate 10 != 29, drop this branch.\n     |- Try 19 * 9 = 171. Evaluate 171 != 29, drop this branch.\n     |- Try 19 \/ 9 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 29 * 10 = 290. Add 290 to the number set. Current number set: [290, 9], target: 29, just two numbers left.\n     |- Try 290 + 9 = 299. Evaluate 299 != 29, drop this branch.\n     |- Try 290 - 9 = 281. Evaluate 281 != 29, drop this branch.\n     |- Try 290 * 9 = 2610. 2610 exceeds the maximum intermediate result, drop this branch.\n     |- Try 290 \/ 9 = 32.2. 32.2 is a decimal, drop this branch.\n    |- Try 29 \/ 10 = 2.9. 2.9 is a decimal, drop this branch.\n   |- Pick two numbers (9, 10) (numbers left: [29]). Try possible operations.\n    |- Try 10 + 9 = 19. Add 19 to the number set. Current number set: [19, 29], target: 29, just two numbers left.\n     |- Try 29 + 19 = 48. Evaluate 48 != 29, drop this branch.\n     |- Try 29 - 19 = 10. Evaluate 10 != 29, drop this branch.\n     |- Try 29 * 19 = 551. Evaluate 551 != 29, drop this branch.\n     |- Try 29 \/ 19 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 10 - 9 = 1. Add 1 to the number set. Current number set: [1, 29], target: 29, just two numbers left.\n     |- Try 29 + 1 = 30. Evaluate 30 != 29, drop this branch.\n     |- Try 29 - 1 = 28. Evaluate 28 != 29, drop this branch.\n     |- Try 29 * 1 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 29 * 1 = 29\nThe step before: 10 - 9 = 1\nThe first step: 21 + 8 = 29\n\nOutput the solution in the required format:\n<Solution>\n21 + 8 = 29\n10 - 9 = 1\n29 * 1 = 29\n<\/Solution>\n","item":{"nums":[8,9,21,10],"solution":["21 + 8 = 29","10 - 9 = 1","29 * 1 = 29"],"target":29}}
+{"instance_id":"countdown_8k_166","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [8, 16, 2, 30]\nTarget: 16","reference_output":"# Search Procedure\nInitial number set: [8, 16, 2, 30], target: 16. Options for choosing two numbers: [(8, 16), (8, 2), (8, 30), (16, 2), (16, 30), (2, 30)].\n |- Pick two numbers (8, 16) (numbers left: [2, 30]). Try possible operations.\n  |- Try 16 + 8 = 24. Add 24 to the number set. Current number set: [24, 2, 30], target: 16. Options for choosing two numbers: [(24, 2), (24, 30), (2, 30)].\n   |- Pick two numbers (24, 2) (numbers left: [30]). Try possible operations.\n    |- Try 24 + 2 = 26. Add 26 to the number set. Current number set: [26, 30], target: 16, just two numbers left.\n     |- Try 30 + 26 = 56. Evaluate 56 != 16, drop this branch.\n     |- Try 30 - 26 = 4. Evaluate 4 != 16, drop this branch.\n     |- Try 30 * 26 = 780. Evaluate 780 != 16, drop this branch.\n     |- Try 30 \/ 26 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 24 - 2 = 22. Add 22 to the number set. Current number set: [22, 30], target: 16, just two numbers left.\n     |- Try 30 + 22 = 52. Evaluate 52 != 16, drop this branch.\n     |- Try 30 - 22 = 8. Evaluate 8 != 16, drop this branch.\n     |- Try 30 * 22 = 660. Evaluate 660 != 16, drop this branch.\n     |- Try 30 \/ 22 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 24 * 2 = 48. Add 48 to the number set. Current number set: [48, 30], target: 16, just two numbers left.\n     |- Try 48 + 30 = 78. Evaluate 78 != 16, drop this branch.\n     |- Try 48 - 30 = 18. Evaluate 18 != 16, drop this branch.\n     |- Try 48 * 30 = 1440. Evaluate 1440 != 16, drop this branch.\n     |- Try 48 \/ 30 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 24 \/ 2 = 12. Add 12 to the number set. Current number set: [12, 30], target: 16, just two numbers left.\n     |- Try 30 + 12 = 42. Evaluate 42 != 16, drop this branch.\n     |- Try 30 - 12 = 18. Evaluate 18 != 16, drop this branch.\n     |- Try 30 * 12 = 360. Evaluate 360 != 16, drop this branch.\n     |- Try 30 \/ 12 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (24, 30) (numbers left: [2]). Try possible operations.\n    |- Try 30 + 24 = 54. Add 54 to the number set. Current number set: [54, 2], target: 16, just two numbers left.\n     |- Try 54 + 2 = 56. Evaluate 56 != 16, drop this branch.\n     |- Try 54 - 2 = 52. Evaluate 52 != 16, drop this branch.\n     |- Try 54 * 2 = 108. Evaluate 108 != 16, drop this branch.\n     |- Try 54 \/ 2 = 27. Evaluate 27 != 16, drop this branch.\n    |- Try 30 - 24 = 6. Add 6 to the number set. Current number set: [6, 2], target: 16, just two numbers left.\n     |- Try 6 + 2 = 8. Evaluate 8 != 16, drop this branch.\n     |- Try 6 - 2 = 4. Evaluate 4 != 16, drop this branch.\n     |- Try 6 * 2 = 12. Evaluate 12 != 16, drop this branch.\n     |- Try 6 \/ 2 = 3. Evaluate 3 != 16, drop this branch.\n    |- Try 30 * 24 = 720. Add 720 to the number set. Current number set: [720, 2], target: 16, just two numbers left.\n     |- Try 720 + 2 = 722. Evaluate 722 != 16, drop this branch.\n     |- Try 720 - 2 = 718. Evaluate 718 != 16, drop this branch.\n     |- Try 720 * 2 = 1440. Evaluate 1440 != 16, drop this branch.\n     |- Try 720 \/ 2 = 360. Evaluate 360 != 16, drop this branch.\n    |- Try 30 \/ 24 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (2, 30) (numbers left: [24]). Try possible operations.\n    |- Try 30 + 2 = 32. Add 32 to the number set. Current number set: [32, 24], target: 16, just two numbers left.\n     |- Try 32 + 24 = 56. Evaluate 56 != 16, drop this branch.\n     |- Try 32 - 24 = 8. Evaluate 8 != 16, drop this branch.\n     |- Try 32 * 24 = 768. Evaluate 768 != 16, drop this branch.\n     |- Try 32 \/ 24 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 30 - 2 = 28. Add 28 to the number set. Current number set: [28, 24], target: 16, just two numbers left.\n     |- Try 28 + 24 = 52. Evaluate 52 != 16, drop this branch.\n     |- Try 28 - 24 = 4. Evaluate 4 != 16, drop this branch.\n     |- Try 28 * 24 = 672. Evaluate 672 != 16, drop this branch.\n     |- Try 28 \/ 24 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 30 * 2 = 60. Add 60 to the number set. Current number set: [60, 24], target: 16, just two numbers left.\n     |- Try 60 + 24 = 84. Evaluate 84 != 16, drop this branch.\n     |- Try 60 - 24 = 36. Evaluate 36 != 16, drop this branch.\n     |- Try 60 * 24 = 1440. Evaluate 1440 != 16, drop this branch.\n     |- Try 60 \/ 24 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 30 \/ 2 = 15. Add 15 to the number set. Current number set: [15, 24], target: 16, just two numbers left.\n     |- Try 24 + 15 = 39. Evaluate 39 != 16, drop this branch.\n     |- Try 24 - 15 = 9. Evaluate 9 != 16, drop this branch.\n     |- Try 24 * 15 = 360. Evaluate 360 != 16, drop this branch.\n     |- Try 24 \/ 15 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 16 - 8 = 8. Add 8 to the number set. Current number set: [8, 2, 30], target: 16. Options for choosing two numbers: [(8, 2), (8, 30), (2, 30)].\n   |- Pick two numbers (8, 2) (numbers left: [30]). Try possible operations.\n    |- Try 8 + 2 = 10. Add 10 to the number set. Current number set: [10, 30], target: 16, just two numbers left.\n     |- Try 30 + 10 = 40. Evaluate 40 != 16, drop this branch.\n     |- Try 30 - 10 = 20. Evaluate 20 != 16, drop this branch.\n     |- Try 30 * 10 = 300. Evaluate 300 != 16, drop this branch.\n     |- Try 30 \/ 10 = 3. Evaluate 3 != 16, drop this branch.\n    |- Try 8 - 2 = 6. Add 6 to the number set. Current number set: [6, 30], target: 16, just two numbers left.\n     |- Try 30 + 6 = 36. Evaluate 36 != 16, drop this branch.\n     |- Try 30 - 6 = 24. Evaluate 24 != 16, drop this branch.\n     |- Try 30 * 6 = 180. Evaluate 180 != 16, drop this branch.\n     |- Try 30 \/ 6 = 5. Evaluate 5 != 16, drop this branch.\n    |- Try 8 * 2 = 16. Add 16 to the number set. Current number set: [16, 30], target: 16, just two numbers left.\n     |- Try 30 + 16 = 46. Evaluate 46 != 16, drop this branch.\n     |- Try 30 - 16 = 14. Evaluate 14 != 16, drop this branch.\n     |- Try 30 * 16 = 480. Evaluate 480 != 16, drop this branch.\n     |- Try 30 \/ 16 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 8 \/ 2 = 4. Add 4 to the number set. Current number set: [4, 30], target: 16, just two numbers left.\n     |- Try 30 + 4 = 34. Evaluate 34 != 16, drop this branch.\n     |- Try 30 - 4 = 26. Evaluate 26 != 16, drop this branch.\n     |- Try 30 * 4 = 120. Evaluate 120 != 16, drop this branch.\n     |- Try 30 \/ 4 = 7.5. 7.5 is a decimal, drop this branch.\n   |- Pick two numbers (8, 30) (numbers left: [2]). Try possible operations.\n    |- Try 30 + 8 = 38. Add 38 to the number set. Current number set: [38, 2], target: 16, just two numbers left.\n     |- Try 38 + 2 = 40. Evaluate 40 != 16, drop this branch.\n     |- Try 38 - 2 = 36. Evaluate 36 != 16, drop this branch.\n     |- Try 38 * 2 = 76. Evaluate 76 != 16, drop this branch.\n     |- Try 38 \/ 2 = 19. Evaluate 19 != 16, drop this branch.\n    |- Try 30 - 8 = 22. Add 22 to the number set. Current number set: [22, 2], target: 16, just two numbers left.\n     |- Try 22 + 2 = 24. Evaluate 24 != 16, drop this branch.\n     |- Try 22 - 2 = 20. Evaluate 20 != 16, drop this branch.\n     |- Try 22 * 2 = 44. Evaluate 44 != 16, drop this branch.\n     |- Try 22 \/ 2 = 11. Evaluate 11 != 16, drop this branch.\n    |- Try 30 * 8 = 240. Add 240 to the number set. Current number set: [240, 2], target: 16, just two numbers left.\n     |- Try 240 + 2 = 242. Evaluate 242 != 16, drop this branch.\n     |- Try 240 - 2 = 238. Evaluate 238 != 16, drop this branch.\n     |- Try 240 * 2 = 480. Evaluate 480 != 16, drop this branch.\n     |- Try 240 \/ 2 = 120. Evaluate 120 != 16, drop this branch.\n    |- Try 30 \/ 8 = 3.8. 3.8 is a decimal, drop this branch.\n   |- Pick two numbers (2, 30) (numbers left: [8]). Try possible operations.\n    |- Try 30 + 2 = 32. Add 32 to the number set. Current number set: [32, 8], target: 16, just two numbers left.\n     |- Try 32 + 8 = 40. Evaluate 40 != 16, drop this branch.\n     |- Try 32 - 8 = 24. Evaluate 24 != 16, drop this branch.\n     |- Try 32 * 8 = 256. Evaluate 256 != 16, drop this branch.\n     |- Try 32 \/ 8 = 4. Evaluate 4 != 16, drop this branch.\n    |- Try 30 - 2 = 28. Add 28 to the number set. Current number set: [28, 8], target: 16, just two numbers left.\n     |- Try 28 + 8 = 36. Evaluate 36 != 16, drop this branch.\n     |- Try 28 - 8 = 20. Evaluate 20 != 16, drop this branch.\n     |- Try 28 * 8 = 224. Evaluate 224 != 16, drop this branch.\n     |- Try 28 \/ 8 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 30 * 2 = 60. Add 60 to the number set. Current number set: [60, 8], target: 16, just two numbers left.\n     |- Try 60 + 8 = 68. Evaluate 68 != 16, drop this branch.\n     |- Try 60 - 8 = 52. Evaluate 52 != 16, drop this branch.\n     |- Try 60 * 8 = 480. Evaluate 480 != 16, drop this branch.\n     |- Try 60 \/ 8 = 7.5. 7.5 is a decimal, drop this branch.\n    |- Try 30 \/ 2 = 15. Add 15 to the number set. Current number set: [15, 8], target: 16, just two numbers left.\n     |- Try 15 + 8 = 23. Evaluate 23 != 16, drop this branch.\n     |- Try 15 - 8 = 7. Evaluate 7 != 16, drop this branch.\n     |- Try 15 * 8 = 120. Evaluate 120 != 16, drop this branch.\n     |- Try 15 \/ 8 = 1.9. 1.9 is a decimal, drop this branch.\n  |- Try 16 * 8 = 128. Add 128 to the number set. Current number set: [128, 2, 30], target: 16. Options for choosing two numbers: [(128, 2), (128, 30), (2, 30)].\n   |- Pick two numbers (128, 2) (numbers left: [30]). Try possible operations.\n    |- Try 128 + 2 = 130. Add 130 to the number set. Current number set: [130, 30], target: 16, just two numbers left.\n     |- Try 130 + 30 = 160. Evaluate 160 != 16, drop this branch.\n     |- Try 130 - 30 = 100. Evaluate 100 != 16, drop this branch.\n     |- Try 130 * 30 = 3900. 3900 exceeds the maximum intermediate result, drop this branch.\n     |- Try 130 \/ 30 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 128 - 2 = 126. Add 126 to the number set. Current number set: [126, 30], target: 16, just two numbers left.\n     |- Try 126 + 30 = 156. Evaluate 156 != 16, drop this branch.\n     |- Try 126 - 30 = 96. Evaluate 96 != 16, drop this branch.\n     |- Try 126 * 30 = 3780. 3780 exceeds the maximum intermediate result, drop this branch.\n     |- Try 126 \/ 30 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 128 * 2 = 256. Add 256 to the number set. Current number set: [256, 30], target: 16, just two numbers left.\n     |- Try 256 + 30 = 286. Evaluate 286 != 16, drop this branch.\n     |- Try 256 - 30 = 226. Evaluate 226 != 16, drop this branch.\n     |- Try 256 * 30 = 7680. 7680 exceeds the maximum intermediate result, drop this branch.\n     |- Try 256 \/ 30 = 8.5. 8.5 is a decimal, drop this branch.\n    |- Try 128 \/ 2 = 64. Add 64 to the number set. Current number set: [64, 30], target: 16, just two numbers left.\n     |- Try 64 + 30 = 94. Evaluate 94 != 16, drop this branch.\n     |- Try 64 - 30 = 34. Evaluate 34 != 16, drop this branch.\n     |- Try 64 * 30 = 1920. Evaluate 1920 != 16, drop this branch.\n     |- Try 64 \/ 30 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (128, 30) (numbers left: [2]). Try possible operations.\n    |- Try 128 + 30 = 158. Add 158 to the number set. Current number set: [158, 2], target: 16, just two numbers left.\n     |- Try 158 + 2 = 160. Evaluate 160 != 16, drop this branch.\n     |- Try 158 - 2 = 156. Evaluate 156 != 16, drop this branch.\n     |- Try 158 * 2 = 316. Evaluate 316 != 16, drop this branch.\n     |- Try 158 \/ 2 = 79. Evaluate 79 != 16, drop this branch.\n    |- Try 128 - 30 = 98. Add 98 to the number set. Current number set: [98, 2], target: 16, just two numbers left.\n     |- Try 98 + 2 = 100. Evaluate 100 != 16, drop this branch.\n     |- Try 98 - 2 = 96. Evaluate 96 != 16, drop this branch.\n     |- Try 98 * 2 = 196. Evaluate 196 != 16, drop this branch.\n     |- Try 98 \/ 2 = 49. Evaluate 49 != 16, drop this branch.\n    |- Try 128 * 30 = 3840. 3840 exceeds the maximum intermediate result, drop this branch.\n    |- Try 128 \/ 30 = 4.3. 4.3 is a decimal, drop this branch.\n   |- Pick two numbers (2, 30) (numbers left: [128]). Try possible operations.\n    |- Try 30 + 2 = 32. Add 32 to the number set. Current number set: [32, 128], target: 16, just two numbers left.\n     |- Try 128 + 32 = 160. Evaluate 160 != 16, drop this branch.\n     |- Try 128 - 32 = 96. Evaluate 96 != 16, drop this branch.\n     |- Try 128 * 32 = 4096. 4096 exceeds the maximum intermediate result, drop this branch.\n     |- Try 128 \/ 32 = 4. Evaluate 4 != 16, drop this branch.\n    |- Try 30 - 2 = 28. Add 28 to the number set. Current number set: [28, 128], target: 16, just two numbers left.\n     |- Try 128 + 28 = 156. Evaluate 156 != 16, drop this branch.\n     |- Try 128 - 28 = 100. Evaluate 100 != 16, drop this branch.\n     |- Try 128 * 28 = 3584. 3584 exceeds the maximum intermediate result, drop this branch.\n     |- Try 128 \/ 28 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 30 * 2 = 60. Add 60 to the number set. Current number set: [60, 128], target: 16, just two numbers left.\n     |- Try 128 + 60 = 188. Evaluate 188 != 16, drop this branch.\n     |- Try 128 - 60 = 68. Evaluate 68 != 16, drop this branch.\n     |- Try 128 * 60 = 7680. 7680 exceeds the maximum intermediate result, drop this branch.\n     |- Try 128 \/ 60 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 30 \/ 2 = 15. Add 15 to the number set. Current number set: [15, 128], target: 16, just two numbers left.\n     |- Try 128 + 15 = 143. Evaluate 143 != 16, drop this branch.\n     |- Try 128 - 15 = 113. Evaluate 113 != 16, drop this branch.\n     |- Try 128 * 15 = 1920. Evaluate 1920 != 16, drop this branch.\n     |- Try 128 \/ 15 = 8.5. 8.5 is a decimal, drop this branch.\n  |- Try 16 \/ 8 = 2. Add 2 to the number set. Current number set: [2, 2, 30], target: 16. Options for choosing two numbers: [(2, 2), (2, 30), (2, 30)].\n   |- Pick two numbers (2, 2) (numbers left: [30]). Try possible operations.\n    |- Try 2 + 2 = 4. Add 4 to the number set. Current number set: [4, 30], target: 16, just two numbers left.\n     |- Try 30 + 4 = 34. Evaluate 34 != 16, drop this branch.\n     |- Try 30 - 4 = 26. Evaluate 26 != 16, drop this branch.\n     |- Try 30 * 4 = 120. Evaluate 120 != 16, drop this branch.\n     |- Try 30 \/ 4 = 7.5. 7.5 is a decimal, drop this branch.\n    |- Try 2 - 2 = 0. Add 0 to the number set. Current number set: [0, 30], target: 16, just two numbers left.\n     |- Try 30 + 0 = 30. Evaluate 30 != 16, drop this branch.\n     |- Try 30 - 0 = 30. Evaluate 30 != 16, drop this branch.\n     |- Try 30 * 0 = 0. Evaluate 0 != 16, drop this branch.\n     |- Try 30 \/ 0 (invalid operation). drop this branch.\n    |- Try 2 * 2 = 4. Add 4 to the number set. Current number set: [4, 30], target: 16, just two numbers left.\n     |- Try 30 + 4 = 34. Evaluate 34 != 16, drop this branch.\n     |- Try 30 - 4 = 26. Evaluate 26 != 16, drop this branch.\n     |- Try 30 * 4 = 120. Evaluate 120 != 16, drop this branch.\n     |- Try 30 \/ 4 = 7.5. 7.5 is a decimal, drop this branch.\n    |- Try 2 \/ 2 = 1. Add 1 to the number set. Current number set: [1, 30], target: 16, just two numbers left.\n     |- Try 30 + 1 = 31. Evaluate 31 != 16, drop this branch.\n     |- Try 30 - 1 = 29. Evaluate 29 != 16, drop this branch.\n     |- Try 30 * 1 = 30. Evaluate 30 != 16, drop this branch.\n     |- Try 30 \/ 1 = 30. Evaluate 30 != 16, drop this branch.\n   |- Pick two numbers (2, 30) (numbers left: [2]). Try possible operations.\n    |- Try 30 + 2 = 32. Add 32 to the number set. Current number set: [32, 2], target: 16, just two numbers left.\n     |- Try 32 + 2 = 34. Evaluate 34 != 16, drop this branch.\n     |- Try 32 - 2 = 30. Evaluate 30 != 16, drop this branch.\n     |- Try 32 * 2 = 64. Evaluate 64 != 16, drop this branch.\n     |- Try 32 \/ 2 = 16. Evaluate 16 == 16, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 32 \/ 2 = 16\nThe step before: 30 + 2 = 32\nThe first step: 16 \/ 8 = 2\n\nOutput the solution in the required format:\n<Solution>\n16 \/ 8 = 2\n30 + 2 = 32\n32 \/ 2 = 16\n<\/Solution>\n","item":{"nums":[8,16,2,30],"solution":["16 \/ 8 = 2","30 + 2 = 32","32 \/ 2 = 16"],"target":16}}
+{"instance_id":"countdown_8k_167","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [18, 2, 31, 43]\nTarget: 21","reference_output":"# Search Procedure\nInitial number set: [18, 2, 31, 43], target: 21. Options for choosing two numbers: [(18, 2), (18, 31), (18, 43), (2, 31), (2, 43), (31, 43)].\n |- Pick two numbers (18, 2) (numbers left: [31, 43]). Try possible operations.\n  |- Try 18 + 2 = 20. Add 20 to the number set. Current number set: [20, 31, 43], target: 21. Options for choosing two numbers: [(20, 31), (20, 43), (31, 43)].\n   |- Pick two numbers (20, 31) (numbers left: [43]). Try possible operations.\n    |- Try 31 + 20 = 51. Add 51 to the number set. Current number set: [51, 43], target: 21, just two numbers left.\n     |- Try 51 + 43 = 94. Evaluate 94 != 21, drop this branch.\n     |- Try 51 - 43 = 8. Evaluate 8 != 21, drop this branch.\n     |- Try 51 * 43 = 2193. 2193 exceeds the maximum intermediate result, drop this branch.\n     |- Try 51 \/ 43 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 31 - 20 = 11. Add 11 to the number set. Current number set: [11, 43], target: 21, just two numbers left.\n     |- Try 43 + 11 = 54. Evaluate 54 != 21, drop this branch.\n     |- Try 43 - 11 = 32. Evaluate 32 != 21, drop this branch.\n     |- Try 43 * 11 = 473. Evaluate 473 != 21, drop this branch.\n     |- Try 43 \/ 11 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 31 * 20 = 620. Add 620 to the number set. Current number set: [620, 43], target: 21, just two numbers left.\n     |- Try 620 + 43 = 663. Evaluate 663 != 21, drop this branch.\n     |- Try 620 - 43 = 577. Evaluate 577 != 21, drop this branch.\n     |- Try 620 * 43 = 26660. 26660 exceeds the maximum intermediate result, drop this branch.\n     |- Try 620 \/ 43 = 14.4. 14.4 is a decimal, drop this branch.\n    |- Try 31 \/ 20 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (20, 43) (numbers left: [31]). Try possible operations.\n    |- Try 43 + 20 = 63. Add 63 to the number set. Current number set: [63, 31], target: 21, just two numbers left.\n     |- Try 63 + 31 = 94. Evaluate 94 != 21, drop this branch.\n     |- Try 63 - 31 = 32. Evaluate 32 != 21, drop this branch.\n     |- Try 63 * 31 = 1953. Evaluate 1953 != 21, drop this branch.\n     |- Try 63 \/ 31 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 43 - 20 = 23. Add 23 to the number set. Current number set: [23, 31], target: 21, just two numbers left.\n     |- Try 31 + 23 = 54. Evaluate 54 != 21, drop this branch.\n     |- Try 31 - 23 = 8. Evaluate 8 != 21, drop this branch.\n     |- Try 31 * 23 = 713. Evaluate 713 != 21, drop this branch.\n     |- Try 31 \/ 23 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 43 * 20 = 860. Add 860 to the number set. Current number set: [860, 31], target: 21, just two numbers left.\n     |- Try 860 + 31 = 891. Evaluate 891 != 21, drop this branch.\n     |- Try 860 - 31 = 829. Evaluate 829 != 21, drop this branch.\n     |- Try 860 * 31 = 26660. 26660 exceeds the maximum intermediate result, drop this branch.\n     |- Try 860 \/ 31 = 27.7. 27.7 is a decimal, drop this branch.\n    |- Try 43 \/ 20 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (31, 43) (numbers left: [20]). Try possible operations.\n    |- Try 43 + 31 = 74. Add 74 to the number set. Current number set: [74, 20], target: 21, just two numbers left.\n     |- Try 74 + 20 = 94. Evaluate 94 != 21, drop this branch.\n     |- Try 74 - 20 = 54. Evaluate 54 != 21, drop this branch.\n     |- Try 74 * 20 = 1480. Evaluate 1480 != 21, drop this branch.\n     |- Try 74 \/ 20 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 43 - 31 = 12. Add 12 to the number set. Current number set: [12, 20], target: 21, just two numbers left.\n     |- Try 20 + 12 = 32. Evaluate 32 != 21, drop this branch.\n     |- Try 20 - 12 = 8. Evaluate 8 != 21, drop this branch.\n     |- Try 20 * 12 = 240. Evaluate 240 != 21, drop this branch.\n     |- Try 20 \/ 12 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 43 * 31 = 1333. Add 1333 to the number set. Current number set: [1333, 20], target: 21, just two numbers left.\n     |- Try 1333 + 20 = 1353. Evaluate 1353 != 21, drop this branch.\n     |- Try 1333 - 20 = 1313. Evaluate 1313 != 21, drop this branch.\n     |- Try 1333 * 20 = 26660. 26660 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1333 \/ 20 = 66.7. 66.7 is a decimal, drop this branch.\n    |- Try 43 \/ 31 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 18 - 2 = 16. Add 16 to the number set. Current number set: [16, 31, 43], target: 21. Options for choosing two numbers: [(16, 31), (16, 43), (31, 43)].\n   |- Pick two numbers (16, 31) (numbers left: [43]). Try possible operations.\n    |- Try 31 + 16 = 47. Add 47 to the number set. Current number set: [47, 43], target: 21, just two numbers left.\n     |- Try 47 + 43 = 90. Evaluate 90 != 21, drop this branch.\n     |- Try 47 - 43 = 4. Evaluate 4 != 21, drop this branch.\n     |- Try 47 * 43 = 2021. 2021 exceeds the maximum intermediate result, drop this branch.\n     |- Try 47 \/ 43 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 31 - 16 = 15. Add 15 to the number set. Current number set: [15, 43], target: 21, just two numbers left.\n     |- Try 43 + 15 = 58. Evaluate 58 != 21, drop this branch.\n     |- Try 43 - 15 = 28. Evaluate 28 != 21, drop this branch.\n     |- Try 43 * 15 = 645. Evaluate 645 != 21, drop this branch.\n     |- Try 43 \/ 15 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 31 * 16 = 496. Add 496 to the number set. Current number set: [496, 43], target: 21, just two numbers left.\n     |- Try 496 + 43 = 539. Evaluate 539 != 21, drop this branch.\n     |- Try 496 - 43 = 453. Evaluate 453 != 21, drop this branch.\n     |- Try 496 * 43 = 21328. 21328 exceeds the maximum intermediate result, drop this branch.\n     |- Try 496 \/ 43 = 11.5. 11.5 is a decimal, drop this branch.\n    |- Try 31 \/ 16 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (16, 43) (numbers left: [31]). Try possible operations.\n    |- Try 43 + 16 = 59. Add 59 to the number set. Current number set: [59, 31], target: 21, just two numbers left.\n     |- Try 59 + 31 = 90. Evaluate 90 != 21, drop this branch.\n     |- Try 59 - 31 = 28. Evaluate 28 != 21, drop this branch.\n     |- Try 59 * 31 = 1829. Evaluate 1829 != 21, drop this branch.\n     |- Try 59 \/ 31 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 43 - 16 = 27. Add 27 to the number set. Current number set: [27, 31], target: 21, just two numbers left.\n     |- Try 31 + 27 = 58. Evaluate 58 != 21, drop this branch.\n     |- Try 31 - 27 = 4. Evaluate 4 != 21, drop this branch.\n     |- Try 31 * 27 = 837. Evaluate 837 != 21, drop this branch.\n     |- Try 31 \/ 27 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 43 * 16 = 688. Add 688 to the number set. Current number set: [688, 31], target: 21, just two numbers left.\n     |- Try 688 + 31 = 719. Evaluate 719 != 21, drop this branch.\n     |- Try 688 - 31 = 657. Evaluate 657 != 21, drop this branch.\n     |- Try 688 * 31 = 21328. 21328 exceeds the maximum intermediate result, drop this branch.\n     |- Try 688 \/ 31 = 22.2. 22.2 is a decimal, drop this branch.\n    |- Try 43 \/ 16 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (31, 43) (numbers left: [16]). Try possible operations.\n    |- Try 43 + 31 = 74. Add 74 to the number set. Current number set: [74, 16], target: 21, just two numbers left.\n     |- Try 74 + 16 = 90. Evaluate 90 != 21, drop this branch.\n     |- Try 74 - 16 = 58. Evaluate 58 != 21, drop this branch.\n     |- Try 74 * 16 = 1184. Evaluate 1184 != 21, drop this branch.\n     |- Try 74 \/ 16 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 43 - 31 = 12. Add 12 to the number set. Current number set: [12, 16], target: 21, just two numbers left.\n     |- Try 16 + 12 = 28. Evaluate 28 != 21, drop this branch.\n     |- Try 16 - 12 = 4. Evaluate 4 != 21, drop this branch.\n     |- Try 16 * 12 = 192. Evaluate 192 != 21, drop this branch.\n     |- Try 16 \/ 12 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 43 * 31 = 1333. Add 1333 to the number set. Current number set: [1333, 16], target: 21, just two numbers left.\n     |- Try 1333 + 16 = 1349. Evaluate 1349 != 21, drop this branch.\n     |- Try 1333 - 16 = 1317. Evaluate 1317 != 21, drop this branch.\n     |- Try 1333 * 16 = 21328. 21328 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1333 \/ 16 = 83.3. 83.3 is a decimal, drop this branch.\n    |- Try 43 \/ 31 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 18 * 2 = 36. Add 36 to the number set. Current number set: [36, 31, 43], target: 21. Options for choosing two numbers: [(36, 31), (36, 43), (31, 43)].\n   |- Pick two numbers (36, 31) (numbers left: [43]). Try possible operations.\n    |- Try 36 + 31 = 67. Add 67 to the number set. Current number set: [67, 43], target: 21, just two numbers left.\n     |- Try 67 + 43 = 110. Evaluate 110 != 21, drop this branch.\n     |- Try 67 - 43 = 24. Evaluate 24 != 21, drop this branch.\n     |- Try 67 * 43 = 2881. 2881 exceeds the maximum intermediate result, drop this branch.\n     |- Try 67 \/ 43 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 36 - 31 = 5. Add 5 to the number set. Current number set: [5, 43], target: 21, just two numbers left.\n     |- Try 43 + 5 = 48. Evaluate 48 != 21, drop this branch.\n     |- Try 43 - 5 = 38. Evaluate 38 != 21, drop this branch.\n     |- Try 43 * 5 = 215. Evaluate 215 != 21, drop this branch.\n     |- Try 43 \/ 5 = 8.6. 8.6 is a decimal, drop this branch.\n    |- Try 36 * 31 = 1116. Add 1116 to the number set. Current number set: [1116, 43], target: 21, just two numbers left.\n     |- Try 1116 + 43 = 1159. Evaluate 1159 != 21, drop this branch.\n     |- Try 1116 - 43 = 1073. Evaluate 1073 != 21, drop this branch.\n     |- Try 1116 * 43 = 47988. 47988 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1116 \/ 43 = 26.0. 26.0 is a decimal, drop this branch.\n    |- Try 36 \/ 31 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (36, 43) (numbers left: [31]). Try possible operations.\n    |- Try 43 + 36 = 79. Add 79 to the number set. Current number set: [79, 31], target: 21, just two numbers left.\n     |- Try 79 + 31 = 110. Evaluate 110 != 21, drop this branch.\n     |- Try 79 - 31 = 48. Evaluate 48 != 21, drop this branch.\n     |- Try 79 * 31 = 2449. 2449 exceeds the maximum intermediate result, drop this branch.\n     |- Try 79 \/ 31 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 43 - 36 = 7. Add 7 to the number set. Current number set: [7, 31], target: 21, just two numbers left.\n     |- Try 31 + 7 = 38. Evaluate 38 != 21, drop this branch.\n     |- Try 31 - 7 = 24. Evaluate 24 != 21, drop this branch.\n     |- Try 31 * 7 = 217. Evaluate 217 != 21, drop this branch.\n     |- Try 31 \/ 7 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 43 * 36 = 1548. Add 1548 to the number set. Current number set: [1548, 31], target: 21, just two numbers left.\n     |- Try 1548 + 31 = 1579. Evaluate 1579 != 21, drop this branch.\n     |- Try 1548 - 31 = 1517. Evaluate 1517 != 21, drop this branch.\n     |- Try 1548 * 31 = 47988. 47988 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1548 \/ 31 = 49.9. 49.9 is a decimal, drop this branch.\n    |- Try 43 \/ 36 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (31, 43) (numbers left: [36]). Try possible operations.\n    |- Try 43 + 31 = 74. Add 74 to the number set. Current number set: [74, 36], target: 21, just two numbers left.\n     |- Try 74 + 36 = 110. Evaluate 110 != 21, drop this branch.\n     |- Try 74 - 36 = 38. Evaluate 38 != 21, drop this branch.\n     |- Try 74 * 36 = 2664. 2664 exceeds the maximum intermediate result, drop this branch.\n     |- Try 74 \/ 36 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 43 - 31 = 12. Add 12 to the number set. Current number set: [12, 36], target: 21, just two numbers left.\n     |- Try 36 + 12 = 48. Evaluate 48 != 21, drop this branch.\n     |- Try 36 - 12 = 24. Evaluate 24 != 21, drop this branch.\n     |- Try 36 * 12 = 432. Evaluate 432 != 21, drop this branch.\n     |- Try 36 \/ 12 = 3. Evaluate 3 != 21, drop this branch.\n    |- Try 43 * 31 = 1333. Add 1333 to the number set. Current number set: [1333, 36], target: 21, just two numbers left.\n     |- Try 1333 + 36 = 1369. Evaluate 1369 != 21, drop this branch.\n     |- Try 1333 - 36 = 1297. Evaluate 1297 != 21, drop this branch.\n     |- Try 1333 * 36 = 47988. 47988 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1333 \/ 36 = 37.0. 37.0 is a decimal, drop this branch.\n    |- Try 43 \/ 31 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 18 \/ 2 = 9. Add 9 to the number set. Current number set: [9, 31, 43], target: 21. Options for choosing two numbers: [(9, 31), (9, 43), (31, 43)].\n   |- Pick two numbers (9, 31) (numbers left: [43]). Try possible operations.\n    |- Try 31 + 9 = 40. Add 40 to the number set. Current number set: [40, 43], target: 21, just two numbers left.\n     |- Try 43 + 40 = 83. Evaluate 83 != 21, drop this branch.\n     |- Try 43 - 40 = 3. Evaluate 3 != 21, drop this branch.\n     |- Try 43 * 40 = 1720. Evaluate 1720 != 21, drop this branch.\n     |- Try 43 \/ 40 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 31 - 9 = 22. Add 22 to the number set. Current number set: [22, 43], target: 21, just two numbers left.\n     |- Try 43 + 22 = 65. Evaluate 65 != 21, drop this branch.\n     |- Try 43 - 22 = 21. Evaluate 21 == 21, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 43 - 22 = 21\nThe step before: 31 - 9 = 22\nThe first step: 18 \/ 2 = 9\n\nOutput the solution in the required format:\n<Solution>\n18 \/ 2 = 9\n31 - 9 = 22\n43 - 22 = 21\n<\/Solution>\n","item":{"nums":[18,2,31,43],"solution":["18 \/ 2 = 9","31 - 9 = 22","43 - 22 = 21"],"target":21}}
+{"instance_id":"countdown_8k_168","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [22, 2, 12, 17]\nTarget: 37","reference_output":"# Search Procedure\nInitial number set: [22, 2, 12, 17], target: 37. Options for choosing two numbers: [(22, 2), (22, 12), (22, 17), (2, 12), (2, 17), (12, 17)].\n |- Pick two numbers (22, 2) (numbers left: [12, 17]). Try possible operations.\n  |- Try 22 + 2 = 24. Add 24 to the number set. Current number set: [24, 12, 17], target: 37. Options for choosing two numbers: [(24, 12), (24, 17), (12, 17)].\n   |- Pick two numbers (24, 12) (numbers left: [17]). Try possible operations.\n    |- Try 24 + 12 = 36. Add 36 to the number set. Current number set: [36, 17], target: 37, just two numbers left.\n     |- Try 36 + 17 = 53. Evaluate 53 != 37, drop this branch.\n     |- Try 36 - 17 = 19. Evaluate 19 != 37, drop this branch.\n     |- Try 36 * 17 = 612. Evaluate 612 != 37, drop this branch.\n     |- Try 36 \/ 17 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 24 - 12 = 12. Add 12 to the number set. Current number set: [12, 17], target: 37, just two numbers left.\n     |- Try 17 + 12 = 29. Evaluate 29 != 37, drop this branch.\n     |- Try 17 - 12 = 5. Evaluate 5 != 37, drop this branch.\n     |- Try 17 * 12 = 204. Evaluate 204 != 37, drop this branch.\n     |- Try 17 \/ 12 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 24 * 12 = 288. Add 288 to the number set. Current number set: [288, 17], target: 37, just two numbers left.\n     |- Try 288 + 17 = 305. Evaluate 305 != 37, drop this branch.\n     |- Try 288 - 17 = 271. Evaluate 271 != 37, drop this branch.\n     |- Try 288 * 17 = 4896. 4896 exceeds the maximum intermediate result, drop this branch.\n     |- Try 288 \/ 17 = 16.9. 16.9 is a decimal, drop this branch.\n    |- Try 24 \/ 12 = 2. Add 2 to the number set. Current number set: [2, 17], target: 37, just two numbers left.\n     |- Try 17 + 2 = 19. Evaluate 19 != 37, drop this branch.\n     |- Try 17 - 2 = 15. Evaluate 15 != 37, drop this branch.\n     |- Try 17 * 2 = 34. Evaluate 34 != 37, drop this branch.\n     |- Try 17 \/ 2 = 8.5. 8.5 is a decimal, drop this branch.\n   |- Pick two numbers (24, 17) (numbers left: [12]). Try possible operations.\n    |- Try 24 + 17 = 41. Add 41 to the number set. Current number set: [41, 12], target: 37, just two numbers left.\n     |- Try 41 + 12 = 53. Evaluate 53 != 37, drop this branch.\n     |- Try 41 - 12 = 29. Evaluate 29 != 37, drop this branch.\n     |- Try 41 * 12 = 492. Evaluate 492 != 37, drop this branch.\n     |- Try 41 \/ 12 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 24 - 17 = 7. Add 7 to the number set. Current number set: [7, 12], target: 37, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 37, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 37, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 37, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 24 * 17 = 408. Add 408 to the number set. Current number set: [408, 12], target: 37, just two numbers left.\n     |- Try 408 + 12 = 420. Evaluate 420 != 37, drop this branch.\n     |- Try 408 - 12 = 396. Evaluate 396 != 37, drop this branch.\n     |- Try 408 * 12 = 4896. 4896 exceeds the maximum intermediate result, drop this branch.\n     |- Try 408 \/ 12 = 34. Evaluate 34 != 37, drop this branch.\n    |- Try 24 \/ 17 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (12, 17) (numbers left: [24]). Try possible operations.\n    |- Try 17 + 12 = 29. Add 29 to the number set. Current number set: [29, 24], target: 37, just two numbers left.\n     |- Try 29 + 24 = 53. Evaluate 53 != 37, drop this branch.\n     |- Try 29 - 24 = 5. Evaluate 5 != 37, drop this branch.\n     |- Try 29 * 24 = 696. Evaluate 696 != 37, drop this branch.\n     |- Try 29 \/ 24 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 17 - 12 = 5. Add 5 to the number set. Current number set: [5, 24], target: 37, just two numbers left.\n     |- Try 24 + 5 = 29. Evaluate 29 != 37, drop this branch.\n     |- Try 24 - 5 = 19. Evaluate 19 != 37, drop this branch.\n     |- Try 24 * 5 = 120. Evaluate 120 != 37, drop this branch.\n     |- Try 24 \/ 5 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 17 * 12 = 204. Add 204 to the number set. Current number set: [204, 24], target: 37, just two numbers left.\n     |- Try 204 + 24 = 228. Evaluate 228 != 37, drop this branch.\n     |- Try 204 - 24 = 180. Evaluate 180 != 37, drop this branch.\n     |- Try 204 * 24 = 4896. 4896 exceeds the maximum intermediate result, drop this branch.\n     |- Try 204 \/ 24 = 8.5. 8.5 is a decimal, drop this branch.\n    |- Try 17 \/ 12 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 22 - 2 = 20. Add 20 to the number set. Current number set: [20, 12, 17], target: 37. Options for choosing two numbers: [(20, 12), (20, 17), (12, 17)].\n   |- Pick two numbers (20, 12) (numbers left: [17]). Try possible operations.\n    |- Try 20 + 12 = 32. Add 32 to the number set. Current number set: [32, 17], target: 37, just two numbers left.\n     |- Try 32 + 17 = 49. Evaluate 49 != 37, drop this branch.\n     |- Try 32 - 17 = 15. Evaluate 15 != 37, drop this branch.\n     |- Try 32 * 17 = 544. Evaluate 544 != 37, drop this branch.\n     |- Try 32 \/ 17 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 20 - 12 = 8. Add 8 to the number set. Current number set: [8, 17], target: 37, just two numbers left.\n     |- Try 17 + 8 = 25. Evaluate 25 != 37, drop this branch.\n     |- Try 17 - 8 = 9. Evaluate 9 != 37, drop this branch.\n     |- Try 17 * 8 = 136. Evaluate 136 != 37, drop this branch.\n     |- Try 17 \/ 8 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 20 * 12 = 240. Add 240 to the number set. Current number set: [240, 17], target: 37, just two numbers left.\n     |- Try 240 + 17 = 257. Evaluate 257 != 37, drop this branch.\n     |- Try 240 - 17 = 223. Evaluate 223 != 37, drop this branch.\n     |- Try 240 * 17 = 4080. 4080 exceeds the maximum intermediate result, drop this branch.\n     |- Try 240 \/ 17 = 14.1. 14.1 is a decimal, drop this branch.\n    |- Try 20 \/ 12 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (20, 17) (numbers left: [12]). Try possible operations.\n    |- Try 20 + 17 = 37. Add 37 to the number set. Current number set: [37, 12], target: 37, just two numbers left.\n     |- Try 37 + 12 = 49. Evaluate 49 != 37, drop this branch.\n     |- Try 37 - 12 = 25. Evaluate 25 != 37, drop this branch.\n     |- Try 37 * 12 = 444. Evaluate 444 != 37, drop this branch.\n     |- Try 37 \/ 12 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 20 - 17 = 3. Add 3 to the number set. Current number set: [3, 12], target: 37, just two numbers left.\n     |- Try 12 + 3 = 15. Evaluate 15 != 37, drop this branch.\n     |- Try 12 - 3 = 9. Evaluate 9 != 37, drop this branch.\n     |- Try 12 * 3 = 36. Evaluate 36 != 37, drop this branch.\n     |- Try 12 \/ 3 = 4. Evaluate 4 != 37, drop this branch.\n    |- Try 20 * 17 = 340. Add 340 to the number set. Current number set: [340, 12], target: 37, just two numbers left.\n     |- Try 340 + 12 = 352. Evaluate 352 != 37, drop this branch.\n     |- Try 340 - 12 = 328. Evaluate 328 != 37, drop this branch.\n     |- Try 340 * 12 = 4080. 4080 exceeds the maximum intermediate result, drop this branch.\n     |- Try 340 \/ 12 = 28.3. 28.3 is a decimal, drop this branch.\n    |- Try 20 \/ 17 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (12, 17) (numbers left: [20]). Try possible operations.\n    |- Try 17 + 12 = 29. Add 29 to the number set. Current number set: [29, 20], target: 37, just two numbers left.\n     |- Try 29 + 20 = 49. Evaluate 49 != 37, drop this branch.\n     |- Try 29 - 20 = 9. Evaluate 9 != 37, drop this branch.\n     |- Try 29 * 20 = 580. Evaluate 580 != 37, drop this branch.\n     |- Try 29 \/ 20 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 17 - 12 = 5. Add 5 to the number set. Current number set: [5, 20], target: 37, just two numbers left.\n     |- Try 20 + 5 = 25. Evaluate 25 != 37, drop this branch.\n     |- Try 20 - 5 = 15. Evaluate 15 != 37, drop this branch.\n     |- Try 20 * 5 = 100. Evaluate 100 != 37, drop this branch.\n     |- Try 20 \/ 5 = 4. Evaluate 4 != 37, drop this branch.\n    |- Try 17 * 12 = 204. Add 204 to the number set. Current number set: [204, 20], target: 37, just two numbers left.\n     |- Try 204 + 20 = 224. Evaluate 224 != 37, drop this branch.\n     |- Try 204 - 20 = 184. Evaluate 184 != 37, drop this branch.\n     |- Try 204 * 20 = 4080. 4080 exceeds the maximum intermediate result, drop this branch.\n     |- Try 204 \/ 20 = 10.2. 10.2 is a decimal, drop this branch.\n    |- Try 17 \/ 12 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 22 * 2 = 44. Add 44 to the number set. Current number set: [44, 12, 17], target: 37. Options for choosing two numbers: [(44, 12), (44, 17), (12, 17)].\n   |- Pick two numbers (44, 12) (numbers left: [17]). Try possible operations.\n    |- Try 44 + 12 = 56. Add 56 to the number set. Current number set: [56, 17], target: 37, just two numbers left.\n     |- Try 56 + 17 = 73. Evaluate 73 != 37, drop this branch.\n     |- Try 56 - 17 = 39. Evaluate 39 != 37, drop this branch.\n     |- Try 56 * 17 = 952. Evaluate 952 != 37, drop this branch.\n     |- Try 56 \/ 17 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 44 - 12 = 32. Add 32 to the number set. Current number set: [32, 17], target: 37, just two numbers left.\n     |- Try 32 + 17 = 49. Evaluate 49 != 37, drop this branch.\n     |- Try 32 - 17 = 15. Evaluate 15 != 37, drop this branch.\n     |- Try 32 * 17 = 544. Evaluate 544 != 37, drop this branch.\n     |- Try 32 \/ 17 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 44 * 12 = 528. Add 528 to the number set. Current number set: [528, 17], target: 37, just two numbers left.\n     |- Try 528 + 17 = 545. Evaluate 545 != 37, drop this branch.\n     |- Try 528 - 17 = 511. Evaluate 511 != 37, drop this branch.\n     |- Try 528 * 17 = 8976. 8976 exceeds the maximum intermediate result, drop this branch.\n     |- Try 528 \/ 17 = 31.1. 31.1 is a decimal, drop this branch.\n    |- Try 44 \/ 12 = 3.7. 3.7 is a decimal, drop this branch.\n   |- Pick two numbers (44, 17) (numbers left: [12]). Try possible operations.\n    |- Try 44 + 17 = 61. Add 61 to the number set. Current number set: [61, 12], target: 37, just two numbers left.\n     |- Try 61 + 12 = 73. Evaluate 73 != 37, drop this branch.\n     |- Try 61 - 12 = 49. Evaluate 49 != 37, drop this branch.\n     |- Try 61 * 12 = 732. Evaluate 732 != 37, drop this branch.\n     |- Try 61 \/ 12 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 44 - 17 = 27. Add 27 to the number set. Current number set: [27, 12], target: 37, just two numbers left.\n     |- Try 27 + 12 = 39. Evaluate 39 != 37, drop this branch.\n     |- Try 27 - 12 = 15. Evaluate 15 != 37, drop this branch.\n     |- Try 27 * 12 = 324. Evaluate 324 != 37, drop this branch.\n     |- Try 27 \/ 12 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 44 * 17 = 748. Add 748 to the number set. Current number set: [748, 12], target: 37, just two numbers left.\n     |- Try 748 + 12 = 760. Evaluate 760 != 37, drop this branch.\n     |- Try 748 - 12 = 736. Evaluate 736 != 37, drop this branch.\n     |- Try 748 * 12 = 8976. 8976 exceeds the maximum intermediate result, drop this branch.\n     |- Try 748 \/ 12 = 62.3. 62.3 is a decimal, drop this branch.\n    |- Try 44 \/ 17 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (12, 17) (numbers left: [44]). Try possible operations.\n    |- Try 17 + 12 = 29. Add 29 to the number set. Current number set: [29, 44], target: 37, just two numbers left.\n     |- Try 44 + 29 = 73. Evaluate 73 != 37, drop this branch.\n     |- Try 44 - 29 = 15. Evaluate 15 != 37, drop this branch.\n     |- Try 44 * 29 = 1276. Evaluate 1276 != 37, drop this branch.\n     |- Try 44 \/ 29 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 17 - 12 = 5. Add 5 to the number set. Current number set: [5, 44], target: 37, just two numbers left.\n     |- Try 44 + 5 = 49. Evaluate 49 != 37, drop this branch.\n     |- Try 44 - 5 = 39. Evaluate 39 != 37, drop this branch.\n     |- Try 44 * 5 = 220. Evaluate 220 != 37, drop this branch.\n     |- Try 44 \/ 5 = 8.8. 8.8 is a decimal, drop this branch.\n    |- Try 17 * 12 = 204. Add 204 to the number set. Current number set: [204, 44], target: 37, just two numbers left.\n     |- Try 204 + 44 = 248. Evaluate 248 != 37, drop this branch.\n     |- Try 204 - 44 = 160. Evaluate 160 != 37, drop this branch.\n     |- Try 204 * 44 = 8976. 8976 exceeds the maximum intermediate result, drop this branch.\n     |- Try 204 \/ 44 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 17 \/ 12 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 22 \/ 2 = 11. Add 11 to the number set. Current number set: [11, 12, 17], target: 37. Options for choosing two numbers: [(11, 12), (11, 17), (12, 17)].\n   |- Pick two numbers (11, 12) (numbers left: [17]). Try possible operations.\n    |- Try 12 + 11 = 23. Add 23 to the number set. Current number set: [23, 17], target: 37, just two numbers left.\n     |- Try 23 + 17 = 40. Evaluate 40 != 37, drop this branch.\n     |- Try 23 - 17 = 6. Evaluate 6 != 37, drop this branch.\n     |- Try 23 * 17 = 391. Evaluate 391 != 37, drop this branch.\n     |- Try 23 \/ 17 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 12 - 11 = 1. Add 1 to the number set. Current number set: [1, 17], target: 37, just two numbers left.\n     |- Try 17 + 1 = 18. Evaluate 18 != 37, drop this branch.\n     |- Try 17 - 1 = 16. Evaluate 16 != 37, drop this branch.\n     |- Try 17 * 1 = 17. Evaluate 17 != 37, drop this branch.\n     |- Try 17 \/ 1 = 17. Evaluate 17 != 37, drop this branch.\n    |- Try 12 * 11 = 132. Add 132 to the number set. Current number set: [132, 17], target: 37, just two numbers left.\n     |- Try 132 + 17 = 149. Evaluate 149 != 37, drop this branch.\n     |- Try 132 - 17 = 115. Evaluate 115 != 37, drop this branch.\n     |- Try 132 * 17 = 2244. 2244 exceeds the maximum intermediate result, drop this branch.\n     |- Try 132 \/ 17 = 7.8. 7.8 is a decimal, drop this branch.\n    |- Try 12 \/ 11 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (11, 17) (numbers left: [12]). Try possible operations.\n    |- Try 17 + 11 = 28. Add 28 to the number set. Current number set: [28, 12], target: 37, just two numbers left.\n     |- Try 28 + 12 = 40. Evaluate 40 != 37, drop this branch.\n     |- Try 28 - 12 = 16. Evaluate 16 != 37, drop this branch.\n     |- Try 28 * 12 = 336. Evaluate 336 != 37, drop this branch.\n     |- Try 28 \/ 12 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 17 - 11 = 6. Add 6 to the number set. Current number set: [6, 12], target: 37, just two numbers left.\n     |- Try 12 + 6 = 18. Evaluate 18 != 37, drop this branch.\n     |- Try 12 - 6 = 6. Evaluate 6 != 37, drop this branch.\n     |- Try 12 * 6 = 72. Evaluate 72 != 37, drop this branch.\n     |- Try 12 \/ 6 = 2. Evaluate 2 != 37, drop this branch.\n    |- Try 17 * 11 = 187. Add 187 to the number set. Current number set: [187, 12], target: 37, just two numbers left.\n     |- Try 187 + 12 = 199. Evaluate 199 != 37, drop this branch.\n     |- Try 187 - 12 = 175. Evaluate 175 != 37, drop this branch.\n     |- Try 187 * 12 = 2244. 2244 exceeds the maximum intermediate result, drop this branch.\n     |- Try 187 \/ 12 = 15.6. 15.6 is a decimal, drop this branch.\n    |- Try 17 \/ 11 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (12, 17) (numbers left: [11]). Try possible operations.\n    |- Try 17 + 12 = 29. Add 29 to the number set. Current number set: [29, 11], target: 37, just two numbers left.\n     |- Try 29 + 11 = 40. Evaluate 40 != 37, drop this branch.\n     |- Try 29 - 11 = 18. Evaluate 18 != 37, drop this branch.\n     |- Try 29 * 11 = 319. Evaluate 319 != 37, drop this branch.\n     |- Try 29 \/ 11 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 17 - 12 = 5. Add 5 to the number set. Current number set: [5, 11], target: 37, just two numbers left.\n     |- Try 11 + 5 = 16. Evaluate 16 != 37, drop this branch.\n     |- Try 11 - 5 = 6. Evaluate 6 != 37, drop this branch.\n     |- Try 11 * 5 = 55. Evaluate 55 != 37, drop this branch.\n     |- Try 11 \/ 5 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 17 * 12 = 204. Add 204 to the number set. Current number set: [204, 11], target: 37, just two numbers left.\n     |- Try 204 + 11 = 215. Evaluate 215 != 37, drop this branch.\n     |- Try 204 - 11 = 193. Evaluate 193 != 37, drop this branch.\n     |- Try 204 * 11 = 2244. 2244 exceeds the maximum intermediate result, drop this branch.\n     |- Try 204 \/ 11 = 18.5. 18.5 is a decimal, drop this branch.\n    |- Try 17 \/ 12 = 1.4. 1.4 is a decimal, drop this branch.\n |- Pick two numbers (22, 12) (numbers left: [2, 17]). Try possible operations.\n  |- Try 22 + 12 = 34. Add 34 to the number set. Current number set: [34, 2, 17], target: 37. Options for choosing two numbers: [(34, 2), (34, 17), (2, 17)].\n   |- Pick two numbers (34, 2) (numbers left: [17]). Try possible operations.\n    |- Try 34 + 2 = 36. Add 36 to the number set. Current number set: [36, 17], target: 37, just two numbers left.\n     |- Try 36 + 17 = 53. Evaluate 53 != 37, drop this branch.\n     |- Try 36 - 17 = 19. Evaluate 19 != 37, drop this branch.\n     |- Try 36 * 17 = 612. Evaluate 612 != 37, drop this branch.\n     |- Try 36 \/ 17 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 34 - 2 = 32. Add 32 to the number set. Current number set: [32, 17], target: 37, just two numbers left.\n     |- Try 32 + 17 = 49. Evaluate 49 != 37, drop this branch.\n     |- Try 32 - 17 = 15. Evaluate 15 != 37, drop this branch.\n     |- Try 32 * 17 = 544. Evaluate 544 != 37, drop this branch.\n     |- Try 32 \/ 17 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 34 * 2 = 68. Add 68 to the number set. Current number set: [68, 17], target: 37, just two numbers left.\n     |- Try 68 + 17 = 85. Evaluate 85 != 37, drop this branch.\n     |- Try 68 - 17 = 51. Evaluate 51 != 37, drop this branch.\n     |- Try 68 * 17 = 1156. Evaluate 1156 != 37, drop this branch.\n     |- Try 68 \/ 17 = 4. Evaluate 4 != 37, drop this branch.\n    |- Try 34 \/ 2 = 17. Add 17 to the number set. Current number set: [17, 17], target: 37, just two numbers left.\n     |- Try 17 + 17 = 34. Evaluate 34 != 37, drop this branch.\n     |- Try 17 - 17 = 0. Evaluate 0 != 37, drop this branch.\n     |- Try 17 * 17 = 289. Evaluate 289 != 37, drop this branch.\n     |- Try 17 \/ 17 = 1. Evaluate 1 != 37, drop this branch.\n   |- Pick two numbers (34, 17) (numbers left: [2]). Try possible operations.\n    |- Try 34 + 17 = 51. Add 51 to the number set. Current number set: [51, 2], target: 37, just two numbers left.\n     |- Try 51 + 2 = 53. Evaluate 53 != 37, drop this branch.\n     |- Try 51 - 2 = 49. Evaluate 49 != 37, drop this branch.\n     |- Try 51 * 2 = 102. Evaluate 102 != 37, drop this branch.\n     |- Try 51 \/ 2 = 25.5. 25.5 is a decimal, drop this branch.\n    |- Try 34 - 17 = 17. Add 17 to the number set. Current number set: [17, 2], target: 37, just two numbers left.\n     |- Try 17 + 2 = 19. Evaluate 19 != 37, drop this branch.\n     |- Try 17 - 2 = 15. Evaluate 15 != 37, drop this branch.\n     |- Try 17 * 2 = 34. Evaluate 34 != 37, drop this branch.\n     |- Try 17 \/ 2 = 8.5. 8.5 is a decimal, drop this branch.\n    |- Try 34 * 17 = 578. Add 578 to the number set. Current number set: [578, 2], target: 37, just two numbers left.\n     |- Try 578 + 2 = 580. Evaluate 580 != 37, drop this branch.\n     |- Try 578 - 2 = 576. Evaluate 576 != 37, drop this branch.\n     |- Try 578 * 2 = 1156. Evaluate 1156 != 37, drop this branch.\n     |- Try 578 \/ 2 = 289. Evaluate 289 != 37, drop this branch.\n    |- Try 34 \/ 17 = 2. Add 2 to the number set. Current number set: [2, 2], target: 37, just two numbers left.\n     |- Try 2 + 2 = 4. Evaluate 4 != 37, drop this branch.\n     |- Try 2 - 2 = 0. Evaluate 0 != 37, drop this branch.\n     |- Try 2 * 2 = 4. Evaluate 4 != 37, drop this branch.\n     |- Try 2 \/ 2 = 1. Evaluate 1 != 37, drop this branch.\n   |- Pick two numbers (2, 17) (numbers left: [34]). Try possible operations.\n    |- Try 17 + 2 = 19. Add 19 to the number set. Current number set: [19, 34], target: 37, just two numbers left.\n     |- Try 34 + 19 = 53. Evaluate 53 != 37, drop this branch.\n     |- Try 34 - 19 = 15. Evaluate 15 != 37, drop this branch.\n     |- Try 34 * 19 = 646. Evaluate 646 != 37, drop this branch.\n     |- Try 34 \/ 19 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 17 - 2 = 15. Add 15 to the number set. Current number set: [15, 34], target: 37, just two numbers left.\n     |- Try 34 + 15 = 49. Evaluate 49 != 37, drop this branch.\n     |- Try 34 - 15 = 19. Evaluate 19 != 37, drop this branch.\n     |- Try 34 * 15 = 510. Evaluate 510 != 37, drop this branch.\n     |- Try 34 \/ 15 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 17 * 2 = 34. Add 34 to the number set. Current number set: [34, 34], target: 37, just two numbers left.\n     |- Try 34 + 34 = 68. Evaluate 68 != 37, drop this branch.\n     |- Try 34 - 34 = 0. Evaluate 0 != 37, drop this branch.\n     |- Try 34 * 34 = 1156. Evaluate 1156 != 37, drop this branch.\n     |- Try 34 \/ 34 = 1. Evaluate 1 != 37, drop this branch.\n    |- Try 17 \/ 2 = 8.5. 8.5 is a decimal, drop this branch.\n  |- Try 22 - 12 = 10. Add 10 to the number set. Current number set: [10, 2, 17], target: 37. Options for choosing two numbers: [(10, 2), (10, 17), (2, 17)].\n   |- Pick two numbers (10, 2) (numbers left: [17]). Try possible operations.\n    |- Try 10 + 2 = 12. Add 12 to the number set. Current number set: [12, 17], target: 37, just two numbers left.\n     |- Try 17 + 12 = 29. Evaluate 29 != 37, drop this branch.\n     |- Try 17 - 12 = 5. Evaluate 5 != 37, drop this branch.\n     |- Try 17 * 12 = 204. Evaluate 204 != 37, drop this branch.\n     |- Try 17 \/ 12 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 10 - 2 = 8. Add 8 to the number set. Current number set: [8, 17], target: 37, just two numbers left.\n     |- Try 17 + 8 = 25. Evaluate 25 != 37, drop this branch.\n     |- Try 17 - 8 = 9. Evaluate 9 != 37, drop this branch.\n     |- Try 17 * 8 = 136. Evaluate 136 != 37, drop this branch.\n     |- Try 17 \/ 8 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 10 * 2 = 20. Add 20 to the number set. Current number set: [20, 17], target: 37, just two numbers left.\n     |- Try 20 + 17 = 37. Evaluate 37 == 37, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 20 + 17 = 37\nThe step before: 10 * 2 = 20\nThe first step: 22 - 12 = 10\n\nOutput the solution in the required format:\n<Solution>\n22 - 12 = 10\n10 * 2 = 20\n20 + 17 = 37\n<\/Solution>\n","item":{"nums":[22,2,12,17],"solution":["22 - 12 = 10","10 * 2 = 20","20 + 17 = 37"],"target":37}}
+{"instance_id":"countdown_8k_169","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [49, 10, 7, 7]\nTarget: 28","reference_output":"# Search Procedure\nInitial number set: [49, 10, 7, 7], target: 28. Options for choosing two numbers: [(49, 10), (49, 7), (49, 7), (10, 7), (10, 7), (7, 7)].\n |- Pick two numbers (49, 10) (numbers left: [7, 7]). Try possible operations.\n  |- Try 49 + 10 = 59. Add 59 to the number set. Current number set: [59, 7, 7], target: 28. Options for choosing two numbers: [(59, 7), (59, 7), (7, 7)].\n   |- Pick two numbers (59, 7) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 7 = 66. Add 66 to the number set. Current number set: [66, 7], target: 28, just two numbers left.\n     |- Try 66 + 7 = 73. Evaluate 73 != 28, drop this branch.\n     |- Try 66 - 7 = 59. Evaluate 59 != 28, drop this branch.\n     |- Try 66 * 7 = 462. Evaluate 462 != 28, drop this branch.\n     |- Try 66 \/ 7 = 9.4. 9.4 is a decimal, drop this branch.\n    |- Try 59 - 7 = 52. Add 52 to the number set. Current number set: [52, 7], target: 28, just two numbers left.\n     |- Try 52 + 7 = 59. Evaluate 59 != 28, drop this branch.\n     |- Try 52 - 7 = 45. Evaluate 45 != 28, drop this branch.\n     |- Try 52 * 7 = 364. Evaluate 364 != 28, drop this branch.\n     |- Try 52 \/ 7 = 7.4. 7.4 is a decimal, drop this branch.\n    |- Try 59 * 7 = 413. Add 413 to the number set. Current number set: [413, 7], target: 28, just two numbers left.\n     |- Try 413 + 7 = 420. Evaluate 420 != 28, drop this branch.\n     |- Try 413 - 7 = 406. Evaluate 406 != 28, drop this branch.\n     |- Try 413 * 7 = 2891. 2891 exceeds the maximum intermediate result, drop this branch.\n     |- Try 413 \/ 7 = 59. Evaluate 59 != 28, drop this branch.\n    |- Try 59 \/ 7 = 8.4. 8.4 is a decimal, drop this branch.\n   |- Pick two numbers (59, 7) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 7 = 66. Add 66 to the number set. Current number set: [66, 7], target: 28, just two numbers left.\n     |- Try 66 + 7 = 73. Evaluate 73 != 28, drop this branch.\n     |- Try 66 - 7 = 59. Evaluate 59 != 28, drop this branch.\n     |- Try 66 * 7 = 462. Evaluate 462 != 28, drop this branch.\n     |- Try 66 \/ 7 = 9.4. 9.4 is a decimal, drop this branch.\n    |- Try 59 - 7 = 52. Add 52 to the number set. Current number set: [52, 7], target: 28, just two numbers left.\n     |- Try 52 + 7 = 59. Evaluate 59 != 28, drop this branch.\n     |- Try 52 - 7 = 45. Evaluate 45 != 28, drop this branch.\n     |- Try 52 * 7 = 364. Evaluate 364 != 28, drop this branch.\n     |- Try 52 \/ 7 = 7.4. 7.4 is a decimal, drop this branch.\n    |- Try 59 * 7 = 413. Add 413 to the number set. Current number set: [413, 7], target: 28, just two numbers left.\n     |- Try 413 + 7 = 420. Evaluate 420 != 28, drop this branch.\n     |- Try 413 - 7 = 406. Evaluate 406 != 28, drop this branch.\n     |- Try 413 * 7 = 2891. 2891 exceeds the maximum intermediate result, drop this branch.\n     |- Try 413 \/ 7 = 59. Evaluate 59 != 28, drop this branch.\n    |- Try 59 \/ 7 = 8.4. 8.4 is a decimal, drop this branch.\n   |- Pick two numbers (7, 7) (numbers left: [59]). Try possible operations.\n    |- Try 7 + 7 = 14. Add 14 to the number set. Current number set: [14, 59], target: 28, just two numbers left.\n     |- Try 59 + 14 = 73. Evaluate 73 != 28, drop this branch.\n     |- Try 59 - 14 = 45. Evaluate 45 != 28, drop this branch.\n     |- Try 59 * 14 = 826. Evaluate 826 != 28, drop this branch.\n     |- Try 59 \/ 14 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 7 - 7 = 0. Add 0 to the number set. Current number set: [0, 59], target: 28, just two numbers left.\n     |- Try 59 + 0 = 59. Evaluate 59 != 28, drop this branch.\n     |- Try 59 - 0 = 59. Evaluate 59 != 28, drop this branch.\n     |- Try 59 * 0 = 0. Evaluate 0 != 28, drop this branch.\n     |- Try 59 \/ 0 (invalid operation). drop this branch.\n    |- Try 7 * 7 = 49. Add 49 to the number set. Current number set: [49, 59], target: 28, just two numbers left.\n     |- Try 59 + 49 = 108. Evaluate 108 != 28, drop this branch.\n     |- Try 59 - 49 = 10. Evaluate 10 != 28, drop this branch.\n     |- Try 59 * 49 = 2891. 2891 exceeds the maximum intermediate result, drop this branch.\n     |- Try 59 \/ 49 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 7 \/ 7 = 1. Add 1 to the number set. Current number set: [1, 59], target: 28, just two numbers left.\n     |- Try 59 + 1 = 60. Evaluate 60 != 28, drop this branch.\n     |- Try 59 - 1 = 58. Evaluate 58 != 28, drop this branch.\n     |- Try 59 * 1 = 59. Evaluate 59 != 28, drop this branch.\n     |- Try 59 \/ 1 = 59. Evaluate 59 != 28, drop this branch.\n  |- Try 49 - 10 = 39. Add 39 to the number set. Current number set: [39, 7, 7], target: 28. Options for choosing two numbers: [(39, 7), (39, 7), (7, 7)].\n   |- Pick two numbers (39, 7) (numbers left: [7]). Try possible operations.\n    |- Try 39 + 7 = 46. Add 46 to the number set. Current number set: [46, 7], target: 28, just two numbers left.\n     |- Try 46 + 7 = 53. Evaluate 53 != 28, drop this branch.\n     |- Try 46 - 7 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 46 * 7 = 322. Evaluate 322 != 28, drop this branch.\n     |- Try 46 \/ 7 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 39 - 7 = 32. Add 32 to the number set. Current number set: [32, 7], target: 28, just two numbers left.\n     |- Try 32 + 7 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 32 - 7 = 25. Evaluate 25 != 28, drop this branch.\n     |- Try 32 * 7 = 224. Evaluate 224 != 28, drop this branch.\n     |- Try 32 \/ 7 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 39 * 7 = 273. Add 273 to the number set. Current number set: [273, 7], target: 28, just two numbers left.\n     |- Try 273 + 7 = 280. Evaluate 280 != 28, drop this branch.\n     |- Try 273 - 7 = 266. Evaluate 266 != 28, drop this branch.\n     |- Try 273 * 7 = 1911. Evaluate 1911 != 28, drop this branch.\n     |- Try 273 \/ 7 = 39. Evaluate 39 != 28, drop this branch.\n    |- Try 39 \/ 7 = 5.6. 5.6 is a decimal, drop this branch.\n   |- Pick two numbers (39, 7) (numbers left: [7]). Try possible operations.\n    |- Try 39 + 7 = 46. Add 46 to the number set. Current number set: [46, 7], target: 28, just two numbers left.\n     |- Try 46 + 7 = 53. Evaluate 53 != 28, drop this branch.\n     |- Try 46 - 7 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 46 * 7 = 322. Evaluate 322 != 28, drop this branch.\n     |- Try 46 \/ 7 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 39 - 7 = 32. Add 32 to the number set. Current number set: [32, 7], target: 28, just two numbers left.\n     |- Try 32 + 7 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 32 - 7 = 25. Evaluate 25 != 28, drop this branch.\n     |- Try 32 * 7 = 224. Evaluate 224 != 28, drop this branch.\n     |- Try 32 \/ 7 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 39 * 7 = 273. Add 273 to the number set. Current number set: [273, 7], target: 28, just two numbers left.\n     |- Try 273 + 7 = 280. Evaluate 280 != 28, drop this branch.\n     |- Try 273 - 7 = 266. Evaluate 266 != 28, drop this branch.\n     |- Try 273 * 7 = 1911. Evaluate 1911 != 28, drop this branch.\n     |- Try 273 \/ 7 = 39. Evaluate 39 != 28, drop this branch.\n    |- Try 39 \/ 7 = 5.6. 5.6 is a decimal, drop this branch.\n   |- Pick two numbers (7, 7) (numbers left: [39]). Try possible operations.\n    |- Try 7 + 7 = 14. Add 14 to the number set. Current number set: [14, 39], target: 28, just two numbers left.\n     |- Try 39 + 14 = 53. Evaluate 53 != 28, drop this branch.\n     |- Try 39 - 14 = 25. Evaluate 25 != 28, drop this branch.\n     |- Try 39 * 14 = 546. Evaluate 546 != 28, drop this branch.\n     |- Try 39 \/ 14 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 7 - 7 = 0. Add 0 to the number set. Current number set: [0, 39], target: 28, just two numbers left.\n     |- Try 39 + 0 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 39 - 0 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 39 * 0 = 0. Evaluate 0 != 28, drop this branch.\n     |- Try 39 \/ 0 (invalid operation). drop this branch.\n    |- Try 7 * 7 = 49. Add 49 to the number set. Current number set: [49, 39], target: 28, just two numbers left.\n     |- Try 49 + 39 = 88. Evaluate 88 != 28, drop this branch.\n     |- Try 49 - 39 = 10. Evaluate 10 != 28, drop this branch.\n     |- Try 49 * 39 = 1911. Evaluate 1911 != 28, drop this branch.\n     |- Try 49 \/ 39 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 7 \/ 7 = 1. Add 1 to the number set. Current number set: [1, 39], target: 28, just two numbers left.\n     |- Try 39 + 1 = 40. Evaluate 40 != 28, drop this branch.\n     |- Try 39 - 1 = 38. Evaluate 38 != 28, drop this branch.\n     |- Try 39 * 1 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 39 \/ 1 = 39. Evaluate 39 != 28, drop this branch.\n  |- Try 49 * 10 = 490. Add 490 to the number set. Current number set: [490, 7, 7], target: 28. Options for choosing two numbers: [(490, 7), (490, 7), (7, 7)].\n   |- Pick two numbers (490, 7) (numbers left: [7]). Try possible operations.\n    |- Try 490 + 7 = 497. Add 497 to the number set. Current number set: [497, 7], target: 28, just two numbers left.\n     |- Try 497 + 7 = 504. Evaluate 504 != 28, drop this branch.\n     |- Try 497 - 7 = 490. Evaluate 490 != 28, drop this branch.\n     |- Try 497 * 7 = 3479. 3479 exceeds the maximum intermediate result, drop this branch.\n     |- Try 497 \/ 7 = 71. Evaluate 71 != 28, drop this branch.\n    |- Try 490 - 7 = 483. Add 483 to the number set. Current number set: [483, 7], target: 28, just two numbers left.\n     |- Try 483 + 7 = 490. Evaluate 490 != 28, drop this branch.\n     |- Try 483 - 7 = 476. Evaluate 476 != 28, drop this branch.\n     |- Try 483 * 7 = 3381. 3381 exceeds the maximum intermediate result, drop this branch.\n     |- Try 483 \/ 7 = 69. Evaluate 69 != 28, drop this branch.\n    |- Try 490 * 7 = 3430. 3430 exceeds the maximum intermediate result, drop this branch.\n    |- Try 490 \/ 7 = 70. Add 70 to the number set. Current number set: [70, 7], target: 28, just two numbers left.\n     |- Try 70 + 7 = 77. Evaluate 77 != 28, drop this branch.\n     |- Try 70 - 7 = 63. Evaluate 63 != 28, drop this branch.\n     |- Try 70 * 7 = 490. Evaluate 490 != 28, drop this branch.\n     |- Try 70 \/ 7 = 10. Evaluate 10 != 28, drop this branch.\n   |- Pick two numbers (490, 7) (numbers left: [7]). Try possible operations.\n    |- Try 490 + 7 = 497. Add 497 to the number set. Current number set: [497, 7], target: 28, just two numbers left.\n     |- Try 497 + 7 = 504. Evaluate 504 != 28, drop this branch.\n     |- Try 497 - 7 = 490. Evaluate 490 != 28, drop this branch.\n     |- Try 497 * 7 = 3479. 3479 exceeds the maximum intermediate result, drop this branch.\n     |- Try 497 \/ 7 = 71. Evaluate 71 != 28, drop this branch.\n    |- Try 490 - 7 = 483. Add 483 to the number set. Current number set: [483, 7], target: 28, just two numbers left.\n     |- Try 483 + 7 = 490. Evaluate 490 != 28, drop this branch.\n     |- Try 483 - 7 = 476. Evaluate 476 != 28, drop this branch.\n     |- Try 483 * 7 = 3381. 3381 exceeds the maximum intermediate result, drop this branch.\n     |- Try 483 \/ 7 = 69. Evaluate 69 != 28, drop this branch.\n    |- Try 490 * 7 = 3430. 3430 exceeds the maximum intermediate result, drop this branch.\n    |- Try 490 \/ 7 = 70. Add 70 to the number set. Current number set: [70, 7], target: 28, just two numbers left.\n     |- Try 70 + 7 = 77. Evaluate 77 != 28, drop this branch.\n     |- Try 70 - 7 = 63. Evaluate 63 != 28, drop this branch.\n     |- Try 70 * 7 = 490. Evaluate 490 != 28, drop this branch.\n     |- Try 70 \/ 7 = 10. Evaluate 10 != 28, drop this branch.\n   |- Pick two numbers (7, 7) (numbers left: [490]). Try possible operations.\n    |- Try 7 + 7 = 14. Add 14 to the number set. Current number set: [14, 490], target: 28, just two numbers left.\n     |- Try 490 + 14 = 504. Evaluate 504 != 28, drop this branch.\n     |- Try 490 - 14 = 476. Evaluate 476 != 28, drop this branch.\n     |- Try 490 * 14 = 6860. 6860 exceeds the maximum intermediate result, drop this branch.\n     |- Try 490 \/ 14 = 35. Evaluate 35 != 28, drop this branch.\n    |- Try 7 - 7 = 0. Add 0 to the number set. Current number set: [0, 490], target: 28, just two numbers left.\n     |- Try 490 + 0 = 490. Evaluate 490 != 28, drop this branch.\n     |- Try 490 - 0 = 490. Evaluate 490 != 28, drop this branch.\n     |- Try 490 * 0 = 0. Evaluate 0 != 28, drop this branch.\n     |- Try 490 \/ 0 (invalid operation). drop this branch.\n    |- Try 7 * 7 = 49. Add 49 to the number set. Current number set: [49, 490], target: 28, just two numbers left.\n     |- Try 490 + 49 = 539. Evaluate 539 != 28, drop this branch.\n     |- Try 490 - 49 = 441. Evaluate 441 != 28, drop this branch.\n     |- Try 490 * 49 = 24010. 24010 exceeds the maximum intermediate result, drop this branch.\n     |- Try 490 \/ 49 = 10. Evaluate 10 != 28, drop this branch.\n    |- Try 7 \/ 7 = 1. Add 1 to the number set. Current number set: [1, 490], target: 28, just two numbers left.\n     |- Try 490 + 1 = 491. Evaluate 491 != 28, drop this branch.\n     |- Try 490 - 1 = 489. Evaluate 489 != 28, drop this branch.\n     |- Try 490 * 1 = 490. Evaluate 490 != 28, drop this branch.\n     |- Try 490 \/ 1 = 490. Evaluate 490 != 28, drop this branch.\n  |- Try 49 \/ 10 = 4.9. 4.9 is a decimal, drop this branch.\n |- Pick two numbers (49, 7) (numbers left: [10, 7]). Try possible operations.\n  |- Try 49 + 7 = 56. Add 56 to the number set. Current number set: [56, 10, 7], target: 28. Options for choosing two numbers: [(56, 10), (56, 7), (10, 7)].\n   |- Pick two numbers (56, 10) (numbers left: [7]). Try possible operations.\n    |- Try 56 + 10 = 66. Add 66 to the number set. Current number set: [66, 7], target: 28, just two numbers left.\n     |- Try 66 + 7 = 73. Evaluate 73 != 28, drop this branch.\n     |- Try 66 - 7 = 59. Evaluate 59 != 28, drop this branch.\n     |- Try 66 * 7 = 462. Evaluate 462 != 28, drop this branch.\n     |- Try 66 \/ 7 = 9.4. 9.4 is a decimal, drop this branch.\n    |- Try 56 - 10 = 46. Add 46 to the number set. Current number set: [46, 7], target: 28, just two numbers left.\n     |- Try 46 + 7 = 53. Evaluate 53 != 28, drop this branch.\n     |- Try 46 - 7 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 46 * 7 = 322. Evaluate 322 != 28, drop this branch.\n     |- Try 46 \/ 7 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 56 * 10 = 560. Add 560 to the number set. Current number set: [560, 7], target: 28, just two numbers left.\n     |- Try 560 + 7 = 567. Evaluate 567 != 28, drop this branch.\n     |- Try 560 - 7 = 553. Evaluate 553 != 28, drop this branch.\n     |- Try 560 * 7 = 3920. 3920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 560 \/ 7 = 80. Evaluate 80 != 28, drop this branch.\n    |- Try 56 \/ 10 = 5.6. 5.6 is a decimal, drop this branch.\n   |- Pick two numbers (56, 7) (numbers left: [10]). Try possible operations.\n    |- Try 56 + 7 = 63. Add 63 to the number set. Current number set: [63, 10], target: 28, just two numbers left.\n     |- Try 63 + 10 = 73. Evaluate 73 != 28, drop this branch.\n     |- Try 63 - 10 = 53. Evaluate 53 != 28, drop this branch.\n     |- Try 63 * 10 = 630. Evaluate 630 != 28, drop this branch.\n     |- Try 63 \/ 10 = 6.3. 6.3 is a decimal, drop this branch.\n    |- Try 56 - 7 = 49. Add 49 to the number set. Current number set: [49, 10], target: 28, just two numbers left.\n     |- Try 49 + 10 = 59. Evaluate 59 != 28, drop this branch.\n     |- Try 49 - 10 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 49 * 10 = 490. Evaluate 490 != 28, drop this branch.\n     |- Try 49 \/ 10 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 56 * 7 = 392. Add 392 to the number set. Current number set: [392, 10], target: 28, just two numbers left.\n     |- Try 392 + 10 = 402. Evaluate 402 != 28, drop this branch.\n     |- Try 392 - 10 = 382. Evaluate 382 != 28, drop this branch.\n     |- Try 392 * 10 = 3920. 3920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 392 \/ 10 = 39.2. 39.2 is a decimal, drop this branch.\n    |- Try 56 \/ 7 = 8. Add 8 to the number set. Current number set: [8, 10], target: 28, just two numbers left.\n     |- Try 10 + 8 = 18. Evaluate 18 != 28, drop this branch.\n     |- Try 10 - 8 = 2. Evaluate 2 != 28, drop this branch.\n     |- Try 10 * 8 = 80. Evaluate 80 != 28, drop this branch.\n     |- Try 10 \/ 8 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (10, 7) (numbers left: [56]). Try possible operations.\n    |- Try 10 + 7 = 17. Add 17 to the number set. Current number set: [17, 56], target: 28, just two numbers left.\n     |- Try 56 + 17 = 73. Evaluate 73 != 28, drop this branch.\n     |- Try 56 - 17 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 56 * 17 = 952. Evaluate 952 != 28, drop this branch.\n     |- Try 56 \/ 17 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 10 - 7 = 3. Add 3 to the number set. Current number set: [3, 56], target: 28, just two numbers left.\n     |- Try 56 + 3 = 59. Evaluate 59 != 28, drop this branch.\n     |- Try 56 - 3 = 53. Evaluate 53 != 28, drop this branch.\n     |- Try 56 * 3 = 168. Evaluate 168 != 28, drop this branch.\n     |- Try 56 \/ 3 = 18.7. 18.7 is a decimal, drop this branch.\n    |- Try 10 * 7 = 70. Add 70 to the number set. Current number set: [70, 56], target: 28, just two numbers left.\n     |- Try 70 + 56 = 126. Evaluate 126 != 28, drop this branch.\n     |- Try 70 - 56 = 14. Evaluate 14 != 28, drop this branch.\n     |- Try 70 * 56 = 3920. 3920 exceeds the maximum intermediate result, drop this branch.\n     |- Try 70 \/ 56 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 10 \/ 7 = 1.4. 1.4 is a decimal, drop this branch.\n  |- Try 49 - 7 = 42. Add 42 to the number set. Current number set: [42, 10, 7], target: 28. Options for choosing two numbers: [(42, 10), (42, 7), (10, 7)].\n   |- Pick two numbers (42, 10) (numbers left: [7]). Try possible operations.\n    |- Try 42 + 10 = 52. Add 52 to the number set. Current number set: [52, 7], target: 28, just two numbers left.\n     |- Try 52 + 7 = 59. Evaluate 59 != 28, drop this branch.\n     |- Try 52 - 7 = 45. Evaluate 45 != 28, drop this branch.\n     |- Try 52 * 7 = 364. Evaluate 364 != 28, drop this branch.\n     |- Try 52 \/ 7 = 7.4. 7.4 is a decimal, drop this branch.\n    |- Try 42 - 10 = 32. Add 32 to the number set. Current number set: [32, 7], target: 28, just two numbers left.\n     |- Try 32 + 7 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 32 - 7 = 25. Evaluate 25 != 28, drop this branch.\n     |- Try 32 * 7 = 224. Evaluate 224 != 28, drop this branch.\n     |- Try 32 \/ 7 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 42 * 10 = 420. Add 420 to the number set. Current number set: [420, 7], target: 28, just two numbers left.\n     |- Try 420 + 7 = 427. Evaluate 427 != 28, drop this branch.\n     |- Try 420 - 7 = 413. Evaluate 413 != 28, drop this branch.\n     |- Try 420 * 7 = 2940. 2940 exceeds the maximum intermediate result, drop this branch.\n     |- Try 420 \/ 7 = 60. Evaluate 60 != 28, drop this branch.\n    |- Try 42 \/ 10 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (42, 7) (numbers left: [10]). Try possible operations.\n    |- Try 42 + 7 = 49. Add 49 to the number set. Current number set: [49, 10], target: 28, just two numbers left.\n     |- Try 49 + 10 = 59. Evaluate 59 != 28, drop this branch.\n     |- Try 49 - 10 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 49 * 10 = 490. Evaluate 490 != 28, drop this branch.\n     |- Try 49 \/ 10 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 42 - 7 = 35. Add 35 to the number set. Current number set: [35, 10], target: 28, just two numbers left.\n     |- Try 35 + 10 = 45. Evaluate 45 != 28, drop this branch.\n     |- Try 35 - 10 = 25. Evaluate 25 != 28, drop this branch.\n     |- Try 35 * 10 = 350. Evaluate 350 != 28, drop this branch.\n     |- Try 35 \/ 10 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 42 * 7 = 294. Add 294 to the number set. Current number set: [294, 10], target: 28, just two numbers left.\n     |- Try 294 + 10 = 304. Evaluate 304 != 28, drop this branch.\n     |- Try 294 - 10 = 284. Evaluate 284 != 28, drop this branch.\n     |- Try 294 * 10 = 2940. 2940 exceeds the maximum intermediate result, drop this branch.\n     |- Try 294 \/ 10 = 29.4. 29.4 is a decimal, drop this branch.\n    |- Try 42 \/ 7 = 6. Add 6 to the number set. Current number set: [6, 10], target: 28, just two numbers left.\n     |- Try 10 + 6 = 16. Evaluate 16 != 28, drop this branch.\n     |- Try 10 - 6 = 4. Evaluate 4 != 28, drop this branch.\n     |- Try 10 * 6 = 60. Evaluate 60 != 28, drop this branch.\n     |- Try 10 \/ 6 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (10, 7) (numbers left: [42]). Try possible operations.\n    |- Try 10 + 7 = 17. Add 17 to the number set. Current number set: [17, 42], target: 28, just two numbers left.\n     |- Try 42 + 17 = 59. Evaluate 59 != 28, drop this branch.\n     |- Try 42 - 17 = 25. Evaluate 25 != 28, drop this branch.\n     |- Try 42 * 17 = 714. Evaluate 714 != 28, drop this branch.\n     |- Try 42 \/ 17 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 10 - 7 = 3. Add 3 to the number set. Current number set: [3, 42], target: 28, just two numbers left.\n     |- Try 42 + 3 = 45. Evaluate 45 != 28, drop this branch.\n     |- Try 42 - 3 = 39. Evaluate 39 != 28, drop this branch.\n     |- Try 42 * 3 = 126. Evaluate 126 != 28, drop this branch.\n     |- Try 42 \/ 3 = 14. Evaluate 14 != 28, drop this branch.\n    |- Try 10 * 7 = 70. Add 70 to the number set. Current number set: [70, 42], target: 28, just two numbers left.\n     |- Try 70 + 42 = 112. Evaluate 112 != 28, drop this branch.\n     |- Try 70 - 42 = 28. Evaluate 28 == 28, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 70 - 42 = 28\nThe step before: 10 * 7 = 70\nThe first step: 49 - 7 = 42\n\nOutput the solution in the required format:\n<Solution>\n49 - 7 = 42\n10 * 7 = 70\n70 - 42 = 28\n<\/Solution>\n","item":{"nums":[49,10,7,7],"solution":["49 - 7 = 42","10 * 7 = 70","70 - 42 = 28"],"target":28}}
+{"instance_id":"countdown_8k_170","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [23, 32, 2, 16]\nTarget: 19","reference_output":"# Search Procedure\nInitial number set: [23, 32, 2, 16], target: 19. Options for choosing two numbers: [(23, 32), (23, 2), (23, 16), (32, 2), (32, 16), (2, 16)].\n |- Pick two numbers (23, 32) (numbers left: [2, 16]). Try possible operations.\n  |- Try 32 + 23 = 55. Add 55 to the number set. Current number set: [55, 2, 16], target: 19. Options for choosing two numbers: [(55, 2), (55, 16), (2, 16)].\n   |- Pick two numbers (55, 2) (numbers left: [16]). Try possible operations.\n    |- Try 55 + 2 = 57. Add 57 to the number set. Current number set: [57, 16], target: 19, just two numbers left.\n     |- Try 57 + 16 = 73. Evaluate 73 != 19, drop this branch.\n     |- Try 57 - 16 = 41. Evaluate 41 != 19, drop this branch.\n     |- Try 57 * 16 = 912. Evaluate 912 != 19, drop this branch.\n     |- Try 57 \/ 16 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 55 - 2 = 53. Add 53 to the number set. Current number set: [53, 16], target: 19, just two numbers left.\n     |- Try 53 + 16 = 69. Evaluate 69 != 19, drop this branch.\n     |- Try 53 - 16 = 37. Evaluate 37 != 19, drop this branch.\n     |- Try 53 * 16 = 848. Evaluate 848 != 19, drop this branch.\n     |- Try 53 \/ 16 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 55 * 2 = 110. Add 110 to the number set. Current number set: [110, 16], target: 19, just two numbers left.\n     |- Try 110 + 16 = 126. Evaluate 126 != 19, drop this branch.\n     |- Try 110 - 16 = 94. Evaluate 94 != 19, drop this branch.\n     |- Try 110 * 16 = 1760. Evaluate 1760 != 19, drop this branch.\n     |- Try 110 \/ 16 = 6.9. 6.9 is a decimal, drop this branch.\n    |- Try 55 \/ 2 = 27.5. 27.5 is a decimal, drop this branch.\n   |- Pick two numbers (55, 16) (numbers left: [2]). Try possible operations.\n    |- Try 55 + 16 = 71. Add 71 to the number set. Current number set: [71, 2], target: 19, just two numbers left.\n     |- Try 71 + 2 = 73. Evaluate 73 != 19, drop this branch.\n     |- Try 71 - 2 = 69. Evaluate 69 != 19, drop this branch.\n     |- Try 71 * 2 = 142. Evaluate 142 != 19, drop this branch.\n     |- Try 71 \/ 2 = 35.5. 35.5 is a decimal, drop this branch.\n    |- Try 55 - 16 = 39. Add 39 to the number set. Current number set: [39, 2], target: 19, just two numbers left.\n     |- Try 39 + 2 = 41. Evaluate 41 != 19, drop this branch.\n     |- Try 39 - 2 = 37. Evaluate 37 != 19, drop this branch.\n     |- Try 39 * 2 = 78. Evaluate 78 != 19, drop this branch.\n     |- Try 39 \/ 2 = 19.5. 19.5 is a decimal, drop this branch.\n    |- Try 55 * 16 = 880. Add 880 to the number set. Current number set: [880, 2], target: 19, just two numbers left.\n     |- Try 880 + 2 = 882. Evaluate 882 != 19, drop this branch.\n     |- Try 880 - 2 = 878. Evaluate 878 != 19, drop this branch.\n     |- Try 880 * 2 = 1760. Evaluate 1760 != 19, drop this branch.\n     |- Try 880 \/ 2 = 440. Evaluate 440 != 19, drop this branch.\n    |- Try 55 \/ 16 = 3.4. 3.4 is a decimal, drop this branch.\n   |- Pick two numbers (2, 16) (numbers left: [55]). Try possible operations.\n    |- Try 16 + 2 = 18. Add 18 to the number set. Current number set: [18, 55], target: 19, just two numbers left.\n     |- Try 55 + 18 = 73. Evaluate 73 != 19, drop this branch.\n     |- Try 55 - 18 = 37. Evaluate 37 != 19, drop this branch.\n     |- Try 55 * 18 = 990. Evaluate 990 != 19, drop this branch.\n     |- Try 55 \/ 18 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 16 - 2 = 14. Add 14 to the number set. Current number set: [14, 55], target: 19, just two numbers left.\n     |- Try 55 + 14 = 69. Evaluate 69 != 19, drop this branch.\n     |- Try 55 - 14 = 41. Evaluate 41 != 19, drop this branch.\n     |- Try 55 * 14 = 770. Evaluate 770 != 19, drop this branch.\n     |- Try 55 \/ 14 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 16 * 2 = 32. Add 32 to the number set. Current number set: [32, 55], target: 19, just two numbers left.\n     |- Try 55 + 32 = 87. Evaluate 87 != 19, drop this branch.\n     |- Try 55 - 32 = 23. Evaluate 23 != 19, drop this branch.\n     |- Try 55 * 32 = 1760. Evaluate 1760 != 19, drop this branch.\n     |- Try 55 \/ 32 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 16 \/ 2 = 8. Add 8 to the number set. Current number set: [8, 55], target: 19, just two numbers left.\n     |- Try 55 + 8 = 63. Evaluate 63 != 19, drop this branch.\n     |- Try 55 - 8 = 47. Evaluate 47 != 19, drop this branch.\n     |- Try 55 * 8 = 440. Evaluate 440 != 19, drop this branch.\n     |- Try 55 \/ 8 = 6.9. 6.9 is a decimal, drop this branch.\n  |- Try 32 - 23 = 9. Add 9 to the number set. Current number set: [9, 2, 16], target: 19. Options for choosing two numbers: [(9, 2), (9, 16), (2, 16)].\n   |- Pick two numbers (9, 2) (numbers left: [16]). Try possible operations.\n    |- Try 9 + 2 = 11. Add 11 to the number set. Current number set: [11, 16], target: 19, just two numbers left.\n     |- Try 16 + 11 = 27. Evaluate 27 != 19, drop this branch.\n     |- Try 16 - 11 = 5. Evaluate 5 != 19, drop this branch.\n     |- Try 16 * 11 = 176. Evaluate 176 != 19, drop this branch.\n     |- Try 16 \/ 11 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 9 - 2 = 7. Add 7 to the number set. Current number set: [7, 16], target: 19, just two numbers left.\n     |- Try 16 + 7 = 23. Evaluate 23 != 19, drop this branch.\n     |- Try 16 - 7 = 9. Evaluate 9 != 19, drop this branch.\n     |- Try 16 * 7 = 112. Evaluate 112 != 19, drop this branch.\n     |- Try 16 \/ 7 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 9 * 2 = 18. Add 18 to the number set. Current number set: [18, 16], target: 19, just two numbers left.\n     |- Try 18 + 16 = 34. Evaluate 34 != 19, drop this branch.\n     |- Try 18 - 16 = 2. Evaluate 2 != 19, drop this branch.\n     |- Try 18 * 16 = 288. Evaluate 288 != 19, drop this branch.\n     |- Try 18 \/ 16 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 9 \/ 2 = 4.5. 4.5 is a decimal, drop this branch.\n   |- Pick two numbers (9, 16) (numbers left: [2]). Try possible operations.\n    |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 2], target: 19, just two numbers left.\n     |- Try 25 + 2 = 27. Evaluate 27 != 19, drop this branch.\n     |- Try 25 - 2 = 23. Evaluate 23 != 19, drop this branch.\n     |- Try 25 * 2 = 50. Evaluate 50 != 19, drop this branch.\n     |- Try 25 \/ 2 = 12.5. 12.5 is a decimal, drop this branch.\n    |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 2], target: 19, just two numbers left.\n     |- Try 7 + 2 = 9. Evaluate 9 != 19, drop this branch.\n     |- Try 7 - 2 = 5. Evaluate 5 != 19, drop this branch.\n     |- Try 7 * 2 = 14. Evaluate 14 != 19, drop this branch.\n     |- Try 7 \/ 2 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 2], target: 19, just two numbers left.\n     |- Try 144 + 2 = 146. Evaluate 146 != 19, drop this branch.\n     |- Try 144 - 2 = 142. Evaluate 142 != 19, drop this branch.\n     |- Try 144 * 2 = 288. Evaluate 288 != 19, drop this branch.\n     |- Try 144 \/ 2 = 72. Evaluate 72 != 19, drop this branch.\n    |- Try 16 \/ 9 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (2, 16) (numbers left: [9]). Try possible operations.\n    |- Try 16 + 2 = 18. Add 18 to the number set. Current number set: [18, 9], target: 19, just two numbers left.\n     |- Try 18 + 9 = 27. Evaluate 27 != 19, drop this branch.\n     |- Try 18 - 9 = 9. Evaluate 9 != 19, drop this branch.\n     |- Try 18 * 9 = 162. Evaluate 162 != 19, drop this branch.\n     |- Try 18 \/ 9 = 2. Evaluate 2 != 19, drop this branch.\n    |- Try 16 - 2 = 14. Add 14 to the number set. Current number set: [14, 9], target: 19, just two numbers left.\n     |- Try 14 + 9 = 23. Evaluate 23 != 19, drop this branch.\n     |- Try 14 - 9 = 5. Evaluate 5 != 19, drop this branch.\n     |- Try 14 * 9 = 126. Evaluate 126 != 19, drop this branch.\n     |- Try 14 \/ 9 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 16 * 2 = 32. Add 32 to the number set. Current number set: [32, 9], target: 19, just two numbers left.\n     |- Try 32 + 9 = 41. Evaluate 41 != 19, drop this branch.\n     |- Try 32 - 9 = 23. Evaluate 23 != 19, drop this branch.\n     |- Try 32 * 9 = 288. Evaluate 288 != 19, drop this branch.\n     |- Try 32 \/ 9 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 16 \/ 2 = 8. Add 8 to the number set. Current number set: [8, 9], target: 19, just two numbers left.\n     |- Try 9 + 8 = 17. Evaluate 17 != 19, drop this branch.\n     |- Try 9 - 8 = 1. Evaluate 1 != 19, drop this branch.\n     |- Try 9 * 8 = 72. Evaluate 72 != 19, drop this branch.\n     |- Try 9 \/ 8 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 32 * 23 = 736. Add 736 to the number set. Current number set: [736, 2, 16], target: 19. Options for choosing two numbers: [(736, 2), (736, 16), (2, 16)].\n   |- Pick two numbers (736, 2) (numbers left: [16]). Try possible operations.\n    |- Try 736 + 2 = 738. Add 738 to the number set. Current number set: [738, 16], target: 19, just two numbers left.\n     |- Try 738 + 16 = 754. Evaluate 754 != 19, drop this branch.\n     |- Try 738 - 16 = 722. Evaluate 722 != 19, drop this branch.\n     |- Try 738 * 16 = 11808. 11808 exceeds the maximum intermediate result, drop this branch.\n     |- Try 738 \/ 16 = 46.1. 46.1 is a decimal, drop this branch.\n    |- Try 736 - 2 = 734. Add 734 to the number set. Current number set: [734, 16], target: 19, just two numbers left.\n     |- Try 734 + 16 = 750. Evaluate 750 != 19, drop this branch.\n     |- Try 734 - 16 = 718. Evaluate 718 != 19, drop this branch.\n     |- Try 734 * 16 = 11744. 11744 exceeds the maximum intermediate result, drop this branch.\n     |- Try 734 \/ 16 = 45.9. 45.9 is a decimal, drop this branch.\n    |- Try 736 * 2 = 1472. Add 1472 to the number set. Current number set: [1472, 16], target: 19, just two numbers left.\n     |- Try 1472 + 16 = 1488. Evaluate 1488 != 19, drop this branch.\n     |- Try 1472 - 16 = 1456. Evaluate 1456 != 19, drop this branch.\n     |- Try 1472 * 16 = 23552. 23552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1472 \/ 16 = 92. Evaluate 92 != 19, drop this branch.\n    |- Try 736 \/ 2 = 368. Add 368 to the number set. Current number set: [368, 16], target: 19, just two numbers left.\n     |- Try 368 + 16 = 384. Evaluate 384 != 19, drop this branch.\n     |- Try 368 - 16 = 352. Evaluate 352 != 19, drop this branch.\n     |- Try 368 * 16 = 5888. 5888 exceeds the maximum intermediate result, drop this branch.\n     |- Try 368 \/ 16 = 23. Evaluate 23 != 19, drop this branch.\n   |- Pick two numbers (736, 16) (numbers left: [2]). Try possible operations.\n    |- Try 736 + 16 = 752. Add 752 to the number set. Current number set: [752, 2], target: 19, just two numbers left.\n     |- Try 752 + 2 = 754. Evaluate 754 != 19, drop this branch.\n     |- Try 752 - 2 = 750. Evaluate 750 != 19, drop this branch.\n     |- Try 752 * 2 = 1504. Evaluate 1504 != 19, drop this branch.\n     |- Try 752 \/ 2 = 376. Evaluate 376 != 19, drop this branch.\n    |- Try 736 - 16 = 720. Add 720 to the number set. Current number set: [720, 2], target: 19, just two numbers left.\n     |- Try 720 + 2 = 722. Evaluate 722 != 19, drop this branch.\n     |- Try 720 - 2 = 718. Evaluate 718 != 19, drop this branch.\n     |- Try 720 * 2 = 1440. Evaluate 1440 != 19, drop this branch.\n     |- Try 720 \/ 2 = 360. Evaluate 360 != 19, drop this branch.\n    |- Try 736 * 16 = 11776. 11776 exceeds the maximum intermediate result, drop this branch.\n    |- Try 736 \/ 16 = 46. Add 46 to the number set. Current number set: [46, 2], target: 19, just two numbers left.\n     |- Try 46 + 2 = 48. Evaluate 48 != 19, drop this branch.\n     |- Try 46 - 2 = 44. Evaluate 44 != 19, drop this branch.\n     |- Try 46 * 2 = 92. Evaluate 92 != 19, drop this branch.\n     |- Try 46 \/ 2 = 23. Evaluate 23 != 19, drop this branch.\n   |- Pick two numbers (2, 16) (numbers left: [736]). Try possible operations.\n    |- Try 16 + 2 = 18. Add 18 to the number set. Current number set: [18, 736], target: 19, just two numbers left.\n     |- Try 736 + 18 = 754. Evaluate 754 != 19, drop this branch.\n     |- Try 736 - 18 = 718. Evaluate 718 != 19, drop this branch.\n     |- Try 736 * 18 = 13248. 13248 exceeds the maximum intermediate result, drop this branch.\n     |- Try 736 \/ 18 = 40.9. 40.9 is a decimal, drop this branch.\n    |- Try 16 - 2 = 14. Add 14 to the number set. Current number set: [14, 736], target: 19, just two numbers left.\n     |- Try 736 + 14 = 750. Evaluate 750 != 19, drop this branch.\n     |- Try 736 - 14 = 722. Evaluate 722 != 19, drop this branch.\n     |- Try 736 * 14 = 10304. 10304 exceeds the maximum intermediate result, drop this branch.\n     |- Try 736 \/ 14 = 52.6. 52.6 is a decimal, drop this branch.\n    |- Try 16 * 2 = 32. Add 32 to the number set. Current number set: [32, 736], target: 19, just two numbers left.\n     |- Try 736 + 32 = 768. Evaluate 768 != 19, drop this branch.\n     |- Try 736 - 32 = 704. Evaluate 704 != 19, drop this branch.\n     |- Try 736 * 32 = 23552. 23552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 736 \/ 32 = 23. Evaluate 23 != 19, drop this branch.\n    |- Try 16 \/ 2 = 8. Add 8 to the number set. Current number set: [8, 736], target: 19, just two numbers left.\n     |- Try 736 + 8 = 744. Evaluate 744 != 19, drop this branch.\n     |- Try 736 - 8 = 728. Evaluate 728 != 19, drop this branch.\n     |- Try 736 * 8 = 5888. 5888 exceeds the maximum intermediate result, drop this branch.\n     |- Try 736 \/ 8 = 92. Evaluate 92 != 19, drop this branch.\n  |- Try 32 \/ 23 = 1.4. 1.4 is a decimal, drop this branch.\n |- Pick two numbers (23, 2) (numbers left: [32, 16]). Try possible operations.\n  |- Try 23 + 2 = 25. Add 25 to the number set. Current number set: [25, 32, 16], target: 19. Options for choosing two numbers: [(25, 32), (25, 16), (32, 16)].\n   |- Pick two numbers (25, 32) (numbers left: [16]). Try possible operations.\n    |- Try 32 + 25 = 57. Add 57 to the number set. Current number set: [57, 16], target: 19, just two numbers left.\n     |- Try 57 + 16 = 73. Evaluate 73 != 19, drop this branch.\n     |- Try 57 - 16 = 41. Evaluate 41 != 19, drop this branch.\n     |- Try 57 * 16 = 912. Evaluate 912 != 19, drop this branch.\n     |- Try 57 \/ 16 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 32 - 25 = 7. Add 7 to the number set. Current number set: [7, 16], target: 19, just two numbers left.\n     |- Try 16 + 7 = 23. Evaluate 23 != 19, drop this branch.\n     |- Try 16 - 7 = 9. Evaluate 9 != 19, drop this branch.\n     |- Try 16 * 7 = 112. Evaluate 112 != 19, drop this branch.\n     |- Try 16 \/ 7 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 32 * 25 = 800. Add 800 to the number set. Current number set: [800, 16], target: 19, just two numbers left.\n     |- Try 800 + 16 = 816. Evaluate 816 != 19, drop this branch.\n     |- Try 800 - 16 = 784. Evaluate 784 != 19, drop this branch.\n     |- Try 800 * 16 = 12800. 12800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 800 \/ 16 = 50. Evaluate 50 != 19, drop this branch.\n    |- Try 32 \/ 25 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (25, 16) (numbers left: [32]). Try possible operations.\n    |- Try 25 + 16 = 41. Add 41 to the number set. Current number set: [41, 32], target: 19, just two numbers left.\n     |- Try 41 + 32 = 73. Evaluate 73 != 19, drop this branch.\n     |- Try 41 - 32 = 9. Evaluate 9 != 19, drop this branch.\n     |- Try 41 * 32 = 1312. Evaluate 1312 != 19, drop this branch.\n     |- Try 41 \/ 32 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 25 - 16 = 9. Add 9 to the number set. Current number set: [9, 32], target: 19, just two numbers left.\n     |- Try 32 + 9 = 41. Evaluate 41 != 19, drop this branch.\n     |- Try 32 - 9 = 23. Evaluate 23 != 19, drop this branch.\n     |- Try 32 * 9 = 288. Evaluate 288 != 19, drop this branch.\n     |- Try 32 \/ 9 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 25 * 16 = 400. Add 400 to the number set. Current number set: [400, 32], target: 19, just two numbers left.\n     |- Try 400 + 32 = 432. Evaluate 432 != 19, drop this branch.\n     |- Try 400 - 32 = 368. Evaluate 368 != 19, drop this branch.\n     |- Try 400 * 32 = 12800. 12800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 400 \/ 32 = 12.5. 12.5 is a decimal, drop this branch.\n    |- Try 25 \/ 16 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (32, 16) (numbers left: [25]). Try possible operations.\n    |- Try 32 + 16 = 48. Add 48 to the number set. Current number set: [48, 25], target: 19, just two numbers left.\n     |- Try 48 + 25 = 73. Evaluate 73 != 19, drop this branch.\n     |- Try 48 - 25 = 23. Evaluate 23 != 19, drop this branch.\n     |- Try 48 * 25 = 1200. Evaluate 1200 != 19, drop this branch.\n     |- Try 48 \/ 25 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 32 - 16 = 16. Add 16 to the number set. Current number set: [16, 25], target: 19, just two numbers left.\n     |- Try 25 + 16 = 41. Evaluate 41 != 19, drop this branch.\n     |- Try 25 - 16 = 9. Evaluate 9 != 19, drop this branch.\n     |- Try 25 * 16 = 400. Evaluate 400 != 19, drop this branch.\n     |- Try 25 \/ 16 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 32 * 16 = 512. Add 512 to the number set. Current number set: [512, 25], target: 19, just two numbers left.\n     |- Try 512 + 25 = 537. Evaluate 537 != 19, drop this branch.\n     |- Try 512 - 25 = 487. Evaluate 487 != 19, drop this branch.\n     |- Try 512 * 25 = 12800. 12800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 512 \/ 25 = 20.5. 20.5 is a decimal, drop this branch.\n    |- Try 32 \/ 16 = 2. Add 2 to the number set. Current number set: [2, 25], target: 19, just two numbers left.\n     |- Try 25 + 2 = 27. Evaluate 27 != 19, drop this branch.\n     |- Try 25 - 2 = 23. Evaluate 23 != 19, drop this branch.\n     |- Try 25 * 2 = 50. Evaluate 50 != 19, drop this branch.\n     |- Try 25 \/ 2 = 12.5. 12.5 is a decimal, drop this branch.\n  |- Try 23 - 2 = 21. Add 21 to the number set. Current number set: [21, 32, 16], target: 19. Options for choosing two numbers: [(21, 32), (21, 16), (32, 16)].\n   |- Pick two numbers (21, 32) (numbers left: [16]). Try possible operations.\n    |- Try 32 + 21 = 53. Add 53 to the number set. Current number set: [53, 16], target: 19, just two numbers left.\n     |- Try 53 + 16 = 69. Evaluate 69 != 19, drop this branch.\n     |- Try 53 - 16 = 37. Evaluate 37 != 19, drop this branch.\n     |- Try 53 * 16 = 848. Evaluate 848 != 19, drop this branch.\n     |- Try 53 \/ 16 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 32 - 21 = 11. Add 11 to the number set. Current number set: [11, 16], target: 19, just two numbers left.\n     |- Try 16 + 11 = 27. Evaluate 27 != 19, drop this branch.\n     |- Try 16 - 11 = 5. Evaluate 5 != 19, drop this branch.\n     |- Try 16 * 11 = 176. Evaluate 176 != 19, drop this branch.\n     |- Try 16 \/ 11 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 32 * 21 = 672. Add 672 to the number set. Current number set: [672, 16], target: 19, just two numbers left.\n     |- Try 672 + 16 = 688. Evaluate 688 != 19, drop this branch.\n     |- Try 672 - 16 = 656. Evaluate 656 != 19, drop this branch.\n     |- Try 672 * 16 = 10752. 10752 exceeds the maximum intermediate result, drop this branch.\n     |- Try 672 \/ 16 = 42. Evaluate 42 != 19, drop this branch.\n    |- Try 32 \/ 21 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (21, 16) (numbers left: [32]). Try possible operations.\n    |- Try 21 + 16 = 37. Add 37 to the number set. Current number set: [37, 32], target: 19, just two numbers left.\n     |- Try 37 + 32 = 69. Evaluate 69 != 19, drop this branch.\n     |- Try 37 - 32 = 5. Evaluate 5 != 19, drop this branch.\n     |- Try 37 * 32 = 1184. Evaluate 1184 != 19, drop this branch.\n     |- Try 37 \/ 32 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 21 - 16 = 5. Add 5 to the number set. Current number set: [5, 32], target: 19, just two numbers left.\n     |- Try 32 + 5 = 37. Evaluate 37 != 19, drop this branch.\n     |- Try 32 - 5 = 27. Evaluate 27 != 19, drop this branch.\n     |- Try 32 * 5 = 160. Evaluate 160 != 19, drop this branch.\n     |- Try 32 \/ 5 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 21 * 16 = 336. Add 336 to the number set. Current number set: [336, 32], target: 19, just two numbers left.\n     |- Try 336 + 32 = 368. Evaluate 368 != 19, drop this branch.\n     |- Try 336 - 32 = 304. Evaluate 304 != 19, drop this branch.\n     |- Try 336 * 32 = 10752. 10752 exceeds the maximum intermediate result, drop this branch.\n     |- Try 336 \/ 32 = 10.5. 10.5 is a decimal, drop this branch.\n    |- Try 21 \/ 16 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (32, 16) (numbers left: [21]). Try possible operations.\n    |- Try 32 + 16 = 48. Add 48 to the number set. Current number set: [48, 21], target: 19, just two numbers left.\n     |- Try 48 + 21 = 69. Evaluate 69 != 19, drop this branch.\n     |- Try 48 - 21 = 27. Evaluate 27 != 19, drop this branch.\n     |- Try 48 * 21 = 1008. Evaluate 1008 != 19, drop this branch.\n     |- Try 48 \/ 21 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 32 - 16 = 16. Add 16 to the number set. Current number set: [16, 21], target: 19, just two numbers left.\n     |- Try 21 + 16 = 37. Evaluate 37 != 19, drop this branch.\n     |- Try 21 - 16 = 5. Evaluate 5 != 19, drop this branch.\n     |- Try 21 * 16 = 336. Evaluate 336 != 19, drop this branch.\n     |- Try 21 \/ 16 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 32 * 16 = 512. Add 512 to the number set. Current number set: [512, 21], target: 19, just two numbers left.\n     |- Try 512 + 21 = 533. Evaluate 533 != 19, drop this branch.\n     |- Try 512 - 21 = 491. Evaluate 491 != 19, drop this branch.\n     |- Try 512 * 21 = 10752. 10752 exceeds the maximum intermediate result, drop this branch.\n     |- Try 512 \/ 21 = 24.4. 24.4 is a decimal, drop this branch.\n    |- Try 32 \/ 16 = 2. Add 2 to the number set. Current number set: [2, 21], target: 19, just two numbers left.\n     |- Try 21 + 2 = 23. Evaluate 23 != 19, drop this branch.\n     |- Try 21 - 2 = 19. Evaluate 19 == 19, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 21 - 2 = 19\nThe step before: 32 \/ 16 = 2\nThe first step: 23 - 2 = 21\n\nOutput the solution in the required format:\n<Solution>\n23 - 2 = 21\n32 \/ 16 = 2\n21 - 2 = 19\n<\/Solution>\n","item":{"nums":[23,32,2,16],"solution":["23 - 2 = 21","32 \/ 16 = 2","21 - 2 = 19"],"target":19}}
+{"instance_id":"countdown_8k_171","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [19, 15, 3, 31]\nTarget: 41","reference_output":"# Search Procedure\nInitial number set: [19, 15, 3, 31], target: 41. Options for choosing two numbers: [(19, 15), (19, 3), (19, 31), (15, 3), (15, 31), (3, 31)].\n |- Pick two numbers (19, 15) (numbers left: [3, 31]). Try possible operations.\n  |- Try 19 + 15 = 34. Add 34 to the number set. Current number set: [34, 3, 31], target: 41. Options for choosing two numbers: [(34, 3), (34, 31), (3, 31)].\n   |- Pick two numbers (34, 3) (numbers left: [31]). Try possible operations.\n    |- Try 34 + 3 = 37. Add 37 to the number set. Current number set: [37, 31], target: 41, just two numbers left.\n     |- Try 37 + 31 = 68. Evaluate 68 != 41, drop this branch.\n     |- Try 37 - 31 = 6. Evaluate 6 != 41, drop this branch.\n     |- Try 37 * 31 = 1147. Evaluate 1147 != 41, drop this branch.\n     |- Try 37 \/ 31 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 34 - 3 = 31. Add 31 to the number set. Current number set: [31, 31], target: 41, just two numbers left.\n     |- Try 31 + 31 = 62. Evaluate 62 != 41, drop this branch.\n     |- Try 31 - 31 = 0. Evaluate 0 != 41, drop this branch.\n     |- Try 31 * 31 = 961. Evaluate 961 != 41, drop this branch.\n     |- Try 31 \/ 31 = 1. Evaluate 1 != 41, drop this branch.\n    |- Try 34 * 3 = 102. Add 102 to the number set. Current number set: [102, 31], target: 41, just two numbers left.\n     |- Try 102 + 31 = 133. Evaluate 133 != 41, drop this branch.\n     |- Try 102 - 31 = 71. Evaluate 71 != 41, drop this branch.\n     |- Try 102 * 31 = 3162. 3162 exceeds the maximum intermediate result, drop this branch.\n     |- Try 102 \/ 31 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 34 \/ 3 = 11.3. 11.3 is a decimal, drop this branch.\n   |- Pick two numbers (34, 31) (numbers left: [3]). Try possible operations.\n    |- Try 34 + 31 = 65. Add 65 to the number set. Current number set: [65, 3], target: 41, just two numbers left.\n     |- Try 65 + 3 = 68. Evaluate 68 != 41, drop this branch.\n     |- Try 65 - 3 = 62. Evaluate 62 != 41, drop this branch.\n     |- Try 65 * 3 = 195. Evaluate 195 != 41, drop this branch.\n     |- Try 65 \/ 3 = 21.7. 21.7 is a decimal, drop this branch.\n    |- Try 34 - 31 = 3. Add 3 to the number set. Current number set: [3, 3], target: 41, just two numbers left.\n     |- Try 3 + 3 = 6. Evaluate 6 != 41, drop this branch.\n     |- Try 3 - 3 = 0. Evaluate 0 != 41, drop this branch.\n     |- Try 3 * 3 = 9. Evaluate 9 != 41, drop this branch.\n     |- Try 3 \/ 3 = 1. Evaluate 1 != 41, drop this branch.\n    |- Try 34 * 31 = 1054. Add 1054 to the number set. Current number set: [1054, 3], target: 41, just two numbers left.\n     |- Try 1054 + 3 = 1057. Evaluate 1057 != 41, drop this branch.\n     |- Try 1054 - 3 = 1051. Evaluate 1051 != 41, drop this branch.\n     |- Try 1054 * 3 = 3162. 3162 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1054 \/ 3 = 351.3. 351.3 is a decimal, drop this branch.\n    |- Try 34 \/ 31 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (3, 31) (numbers left: [34]). Try possible operations.\n    |- Try 31 + 3 = 34. Add 34 to the number set. Current number set: [34, 34], target: 41, just two numbers left.\n     |- Try 34 + 34 = 68. Evaluate 68 != 41, drop this branch.\n     |- Try 34 - 34 = 0. Evaluate 0 != 41, drop this branch.\n     |- Try 34 * 34 = 1156. Evaluate 1156 != 41, drop this branch.\n     |- Try 34 \/ 34 = 1. Evaluate 1 != 41, drop this branch.\n    |- Try 31 - 3 = 28. Add 28 to the number set. Current number set: [28, 34], target: 41, just two numbers left.\n     |- Try 34 + 28 = 62. Evaluate 62 != 41, drop this branch.\n     |- Try 34 - 28 = 6. Evaluate 6 != 41, drop this branch.\n     |- Try 34 * 28 = 952. Evaluate 952 != 41, drop this branch.\n     |- Try 34 \/ 28 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 31 * 3 = 93. Add 93 to the number set. Current number set: [93, 34], target: 41, just two numbers left.\n     |- Try 93 + 34 = 127. Evaluate 127 != 41, drop this branch.\n     |- Try 93 - 34 = 59. Evaluate 59 != 41, drop this branch.\n     |- Try 93 * 34 = 3162. 3162 exceeds the maximum intermediate result, drop this branch.\n     |- Try 93 \/ 34 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 31 \/ 3 = 10.3. 10.3 is a decimal, drop this branch.\n  |- Try 19 - 15 = 4. Add 4 to the number set. Current number set: [4, 3, 31], target: 41. Options for choosing two numbers: [(4, 3), (4, 31), (3, 31)].\n   |- Pick two numbers (4, 3) (numbers left: [31]). Try possible operations.\n    |- Try 4 + 3 = 7. Add 7 to the number set. Current number set: [7, 31], target: 41, just two numbers left.\n     |- Try 31 + 7 = 38. Evaluate 38 != 41, drop this branch.\n     |- Try 31 - 7 = 24. Evaluate 24 != 41, drop this branch.\n     |- Try 31 * 7 = 217. Evaluate 217 != 41, drop this branch.\n     |- Try 31 \/ 7 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 4 - 3 = 1. Add 1 to the number set. Current number set: [1, 31], target: 41, just two numbers left.\n     |- Try 31 + 1 = 32. Evaluate 32 != 41, drop this branch.\n     |- Try 31 - 1 = 30. Evaluate 30 != 41, drop this branch.\n     |- Try 31 * 1 = 31. Evaluate 31 != 41, drop this branch.\n     |- Try 31 \/ 1 = 31. Evaluate 31 != 41, drop this branch.\n    |- Try 4 * 3 = 12. Add 12 to the number set. Current number set: [12, 31], target: 41, just two numbers left.\n     |- Try 31 + 12 = 43. Evaluate 43 != 41, drop this branch.\n     |- Try 31 - 12 = 19. Evaluate 19 != 41, drop this branch.\n     |- Try 31 * 12 = 372. Evaluate 372 != 41, drop this branch.\n     |- Try 31 \/ 12 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 4 \/ 3 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (4, 31) (numbers left: [3]). Try possible operations.\n    |- Try 31 + 4 = 35. Add 35 to the number set. Current number set: [35, 3], target: 41, just two numbers left.\n     |- Try 35 + 3 = 38. Evaluate 38 != 41, drop this branch.\n     |- Try 35 - 3 = 32. Evaluate 32 != 41, drop this branch.\n     |- Try 35 * 3 = 105. Evaluate 105 != 41, drop this branch.\n     |- Try 35 \/ 3 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 31 - 4 = 27. Add 27 to the number set. Current number set: [27, 3], target: 41, just two numbers left.\n     |- Try 27 + 3 = 30. Evaluate 30 != 41, drop this branch.\n     |- Try 27 - 3 = 24. Evaluate 24 != 41, drop this branch.\n     |- Try 27 * 3 = 81. Evaluate 81 != 41, drop this branch.\n     |- Try 27 \/ 3 = 9. Evaluate 9 != 41, drop this branch.\n    |- Try 31 * 4 = 124. Add 124 to the number set. Current number set: [124, 3], target: 41, just two numbers left.\n     |- Try 124 + 3 = 127. Evaluate 127 != 41, drop this branch.\n     |- Try 124 - 3 = 121. Evaluate 121 != 41, drop this branch.\n     |- Try 124 * 3 = 372. Evaluate 372 != 41, drop this branch.\n     |- Try 124 \/ 3 = 41.3. 41.3 is a decimal, drop this branch.\n    |- Try 31 \/ 4 = 7.8. 7.8 is a decimal, drop this branch.\n   |- Pick two numbers (3, 31) (numbers left: [4]). Try possible operations.\n    |- Try 31 + 3 = 34. Add 34 to the number set. Current number set: [34, 4], target: 41, just two numbers left.\n     |- Try 34 + 4 = 38. Evaluate 38 != 41, drop this branch.\n     |- Try 34 - 4 = 30. Evaluate 30 != 41, drop this branch.\n     |- Try 34 * 4 = 136. Evaluate 136 != 41, drop this branch.\n     |- Try 34 \/ 4 = 8.5. 8.5 is a decimal, drop this branch.\n    |- Try 31 - 3 = 28. Add 28 to the number set. Current number set: [28, 4], target: 41, just two numbers left.\n     |- Try 28 + 4 = 32. Evaluate 32 != 41, drop this branch.\n     |- Try 28 - 4 = 24. Evaluate 24 != 41, drop this branch.\n     |- Try 28 * 4 = 112. Evaluate 112 != 41, drop this branch.\n     |- Try 28 \/ 4 = 7. Evaluate 7 != 41, drop this branch.\n    |- Try 31 * 3 = 93. Add 93 to the number set. Current number set: [93, 4], target: 41, just two numbers left.\n     |- Try 93 + 4 = 97. Evaluate 97 != 41, drop this branch.\n     |- Try 93 - 4 = 89. Evaluate 89 != 41, drop this branch.\n     |- Try 93 * 4 = 372. Evaluate 372 != 41, drop this branch.\n     |- Try 93 \/ 4 = 23.2. 23.2 is a decimal, drop this branch.\n    |- Try 31 \/ 3 = 10.3. 10.3 is a decimal, drop this branch.\n  |- Try 19 * 15 = 285. Add 285 to the number set. Current number set: [285, 3, 31], target: 41. Options for choosing two numbers: [(285, 3), (285, 31), (3, 31)].\n   |- Pick two numbers (285, 3) (numbers left: [31]). Try possible operations.\n    |- Try 285 + 3 = 288. Add 288 to the number set. Current number set: [288, 31], target: 41, just two numbers left.\n     |- Try 288 + 31 = 319. Evaluate 319 != 41, drop this branch.\n     |- Try 288 - 31 = 257. Evaluate 257 != 41, drop this branch.\n     |- Try 288 * 31 = 8928. 8928 exceeds the maximum intermediate result, drop this branch.\n     |- Try 288 \/ 31 = 9.3. 9.3 is a decimal, drop this branch.\n    |- Try 285 - 3 = 282. Add 282 to the number set. Current number set: [282, 31], target: 41, just two numbers left.\n     |- Try 282 + 31 = 313. Evaluate 313 != 41, drop this branch.\n     |- Try 282 - 31 = 251. Evaluate 251 != 41, drop this branch.\n     |- Try 282 * 31 = 8742. 8742 exceeds the maximum intermediate result, drop this branch.\n     |- Try 282 \/ 31 = 9.1. 9.1 is a decimal, drop this branch.\n    |- Try 285 * 3 = 855. Add 855 to the number set. Current number set: [855, 31], target: 41, just two numbers left.\n     |- Try 855 + 31 = 886. Evaluate 886 != 41, drop this branch.\n     |- Try 855 - 31 = 824. Evaluate 824 != 41, drop this branch.\n     |- Try 855 * 31 = 26505. 26505 exceeds the maximum intermediate result, drop this branch.\n     |- Try 855 \/ 31 = 27.6. 27.6 is a decimal, drop this branch.\n    |- Try 285 \/ 3 = 95. Add 95 to the number set. Current number set: [95, 31], target: 41, just two numbers left.\n     |- Try 95 + 31 = 126. Evaluate 126 != 41, drop this branch.\n     |- Try 95 - 31 = 64. Evaluate 64 != 41, drop this branch.\n     |- Try 95 * 31 = 2945. 2945 exceeds the maximum intermediate result, drop this branch.\n     |- Try 95 \/ 31 = 3.1. 3.1 is a decimal, drop this branch.\n   |- Pick two numbers (285, 31) (numbers left: [3]). Try possible operations.\n    |- Try 285 + 31 = 316. Add 316 to the number set. Current number set: [316, 3], target: 41, just two numbers left.\n     |- Try 316 + 3 = 319. Evaluate 319 != 41, drop this branch.\n     |- Try 316 - 3 = 313. Evaluate 313 != 41, drop this branch.\n     |- Try 316 * 3 = 948. Evaluate 948 != 41, drop this branch.\n     |- Try 316 \/ 3 = 105.3. 105.3 is a decimal, drop this branch.\n    |- Try 285 - 31 = 254. Add 254 to the number set. Current number set: [254, 3], target: 41, just two numbers left.\n     |- Try 254 + 3 = 257. Evaluate 257 != 41, drop this branch.\n     |- Try 254 - 3 = 251. Evaluate 251 != 41, drop this branch.\n     |- Try 254 * 3 = 762. Evaluate 762 != 41, drop this branch.\n     |- Try 254 \/ 3 = 84.7. 84.7 is a decimal, drop this branch.\n    |- Try 285 * 31 = 8835. 8835 exceeds the maximum intermediate result, drop this branch.\n    |- Try 285 \/ 31 = 9.2. 9.2 is a decimal, drop this branch.\n   |- Pick two numbers (3, 31) (numbers left: [285]). Try possible operations.\n    |- Try 31 + 3 = 34. Add 34 to the number set. Current number set: [34, 285], target: 41, just two numbers left.\n     |- Try 285 + 34 = 319. Evaluate 319 != 41, drop this branch.\n     |- Try 285 - 34 = 251. Evaluate 251 != 41, drop this branch.\n     |- Try 285 * 34 = 9690. 9690 exceeds the maximum intermediate result, drop this branch.\n     |- Try 285 \/ 34 = 8.4. 8.4 is a decimal, drop this branch.\n    |- Try 31 - 3 = 28. Add 28 to the number set. Current number set: [28, 285], target: 41, just two numbers left.\n     |- Try 285 + 28 = 313. Evaluate 313 != 41, drop this branch.\n     |- Try 285 - 28 = 257. Evaluate 257 != 41, drop this branch.\n     |- Try 285 * 28 = 7980. 7980 exceeds the maximum intermediate result, drop this branch.\n     |- Try 285 \/ 28 = 10.2. 10.2 is a decimal, drop this branch.\n    |- Try 31 * 3 = 93. Add 93 to the number set. Current number set: [93, 285], target: 41, just two numbers left.\n     |- Try 285 + 93 = 378. Evaluate 378 != 41, drop this branch.\n     |- Try 285 - 93 = 192. Evaluate 192 != 41, drop this branch.\n     |- Try 285 * 93 = 26505. 26505 exceeds the maximum intermediate result, drop this branch.\n     |- Try 285 \/ 93 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 31 \/ 3 = 10.3. 10.3 is a decimal, drop this branch.\n  |- Try 19 \/ 15 = 1.3. 1.3 is a decimal, drop this branch.\n |- Pick two numbers (19, 3) (numbers left: [15, 31]). Try possible operations.\n  |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 15, 31], target: 41. Options for choosing two numbers: [(22, 15), (22, 31), (15, 31)].\n   |- Pick two numbers (22, 15) (numbers left: [31]). Try possible operations.\n    |- Try 22 + 15 = 37. Add 37 to the number set. Current number set: [37, 31], target: 41, just two numbers left.\n     |- Try 37 + 31 = 68. Evaluate 68 != 41, drop this branch.\n     |- Try 37 - 31 = 6. Evaluate 6 != 41, drop this branch.\n     |- Try 37 * 31 = 1147. Evaluate 1147 != 41, drop this branch.\n     |- Try 37 \/ 31 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 22 - 15 = 7. Add 7 to the number set. Current number set: [7, 31], target: 41, just two numbers left.\n     |- Try 31 + 7 = 38. Evaluate 38 != 41, drop this branch.\n     |- Try 31 - 7 = 24. Evaluate 24 != 41, drop this branch.\n     |- Try 31 * 7 = 217. Evaluate 217 != 41, drop this branch.\n     |- Try 31 \/ 7 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 22 * 15 = 330. Add 330 to the number set. Current number set: [330, 31], target: 41, just two numbers left.\n     |- Try 330 + 31 = 361. Evaluate 361 != 41, drop this branch.\n     |- Try 330 - 31 = 299. Evaluate 299 != 41, drop this branch.\n     |- Try 330 * 31 = 10230. 10230 exceeds the maximum intermediate result, drop this branch.\n     |- Try 330 \/ 31 = 10.6. 10.6 is a decimal, drop this branch.\n    |- Try 22 \/ 15 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (22, 31) (numbers left: [15]). Try possible operations.\n    |- Try 31 + 22 = 53. Add 53 to the number set. Current number set: [53, 15], target: 41, just two numbers left.\n     |- Try 53 + 15 = 68. Evaluate 68 != 41, drop this branch.\n     |- Try 53 - 15 = 38. Evaluate 38 != 41, drop this branch.\n     |- Try 53 * 15 = 795. Evaluate 795 != 41, drop this branch.\n     |- Try 53 \/ 15 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 31 - 22 = 9. Add 9 to the number set. Current number set: [9, 15], target: 41, just two numbers left.\n     |- Try 15 + 9 = 24. Evaluate 24 != 41, drop this branch.\n     |- Try 15 - 9 = 6. Evaluate 6 != 41, drop this branch.\n     |- Try 15 * 9 = 135. Evaluate 135 != 41, drop this branch.\n     |- Try 15 \/ 9 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 31 * 22 = 682. Add 682 to the number set. Current number set: [682, 15], target: 41, just two numbers left.\n     |- Try 682 + 15 = 697. Evaluate 697 != 41, drop this branch.\n     |- Try 682 - 15 = 667. Evaluate 667 != 41, drop this branch.\n     |- Try 682 * 15 = 10230. 10230 exceeds the maximum intermediate result, drop this branch.\n     |- Try 682 \/ 15 = 45.5. 45.5 is a decimal, drop this branch.\n    |- Try 31 \/ 22 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (15, 31) (numbers left: [22]). Try possible operations.\n    |- Try 31 + 15 = 46. Add 46 to the number set. Current number set: [46, 22], target: 41, just two numbers left.\n     |- Try 46 + 22 = 68. Evaluate 68 != 41, drop this branch.\n     |- Try 46 - 22 = 24. Evaluate 24 != 41, drop this branch.\n     |- Try 46 * 22 = 1012. Evaluate 1012 != 41, drop this branch.\n     |- Try 46 \/ 22 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 31 - 15 = 16. Add 16 to the number set. Current number set: [16, 22], target: 41, just two numbers left.\n     |- Try 22 + 16 = 38. Evaluate 38 != 41, drop this branch.\n     |- Try 22 - 16 = 6. Evaluate 6 != 41, drop this branch.\n     |- Try 22 * 16 = 352. Evaluate 352 != 41, drop this branch.\n     |- Try 22 \/ 16 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 31 * 15 = 465. Add 465 to the number set. Current number set: [465, 22], target: 41, just two numbers left.\n     |- Try 465 + 22 = 487. Evaluate 487 != 41, drop this branch.\n     |- Try 465 - 22 = 443. Evaluate 443 != 41, drop this branch.\n     |- Try 465 * 22 = 10230. 10230 exceeds the maximum intermediate result, drop this branch.\n     |- Try 465 \/ 22 = 21.1. 21.1 is a decimal, drop this branch.\n    |- Try 31 \/ 15 = 2.1. 2.1 is a decimal, drop this branch.\n  |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 15, 31], target: 41. Options for choosing two numbers: [(16, 15), (16, 31), (15, 31)].\n   |- Pick two numbers (16, 15) (numbers left: [31]). Try possible operations.\n    |- Try 16 + 15 = 31. Add 31 to the number set. Current number set: [31, 31], target: 41, just two numbers left.\n     |- Try 31 + 31 = 62. Evaluate 62 != 41, drop this branch.\n     |- Try 31 - 31 = 0. Evaluate 0 != 41, drop this branch.\n     |- Try 31 * 31 = 961. Evaluate 961 != 41, drop this branch.\n     |- Try 31 \/ 31 = 1. Evaluate 1 != 41, drop this branch.\n    |- Try 16 - 15 = 1. Add 1 to the number set. Current number set: [1, 31], target: 41, just two numbers left.\n     |- Try 31 + 1 = 32. Evaluate 32 != 41, drop this branch.\n     |- Try 31 - 1 = 30. Evaluate 30 != 41, drop this branch.\n     |- Try 31 * 1 = 31. Evaluate 31 != 41, drop this branch.\n     |- Try 31 \/ 1 = 31. Evaluate 31 != 41, drop this branch.\n    |- Try 16 * 15 = 240. Add 240 to the number set. Current number set: [240, 31], target: 41, just two numbers left.\n     |- Try 240 + 31 = 271. Evaluate 271 != 41, drop this branch.\n     |- Try 240 - 31 = 209. Evaluate 209 != 41, drop this branch.\n     |- Try 240 * 31 = 7440. 7440 exceeds the maximum intermediate result, drop this branch.\n     |- Try 240 \/ 31 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 16 \/ 15 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (16, 31) (numbers left: [15]). Try possible operations.\n    |- Try 31 + 16 = 47. Add 47 to the number set. Current number set: [47, 15], target: 41, just two numbers left.\n     |- Try 47 + 15 = 62. Evaluate 62 != 41, drop this branch.\n     |- Try 47 - 15 = 32. Evaluate 32 != 41, drop this branch.\n     |- Try 47 * 15 = 705. Evaluate 705 != 41, drop this branch.\n     |- Try 47 \/ 15 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 31 - 16 = 15. Add 15 to the number set. Current number set: [15, 15], target: 41, just two numbers left.\n     |- Try 15 + 15 = 30. Evaluate 30 != 41, drop this branch.\n     |- Try 15 - 15 = 0. Evaluate 0 != 41, drop this branch.\n     |- Try 15 * 15 = 225. Evaluate 225 != 41, drop this branch.\n     |- Try 15 \/ 15 = 1. Evaluate 1 != 41, drop this branch.\n    |- Try 31 * 16 = 496. Add 496 to the number set. Current number set: [496, 15], target: 41, just two numbers left.\n     |- Try 496 + 15 = 511. Evaluate 511 != 41, drop this branch.\n     |- Try 496 - 15 = 481. Evaluate 481 != 41, drop this branch.\n     |- Try 496 * 15 = 7440. 7440 exceeds the maximum intermediate result, drop this branch.\n     |- Try 496 \/ 15 = 33.1. 33.1 is a decimal, drop this branch.\n    |- Try 31 \/ 16 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (15, 31) (numbers left: [16]). Try possible operations.\n    |- Try 31 + 15 = 46. Add 46 to the number set. Current number set: [46, 16], target: 41, just two numbers left.\n     |- Try 46 + 16 = 62. Evaluate 62 != 41, drop this branch.\n     |- Try 46 - 16 = 30. Evaluate 30 != 41, drop this branch.\n     |- Try 46 * 16 = 736. Evaluate 736 != 41, drop this branch.\n     |- Try 46 \/ 16 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 31 - 15 = 16. Add 16 to the number set. Current number set: [16, 16], target: 41, just two numbers left.\n     |- Try 16 + 16 = 32. Evaluate 32 != 41, drop this branch.\n     |- Try 16 - 16 = 0. Evaluate 0 != 41, drop this branch.\n     |- Try 16 * 16 = 256. Evaluate 256 != 41, drop this branch.\n     |- Try 16 \/ 16 = 1. Evaluate 1 != 41, drop this branch.\n    |- Try 31 * 15 = 465. Add 465 to the number set. Current number set: [465, 16], target: 41, just two numbers left.\n     |- Try 465 + 16 = 481. Evaluate 481 != 41, drop this branch.\n     |- Try 465 - 16 = 449. Evaluate 449 != 41, drop this branch.\n     |- Try 465 * 16 = 7440. 7440 exceeds the maximum intermediate result, drop this branch.\n     |- Try 465 \/ 16 = 29.1. 29.1 is a decimal, drop this branch.\n    |- Try 31 \/ 15 = 2.1. 2.1 is a decimal, drop this branch.\n  |- Try 19 * 3 = 57. Add 57 to the number set. Current number set: [57, 15, 31], target: 41. Options for choosing two numbers: [(57, 15), (57, 31), (15, 31)].\n   |- Pick two numbers (57, 15) (numbers left: [31]). Try possible operations.\n    |- Try 57 + 15 = 72. Add 72 to the number set. Current number set: [72, 31], target: 41, just two numbers left.\n     |- Try 72 + 31 = 103. Evaluate 103 != 41, drop this branch.\n     |- Try 72 - 31 = 41. Evaluate 41 == 41, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 72 - 31 = 41\nThe step before: 57 + 15 = 72\nThe first step: 19 * 3 = 57\n\nOutput the solution in the required format:\n<Solution>\n19 * 3 = 57\n57 + 15 = 72\n72 - 31 = 41\n<\/Solution>\n","item":{"nums":[19,15,3,31],"solution":["19 * 3 = 57","57 + 15 = 72","72 - 31 = 41"],"target":41}}
+{"instance_id":"countdown_8k_172","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [32, 29, 44, 19]\nTarget: 33","reference_output":"# Search Procedure\nInitial number set: [32, 29, 44, 19], target: 33. Options for choosing two numbers: [(32, 29), (32, 44), (32, 19), (29, 44), (29, 19), (44, 19)].\n |- Pick two numbers (32, 29) (numbers left: [44, 19]). Try possible operations.\n  |- Try 32 + 29 = 61. Add 61 to the number set. Current number set: [61, 44, 19], target: 33. Options for choosing two numbers: [(61, 44), (61, 19), (44, 19)].\n   |- Pick two numbers (61, 44) (numbers left: [19]). Try possible operations.\n    |- Try 61 + 44 = 105. Add 105 to the number set. Current number set: [105, 19], target: 33, just two numbers left.\n     |- Try 105 + 19 = 124. Evaluate 124 != 33, drop this branch.\n     |- Try 105 - 19 = 86. Evaluate 86 != 33, drop this branch.\n     |- Try 105 * 19 = 1995. Evaluate 1995 != 33, drop this branch.\n     |- Try 105 \/ 19 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 61 - 44 = 17. Add 17 to the number set. Current number set: [17, 19], target: 33, just two numbers left.\n     |- Try 19 + 17 = 36. Evaluate 36 != 33, drop this branch.\n     |- Try 19 - 17 = 2. Evaluate 2 != 33, drop this branch.\n     |- Try 19 * 17 = 323. Evaluate 323 != 33, drop this branch.\n     |- Try 19 \/ 17 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 61 * 44 = 2684. 2684 exceeds the maximum intermediate result, drop this branch.\n    |- Try 61 \/ 44 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (61, 19) (numbers left: [44]). Try possible operations.\n    |- Try 61 + 19 = 80. Add 80 to the number set. Current number set: [80, 44], target: 33, just two numbers left.\n     |- Try 80 + 44 = 124. Evaluate 124 != 33, drop this branch.\n     |- Try 80 - 44 = 36. Evaluate 36 != 33, drop this branch.\n     |- Try 80 * 44 = 3520. 3520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 80 \/ 44 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 61 - 19 = 42. Add 42 to the number set. Current number set: [42, 44], target: 33, just two numbers left.\n     |- Try 44 + 42 = 86. Evaluate 86 != 33, drop this branch.\n     |- Try 44 - 42 = 2. Evaluate 2 != 33, drop this branch.\n     |- Try 44 * 42 = 1848. Evaluate 1848 != 33, drop this branch.\n     |- Try 44 \/ 42 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 61 * 19 = 1159. Add 1159 to the number set. Current number set: [1159, 44], target: 33, just two numbers left.\n     |- Try 1159 + 44 = 1203. Evaluate 1203 != 33, drop this branch.\n     |- Try 1159 - 44 = 1115. Evaluate 1115 != 33, drop this branch.\n     |- Try 1159 * 44 = 50996. 50996 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1159 \/ 44 = 26.3. 26.3 is a decimal, drop this branch.\n    |- Try 61 \/ 19 = 3.2. 3.2 is a decimal, drop this branch.\n   |- Pick two numbers (44, 19) (numbers left: [61]). Try possible operations.\n    |- Try 44 + 19 = 63. Add 63 to the number set. Current number set: [63, 61], target: 33, just two numbers left.\n     |- Try 63 + 61 = 124. Evaluate 124 != 33, drop this branch.\n     |- Try 63 - 61 = 2. Evaluate 2 != 33, drop this branch.\n     |- Try 63 * 61 = 3843. 3843 exceeds the maximum intermediate result, drop this branch.\n     |- Try 63 \/ 61 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 44 - 19 = 25. Add 25 to the number set. Current number set: [25, 61], target: 33, just two numbers left.\n     |- Try 61 + 25 = 86. Evaluate 86 != 33, drop this branch.\n     |- Try 61 - 25 = 36. Evaluate 36 != 33, drop this branch.\n     |- Try 61 * 25 = 1525. Evaluate 1525 != 33, drop this branch.\n     |- Try 61 \/ 25 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 44 * 19 = 836. Add 836 to the number set. Current number set: [836, 61], target: 33, just two numbers left.\n     |- Try 836 + 61 = 897. Evaluate 897 != 33, drop this branch.\n     |- Try 836 - 61 = 775. Evaluate 775 != 33, drop this branch.\n     |- Try 836 * 61 = 50996. 50996 exceeds the maximum intermediate result, drop this branch.\n     |- Try 836 \/ 61 = 13.7. 13.7 is a decimal, drop this branch.\n    |- Try 44 \/ 19 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 32 - 29 = 3. Add 3 to the number set. Current number set: [3, 44, 19], target: 33. Options for choosing two numbers: [(3, 44), (3, 19), (44, 19)].\n   |- Pick two numbers (3, 44) (numbers left: [19]). Try possible operations.\n    |- Try 44 + 3 = 47. Add 47 to the number set. Current number set: [47, 19], target: 33, just two numbers left.\n     |- Try 47 + 19 = 66. Evaluate 66 != 33, drop this branch.\n     |- Try 47 - 19 = 28. Evaluate 28 != 33, drop this branch.\n     |- Try 47 * 19 = 893. Evaluate 893 != 33, drop this branch.\n     |- Try 47 \/ 19 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 44 - 3 = 41. Add 41 to the number set. Current number set: [41, 19], target: 33, just two numbers left.\n     |- Try 41 + 19 = 60. Evaluate 60 != 33, drop this branch.\n     |- Try 41 - 19 = 22. Evaluate 22 != 33, drop this branch.\n     |- Try 41 * 19 = 779. Evaluate 779 != 33, drop this branch.\n     |- Try 41 \/ 19 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 44 * 3 = 132. Add 132 to the number set. Current number set: [132, 19], target: 33, just two numbers left.\n     |- Try 132 + 19 = 151. Evaluate 151 != 33, drop this branch.\n     |- Try 132 - 19 = 113. Evaluate 113 != 33, drop this branch.\n     |- Try 132 * 19 = 2508. 2508 exceeds the maximum intermediate result, drop this branch.\n     |- Try 132 \/ 19 = 6.9. 6.9 is a decimal, drop this branch.\n    |- Try 44 \/ 3 = 14.7. 14.7 is a decimal, drop this branch.\n   |- Pick two numbers (3, 19) (numbers left: [44]). Try possible operations.\n    |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 44], target: 33, just two numbers left.\n     |- Try 44 + 22 = 66. Evaluate 66 != 33, drop this branch.\n     |- Try 44 - 22 = 22. Evaluate 22 != 33, drop this branch.\n     |- Try 44 * 22 = 968. Evaluate 968 != 33, drop this branch.\n     |- Try 44 \/ 22 = 2. Evaluate 2 != 33, drop this branch.\n    |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 44], target: 33, just two numbers left.\n     |- Try 44 + 16 = 60. Evaluate 60 != 33, drop this branch.\n     |- Try 44 - 16 = 28. Evaluate 28 != 33, drop this branch.\n     |- Try 44 * 16 = 704. Evaluate 704 != 33, drop this branch.\n     |- Try 44 \/ 16 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 19 * 3 = 57. Add 57 to the number set. Current number set: [57, 44], target: 33, just two numbers left.\n     |- Try 57 + 44 = 101. Evaluate 101 != 33, drop this branch.\n     |- Try 57 - 44 = 13. Evaluate 13 != 33, drop this branch.\n     |- Try 57 * 44 = 2508. 2508 exceeds the maximum intermediate result, drop this branch.\n     |- Try 57 \/ 44 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 19 \/ 3 = 6.3. 6.3 is a decimal, drop this branch.\n   |- Pick two numbers (44, 19) (numbers left: [3]). Try possible operations.\n    |- Try 44 + 19 = 63. Add 63 to the number set. Current number set: [63, 3], target: 33, just two numbers left.\n     |- Try 63 + 3 = 66. Evaluate 66 != 33, drop this branch.\n     |- Try 63 - 3 = 60. Evaluate 60 != 33, drop this branch.\n     |- Try 63 * 3 = 189. Evaluate 189 != 33, drop this branch.\n     |- Try 63 \/ 3 = 21. Evaluate 21 != 33, drop this branch.\n    |- Try 44 - 19 = 25. Add 25 to the number set. Current number set: [25, 3], target: 33, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 33, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 33, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 33, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 44 * 19 = 836. Add 836 to the number set. Current number set: [836, 3], target: 33, just two numbers left.\n     |- Try 836 + 3 = 839. Evaluate 839 != 33, drop this branch.\n     |- Try 836 - 3 = 833. Evaluate 833 != 33, drop this branch.\n     |- Try 836 * 3 = 2508. 2508 exceeds the maximum intermediate result, drop this branch.\n     |- Try 836 \/ 3 = 278.7. 278.7 is a decimal, drop this branch.\n    |- Try 44 \/ 19 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 32 * 29 = 928. Add 928 to the number set. Current number set: [928, 44, 19], target: 33. Options for choosing two numbers: [(928, 44), (928, 19), (44, 19)].\n   |- Pick two numbers (928, 44) (numbers left: [19]). Try possible operations.\n    |- Try 928 + 44 = 972. Add 972 to the number set. Current number set: [972, 19], target: 33, just two numbers left.\n     |- Try 972 + 19 = 991. Evaluate 991 != 33, drop this branch.\n     |- Try 972 - 19 = 953. Evaluate 953 != 33, drop this branch.\n     |- Try 972 * 19 = 18468. 18468 exceeds the maximum intermediate result, drop this branch.\n     |- Try 972 \/ 19 = 51.2. 51.2 is a decimal, drop this branch.\n    |- Try 928 - 44 = 884. Add 884 to the number set. Current number set: [884, 19], target: 33, just two numbers left.\n     |- Try 884 + 19 = 903. Evaluate 903 != 33, drop this branch.\n     |- Try 884 - 19 = 865. Evaluate 865 != 33, drop this branch.\n     |- Try 884 * 19 = 16796. 16796 exceeds the maximum intermediate result, drop this branch.\n     |- Try 884 \/ 19 = 46.5. 46.5 is a decimal, drop this branch.\n    |- Try 928 * 44 = 40832. 40832 exceeds the maximum intermediate result, drop this branch.\n    |- Try 928 \/ 44 = 21.1. 21.1 is a decimal, drop this branch.\n   |- Pick two numbers (928, 19) (numbers left: [44]). Try possible operations.\n    |- Try 928 + 19 = 947. Add 947 to the number set. Current number set: [947, 44], target: 33, just two numbers left.\n     |- Try 947 + 44 = 991. Evaluate 991 != 33, drop this branch.\n     |- Try 947 - 44 = 903. Evaluate 903 != 33, drop this branch.\n     |- Try 947 * 44 = 41668. 41668 exceeds the maximum intermediate result, drop this branch.\n     |- Try 947 \/ 44 = 21.5. 21.5 is a decimal, drop this branch.\n    |- Try 928 - 19 = 909. Add 909 to the number set. Current number set: [909, 44], target: 33, just two numbers left.\n     |- Try 909 + 44 = 953. Evaluate 953 != 33, drop this branch.\n     |- Try 909 - 44 = 865. Evaluate 865 != 33, drop this branch.\n     |- Try 909 * 44 = 39996. 39996 exceeds the maximum intermediate result, drop this branch.\n     |- Try 909 \/ 44 = 20.7. 20.7 is a decimal, drop this branch.\n    |- Try 928 * 19 = 17632. 17632 exceeds the maximum intermediate result, drop this branch.\n    |- Try 928 \/ 19 = 48.8. 48.8 is a decimal, drop this branch.\n   |- Pick two numbers (44, 19) (numbers left: [928]). Try possible operations.\n    |- Try 44 + 19 = 63. Add 63 to the number set. Current number set: [63, 928], target: 33, just two numbers left.\n     |- Try 928 + 63 = 991. Evaluate 991 != 33, drop this branch.\n     |- Try 928 - 63 = 865. Evaluate 865 != 33, drop this branch.\n     |- Try 928 * 63 = 58464. 58464 exceeds the maximum intermediate result, drop this branch.\n     |- Try 928 \/ 63 = 14.7. 14.7 is a decimal, drop this branch.\n    |- Try 44 - 19 = 25. Add 25 to the number set. Current number set: [25, 928], target: 33, just two numbers left.\n     |- Try 928 + 25 = 953. Evaluate 953 != 33, drop this branch.\n     |- Try 928 - 25 = 903. Evaluate 903 != 33, drop this branch.\n     |- Try 928 * 25 = 23200. 23200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 928 \/ 25 = 37.1. 37.1 is a decimal, drop this branch.\n    |- Try 44 * 19 = 836. Add 836 to the number set. Current number set: [836, 928], target: 33, just two numbers left.\n     |- Try 928 + 836 = 1764. Evaluate 1764 != 33, drop this branch.\n     |- Try 928 - 836 = 92. Evaluate 92 != 33, drop this branch.\n     |- Try 928 * 836 = 775808. 775808 exceeds the maximum intermediate result, drop this branch.\n     |- Try 928 \/ 836 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 44 \/ 19 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 32 \/ 29 = 1.1. 1.1 is a decimal, drop this branch.\n |- Pick two numbers (32, 44) (numbers left: [29, 19]). Try possible operations.\n  |- Try 44 + 32 = 76. Add 76 to the number set. Current number set: [76, 29, 19], target: 33. Options for choosing two numbers: [(76, 29), (76, 19), (29, 19)].\n   |- Pick two numbers (76, 29) (numbers left: [19]). Try possible operations.\n    |- Try 76 + 29 = 105. Add 105 to the number set. Current number set: [105, 19], target: 33, just two numbers left.\n     |- Try 105 + 19 = 124. Evaluate 124 != 33, drop this branch.\n     |- Try 105 - 19 = 86. Evaluate 86 != 33, drop this branch.\n     |- Try 105 * 19 = 1995. Evaluate 1995 != 33, drop this branch.\n     |- Try 105 \/ 19 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 76 - 29 = 47. Add 47 to the number set. Current number set: [47, 19], target: 33, just two numbers left.\n     |- Try 47 + 19 = 66. Evaluate 66 != 33, drop this branch.\n     |- Try 47 - 19 = 28. Evaluate 28 != 33, drop this branch.\n     |- Try 47 * 19 = 893. Evaluate 893 != 33, drop this branch.\n     |- Try 47 \/ 19 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 76 * 29 = 2204. 2204 exceeds the maximum intermediate result, drop this branch.\n    |- Try 76 \/ 29 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (76, 19) (numbers left: [29]). Try possible operations.\n    |- Try 76 + 19 = 95. Add 95 to the number set. Current number set: [95, 29], target: 33, just two numbers left.\n     |- Try 95 + 29 = 124. Evaluate 124 != 33, drop this branch.\n     |- Try 95 - 29 = 66. Evaluate 66 != 33, drop this branch.\n     |- Try 95 * 29 = 2755. 2755 exceeds the maximum intermediate result, drop this branch.\n     |- Try 95 \/ 29 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 76 - 19 = 57. Add 57 to the number set. Current number set: [57, 29], target: 33, just two numbers left.\n     |- Try 57 + 29 = 86. Evaluate 86 != 33, drop this branch.\n     |- Try 57 - 29 = 28. Evaluate 28 != 33, drop this branch.\n     |- Try 57 * 29 = 1653. Evaluate 1653 != 33, drop this branch.\n     |- Try 57 \/ 29 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 76 * 19 = 1444. Add 1444 to the number set. Current number set: [1444, 29], target: 33, just two numbers left.\n     |- Try 1444 + 29 = 1473. Evaluate 1473 != 33, drop this branch.\n     |- Try 1444 - 29 = 1415. Evaluate 1415 != 33, drop this branch.\n     |- Try 1444 * 29 = 41876. 41876 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1444 \/ 29 = 49.8. 49.8 is a decimal, drop this branch.\n    |- Try 76 \/ 19 = 4. Add 4 to the number set. Current number set: [4, 29], target: 33, just two numbers left.\n     |- Try 29 + 4 = 33. Evaluate 33 == 33, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 29 + 4 = 33\nThe step before: 76 \/ 19 = 4\nThe first step: 44 + 32 = 76\n\nOutput the solution in the required format:\n<Solution>\n44 + 32 = 76\n76 \/ 19 = 4\n29 + 4 = 33\n<\/Solution>\n","item":{"nums":[32,29,44,19],"solution":["44 + 32 = 76","76 \/ 19 = 4","29 + 4 = 33"],"target":33}}
+{"instance_id":"countdown_8k_173","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [22, 2, 15, 19]\nTarget: 44","reference_output":"# Search Procedure\nInitial number set: [22, 2, 15, 19], target: 44. Options for choosing two numbers: [(22, 2), (22, 15), (22, 19), (2, 15), (2, 19), (15, 19)].\n |- Pick two numbers (22, 2) (numbers left: [15, 19]). Try possible operations.\n  |- Try 22 + 2 = 24. Add 24 to the number set. Current number set: [24, 15, 19], target: 44. Options for choosing two numbers: [(24, 15), (24, 19), (15, 19)].\n   |- Pick two numbers (24, 15) (numbers left: [19]). Try possible operations.\n    |- Try 24 + 15 = 39. Add 39 to the number set. Current number set: [39, 19], target: 44, just two numbers left.\n     |- Try 39 + 19 = 58. Evaluate 58 != 44, drop this branch.\n     |- Try 39 - 19 = 20. Evaluate 20 != 44, drop this branch.\n     |- Try 39 * 19 = 741. Evaluate 741 != 44, drop this branch.\n     |- Try 39 \/ 19 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 24 - 15 = 9. Add 9 to the number set. Current number set: [9, 19], target: 44, just two numbers left.\n     |- Try 19 + 9 = 28. Evaluate 28 != 44, drop this branch.\n     |- Try 19 - 9 = 10. Evaluate 10 != 44, drop this branch.\n     |- Try 19 * 9 = 171. Evaluate 171 != 44, drop this branch.\n     |- Try 19 \/ 9 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 24 * 15 = 360. Add 360 to the number set. Current number set: [360, 19], target: 44, just two numbers left.\n     |- Try 360 + 19 = 379. Evaluate 379 != 44, drop this branch.\n     |- Try 360 - 19 = 341. Evaluate 341 != 44, drop this branch.\n     |- Try 360 * 19 = 6840. 6840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 360 \/ 19 = 18.9. 18.9 is a decimal, drop this branch.\n    |- Try 24 \/ 15 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (24, 19) (numbers left: [15]). Try possible operations.\n    |- Try 24 + 19 = 43. Add 43 to the number set. Current number set: [43, 15], target: 44, just two numbers left.\n     |- Try 43 + 15 = 58. Evaluate 58 != 44, drop this branch.\n     |- Try 43 - 15 = 28. Evaluate 28 != 44, drop this branch.\n     |- Try 43 * 15 = 645. Evaluate 645 != 44, drop this branch.\n     |- Try 43 \/ 15 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 24 - 19 = 5. Add 5 to the number set. Current number set: [5, 15], target: 44, just two numbers left.\n     |- Try 15 + 5 = 20. Evaluate 20 != 44, drop this branch.\n     |- Try 15 - 5 = 10. Evaluate 10 != 44, drop this branch.\n     |- Try 15 * 5 = 75. Evaluate 75 != 44, drop this branch.\n     |- Try 15 \/ 5 = 3. Evaluate 3 != 44, drop this branch.\n    |- Try 24 * 19 = 456. Add 456 to the number set. Current number set: [456, 15], target: 44, just two numbers left.\n     |- Try 456 + 15 = 471. Evaluate 471 != 44, drop this branch.\n     |- Try 456 - 15 = 441. Evaluate 441 != 44, drop this branch.\n     |- Try 456 * 15 = 6840. 6840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 456 \/ 15 = 30.4. 30.4 is a decimal, drop this branch.\n    |- Try 24 \/ 19 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (15, 19) (numbers left: [24]). Try possible operations.\n    |- Try 19 + 15 = 34. Add 34 to the number set. Current number set: [34, 24], target: 44, just two numbers left.\n     |- Try 34 + 24 = 58. Evaluate 58 != 44, drop this branch.\n     |- Try 34 - 24 = 10. Evaluate 10 != 44, drop this branch.\n     |- Try 34 * 24 = 816. Evaluate 816 != 44, drop this branch.\n     |- Try 34 \/ 24 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 19 - 15 = 4. Add 4 to the number set. Current number set: [4, 24], target: 44, just two numbers left.\n     |- Try 24 + 4 = 28. Evaluate 28 != 44, drop this branch.\n     |- Try 24 - 4 = 20. Evaluate 20 != 44, drop this branch.\n     |- Try 24 * 4 = 96. Evaluate 96 != 44, drop this branch.\n     |- Try 24 \/ 4 = 6. Evaluate 6 != 44, drop this branch.\n    |- Try 19 * 15 = 285. Add 285 to the number set. Current number set: [285, 24], target: 44, just two numbers left.\n     |- Try 285 + 24 = 309. Evaluate 309 != 44, drop this branch.\n     |- Try 285 - 24 = 261. Evaluate 261 != 44, drop this branch.\n     |- Try 285 * 24 = 6840. 6840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 285 \/ 24 = 11.9. 11.9 is a decimal, drop this branch.\n    |- Try 19 \/ 15 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 22 - 2 = 20. Add 20 to the number set. Current number set: [20, 15, 19], target: 44. Options for choosing two numbers: [(20, 15), (20, 19), (15, 19)].\n   |- Pick two numbers (20, 15) (numbers left: [19]). Try possible operations.\n    |- Try 20 + 15 = 35. Add 35 to the number set. Current number set: [35, 19], target: 44, just two numbers left.\n     |- Try 35 + 19 = 54. Evaluate 54 != 44, drop this branch.\n     |- Try 35 - 19 = 16. Evaluate 16 != 44, drop this branch.\n     |- Try 35 * 19 = 665. Evaluate 665 != 44, drop this branch.\n     |- Try 35 \/ 19 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 20 - 15 = 5. Add 5 to the number set. Current number set: [5, 19], target: 44, just two numbers left.\n     |- Try 19 + 5 = 24. Evaluate 24 != 44, drop this branch.\n     |- Try 19 - 5 = 14. Evaluate 14 != 44, drop this branch.\n     |- Try 19 * 5 = 95. Evaluate 95 != 44, drop this branch.\n     |- Try 19 \/ 5 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 20 * 15 = 300. Add 300 to the number set. Current number set: [300, 19], target: 44, just two numbers left.\n     |- Try 300 + 19 = 319. Evaluate 319 != 44, drop this branch.\n     |- Try 300 - 19 = 281. Evaluate 281 != 44, drop this branch.\n     |- Try 300 * 19 = 5700. 5700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 300 \/ 19 = 15.8. 15.8 is a decimal, drop this branch.\n    |- Try 20 \/ 15 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (20, 19) (numbers left: [15]). Try possible operations.\n    |- Try 20 + 19 = 39. Add 39 to the number set. Current number set: [39, 15], target: 44, just two numbers left.\n     |- Try 39 + 15 = 54. Evaluate 54 != 44, drop this branch.\n     |- Try 39 - 15 = 24. Evaluate 24 != 44, drop this branch.\n     |- Try 39 * 15 = 585. Evaluate 585 != 44, drop this branch.\n     |- Try 39 \/ 15 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 20 - 19 = 1. Add 1 to the number set. Current number set: [1, 15], target: 44, just two numbers left.\n     |- Try 15 + 1 = 16. Evaluate 16 != 44, drop this branch.\n     |- Try 15 - 1 = 14. Evaluate 14 != 44, drop this branch.\n     |- Try 15 * 1 = 15. Evaluate 15 != 44, drop this branch.\n     |- Try 15 \/ 1 = 15. Evaluate 15 != 44, drop this branch.\n    |- Try 20 * 19 = 380. Add 380 to the number set. Current number set: [380, 15], target: 44, just two numbers left.\n     |- Try 380 + 15 = 395. Evaluate 395 != 44, drop this branch.\n     |- Try 380 - 15 = 365. Evaluate 365 != 44, drop this branch.\n     |- Try 380 * 15 = 5700. 5700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 380 \/ 15 = 25.3. 25.3 is a decimal, drop this branch.\n    |- Try 20 \/ 19 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (15, 19) (numbers left: [20]). Try possible operations.\n    |- Try 19 + 15 = 34. Add 34 to the number set. Current number set: [34, 20], target: 44, just two numbers left.\n     |- Try 34 + 20 = 54. Evaluate 54 != 44, drop this branch.\n     |- Try 34 - 20 = 14. Evaluate 14 != 44, drop this branch.\n     |- Try 34 * 20 = 680. Evaluate 680 != 44, drop this branch.\n     |- Try 34 \/ 20 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 19 - 15 = 4. Add 4 to the number set. Current number set: [4, 20], target: 44, just two numbers left.\n     |- Try 20 + 4 = 24. Evaluate 24 != 44, drop this branch.\n     |- Try 20 - 4 = 16. Evaluate 16 != 44, drop this branch.\n     |- Try 20 * 4 = 80. Evaluate 80 != 44, drop this branch.\n     |- Try 20 \/ 4 = 5. Evaluate 5 != 44, drop this branch.\n    |- Try 19 * 15 = 285. Add 285 to the number set. Current number set: [285, 20], target: 44, just two numbers left.\n     |- Try 285 + 20 = 305. Evaluate 305 != 44, drop this branch.\n     |- Try 285 - 20 = 265. Evaluate 265 != 44, drop this branch.\n     |- Try 285 * 20 = 5700. 5700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 285 \/ 20 = 14.2. 14.2 is a decimal, drop this branch.\n    |- Try 19 \/ 15 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 22 * 2 = 44. Add 44 to the number set. Current number set: [44, 15, 19], target: 44. Options for choosing two numbers: [(44, 15), (44, 19), (15, 19)].\n   |- Pick two numbers (44, 15) (numbers left: [19]). Try possible operations.\n    |- Try 44 + 15 = 59. Add 59 to the number set. Current number set: [59, 19], target: 44, just two numbers left.\n     |- Try 59 + 19 = 78. Evaluate 78 != 44, drop this branch.\n     |- Try 59 - 19 = 40. Evaluate 40 != 44, drop this branch.\n     |- Try 59 * 19 = 1121. Evaluate 1121 != 44, drop this branch.\n     |- Try 59 \/ 19 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 44 - 15 = 29. Add 29 to the number set. Current number set: [29, 19], target: 44, just two numbers left.\n     |- Try 29 + 19 = 48. Evaluate 48 != 44, drop this branch.\n     |- Try 29 - 19 = 10. Evaluate 10 != 44, drop this branch.\n     |- Try 29 * 19 = 551. Evaluate 551 != 44, drop this branch.\n     |- Try 29 \/ 19 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 44 * 15 = 660. Add 660 to the number set. Current number set: [660, 19], target: 44, just two numbers left.\n     |- Try 660 + 19 = 679. Evaluate 679 != 44, drop this branch.\n     |- Try 660 - 19 = 641. Evaluate 641 != 44, drop this branch.\n     |- Try 660 * 19 = 12540. 12540 exceeds the maximum intermediate result, drop this branch.\n     |- Try 660 \/ 19 = 34.7. 34.7 is a decimal, drop this branch.\n    |- Try 44 \/ 15 = 2.9. 2.9 is a decimal, drop this branch.\n   |- Pick two numbers (44, 19) (numbers left: [15]). Try possible operations.\n    |- Try 44 + 19 = 63. Add 63 to the number set. Current number set: [63, 15], target: 44, just two numbers left.\n     |- Try 63 + 15 = 78. Evaluate 78 != 44, drop this branch.\n     |- Try 63 - 15 = 48. Evaluate 48 != 44, drop this branch.\n     |- Try 63 * 15 = 945. Evaluate 945 != 44, drop this branch.\n     |- Try 63 \/ 15 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 44 - 19 = 25. Add 25 to the number set. Current number set: [25, 15], target: 44, just two numbers left.\n     |- Try 25 + 15 = 40. Evaluate 40 != 44, drop this branch.\n     |- Try 25 - 15 = 10. Evaluate 10 != 44, drop this branch.\n     |- Try 25 * 15 = 375. Evaluate 375 != 44, drop this branch.\n     |- Try 25 \/ 15 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 44 * 19 = 836. Add 836 to the number set. Current number set: [836, 15], target: 44, just two numbers left.\n     |- Try 836 + 15 = 851. Evaluate 851 != 44, drop this branch.\n     |- Try 836 - 15 = 821. Evaluate 821 != 44, drop this branch.\n     |- Try 836 * 15 = 12540. 12540 exceeds the maximum intermediate result, drop this branch.\n     |- Try 836 \/ 15 = 55.7. 55.7 is a decimal, drop this branch.\n    |- Try 44 \/ 19 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (15, 19) (numbers left: [44]). Try possible operations.\n    |- Try 19 + 15 = 34. Add 34 to the number set. Current number set: [34, 44], target: 44, just two numbers left.\n     |- Try 44 + 34 = 78. Evaluate 78 != 44, drop this branch.\n     |- Try 44 - 34 = 10. Evaluate 10 != 44, drop this branch.\n     |- Try 44 * 34 = 1496. Evaluate 1496 != 44, drop this branch.\n     |- Try 44 \/ 34 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 19 - 15 = 4. Add 4 to the number set. Current number set: [4, 44], target: 44, just two numbers left.\n     |- Try 44 + 4 = 48. Evaluate 48 != 44, drop this branch.\n     |- Try 44 - 4 = 40. Evaluate 40 != 44, drop this branch.\n     |- Try 44 * 4 = 176. Evaluate 176 != 44, drop this branch.\n     |- Try 44 \/ 4 = 11. Evaluate 11 != 44, drop this branch.\n    |- Try 19 * 15 = 285. Add 285 to the number set. Current number set: [285, 44], target: 44, just two numbers left.\n     |- Try 285 + 44 = 329. Evaluate 329 != 44, drop this branch.\n     |- Try 285 - 44 = 241. Evaluate 241 != 44, drop this branch.\n     |- Try 285 * 44 = 12540. 12540 exceeds the maximum intermediate result, drop this branch.\n     |- Try 285 \/ 44 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 19 \/ 15 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 22 \/ 2 = 11. Add 11 to the number set. Current number set: [11, 15, 19], target: 44. Options for choosing two numbers: [(11, 15), (11, 19), (15, 19)].\n   |- Pick two numbers (11, 15) (numbers left: [19]). Try possible operations.\n    |- Try 15 + 11 = 26. Add 26 to the number set. Current number set: [26, 19], target: 44, just two numbers left.\n     |- Try 26 + 19 = 45. Evaluate 45 != 44, drop this branch.\n     |- Try 26 - 19 = 7. Evaluate 7 != 44, drop this branch.\n     |- Try 26 * 19 = 494. Evaluate 494 != 44, drop this branch.\n     |- Try 26 \/ 19 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 15 - 11 = 4. Add 4 to the number set. Current number set: [4, 19], target: 44, just two numbers left.\n     |- Try 19 + 4 = 23. Evaluate 23 != 44, drop this branch.\n     |- Try 19 - 4 = 15. Evaluate 15 != 44, drop this branch.\n     |- Try 19 * 4 = 76. Evaluate 76 != 44, drop this branch.\n     |- Try 19 \/ 4 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 15 * 11 = 165. Add 165 to the number set. Current number set: [165, 19], target: 44, just two numbers left.\n     |- Try 165 + 19 = 184. Evaluate 184 != 44, drop this branch.\n     |- Try 165 - 19 = 146. Evaluate 146 != 44, drop this branch.\n     |- Try 165 * 19 = 3135. 3135 exceeds the maximum intermediate result, drop this branch.\n     |- Try 165 \/ 19 = 8.7. 8.7 is a decimal, drop this branch.\n    |- Try 15 \/ 11 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (11, 19) (numbers left: [15]). Try possible operations.\n    |- Try 19 + 11 = 30. Add 30 to the number set. Current number set: [30, 15], target: 44, just two numbers left.\n     |- Try 30 + 15 = 45. Evaluate 45 != 44, drop this branch.\n     |- Try 30 - 15 = 15. Evaluate 15 != 44, drop this branch.\n     |- Try 30 * 15 = 450. Evaluate 450 != 44, drop this branch.\n     |- Try 30 \/ 15 = 2. Evaluate 2 != 44, drop this branch.\n    |- Try 19 - 11 = 8. Add 8 to the number set. Current number set: [8, 15], target: 44, just two numbers left.\n     |- Try 15 + 8 = 23. Evaluate 23 != 44, drop this branch.\n     |- Try 15 - 8 = 7. Evaluate 7 != 44, drop this branch.\n     |- Try 15 * 8 = 120. Evaluate 120 != 44, drop this branch.\n     |- Try 15 \/ 8 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 19 * 11 = 209. Add 209 to the number set. Current number set: [209, 15], target: 44, just two numbers left.\n     |- Try 209 + 15 = 224. Evaluate 224 != 44, drop this branch.\n     |- Try 209 - 15 = 194. Evaluate 194 != 44, drop this branch.\n     |- Try 209 * 15 = 3135. 3135 exceeds the maximum intermediate result, drop this branch.\n     |- Try 209 \/ 15 = 13.9. 13.9 is a decimal, drop this branch.\n    |- Try 19 \/ 11 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (15, 19) (numbers left: [11]). Try possible operations.\n    |- Try 19 + 15 = 34. Add 34 to the number set. Current number set: [34, 11], target: 44, just two numbers left.\n     |- Try 34 + 11 = 45. Evaluate 45 != 44, drop this branch.\n     |- Try 34 - 11 = 23. Evaluate 23 != 44, drop this branch.\n     |- Try 34 * 11 = 374. Evaluate 374 != 44, drop this branch.\n     |- Try 34 \/ 11 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 19 - 15 = 4. Add 4 to the number set. Current number set: [4, 11], target: 44, just two numbers left.\n     |- Try 11 + 4 = 15. Evaluate 15 != 44, drop this branch.\n     |- Try 11 - 4 = 7. Evaluate 7 != 44, drop this branch.\n     |- Try 11 * 4 = 44. Evaluate 44 == 44, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 11 * 4 = 44\nThe step before: 19 - 15 = 4\nThe first step: 22 \/ 2 = 11\n\nOutput the solution in the required format:\n<Solution>\n22 \/ 2 = 11\n19 - 15 = 4\n11 * 4 = 44\n<\/Solution>\n","item":{"nums":[22,2,15,19],"solution":["22 \/ 2 = 11","19 - 15 = 4","11 * 4 = 44"],"target":44}}
+{"instance_id":"countdown_8k_174","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [13, 22, 49, 4]\nTarget: 26","reference_output":"# Search Procedure\nInitial number set: [13, 22, 49, 4], target: 26. Options for choosing two numbers: [(13, 22), (13, 49), (13, 4), (22, 49), (22, 4), (49, 4)].\n |- Pick two numbers (13, 22) (numbers left: [49, 4]). Try possible operations.\n  |- Try 22 + 13 = 35. Add 35 to the number set. Current number set: [35, 49, 4], target: 26. Options for choosing two numbers: [(35, 49), (35, 4), (49, 4)].\n   |- Pick two numbers (35, 49) (numbers left: [4]). Try possible operations.\n    |- Try 49 + 35 = 84. Add 84 to the number set. Current number set: [84, 4], target: 26, just two numbers left.\n     |- Try 84 + 4 = 88. Evaluate 88 != 26, drop this branch.\n     |- Try 84 - 4 = 80. Evaluate 80 != 26, drop this branch.\n     |- Try 84 * 4 = 336. Evaluate 336 != 26, drop this branch.\n     |- Try 84 \/ 4 = 21. Evaluate 21 != 26, drop this branch.\n    |- Try 49 - 35 = 14. Add 14 to the number set. Current number set: [14, 4], target: 26, just two numbers left.\n     |- Try 14 + 4 = 18. Evaluate 18 != 26, drop this branch.\n     |- Try 14 - 4 = 10. Evaluate 10 != 26, drop this branch.\n     |- Try 14 * 4 = 56. Evaluate 56 != 26, drop this branch.\n     |- Try 14 \/ 4 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 49 * 35 = 1715. Add 1715 to the number set. Current number set: [1715, 4], target: 26, just two numbers left.\n     |- Try 1715 + 4 = 1719. Evaluate 1719 != 26, drop this branch.\n     |- Try 1715 - 4 = 1711. Evaluate 1711 != 26, drop this branch.\n     |- Try 1715 * 4 = 6860. 6860 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1715 \/ 4 = 428.8. 428.8 is a decimal, drop this branch.\n    |- Try 49 \/ 35 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (35, 4) (numbers left: [49]). Try possible operations.\n    |- Try 35 + 4 = 39. Add 39 to the number set. Current number set: [39, 49], target: 26, just two numbers left.\n     |- Try 49 + 39 = 88. Evaluate 88 != 26, drop this branch.\n     |- Try 49 - 39 = 10. Evaluate 10 != 26, drop this branch.\n     |- Try 49 * 39 = 1911. Evaluate 1911 != 26, drop this branch.\n     |- Try 49 \/ 39 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 35 - 4 = 31. Add 31 to the number set. Current number set: [31, 49], target: 26, just two numbers left.\n     |- Try 49 + 31 = 80. Evaluate 80 != 26, drop this branch.\n     |- Try 49 - 31 = 18. Evaluate 18 != 26, drop this branch.\n     |- Try 49 * 31 = 1519. Evaluate 1519 != 26, drop this branch.\n     |- Try 49 \/ 31 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 35 * 4 = 140. Add 140 to the number set. Current number set: [140, 49], target: 26, just two numbers left.\n     |- Try 140 + 49 = 189. Evaluate 189 != 26, drop this branch.\n     |- Try 140 - 49 = 91. Evaluate 91 != 26, drop this branch.\n     |- Try 140 * 49 = 6860. 6860 exceeds the maximum intermediate result, drop this branch.\n     |- Try 140 \/ 49 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 35 \/ 4 = 8.8. 8.8 is a decimal, drop this branch.\n   |- Pick two numbers (49, 4) (numbers left: [35]). Try possible operations.\n    |- Try 49 + 4 = 53. Add 53 to the number set. Current number set: [53, 35], target: 26, just two numbers left.\n     |- Try 53 + 35 = 88. Evaluate 88 != 26, drop this branch.\n     |- Try 53 - 35 = 18. Evaluate 18 != 26, drop this branch.\n     |- Try 53 * 35 = 1855. Evaluate 1855 != 26, drop this branch.\n     |- Try 53 \/ 35 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 49 - 4 = 45. Add 45 to the number set. Current number set: [45, 35], target: 26, just two numbers left.\n     |- Try 45 + 35 = 80. Evaluate 80 != 26, drop this branch.\n     |- Try 45 - 35 = 10. Evaluate 10 != 26, drop this branch.\n     |- Try 45 * 35 = 1575. Evaluate 1575 != 26, drop this branch.\n     |- Try 45 \/ 35 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 49 * 4 = 196. Add 196 to the number set. Current number set: [196, 35], target: 26, just two numbers left.\n     |- Try 196 + 35 = 231. Evaluate 231 != 26, drop this branch.\n     |- Try 196 - 35 = 161. Evaluate 161 != 26, drop this branch.\n     |- Try 196 * 35 = 6860. 6860 exceeds the maximum intermediate result, drop this branch.\n     |- Try 196 \/ 35 = 5.6. 5.6 is a decimal, drop this branch.\n    |- Try 49 \/ 4 = 12.2. 12.2 is a decimal, drop this branch.\n  |- Try 22 - 13 = 9. Add 9 to the number set. Current number set: [9, 49, 4], target: 26. Options for choosing two numbers: [(9, 49), (9, 4), (49, 4)].\n   |- Pick two numbers (9, 49) (numbers left: [4]). Try possible operations.\n    |- Try 49 + 9 = 58. Add 58 to the number set. Current number set: [58, 4], target: 26, just two numbers left.\n     |- Try 58 + 4 = 62. Evaluate 62 != 26, drop this branch.\n     |- Try 58 - 4 = 54. Evaluate 54 != 26, drop this branch.\n     |- Try 58 * 4 = 232. Evaluate 232 != 26, drop this branch.\n     |- Try 58 \/ 4 = 14.5. 14.5 is a decimal, drop this branch.\n    |- Try 49 - 9 = 40. Add 40 to the number set. Current number set: [40, 4], target: 26, just two numbers left.\n     |- Try 40 + 4 = 44. Evaluate 44 != 26, drop this branch.\n     |- Try 40 - 4 = 36. Evaluate 36 != 26, drop this branch.\n     |- Try 40 * 4 = 160. Evaluate 160 != 26, drop this branch.\n     |- Try 40 \/ 4 = 10. Evaluate 10 != 26, drop this branch.\n    |- Try 49 * 9 = 441. Add 441 to the number set. Current number set: [441, 4], target: 26, just two numbers left.\n     |- Try 441 + 4 = 445. Evaluate 445 != 26, drop this branch.\n     |- Try 441 - 4 = 437. Evaluate 437 != 26, drop this branch.\n     |- Try 441 * 4 = 1764. Evaluate 1764 != 26, drop this branch.\n     |- Try 441 \/ 4 = 110.2. 110.2 is a decimal, drop this branch.\n    |- Try 49 \/ 9 = 5.4. 5.4 is a decimal, drop this branch.\n   |- Pick two numbers (9, 4) (numbers left: [49]). Try possible operations.\n    |- Try 9 + 4 = 13. Add 13 to the number set. Current number set: [13, 49], target: 26, just two numbers left.\n     |- Try 49 + 13 = 62. Evaluate 62 != 26, drop this branch.\n     |- Try 49 - 13 = 36. Evaluate 36 != 26, drop this branch.\n     |- Try 49 * 13 = 637. Evaluate 637 != 26, drop this branch.\n     |- Try 49 \/ 13 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 9 - 4 = 5. Add 5 to the number set. Current number set: [5, 49], target: 26, just two numbers left.\n     |- Try 49 + 5 = 54. Evaluate 54 != 26, drop this branch.\n     |- Try 49 - 5 = 44. Evaluate 44 != 26, drop this branch.\n     |- Try 49 * 5 = 245. Evaluate 245 != 26, drop this branch.\n     |- Try 49 \/ 5 = 9.8. 9.8 is a decimal, drop this branch.\n    |- Try 9 * 4 = 36. Add 36 to the number set. Current number set: [36, 49], target: 26, just two numbers left.\n     |- Try 49 + 36 = 85. Evaluate 85 != 26, drop this branch.\n     |- Try 49 - 36 = 13. Evaluate 13 != 26, drop this branch.\n     |- Try 49 * 36 = 1764. Evaluate 1764 != 26, drop this branch.\n     |- Try 49 \/ 36 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 9 \/ 4 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (49, 4) (numbers left: [9]). Try possible operations.\n    |- Try 49 + 4 = 53. Add 53 to the number set. Current number set: [53, 9], target: 26, just two numbers left.\n     |- Try 53 + 9 = 62. Evaluate 62 != 26, drop this branch.\n     |- Try 53 - 9 = 44. Evaluate 44 != 26, drop this branch.\n     |- Try 53 * 9 = 477. Evaluate 477 != 26, drop this branch.\n     |- Try 53 \/ 9 = 5.9. 5.9 is a decimal, drop this branch.\n    |- Try 49 - 4 = 45. Add 45 to the number set. Current number set: [45, 9], target: 26, just two numbers left.\n     |- Try 45 + 9 = 54. Evaluate 54 != 26, drop this branch.\n     |- Try 45 - 9 = 36. Evaluate 36 != 26, drop this branch.\n     |- Try 45 * 9 = 405. Evaluate 405 != 26, drop this branch.\n     |- Try 45 \/ 9 = 5. Evaluate 5 != 26, drop this branch.\n    |- Try 49 * 4 = 196. Add 196 to the number set. Current number set: [196, 9], target: 26, just two numbers left.\n     |- Try 196 + 9 = 205. Evaluate 205 != 26, drop this branch.\n     |- Try 196 - 9 = 187. Evaluate 187 != 26, drop this branch.\n     |- Try 196 * 9 = 1764. Evaluate 1764 != 26, drop this branch.\n     |- Try 196 \/ 9 = 21.8. 21.8 is a decimal, drop this branch.\n    |- Try 49 \/ 4 = 12.2. 12.2 is a decimal, drop this branch.\n  |- Try 22 * 13 = 286. Add 286 to the number set. Current number set: [286, 49, 4], target: 26. Options for choosing two numbers: [(286, 49), (286, 4), (49, 4)].\n   |- Pick two numbers (286, 49) (numbers left: [4]). Try possible operations.\n    |- Try 286 + 49 = 335. Add 335 to the number set. Current number set: [335, 4], target: 26, just two numbers left.\n     |- Try 335 + 4 = 339. Evaluate 339 != 26, drop this branch.\n     |- Try 335 - 4 = 331. Evaluate 331 != 26, drop this branch.\n     |- Try 335 * 4 = 1340. Evaluate 1340 != 26, drop this branch.\n     |- Try 335 \/ 4 = 83.8. 83.8 is a decimal, drop this branch.\n    |- Try 286 - 49 = 237. Add 237 to the number set. Current number set: [237, 4], target: 26, just two numbers left.\n     |- Try 237 + 4 = 241. Evaluate 241 != 26, drop this branch.\n     |- Try 237 - 4 = 233. Evaluate 233 != 26, drop this branch.\n     |- Try 237 * 4 = 948. Evaluate 948 != 26, drop this branch.\n     |- Try 237 \/ 4 = 59.2. 59.2 is a decimal, drop this branch.\n    |- Try 286 * 49 = 14014. 14014 exceeds the maximum intermediate result, drop this branch.\n    |- Try 286 \/ 49 = 5.8. 5.8 is a decimal, drop this branch.\n   |- Pick two numbers (286, 4) (numbers left: [49]). Try possible operations.\n    |- Try 286 + 4 = 290. Add 290 to the number set. Current number set: [290, 49], target: 26, just two numbers left.\n     |- Try 290 + 49 = 339. Evaluate 339 != 26, drop this branch.\n     |- Try 290 - 49 = 241. Evaluate 241 != 26, drop this branch.\n     |- Try 290 * 49 = 14210. 14210 exceeds the maximum intermediate result, drop this branch.\n     |- Try 290 \/ 49 = 5.9. 5.9 is a decimal, drop this branch.\n    |- Try 286 - 4 = 282. Add 282 to the number set. Current number set: [282, 49], target: 26, just two numbers left.\n     |- Try 282 + 49 = 331. Evaluate 331 != 26, drop this branch.\n     |- Try 282 - 49 = 233. Evaluate 233 != 26, drop this branch.\n     |- Try 282 * 49 = 13818. 13818 exceeds the maximum intermediate result, drop this branch.\n     |- Try 282 \/ 49 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 286 * 4 = 1144. Add 1144 to the number set. Current number set: [1144, 49], target: 26, just two numbers left.\n     |- Try 1144 + 49 = 1193. Evaluate 1193 != 26, drop this branch.\n     |- Try 1144 - 49 = 1095. Evaluate 1095 != 26, drop this branch.\n     |- Try 1144 * 49 = 56056. 56056 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1144 \/ 49 = 23.3. 23.3 is a decimal, drop this branch.\n    |- Try 286 \/ 4 = 71.5. 71.5 is a decimal, drop this branch.\n   |- Pick two numbers (49, 4) (numbers left: [286]). Try possible operations.\n    |- Try 49 + 4 = 53. Add 53 to the number set. Current number set: [53, 286], target: 26, just two numbers left.\n     |- Try 286 + 53 = 339. Evaluate 339 != 26, drop this branch.\n     |- Try 286 - 53 = 233. Evaluate 233 != 26, drop this branch.\n     |- Try 286 * 53 = 15158. 15158 exceeds the maximum intermediate result, drop this branch.\n     |- Try 286 \/ 53 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 49 - 4 = 45. Add 45 to the number set. Current number set: [45, 286], target: 26, just two numbers left.\n     |- Try 286 + 45 = 331. Evaluate 331 != 26, drop this branch.\n     |- Try 286 - 45 = 241. Evaluate 241 != 26, drop this branch.\n     |- Try 286 * 45 = 12870. 12870 exceeds the maximum intermediate result, drop this branch.\n     |- Try 286 \/ 45 = 6.4. 6.4 is a decimal, drop this branch.\n    |- Try 49 * 4 = 196. Add 196 to the number set. Current number set: [196, 286], target: 26, just two numbers left.\n     |- Try 286 + 196 = 482. Evaluate 482 != 26, drop this branch.\n     |- Try 286 - 196 = 90. Evaluate 90 != 26, drop this branch.\n     |- Try 286 * 196 = 56056. 56056 exceeds the maximum intermediate result, drop this branch.\n     |- Try 286 \/ 196 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 49 \/ 4 = 12.2. 12.2 is a decimal, drop this branch.\n  |- Try 22 \/ 13 = 1.7. 1.7 is a decimal, drop this branch.\n |- Pick two numbers (13, 49) (numbers left: [22, 4]). Try possible operations.\n  |- Try 49 + 13 = 62. Add 62 to the number set. Current number set: [62, 22, 4], target: 26. Options for choosing two numbers: [(62, 22), (62, 4), (22, 4)].\n   |- Pick two numbers (62, 22) (numbers left: [4]). Try possible operations.\n    |- Try 62 + 22 = 84. Add 84 to the number set. Current number set: [84, 4], target: 26, just two numbers left.\n     |- Try 84 + 4 = 88. Evaluate 88 != 26, drop this branch.\n     |- Try 84 - 4 = 80. Evaluate 80 != 26, drop this branch.\n     |- Try 84 * 4 = 336. Evaluate 336 != 26, drop this branch.\n     |- Try 84 \/ 4 = 21. Evaluate 21 != 26, drop this branch.\n    |- Try 62 - 22 = 40. Add 40 to the number set. Current number set: [40, 4], target: 26, just two numbers left.\n     |- Try 40 + 4 = 44. Evaluate 44 != 26, drop this branch.\n     |- Try 40 - 4 = 36. Evaluate 36 != 26, drop this branch.\n     |- Try 40 * 4 = 160. Evaluate 160 != 26, drop this branch.\n     |- Try 40 \/ 4 = 10. Evaluate 10 != 26, drop this branch.\n    |- Try 62 * 22 = 1364. Add 1364 to the number set. Current number set: [1364, 4], target: 26, just two numbers left.\n     |- Try 1364 + 4 = 1368. Evaluate 1368 != 26, drop this branch.\n     |- Try 1364 - 4 = 1360. Evaluate 1360 != 26, drop this branch.\n     |- Try 1364 * 4 = 5456. 5456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1364 \/ 4 = 341. Evaluate 341 != 26, drop this branch.\n    |- Try 62 \/ 22 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (62, 4) (numbers left: [22]). Try possible operations.\n    |- Try 62 + 4 = 66. Add 66 to the number set. Current number set: [66, 22], target: 26, just two numbers left.\n     |- Try 66 + 22 = 88. Evaluate 88 != 26, drop this branch.\n     |- Try 66 - 22 = 44. Evaluate 44 != 26, drop this branch.\n     |- Try 66 * 22 = 1452. Evaluate 1452 != 26, drop this branch.\n     |- Try 66 \/ 22 = 3. Evaluate 3 != 26, drop this branch.\n    |- Try 62 - 4 = 58. Add 58 to the number set. Current number set: [58, 22], target: 26, just two numbers left.\n     |- Try 58 + 22 = 80. Evaluate 80 != 26, drop this branch.\n     |- Try 58 - 22 = 36. Evaluate 36 != 26, drop this branch.\n     |- Try 58 * 22 = 1276. Evaluate 1276 != 26, drop this branch.\n     |- Try 58 \/ 22 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 62 * 4 = 248. Add 248 to the number set. Current number set: [248, 22], target: 26, just two numbers left.\n     |- Try 248 + 22 = 270. Evaluate 270 != 26, drop this branch.\n     |- Try 248 - 22 = 226. Evaluate 226 != 26, drop this branch.\n     |- Try 248 * 22 = 5456. 5456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 248 \/ 22 = 11.3. 11.3 is a decimal, drop this branch.\n    |- Try 62 \/ 4 = 15.5. 15.5 is a decimal, drop this branch.\n   |- Pick two numbers (22, 4) (numbers left: [62]). Try possible operations.\n    |- Try 22 + 4 = 26. Add 26 to the number set. Current number set: [26, 62], target: 26, just two numbers left.\n     |- Try 62 + 26 = 88. Evaluate 88 != 26, drop this branch.\n     |- Try 62 - 26 = 36. Evaluate 36 != 26, drop this branch.\n     |- Try 62 * 26 = 1612. Evaluate 1612 != 26, drop this branch.\n     |- Try 62 \/ 26 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 22 - 4 = 18. Add 18 to the number set. Current number set: [18, 62], target: 26, just two numbers left.\n     |- Try 62 + 18 = 80. Evaluate 80 != 26, drop this branch.\n     |- Try 62 - 18 = 44. Evaluate 44 != 26, drop this branch.\n     |- Try 62 * 18 = 1116. Evaluate 1116 != 26, drop this branch.\n     |- Try 62 \/ 18 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 22 * 4 = 88. Add 88 to the number set. Current number set: [88, 62], target: 26, just two numbers left.\n     |- Try 88 + 62 = 150. Evaluate 150 != 26, drop this branch.\n     |- Try 88 - 62 = 26. Evaluate 26 == 26, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 88 - 62 = 26\nThe step before: 22 * 4 = 88\nThe first step: 49 + 13 = 62\n\nOutput the solution in the required format:\n<Solution>\n49 + 13 = 62\n22 * 4 = 88\n88 - 62 = 26\n<\/Solution>\n","item":{"nums":[13,22,49,4],"solution":["49 + 13 = 62","22 * 4 = 88","88 - 62 = 26"],"target":26}}
+{"instance_id":"countdown_8k_175","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [49, 3, 23, 5]\nTarget: 41","reference_output":"# Search Procedure\nInitial number set: [49, 3, 23, 5], target: 41. Options for choosing two numbers: [(49, 3), (49, 23), (49, 5), (3, 23), (3, 5), (23, 5)].\n |- Pick two numbers (49, 3) (numbers left: [23, 5]). Try possible operations.\n  |- Try 49 + 3 = 52. Add 52 to the number set. Current number set: [52, 23, 5], target: 41. Options for choosing two numbers: [(52, 23), (52, 5), (23, 5)].\n   |- Pick two numbers (52, 23) (numbers left: [5]). Try possible operations.\n    |- Try 52 + 23 = 75. Add 75 to the number set. Current number set: [75, 5], target: 41, just two numbers left.\n     |- Try 75 + 5 = 80. Evaluate 80 != 41, drop this branch.\n     |- Try 75 - 5 = 70. Evaluate 70 != 41, drop this branch.\n     |- Try 75 * 5 = 375. Evaluate 375 != 41, drop this branch.\n     |- Try 75 \/ 5 = 15. Evaluate 15 != 41, drop this branch.\n    |- Try 52 - 23 = 29. Add 29 to the number set. Current number set: [29, 5], target: 41, just two numbers left.\n     |- Try 29 + 5 = 34. Evaluate 34 != 41, drop this branch.\n     |- Try 29 - 5 = 24. Evaluate 24 != 41, drop this branch.\n     |- Try 29 * 5 = 145. Evaluate 145 != 41, drop this branch.\n     |- Try 29 \/ 5 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 52 * 23 = 1196. Add 1196 to the number set. Current number set: [1196, 5], target: 41, just two numbers left.\n     |- Try 1196 + 5 = 1201. Evaluate 1201 != 41, drop this branch.\n     |- Try 1196 - 5 = 1191. Evaluate 1191 != 41, drop this branch.\n     |- Try 1196 * 5 = 5980. 5980 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1196 \/ 5 = 239.2. 239.2 is a decimal, drop this branch.\n    |- Try 52 \/ 23 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (52, 5) (numbers left: [23]). Try possible operations.\n    |- Try 52 + 5 = 57. Add 57 to the number set. Current number set: [57, 23], target: 41, just two numbers left.\n     |- Try 57 + 23 = 80. Evaluate 80 != 41, drop this branch.\n     |- Try 57 - 23 = 34. Evaluate 34 != 41, drop this branch.\n     |- Try 57 * 23 = 1311. Evaluate 1311 != 41, drop this branch.\n     |- Try 57 \/ 23 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 52 - 5 = 47. Add 47 to the number set. Current number set: [47, 23], target: 41, just two numbers left.\n     |- Try 47 + 23 = 70. Evaluate 70 != 41, drop this branch.\n     |- Try 47 - 23 = 24. Evaluate 24 != 41, drop this branch.\n     |- Try 47 * 23 = 1081. Evaluate 1081 != 41, drop this branch.\n     |- Try 47 \/ 23 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 52 * 5 = 260. Add 260 to the number set. Current number set: [260, 23], target: 41, just two numbers left.\n     |- Try 260 + 23 = 283. Evaluate 283 != 41, drop this branch.\n     |- Try 260 - 23 = 237. Evaluate 237 != 41, drop this branch.\n     |- Try 260 * 23 = 5980. 5980 exceeds the maximum intermediate result, drop this branch.\n     |- Try 260 \/ 23 = 11.3. 11.3 is a decimal, drop this branch.\n    |- Try 52 \/ 5 = 10.4. 10.4 is a decimal, drop this branch.\n   |- Pick two numbers (23, 5) (numbers left: [52]). Try possible operations.\n    |- Try 23 + 5 = 28. Add 28 to the number set. Current number set: [28, 52], target: 41, just two numbers left.\n     |- Try 52 + 28 = 80. Evaluate 80 != 41, drop this branch.\n     |- Try 52 - 28 = 24. Evaluate 24 != 41, drop this branch.\n     |- Try 52 * 28 = 1456. Evaluate 1456 != 41, drop this branch.\n     |- Try 52 \/ 28 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 23 - 5 = 18. Add 18 to the number set. Current number set: [18, 52], target: 41, just two numbers left.\n     |- Try 52 + 18 = 70. Evaluate 70 != 41, drop this branch.\n     |- Try 52 - 18 = 34. Evaluate 34 != 41, drop this branch.\n     |- Try 52 * 18 = 936. Evaluate 936 != 41, drop this branch.\n     |- Try 52 \/ 18 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 23 * 5 = 115. Add 115 to the number set. Current number set: [115, 52], target: 41, just two numbers left.\n     |- Try 115 + 52 = 167. Evaluate 167 != 41, drop this branch.\n     |- Try 115 - 52 = 63. Evaluate 63 != 41, drop this branch.\n     |- Try 115 * 52 = 5980. 5980 exceeds the maximum intermediate result, drop this branch.\n     |- Try 115 \/ 52 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 23 \/ 5 = 4.6. 4.6 is a decimal, drop this branch.\n  |- Try 49 - 3 = 46. Add 46 to the number set. Current number set: [46, 23, 5], target: 41. Options for choosing two numbers: [(46, 23), (46, 5), (23, 5)].\n   |- Pick two numbers (46, 23) (numbers left: [5]). Try possible operations.\n    |- Try 46 + 23 = 69. Add 69 to the number set. Current number set: [69, 5], target: 41, just two numbers left.\n     |- Try 69 + 5 = 74. Evaluate 74 != 41, drop this branch.\n     |- Try 69 - 5 = 64. Evaluate 64 != 41, drop this branch.\n     |- Try 69 * 5 = 345. Evaluate 345 != 41, drop this branch.\n     |- Try 69 \/ 5 = 13.8. 13.8 is a decimal, drop this branch.\n    |- Try 46 - 23 = 23. Add 23 to the number set. Current number set: [23, 5], target: 41, just two numbers left.\n     |- Try 23 + 5 = 28. Evaluate 28 != 41, drop this branch.\n     |- Try 23 - 5 = 18. Evaluate 18 != 41, drop this branch.\n     |- Try 23 * 5 = 115. Evaluate 115 != 41, drop this branch.\n     |- Try 23 \/ 5 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 46 * 23 = 1058. Add 1058 to the number set. Current number set: [1058, 5], target: 41, just two numbers left.\n     |- Try 1058 + 5 = 1063. Evaluate 1063 != 41, drop this branch.\n     |- Try 1058 - 5 = 1053. Evaluate 1053 != 41, drop this branch.\n     |- Try 1058 * 5 = 5290. 5290 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1058 \/ 5 = 211.6. 211.6 is a decimal, drop this branch.\n    |- Try 46 \/ 23 = 2. Add 2 to the number set. Current number set: [2, 5], target: 41, just two numbers left.\n     |- Try 5 + 2 = 7. Evaluate 7 != 41, drop this branch.\n     |- Try 5 - 2 = 3. Evaluate 3 != 41, drop this branch.\n     |- Try 5 * 2 = 10. Evaluate 10 != 41, drop this branch.\n     |- Try 5 \/ 2 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (46, 5) (numbers left: [23]). Try possible operations.\n    |- Try 46 + 5 = 51. Add 51 to the number set. Current number set: [51, 23], target: 41, just two numbers left.\n     |- Try 51 + 23 = 74. Evaluate 74 != 41, drop this branch.\n     |- Try 51 - 23 = 28. Evaluate 28 != 41, drop this branch.\n     |- Try 51 * 23 = 1173. Evaluate 1173 != 41, drop this branch.\n     |- Try 51 \/ 23 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 46 - 5 = 41. Add 41 to the number set. Current number set: [41, 23], target: 41, just two numbers left.\n     |- Try 41 + 23 = 64. Evaluate 64 != 41, drop this branch.\n     |- Try 41 - 23 = 18. Evaluate 18 != 41, drop this branch.\n     |- Try 41 * 23 = 943. Evaluate 943 != 41, drop this branch.\n     |- Try 41 \/ 23 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 46 * 5 = 230. Add 230 to the number set. Current number set: [230, 23], target: 41, just two numbers left.\n     |- Try 230 + 23 = 253. Evaluate 253 != 41, drop this branch.\n     |- Try 230 - 23 = 207. Evaluate 207 != 41, drop this branch.\n     |- Try 230 * 23 = 5290. 5290 exceeds the maximum intermediate result, drop this branch.\n     |- Try 230 \/ 23 = 10. Evaluate 10 != 41, drop this branch.\n    |- Try 46 \/ 5 = 9.2. 9.2 is a decimal, drop this branch.\n   |- Pick two numbers (23, 5) (numbers left: [46]). Try possible operations.\n    |- Try 23 + 5 = 28. Add 28 to the number set. Current number set: [28, 46], target: 41, just two numbers left.\n     |- Try 46 + 28 = 74. Evaluate 74 != 41, drop this branch.\n     |- Try 46 - 28 = 18. Evaluate 18 != 41, drop this branch.\n     |- Try 46 * 28 = 1288. Evaluate 1288 != 41, drop this branch.\n     |- Try 46 \/ 28 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 23 - 5 = 18. Add 18 to the number set. Current number set: [18, 46], target: 41, just two numbers left.\n     |- Try 46 + 18 = 64. Evaluate 64 != 41, drop this branch.\n     |- Try 46 - 18 = 28. Evaluate 28 != 41, drop this branch.\n     |- Try 46 * 18 = 828. Evaluate 828 != 41, drop this branch.\n     |- Try 46 \/ 18 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 23 * 5 = 115. Add 115 to the number set. Current number set: [115, 46], target: 41, just two numbers left.\n     |- Try 115 + 46 = 161. Evaluate 161 != 41, drop this branch.\n     |- Try 115 - 46 = 69. Evaluate 69 != 41, drop this branch.\n     |- Try 115 * 46 = 5290. 5290 exceeds the maximum intermediate result, drop this branch.\n     |- Try 115 \/ 46 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 23 \/ 5 = 4.6. 4.6 is a decimal, drop this branch.\n  |- Try 49 * 3 = 147. Add 147 to the number set. Current number set: [147, 23, 5], target: 41. Options for choosing two numbers: [(147, 23), (147, 5), (23, 5)].\n   |- Pick two numbers (147, 23) (numbers left: [5]). Try possible operations.\n    |- Try 147 + 23 = 170. Add 170 to the number set. Current number set: [170, 5], target: 41, just two numbers left.\n     |- Try 170 + 5 = 175. Evaluate 175 != 41, drop this branch.\n     |- Try 170 - 5 = 165. Evaluate 165 != 41, drop this branch.\n     |- Try 170 * 5 = 850. Evaluate 850 != 41, drop this branch.\n     |- Try 170 \/ 5 = 34. Evaluate 34 != 41, drop this branch.\n    |- Try 147 - 23 = 124. Add 124 to the number set. Current number set: [124, 5], target: 41, just two numbers left.\n     |- Try 124 + 5 = 129. Evaluate 129 != 41, drop this branch.\n     |- Try 124 - 5 = 119. Evaluate 119 != 41, drop this branch.\n     |- Try 124 * 5 = 620. Evaluate 620 != 41, drop this branch.\n     |- Try 124 \/ 5 = 24.8. 24.8 is a decimal, drop this branch.\n    |- Try 147 * 23 = 3381. 3381 exceeds the maximum intermediate result, drop this branch.\n    |- Try 147 \/ 23 = 6.4. 6.4 is a decimal, drop this branch.\n   |- Pick two numbers (147, 5) (numbers left: [23]). Try possible operations.\n    |- Try 147 + 5 = 152. Add 152 to the number set. Current number set: [152, 23], target: 41, just two numbers left.\n     |- Try 152 + 23 = 175. Evaluate 175 != 41, drop this branch.\n     |- Try 152 - 23 = 129. Evaluate 129 != 41, drop this branch.\n     |- Try 152 * 23 = 3496. 3496 exceeds the maximum intermediate result, drop this branch.\n     |- Try 152 \/ 23 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 147 - 5 = 142. Add 142 to the number set. Current number set: [142, 23], target: 41, just two numbers left.\n     |- Try 142 + 23 = 165. Evaluate 165 != 41, drop this branch.\n     |- Try 142 - 23 = 119. Evaluate 119 != 41, drop this branch.\n     |- Try 142 * 23 = 3266. 3266 exceeds the maximum intermediate result, drop this branch.\n     |- Try 142 \/ 23 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 147 * 5 = 735. Add 735 to the number set. Current number set: [735, 23], target: 41, just two numbers left.\n     |- Try 735 + 23 = 758. Evaluate 758 != 41, drop this branch.\n     |- Try 735 - 23 = 712. Evaluate 712 != 41, drop this branch.\n     |- Try 735 * 23 = 16905. 16905 exceeds the maximum intermediate result, drop this branch.\n     |- Try 735 \/ 23 = 32.0. 32.0 is a decimal, drop this branch.\n    |- Try 147 \/ 5 = 29.4. 29.4 is a decimal, drop this branch.\n   |- Pick two numbers (23, 5) (numbers left: [147]). Try possible operations.\n    |- Try 23 + 5 = 28. Add 28 to the number set. Current number set: [28, 147], target: 41, just two numbers left.\n     |- Try 147 + 28 = 175. Evaluate 175 != 41, drop this branch.\n     |- Try 147 - 28 = 119. Evaluate 119 != 41, drop this branch.\n     |- Try 147 * 28 = 4116. 4116 exceeds the maximum intermediate result, drop this branch.\n     |- Try 147 \/ 28 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 23 - 5 = 18. Add 18 to the number set. Current number set: [18, 147], target: 41, just two numbers left.\n     |- Try 147 + 18 = 165. Evaluate 165 != 41, drop this branch.\n     |- Try 147 - 18 = 129. Evaluate 129 != 41, drop this branch.\n     |- Try 147 * 18 = 2646. 2646 exceeds the maximum intermediate result, drop this branch.\n     |- Try 147 \/ 18 = 8.2. 8.2 is a decimal, drop this branch.\n    |- Try 23 * 5 = 115. Add 115 to the number set. Current number set: [115, 147], target: 41, just two numbers left.\n     |- Try 147 + 115 = 262. Evaluate 262 != 41, drop this branch.\n     |- Try 147 - 115 = 32. Evaluate 32 != 41, drop this branch.\n     |- Try 147 * 115 = 16905. 16905 exceeds the maximum intermediate result, drop this branch.\n     |- Try 147 \/ 115 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 23 \/ 5 = 4.6. 4.6 is a decimal, drop this branch.\n  |- Try 49 \/ 3 = 16.3. 16.3 is a decimal, drop this branch.\n |- Pick two numbers (49, 23) (numbers left: [3, 5]). Try possible operations.\n  |- Try 49 + 23 = 72. Add 72 to the number set. Current number set: [72, 3, 5], target: 41. Options for choosing two numbers: [(72, 3), (72, 5), (3, 5)].\n   |- Pick two numbers (72, 3) (numbers left: [5]). Try possible operations.\n    |- Try 72 + 3 = 75. Add 75 to the number set. Current number set: [75, 5], target: 41, just two numbers left.\n     |- Try 75 + 5 = 80. Evaluate 80 != 41, drop this branch.\n     |- Try 75 - 5 = 70. Evaluate 70 != 41, drop this branch.\n     |- Try 75 * 5 = 375. Evaluate 375 != 41, drop this branch.\n     |- Try 75 \/ 5 = 15. Evaluate 15 != 41, drop this branch.\n    |- Try 72 - 3 = 69. Add 69 to the number set. Current number set: [69, 5], target: 41, just two numbers left.\n     |- Try 69 + 5 = 74. Evaluate 74 != 41, drop this branch.\n     |- Try 69 - 5 = 64. Evaluate 64 != 41, drop this branch.\n     |- Try 69 * 5 = 345. Evaluate 345 != 41, drop this branch.\n     |- Try 69 \/ 5 = 13.8. 13.8 is a decimal, drop this branch.\n    |- Try 72 * 3 = 216. Add 216 to the number set. Current number set: [216, 5], target: 41, just two numbers left.\n     |- Try 216 + 5 = 221. Evaluate 221 != 41, drop this branch.\n     |- Try 216 - 5 = 211. Evaluate 211 != 41, drop this branch.\n     |- Try 216 * 5 = 1080. Evaluate 1080 != 41, drop this branch.\n     |- Try 216 \/ 5 = 43.2. 43.2 is a decimal, drop this branch.\n    |- Try 72 \/ 3 = 24. Add 24 to the number set. Current number set: [24, 5], target: 41, just two numbers left.\n     |- Try 24 + 5 = 29. Evaluate 29 != 41, drop this branch.\n     |- Try 24 - 5 = 19. Evaluate 19 != 41, drop this branch.\n     |- Try 24 * 5 = 120. Evaluate 120 != 41, drop this branch.\n     |- Try 24 \/ 5 = 4.8. 4.8 is a decimal, drop this branch.\n   |- Pick two numbers (72, 5) (numbers left: [3]). Try possible operations.\n    |- Try 72 + 5 = 77. Add 77 to the number set. Current number set: [77, 3], target: 41, just two numbers left.\n     |- Try 77 + 3 = 80. Evaluate 80 != 41, drop this branch.\n     |- Try 77 - 3 = 74. Evaluate 74 != 41, drop this branch.\n     |- Try 77 * 3 = 231. Evaluate 231 != 41, drop this branch.\n     |- Try 77 \/ 3 = 25.7. 25.7 is a decimal, drop this branch.\n    |- Try 72 - 5 = 67. Add 67 to the number set. Current number set: [67, 3], target: 41, just two numbers left.\n     |- Try 67 + 3 = 70. Evaluate 70 != 41, drop this branch.\n     |- Try 67 - 3 = 64. Evaluate 64 != 41, drop this branch.\n     |- Try 67 * 3 = 201. Evaluate 201 != 41, drop this branch.\n     |- Try 67 \/ 3 = 22.3. 22.3 is a decimal, drop this branch.\n    |- Try 72 * 5 = 360. Add 360 to the number set. Current number set: [360, 3], target: 41, just two numbers left.\n     |- Try 360 + 3 = 363. Evaluate 363 != 41, drop this branch.\n     |- Try 360 - 3 = 357. Evaluate 357 != 41, drop this branch.\n     |- Try 360 * 3 = 1080. Evaluate 1080 != 41, drop this branch.\n     |- Try 360 \/ 3 = 120. Evaluate 120 != 41, drop this branch.\n    |- Try 72 \/ 5 = 14.4. 14.4 is a decimal, drop this branch.\n   |- Pick two numbers (3, 5) (numbers left: [72]). Try possible operations.\n    |- Try 5 + 3 = 8. Add 8 to the number set. Current number set: [8, 72], target: 41, just two numbers left.\n     |- Try 72 + 8 = 80. Evaluate 80 != 41, drop this branch.\n     |- Try 72 - 8 = 64. Evaluate 64 != 41, drop this branch.\n     |- Try 72 * 8 = 576. Evaluate 576 != 41, drop this branch.\n     |- Try 72 \/ 8 = 9. Evaluate 9 != 41, drop this branch.\n    |- Try 5 - 3 = 2. Add 2 to the number set. Current number set: [2, 72], target: 41, just two numbers left.\n     |- Try 72 + 2 = 74. Evaluate 74 != 41, drop this branch.\n     |- Try 72 - 2 = 70. Evaluate 70 != 41, drop this branch.\n     |- Try 72 * 2 = 144. Evaluate 144 != 41, drop this branch.\n     |- Try 72 \/ 2 = 36. Evaluate 36 != 41, drop this branch.\n    |- Try 5 * 3 = 15. Add 15 to the number set. Current number set: [15, 72], target: 41, just two numbers left.\n     |- Try 72 + 15 = 87. Evaluate 87 != 41, drop this branch.\n     |- Try 72 - 15 = 57. Evaluate 57 != 41, drop this branch.\n     |- Try 72 * 15 = 1080. Evaluate 1080 != 41, drop this branch.\n     |- Try 72 \/ 15 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 5 \/ 3 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 49 - 23 = 26. Add 26 to the number set. Current number set: [26, 3, 5], target: 41. Options for choosing two numbers: [(26, 3), (26, 5), (3, 5)].\n   |- Pick two numbers (26, 3) (numbers left: [5]). Try possible operations.\n    |- Try 26 + 3 = 29. Add 29 to the number set. Current number set: [29, 5], target: 41, just two numbers left.\n     |- Try 29 + 5 = 34. Evaluate 34 != 41, drop this branch.\n     |- Try 29 - 5 = 24. Evaluate 24 != 41, drop this branch.\n     |- Try 29 * 5 = 145. Evaluate 145 != 41, drop this branch.\n     |- Try 29 \/ 5 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 26 - 3 = 23. Add 23 to the number set. Current number set: [23, 5], target: 41, just two numbers left.\n     |- Try 23 + 5 = 28. Evaluate 28 != 41, drop this branch.\n     |- Try 23 - 5 = 18. Evaluate 18 != 41, drop this branch.\n     |- Try 23 * 5 = 115. Evaluate 115 != 41, drop this branch.\n     |- Try 23 \/ 5 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 26 * 3 = 78. Add 78 to the number set. Current number set: [78, 5], target: 41, just two numbers left.\n     |- Try 78 + 5 = 83. Evaluate 83 != 41, drop this branch.\n     |- Try 78 - 5 = 73. Evaluate 73 != 41, drop this branch.\n     |- Try 78 * 5 = 390. Evaluate 390 != 41, drop this branch.\n     |- Try 78 \/ 5 = 15.6. 15.6 is a decimal, drop this branch.\n    |- Try 26 \/ 3 = 8.7. 8.7 is a decimal, drop this branch.\n   |- Pick two numbers (26, 5) (numbers left: [3]). Try possible operations.\n    |- Try 26 + 5 = 31. Add 31 to the number set. Current number set: [31, 3], target: 41, just two numbers left.\n     |- Try 31 + 3 = 34. Evaluate 34 != 41, drop this branch.\n     |- Try 31 - 3 = 28. Evaluate 28 != 41, drop this branch.\n     |- Try 31 * 3 = 93. Evaluate 93 != 41, drop this branch.\n     |- Try 31 \/ 3 = 10.3. 10.3 is a decimal, drop this branch.\n    |- Try 26 - 5 = 21. Add 21 to the number set. Current number set: [21, 3], target: 41, just two numbers left.\n     |- Try 21 + 3 = 24. Evaluate 24 != 41, drop this branch.\n     |- Try 21 - 3 = 18. Evaluate 18 != 41, drop this branch.\n     |- Try 21 * 3 = 63. Evaluate 63 != 41, drop this branch.\n     |- Try 21 \/ 3 = 7. Evaluate 7 != 41, drop this branch.\n    |- Try 26 * 5 = 130. Add 130 to the number set. Current number set: [130, 3], target: 41, just two numbers left.\n     |- Try 130 + 3 = 133. Evaluate 133 != 41, drop this branch.\n     |- Try 130 - 3 = 127. Evaluate 127 != 41, drop this branch.\n     |- Try 130 * 3 = 390. Evaluate 390 != 41, drop this branch.\n     |- Try 130 \/ 3 = 43.3. 43.3 is a decimal, drop this branch.\n    |- Try 26 \/ 5 = 5.2. 5.2 is a decimal, drop this branch.\n   |- Pick two numbers (3, 5) (numbers left: [26]). Try possible operations.\n    |- Try 5 + 3 = 8. Add 8 to the number set. Current number set: [8, 26], target: 41, just two numbers left.\n     |- Try 26 + 8 = 34. Evaluate 34 != 41, drop this branch.\n     |- Try 26 - 8 = 18. Evaluate 18 != 41, drop this branch.\n     |- Try 26 * 8 = 208. Evaluate 208 != 41, drop this branch.\n     |- Try 26 \/ 8 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 5 - 3 = 2. Add 2 to the number set. Current number set: [2, 26], target: 41, just two numbers left.\n     |- Try 26 + 2 = 28. Evaluate 28 != 41, drop this branch.\n     |- Try 26 - 2 = 24. Evaluate 24 != 41, drop this branch.\n     |- Try 26 * 2 = 52. Evaluate 52 != 41, drop this branch.\n     |- Try 26 \/ 2 = 13. Evaluate 13 != 41, drop this branch.\n    |- Try 5 * 3 = 15. Add 15 to the number set. Current number set: [15, 26], target: 41, just two numbers left.\n     |- Try 26 + 15 = 41. Evaluate 41 == 41, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 26 + 15 = 41\nThe step before: 5 * 3 = 15\nThe first step: 49 - 23 = 26\n\nOutput the solution in the required format:\n<Solution>\n49 - 23 = 26\n5 * 3 = 15\n26 + 15 = 41\n<\/Solution>\n","item":{"nums":[49,3,23,5],"solution":["49 - 23 = 26","5 * 3 = 15","26 + 15 = 41"],"target":41}}
+{"instance_id":"countdown_8k_176","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [16, 4, 5, 4]\nTarget: 24","reference_output":"# Search Procedure\nInitial number set: [16, 4, 5, 4], target: 24. Options for choosing two numbers: [(16, 4), (16, 5), (16, 4), (4, 5), (4, 4), (5, 4)].\n |- Pick two numbers (16, 4) (numbers left: [5, 4]). Try possible operations.\n  |- Try 16 + 4 = 20. Add 20 to the number set. Current number set: [20, 5, 4], target: 24. Options for choosing two numbers: [(20, 5), (20, 4), (5, 4)].\n   |- Pick two numbers (20, 5) (numbers left: [4]). Try possible operations.\n    |- Try 20 + 5 = 25. Add 25 to the number set. Current number set: [25, 4], target: 24, just two numbers left.\n     |- Try 25 + 4 = 29. Evaluate 29 != 24, drop this branch.\n     |- Try 25 - 4 = 21. Evaluate 21 != 24, drop this branch.\n     |- Try 25 * 4 = 100. Evaluate 100 != 24, drop this branch.\n     |- Try 25 \/ 4 = 6.2. 6.2 is a decimal, drop this branch.\n    |- Try 20 - 5 = 15. Add 15 to the number set. Current number set: [15, 4], target: 24, just two numbers left.\n     |- Try 15 + 4 = 19. Evaluate 19 != 24, drop this branch.\n     |- Try 15 - 4 = 11. Evaluate 11 != 24, drop this branch.\n     |- Try 15 * 4 = 60. Evaluate 60 != 24, drop this branch.\n     |- Try 15 \/ 4 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 20 * 5 = 100. Add 100 to the number set. Current number set: [100, 4], target: 24, just two numbers left.\n     |- Try 100 + 4 = 104. Evaluate 104 != 24, drop this branch.\n     |- Try 100 - 4 = 96. Evaluate 96 != 24, drop this branch.\n     |- Try 100 * 4 = 400. Evaluate 400 != 24, drop this branch.\n     |- Try 100 \/ 4 = 25. Evaluate 25 != 24, drop this branch.\n    |- Try 20 \/ 5 = 4. Add 4 to the number set. Current number set: [4, 4], target: 24, just two numbers left.\n     |- Try 4 + 4 = 8. Evaluate 8 != 24, drop this branch.\n     |- Try 4 - 4 = 0. Evaluate 0 != 24, drop this branch.\n     |- Try 4 * 4 = 16. Evaluate 16 != 24, drop this branch.\n     |- Try 4 \/ 4 = 1. Evaluate 1 != 24, drop this branch.\n   |- Pick two numbers (20, 4) (numbers left: [5]). Try possible operations.\n    |- Try 20 + 4 = 24. Add 24 to the number set. Current number set: [24, 5], target: 24, just two numbers left.\n     |- Try 24 + 5 = 29. Evaluate 29 != 24, drop this branch.\n     |- Try 24 - 5 = 19. Evaluate 19 != 24, drop this branch.\n     |- Try 24 * 5 = 120. Evaluate 120 != 24, drop this branch.\n     |- Try 24 \/ 5 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 20 - 4 = 16. Add 16 to the number set. Current number set: [16, 5], target: 24, just two numbers left.\n     |- Try 16 + 5 = 21. Evaluate 21 != 24, drop this branch.\n     |- Try 16 - 5 = 11. Evaluate 11 != 24, drop this branch.\n     |- Try 16 * 5 = 80. Evaluate 80 != 24, drop this branch.\n     |- Try 16 \/ 5 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 20 * 4 = 80. Add 80 to the number set. Current number set: [80, 5], target: 24, just two numbers left.\n     |- Try 80 + 5 = 85. Evaluate 85 != 24, drop this branch.\n     |- Try 80 - 5 = 75. Evaluate 75 != 24, drop this branch.\n     |- Try 80 * 5 = 400. Evaluate 400 != 24, drop this branch.\n     |- Try 80 \/ 5 = 16. Evaluate 16 != 24, drop this branch.\n    |- Try 20 \/ 4 = 5. Add 5 to the number set. Current number set: [5, 5], target: 24, just two numbers left.\n     |- Try 5 + 5 = 10. Evaluate 10 != 24, drop this branch.\n     |- Try 5 - 5 = 0. Evaluate 0 != 24, drop this branch.\n     |- Try 5 * 5 = 25. Evaluate 25 != 24, drop this branch.\n     |- Try 5 \/ 5 = 1. Evaluate 1 != 24, drop this branch.\n   |- Pick two numbers (5, 4) (numbers left: [20]). Try possible operations.\n    |- Try 5 + 4 = 9. Add 9 to the number set. Current number set: [9, 20], target: 24, just two numbers left.\n     |- Try 20 + 9 = 29. Evaluate 29 != 24, drop this branch.\n     |- Try 20 - 9 = 11. Evaluate 11 != 24, drop this branch.\n     |- Try 20 * 9 = 180. Evaluate 180 != 24, drop this branch.\n     |- Try 20 \/ 9 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 5 - 4 = 1. Add 1 to the number set. Current number set: [1, 20], target: 24, just two numbers left.\n     |- Try 20 + 1 = 21. Evaluate 21 != 24, drop this branch.\n     |- Try 20 - 1 = 19. Evaluate 19 != 24, drop this branch.\n     |- Try 20 * 1 = 20. Evaluate 20 != 24, drop this branch.\n     |- Try 20 \/ 1 = 20. Evaluate 20 != 24, drop this branch.\n    |- Try 5 * 4 = 20. Add 20 to the number set. Current number set: [20, 20], target: 24, just two numbers left.\n     |- Try 20 + 20 = 40. Evaluate 40 != 24, drop this branch.\n     |- Try 20 - 20 = 0. Evaluate 0 != 24, drop this branch.\n     |- Try 20 * 20 = 400. Evaluate 400 != 24, drop this branch.\n     |- Try 20 \/ 20 = 1. Evaluate 1 != 24, drop this branch.\n    |- Try 5 \/ 4 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 16 - 4 = 12. Add 12 to the number set. Current number set: [12, 5, 4], target: 24. Options for choosing two numbers: [(12, 5), (12, 4), (5, 4)].\n   |- Pick two numbers (12, 5) (numbers left: [4]). Try possible operations.\n    |- Try 12 + 5 = 17. Add 17 to the number set. Current number set: [17, 4], target: 24, just two numbers left.\n     |- Try 17 + 4 = 21. Evaluate 21 != 24, drop this branch.\n     |- Try 17 - 4 = 13. Evaluate 13 != 24, drop this branch.\n     |- Try 17 * 4 = 68. Evaluate 68 != 24, drop this branch.\n     |- Try 17 \/ 4 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 12 - 5 = 7. Add 7 to the number set. Current number set: [7, 4], target: 24, just two numbers left.\n     |- Try 7 + 4 = 11. Evaluate 11 != 24, drop this branch.\n     |- Try 7 - 4 = 3. Evaluate 3 != 24, drop this branch.\n     |- Try 7 * 4 = 28. Evaluate 28 != 24, drop this branch.\n     |- Try 7 \/ 4 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 12 * 5 = 60. Add 60 to the number set. Current number set: [60, 4], target: 24, just two numbers left.\n     |- Try 60 + 4 = 64. Evaluate 64 != 24, drop this branch.\n     |- Try 60 - 4 = 56. Evaluate 56 != 24, drop this branch.\n     |- Try 60 * 4 = 240. Evaluate 240 != 24, drop this branch.\n     |- Try 60 \/ 4 = 15. Evaluate 15 != 24, drop this branch.\n    |- Try 12 \/ 5 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (12, 4) (numbers left: [5]). Try possible operations.\n    |- Try 12 + 4 = 16. Add 16 to the number set. Current number set: [16, 5], target: 24, just two numbers left.\n     |- Try 16 + 5 = 21. Evaluate 21 != 24, drop this branch.\n     |- Try 16 - 5 = 11. Evaluate 11 != 24, drop this branch.\n     |- Try 16 * 5 = 80. Evaluate 80 != 24, drop this branch.\n     |- Try 16 \/ 5 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 12 - 4 = 8. Add 8 to the number set. Current number set: [8, 5], target: 24, just two numbers left.\n     |- Try 8 + 5 = 13. Evaluate 13 != 24, drop this branch.\n     |- Try 8 - 5 = 3. Evaluate 3 != 24, drop this branch.\n     |- Try 8 * 5 = 40. Evaluate 40 != 24, drop this branch.\n     |- Try 8 \/ 5 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 12 * 4 = 48. Add 48 to the number set. Current number set: [48, 5], target: 24, just two numbers left.\n     |- Try 48 + 5 = 53. Evaluate 53 != 24, drop this branch.\n     |- Try 48 - 5 = 43. Evaluate 43 != 24, drop this branch.\n     |- Try 48 * 5 = 240. Evaluate 240 != 24, drop this branch.\n     |- Try 48 \/ 5 = 9.6. 9.6 is a decimal, drop this branch.\n    |- Try 12 \/ 4 = 3. Add 3 to the number set. Current number set: [3, 5], target: 24, just two numbers left.\n     |- Try 5 + 3 = 8. Evaluate 8 != 24, drop this branch.\n     |- Try 5 - 3 = 2. Evaluate 2 != 24, drop this branch.\n     |- Try 5 * 3 = 15. Evaluate 15 != 24, drop this branch.\n     |- Try 5 \/ 3 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (5, 4) (numbers left: [12]). Try possible operations.\n    |- Try 5 + 4 = 9. Add 9 to the number set. Current number set: [9, 12], target: 24, just two numbers left.\n     |- Try 12 + 9 = 21. Evaluate 21 != 24, drop this branch.\n     |- Try 12 - 9 = 3. Evaluate 3 != 24, drop this branch.\n     |- Try 12 * 9 = 108. Evaluate 108 != 24, drop this branch.\n     |- Try 12 \/ 9 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 5 - 4 = 1. Add 1 to the number set. Current number set: [1, 12], target: 24, just two numbers left.\n     |- Try 12 + 1 = 13. Evaluate 13 != 24, drop this branch.\n     |- Try 12 - 1 = 11. Evaluate 11 != 24, drop this branch.\n     |- Try 12 * 1 = 12. Evaluate 12 != 24, drop this branch.\n     |- Try 12 \/ 1 = 12. Evaluate 12 != 24, drop this branch.\n    |- Try 5 * 4 = 20. Add 20 to the number set. Current number set: [20, 12], target: 24, just two numbers left.\n     |- Try 20 + 12 = 32. Evaluate 32 != 24, drop this branch.\n     |- Try 20 - 12 = 8. Evaluate 8 != 24, drop this branch.\n     |- Try 20 * 12 = 240. Evaluate 240 != 24, drop this branch.\n     |- Try 20 \/ 12 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 5 \/ 4 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 16 * 4 = 64. Add 64 to the number set. Current number set: [64, 5, 4], target: 24. Options for choosing two numbers: [(64, 5), (64, 4), (5, 4)].\n   |- Pick two numbers (64, 5) (numbers left: [4]). Try possible operations.\n    |- Try 64 + 5 = 69. Add 69 to the number set. Current number set: [69, 4], target: 24, just two numbers left.\n     |- Try 69 + 4 = 73. Evaluate 73 != 24, drop this branch.\n     |- Try 69 - 4 = 65. Evaluate 65 != 24, drop this branch.\n     |- Try 69 * 4 = 276. Evaluate 276 != 24, drop this branch.\n     |- Try 69 \/ 4 = 17.2. 17.2 is a decimal, drop this branch.\n    |- Try 64 - 5 = 59. Add 59 to the number set. Current number set: [59, 4], target: 24, just two numbers left.\n     |- Try 59 + 4 = 63. Evaluate 63 != 24, drop this branch.\n     |- Try 59 - 4 = 55. Evaluate 55 != 24, drop this branch.\n     |- Try 59 * 4 = 236. Evaluate 236 != 24, drop this branch.\n     |- Try 59 \/ 4 = 14.8. 14.8 is a decimal, drop this branch.\n    |- Try 64 * 5 = 320. Add 320 to the number set. Current number set: [320, 4], target: 24, just two numbers left.\n     |- Try 320 + 4 = 324. Evaluate 324 != 24, drop this branch.\n     |- Try 320 - 4 = 316. Evaluate 316 != 24, drop this branch.\n     |- Try 320 * 4 = 1280. Evaluate 1280 != 24, drop this branch.\n     |- Try 320 \/ 4 = 80. Evaluate 80 != 24, drop this branch.\n    |- Try 64 \/ 5 = 12.8. 12.8 is a decimal, drop this branch.\n   |- Pick two numbers (64, 4) (numbers left: [5]). Try possible operations.\n    |- Try 64 + 4 = 68. Add 68 to the number set. Current number set: [68, 5], target: 24, just two numbers left.\n     |- Try 68 + 5 = 73. Evaluate 73 != 24, drop this branch.\n     |- Try 68 - 5 = 63. Evaluate 63 != 24, drop this branch.\n     |- Try 68 * 5 = 340. Evaluate 340 != 24, drop this branch.\n     |- Try 68 \/ 5 = 13.6. 13.6 is a decimal, drop this branch.\n    |- Try 64 - 4 = 60. Add 60 to the number set. Current number set: [60, 5], target: 24, just two numbers left.\n     |- Try 60 + 5 = 65. Evaluate 65 != 24, drop this branch.\n     |- Try 60 - 5 = 55. Evaluate 55 != 24, drop this branch.\n     |- Try 60 * 5 = 300. Evaluate 300 != 24, drop this branch.\n     |- Try 60 \/ 5 = 12. Evaluate 12 != 24, drop this branch.\n    |- Try 64 * 4 = 256. Add 256 to the number set. Current number set: [256, 5], target: 24, just two numbers left.\n     |- Try 256 + 5 = 261. Evaluate 261 != 24, drop this branch.\n     |- Try 256 - 5 = 251. Evaluate 251 != 24, drop this branch.\n     |- Try 256 * 5 = 1280. Evaluate 1280 != 24, drop this branch.\n     |- Try 256 \/ 5 = 51.2. 51.2 is a decimal, drop this branch.\n    |- Try 64 \/ 4 = 16. Add 16 to the number set. Current number set: [16, 5], target: 24, just two numbers left.\n     |- Try 16 + 5 = 21. Evaluate 21 != 24, drop this branch.\n     |- Try 16 - 5 = 11. Evaluate 11 != 24, drop this branch.\n     |- Try 16 * 5 = 80. Evaluate 80 != 24, drop this branch.\n     |- Try 16 \/ 5 = 3.2. 3.2 is a decimal, drop this branch.\n   |- Pick two numbers (5, 4) (numbers left: [64]). Try possible operations.\n    |- Try 5 + 4 = 9. Add 9 to the number set. Current number set: [9, 64], target: 24, just two numbers left.\n     |- Try 64 + 9 = 73. Evaluate 73 != 24, drop this branch.\n     |- Try 64 - 9 = 55. Evaluate 55 != 24, drop this branch.\n     |- Try 64 * 9 = 576. Evaluate 576 != 24, drop this branch.\n     |- Try 64 \/ 9 = 7.1. 7.1 is a decimal, drop this branch.\n    |- Try 5 - 4 = 1. Add 1 to the number set. Current number set: [1, 64], target: 24, just two numbers left.\n     |- Try 64 + 1 = 65. Evaluate 65 != 24, drop this branch.\n     |- Try 64 - 1 = 63. Evaluate 63 != 24, drop this branch.\n     |- Try 64 * 1 = 64. Evaluate 64 != 24, drop this branch.\n     |- Try 64 \/ 1 = 64. Evaluate 64 != 24, drop this branch.\n    |- Try 5 * 4 = 20. Add 20 to the number set. Current number set: [20, 64], target: 24, just two numbers left.\n     |- Try 64 + 20 = 84. Evaluate 84 != 24, drop this branch.\n     |- Try 64 - 20 = 44. Evaluate 44 != 24, drop this branch.\n     |- Try 64 * 20 = 1280. Evaluate 1280 != 24, drop this branch.\n     |- Try 64 \/ 20 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 5 \/ 4 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 16 \/ 4 = 4. Add 4 to the number set. Current number set: [4, 5, 4], target: 24. Options for choosing two numbers: [(4, 5), (4, 4), (5, 4)].\n   |- Pick two numbers (4, 5) (numbers left: [4]). Try possible operations.\n    |- Try 5 + 4 = 9. Add 9 to the number set. Current number set: [9, 4], target: 24, just two numbers left.\n     |- Try 9 + 4 = 13. Evaluate 13 != 24, drop this branch.\n     |- Try 9 - 4 = 5. Evaluate 5 != 24, drop this branch.\n     |- Try 9 * 4 = 36. Evaluate 36 != 24, drop this branch.\n     |- Try 9 \/ 4 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 5 - 4 = 1. Add 1 to the number set. Current number set: [1, 4], target: 24, just two numbers left.\n     |- Try 4 + 1 = 5. Evaluate 5 != 24, drop this branch.\n     |- Try 4 - 1 = 3. Evaluate 3 != 24, drop this branch.\n     |- Try 4 * 1 = 4. Evaluate 4 != 24, drop this branch.\n     |- Try 4 \/ 1 = 4. Evaluate 4 != 24, drop this branch.\n    |- Try 5 * 4 = 20. Add 20 to the number set. Current number set: [20, 4], target: 24, just two numbers left.\n     |- Try 20 + 4 = 24. Evaluate 24 == 24, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 20 + 4 = 24\nThe step before: 5 * 4 = 20\nThe first step: 16 \/ 4 = 4\n\nOutput the solution in the required format:\n<Solution>\n16 \/ 4 = 4\n5 * 4 = 20\n20 + 4 = 24\n<\/Solution>\n","item":{"nums":[16,4,5,4],"solution":["16 \/ 4 = 4","5 * 4 = 20","20 + 4 = 24"],"target":24}}
+{"instance_id":"countdown_8k_177","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [29, 12, 19, 3]\nTarget: 18","reference_output":"# Search Procedure\nInitial number set: [29, 12, 19, 3], target: 18. Options for choosing two numbers: [(29, 12), (29, 19), (29, 3), (12, 19), (12, 3), (19, 3)].\n |- Pick two numbers (29, 12) (numbers left: [19, 3]). Try possible operations.\n  |- Try 29 + 12 = 41. Add 41 to the number set. Current number set: [41, 19, 3], target: 18. Options for choosing two numbers: [(41, 19), (41, 3), (19, 3)].\n   |- Pick two numbers (41, 19) (numbers left: [3]). Try possible operations.\n    |- Try 41 + 19 = 60. Add 60 to the number set. Current number set: [60, 3], target: 18, just two numbers left.\n     |- Try 60 + 3 = 63. Evaluate 63 != 18, drop this branch.\n     |- Try 60 - 3 = 57. Evaluate 57 != 18, drop this branch.\n     |- Try 60 * 3 = 180. Evaluate 180 != 18, drop this branch.\n     |- Try 60 \/ 3 = 20. Evaluate 20 != 18, drop this branch.\n    |- Try 41 - 19 = 22. Add 22 to the number set. Current number set: [22, 3], target: 18, just two numbers left.\n     |- Try 22 + 3 = 25. Evaluate 25 != 18, drop this branch.\n     |- Try 22 - 3 = 19. Evaluate 19 != 18, drop this branch.\n     |- Try 22 * 3 = 66. Evaluate 66 != 18, drop this branch.\n     |- Try 22 \/ 3 = 7.3. 7.3 is a decimal, drop this branch.\n    |- Try 41 * 19 = 779. Add 779 to the number set. Current number set: [779, 3], target: 18, just two numbers left.\n     |- Try 779 + 3 = 782. Evaluate 782 != 18, drop this branch.\n     |- Try 779 - 3 = 776. Evaluate 776 != 18, drop this branch.\n     |- Try 779 * 3 = 2337. 2337 exceeds the maximum intermediate result, drop this branch.\n     |- Try 779 \/ 3 = 259.7. 259.7 is a decimal, drop this branch.\n    |- Try 41 \/ 19 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (41, 3) (numbers left: [19]). Try possible operations.\n    |- Try 41 + 3 = 44. Add 44 to the number set. Current number set: [44, 19], target: 18, just two numbers left.\n     |- Try 44 + 19 = 63. Evaluate 63 != 18, drop this branch.\n     |- Try 44 - 19 = 25. Evaluate 25 != 18, drop this branch.\n     |- Try 44 * 19 = 836. Evaluate 836 != 18, drop this branch.\n     |- Try 44 \/ 19 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 41 - 3 = 38. Add 38 to the number set. Current number set: [38, 19], target: 18, just two numbers left.\n     |- Try 38 + 19 = 57. Evaluate 57 != 18, drop this branch.\n     |- Try 38 - 19 = 19. Evaluate 19 != 18, drop this branch.\n     |- Try 38 * 19 = 722. Evaluate 722 != 18, drop this branch.\n     |- Try 38 \/ 19 = 2. Evaluate 2 != 18, drop this branch.\n    |- Try 41 * 3 = 123. Add 123 to the number set. Current number set: [123, 19], target: 18, just two numbers left.\n     |- Try 123 + 19 = 142. Evaluate 142 != 18, drop this branch.\n     |- Try 123 - 19 = 104. Evaluate 104 != 18, drop this branch.\n     |- Try 123 * 19 = 2337. 2337 exceeds the maximum intermediate result, drop this branch.\n     |- Try 123 \/ 19 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 41 \/ 3 = 13.7. 13.7 is a decimal, drop this branch.\n   |- Pick two numbers (19, 3) (numbers left: [41]). Try possible operations.\n    |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 41], target: 18, just two numbers left.\n     |- Try 41 + 22 = 63. Evaluate 63 != 18, drop this branch.\n     |- Try 41 - 22 = 19. Evaluate 19 != 18, drop this branch.\n     |- Try 41 * 22 = 902. Evaluate 902 != 18, drop this branch.\n     |- Try 41 \/ 22 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 41], target: 18, just two numbers left.\n     |- Try 41 + 16 = 57. Evaluate 57 != 18, drop this branch.\n     |- Try 41 - 16 = 25. Evaluate 25 != 18, drop this branch.\n     |- Try 41 * 16 = 656. Evaluate 656 != 18, drop this branch.\n     |- Try 41 \/ 16 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 19 * 3 = 57. Add 57 to the number set. Current number set: [57, 41], target: 18, just two numbers left.\n     |- Try 57 + 41 = 98. Evaluate 98 != 18, drop this branch.\n     |- Try 57 - 41 = 16. Evaluate 16 != 18, drop this branch.\n     |- Try 57 * 41 = 2337. 2337 exceeds the maximum intermediate result, drop this branch.\n     |- Try 57 \/ 41 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 19 \/ 3 = 6.3. 6.3 is a decimal, drop this branch.\n  |- Try 29 - 12 = 17. Add 17 to the number set. Current number set: [17, 19, 3], target: 18. Options for choosing two numbers: [(17, 19), (17, 3), (19, 3)].\n   |- Pick two numbers (17, 19) (numbers left: [3]). Try possible operations.\n    |- Try 19 + 17 = 36. Add 36 to the number set. Current number set: [36, 3], target: 18, just two numbers left.\n     |- Try 36 + 3 = 39. Evaluate 39 != 18, drop this branch.\n     |- Try 36 - 3 = 33. Evaluate 33 != 18, drop this branch.\n     |- Try 36 * 3 = 108. Evaluate 108 != 18, drop this branch.\n     |- Try 36 \/ 3 = 12. Evaluate 12 != 18, drop this branch.\n    |- Try 19 - 17 = 2. Add 2 to the number set. Current number set: [2, 3], target: 18, just two numbers left.\n     |- Try 3 + 2 = 5. Evaluate 5 != 18, drop this branch.\n     |- Try 3 - 2 = 1. Evaluate 1 != 18, drop this branch.\n     |- Try 3 * 2 = 6. Evaluate 6 != 18, drop this branch.\n     |- Try 3 \/ 2 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 19 * 17 = 323. Add 323 to the number set. Current number set: [323, 3], target: 18, just two numbers left.\n     |- Try 323 + 3 = 326. Evaluate 326 != 18, drop this branch.\n     |- Try 323 - 3 = 320. Evaluate 320 != 18, drop this branch.\n     |- Try 323 * 3 = 969. Evaluate 969 != 18, drop this branch.\n     |- Try 323 \/ 3 = 107.7. 107.7 is a decimal, drop this branch.\n    |- Try 19 \/ 17 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (17, 3) (numbers left: [19]). Try possible operations.\n    |- Try 17 + 3 = 20. Add 20 to the number set. Current number set: [20, 19], target: 18, just two numbers left.\n     |- Try 20 + 19 = 39. Evaluate 39 != 18, drop this branch.\n     |- Try 20 - 19 = 1. Evaluate 1 != 18, drop this branch.\n     |- Try 20 * 19 = 380. Evaluate 380 != 18, drop this branch.\n     |- Try 20 \/ 19 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 17 - 3 = 14. Add 14 to the number set. Current number set: [14, 19], target: 18, just two numbers left.\n     |- Try 19 + 14 = 33. Evaluate 33 != 18, drop this branch.\n     |- Try 19 - 14 = 5. Evaluate 5 != 18, drop this branch.\n     |- Try 19 * 14 = 266. Evaluate 266 != 18, drop this branch.\n     |- Try 19 \/ 14 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 17 * 3 = 51. Add 51 to the number set. Current number set: [51, 19], target: 18, just two numbers left.\n     |- Try 51 + 19 = 70. Evaluate 70 != 18, drop this branch.\n     |- Try 51 - 19 = 32. Evaluate 32 != 18, drop this branch.\n     |- Try 51 * 19 = 969. Evaluate 969 != 18, drop this branch.\n     |- Try 51 \/ 19 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 17 \/ 3 = 5.7. 5.7 is a decimal, drop this branch.\n   |- Pick two numbers (19, 3) (numbers left: [17]). Try possible operations.\n    |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 17], target: 18, just two numbers left.\n     |- Try 22 + 17 = 39. Evaluate 39 != 18, drop this branch.\n     |- Try 22 - 17 = 5. Evaluate 5 != 18, drop this branch.\n     |- Try 22 * 17 = 374. Evaluate 374 != 18, drop this branch.\n     |- Try 22 \/ 17 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 17], target: 18, just two numbers left.\n     |- Try 17 + 16 = 33. Evaluate 33 != 18, drop this branch.\n     |- Try 17 - 16 = 1. Evaluate 1 != 18, drop this branch.\n     |- Try 17 * 16 = 272. Evaluate 272 != 18, drop this branch.\n     |- Try 17 \/ 16 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 19 * 3 = 57. Add 57 to the number set. Current number set: [57, 17], target: 18, just two numbers left.\n     |- Try 57 + 17 = 74. Evaluate 74 != 18, drop this branch.\n     |- Try 57 - 17 = 40. Evaluate 40 != 18, drop this branch.\n     |- Try 57 * 17 = 969. Evaluate 969 != 18, drop this branch.\n     |- Try 57 \/ 17 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 19 \/ 3 = 6.3. 6.3 is a decimal, drop this branch.\n  |- Try 29 * 12 = 348. Add 348 to the number set. Current number set: [348, 19, 3], target: 18. Options for choosing two numbers: [(348, 19), (348, 3), (19, 3)].\n   |- Pick two numbers (348, 19) (numbers left: [3]). Try possible operations.\n    |- Try 348 + 19 = 367. Add 367 to the number set. Current number set: [367, 3], target: 18, just two numbers left.\n     |- Try 367 + 3 = 370. Evaluate 370 != 18, drop this branch.\n     |- Try 367 - 3 = 364. Evaluate 364 != 18, drop this branch.\n     |- Try 367 * 3 = 1101. Evaluate 1101 != 18, drop this branch.\n     |- Try 367 \/ 3 = 122.3. 122.3 is a decimal, drop this branch.\n    |- Try 348 - 19 = 329. Add 329 to the number set. Current number set: [329, 3], target: 18, just two numbers left.\n     |- Try 329 + 3 = 332. Evaluate 332 != 18, drop this branch.\n     |- Try 329 - 3 = 326. Evaluate 326 != 18, drop this branch.\n     |- Try 329 * 3 = 987. Evaluate 987 != 18, drop this branch.\n     |- Try 329 \/ 3 = 109.7. 109.7 is a decimal, drop this branch.\n    |- Try 348 * 19 = 6612. 6612 exceeds the maximum intermediate result, drop this branch.\n    |- Try 348 \/ 19 = 18.3. 18.3 is a decimal, drop this branch.\n   |- Pick two numbers (348, 3) (numbers left: [19]). Try possible operations.\n    |- Try 348 + 3 = 351. Add 351 to the number set. Current number set: [351, 19], target: 18, just two numbers left.\n     |- Try 351 + 19 = 370. Evaluate 370 != 18, drop this branch.\n     |- Try 351 - 19 = 332. Evaluate 332 != 18, drop this branch.\n     |- Try 351 * 19 = 6669. 6669 exceeds the maximum intermediate result, drop this branch.\n     |- Try 351 \/ 19 = 18.5. 18.5 is a decimal, drop this branch.\n    |- Try 348 - 3 = 345. Add 345 to the number set. Current number set: [345, 19], target: 18, just two numbers left.\n     |- Try 345 + 19 = 364. Evaluate 364 != 18, drop this branch.\n     |- Try 345 - 19 = 326. Evaluate 326 != 18, drop this branch.\n     |- Try 345 * 19 = 6555. 6555 exceeds the maximum intermediate result, drop this branch.\n     |- Try 345 \/ 19 = 18.2. 18.2 is a decimal, drop this branch.\n    |- Try 348 * 3 = 1044. Add 1044 to the number set. Current number set: [1044, 19], target: 18, just two numbers left.\n     |- Try 1044 + 19 = 1063. Evaluate 1063 != 18, drop this branch.\n     |- Try 1044 - 19 = 1025. Evaluate 1025 != 18, drop this branch.\n     |- Try 1044 * 19 = 19836. 19836 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1044 \/ 19 = 54.9. 54.9 is a decimal, drop this branch.\n    |- Try 348 \/ 3 = 116. Add 116 to the number set. Current number set: [116, 19], target: 18, just two numbers left.\n     |- Try 116 + 19 = 135. Evaluate 135 != 18, drop this branch.\n     |- Try 116 - 19 = 97. Evaluate 97 != 18, drop this branch.\n     |- Try 116 * 19 = 2204. 2204 exceeds the maximum intermediate result, drop this branch.\n     |- Try 116 \/ 19 = 6.1. 6.1 is a decimal, drop this branch.\n   |- Pick two numbers (19, 3) (numbers left: [348]). Try possible operations.\n    |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 348], target: 18, just two numbers left.\n     |- Try 348 + 22 = 370. Evaluate 370 != 18, drop this branch.\n     |- Try 348 - 22 = 326. Evaluate 326 != 18, drop this branch.\n     |- Try 348 * 22 = 7656. 7656 exceeds the maximum intermediate result, drop this branch.\n     |- Try 348 \/ 22 = 15.8. 15.8 is a decimal, drop this branch.\n    |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 348], target: 18, just two numbers left.\n     |- Try 348 + 16 = 364. Evaluate 364 != 18, drop this branch.\n     |- Try 348 - 16 = 332. Evaluate 332 != 18, drop this branch.\n     |- Try 348 * 16 = 5568. 5568 exceeds the maximum intermediate result, drop this branch.\n     |- Try 348 \/ 16 = 21.8. 21.8 is a decimal, drop this branch.\n    |- Try 19 * 3 = 57. Add 57 to the number set. Current number set: [57, 348], target: 18, just two numbers left.\n     |- Try 348 + 57 = 405. Evaluate 405 != 18, drop this branch.\n     |- Try 348 - 57 = 291. Evaluate 291 != 18, drop this branch.\n     |- Try 348 * 57 = 19836. 19836 exceeds the maximum intermediate result, drop this branch.\n     |- Try 348 \/ 57 = 6.1. 6.1 is a decimal, drop this branch.\n    |- Try 19 \/ 3 = 6.3. 6.3 is a decimal, drop this branch.\n  |- Try 29 \/ 12 = 2.4. 2.4 is a decimal, drop this branch.\n |- Pick two numbers (29, 19) (numbers left: [12, 3]). Try possible operations.\n  |- Try 29 + 19 = 48. Add 48 to the number set. Current number set: [48, 12, 3], target: 18. Options for choosing two numbers: [(48, 12), (48, 3), (12, 3)].\n   |- Pick two numbers (48, 12) (numbers left: [3]). Try possible operations.\n    |- Try 48 + 12 = 60. Add 60 to the number set. Current number set: [60, 3], target: 18, just two numbers left.\n     |- Try 60 + 3 = 63. Evaluate 63 != 18, drop this branch.\n     |- Try 60 - 3 = 57. Evaluate 57 != 18, drop this branch.\n     |- Try 60 * 3 = 180. Evaluate 180 != 18, drop this branch.\n     |- Try 60 \/ 3 = 20. Evaluate 20 != 18, drop this branch.\n    |- Try 48 - 12 = 36. Add 36 to the number set. Current number set: [36, 3], target: 18, just two numbers left.\n     |- Try 36 + 3 = 39. Evaluate 39 != 18, drop this branch.\n     |- Try 36 - 3 = 33. Evaluate 33 != 18, drop this branch.\n     |- Try 36 * 3 = 108. Evaluate 108 != 18, drop this branch.\n     |- Try 36 \/ 3 = 12. Evaluate 12 != 18, drop this branch.\n    |- Try 48 * 12 = 576. Add 576 to the number set. Current number set: [576, 3], target: 18, just two numbers left.\n     |- Try 576 + 3 = 579. Evaluate 579 != 18, drop this branch.\n     |- Try 576 - 3 = 573. Evaluate 573 != 18, drop this branch.\n     |- Try 576 * 3 = 1728. Evaluate 1728 != 18, drop this branch.\n     |- Try 576 \/ 3 = 192. Evaluate 192 != 18, drop this branch.\n    |- Try 48 \/ 12 = 4. Add 4 to the number set. Current number set: [4, 3], target: 18, just two numbers left.\n     |- Try 4 + 3 = 7. Evaluate 7 != 18, drop this branch.\n     |- Try 4 - 3 = 1. Evaluate 1 != 18, drop this branch.\n     |- Try 4 * 3 = 12. Evaluate 12 != 18, drop this branch.\n     |- Try 4 \/ 3 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (48, 3) (numbers left: [12]). Try possible operations.\n    |- Try 48 + 3 = 51. Add 51 to the number set. Current number set: [51, 12], target: 18, just two numbers left.\n     |- Try 51 + 12 = 63. Evaluate 63 != 18, drop this branch.\n     |- Try 51 - 12 = 39. Evaluate 39 != 18, drop this branch.\n     |- Try 51 * 12 = 612. Evaluate 612 != 18, drop this branch.\n     |- Try 51 \/ 12 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 48 - 3 = 45. Add 45 to the number set. Current number set: [45, 12], target: 18, just two numbers left.\n     |- Try 45 + 12 = 57. Evaluate 57 != 18, drop this branch.\n     |- Try 45 - 12 = 33. Evaluate 33 != 18, drop this branch.\n     |- Try 45 * 12 = 540. Evaluate 540 != 18, drop this branch.\n     |- Try 45 \/ 12 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 48 * 3 = 144. Add 144 to the number set. Current number set: [144, 12], target: 18, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 18, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 18, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 18, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 != 18, drop this branch.\n    |- Try 48 \/ 3 = 16. Add 16 to the number set. Current number set: [16, 12], target: 18, just two numbers left.\n     |- Try 16 + 12 = 28. Evaluate 28 != 18, drop this branch.\n     |- Try 16 - 12 = 4. Evaluate 4 != 18, drop this branch.\n     |- Try 16 * 12 = 192. Evaluate 192 != 18, drop this branch.\n     |- Try 16 \/ 12 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (12, 3) (numbers left: [48]). Try possible operations.\n    |- Try 12 + 3 = 15. Add 15 to the number set. Current number set: [15, 48], target: 18, just two numbers left.\n     |- Try 48 + 15 = 63. Evaluate 63 != 18, drop this branch.\n     |- Try 48 - 15 = 33. Evaluate 33 != 18, drop this branch.\n     |- Try 48 * 15 = 720. Evaluate 720 != 18, drop this branch.\n     |- Try 48 \/ 15 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 12 - 3 = 9. Add 9 to the number set. Current number set: [9, 48], target: 18, just two numbers left.\n     |- Try 48 + 9 = 57. Evaluate 57 != 18, drop this branch.\n     |- Try 48 - 9 = 39. Evaluate 39 != 18, drop this branch.\n     |- Try 48 * 9 = 432. Evaluate 432 != 18, drop this branch.\n     |- Try 48 \/ 9 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 12 * 3 = 36. Add 36 to the number set. Current number set: [36, 48], target: 18, just two numbers left.\n     |- Try 48 + 36 = 84. Evaluate 84 != 18, drop this branch.\n     |- Try 48 - 36 = 12. Evaluate 12 != 18, drop this branch.\n     |- Try 48 * 36 = 1728. Evaluate 1728 != 18, drop this branch.\n     |- Try 48 \/ 36 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 12 \/ 3 = 4. Add 4 to the number set. Current number set: [4, 48], target: 18, just two numbers left.\n     |- Try 48 + 4 = 52. Evaluate 52 != 18, drop this branch.\n     |- Try 48 - 4 = 44. Evaluate 44 != 18, drop this branch.\n     |- Try 48 * 4 = 192. Evaluate 192 != 18, drop this branch.\n     |- Try 48 \/ 4 = 12. Evaluate 12 != 18, drop this branch.\n  |- Try 29 - 19 = 10. Add 10 to the number set. Current number set: [10, 12, 3], target: 18. Options for choosing two numbers: [(10, 12), (10, 3), (12, 3)].\n   |- Pick two numbers (10, 12) (numbers left: [3]). Try possible operations.\n    |- Try 12 + 10 = 22. Add 22 to the number set. Current number set: [22, 3], target: 18, just two numbers left.\n     |- Try 22 + 3 = 25. Evaluate 25 != 18, drop this branch.\n     |- Try 22 - 3 = 19. Evaluate 19 != 18, drop this branch.\n     |- Try 22 * 3 = 66. Evaluate 66 != 18, drop this branch.\n     |- Try 22 \/ 3 = 7.3. 7.3 is a decimal, drop this branch.\n    |- Try 12 - 10 = 2. Add 2 to the number set. Current number set: [2, 3], target: 18, just two numbers left.\n     |- Try 3 + 2 = 5. Evaluate 5 != 18, drop this branch.\n     |- Try 3 - 2 = 1. Evaluate 1 != 18, drop this branch.\n     |- Try 3 * 2 = 6. Evaluate 6 != 18, drop this branch.\n     |- Try 3 \/ 2 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 12 * 10 = 120. Add 120 to the number set. Current number set: [120, 3], target: 18, just two numbers left.\n     |- Try 120 + 3 = 123. Evaluate 123 != 18, drop this branch.\n     |- Try 120 - 3 = 117. Evaluate 117 != 18, drop this branch.\n     |- Try 120 * 3 = 360. Evaluate 360 != 18, drop this branch.\n     |- Try 120 \/ 3 = 40. Evaluate 40 != 18, drop this branch.\n    |- Try 12 \/ 10 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (10, 3) (numbers left: [12]). Try possible operations.\n    |- Try 10 + 3 = 13. Add 13 to the number set. Current number set: [13, 12], target: 18, just two numbers left.\n     |- Try 13 + 12 = 25. Evaluate 25 != 18, drop this branch.\n     |- Try 13 - 12 = 1. Evaluate 1 != 18, drop this branch.\n     |- Try 13 * 12 = 156. Evaluate 156 != 18, drop this branch.\n     |- Try 13 \/ 12 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 10 - 3 = 7. Add 7 to the number set. Current number set: [7, 12], target: 18, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 18, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 18, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 18, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 10 * 3 = 30. Add 30 to the number set. Current number set: [30, 12], target: 18, just two numbers left.\n     |- Try 30 + 12 = 42. Evaluate 42 != 18, drop this branch.\n     |- Try 30 - 12 = 18. Evaluate 18 == 18, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 30 - 12 = 18\nThe step before: 10 * 3 = 30\nThe first step: 29 - 19 = 10\n\nOutput the solution in the required format:\n<Solution>\n29 - 19 = 10\n10 * 3 = 30\n30 - 12 = 18\n<\/Solution>\n","item":{"nums":[29,12,19,3],"solution":["29 - 19 = 10","10 * 3 = 30","30 - 12 = 18"],"target":18}}
+{"instance_id":"countdown_8k_178","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [35, 30, 28, 37]\nTarget: 49","reference_output":"# Search Procedure\nInitial number set: [35, 30, 28, 37], target: 49. Options for choosing two numbers: [(35, 30), (35, 28), (35, 37), (30, 28), (30, 37), (28, 37)].\n |- Pick two numbers (35, 30) (numbers left: [28, 37]). Try possible operations.\n  |- Try 35 + 30 = 65. Add 65 to the number set. Current number set: [65, 28, 37], target: 49. Options for choosing two numbers: [(65, 28), (65, 37), (28, 37)].\n   |- Pick two numbers (65, 28) (numbers left: [37]). Try possible operations.\n    |- Try 65 + 28 = 93. Add 93 to the number set. Current number set: [93, 37], target: 49, just two numbers left.\n     |- Try 93 + 37 = 130. Evaluate 130 != 49, drop this branch.\n     |- Try 93 - 37 = 56. Evaluate 56 != 49, drop this branch.\n     |- Try 93 * 37 = 3441. 3441 exceeds the maximum intermediate result, drop this branch.\n     |- Try 93 \/ 37 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 65 - 28 = 37. Add 37 to the number set. Current number set: [37, 37], target: 49, just two numbers left.\n     |- Try 37 + 37 = 74. Evaluate 74 != 49, drop this branch.\n     |- Try 37 - 37 = 0. Evaluate 0 != 49, drop this branch.\n     |- Try 37 * 37 = 1369. Evaluate 1369 != 49, drop this branch.\n     |- Try 37 \/ 37 = 1. Evaluate 1 != 49, drop this branch.\n    |- Try 65 * 28 = 1820. Add 1820 to the number set. Current number set: [1820, 37], target: 49, just two numbers left.\n     |- Try 1820 + 37 = 1857. Evaluate 1857 != 49, drop this branch.\n     |- Try 1820 - 37 = 1783. Evaluate 1783 != 49, drop this branch.\n     |- Try 1820 * 37 = 67340. 67340 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1820 \/ 37 = 49.2. 49.2 is a decimal, drop this branch.\n    |- Try 65 \/ 28 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (65, 37) (numbers left: [28]). Try possible operations.\n    |- Try 65 + 37 = 102. Add 102 to the number set. Current number set: [102, 28], target: 49, just two numbers left.\n     |- Try 102 + 28 = 130. Evaluate 130 != 49, drop this branch.\n     |- Try 102 - 28 = 74. Evaluate 74 != 49, drop this branch.\n     |- Try 102 * 28 = 2856. 2856 exceeds the maximum intermediate result, drop this branch.\n     |- Try 102 \/ 28 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 65 - 37 = 28. Add 28 to the number set. Current number set: [28, 28], target: 49, just two numbers left.\n     |- Try 28 + 28 = 56. Evaluate 56 != 49, drop this branch.\n     |- Try 28 - 28 = 0. Evaluate 0 != 49, drop this branch.\n     |- Try 28 * 28 = 784. Evaluate 784 != 49, drop this branch.\n     |- Try 28 \/ 28 = 1. Evaluate 1 != 49, drop this branch.\n    |- Try 65 * 37 = 2405. 2405 exceeds the maximum intermediate result, drop this branch.\n    |- Try 65 \/ 37 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (28, 37) (numbers left: [65]). Try possible operations.\n    |- Try 37 + 28 = 65. Add 65 to the number set. Current number set: [65, 65], target: 49, just two numbers left.\n     |- Try 65 + 65 = 130. Evaluate 130 != 49, drop this branch.\n     |- Try 65 - 65 = 0. Evaluate 0 != 49, drop this branch.\n     |- Try 65 * 65 = 4225. 4225 exceeds the maximum intermediate result, drop this branch.\n     |- Try 65 \/ 65 = 1. Evaluate 1 != 49, drop this branch.\n    |- Try 37 - 28 = 9. Add 9 to the number set. Current number set: [9, 65], target: 49, just two numbers left.\n     |- Try 65 + 9 = 74. Evaluate 74 != 49, drop this branch.\n     |- Try 65 - 9 = 56. Evaluate 56 != 49, drop this branch.\n     |- Try 65 * 9 = 585. Evaluate 585 != 49, drop this branch.\n     |- Try 65 \/ 9 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 37 * 28 = 1036. Add 1036 to the number set. Current number set: [1036, 65], target: 49, just two numbers left.\n     |- Try 1036 + 65 = 1101. Evaluate 1101 != 49, drop this branch.\n     |- Try 1036 - 65 = 971. Evaluate 971 != 49, drop this branch.\n     |- Try 1036 * 65 = 67340. 67340 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1036 \/ 65 = 15.9. 15.9 is a decimal, drop this branch.\n    |- Try 37 \/ 28 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 35 - 30 = 5. Add 5 to the number set. Current number set: [5, 28, 37], target: 49. Options for choosing two numbers: [(5, 28), (5, 37), (28, 37)].\n   |- Pick two numbers (5, 28) (numbers left: [37]). Try possible operations.\n    |- Try 28 + 5 = 33. Add 33 to the number set. Current number set: [33, 37], target: 49, just two numbers left.\n     |- Try 37 + 33 = 70. Evaluate 70 != 49, drop this branch.\n     |- Try 37 - 33 = 4. Evaluate 4 != 49, drop this branch.\n     |- Try 37 * 33 = 1221. Evaluate 1221 != 49, drop this branch.\n     |- Try 37 \/ 33 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 28 - 5 = 23. Add 23 to the number set. Current number set: [23, 37], target: 49, just two numbers left.\n     |- Try 37 + 23 = 60. Evaluate 60 != 49, drop this branch.\n     |- Try 37 - 23 = 14. Evaluate 14 != 49, drop this branch.\n     |- Try 37 * 23 = 851. Evaluate 851 != 49, drop this branch.\n     |- Try 37 \/ 23 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 28 * 5 = 140. Add 140 to the number set. Current number set: [140, 37], target: 49, just two numbers left.\n     |- Try 140 + 37 = 177. Evaluate 177 != 49, drop this branch.\n     |- Try 140 - 37 = 103. Evaluate 103 != 49, drop this branch.\n     |- Try 140 * 37 = 5180. 5180 exceeds the maximum intermediate result, drop this branch.\n     |- Try 140 \/ 37 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 28 \/ 5 = 5.6. 5.6 is a decimal, drop this branch.\n   |- Pick two numbers (5, 37) (numbers left: [28]). Try possible operations.\n    |- Try 37 + 5 = 42. Add 42 to the number set. Current number set: [42, 28], target: 49, just two numbers left.\n     |- Try 42 + 28 = 70. Evaluate 70 != 49, drop this branch.\n     |- Try 42 - 28 = 14. Evaluate 14 != 49, drop this branch.\n     |- Try 42 * 28 = 1176. Evaluate 1176 != 49, drop this branch.\n     |- Try 42 \/ 28 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 37 - 5 = 32. Add 32 to the number set. Current number set: [32, 28], target: 49, just two numbers left.\n     |- Try 32 + 28 = 60. Evaluate 60 != 49, drop this branch.\n     |- Try 32 - 28 = 4. Evaluate 4 != 49, drop this branch.\n     |- Try 32 * 28 = 896. Evaluate 896 != 49, drop this branch.\n     |- Try 32 \/ 28 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 37 * 5 = 185. Add 185 to the number set. Current number set: [185, 28], target: 49, just two numbers left.\n     |- Try 185 + 28 = 213. Evaluate 213 != 49, drop this branch.\n     |- Try 185 - 28 = 157. Evaluate 157 != 49, drop this branch.\n     |- Try 185 * 28 = 5180. 5180 exceeds the maximum intermediate result, drop this branch.\n     |- Try 185 \/ 28 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 37 \/ 5 = 7.4. 7.4 is a decimal, drop this branch.\n   |- Pick two numbers (28, 37) (numbers left: [5]). Try possible operations.\n    |- Try 37 + 28 = 65. Add 65 to the number set. Current number set: [65, 5], target: 49, just two numbers left.\n     |- Try 65 + 5 = 70. Evaluate 70 != 49, drop this branch.\n     |- Try 65 - 5 = 60. Evaluate 60 != 49, drop this branch.\n     |- Try 65 * 5 = 325. Evaluate 325 != 49, drop this branch.\n     |- Try 65 \/ 5 = 13. Evaluate 13 != 49, drop this branch.\n    |- Try 37 - 28 = 9. Add 9 to the number set. Current number set: [9, 5], target: 49, just two numbers left.\n     |- Try 9 + 5 = 14. Evaluate 14 != 49, drop this branch.\n     |- Try 9 - 5 = 4. Evaluate 4 != 49, drop this branch.\n     |- Try 9 * 5 = 45. Evaluate 45 != 49, drop this branch.\n     |- Try 9 \/ 5 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 37 * 28 = 1036. Add 1036 to the number set. Current number set: [1036, 5], target: 49, just two numbers left.\n     |- Try 1036 + 5 = 1041. Evaluate 1041 != 49, drop this branch.\n     |- Try 1036 - 5 = 1031. Evaluate 1031 != 49, drop this branch.\n     |- Try 1036 * 5 = 5180. 5180 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1036 \/ 5 = 207.2. 207.2 is a decimal, drop this branch.\n    |- Try 37 \/ 28 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 35 * 30 = 1050. Add 1050 to the number set. Current number set: [1050, 28, 37], target: 49. Options for choosing two numbers: [(1050, 28), (1050, 37), (28, 37)].\n   |- Pick two numbers (1050, 28) (numbers left: [37]). Try possible operations.\n    |- Try 1050 + 28 = 1078. Add 1078 to the number set. Current number set: [1078, 37], target: 49, just two numbers left.\n     |- Try 1078 + 37 = 1115. Evaluate 1115 != 49, drop this branch.\n     |- Try 1078 - 37 = 1041. Evaluate 1041 != 49, drop this branch.\n     |- Try 1078 * 37 = 39886. 39886 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1078 \/ 37 = 29.1. 29.1 is a decimal, drop this branch.\n    |- Try 1050 - 28 = 1022. Add 1022 to the number set. Current number set: [1022, 37], target: 49, just two numbers left.\n     |- Try 1022 + 37 = 1059. Evaluate 1059 != 49, drop this branch.\n     |- Try 1022 - 37 = 985. Evaluate 985 != 49, drop this branch.\n     |- Try 1022 * 37 = 37814. 37814 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1022 \/ 37 = 27.6. 27.6 is a decimal, drop this branch.\n    |- Try 1050 * 28 = 29400. 29400 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1050 \/ 28 = 37.5. 37.5 is a decimal, drop this branch.\n   |- Pick two numbers (1050, 37) (numbers left: [28]). Try possible operations.\n    |- Try 1050 + 37 = 1087. Add 1087 to the number set. Current number set: [1087, 28], target: 49, just two numbers left.\n     |- Try 1087 + 28 = 1115. Evaluate 1115 != 49, drop this branch.\n     |- Try 1087 - 28 = 1059. Evaluate 1059 != 49, drop this branch.\n     |- Try 1087 * 28 = 30436. 30436 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1087 \/ 28 = 38.8. 38.8 is a decimal, drop this branch.\n    |- Try 1050 - 37 = 1013. Add 1013 to the number set. Current number set: [1013, 28], target: 49, just two numbers left.\n     |- Try 1013 + 28 = 1041. Evaluate 1041 != 49, drop this branch.\n     |- Try 1013 - 28 = 985. Evaluate 985 != 49, drop this branch.\n     |- Try 1013 * 28 = 28364. 28364 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1013 \/ 28 = 36.2. 36.2 is a decimal, drop this branch.\n    |- Try 1050 * 37 = 38850. 38850 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1050 \/ 37 = 28.4. 28.4 is a decimal, drop this branch.\n   |- Pick two numbers (28, 37) (numbers left: [1050]). Try possible operations.\n    |- Try 37 + 28 = 65. Add 65 to the number set. Current number set: [65, 1050], target: 49, just two numbers left.\n     |- Try 1050 + 65 = 1115. Evaluate 1115 != 49, drop this branch.\n     |- Try 1050 - 65 = 985. Evaluate 985 != 49, drop this branch.\n     |- Try 1050 * 65 = 68250. 68250 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1050 \/ 65 = 16.2. 16.2 is a decimal, drop this branch.\n    |- Try 37 - 28 = 9. Add 9 to the number set. Current number set: [9, 1050], target: 49, just two numbers left.\n     |- Try 1050 + 9 = 1059. Evaluate 1059 != 49, drop this branch.\n     |- Try 1050 - 9 = 1041. Evaluate 1041 != 49, drop this branch.\n     |- Try 1050 * 9 = 9450. 9450 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1050 \/ 9 = 116.7. 116.7 is a decimal, drop this branch.\n    |- Try 37 * 28 = 1036. Add 1036 to the number set. Current number set: [1036, 1050], target: 49, just two numbers left.\n     |- Try 1050 + 1036 = 2086. 2086 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1050 - 1036 = 14. Evaluate 14 != 49, drop this branch.\n     |- Try 1050 * 1036 = 1087800. 1087800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1050 \/ 1036 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 37 \/ 28 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 35 \/ 30 = 1.2. 1.2 is a decimal, drop this branch.\n |- Pick two numbers (35, 28) (numbers left: [30, 37]). Try possible operations.\n  |- Try 35 + 28 = 63. Add 63 to the number set. Current number set: [63, 30, 37], target: 49. Options for choosing two numbers: [(63, 30), (63, 37), (30, 37)].\n   |- Pick two numbers (63, 30) (numbers left: [37]). Try possible operations.\n    |- Try 63 + 30 = 93. Add 93 to the number set. Current number set: [93, 37], target: 49, just two numbers left.\n     |- Try 93 + 37 = 130. Evaluate 130 != 49, drop this branch.\n     |- Try 93 - 37 = 56. Evaluate 56 != 49, drop this branch.\n     |- Try 93 * 37 = 3441. 3441 exceeds the maximum intermediate result, drop this branch.\n     |- Try 93 \/ 37 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 63 - 30 = 33. Add 33 to the number set. Current number set: [33, 37], target: 49, just two numbers left.\n     |- Try 37 + 33 = 70. Evaluate 70 != 49, drop this branch.\n     |- Try 37 - 33 = 4. Evaluate 4 != 49, drop this branch.\n     |- Try 37 * 33 = 1221. Evaluate 1221 != 49, drop this branch.\n     |- Try 37 \/ 33 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 63 * 30 = 1890. Add 1890 to the number set. Current number set: [1890, 37], target: 49, just two numbers left.\n     |- Try 1890 + 37 = 1927. Evaluate 1927 != 49, drop this branch.\n     |- Try 1890 - 37 = 1853. Evaluate 1853 != 49, drop this branch.\n     |- Try 1890 * 37 = 69930. 69930 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1890 \/ 37 = 51.1. 51.1 is a decimal, drop this branch.\n    |- Try 63 \/ 30 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (63, 37) (numbers left: [30]). Try possible operations.\n    |- Try 63 + 37 = 100. Add 100 to the number set. Current number set: [100, 30], target: 49, just two numbers left.\n     |- Try 100 + 30 = 130. Evaluate 130 != 49, drop this branch.\n     |- Try 100 - 30 = 70. Evaluate 70 != 49, drop this branch.\n     |- Try 100 * 30 = 3000. 3000 exceeds the maximum intermediate result, drop this branch.\n     |- Try 100 \/ 30 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 63 - 37 = 26. Add 26 to the number set. Current number set: [26, 30], target: 49, just two numbers left.\n     |- Try 30 + 26 = 56. Evaluate 56 != 49, drop this branch.\n     |- Try 30 - 26 = 4. Evaluate 4 != 49, drop this branch.\n     |- Try 30 * 26 = 780. Evaluate 780 != 49, drop this branch.\n     |- Try 30 \/ 26 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 63 * 37 = 2331. 2331 exceeds the maximum intermediate result, drop this branch.\n    |- Try 63 \/ 37 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (30, 37) (numbers left: [63]). Try possible operations.\n    |- Try 37 + 30 = 67. Add 67 to the number set. Current number set: [67, 63], target: 49, just two numbers left.\n     |- Try 67 + 63 = 130. Evaluate 130 != 49, drop this branch.\n     |- Try 67 - 63 = 4. Evaluate 4 != 49, drop this branch.\n     |- Try 67 * 63 = 4221. 4221 exceeds the maximum intermediate result, drop this branch.\n     |- Try 67 \/ 63 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 37 - 30 = 7. Add 7 to the number set. Current number set: [7, 63], target: 49, just two numbers left.\n     |- Try 63 + 7 = 70. Evaluate 70 != 49, drop this branch.\n     |- Try 63 - 7 = 56. Evaluate 56 != 49, drop this branch.\n     |- Try 63 * 7 = 441. Evaluate 441 != 49, drop this branch.\n     |- Try 63 \/ 7 = 9. Evaluate 9 != 49, drop this branch.\n    |- Try 37 * 30 = 1110. Add 1110 to the number set. Current number set: [1110, 63], target: 49, just two numbers left.\n     |- Try 1110 + 63 = 1173. Evaluate 1173 != 49, drop this branch.\n     |- Try 1110 - 63 = 1047. Evaluate 1047 != 49, drop this branch.\n     |- Try 1110 * 63 = 69930. 69930 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1110 \/ 63 = 17.6. 17.6 is a decimal, drop this branch.\n    |- Try 37 \/ 30 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 35 - 28 = 7. Add 7 to the number set. Current number set: [7, 30, 37], target: 49. Options for choosing two numbers: [(7, 30), (7, 37), (30, 37)].\n   |- Pick two numbers (7, 30) (numbers left: [37]). Try possible operations.\n    |- Try 30 + 7 = 37. Add 37 to the number set. Current number set: [37, 37], target: 49, just two numbers left.\n     |- Try 37 + 37 = 74. Evaluate 74 != 49, drop this branch.\n     |- Try 37 - 37 = 0. Evaluate 0 != 49, drop this branch.\n     |- Try 37 * 37 = 1369. Evaluate 1369 != 49, drop this branch.\n     |- Try 37 \/ 37 = 1. Evaluate 1 != 49, drop this branch.\n    |- Try 30 - 7 = 23. Add 23 to the number set. Current number set: [23, 37], target: 49, just two numbers left.\n     |- Try 37 + 23 = 60. Evaluate 60 != 49, drop this branch.\n     |- Try 37 - 23 = 14. Evaluate 14 != 49, drop this branch.\n     |- Try 37 * 23 = 851. Evaluate 851 != 49, drop this branch.\n     |- Try 37 \/ 23 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 30 * 7 = 210. Add 210 to the number set. Current number set: [210, 37], target: 49, just two numbers left.\n     |- Try 210 + 37 = 247. Evaluate 247 != 49, drop this branch.\n     |- Try 210 - 37 = 173. Evaluate 173 != 49, drop this branch.\n     |- Try 210 * 37 = 7770. 7770 exceeds the maximum intermediate result, drop this branch.\n     |- Try 210 \/ 37 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 30 \/ 7 = 4.3. 4.3 is a decimal, drop this branch.\n   |- Pick two numbers (7, 37) (numbers left: [30]). Try possible operations.\n    |- Try 37 + 7 = 44. Add 44 to the number set. Current number set: [44, 30], target: 49, just two numbers left.\n     |- Try 44 + 30 = 74. Evaluate 74 != 49, drop this branch.\n     |- Try 44 - 30 = 14. Evaluate 14 != 49, drop this branch.\n     |- Try 44 * 30 = 1320. Evaluate 1320 != 49, drop this branch.\n     |- Try 44 \/ 30 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 37 - 7 = 30. Add 30 to the number set. Current number set: [30, 30], target: 49, just two numbers left.\n     |- Try 30 + 30 = 60. Evaluate 60 != 49, drop this branch.\n     |- Try 30 - 30 = 0. Evaluate 0 != 49, drop this branch.\n     |- Try 30 * 30 = 900. Evaluate 900 != 49, drop this branch.\n     |- Try 30 \/ 30 = 1. Evaluate 1 != 49, drop this branch.\n    |- Try 37 * 7 = 259. Add 259 to the number set. Current number set: [259, 30], target: 49, just two numbers left.\n     |- Try 259 + 30 = 289. Evaluate 289 != 49, drop this branch.\n     |- Try 259 - 30 = 229. Evaluate 229 != 49, drop this branch.\n     |- Try 259 * 30 = 7770. 7770 exceeds the maximum intermediate result, drop this branch.\n     |- Try 259 \/ 30 = 8.6. 8.6 is a decimal, drop this branch.\n    |- Try 37 \/ 7 = 5.3. 5.3 is a decimal, drop this branch.\n   |- Pick two numbers (30, 37) (numbers left: [7]). Try possible operations.\n    |- Try 37 + 30 = 67. Add 67 to the number set. Current number set: [67, 7], target: 49, just two numbers left.\n     |- Try 67 + 7 = 74. Evaluate 74 != 49, drop this branch.\n     |- Try 67 - 7 = 60. Evaluate 60 != 49, drop this branch.\n     |- Try 67 * 7 = 469. Evaluate 469 != 49, drop this branch.\n     |- Try 67 \/ 7 = 9.6. 9.6 is a decimal, drop this branch.\n    |- Try 37 - 30 = 7. Add 7 to the number set. Current number set: [7, 7], target: 49, just two numbers left.\n     |- Try 7 + 7 = 14. Evaluate 14 != 49, drop this branch.\n     |- Try 7 - 7 = 0. Evaluate 0 != 49, drop this branch.\n     |- Try 7 * 7 = 49. Evaluate 49 == 49, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 7 * 7 = 49\nThe step before: 37 - 30 = 7\nThe first step: 35 - 28 = 7\n\nOutput the solution in the required format:\n<Solution>\n35 - 28 = 7\n37 - 30 = 7\n7 * 7 = 49\n<\/Solution>\n","item":{"nums":[35,30,28,37],"solution":["35 - 28 = 7","37 - 30 = 7","7 * 7 = 49"],"target":49}}
+{"instance_id":"countdown_8k_179","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [1, 18, 44, 18]\nTarget: 46","reference_output":"# Search Procedure\nInitial number set: [1, 18, 44, 18], target: 46. Options for choosing two numbers: [(1, 18), (1, 44), (1, 18), (18, 44), (18, 18), (44, 18)].\n |- Pick two numbers (1, 18) (numbers left: [44, 18]). Try possible operations.\n  |- Try 18 + 1 = 19. Add 19 to the number set. Current number set: [19, 44, 18], target: 46. Options for choosing two numbers: [(19, 44), (19, 18), (44, 18)].\n   |- Pick two numbers (19, 44) (numbers left: [18]). Try possible operations.\n    |- Try 44 + 19 = 63. Add 63 to the number set. Current number set: [63, 18], target: 46, just two numbers left.\n     |- Try 63 + 18 = 81. Evaluate 81 != 46, drop this branch.\n     |- Try 63 - 18 = 45. Evaluate 45 != 46, drop this branch.\n     |- Try 63 * 18 = 1134. Evaluate 1134 != 46, drop this branch.\n     |- Try 63 \/ 18 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 44 - 19 = 25. Add 25 to the number set. Current number set: [25, 18], target: 46, just two numbers left.\n     |- Try 25 + 18 = 43. Evaluate 43 != 46, drop this branch.\n     |- Try 25 - 18 = 7. Evaluate 7 != 46, drop this branch.\n     |- Try 25 * 18 = 450. Evaluate 450 != 46, drop this branch.\n     |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 44 * 19 = 836. Add 836 to the number set. Current number set: [836, 18], target: 46, just two numbers left.\n     |- Try 836 + 18 = 854. Evaluate 854 != 46, drop this branch.\n     |- Try 836 - 18 = 818. Evaluate 818 != 46, drop this branch.\n     |- Try 836 * 18 = 15048. 15048 exceeds the maximum intermediate result, drop this branch.\n     |- Try 836 \/ 18 = 46.4. 46.4 is a decimal, drop this branch.\n    |- Try 44 \/ 19 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (19, 18) (numbers left: [44]). Try possible operations.\n    |- Try 19 + 18 = 37. Add 37 to the number set. Current number set: [37, 44], target: 46, just two numbers left.\n     |- Try 44 + 37 = 81. Evaluate 81 != 46, drop this branch.\n     |- Try 44 - 37 = 7. Evaluate 7 != 46, drop this branch.\n     |- Try 44 * 37 = 1628. Evaluate 1628 != 46, drop this branch.\n     |- Try 44 \/ 37 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 19 - 18 = 1. Add 1 to the number set. Current number set: [1, 44], target: 46, just two numbers left.\n     |- Try 44 + 1 = 45. Evaluate 45 != 46, drop this branch.\n     |- Try 44 - 1 = 43. Evaluate 43 != 46, drop this branch.\n     |- Try 44 * 1 = 44. Evaluate 44 != 46, drop this branch.\n     |- Try 44 \/ 1 = 44. Evaluate 44 != 46, drop this branch.\n    |- Try 19 * 18 = 342. Add 342 to the number set. Current number set: [342, 44], target: 46, just two numbers left.\n     |- Try 342 + 44 = 386. Evaluate 386 != 46, drop this branch.\n     |- Try 342 - 44 = 298. Evaluate 298 != 46, drop this branch.\n     |- Try 342 * 44 = 15048. 15048 exceeds the maximum intermediate result, drop this branch.\n     |- Try 342 \/ 44 = 7.8. 7.8 is a decimal, drop this branch.\n    |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (44, 18) (numbers left: [19]). Try possible operations.\n    |- Try 44 + 18 = 62. Add 62 to the number set. Current number set: [62, 19], target: 46, just two numbers left.\n     |- Try 62 + 19 = 81. Evaluate 81 != 46, drop this branch.\n     |- Try 62 - 19 = 43. Evaluate 43 != 46, drop this branch.\n     |- Try 62 * 19 = 1178. Evaluate 1178 != 46, drop this branch.\n     |- Try 62 \/ 19 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 44 - 18 = 26. Add 26 to the number set. Current number set: [26, 19], target: 46, just two numbers left.\n     |- Try 26 + 19 = 45. Evaluate 45 != 46, drop this branch.\n     |- Try 26 - 19 = 7. Evaluate 7 != 46, drop this branch.\n     |- Try 26 * 19 = 494. Evaluate 494 != 46, drop this branch.\n     |- Try 26 \/ 19 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 44 * 18 = 792. Add 792 to the number set. Current number set: [792, 19], target: 46, just two numbers left.\n     |- Try 792 + 19 = 811. Evaluate 811 != 46, drop this branch.\n     |- Try 792 - 19 = 773. Evaluate 773 != 46, drop this branch.\n     |- Try 792 * 19 = 15048. 15048 exceeds the maximum intermediate result, drop this branch.\n     |- Try 792 \/ 19 = 41.7. 41.7 is a decimal, drop this branch.\n    |- Try 44 \/ 18 = 2.4. 2.4 is a decimal, drop this branch.\n  |- Try 18 - 1 = 17. Add 17 to the number set. Current number set: [17, 44, 18], target: 46. Options for choosing two numbers: [(17, 44), (17, 18), (44, 18)].\n   |- Pick two numbers (17, 44) (numbers left: [18]). Try possible operations.\n    |- Try 44 + 17 = 61. Add 61 to the number set. Current number set: [61, 18], target: 46, just two numbers left.\n     |- Try 61 + 18 = 79. Evaluate 79 != 46, drop this branch.\n     |- Try 61 - 18 = 43. Evaluate 43 != 46, drop this branch.\n     |- Try 61 * 18 = 1098. Evaluate 1098 != 46, drop this branch.\n     |- Try 61 \/ 18 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 44 - 17 = 27. Add 27 to the number set. Current number set: [27, 18], target: 46, just two numbers left.\n     |- Try 27 + 18 = 45. Evaluate 45 != 46, drop this branch.\n     |- Try 27 - 18 = 9. Evaluate 9 != 46, drop this branch.\n     |- Try 27 * 18 = 486. Evaluate 486 != 46, drop this branch.\n     |- Try 27 \/ 18 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 44 * 17 = 748. Add 748 to the number set. Current number set: [748, 18], target: 46, just two numbers left.\n     |- Try 748 + 18 = 766. Evaluate 766 != 46, drop this branch.\n     |- Try 748 - 18 = 730. Evaluate 730 != 46, drop this branch.\n     |- Try 748 * 18 = 13464. 13464 exceeds the maximum intermediate result, drop this branch.\n     |- Try 748 \/ 18 = 41.6. 41.6 is a decimal, drop this branch.\n    |- Try 44 \/ 17 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (17, 18) (numbers left: [44]). Try possible operations.\n    |- Try 18 + 17 = 35. Add 35 to the number set. Current number set: [35, 44], target: 46, just two numbers left.\n     |- Try 44 + 35 = 79. Evaluate 79 != 46, drop this branch.\n     |- Try 44 - 35 = 9. Evaluate 9 != 46, drop this branch.\n     |- Try 44 * 35 = 1540. Evaluate 1540 != 46, drop this branch.\n     |- Try 44 \/ 35 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 18 - 17 = 1. Add 1 to the number set. Current number set: [1, 44], target: 46, just two numbers left.\n     |- Try 44 + 1 = 45. Evaluate 45 != 46, drop this branch.\n     |- Try 44 - 1 = 43. Evaluate 43 != 46, drop this branch.\n     |- Try 44 * 1 = 44. Evaluate 44 != 46, drop this branch.\n     |- Try 44 \/ 1 = 44. Evaluate 44 != 46, drop this branch.\n    |- Try 18 * 17 = 306. Add 306 to the number set. Current number set: [306, 44], target: 46, just two numbers left.\n     |- Try 306 + 44 = 350. Evaluate 350 != 46, drop this branch.\n     |- Try 306 - 44 = 262. Evaluate 262 != 46, drop this branch.\n     |- Try 306 * 44 = 13464. 13464 exceeds the maximum intermediate result, drop this branch.\n     |- Try 306 \/ 44 = 7.0. 7.0 is a decimal, drop this branch.\n    |- Try 18 \/ 17 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (44, 18) (numbers left: [17]). Try possible operations.\n    |- Try 44 + 18 = 62. Add 62 to the number set. Current number set: [62, 17], target: 46, just two numbers left.\n     |- Try 62 + 17 = 79. Evaluate 79 != 46, drop this branch.\n     |- Try 62 - 17 = 45. Evaluate 45 != 46, drop this branch.\n     |- Try 62 * 17 = 1054. Evaluate 1054 != 46, drop this branch.\n     |- Try 62 \/ 17 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 44 - 18 = 26. Add 26 to the number set. Current number set: [26, 17], target: 46, just two numbers left.\n     |- Try 26 + 17 = 43. Evaluate 43 != 46, drop this branch.\n     |- Try 26 - 17 = 9. Evaluate 9 != 46, drop this branch.\n     |- Try 26 * 17 = 442. Evaluate 442 != 46, drop this branch.\n     |- Try 26 \/ 17 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 44 * 18 = 792. Add 792 to the number set. Current number set: [792, 17], target: 46, just two numbers left.\n     |- Try 792 + 17 = 809. Evaluate 809 != 46, drop this branch.\n     |- Try 792 - 17 = 775. Evaluate 775 != 46, drop this branch.\n     |- Try 792 * 17 = 13464. 13464 exceeds the maximum intermediate result, drop this branch.\n     |- Try 792 \/ 17 = 46.6. 46.6 is a decimal, drop this branch.\n    |- Try 44 \/ 18 = 2.4. 2.4 is a decimal, drop this branch.\n  |- Try 18 * 1 = 18. Add 18 to the number set. Current number set: [18, 44, 18], target: 46. Options for choosing two numbers: [(18, 44), (18, 18), (44, 18)].\n   |- Pick two numbers (18, 44) (numbers left: [18]). Try possible operations.\n    |- Try 44 + 18 = 62. Add 62 to the number set. Current number set: [62, 18], target: 46, just two numbers left.\n     |- Try 62 + 18 = 80. Evaluate 80 != 46, drop this branch.\n     |- Try 62 - 18 = 44. Evaluate 44 != 46, drop this branch.\n     |- Try 62 * 18 = 1116. Evaluate 1116 != 46, drop this branch.\n     |- Try 62 \/ 18 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 44 - 18 = 26. Add 26 to the number set. Current number set: [26, 18], target: 46, just two numbers left.\n     |- Try 26 + 18 = 44. Evaluate 44 != 46, drop this branch.\n     |- Try 26 - 18 = 8. Evaluate 8 != 46, drop this branch.\n     |- Try 26 * 18 = 468. Evaluate 468 != 46, drop this branch.\n     |- Try 26 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 44 * 18 = 792. Add 792 to the number set. Current number set: [792, 18], target: 46, just two numbers left.\n     |- Try 792 + 18 = 810. Evaluate 810 != 46, drop this branch.\n     |- Try 792 - 18 = 774. Evaluate 774 != 46, drop this branch.\n     |- Try 792 * 18 = 14256. 14256 exceeds the maximum intermediate result, drop this branch.\n     |- Try 792 \/ 18 = 44. Evaluate 44 != 46, drop this branch.\n    |- Try 44 \/ 18 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (18, 18) (numbers left: [44]). Try possible operations.\n    |- Try 18 + 18 = 36. Add 36 to the number set. Current number set: [36, 44], target: 46, just two numbers left.\n     |- Try 44 + 36 = 80. Evaluate 80 != 46, drop this branch.\n     |- Try 44 - 36 = 8. Evaluate 8 != 46, drop this branch.\n     |- Try 44 * 36 = 1584. Evaluate 1584 != 46, drop this branch.\n     |- Try 44 \/ 36 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 18 - 18 = 0. Add 0 to the number set. Current number set: [0, 44], target: 46, just two numbers left.\n     |- Try 44 + 0 = 44. Evaluate 44 != 46, drop this branch.\n     |- Try 44 - 0 = 44. Evaluate 44 != 46, drop this branch.\n     |- Try 44 * 0 = 0. Evaluate 0 != 46, drop this branch.\n     |- Try 44 \/ 0 (invalid operation). drop this branch.\n    |- Try 18 * 18 = 324. Add 324 to the number set. Current number set: [324, 44], target: 46, just two numbers left.\n     |- Try 324 + 44 = 368. Evaluate 368 != 46, drop this branch.\n     |- Try 324 - 44 = 280. Evaluate 280 != 46, drop this branch.\n     |- Try 324 * 44 = 14256. 14256 exceeds the maximum intermediate result, drop this branch.\n     |- Try 324 \/ 44 = 7.4. 7.4 is a decimal, drop this branch.\n    |- Try 18 \/ 18 = 1. Add 1 to the number set. Current number set: [1, 44], target: 46, just two numbers left.\n     |- Try 44 + 1 = 45. Evaluate 45 != 46, drop this branch.\n     |- Try 44 - 1 = 43. Evaluate 43 != 46, drop this branch.\n     |- Try 44 * 1 = 44. Evaluate 44 != 46, drop this branch.\n     |- Try 44 \/ 1 = 44. Evaluate 44 != 46, drop this branch.\n   |- Pick two numbers (44, 18) (numbers left: [18]). Try possible operations.\n    |- Try 44 + 18 = 62. Add 62 to the number set. Current number set: [62, 18], target: 46, just two numbers left.\n     |- Try 62 + 18 = 80. Evaluate 80 != 46, drop this branch.\n     |- Try 62 - 18 = 44. Evaluate 44 != 46, drop this branch.\n     |- Try 62 * 18 = 1116. Evaluate 1116 != 46, drop this branch.\n     |- Try 62 \/ 18 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 44 - 18 = 26. Add 26 to the number set. Current number set: [26, 18], target: 46, just two numbers left.\n     |- Try 26 + 18 = 44. Evaluate 44 != 46, drop this branch.\n     |- Try 26 - 18 = 8. Evaluate 8 != 46, drop this branch.\n     |- Try 26 * 18 = 468. Evaluate 468 != 46, drop this branch.\n     |- Try 26 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 44 * 18 = 792. Add 792 to the number set. Current number set: [792, 18], target: 46, just two numbers left.\n     |- Try 792 + 18 = 810. Evaluate 810 != 46, drop this branch.\n     |- Try 792 - 18 = 774. Evaluate 774 != 46, drop this branch.\n     |- Try 792 * 18 = 14256. 14256 exceeds the maximum intermediate result, drop this branch.\n     |- Try 792 \/ 18 = 44. Evaluate 44 != 46, drop this branch.\n    |- Try 44 \/ 18 = 2.4. 2.4 is a decimal, drop this branch.\n  |- Try 18 \/ 1 = 18. Add 18 to the number set. Current number set: [18, 44, 18], target: 46. Options for choosing two numbers: [(18, 44), (18, 18), (44, 18)].\n   |- Pick two numbers (18, 44) (numbers left: [18]). Try possible operations.\n    |- Try 44 + 18 = 62. Add 62 to the number set. Current number set: [62, 18], target: 46, just two numbers left.\n     |- Try 62 + 18 = 80. Evaluate 80 != 46, drop this branch.\n     |- Try 62 - 18 = 44. Evaluate 44 != 46, drop this branch.\n     |- Try 62 * 18 = 1116. Evaluate 1116 != 46, drop this branch.\n     |- Try 62 \/ 18 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 44 - 18 = 26. Add 26 to the number set. Current number set: [26, 18], target: 46, just two numbers left.\n     |- Try 26 + 18 = 44. Evaluate 44 != 46, drop this branch.\n     |- Try 26 - 18 = 8. Evaluate 8 != 46, drop this branch.\n     |- Try 26 * 18 = 468. Evaluate 468 != 46, drop this branch.\n     |- Try 26 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 44 * 18 = 792. Add 792 to the number set. Current number set: [792, 18], target: 46, just two numbers left.\n     |- Try 792 + 18 = 810. Evaluate 810 != 46, drop this branch.\n     |- Try 792 - 18 = 774. Evaluate 774 != 46, drop this branch.\n     |- Try 792 * 18 = 14256. 14256 exceeds the maximum intermediate result, drop this branch.\n     |- Try 792 \/ 18 = 44. Evaluate 44 != 46, drop this branch.\n    |- Try 44 \/ 18 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (18, 18) (numbers left: [44]). Try possible operations.\n    |- Try 18 + 18 = 36. Add 36 to the number set. Current number set: [36, 44], target: 46, just two numbers left.\n     |- Try 44 + 36 = 80. Evaluate 80 != 46, drop this branch.\n     |- Try 44 - 36 = 8. Evaluate 8 != 46, drop this branch.\n     |- Try 44 * 36 = 1584. Evaluate 1584 != 46, drop this branch.\n     |- Try 44 \/ 36 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 18 - 18 = 0. Add 0 to the number set. Current number set: [0, 44], target: 46, just two numbers left.\n     |- Try 44 + 0 = 44. Evaluate 44 != 46, drop this branch.\n     |- Try 44 - 0 = 44. Evaluate 44 != 46, drop this branch.\n     |- Try 44 * 0 = 0. Evaluate 0 != 46, drop this branch.\n     |- Try 44 \/ 0 (invalid operation). drop this branch.\n    |- Try 18 * 18 = 324. Add 324 to the number set. Current number set: [324, 44], target: 46, just two numbers left.\n     |- Try 324 + 44 = 368. Evaluate 368 != 46, drop this branch.\n     |- Try 324 - 44 = 280. Evaluate 280 != 46, drop this branch.\n     |- Try 324 * 44 = 14256. 14256 exceeds the maximum intermediate result, drop this branch.\n     |- Try 324 \/ 44 = 7.4. 7.4 is a decimal, drop this branch.\n    |- Try 18 \/ 18 = 1. Add 1 to the number set. Current number set: [1, 44], target: 46, just two numbers left.\n     |- Try 44 + 1 = 45. Evaluate 45 != 46, drop this branch.\n     |- Try 44 - 1 = 43. Evaluate 43 != 46, drop this branch.\n     |- Try 44 * 1 = 44. Evaluate 44 != 46, drop this branch.\n     |- Try 44 \/ 1 = 44. Evaluate 44 != 46, drop this branch.\n   |- Pick two numbers (44, 18) (numbers left: [18]). Try possible operations.\n    |- Try 44 + 18 = 62. Add 62 to the number set. Current number set: [62, 18], target: 46, just two numbers left.\n     |- Try 62 + 18 = 80. Evaluate 80 != 46, drop this branch.\n     |- Try 62 - 18 = 44. Evaluate 44 != 46, drop this branch.\n     |- Try 62 * 18 = 1116. Evaluate 1116 != 46, drop this branch.\n     |- Try 62 \/ 18 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 44 - 18 = 26. Add 26 to the number set. Current number set: [26, 18], target: 46, just two numbers left.\n     |- Try 26 + 18 = 44. Evaluate 44 != 46, drop this branch.\n     |- Try 26 - 18 = 8. Evaluate 8 != 46, drop this branch.\n     |- Try 26 * 18 = 468. Evaluate 468 != 46, drop this branch.\n     |- Try 26 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 44 * 18 = 792. Add 792 to the number set. Current number set: [792, 18], target: 46, just two numbers left.\n     |- Try 792 + 18 = 810. Evaluate 810 != 46, drop this branch.\n     |- Try 792 - 18 = 774. Evaluate 774 != 46, drop this branch.\n     |- Try 792 * 18 = 14256. 14256 exceeds the maximum intermediate result, drop this branch.\n     |- Try 792 \/ 18 = 44. Evaluate 44 != 46, drop this branch.\n    |- Try 44 \/ 18 = 2.4. 2.4 is a decimal, drop this branch.\n |- Pick two numbers (1, 44) (numbers left: [18, 18]). Try possible operations.\n  |- Try 44 + 1 = 45. Add 45 to the number set. Current number set: [45, 18, 18], target: 46. Options for choosing two numbers: [(45, 18), (45, 18), (18, 18)].\n   |- Pick two numbers (45, 18) (numbers left: [18]). Try possible operations.\n    |- Try 45 + 18 = 63. Add 63 to the number set. Current number set: [63, 18], target: 46, just two numbers left.\n     |- Try 63 + 18 = 81. Evaluate 81 != 46, drop this branch.\n     |- Try 63 - 18 = 45. Evaluate 45 != 46, drop this branch.\n     |- Try 63 * 18 = 1134. Evaluate 1134 != 46, drop this branch.\n     |- Try 63 \/ 18 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 45 - 18 = 27. Add 27 to the number set. Current number set: [27, 18], target: 46, just two numbers left.\n     |- Try 27 + 18 = 45. Evaluate 45 != 46, drop this branch.\n     |- Try 27 - 18 = 9. Evaluate 9 != 46, drop this branch.\n     |- Try 27 * 18 = 486. Evaluate 486 != 46, drop this branch.\n     |- Try 27 \/ 18 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 45 * 18 = 810. Add 810 to the number set. Current number set: [810, 18], target: 46, just two numbers left.\n     |- Try 810 + 18 = 828. Evaluate 828 != 46, drop this branch.\n     |- Try 810 - 18 = 792. Evaluate 792 != 46, drop this branch.\n     |- Try 810 * 18 = 14580. 14580 exceeds the maximum intermediate result, drop this branch.\n     |- Try 810 \/ 18 = 45. Evaluate 45 != 46, drop this branch.\n    |- Try 45 \/ 18 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (45, 18) (numbers left: [18]). Try possible operations.\n    |- Try 45 + 18 = 63. Add 63 to the number set. Current number set: [63, 18], target: 46, just two numbers left.\n     |- Try 63 + 18 = 81. Evaluate 81 != 46, drop this branch.\n     |- Try 63 - 18 = 45. Evaluate 45 != 46, drop this branch.\n     |- Try 63 * 18 = 1134. Evaluate 1134 != 46, drop this branch.\n     |- Try 63 \/ 18 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 45 - 18 = 27. Add 27 to the number set. Current number set: [27, 18], target: 46, just two numbers left.\n     |- Try 27 + 18 = 45. Evaluate 45 != 46, drop this branch.\n     |- Try 27 - 18 = 9. Evaluate 9 != 46, drop this branch.\n     |- Try 27 * 18 = 486. Evaluate 486 != 46, drop this branch.\n     |- Try 27 \/ 18 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 45 * 18 = 810. Add 810 to the number set. Current number set: [810, 18], target: 46, just two numbers left.\n     |- Try 810 + 18 = 828. Evaluate 828 != 46, drop this branch.\n     |- Try 810 - 18 = 792. Evaluate 792 != 46, drop this branch.\n     |- Try 810 * 18 = 14580. 14580 exceeds the maximum intermediate result, drop this branch.\n     |- Try 810 \/ 18 = 45. Evaluate 45 != 46, drop this branch.\n    |- Try 45 \/ 18 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (18, 18) (numbers left: [45]). Try possible operations.\n    |- Try 18 + 18 = 36. Add 36 to the number set. Current number set: [36, 45], target: 46, just two numbers left.\n     |- Try 45 + 36 = 81. Evaluate 81 != 46, drop this branch.\n     |- Try 45 - 36 = 9. Evaluate 9 != 46, drop this branch.\n     |- Try 45 * 36 = 1620. Evaluate 1620 != 46, drop this branch.\n     |- Try 45 \/ 36 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 18 - 18 = 0. Add 0 to the number set. Current number set: [0, 45], target: 46, just two numbers left.\n     |- Try 45 + 0 = 45. Evaluate 45 != 46, drop this branch.\n     |- Try 45 - 0 = 45. Evaluate 45 != 46, drop this branch.\n     |- Try 45 * 0 = 0. Evaluate 0 != 46, drop this branch.\n     |- Try 45 \/ 0 (invalid operation). drop this branch.\n    |- Try 18 * 18 = 324. Add 324 to the number set. Current number set: [324, 45], target: 46, just two numbers left.\n     |- Try 324 + 45 = 369. Evaluate 369 != 46, drop this branch.\n     |- Try 324 - 45 = 279. Evaluate 279 != 46, drop this branch.\n     |- Try 324 * 45 = 14580. 14580 exceeds the maximum intermediate result, drop this branch.\n     |- Try 324 \/ 45 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 18 \/ 18 = 1. Add 1 to the number set. Current number set: [1, 45], target: 46, just two numbers left.\n     |- Try 45 + 1 = 46. Evaluate 46 == 46, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 45 + 1 = 46\nThe step before: 18 \/ 18 = 1\nThe first step: 44 + 1 = 45\n\nOutput the solution in the required format:\n<Solution>\n44 + 1 = 45\n18 \/ 18 = 1\n45 + 1 = 46\n<\/Solution>\n","item":{"nums":[1,18,44,18],"solution":["44 + 1 = 45","18 \/ 18 = 1","45 + 1 = 46"],"target":46}}
+{"instance_id":"countdown_8k_180","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [23, 31, 41, 36]\nTarget: 29","reference_output":"# Search Procedure\nInitial number set: [23, 31, 41, 36], target: 29. Options for choosing two numbers: [(23, 31), (23, 41), (23, 36), (31, 41), (31, 36), (41, 36)].\n |- Pick two numbers (23, 31) (numbers left: [41, 36]). Try possible operations.\n  |- Try 31 + 23 = 54. Add 54 to the number set. Current number set: [54, 41, 36], target: 29. Options for choosing two numbers: [(54, 41), (54, 36), (41, 36)].\n   |- Pick two numbers (54, 41) (numbers left: [36]). Try possible operations.\n    |- Try 54 + 41 = 95. Add 95 to the number set. Current number set: [95, 36], target: 29, just two numbers left.\n     |- Try 95 + 36 = 131. Evaluate 131 != 29, drop this branch.\n     |- Try 95 - 36 = 59. Evaluate 59 != 29, drop this branch.\n     |- Try 95 * 36 = 3420. 3420 exceeds the maximum intermediate result, drop this branch.\n     |- Try 95 \/ 36 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 54 - 41 = 13. Add 13 to the number set. Current number set: [13, 36], target: 29, just two numbers left.\n     |- Try 36 + 13 = 49. Evaluate 49 != 29, drop this branch.\n     |- Try 36 - 13 = 23. Evaluate 23 != 29, drop this branch.\n     |- Try 36 * 13 = 468. Evaluate 468 != 29, drop this branch.\n     |- Try 36 \/ 13 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 54 * 41 = 2214. 2214 exceeds the maximum intermediate result, drop this branch.\n    |- Try 54 \/ 41 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (54, 36) (numbers left: [41]). Try possible operations.\n    |- Try 54 + 36 = 90. Add 90 to the number set. Current number set: [90, 41], target: 29, just two numbers left.\n     |- Try 90 + 41 = 131. Evaluate 131 != 29, drop this branch.\n     |- Try 90 - 41 = 49. Evaluate 49 != 29, drop this branch.\n     |- Try 90 * 41 = 3690. 3690 exceeds the maximum intermediate result, drop this branch.\n     |- Try 90 \/ 41 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 54 - 36 = 18. Add 18 to the number set. Current number set: [18, 41], target: 29, just two numbers left.\n     |- Try 41 + 18 = 59. Evaluate 59 != 29, drop this branch.\n     |- Try 41 - 18 = 23. Evaluate 23 != 29, drop this branch.\n     |- Try 41 * 18 = 738. Evaluate 738 != 29, drop this branch.\n     |- Try 41 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 54 * 36 = 1944. Add 1944 to the number set. Current number set: [1944, 41], target: 29, just two numbers left.\n     |- Try 1944 + 41 = 1985. Evaluate 1985 != 29, drop this branch.\n     |- Try 1944 - 41 = 1903. Evaluate 1903 != 29, drop this branch.\n     |- Try 1944 * 41 = 79704. 79704 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1944 \/ 41 = 47.4. 47.4 is a decimal, drop this branch.\n    |- Try 54 \/ 36 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (41, 36) (numbers left: [54]). Try possible operations.\n    |- Try 41 + 36 = 77. Add 77 to the number set. Current number set: [77, 54], target: 29, just two numbers left.\n     |- Try 77 + 54 = 131. Evaluate 131 != 29, drop this branch.\n     |- Try 77 - 54 = 23. Evaluate 23 != 29, drop this branch.\n     |- Try 77 * 54 = 4158. 4158 exceeds the maximum intermediate result, drop this branch.\n     |- Try 77 \/ 54 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 41 - 36 = 5. Add 5 to the number set. Current number set: [5, 54], target: 29, just two numbers left.\n     |- Try 54 + 5 = 59. Evaluate 59 != 29, drop this branch.\n     |- Try 54 - 5 = 49. Evaluate 49 != 29, drop this branch.\n     |- Try 54 * 5 = 270. Evaluate 270 != 29, drop this branch.\n     |- Try 54 \/ 5 = 10.8. 10.8 is a decimal, drop this branch.\n    |- Try 41 * 36 = 1476. Add 1476 to the number set. Current number set: [1476, 54], target: 29, just two numbers left.\n     |- Try 1476 + 54 = 1530. Evaluate 1530 != 29, drop this branch.\n     |- Try 1476 - 54 = 1422. Evaluate 1422 != 29, drop this branch.\n     |- Try 1476 * 54 = 79704. 79704 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1476 \/ 54 = 27.3. 27.3 is a decimal, drop this branch.\n    |- Try 41 \/ 36 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 31 - 23 = 8. Add 8 to the number set. Current number set: [8, 41, 36], target: 29. Options for choosing two numbers: [(8, 41), (8, 36), (41, 36)].\n   |- Pick two numbers (8, 41) (numbers left: [36]). Try possible operations.\n    |- Try 41 + 8 = 49. Add 49 to the number set. Current number set: [49, 36], target: 29, just two numbers left.\n     |- Try 49 + 36 = 85. Evaluate 85 != 29, drop this branch.\n     |- Try 49 - 36 = 13. Evaluate 13 != 29, drop this branch.\n     |- Try 49 * 36 = 1764. Evaluate 1764 != 29, drop this branch.\n     |- Try 49 \/ 36 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 41 - 8 = 33. Add 33 to the number set. Current number set: [33, 36], target: 29, just two numbers left.\n     |- Try 36 + 33 = 69. Evaluate 69 != 29, drop this branch.\n     |- Try 36 - 33 = 3. Evaluate 3 != 29, drop this branch.\n     |- Try 36 * 33 = 1188. Evaluate 1188 != 29, drop this branch.\n     |- Try 36 \/ 33 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 41 * 8 = 328. Add 328 to the number set. Current number set: [328, 36], target: 29, just two numbers left.\n     |- Try 328 + 36 = 364. Evaluate 364 != 29, drop this branch.\n     |- Try 328 - 36 = 292. Evaluate 292 != 29, drop this branch.\n     |- Try 328 * 36 = 11808. 11808 exceeds the maximum intermediate result, drop this branch.\n     |- Try 328 \/ 36 = 9.1. 9.1 is a decimal, drop this branch.\n    |- Try 41 \/ 8 = 5.1. 5.1 is a decimal, drop this branch.\n   |- Pick two numbers (8, 36) (numbers left: [41]). Try possible operations.\n    |- Try 36 + 8 = 44. Add 44 to the number set. Current number set: [44, 41], target: 29, just two numbers left.\n     |- Try 44 + 41 = 85. Evaluate 85 != 29, drop this branch.\n     |- Try 44 - 41 = 3. Evaluate 3 != 29, drop this branch.\n     |- Try 44 * 41 = 1804. Evaluate 1804 != 29, drop this branch.\n     |- Try 44 \/ 41 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 36 - 8 = 28. Add 28 to the number set. Current number set: [28, 41], target: 29, just two numbers left.\n     |- Try 41 + 28 = 69. Evaluate 69 != 29, drop this branch.\n     |- Try 41 - 28 = 13. Evaluate 13 != 29, drop this branch.\n     |- Try 41 * 28 = 1148. Evaluate 1148 != 29, drop this branch.\n     |- Try 41 \/ 28 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 36 * 8 = 288. Add 288 to the number set. Current number set: [288, 41], target: 29, just two numbers left.\n     |- Try 288 + 41 = 329. Evaluate 329 != 29, drop this branch.\n     |- Try 288 - 41 = 247. Evaluate 247 != 29, drop this branch.\n     |- Try 288 * 41 = 11808. 11808 exceeds the maximum intermediate result, drop this branch.\n     |- Try 288 \/ 41 = 7.0. 7.0 is a decimal, drop this branch.\n    |- Try 36 \/ 8 = 4.5. 4.5 is a decimal, drop this branch.\n   |- Pick two numbers (41, 36) (numbers left: [8]). Try possible operations.\n    |- Try 41 + 36 = 77. Add 77 to the number set. Current number set: [77, 8], target: 29, just two numbers left.\n     |- Try 77 + 8 = 85. Evaluate 85 != 29, drop this branch.\n     |- Try 77 - 8 = 69. Evaluate 69 != 29, drop this branch.\n     |- Try 77 * 8 = 616. Evaluate 616 != 29, drop this branch.\n     |- Try 77 \/ 8 = 9.6. 9.6 is a decimal, drop this branch.\n    |- Try 41 - 36 = 5. Add 5 to the number set. Current number set: [5, 8], target: 29, just two numbers left.\n     |- Try 8 + 5 = 13. Evaluate 13 != 29, drop this branch.\n     |- Try 8 - 5 = 3. Evaluate 3 != 29, drop this branch.\n     |- Try 8 * 5 = 40. Evaluate 40 != 29, drop this branch.\n     |- Try 8 \/ 5 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 41 * 36 = 1476. Add 1476 to the number set. Current number set: [1476, 8], target: 29, just two numbers left.\n     |- Try 1476 + 8 = 1484. Evaluate 1484 != 29, drop this branch.\n     |- Try 1476 - 8 = 1468. Evaluate 1468 != 29, drop this branch.\n     |- Try 1476 * 8 = 11808. 11808 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1476 \/ 8 = 184.5. 184.5 is a decimal, drop this branch.\n    |- Try 41 \/ 36 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 31 * 23 = 713. Add 713 to the number set. Current number set: [713, 41, 36], target: 29. Options for choosing two numbers: [(713, 41), (713, 36), (41, 36)].\n   |- Pick two numbers (713, 41) (numbers left: [36]). Try possible operations.\n    |- Try 713 + 41 = 754. Add 754 to the number set. Current number set: [754, 36], target: 29, just two numbers left.\n     |- Try 754 + 36 = 790. Evaluate 790 != 29, drop this branch.\n     |- Try 754 - 36 = 718. Evaluate 718 != 29, drop this branch.\n     |- Try 754 * 36 = 27144. 27144 exceeds the maximum intermediate result, drop this branch.\n     |- Try 754 \/ 36 = 20.9. 20.9 is a decimal, drop this branch.\n    |- Try 713 - 41 = 672. Add 672 to the number set. Current number set: [672, 36], target: 29, just two numbers left.\n     |- Try 672 + 36 = 708. Evaluate 708 != 29, drop this branch.\n     |- Try 672 - 36 = 636. Evaluate 636 != 29, drop this branch.\n     |- Try 672 * 36 = 24192. 24192 exceeds the maximum intermediate result, drop this branch.\n     |- Try 672 \/ 36 = 18.7. 18.7 is a decimal, drop this branch.\n    |- Try 713 * 41 = 29233. 29233 exceeds the maximum intermediate result, drop this branch.\n    |- Try 713 \/ 41 = 17.4. 17.4 is a decimal, drop this branch.\n   |- Pick two numbers (713, 36) (numbers left: [41]). Try possible operations.\n    |- Try 713 + 36 = 749. Add 749 to the number set. Current number set: [749, 41], target: 29, just two numbers left.\n     |- Try 749 + 41 = 790. Evaluate 790 != 29, drop this branch.\n     |- Try 749 - 41 = 708. Evaluate 708 != 29, drop this branch.\n     |- Try 749 * 41 = 30709. 30709 exceeds the maximum intermediate result, drop this branch.\n     |- Try 749 \/ 41 = 18.3. 18.3 is a decimal, drop this branch.\n    |- Try 713 - 36 = 677. Add 677 to the number set. Current number set: [677, 41], target: 29, just two numbers left.\n     |- Try 677 + 41 = 718. Evaluate 718 != 29, drop this branch.\n     |- Try 677 - 41 = 636. Evaluate 636 != 29, drop this branch.\n     |- Try 677 * 41 = 27757. 27757 exceeds the maximum intermediate result, drop this branch.\n     |- Try 677 \/ 41 = 16.5. 16.5 is a decimal, drop this branch.\n    |- Try 713 * 36 = 25668. 25668 exceeds the maximum intermediate result, drop this branch.\n    |- Try 713 \/ 36 = 19.8. 19.8 is a decimal, drop this branch.\n   |- Pick two numbers (41, 36) (numbers left: [713]). Try possible operations.\n    |- Try 41 + 36 = 77. Add 77 to the number set. Current number set: [77, 713], target: 29, just two numbers left.\n     |- Try 713 + 77 = 790. Evaluate 790 != 29, drop this branch.\n     |- Try 713 - 77 = 636. Evaluate 636 != 29, drop this branch.\n     |- Try 713 * 77 = 54901. 54901 exceeds the maximum intermediate result, drop this branch.\n     |- Try 713 \/ 77 = 9.3. 9.3 is a decimal, drop this branch.\n    |- Try 41 - 36 = 5. Add 5 to the number set. Current number set: [5, 713], target: 29, just two numbers left.\n     |- Try 713 + 5 = 718. Evaluate 718 != 29, drop this branch.\n     |- Try 713 - 5 = 708. Evaluate 708 != 29, drop this branch.\n     |- Try 713 * 5 = 3565. 3565 exceeds the maximum intermediate result, drop this branch.\n     |- Try 713 \/ 5 = 142.6. 142.6 is a decimal, drop this branch.\n    |- Try 41 * 36 = 1476. Add 1476 to the number set. Current number set: [1476, 713], target: 29, just two numbers left.\n     |- Try 1476 + 713 = 2189. 2189 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1476 - 713 = 763. Evaluate 763 != 29, drop this branch.\n     |- Try 1476 * 713 = 1052388. 1052388 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1476 \/ 713 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 41 \/ 36 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 31 \/ 23 = 1.3. 1.3 is a decimal, drop this branch.\n |- Pick two numbers (23, 41) (numbers left: [31, 36]). Try possible operations.\n  |- Try 41 + 23 = 64. Add 64 to the number set. Current number set: [64, 31, 36], target: 29. Options for choosing two numbers: [(64, 31), (64, 36), (31, 36)].\n   |- Pick two numbers (64, 31) (numbers left: [36]). Try possible operations.\n    |- Try 64 + 31 = 95. Add 95 to the number set. Current number set: [95, 36], target: 29, just two numbers left.\n     |- Try 95 + 36 = 131. Evaluate 131 != 29, drop this branch.\n     |- Try 95 - 36 = 59. Evaluate 59 != 29, drop this branch.\n     |- Try 95 * 36 = 3420. 3420 exceeds the maximum intermediate result, drop this branch.\n     |- Try 95 \/ 36 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 64 - 31 = 33. Add 33 to the number set. Current number set: [33, 36], target: 29, just two numbers left.\n     |- Try 36 + 33 = 69. Evaluate 69 != 29, drop this branch.\n     |- Try 36 - 33 = 3. Evaluate 3 != 29, drop this branch.\n     |- Try 36 * 33 = 1188. Evaluate 1188 != 29, drop this branch.\n     |- Try 36 \/ 33 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 64 * 31 = 1984. Add 1984 to the number set. Current number set: [1984, 36], target: 29, just two numbers left.\n     |- Try 1984 + 36 = 2020. 2020 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1984 - 36 = 1948. Evaluate 1948 != 29, drop this branch.\n     |- Try 1984 * 36 = 71424. 71424 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1984 \/ 36 = 55.1. 55.1 is a decimal, drop this branch.\n    |- Try 64 \/ 31 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (64, 36) (numbers left: [31]). Try possible operations.\n    |- Try 64 + 36 = 100. Add 100 to the number set. Current number set: [100, 31], target: 29, just two numbers left.\n     |- Try 100 + 31 = 131. Evaluate 131 != 29, drop this branch.\n     |- Try 100 - 31 = 69. Evaluate 69 != 29, drop this branch.\n     |- Try 100 * 31 = 3100. 3100 exceeds the maximum intermediate result, drop this branch.\n     |- Try 100 \/ 31 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 64 - 36 = 28. Add 28 to the number set. Current number set: [28, 31], target: 29, just two numbers left.\n     |- Try 31 + 28 = 59. Evaluate 59 != 29, drop this branch.\n     |- Try 31 - 28 = 3. Evaluate 3 != 29, drop this branch.\n     |- Try 31 * 28 = 868. Evaluate 868 != 29, drop this branch.\n     |- Try 31 \/ 28 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 64 * 36 = 2304. 2304 exceeds the maximum intermediate result, drop this branch.\n    |- Try 64 \/ 36 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (31, 36) (numbers left: [64]). Try possible operations.\n    |- Try 36 + 31 = 67. Add 67 to the number set. Current number set: [67, 64], target: 29, just two numbers left.\n     |- Try 67 + 64 = 131. Evaluate 131 != 29, drop this branch.\n     |- Try 67 - 64 = 3. Evaluate 3 != 29, drop this branch.\n     |- Try 67 * 64 = 4288. 4288 exceeds the maximum intermediate result, drop this branch.\n     |- Try 67 \/ 64 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 36 - 31 = 5. Add 5 to the number set. Current number set: [5, 64], target: 29, just two numbers left.\n     |- Try 64 + 5 = 69. Evaluate 69 != 29, drop this branch.\n     |- Try 64 - 5 = 59. Evaluate 59 != 29, drop this branch.\n     |- Try 64 * 5 = 320. Evaluate 320 != 29, drop this branch.\n     |- Try 64 \/ 5 = 12.8. 12.8 is a decimal, drop this branch.\n    |- Try 36 * 31 = 1116. Add 1116 to the number set. Current number set: [1116, 64], target: 29, just two numbers left.\n     |- Try 1116 + 64 = 1180. Evaluate 1180 != 29, drop this branch.\n     |- Try 1116 - 64 = 1052. Evaluate 1052 != 29, drop this branch.\n     |- Try 1116 * 64 = 71424. 71424 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1116 \/ 64 = 17.4. 17.4 is a decimal, drop this branch.\n    |- Try 36 \/ 31 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 41 - 23 = 18. Add 18 to the number set. Current number set: [18, 31, 36], target: 29. Options for choosing two numbers: [(18, 31), (18, 36), (31, 36)].\n   |- Pick two numbers (18, 31) (numbers left: [36]). Try possible operations.\n    |- Try 31 + 18 = 49. Add 49 to the number set. Current number set: [49, 36], target: 29, just two numbers left.\n     |- Try 49 + 36 = 85. Evaluate 85 != 29, drop this branch.\n     |- Try 49 - 36 = 13. Evaluate 13 != 29, drop this branch.\n     |- Try 49 * 36 = 1764. Evaluate 1764 != 29, drop this branch.\n     |- Try 49 \/ 36 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 31 - 18 = 13. Add 13 to the number set. Current number set: [13, 36], target: 29, just two numbers left.\n     |- Try 36 + 13 = 49. Evaluate 49 != 29, drop this branch.\n     |- Try 36 - 13 = 23. Evaluate 23 != 29, drop this branch.\n     |- Try 36 * 13 = 468. Evaluate 468 != 29, drop this branch.\n     |- Try 36 \/ 13 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 31 * 18 = 558. Add 558 to the number set. Current number set: [558, 36], target: 29, just two numbers left.\n     |- Try 558 + 36 = 594. Evaluate 594 != 29, drop this branch.\n     |- Try 558 - 36 = 522. Evaluate 522 != 29, drop this branch.\n     |- Try 558 * 36 = 20088. 20088 exceeds the maximum intermediate result, drop this branch.\n     |- Try 558 \/ 36 = 15.5. 15.5 is a decimal, drop this branch.\n    |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (18, 36) (numbers left: [31]). Try possible operations.\n    |- Try 36 + 18 = 54. Add 54 to the number set. Current number set: [54, 31], target: 29, just two numbers left.\n     |- Try 54 + 31 = 85. Evaluate 85 != 29, drop this branch.\n     |- Try 54 - 31 = 23. Evaluate 23 != 29, drop this branch.\n     |- Try 54 * 31 = 1674. Evaluate 1674 != 29, drop this branch.\n     |- Try 54 \/ 31 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 36 - 18 = 18. Add 18 to the number set. Current number set: [18, 31], target: 29, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 29, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 29, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 29, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 36 * 18 = 648. Add 648 to the number set. Current number set: [648, 31], target: 29, just two numbers left.\n     |- Try 648 + 31 = 679. Evaluate 679 != 29, drop this branch.\n     |- Try 648 - 31 = 617. Evaluate 617 != 29, drop this branch.\n     |- Try 648 * 31 = 20088. 20088 exceeds the maximum intermediate result, drop this branch.\n     |- Try 648 \/ 31 = 20.9. 20.9 is a decimal, drop this branch.\n    |- Try 36 \/ 18 = 2. Add 2 to the number set. Current number set: [2, 31], target: 29, just two numbers left.\n     |- Try 31 + 2 = 33. Evaluate 33 != 29, drop this branch.\n     |- Try 31 - 2 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 31 - 2 = 29\nThe step before: 36 \/ 18 = 2\nThe first step: 41 - 23 = 18\n\nOutput the solution in the required format:\n<Solution>\n41 - 23 = 18\n36 \/ 18 = 2\n31 - 2 = 29\n<\/Solution>\n","item":{"nums":[23,31,41,36],"solution":["41 - 23 = 18","36 \/ 18 = 2","31 - 2 = 29"],"target":29}}
+{"instance_id":"countdown_8k_181","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [42, 4, 15, 8]\nTarget: 24","reference_output":"# Search Procedure\nInitial number set: [42, 4, 15, 8], target: 24. Options for choosing two numbers: [(42, 4), (42, 15), (42, 8), (4, 15), (4, 8), (15, 8)].\n |- Pick two numbers (42, 4) (numbers left: [15, 8]). Try possible operations.\n  |- Try 42 + 4 = 46. Add 46 to the number set. Current number set: [46, 15, 8], target: 24. Options for choosing two numbers: [(46, 15), (46, 8), (15, 8)].\n   |- Pick two numbers (46, 15) (numbers left: [8]). Try possible operations.\n    |- Try 46 + 15 = 61. Add 61 to the number set. Current number set: [61, 8], target: 24, just two numbers left.\n     |- Try 61 + 8 = 69. Evaluate 69 != 24, drop this branch.\n     |- Try 61 - 8 = 53. Evaluate 53 != 24, drop this branch.\n     |- Try 61 * 8 = 488. Evaluate 488 != 24, drop this branch.\n     |- Try 61 \/ 8 = 7.6. 7.6 is a decimal, drop this branch.\n    |- Try 46 - 15 = 31. Add 31 to the number set. Current number set: [31, 8], target: 24, just two numbers left.\n     |- Try 31 + 8 = 39. Evaluate 39 != 24, drop this branch.\n     |- Try 31 - 8 = 23. Evaluate 23 != 24, drop this branch.\n     |- Try 31 * 8 = 248. Evaluate 248 != 24, drop this branch.\n     |- Try 31 \/ 8 = 3.9. 3.9 is a decimal, drop this branch.\n    |- Try 46 * 15 = 690. Add 690 to the number set. Current number set: [690, 8], target: 24, just two numbers left.\n     |- Try 690 + 8 = 698. Evaluate 698 != 24, drop this branch.\n     |- Try 690 - 8 = 682. Evaluate 682 != 24, drop this branch.\n     |- Try 690 * 8 = 5520. 5520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 690 \/ 8 = 86.2. 86.2 is a decimal, drop this branch.\n    |- Try 46 \/ 15 = 3.1. 3.1 is a decimal, drop this branch.\n   |- Pick two numbers (46, 8) (numbers left: [15]). Try possible operations.\n    |- Try 46 + 8 = 54. Add 54 to the number set. Current number set: [54, 15], target: 24, just two numbers left.\n     |- Try 54 + 15 = 69. Evaluate 69 != 24, drop this branch.\n     |- Try 54 - 15 = 39. Evaluate 39 != 24, drop this branch.\n     |- Try 54 * 15 = 810. Evaluate 810 != 24, drop this branch.\n     |- Try 54 \/ 15 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 46 - 8 = 38. Add 38 to the number set. Current number set: [38, 15], target: 24, just two numbers left.\n     |- Try 38 + 15 = 53. Evaluate 53 != 24, drop this branch.\n     |- Try 38 - 15 = 23. Evaluate 23 != 24, drop this branch.\n     |- Try 38 * 15 = 570. Evaluate 570 != 24, drop this branch.\n     |- Try 38 \/ 15 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 46 * 8 = 368. Add 368 to the number set. Current number set: [368, 15], target: 24, just two numbers left.\n     |- Try 368 + 15 = 383. Evaluate 383 != 24, drop this branch.\n     |- Try 368 - 15 = 353. Evaluate 353 != 24, drop this branch.\n     |- Try 368 * 15 = 5520. 5520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 368 \/ 15 = 24.5. 24.5 is a decimal, drop this branch.\n    |- Try 46 \/ 8 = 5.8. 5.8 is a decimal, drop this branch.\n   |- Pick two numbers (15, 8) (numbers left: [46]). Try possible operations.\n    |- Try 15 + 8 = 23. Add 23 to the number set. Current number set: [23, 46], target: 24, just two numbers left.\n     |- Try 46 + 23 = 69. Evaluate 69 != 24, drop this branch.\n     |- Try 46 - 23 = 23. Evaluate 23 != 24, drop this branch.\n     |- Try 46 * 23 = 1058. Evaluate 1058 != 24, drop this branch.\n     |- Try 46 \/ 23 = 2. Evaluate 2 != 24, drop this branch.\n    |- Try 15 - 8 = 7. Add 7 to the number set. Current number set: [7, 46], target: 24, just two numbers left.\n     |- Try 46 + 7 = 53. Evaluate 53 != 24, drop this branch.\n     |- Try 46 - 7 = 39. Evaluate 39 != 24, drop this branch.\n     |- Try 46 * 7 = 322. Evaluate 322 != 24, drop this branch.\n     |- Try 46 \/ 7 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 15 * 8 = 120. Add 120 to the number set. Current number set: [120, 46], target: 24, just two numbers left.\n     |- Try 120 + 46 = 166. Evaluate 166 != 24, drop this branch.\n     |- Try 120 - 46 = 74. Evaluate 74 != 24, drop this branch.\n     |- Try 120 * 46 = 5520. 5520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 120 \/ 46 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 15 \/ 8 = 1.9. 1.9 is a decimal, drop this branch.\n  |- Try 42 - 4 = 38. Add 38 to the number set. Current number set: [38, 15, 8], target: 24. Options for choosing two numbers: [(38, 15), (38, 8), (15, 8)].\n   |- Pick two numbers (38, 15) (numbers left: [8]). Try possible operations.\n    |- Try 38 + 15 = 53. Add 53 to the number set. Current number set: [53, 8], target: 24, just two numbers left.\n     |- Try 53 + 8 = 61. Evaluate 61 != 24, drop this branch.\n     |- Try 53 - 8 = 45. Evaluate 45 != 24, drop this branch.\n     |- Try 53 * 8 = 424. Evaluate 424 != 24, drop this branch.\n     |- Try 53 \/ 8 = 6.6. 6.6 is a decimal, drop this branch.\n    |- Try 38 - 15 = 23. Add 23 to the number set. Current number set: [23, 8], target: 24, just two numbers left.\n     |- Try 23 + 8 = 31. Evaluate 31 != 24, drop this branch.\n     |- Try 23 - 8 = 15. Evaluate 15 != 24, drop this branch.\n     |- Try 23 * 8 = 184. Evaluate 184 != 24, drop this branch.\n     |- Try 23 \/ 8 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 38 * 15 = 570. Add 570 to the number set. Current number set: [570, 8], target: 24, just two numbers left.\n     |- Try 570 + 8 = 578. Evaluate 578 != 24, drop this branch.\n     |- Try 570 - 8 = 562. Evaluate 562 != 24, drop this branch.\n     |- Try 570 * 8 = 4560. 4560 exceeds the maximum intermediate result, drop this branch.\n     |- Try 570 \/ 8 = 71.2. 71.2 is a decimal, drop this branch.\n    |- Try 38 \/ 15 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (38, 8) (numbers left: [15]). Try possible operations.\n    |- Try 38 + 8 = 46. Add 46 to the number set. Current number set: [46, 15], target: 24, just two numbers left.\n     |- Try 46 + 15 = 61. Evaluate 61 != 24, drop this branch.\n     |- Try 46 - 15 = 31. Evaluate 31 != 24, drop this branch.\n     |- Try 46 * 15 = 690. Evaluate 690 != 24, drop this branch.\n     |- Try 46 \/ 15 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 38 - 8 = 30. Add 30 to the number set. Current number set: [30, 15], target: 24, just two numbers left.\n     |- Try 30 + 15 = 45. Evaluate 45 != 24, drop this branch.\n     |- Try 30 - 15 = 15. Evaluate 15 != 24, drop this branch.\n     |- Try 30 * 15 = 450. Evaluate 450 != 24, drop this branch.\n     |- Try 30 \/ 15 = 2. Evaluate 2 != 24, drop this branch.\n    |- Try 38 * 8 = 304. Add 304 to the number set. Current number set: [304, 15], target: 24, just two numbers left.\n     |- Try 304 + 15 = 319. Evaluate 319 != 24, drop this branch.\n     |- Try 304 - 15 = 289. Evaluate 289 != 24, drop this branch.\n     |- Try 304 * 15 = 4560. 4560 exceeds the maximum intermediate result, drop this branch.\n     |- Try 304 \/ 15 = 20.3. 20.3 is a decimal, drop this branch.\n    |- Try 38 \/ 8 = 4.8. 4.8 is a decimal, drop this branch.\n   |- Pick two numbers (15, 8) (numbers left: [38]). Try possible operations.\n    |- Try 15 + 8 = 23. Add 23 to the number set. Current number set: [23, 38], target: 24, just two numbers left.\n     |- Try 38 + 23 = 61. Evaluate 61 != 24, drop this branch.\n     |- Try 38 - 23 = 15. Evaluate 15 != 24, drop this branch.\n     |- Try 38 * 23 = 874. Evaluate 874 != 24, drop this branch.\n     |- Try 38 \/ 23 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 15 - 8 = 7. Add 7 to the number set. Current number set: [7, 38], target: 24, just two numbers left.\n     |- Try 38 + 7 = 45. Evaluate 45 != 24, drop this branch.\n     |- Try 38 - 7 = 31. Evaluate 31 != 24, drop this branch.\n     |- Try 38 * 7 = 266. Evaluate 266 != 24, drop this branch.\n     |- Try 38 \/ 7 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 15 * 8 = 120. Add 120 to the number set. Current number set: [120, 38], target: 24, just two numbers left.\n     |- Try 120 + 38 = 158. Evaluate 158 != 24, drop this branch.\n     |- Try 120 - 38 = 82. Evaluate 82 != 24, drop this branch.\n     |- Try 120 * 38 = 4560. 4560 exceeds the maximum intermediate result, drop this branch.\n     |- Try 120 \/ 38 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 15 \/ 8 = 1.9. 1.9 is a decimal, drop this branch.\n  |- Try 42 * 4 = 168. Add 168 to the number set. Current number set: [168, 15, 8], target: 24. Options for choosing two numbers: [(168, 15), (168, 8), (15, 8)].\n   |- Pick two numbers (168, 15) (numbers left: [8]). Try possible operations.\n    |- Try 168 + 15 = 183. Add 183 to the number set. Current number set: [183, 8], target: 24, just two numbers left.\n     |- Try 183 + 8 = 191. Evaluate 191 != 24, drop this branch.\n     |- Try 183 - 8 = 175. Evaluate 175 != 24, drop this branch.\n     |- Try 183 * 8 = 1464. Evaluate 1464 != 24, drop this branch.\n     |- Try 183 \/ 8 = 22.9. 22.9 is a decimal, drop this branch.\n    |- Try 168 - 15 = 153. Add 153 to the number set. Current number set: [153, 8], target: 24, just two numbers left.\n     |- Try 153 + 8 = 161. Evaluate 161 != 24, drop this branch.\n     |- Try 153 - 8 = 145. Evaluate 145 != 24, drop this branch.\n     |- Try 153 * 8 = 1224. Evaluate 1224 != 24, drop this branch.\n     |- Try 153 \/ 8 = 19.1. 19.1 is a decimal, drop this branch.\n    |- Try 168 * 15 = 2520. 2520 exceeds the maximum intermediate result, drop this branch.\n    |- Try 168 \/ 15 = 11.2. 11.2 is a decimal, drop this branch.\n   |- Pick two numbers (168, 8) (numbers left: [15]). Try possible operations.\n    |- Try 168 + 8 = 176. Add 176 to the number set. Current number set: [176, 15], target: 24, just two numbers left.\n     |- Try 176 + 15 = 191. Evaluate 191 != 24, drop this branch.\n     |- Try 176 - 15 = 161. Evaluate 161 != 24, drop this branch.\n     |- Try 176 * 15 = 2640. 2640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 176 \/ 15 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 168 - 8 = 160. Add 160 to the number set. Current number set: [160, 15], target: 24, just two numbers left.\n     |- Try 160 + 15 = 175. Evaluate 175 != 24, drop this branch.\n     |- Try 160 - 15 = 145. Evaluate 145 != 24, drop this branch.\n     |- Try 160 * 15 = 2400. 2400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 160 \/ 15 = 10.7. 10.7 is a decimal, drop this branch.\n    |- Try 168 * 8 = 1344. Add 1344 to the number set. Current number set: [1344, 15], target: 24, just two numbers left.\n     |- Try 1344 + 15 = 1359. Evaluate 1359 != 24, drop this branch.\n     |- Try 1344 - 15 = 1329. Evaluate 1329 != 24, drop this branch.\n     |- Try 1344 * 15 = 20160. 20160 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1344 \/ 15 = 89.6. 89.6 is a decimal, drop this branch.\n    |- Try 168 \/ 8 = 21. Add 21 to the number set. Current number set: [21, 15], target: 24, just two numbers left.\n     |- Try 21 + 15 = 36. Evaluate 36 != 24, drop this branch.\n     |- Try 21 - 15 = 6. Evaluate 6 != 24, drop this branch.\n     |- Try 21 * 15 = 315. Evaluate 315 != 24, drop this branch.\n     |- Try 21 \/ 15 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (15, 8) (numbers left: [168]). Try possible operations.\n    |- Try 15 + 8 = 23. Add 23 to the number set. Current number set: [23, 168], target: 24, just two numbers left.\n     |- Try 168 + 23 = 191. Evaluate 191 != 24, drop this branch.\n     |- Try 168 - 23 = 145. Evaluate 145 != 24, drop this branch.\n     |- Try 168 * 23 = 3864. 3864 exceeds the maximum intermediate result, drop this branch.\n     |- Try 168 \/ 23 = 7.3. 7.3 is a decimal, drop this branch.\n    |- Try 15 - 8 = 7. Add 7 to the number set. Current number set: [7, 168], target: 24, just two numbers left.\n     |- Try 168 + 7 = 175. Evaluate 175 != 24, drop this branch.\n     |- Try 168 - 7 = 161. Evaluate 161 != 24, drop this branch.\n     |- Try 168 * 7 = 1176. Evaluate 1176 != 24, drop this branch.\n     |- Try 168 \/ 7 = 24. Evaluate 24 == 24, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 168 \/ 7 = 24\nThe step before: 15 - 8 = 7\nThe first step: 42 * 4 = 168\n\nOutput the solution in the required format:\n<Solution>\n42 * 4 = 168\n15 - 8 = 7\n168 \/ 7 = 24\n<\/Solution>\n","item":{"nums":[42,4,15,8],"solution":["42 * 4 = 168","15 - 8 = 7","168 \/ 7 = 24"],"target":24}}
+{"instance_id":"countdown_8k_182","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [5, 15, 37, 33]\nTarget: 15","reference_output":"# Search Procedure\nInitial number set: [5, 15, 37, 33], target: 15. Options for choosing two numbers: [(5, 15), (5, 37), (5, 33), (15, 37), (15, 33), (37, 33)].\n |- Pick two numbers (5, 15) (numbers left: [37, 33]). Try possible operations.\n  |- Try 15 + 5 = 20. Add 20 to the number set. Current number set: [20, 37, 33], target: 15. Options for choosing two numbers: [(20, 37), (20, 33), (37, 33)].\n   |- Pick two numbers (20, 37) (numbers left: [33]). Try possible operations.\n    |- Try 37 + 20 = 57. Add 57 to the number set. Current number set: [57, 33], target: 15, just two numbers left.\n     |- Try 57 + 33 = 90. Evaluate 90 != 15, drop this branch.\n     |- Try 57 - 33 = 24. Evaluate 24 != 15, drop this branch.\n     |- Try 57 * 33 = 1881. Evaluate 1881 != 15, drop this branch.\n     |- Try 57 \/ 33 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 37 - 20 = 17. Add 17 to the number set. Current number set: [17, 33], target: 15, just two numbers left.\n     |- Try 33 + 17 = 50. Evaluate 50 != 15, drop this branch.\n     |- Try 33 - 17 = 16. Evaluate 16 != 15, drop this branch.\n     |- Try 33 * 17 = 561. Evaluate 561 != 15, drop this branch.\n     |- Try 33 \/ 17 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 37 * 20 = 740. Add 740 to the number set. Current number set: [740, 33], target: 15, just two numbers left.\n     |- Try 740 + 33 = 773. Evaluate 773 != 15, drop this branch.\n     |- Try 740 - 33 = 707. Evaluate 707 != 15, drop this branch.\n     |- Try 740 * 33 = 24420. 24420 exceeds the maximum intermediate result, drop this branch.\n     |- Try 740 \/ 33 = 22.4. 22.4 is a decimal, drop this branch.\n    |- Try 37 \/ 20 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (20, 33) (numbers left: [37]). Try possible operations.\n    |- Try 33 + 20 = 53. Add 53 to the number set. Current number set: [53, 37], target: 15, just two numbers left.\n     |- Try 53 + 37 = 90. Evaluate 90 != 15, drop this branch.\n     |- Try 53 - 37 = 16. Evaluate 16 != 15, drop this branch.\n     |- Try 53 * 37 = 1961. Evaluate 1961 != 15, drop this branch.\n     |- Try 53 \/ 37 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 33 - 20 = 13. Add 13 to the number set. Current number set: [13, 37], target: 15, just two numbers left.\n     |- Try 37 + 13 = 50. Evaluate 50 != 15, drop this branch.\n     |- Try 37 - 13 = 24. Evaluate 24 != 15, drop this branch.\n     |- Try 37 * 13 = 481. Evaluate 481 != 15, drop this branch.\n     |- Try 37 \/ 13 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 33 * 20 = 660. Add 660 to the number set. Current number set: [660, 37], target: 15, just two numbers left.\n     |- Try 660 + 37 = 697. Evaluate 697 != 15, drop this branch.\n     |- Try 660 - 37 = 623. Evaluate 623 != 15, drop this branch.\n     |- Try 660 * 37 = 24420. 24420 exceeds the maximum intermediate result, drop this branch.\n     |- Try 660 \/ 37 = 17.8. 17.8 is a decimal, drop this branch.\n    |- Try 33 \/ 20 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (37, 33) (numbers left: [20]). Try possible operations.\n    |- Try 37 + 33 = 70. Add 70 to the number set. Current number set: [70, 20], target: 15, just two numbers left.\n     |- Try 70 + 20 = 90. Evaluate 90 != 15, drop this branch.\n     |- Try 70 - 20 = 50. Evaluate 50 != 15, drop this branch.\n     |- Try 70 * 20 = 1400. Evaluate 1400 != 15, drop this branch.\n     |- Try 70 \/ 20 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 37 - 33 = 4. Add 4 to the number set. Current number set: [4, 20], target: 15, just two numbers left.\n     |- Try 20 + 4 = 24. Evaluate 24 != 15, drop this branch.\n     |- Try 20 - 4 = 16. Evaluate 16 != 15, drop this branch.\n     |- Try 20 * 4 = 80. Evaluate 80 != 15, drop this branch.\n     |- Try 20 \/ 4 = 5. Evaluate 5 != 15, drop this branch.\n    |- Try 37 * 33 = 1221. Add 1221 to the number set. Current number set: [1221, 20], target: 15, just two numbers left.\n     |- Try 1221 + 20 = 1241. Evaluate 1241 != 15, drop this branch.\n     |- Try 1221 - 20 = 1201. Evaluate 1201 != 15, drop this branch.\n     |- Try 1221 * 20 = 24420. 24420 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1221 \/ 20 = 61.0. 61.0 is a decimal, drop this branch.\n    |- Try 37 \/ 33 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 15 - 5 = 10. Add 10 to the number set. Current number set: [10, 37, 33], target: 15. Options for choosing two numbers: [(10, 37), (10, 33), (37, 33)].\n   |- Pick two numbers (10, 37) (numbers left: [33]). Try possible operations.\n    |- Try 37 + 10 = 47. Add 47 to the number set. Current number set: [47, 33], target: 15, just two numbers left.\n     |- Try 47 + 33 = 80. Evaluate 80 != 15, drop this branch.\n     |- Try 47 - 33 = 14. Evaluate 14 != 15, drop this branch.\n     |- Try 47 * 33 = 1551. Evaluate 1551 != 15, drop this branch.\n     |- Try 47 \/ 33 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 37 - 10 = 27. Add 27 to the number set. Current number set: [27, 33], target: 15, just two numbers left.\n     |- Try 33 + 27 = 60. Evaluate 60 != 15, drop this branch.\n     |- Try 33 - 27 = 6. Evaluate 6 != 15, drop this branch.\n     |- Try 33 * 27 = 891. Evaluate 891 != 15, drop this branch.\n     |- Try 33 \/ 27 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 37 * 10 = 370. Add 370 to the number set. Current number set: [370, 33], target: 15, just two numbers left.\n     |- Try 370 + 33 = 403. Evaluate 403 != 15, drop this branch.\n     |- Try 370 - 33 = 337. Evaluate 337 != 15, drop this branch.\n     |- Try 370 * 33 = 12210. 12210 exceeds the maximum intermediate result, drop this branch.\n     |- Try 370 \/ 33 = 11.2. 11.2 is a decimal, drop this branch.\n    |- Try 37 \/ 10 = 3.7. 3.7 is a decimal, drop this branch.\n   |- Pick two numbers (10, 33) (numbers left: [37]). Try possible operations.\n    |- Try 33 + 10 = 43. Add 43 to the number set. Current number set: [43, 37], target: 15, just two numbers left.\n     |- Try 43 + 37 = 80. Evaluate 80 != 15, drop this branch.\n     |- Try 43 - 37 = 6. Evaluate 6 != 15, drop this branch.\n     |- Try 43 * 37 = 1591. Evaluate 1591 != 15, drop this branch.\n     |- Try 43 \/ 37 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 33 - 10 = 23. Add 23 to the number set. Current number set: [23, 37], target: 15, just two numbers left.\n     |- Try 37 + 23 = 60. Evaluate 60 != 15, drop this branch.\n     |- Try 37 - 23 = 14. Evaluate 14 != 15, drop this branch.\n     |- Try 37 * 23 = 851. Evaluate 851 != 15, drop this branch.\n     |- Try 37 \/ 23 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 33 * 10 = 330. Add 330 to the number set. Current number set: [330, 37], target: 15, just two numbers left.\n     |- Try 330 + 37 = 367. Evaluate 367 != 15, drop this branch.\n     |- Try 330 - 37 = 293. Evaluate 293 != 15, drop this branch.\n     |- Try 330 * 37 = 12210. 12210 exceeds the maximum intermediate result, drop this branch.\n     |- Try 330 \/ 37 = 8.9. 8.9 is a decimal, drop this branch.\n    |- Try 33 \/ 10 = 3.3. 3.3 is a decimal, drop this branch.\n   |- Pick two numbers (37, 33) (numbers left: [10]). Try possible operations.\n    |- Try 37 + 33 = 70. Add 70 to the number set. Current number set: [70, 10], target: 15, just two numbers left.\n     |- Try 70 + 10 = 80. Evaluate 80 != 15, drop this branch.\n     |- Try 70 - 10 = 60. Evaluate 60 != 15, drop this branch.\n     |- Try 70 * 10 = 700. Evaluate 700 != 15, drop this branch.\n     |- Try 70 \/ 10 = 7. Evaluate 7 != 15, drop this branch.\n    |- Try 37 - 33 = 4. Add 4 to the number set. Current number set: [4, 10], target: 15, just two numbers left.\n     |- Try 10 + 4 = 14. Evaluate 14 != 15, drop this branch.\n     |- Try 10 - 4 = 6. Evaluate 6 != 15, drop this branch.\n     |- Try 10 * 4 = 40. Evaluate 40 != 15, drop this branch.\n     |- Try 10 \/ 4 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 37 * 33 = 1221. Add 1221 to the number set. Current number set: [1221, 10], target: 15, just two numbers left.\n     |- Try 1221 + 10 = 1231. Evaluate 1231 != 15, drop this branch.\n     |- Try 1221 - 10 = 1211. Evaluate 1211 != 15, drop this branch.\n     |- Try 1221 * 10 = 12210. 12210 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1221 \/ 10 = 122.1. 122.1 is a decimal, drop this branch.\n    |- Try 37 \/ 33 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 15 * 5 = 75. Add 75 to the number set. Current number set: [75, 37, 33], target: 15. Options for choosing two numbers: [(75, 37), (75, 33), (37, 33)].\n   |- Pick two numbers (75, 37) (numbers left: [33]). Try possible operations.\n    |- Try 75 + 37 = 112. Add 112 to the number set. Current number set: [112, 33], target: 15, just two numbers left.\n     |- Try 112 + 33 = 145. Evaluate 145 != 15, drop this branch.\n     |- Try 112 - 33 = 79. Evaluate 79 != 15, drop this branch.\n     |- Try 112 * 33 = 3696. 3696 exceeds the maximum intermediate result, drop this branch.\n     |- Try 112 \/ 33 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 75 - 37 = 38. Add 38 to the number set. Current number set: [38, 33], target: 15, just two numbers left.\n     |- Try 38 + 33 = 71. Evaluate 71 != 15, drop this branch.\n     |- Try 38 - 33 = 5. Evaluate 5 != 15, drop this branch.\n     |- Try 38 * 33 = 1254. Evaluate 1254 != 15, drop this branch.\n     |- Try 38 \/ 33 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 75 * 37 = 2775. 2775 exceeds the maximum intermediate result, drop this branch.\n    |- Try 75 \/ 37 = 2.0. 2.0 is a decimal, drop this branch.\n   |- Pick two numbers (75, 33) (numbers left: [37]). Try possible operations.\n    |- Try 75 + 33 = 108. Add 108 to the number set. Current number set: [108, 37], target: 15, just two numbers left.\n     |- Try 108 + 37 = 145. Evaluate 145 != 15, drop this branch.\n     |- Try 108 - 37 = 71. Evaluate 71 != 15, drop this branch.\n     |- Try 108 * 37 = 3996. 3996 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 37 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 75 - 33 = 42. Add 42 to the number set. Current number set: [42, 37], target: 15, just two numbers left.\n     |- Try 42 + 37 = 79. Evaluate 79 != 15, drop this branch.\n     |- Try 42 - 37 = 5. Evaluate 5 != 15, drop this branch.\n     |- Try 42 * 37 = 1554. Evaluate 1554 != 15, drop this branch.\n     |- Try 42 \/ 37 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 75 * 33 = 2475. 2475 exceeds the maximum intermediate result, drop this branch.\n    |- Try 75 \/ 33 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (37, 33) (numbers left: [75]). Try possible operations.\n    |- Try 37 + 33 = 70. Add 70 to the number set. Current number set: [70, 75], target: 15, just two numbers left.\n     |- Try 75 + 70 = 145. Evaluate 145 != 15, drop this branch.\n     |- Try 75 - 70 = 5. Evaluate 5 != 15, drop this branch.\n     |- Try 75 * 70 = 5250. 5250 exceeds the maximum intermediate result, drop this branch.\n     |- Try 75 \/ 70 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 37 - 33 = 4. Add 4 to the number set. Current number set: [4, 75], target: 15, just two numbers left.\n     |- Try 75 + 4 = 79. Evaluate 79 != 15, drop this branch.\n     |- Try 75 - 4 = 71. Evaluate 71 != 15, drop this branch.\n     |- Try 75 * 4 = 300. Evaluate 300 != 15, drop this branch.\n     |- Try 75 \/ 4 = 18.8. 18.8 is a decimal, drop this branch.\n    |- Try 37 * 33 = 1221. Add 1221 to the number set. Current number set: [1221, 75], target: 15, just two numbers left.\n     |- Try 1221 + 75 = 1296. Evaluate 1296 != 15, drop this branch.\n     |- Try 1221 - 75 = 1146. Evaluate 1146 != 15, drop this branch.\n     |- Try 1221 * 75 = 91575. 91575 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1221 \/ 75 = 16.3. 16.3 is a decimal, drop this branch.\n    |- Try 37 \/ 33 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 15 \/ 5 = 3. Add 3 to the number set. Current number set: [3, 37, 33], target: 15. Options for choosing two numbers: [(3, 37), (3, 33), (37, 33)].\n   |- Pick two numbers (3, 37) (numbers left: [33]). Try possible operations.\n    |- Try 37 + 3 = 40. Add 40 to the number set. Current number set: [40, 33], target: 15, just two numbers left.\n     |- Try 40 + 33 = 73. Evaluate 73 != 15, drop this branch.\n     |- Try 40 - 33 = 7. Evaluate 7 != 15, drop this branch.\n     |- Try 40 * 33 = 1320. Evaluate 1320 != 15, drop this branch.\n     |- Try 40 \/ 33 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 37 - 3 = 34. Add 34 to the number set. Current number set: [34, 33], target: 15, just two numbers left.\n     |- Try 34 + 33 = 67. Evaluate 67 != 15, drop this branch.\n     |- Try 34 - 33 = 1. Evaluate 1 != 15, drop this branch.\n     |- Try 34 * 33 = 1122. Evaluate 1122 != 15, drop this branch.\n     |- Try 34 \/ 33 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 37 * 3 = 111. Add 111 to the number set. Current number set: [111, 33], target: 15, just two numbers left.\n     |- Try 111 + 33 = 144. Evaluate 144 != 15, drop this branch.\n     |- Try 111 - 33 = 78. Evaluate 78 != 15, drop this branch.\n     |- Try 111 * 33 = 3663. 3663 exceeds the maximum intermediate result, drop this branch.\n     |- Try 111 \/ 33 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 37 \/ 3 = 12.3. 12.3 is a decimal, drop this branch.\n   |- Pick two numbers (3, 33) (numbers left: [37]). Try possible operations.\n    |- Try 33 + 3 = 36. Add 36 to the number set. Current number set: [36, 37], target: 15, just two numbers left.\n     |- Try 37 + 36 = 73. Evaluate 73 != 15, drop this branch.\n     |- Try 37 - 36 = 1. Evaluate 1 != 15, drop this branch.\n     |- Try 37 * 36 = 1332. Evaluate 1332 != 15, drop this branch.\n     |- Try 37 \/ 36 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 33 - 3 = 30. Add 30 to the number set. Current number set: [30, 37], target: 15, just two numbers left.\n     |- Try 37 + 30 = 67. Evaluate 67 != 15, drop this branch.\n     |- Try 37 - 30 = 7. Evaluate 7 != 15, drop this branch.\n     |- Try 37 * 30 = 1110. Evaluate 1110 != 15, drop this branch.\n     |- Try 37 \/ 30 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 33 * 3 = 99. Add 99 to the number set. Current number set: [99, 37], target: 15, just two numbers left.\n     |- Try 99 + 37 = 136. Evaluate 136 != 15, drop this branch.\n     |- Try 99 - 37 = 62. Evaluate 62 != 15, drop this branch.\n     |- Try 99 * 37 = 3663. 3663 exceeds the maximum intermediate result, drop this branch.\n     |- Try 99 \/ 37 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 33 \/ 3 = 11. Add 11 to the number set. Current number set: [11, 37], target: 15, just two numbers left.\n     |- Try 37 + 11 = 48. Evaluate 48 != 15, drop this branch.\n     |- Try 37 - 11 = 26. Evaluate 26 != 15, drop this branch.\n     |- Try 37 * 11 = 407. Evaluate 407 != 15, drop this branch.\n     |- Try 37 \/ 11 = 3.4. 3.4 is a decimal, drop this branch.\n   |- Pick two numbers (37, 33) (numbers left: [3]). Try possible operations.\n    |- Try 37 + 33 = 70. Add 70 to the number set. Current number set: [70, 3], target: 15, just two numbers left.\n     |- Try 70 + 3 = 73. Evaluate 73 != 15, drop this branch.\n     |- Try 70 - 3 = 67. Evaluate 67 != 15, drop this branch.\n     |- Try 70 * 3 = 210. Evaluate 210 != 15, drop this branch.\n     |- Try 70 \/ 3 = 23.3. 23.3 is a decimal, drop this branch.\n    |- Try 37 - 33 = 4. Add 4 to the number set. Current number set: [4, 3], target: 15, just two numbers left.\n     |- Try 4 + 3 = 7. Evaluate 7 != 15, drop this branch.\n     |- Try 4 - 3 = 1. Evaluate 1 != 15, drop this branch.\n     |- Try 4 * 3 = 12. Evaluate 12 != 15, drop this branch.\n     |- Try 4 \/ 3 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 37 * 33 = 1221. Add 1221 to the number set. Current number set: [1221, 3], target: 15, just two numbers left.\n     |- Try 1221 + 3 = 1224. Evaluate 1224 != 15, drop this branch.\n     |- Try 1221 - 3 = 1218. Evaluate 1218 != 15, drop this branch.\n     |- Try 1221 * 3 = 3663. 3663 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1221 \/ 3 = 407. Evaluate 407 != 15, drop this branch.\n    |- Try 37 \/ 33 = 1.1. 1.1 is a decimal, drop this branch.\n |- Pick two numbers (5, 37) (numbers left: [15, 33]). Try possible operations.\n  |- Try 37 + 5 = 42. Add 42 to the number set. Current number set: [42, 15, 33], target: 15. Options for choosing two numbers: [(42, 15), (42, 33), (15, 33)].\n   |- Pick two numbers (42, 15) (numbers left: [33]). Try possible operations.\n    |- Try 42 + 15 = 57. Add 57 to the number set. Current number set: [57, 33], target: 15, just two numbers left.\n     |- Try 57 + 33 = 90. Evaluate 90 != 15, drop this branch.\n     |- Try 57 - 33 = 24. Evaluate 24 != 15, drop this branch.\n     |- Try 57 * 33 = 1881. Evaluate 1881 != 15, drop this branch.\n     |- Try 57 \/ 33 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 42 - 15 = 27. Add 27 to the number set. Current number set: [27, 33], target: 15, just two numbers left.\n     |- Try 33 + 27 = 60. Evaluate 60 != 15, drop this branch.\n     |- Try 33 - 27 = 6. Evaluate 6 != 15, drop this branch.\n     |- Try 33 * 27 = 891. Evaluate 891 != 15, drop this branch.\n     |- Try 33 \/ 27 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 42 * 15 = 630. Add 630 to the number set. Current number set: [630, 33], target: 15, just two numbers left.\n     |- Try 630 + 33 = 663. Evaluate 663 != 15, drop this branch.\n     |- Try 630 - 33 = 597. Evaluate 597 != 15, drop this branch.\n     |- Try 630 * 33 = 20790. 20790 exceeds the maximum intermediate result, drop this branch.\n     |- Try 630 \/ 33 = 19.1. 19.1 is a decimal, drop this branch.\n    |- Try 42 \/ 15 = 2.8. 2.8 is a decimal, drop this branch.\n   |- Pick two numbers (42, 33) (numbers left: [15]). Try possible operations.\n    |- Try 42 + 33 = 75. Add 75 to the number set. Current number set: [75, 15], target: 15, just two numbers left.\n     |- Try 75 + 15 = 90. Evaluate 90 != 15, drop this branch.\n     |- Try 75 - 15 = 60. Evaluate 60 != 15, drop this branch.\n     |- Try 75 * 15 = 1125. Evaluate 1125 != 15, drop this branch.\n     |- Try 75 \/ 15 = 5. Evaluate 5 != 15, drop this branch.\n    |- Try 42 - 33 = 9. Add 9 to the number set. Current number set: [9, 15], target: 15, just two numbers left.\n     |- Try 15 + 9 = 24. Evaluate 24 != 15, drop this branch.\n     |- Try 15 - 9 = 6. Evaluate 6 != 15, drop this branch.\n     |- Try 15 * 9 = 135. Evaluate 135 != 15, drop this branch.\n     |- Try 15 \/ 9 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 42 * 33 = 1386. Add 1386 to the number set. Current number set: [1386, 15], target: 15, just two numbers left.\n     |- Try 1386 + 15 = 1401. Evaluate 1401 != 15, drop this branch.\n     |- Try 1386 - 15 = 1371. Evaluate 1371 != 15, drop this branch.\n     |- Try 1386 * 15 = 20790. 20790 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1386 \/ 15 = 92.4. 92.4 is a decimal, drop this branch.\n    |- Try 42 \/ 33 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (15, 33) (numbers left: [42]). Try possible operations.\n    |- Try 33 + 15 = 48. Add 48 to the number set. Current number set: [48, 42], target: 15, just two numbers left.\n     |- Try 48 + 42 = 90. Evaluate 90 != 15, drop this branch.\n     |- Try 48 - 42 = 6. Evaluate 6 != 15, drop this branch.\n     |- Try 48 * 42 = 2016. 2016 exceeds the maximum intermediate result, drop this branch.\n     |- Try 48 \/ 42 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 33 - 15 = 18. Add 18 to the number set. Current number set: [18, 42], target: 15, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 15, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 15, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 15, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 33 * 15 = 495. Add 495 to the number set. Current number set: [495, 42], target: 15, just two numbers left.\n     |- Try 495 + 42 = 537. Evaluate 537 != 15, drop this branch.\n     |- Try 495 - 42 = 453. Evaluate 453 != 15, drop this branch.\n     |- Try 495 * 42 = 20790. 20790 exceeds the maximum intermediate result, drop this branch.\n     |- Try 495 \/ 42 = 11.8. 11.8 is a decimal, drop this branch.\n    |- Try 33 \/ 15 = 2.2. 2.2 is a decimal, drop this branch.\n  |- Try 37 - 5 = 32. Add 32 to the number set. Current number set: [32, 15, 33], target: 15. Options for choosing two numbers: [(32, 15), (32, 33), (15, 33)].\n   |- Pick two numbers (32, 15) (numbers left: [33]). Try possible operations.\n    |- Try 32 + 15 = 47. Add 47 to the number set. Current number set: [47, 33], target: 15, just two numbers left.\n     |- Try 47 + 33 = 80. Evaluate 80 != 15, drop this branch.\n     |- Try 47 - 33 = 14. Evaluate 14 != 15, drop this branch.\n     |- Try 47 * 33 = 1551. Evaluate 1551 != 15, drop this branch.\n     |- Try 47 \/ 33 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 32 - 15 = 17. Add 17 to the number set. Current number set: [17, 33], target: 15, just two numbers left.\n     |- Try 33 + 17 = 50. Evaluate 50 != 15, drop this branch.\n     |- Try 33 - 17 = 16. Evaluate 16 != 15, drop this branch.\n     |- Try 33 * 17 = 561. Evaluate 561 != 15, drop this branch.\n     |- Try 33 \/ 17 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 32 * 15 = 480. Add 480 to the number set. Current number set: [480, 33], target: 15, just two numbers left.\n     |- Try 480 + 33 = 513. Evaluate 513 != 15, drop this branch.\n     |- Try 480 - 33 = 447. Evaluate 447 != 15, drop this branch.\n     |- Try 480 * 33 = 15840. 15840 exceeds the maximum intermediate result, drop this branch.\n     |- Try 480 \/ 33 = 14.5. 14.5 is a decimal, drop this branch.\n    |- Try 32 \/ 15 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (32, 33) (numbers left: [15]). Try possible operations.\n    |- Try 33 + 32 = 65. Add 65 to the number set. Current number set: [65, 15], target: 15, just two numbers left.\n     |- Try 65 + 15 = 80. Evaluate 80 != 15, drop this branch.\n     |- Try 65 - 15 = 50. Evaluate 50 != 15, drop this branch.\n     |- Try 65 * 15 = 975. Evaluate 975 != 15, drop this branch.\n     |- Try 65 \/ 15 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 33 - 32 = 1. Add 1 to the number set. Current number set: [1, 15], target: 15, just two numbers left.\n     |- Try 15 + 1 = 16. Evaluate 16 != 15, drop this branch.\n     |- Try 15 - 1 = 14. Evaluate 14 != 15, drop this branch.\n     |- Try 15 * 1 = 15. Evaluate 15 == 15, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 15 * 1 = 15\nThe step before: 33 - 32 = 1\nThe first step: 37 - 5 = 32\n\nOutput the solution in the required format:\n<Solution>\n37 - 5 = 32\n33 - 32 = 1\n15 * 1 = 15\n<\/Solution>\n","item":{"nums":[5,15,37,33],"solution":["37 - 5 = 32","33 - 32 = 1","15 * 1 = 15"],"target":15}}
+{"instance_id":"countdown_8k_183","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [7, 47, 3, 5]\nTarget: 49","reference_output":"# Search Procedure\nInitial number set: [7, 47, 3, 5], target: 49. Options for choosing two numbers: [(7, 47), (7, 3), (7, 5), (47, 3), (47, 5), (3, 5)].\n |- Pick two numbers (7, 47) (numbers left: [3, 5]). Try possible operations.\n  |- Try 47 + 7 = 54. Add 54 to the number set. Current number set: [54, 3, 5], target: 49. Options for choosing two numbers: [(54, 3), (54, 5), (3, 5)].\n   |- Pick two numbers (54, 3) (numbers left: [5]). Try possible operations.\n    |- Try 54 + 3 = 57. Add 57 to the number set. Current number set: [57, 5], target: 49, just two numbers left.\n     |- Try 57 + 5 = 62. Evaluate 62 != 49, drop this branch.\n     |- Try 57 - 5 = 52. Evaluate 52 != 49, drop this branch.\n     |- Try 57 * 5 = 285. Evaluate 285 != 49, drop this branch.\n     |- Try 57 \/ 5 = 11.4. 11.4 is a decimal, drop this branch.\n    |- Try 54 - 3 = 51. Add 51 to the number set. Current number set: [51, 5], target: 49, just two numbers left.\n     |- Try 51 + 5 = 56. Evaluate 56 != 49, drop this branch.\n     |- Try 51 - 5 = 46. Evaluate 46 != 49, drop this branch.\n     |- Try 51 * 5 = 255. Evaluate 255 != 49, drop this branch.\n     |- Try 51 \/ 5 = 10.2. 10.2 is a decimal, drop this branch.\n    |- Try 54 * 3 = 162. Add 162 to the number set. Current number set: [162, 5], target: 49, just two numbers left.\n     |- Try 162 + 5 = 167. Evaluate 167 != 49, drop this branch.\n     |- Try 162 - 5 = 157. Evaluate 157 != 49, drop this branch.\n     |- Try 162 * 5 = 810. Evaluate 810 != 49, drop this branch.\n     |- Try 162 \/ 5 = 32.4. 32.4 is a decimal, drop this branch.\n    |- Try 54 \/ 3 = 18. Add 18 to the number set. Current number set: [18, 5], target: 49, just two numbers left.\n     |- Try 18 + 5 = 23. Evaluate 23 != 49, drop this branch.\n     |- Try 18 - 5 = 13. Evaluate 13 != 49, drop this branch.\n     |- Try 18 * 5 = 90. Evaluate 90 != 49, drop this branch.\n     |- Try 18 \/ 5 = 3.6. 3.6 is a decimal, drop this branch.\n   |- Pick two numbers (54, 5) (numbers left: [3]). Try possible operations.\n    |- Try 54 + 5 = 59. Add 59 to the number set. Current number set: [59, 3], target: 49, just two numbers left.\n     |- Try 59 + 3 = 62. Evaluate 62 != 49, drop this branch.\n     |- Try 59 - 3 = 56. Evaluate 56 != 49, drop this branch.\n     |- Try 59 * 3 = 177. Evaluate 177 != 49, drop this branch.\n     |- Try 59 \/ 3 = 19.7. 19.7 is a decimal, drop this branch.\n    |- Try 54 - 5 = 49. Add 49 to the number set. Current number set: [49, 3], target: 49, just two numbers left.\n     |- Try 49 + 3 = 52. Evaluate 52 != 49, drop this branch.\n     |- Try 49 - 3 = 46. Evaluate 46 != 49, drop this branch.\n     |- Try 49 * 3 = 147. Evaluate 147 != 49, drop this branch.\n     |- Try 49 \/ 3 = 16.3. 16.3 is a decimal, drop this branch.\n    |- Try 54 * 5 = 270. Add 270 to the number set. Current number set: [270, 3], target: 49, just two numbers left.\n     |- Try 270 + 3 = 273. Evaluate 273 != 49, drop this branch.\n     |- Try 270 - 3 = 267. Evaluate 267 != 49, drop this branch.\n     |- Try 270 * 3 = 810. Evaluate 810 != 49, drop this branch.\n     |- Try 270 \/ 3 = 90. Evaluate 90 != 49, drop this branch.\n    |- Try 54 \/ 5 = 10.8. 10.8 is a decimal, drop this branch.\n   |- Pick two numbers (3, 5) (numbers left: [54]). Try possible operations.\n    |- Try 5 + 3 = 8. Add 8 to the number set. Current number set: [8, 54], target: 49, just two numbers left.\n     |- Try 54 + 8 = 62. Evaluate 62 != 49, drop this branch.\n     |- Try 54 - 8 = 46. Evaluate 46 != 49, drop this branch.\n     |- Try 54 * 8 = 432. Evaluate 432 != 49, drop this branch.\n     |- Try 54 \/ 8 = 6.8. 6.8 is a decimal, drop this branch.\n    |- Try 5 - 3 = 2. Add 2 to the number set. Current number set: [2, 54], target: 49, just two numbers left.\n     |- Try 54 + 2 = 56. Evaluate 56 != 49, drop this branch.\n     |- Try 54 - 2 = 52. Evaluate 52 != 49, drop this branch.\n     |- Try 54 * 2 = 108. Evaluate 108 != 49, drop this branch.\n     |- Try 54 \/ 2 = 27. Evaluate 27 != 49, drop this branch.\n    |- Try 5 * 3 = 15. Add 15 to the number set. Current number set: [15, 54], target: 49, just two numbers left.\n     |- Try 54 + 15 = 69. Evaluate 69 != 49, drop this branch.\n     |- Try 54 - 15 = 39. Evaluate 39 != 49, drop this branch.\n     |- Try 54 * 15 = 810. Evaluate 810 != 49, drop this branch.\n     |- Try 54 \/ 15 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 5 \/ 3 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 47 - 7 = 40. Add 40 to the number set. Current number set: [40, 3, 5], target: 49. Options for choosing two numbers: [(40, 3), (40, 5), (3, 5)].\n   |- Pick two numbers (40, 3) (numbers left: [5]). Try possible operations.\n    |- Try 40 + 3 = 43. Add 43 to the number set. Current number set: [43, 5], target: 49, just two numbers left.\n     |- Try 43 + 5 = 48. Evaluate 48 != 49, drop this branch.\n     |- Try 43 - 5 = 38. Evaluate 38 != 49, drop this branch.\n     |- Try 43 * 5 = 215. Evaluate 215 != 49, drop this branch.\n     |- Try 43 \/ 5 = 8.6. 8.6 is a decimal, drop this branch.\n    |- Try 40 - 3 = 37. Add 37 to the number set. Current number set: [37, 5], target: 49, just two numbers left.\n     |- Try 37 + 5 = 42. Evaluate 42 != 49, drop this branch.\n     |- Try 37 - 5 = 32. Evaluate 32 != 49, drop this branch.\n     |- Try 37 * 5 = 185. Evaluate 185 != 49, drop this branch.\n     |- Try 37 \/ 5 = 7.4. 7.4 is a decimal, drop this branch.\n    |- Try 40 * 3 = 120. Add 120 to the number set. Current number set: [120, 5], target: 49, just two numbers left.\n     |- Try 120 + 5 = 125. Evaluate 125 != 49, drop this branch.\n     |- Try 120 - 5 = 115. Evaluate 115 != 49, drop this branch.\n     |- Try 120 * 5 = 600. Evaluate 600 != 49, drop this branch.\n     |- Try 120 \/ 5 = 24. Evaluate 24 != 49, drop this branch.\n    |- Try 40 \/ 3 = 13.3. 13.3 is a decimal, drop this branch.\n   |- Pick two numbers (40, 5) (numbers left: [3]). Try possible operations.\n    |- Try 40 + 5 = 45. Add 45 to the number set. Current number set: [45, 3], target: 49, just two numbers left.\n     |- Try 45 + 3 = 48. Evaluate 48 != 49, drop this branch.\n     |- Try 45 - 3 = 42. Evaluate 42 != 49, drop this branch.\n     |- Try 45 * 3 = 135. Evaluate 135 != 49, drop this branch.\n     |- Try 45 \/ 3 = 15. Evaluate 15 != 49, drop this branch.\n    |- Try 40 - 5 = 35. Add 35 to the number set. Current number set: [35, 3], target: 49, just two numbers left.\n     |- Try 35 + 3 = 38. Evaluate 38 != 49, drop this branch.\n     |- Try 35 - 3 = 32. Evaluate 32 != 49, drop this branch.\n     |- Try 35 * 3 = 105. Evaluate 105 != 49, drop this branch.\n     |- Try 35 \/ 3 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 40 * 5 = 200. Add 200 to the number set. Current number set: [200, 3], target: 49, just two numbers left.\n     |- Try 200 + 3 = 203. Evaluate 203 != 49, drop this branch.\n     |- Try 200 - 3 = 197. Evaluate 197 != 49, drop this branch.\n     |- Try 200 * 3 = 600. Evaluate 600 != 49, drop this branch.\n     |- Try 200 \/ 3 = 66.7. 66.7 is a decimal, drop this branch.\n    |- Try 40 \/ 5 = 8. Add 8 to the number set. Current number set: [8, 3], target: 49, just two numbers left.\n     |- Try 8 + 3 = 11. Evaluate 11 != 49, drop this branch.\n     |- Try 8 - 3 = 5. Evaluate 5 != 49, drop this branch.\n     |- Try 8 * 3 = 24. Evaluate 24 != 49, drop this branch.\n     |- Try 8 \/ 3 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (3, 5) (numbers left: [40]). Try possible operations.\n    |- Try 5 + 3 = 8. Add 8 to the number set. Current number set: [8, 40], target: 49, just two numbers left.\n     |- Try 40 + 8 = 48. Evaluate 48 != 49, drop this branch.\n     |- Try 40 - 8 = 32. Evaluate 32 != 49, drop this branch.\n     |- Try 40 * 8 = 320. Evaluate 320 != 49, drop this branch.\n     |- Try 40 \/ 8 = 5. Evaluate 5 != 49, drop this branch.\n    |- Try 5 - 3 = 2. Add 2 to the number set. Current number set: [2, 40], target: 49, just two numbers left.\n     |- Try 40 + 2 = 42. Evaluate 42 != 49, drop this branch.\n     |- Try 40 - 2 = 38. Evaluate 38 != 49, drop this branch.\n     |- Try 40 * 2 = 80. Evaluate 80 != 49, drop this branch.\n     |- Try 40 \/ 2 = 20. Evaluate 20 != 49, drop this branch.\n    |- Try 5 * 3 = 15. Add 15 to the number set. Current number set: [15, 40], target: 49, just two numbers left.\n     |- Try 40 + 15 = 55. Evaluate 55 != 49, drop this branch.\n     |- Try 40 - 15 = 25. Evaluate 25 != 49, drop this branch.\n     |- Try 40 * 15 = 600. Evaluate 600 != 49, drop this branch.\n     |- Try 40 \/ 15 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 5 \/ 3 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 47 * 7 = 329. Add 329 to the number set. Current number set: [329, 3, 5], target: 49. Options for choosing two numbers: [(329, 3), (329, 5), (3, 5)].\n   |- Pick two numbers (329, 3) (numbers left: [5]). Try possible operations.\n    |- Try 329 + 3 = 332. Add 332 to the number set. Current number set: [332, 5], target: 49, just two numbers left.\n     |- Try 332 + 5 = 337. Evaluate 337 != 49, drop this branch.\n     |- Try 332 - 5 = 327. Evaluate 327 != 49, drop this branch.\n     |- Try 332 * 5 = 1660. Evaluate 1660 != 49, drop this branch.\n     |- Try 332 \/ 5 = 66.4. 66.4 is a decimal, drop this branch.\n    |- Try 329 - 3 = 326. Add 326 to the number set. Current number set: [326, 5], target: 49, just two numbers left.\n     |- Try 326 + 5 = 331. Evaluate 331 != 49, drop this branch.\n     |- Try 326 - 5 = 321. Evaluate 321 != 49, drop this branch.\n     |- Try 326 * 5 = 1630. Evaluate 1630 != 49, drop this branch.\n     |- Try 326 \/ 5 = 65.2. 65.2 is a decimal, drop this branch.\n    |- Try 329 * 3 = 987. Add 987 to the number set. Current number set: [987, 5], target: 49, just two numbers left.\n     |- Try 987 + 5 = 992. Evaluate 992 != 49, drop this branch.\n     |- Try 987 - 5 = 982. Evaluate 982 != 49, drop this branch.\n     |- Try 987 * 5 = 4935. 4935 exceeds the maximum intermediate result, drop this branch.\n     |- Try 987 \/ 5 = 197.4. 197.4 is a decimal, drop this branch.\n    |- Try 329 \/ 3 = 109.7. 109.7 is a decimal, drop this branch.\n   |- Pick two numbers (329, 5) (numbers left: [3]). Try possible operations.\n    |- Try 329 + 5 = 334. Add 334 to the number set. Current number set: [334, 3], target: 49, just two numbers left.\n     |- Try 334 + 3 = 337. Evaluate 337 != 49, drop this branch.\n     |- Try 334 - 3 = 331. Evaluate 331 != 49, drop this branch.\n     |- Try 334 * 3 = 1002. Evaluate 1002 != 49, drop this branch.\n     |- Try 334 \/ 3 = 111.3. 111.3 is a decimal, drop this branch.\n    |- Try 329 - 5 = 324. Add 324 to the number set. Current number set: [324, 3], target: 49, just two numbers left.\n     |- Try 324 + 3 = 327. Evaluate 327 != 49, drop this branch.\n     |- Try 324 - 3 = 321. Evaluate 321 != 49, drop this branch.\n     |- Try 324 * 3 = 972. Evaluate 972 != 49, drop this branch.\n     |- Try 324 \/ 3 = 108. Evaluate 108 != 49, drop this branch.\n    |- Try 329 * 5 = 1645. Add 1645 to the number set. Current number set: [1645, 3], target: 49, just two numbers left.\n     |- Try 1645 + 3 = 1648. Evaluate 1648 != 49, drop this branch.\n     |- Try 1645 - 3 = 1642. Evaluate 1642 != 49, drop this branch.\n     |- Try 1645 * 3 = 4935. 4935 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1645 \/ 3 = 548.3. 548.3 is a decimal, drop this branch.\n    |- Try 329 \/ 5 = 65.8. 65.8 is a decimal, drop this branch.\n   |- Pick two numbers (3, 5) (numbers left: [329]). Try possible operations.\n    |- Try 5 + 3 = 8. Add 8 to the number set. Current number set: [8, 329], target: 49, just two numbers left.\n     |- Try 329 + 8 = 337. Evaluate 337 != 49, drop this branch.\n     |- Try 329 - 8 = 321. Evaluate 321 != 49, drop this branch.\n     |- Try 329 * 8 = 2632. 2632 exceeds the maximum intermediate result, drop this branch.\n     |- Try 329 \/ 8 = 41.1. 41.1 is a decimal, drop this branch.\n    |- Try 5 - 3 = 2. Add 2 to the number set. Current number set: [2, 329], target: 49, just two numbers left.\n     |- Try 329 + 2 = 331. Evaluate 331 != 49, drop this branch.\n     |- Try 329 - 2 = 327. Evaluate 327 != 49, drop this branch.\n     |- Try 329 * 2 = 658. Evaluate 658 != 49, drop this branch.\n     |- Try 329 \/ 2 = 164.5. 164.5 is a decimal, drop this branch.\n    |- Try 5 * 3 = 15. Add 15 to the number set. Current number set: [15, 329], target: 49, just two numbers left.\n     |- Try 329 + 15 = 344. Evaluate 344 != 49, drop this branch.\n     |- Try 329 - 15 = 314. Evaluate 314 != 49, drop this branch.\n     |- Try 329 * 15 = 4935. 4935 exceeds the maximum intermediate result, drop this branch.\n     |- Try 329 \/ 15 = 21.9. 21.9 is a decimal, drop this branch.\n    |- Try 5 \/ 3 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 47 \/ 7 = 6.7. 6.7 is a decimal, drop this branch.\n |- Pick two numbers (7, 3) (numbers left: [47, 5]). Try possible operations.\n  |- Try 7 + 3 = 10. Add 10 to the number set. Current number set: [10, 47, 5], target: 49. Options for choosing two numbers: [(10, 47), (10, 5), (47, 5)].\n   |- Pick two numbers (10, 47) (numbers left: [5]). Try possible operations.\n    |- Try 47 + 10 = 57. Add 57 to the number set. Current number set: [57, 5], target: 49, just two numbers left.\n     |- Try 57 + 5 = 62. Evaluate 62 != 49, drop this branch.\n     |- Try 57 - 5 = 52. Evaluate 52 != 49, drop this branch.\n     |- Try 57 * 5 = 285. Evaluate 285 != 49, drop this branch.\n     |- Try 57 \/ 5 = 11.4. 11.4 is a decimal, drop this branch.\n    |- Try 47 - 10 = 37. Add 37 to the number set. Current number set: [37, 5], target: 49, just two numbers left.\n     |- Try 37 + 5 = 42. Evaluate 42 != 49, drop this branch.\n     |- Try 37 - 5 = 32. Evaluate 32 != 49, drop this branch.\n     |- Try 37 * 5 = 185. Evaluate 185 != 49, drop this branch.\n     |- Try 37 \/ 5 = 7.4. 7.4 is a decimal, drop this branch.\n    |- Try 47 * 10 = 470. Add 470 to the number set. Current number set: [470, 5], target: 49, just two numbers left.\n     |- Try 470 + 5 = 475. Evaluate 475 != 49, drop this branch.\n     |- Try 470 - 5 = 465. Evaluate 465 != 49, drop this branch.\n     |- Try 470 * 5 = 2350. 2350 exceeds the maximum intermediate result, drop this branch.\n     |- Try 470 \/ 5 = 94. Evaluate 94 != 49, drop this branch.\n    |- Try 47 \/ 10 = 4.7. 4.7 is a decimal, drop this branch.\n   |- Pick two numbers (10, 5) (numbers left: [47]). Try possible operations.\n    |- Try 10 + 5 = 15. Add 15 to the number set. Current number set: [15, 47], target: 49, just two numbers left.\n     |- Try 47 + 15 = 62. Evaluate 62 != 49, drop this branch.\n     |- Try 47 - 15 = 32. Evaluate 32 != 49, drop this branch.\n     |- Try 47 * 15 = 705. Evaluate 705 != 49, drop this branch.\n     |- Try 47 \/ 15 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 10 - 5 = 5. Add 5 to the number set. Current number set: [5, 47], target: 49, just two numbers left.\n     |- Try 47 + 5 = 52. Evaluate 52 != 49, drop this branch.\n     |- Try 47 - 5 = 42. Evaluate 42 != 49, drop this branch.\n     |- Try 47 * 5 = 235. Evaluate 235 != 49, drop this branch.\n     |- Try 47 \/ 5 = 9.4. 9.4 is a decimal, drop this branch.\n    |- Try 10 * 5 = 50. Add 50 to the number set. Current number set: [50, 47], target: 49, just two numbers left.\n     |- Try 50 + 47 = 97. Evaluate 97 != 49, drop this branch.\n     |- Try 50 - 47 = 3. Evaluate 3 != 49, drop this branch.\n     |- Try 50 * 47 = 2350. 2350 exceeds the maximum intermediate result, drop this branch.\n     |- Try 50 \/ 47 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 10 \/ 5 = 2. Add 2 to the number set. Current number set: [2, 47], target: 49, just two numbers left.\n     |- Try 47 + 2 = 49. Evaluate 49 == 49, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 47 + 2 = 49\nThe step before: 10 \/ 5 = 2\nThe first step: 7 + 3 = 10\n\nOutput the solution in the required format:\n<Solution>\n7 + 3 = 10\n10 \/ 5 = 2\n47 + 2 = 49\n<\/Solution>\n","item":{"nums":[7,47,3,5],"solution":["7 + 3 = 10","10 \/ 5 = 2","47 + 2 = 49"],"target":49}}
+{"instance_id":"countdown_8k_184","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [6, 10, 1, 38]\nTarget: 32","reference_output":"# Search Procedure\nInitial number set: [6, 10, 1, 38], target: 32. Options for choosing two numbers: [(6, 10), (6, 1), (6, 38), (10, 1), (10, 38), (1, 38)].\n |- Pick two numbers (6, 10) (numbers left: [1, 38]). Try possible operations.\n  |- Try 10 + 6 = 16. Add 16 to the number set. Current number set: [16, 1, 38], target: 32. Options for choosing two numbers: [(16, 1), (16, 38), (1, 38)].\n   |- Pick two numbers (16, 1) (numbers left: [38]). Try possible operations.\n    |- Try 16 + 1 = 17. Add 17 to the number set. Current number set: [17, 38], target: 32, just two numbers left.\n     |- Try 38 + 17 = 55. Evaluate 55 != 32, drop this branch.\n     |- Try 38 - 17 = 21. Evaluate 21 != 32, drop this branch.\n     |- Try 38 * 17 = 646. Evaluate 646 != 32, drop this branch.\n     |- Try 38 \/ 17 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 16 - 1 = 15. Add 15 to the number set. Current number set: [15, 38], target: 32, just two numbers left.\n     |- Try 38 + 15 = 53. Evaluate 53 != 32, drop this branch.\n     |- Try 38 - 15 = 23. Evaluate 23 != 32, drop this branch.\n     |- Try 38 * 15 = 570. Evaluate 570 != 32, drop this branch.\n     |- Try 38 \/ 15 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 16 * 1 = 16. Add 16 to the number set. Current number set: [16, 38], target: 32, just two numbers left.\n     |- Try 38 + 16 = 54. Evaluate 54 != 32, drop this branch.\n     |- Try 38 - 16 = 22. Evaluate 22 != 32, drop this branch.\n     |- Try 38 * 16 = 608. Evaluate 608 != 32, drop this branch.\n     |- Try 38 \/ 16 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 16 \/ 1 = 16. Add 16 to the number set. Current number set: [16, 38], target: 32, just two numbers left.\n     |- Try 38 + 16 = 54. Evaluate 54 != 32, drop this branch.\n     |- Try 38 - 16 = 22. Evaluate 22 != 32, drop this branch.\n     |- Try 38 * 16 = 608. Evaluate 608 != 32, drop this branch.\n     |- Try 38 \/ 16 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (16, 38) (numbers left: [1]). Try possible operations.\n    |- Try 38 + 16 = 54. Add 54 to the number set. Current number set: [54, 1], target: 32, just two numbers left.\n     |- Try 54 + 1 = 55. Evaluate 55 != 32, drop this branch.\n     |- Try 54 - 1 = 53. Evaluate 53 != 32, drop this branch.\n     |- Try 54 * 1 = 54. Evaluate 54 != 32, drop this branch.\n     |- Try 54 \/ 1 = 54. Evaluate 54 != 32, drop this branch.\n    |- Try 38 - 16 = 22. Add 22 to the number set. Current number set: [22, 1], target: 32, just two numbers left.\n     |- Try 22 + 1 = 23. Evaluate 23 != 32, drop this branch.\n     |- Try 22 - 1 = 21. Evaluate 21 != 32, drop this branch.\n     |- Try 22 * 1 = 22. Evaluate 22 != 32, drop this branch.\n     |- Try 22 \/ 1 = 22. Evaluate 22 != 32, drop this branch.\n    |- Try 38 * 16 = 608. Add 608 to the number set. Current number set: [608, 1], target: 32, just two numbers left.\n     |- Try 608 + 1 = 609. Evaluate 609 != 32, drop this branch.\n     |- Try 608 - 1 = 607. Evaluate 607 != 32, drop this branch.\n     |- Try 608 * 1 = 608. Evaluate 608 != 32, drop this branch.\n     |- Try 608 \/ 1 = 608. Evaluate 608 != 32, drop this branch.\n    |- Try 38 \/ 16 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (1, 38) (numbers left: [16]). Try possible operations.\n    |- Try 38 + 1 = 39. Add 39 to the number set. Current number set: [39, 16], target: 32, just two numbers left.\n     |- Try 39 + 16 = 55. Evaluate 55 != 32, drop this branch.\n     |- Try 39 - 16 = 23. Evaluate 23 != 32, drop this branch.\n     |- Try 39 * 16 = 624. Evaluate 624 != 32, drop this branch.\n     |- Try 39 \/ 16 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 38 - 1 = 37. Add 37 to the number set. Current number set: [37, 16], target: 32, just two numbers left.\n     |- Try 37 + 16 = 53. Evaluate 53 != 32, drop this branch.\n     |- Try 37 - 16 = 21. Evaluate 21 != 32, drop this branch.\n     |- Try 37 * 16 = 592. Evaluate 592 != 32, drop this branch.\n     |- Try 37 \/ 16 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 38 * 1 = 38. Add 38 to the number set. Current number set: [38, 16], target: 32, just two numbers left.\n     |- Try 38 + 16 = 54. Evaluate 54 != 32, drop this branch.\n     |- Try 38 - 16 = 22. Evaluate 22 != 32, drop this branch.\n     |- Try 38 * 16 = 608. Evaluate 608 != 32, drop this branch.\n     |- Try 38 \/ 16 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 38 \/ 1 = 38. Add 38 to the number set. Current number set: [38, 16], target: 32, just two numbers left.\n     |- Try 38 + 16 = 54. Evaluate 54 != 32, drop this branch.\n     |- Try 38 - 16 = 22. Evaluate 22 != 32, drop this branch.\n     |- Try 38 * 16 = 608. Evaluate 608 != 32, drop this branch.\n     |- Try 38 \/ 16 = 2.4. 2.4 is a decimal, drop this branch.\n  |- Try 10 - 6 = 4. Add 4 to the number set. Current number set: [4, 1, 38], target: 32. Options for choosing two numbers: [(4, 1), (4, 38), (1, 38)].\n   |- Pick two numbers (4, 1) (numbers left: [38]). Try possible operations.\n    |- Try 4 + 1 = 5. Add 5 to the number set. Current number set: [5, 38], target: 32, just two numbers left.\n     |- Try 38 + 5 = 43. Evaluate 43 != 32, drop this branch.\n     |- Try 38 - 5 = 33. Evaluate 33 != 32, drop this branch.\n     |- Try 38 * 5 = 190. Evaluate 190 != 32, drop this branch.\n     |- Try 38 \/ 5 = 7.6. 7.6 is a decimal, drop this branch.\n    |- Try 4 - 1 = 3. Add 3 to the number set. Current number set: [3, 38], target: 32, just two numbers left.\n     |- Try 38 + 3 = 41. Evaluate 41 != 32, drop this branch.\n     |- Try 38 - 3 = 35. Evaluate 35 != 32, drop this branch.\n     |- Try 38 * 3 = 114. Evaluate 114 != 32, drop this branch.\n     |- Try 38 \/ 3 = 12.7. 12.7 is a decimal, drop this branch.\n    |- Try 4 * 1 = 4. Add 4 to the number set. Current number set: [4, 38], target: 32, just two numbers left.\n     |- Try 38 + 4 = 42. Evaluate 42 != 32, drop this branch.\n     |- Try 38 - 4 = 34. Evaluate 34 != 32, drop this branch.\n     |- Try 38 * 4 = 152. Evaluate 152 != 32, drop this branch.\n     |- Try 38 \/ 4 = 9.5. 9.5 is a decimal, drop this branch.\n    |- Try 4 \/ 1 = 4. Add 4 to the number set. Current number set: [4, 38], target: 32, just two numbers left.\n     |- Try 38 + 4 = 42. Evaluate 42 != 32, drop this branch.\n     |- Try 38 - 4 = 34. Evaluate 34 != 32, drop this branch.\n     |- Try 38 * 4 = 152. Evaluate 152 != 32, drop this branch.\n     |- Try 38 \/ 4 = 9.5. 9.5 is a decimal, drop this branch.\n   |- Pick two numbers (4, 38) (numbers left: [1]). Try possible operations.\n    |- Try 38 + 4 = 42. Add 42 to the number set. Current number set: [42, 1], target: 32, just two numbers left.\n     |- Try 42 + 1 = 43. Evaluate 43 != 32, drop this branch.\n     |- Try 42 - 1 = 41. Evaluate 41 != 32, drop this branch.\n     |- Try 42 * 1 = 42. Evaluate 42 != 32, drop this branch.\n     |- Try 42 \/ 1 = 42. Evaluate 42 != 32, drop this branch.\n    |- Try 38 - 4 = 34. Add 34 to the number set. Current number set: [34, 1], target: 32, just two numbers left.\n     |- Try 34 + 1 = 35. Evaluate 35 != 32, drop this branch.\n     |- Try 34 - 1 = 33. Evaluate 33 != 32, drop this branch.\n     |- Try 34 * 1 = 34. Evaluate 34 != 32, drop this branch.\n     |- Try 34 \/ 1 = 34. Evaluate 34 != 32, drop this branch.\n    |- Try 38 * 4 = 152. Add 152 to the number set. Current number set: [152, 1], target: 32, just two numbers left.\n     |- Try 152 + 1 = 153. Evaluate 153 != 32, drop this branch.\n     |- Try 152 - 1 = 151. Evaluate 151 != 32, drop this branch.\n     |- Try 152 * 1 = 152. Evaluate 152 != 32, drop this branch.\n     |- Try 152 \/ 1 = 152. Evaluate 152 != 32, drop this branch.\n    |- Try 38 \/ 4 = 9.5. 9.5 is a decimal, drop this branch.\n   |- Pick two numbers (1, 38) (numbers left: [4]). Try possible operations.\n    |- Try 38 + 1 = 39. Add 39 to the number set. Current number set: [39, 4], target: 32, just two numbers left.\n     |- Try 39 + 4 = 43. Evaluate 43 != 32, drop this branch.\n     |- Try 39 - 4 = 35. Evaluate 35 != 32, drop this branch.\n     |- Try 39 * 4 = 156. Evaluate 156 != 32, drop this branch.\n     |- Try 39 \/ 4 = 9.8. 9.8 is a decimal, drop this branch.\n    |- Try 38 - 1 = 37. Add 37 to the number set. Current number set: [37, 4], target: 32, just two numbers left.\n     |- Try 37 + 4 = 41. Evaluate 41 != 32, drop this branch.\n     |- Try 37 - 4 = 33. Evaluate 33 != 32, drop this branch.\n     |- Try 37 * 4 = 148. Evaluate 148 != 32, drop this branch.\n     |- Try 37 \/ 4 = 9.2. 9.2 is a decimal, drop this branch.\n    |- Try 38 * 1 = 38. Add 38 to the number set. Current number set: [38, 4], target: 32, just two numbers left.\n     |- Try 38 + 4 = 42. Evaluate 42 != 32, drop this branch.\n     |- Try 38 - 4 = 34. Evaluate 34 != 32, drop this branch.\n     |- Try 38 * 4 = 152. Evaluate 152 != 32, drop this branch.\n     |- Try 38 \/ 4 = 9.5. 9.5 is a decimal, drop this branch.\n    |- Try 38 \/ 1 = 38. Add 38 to the number set. Current number set: [38, 4], target: 32, just two numbers left.\n     |- Try 38 + 4 = 42. Evaluate 42 != 32, drop this branch.\n     |- Try 38 - 4 = 34. Evaluate 34 != 32, drop this branch.\n     |- Try 38 * 4 = 152. Evaluate 152 != 32, drop this branch.\n     |- Try 38 \/ 4 = 9.5. 9.5 is a decimal, drop this branch.\n  |- Try 10 * 6 = 60. Add 60 to the number set. Current number set: [60, 1, 38], target: 32. Options for choosing two numbers: [(60, 1), (60, 38), (1, 38)].\n   |- Pick two numbers (60, 1) (numbers left: [38]). Try possible operations.\n    |- Try 60 + 1 = 61. Add 61 to the number set. Current number set: [61, 38], target: 32, just two numbers left.\n     |- Try 61 + 38 = 99. Evaluate 99 != 32, drop this branch.\n     |- Try 61 - 38 = 23. Evaluate 23 != 32, drop this branch.\n     |- Try 61 * 38 = 2318. 2318 exceeds the maximum intermediate result, drop this branch.\n     |- Try 61 \/ 38 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 60 - 1 = 59. Add 59 to the number set. Current number set: [59, 38], target: 32, just two numbers left.\n     |- Try 59 + 38 = 97. Evaluate 97 != 32, drop this branch.\n     |- Try 59 - 38 = 21. Evaluate 21 != 32, drop this branch.\n     |- Try 59 * 38 = 2242. 2242 exceeds the maximum intermediate result, drop this branch.\n     |- Try 59 \/ 38 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 60 * 1 = 60. Add 60 to the number set. Current number set: [60, 38], target: 32, just two numbers left.\n     |- Try 60 + 38 = 98. Evaluate 98 != 32, drop this branch.\n     |- Try 60 - 38 = 22. Evaluate 22 != 32, drop this branch.\n     |- Try 60 * 38 = 2280. 2280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 60 \/ 38 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 60 \/ 1 = 60. Add 60 to the number set. Current number set: [60, 38], target: 32, just two numbers left.\n     |- Try 60 + 38 = 98. Evaluate 98 != 32, drop this branch.\n     |- Try 60 - 38 = 22. Evaluate 22 != 32, drop this branch.\n     |- Try 60 * 38 = 2280. 2280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 60 \/ 38 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (60, 38) (numbers left: [1]). Try possible operations.\n    |- Try 60 + 38 = 98. Add 98 to the number set. Current number set: [98, 1], target: 32, just two numbers left.\n     |- Try 98 + 1 = 99. Evaluate 99 != 32, drop this branch.\n     |- Try 98 - 1 = 97. Evaluate 97 != 32, drop this branch.\n     |- Try 98 * 1 = 98. Evaluate 98 != 32, drop this branch.\n     |- Try 98 \/ 1 = 98. Evaluate 98 != 32, drop this branch.\n    |- Try 60 - 38 = 22. Add 22 to the number set. Current number set: [22, 1], target: 32, just two numbers left.\n     |- Try 22 + 1 = 23. Evaluate 23 != 32, drop this branch.\n     |- Try 22 - 1 = 21. Evaluate 21 != 32, drop this branch.\n     |- Try 22 * 1 = 22. Evaluate 22 != 32, drop this branch.\n     |- Try 22 \/ 1 = 22. Evaluate 22 != 32, drop this branch.\n    |- Try 60 * 38 = 2280. 2280 exceeds the maximum intermediate result, drop this branch.\n    |- Try 60 \/ 38 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (1, 38) (numbers left: [60]). Try possible operations.\n    |- Try 38 + 1 = 39. Add 39 to the number set. Current number set: [39, 60], target: 32, just two numbers left.\n     |- Try 60 + 39 = 99. Evaluate 99 != 32, drop this branch.\n     |- Try 60 - 39 = 21. Evaluate 21 != 32, drop this branch.\n     |- Try 60 * 39 = 2340. 2340 exceeds the maximum intermediate result, drop this branch.\n     |- Try 60 \/ 39 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 38 - 1 = 37. Add 37 to the number set. Current number set: [37, 60], target: 32, just two numbers left.\n     |- Try 60 + 37 = 97. Evaluate 97 != 32, drop this branch.\n     |- Try 60 - 37 = 23. Evaluate 23 != 32, drop this branch.\n     |- Try 60 * 37 = 2220. 2220 exceeds the maximum intermediate result, drop this branch.\n     |- Try 60 \/ 37 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 38 * 1 = 38. Add 38 to the number set. Current number set: [38, 60], target: 32, just two numbers left.\n     |- Try 60 + 38 = 98. Evaluate 98 != 32, drop this branch.\n     |- Try 60 - 38 = 22. Evaluate 22 != 32, drop this branch.\n     |- Try 60 * 38 = 2280. 2280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 60 \/ 38 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 38 \/ 1 = 38. Add 38 to the number set. Current number set: [38, 60], target: 32, just two numbers left.\n     |- Try 60 + 38 = 98. Evaluate 98 != 32, drop this branch.\n     |- Try 60 - 38 = 22. Evaluate 22 != 32, drop this branch.\n     |- Try 60 * 38 = 2280. 2280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 60 \/ 38 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 10 \/ 6 = 1.7. 1.7 is a decimal, drop this branch.\n |- Pick two numbers (6, 1) (numbers left: [10, 38]). Try possible operations.\n  |- Try 6 + 1 = 7. Add 7 to the number set. Current number set: [7, 10, 38], target: 32. Options for choosing two numbers: [(7, 10), (7, 38), (10, 38)].\n   |- Pick two numbers (7, 10) (numbers left: [38]). Try possible operations.\n    |- Try 10 + 7 = 17. Add 17 to the number set. Current number set: [17, 38], target: 32, just two numbers left.\n     |- Try 38 + 17 = 55. Evaluate 55 != 32, drop this branch.\n     |- Try 38 - 17 = 21. Evaluate 21 != 32, drop this branch.\n     |- Try 38 * 17 = 646. Evaluate 646 != 32, drop this branch.\n     |- Try 38 \/ 17 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 10 - 7 = 3. Add 3 to the number set. Current number set: [3, 38], target: 32, just two numbers left.\n     |- Try 38 + 3 = 41. Evaluate 41 != 32, drop this branch.\n     |- Try 38 - 3 = 35. Evaluate 35 != 32, drop this branch.\n     |- Try 38 * 3 = 114. Evaluate 114 != 32, drop this branch.\n     |- Try 38 \/ 3 = 12.7. 12.7 is a decimal, drop this branch.\n    |- Try 10 * 7 = 70. Add 70 to the number set. Current number set: [70, 38], target: 32, just two numbers left.\n     |- Try 70 + 38 = 108. Evaluate 108 != 32, drop this branch.\n     |- Try 70 - 38 = 32. Evaluate 32 == 32, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 70 - 38 = 32\nThe step before: 10 * 7 = 70\nThe first step: 6 + 1 = 7\n\nOutput the solution in the required format:\n<Solution>\n6 + 1 = 7\n10 * 7 = 70\n70 - 38 = 32\n<\/Solution>\n","item":{"nums":[6,10,1,38],"solution":["6 + 1 = 7","10 * 7 = 70","70 - 38 = 32"],"target":32}}
+{"instance_id":"countdown_8k_185","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [20, 32, 22, 4]\nTarget: 24","reference_output":"# Search Procedure\nInitial number set: [20, 32, 22, 4], target: 24. Options for choosing two numbers: [(20, 32), (20, 22), (20, 4), (32, 22), (32, 4), (22, 4)].\n |- Pick two numbers (20, 32) (numbers left: [22, 4]). Try possible operations.\n  |- Try 32 + 20 = 52. Add 52 to the number set. Current number set: [52, 22, 4], target: 24. Options for choosing two numbers: [(52, 22), (52, 4), (22, 4)].\n   |- Pick two numbers (52, 22) (numbers left: [4]). Try possible operations.\n    |- Try 52 + 22 = 74. Add 74 to the number set. Current number set: [74, 4], target: 24, just two numbers left.\n     |- Try 74 + 4 = 78. Evaluate 78 != 24, drop this branch.\n     |- Try 74 - 4 = 70. Evaluate 70 != 24, drop this branch.\n     |- Try 74 * 4 = 296. Evaluate 296 != 24, drop this branch.\n     |- Try 74 \/ 4 = 18.5. 18.5 is a decimal, drop this branch.\n    |- Try 52 - 22 = 30. Add 30 to the number set. Current number set: [30, 4], target: 24, just two numbers left.\n     |- Try 30 + 4 = 34. Evaluate 34 != 24, drop this branch.\n     |- Try 30 - 4 = 26. Evaluate 26 != 24, drop this branch.\n     |- Try 30 * 4 = 120. Evaluate 120 != 24, drop this branch.\n     |- Try 30 \/ 4 = 7.5. 7.5 is a decimal, drop this branch.\n    |- Try 52 * 22 = 1144. Add 1144 to the number set. Current number set: [1144, 4], target: 24, just two numbers left.\n     |- Try 1144 + 4 = 1148. Evaluate 1148 != 24, drop this branch.\n     |- Try 1144 - 4 = 1140. Evaluate 1140 != 24, drop this branch.\n     |- Try 1144 * 4 = 4576. 4576 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1144 \/ 4 = 286. Evaluate 286 != 24, drop this branch.\n    |- Try 52 \/ 22 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (52, 4) (numbers left: [22]). Try possible operations.\n    |- Try 52 + 4 = 56. Add 56 to the number set. Current number set: [56, 22], target: 24, just two numbers left.\n     |- Try 56 + 22 = 78. Evaluate 78 != 24, drop this branch.\n     |- Try 56 - 22 = 34. Evaluate 34 != 24, drop this branch.\n     |- Try 56 * 22 = 1232. Evaluate 1232 != 24, drop this branch.\n     |- Try 56 \/ 22 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 52 - 4 = 48. Add 48 to the number set. Current number set: [48, 22], target: 24, just two numbers left.\n     |- Try 48 + 22 = 70. Evaluate 70 != 24, drop this branch.\n     |- Try 48 - 22 = 26. Evaluate 26 != 24, drop this branch.\n     |- Try 48 * 22 = 1056. Evaluate 1056 != 24, drop this branch.\n     |- Try 48 \/ 22 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 52 * 4 = 208. Add 208 to the number set. Current number set: [208, 22], target: 24, just two numbers left.\n     |- Try 208 + 22 = 230. Evaluate 230 != 24, drop this branch.\n     |- Try 208 - 22 = 186. Evaluate 186 != 24, drop this branch.\n     |- Try 208 * 22 = 4576. 4576 exceeds the maximum intermediate result, drop this branch.\n     |- Try 208 \/ 22 = 9.5. 9.5 is a decimal, drop this branch.\n    |- Try 52 \/ 4 = 13. Add 13 to the number set. Current number set: [13, 22], target: 24, just two numbers left.\n     |- Try 22 + 13 = 35. Evaluate 35 != 24, drop this branch.\n     |- Try 22 - 13 = 9. Evaluate 9 != 24, drop this branch.\n     |- Try 22 * 13 = 286. Evaluate 286 != 24, drop this branch.\n     |- Try 22 \/ 13 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (22, 4) (numbers left: [52]). Try possible operations.\n    |- Try 22 + 4 = 26. Add 26 to the number set. Current number set: [26, 52], target: 24, just two numbers left.\n     |- Try 52 + 26 = 78. Evaluate 78 != 24, drop this branch.\n     |- Try 52 - 26 = 26. Evaluate 26 != 24, drop this branch.\n     |- Try 52 * 26 = 1352. Evaluate 1352 != 24, drop this branch.\n     |- Try 52 \/ 26 = 2. Evaluate 2 != 24, drop this branch.\n    |- Try 22 - 4 = 18. Add 18 to the number set. Current number set: [18, 52], target: 24, just two numbers left.\n     |- Try 52 + 18 = 70. Evaluate 70 != 24, drop this branch.\n     |- Try 52 - 18 = 34. Evaluate 34 != 24, drop this branch.\n     |- Try 52 * 18 = 936. Evaluate 936 != 24, drop this branch.\n     |- Try 52 \/ 18 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 22 * 4 = 88. Add 88 to the number set. Current number set: [88, 52], target: 24, just two numbers left.\n     |- Try 88 + 52 = 140. Evaluate 140 != 24, drop this branch.\n     |- Try 88 - 52 = 36. Evaluate 36 != 24, drop this branch.\n     |- Try 88 * 52 = 4576. 4576 exceeds the maximum intermediate result, drop this branch.\n     |- Try 88 \/ 52 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 22 \/ 4 = 5.5. 5.5 is a decimal, drop this branch.\n  |- Try 32 - 20 = 12. Add 12 to the number set. Current number set: [12, 22, 4], target: 24. Options for choosing two numbers: [(12, 22), (12, 4), (22, 4)].\n   |- Pick two numbers (12, 22) (numbers left: [4]). Try possible operations.\n    |- Try 22 + 12 = 34. Add 34 to the number set. Current number set: [34, 4], target: 24, just two numbers left.\n     |- Try 34 + 4 = 38. Evaluate 38 != 24, drop this branch.\n     |- Try 34 - 4 = 30. Evaluate 30 != 24, drop this branch.\n     |- Try 34 * 4 = 136. Evaluate 136 != 24, drop this branch.\n     |- Try 34 \/ 4 = 8.5. 8.5 is a decimal, drop this branch.\n    |- Try 22 - 12 = 10. Add 10 to the number set. Current number set: [10, 4], target: 24, just two numbers left.\n     |- Try 10 + 4 = 14. Evaluate 14 != 24, drop this branch.\n     |- Try 10 - 4 = 6. Evaluate 6 != 24, drop this branch.\n     |- Try 10 * 4 = 40. Evaluate 40 != 24, drop this branch.\n     |- Try 10 \/ 4 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 22 * 12 = 264. Add 264 to the number set. Current number set: [264, 4], target: 24, just two numbers left.\n     |- Try 264 + 4 = 268. Evaluate 268 != 24, drop this branch.\n     |- Try 264 - 4 = 260. Evaluate 260 != 24, drop this branch.\n     |- Try 264 * 4 = 1056. Evaluate 1056 != 24, drop this branch.\n     |- Try 264 \/ 4 = 66. Evaluate 66 != 24, drop this branch.\n    |- Try 22 \/ 12 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (12, 4) (numbers left: [22]). Try possible operations.\n    |- Try 12 + 4 = 16. Add 16 to the number set. Current number set: [16, 22], target: 24, just two numbers left.\n     |- Try 22 + 16 = 38. Evaluate 38 != 24, drop this branch.\n     |- Try 22 - 16 = 6. Evaluate 6 != 24, drop this branch.\n     |- Try 22 * 16 = 352. Evaluate 352 != 24, drop this branch.\n     |- Try 22 \/ 16 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 12 - 4 = 8. Add 8 to the number set. Current number set: [8, 22], target: 24, just two numbers left.\n     |- Try 22 + 8 = 30. Evaluate 30 != 24, drop this branch.\n     |- Try 22 - 8 = 14. Evaluate 14 != 24, drop this branch.\n     |- Try 22 * 8 = 176. Evaluate 176 != 24, drop this branch.\n     |- Try 22 \/ 8 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 12 * 4 = 48. Add 48 to the number set. Current number set: [48, 22], target: 24, just two numbers left.\n     |- Try 48 + 22 = 70. Evaluate 70 != 24, drop this branch.\n     |- Try 48 - 22 = 26. Evaluate 26 != 24, drop this branch.\n     |- Try 48 * 22 = 1056. Evaluate 1056 != 24, drop this branch.\n     |- Try 48 \/ 22 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 12 \/ 4 = 3. Add 3 to the number set. Current number set: [3, 22], target: 24, just two numbers left.\n     |- Try 22 + 3 = 25. Evaluate 25 != 24, drop this branch.\n     |- Try 22 - 3 = 19. Evaluate 19 != 24, drop this branch.\n     |- Try 22 * 3 = 66. Evaluate 66 != 24, drop this branch.\n     |- Try 22 \/ 3 = 7.3. 7.3 is a decimal, drop this branch.\n   |- Pick two numbers (22, 4) (numbers left: [12]). Try possible operations.\n    |- Try 22 + 4 = 26. Add 26 to the number set. Current number set: [26, 12], target: 24, just two numbers left.\n     |- Try 26 + 12 = 38. Evaluate 38 != 24, drop this branch.\n     |- Try 26 - 12 = 14. Evaluate 14 != 24, drop this branch.\n     |- Try 26 * 12 = 312. Evaluate 312 != 24, drop this branch.\n     |- Try 26 \/ 12 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 22 - 4 = 18. Add 18 to the number set. Current number set: [18, 12], target: 24, just two numbers left.\n     |- Try 18 + 12 = 30. Evaluate 30 != 24, drop this branch.\n     |- Try 18 - 12 = 6. Evaluate 6 != 24, drop this branch.\n     |- Try 18 * 12 = 216. Evaluate 216 != 24, drop this branch.\n     |- Try 18 \/ 12 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 22 * 4 = 88. Add 88 to the number set. Current number set: [88, 12], target: 24, just two numbers left.\n     |- Try 88 + 12 = 100. Evaluate 100 != 24, drop this branch.\n     |- Try 88 - 12 = 76. Evaluate 76 != 24, drop this branch.\n     |- Try 88 * 12 = 1056. Evaluate 1056 != 24, drop this branch.\n     |- Try 88 \/ 12 = 7.3. 7.3 is a decimal, drop this branch.\n    |- Try 22 \/ 4 = 5.5. 5.5 is a decimal, drop this branch.\n  |- Try 32 * 20 = 640. Add 640 to the number set. Current number set: [640, 22, 4], target: 24. Options for choosing two numbers: [(640, 22), (640, 4), (22, 4)].\n   |- Pick two numbers (640, 22) (numbers left: [4]). Try possible operations.\n    |- Try 640 + 22 = 662. Add 662 to the number set. Current number set: [662, 4], target: 24, just two numbers left.\n     |- Try 662 + 4 = 666. Evaluate 666 != 24, drop this branch.\n     |- Try 662 - 4 = 658. Evaluate 658 != 24, drop this branch.\n     |- Try 662 * 4 = 2648. 2648 exceeds the maximum intermediate result, drop this branch.\n     |- Try 662 \/ 4 = 165.5. 165.5 is a decimal, drop this branch.\n    |- Try 640 - 22 = 618. Add 618 to the number set. Current number set: [618, 4], target: 24, just two numbers left.\n     |- Try 618 + 4 = 622. Evaluate 622 != 24, drop this branch.\n     |- Try 618 - 4 = 614. Evaluate 614 != 24, drop this branch.\n     |- Try 618 * 4 = 2472. 2472 exceeds the maximum intermediate result, drop this branch.\n     |- Try 618 \/ 4 = 154.5. 154.5 is a decimal, drop this branch.\n    |- Try 640 * 22 = 14080. 14080 exceeds the maximum intermediate result, drop this branch.\n    |- Try 640 \/ 22 = 29.1. 29.1 is a decimal, drop this branch.\n   |- Pick two numbers (640, 4) (numbers left: [22]). Try possible operations.\n    |- Try 640 + 4 = 644. Add 644 to the number set. Current number set: [644, 22], target: 24, just two numbers left.\n     |- Try 644 + 22 = 666. Evaluate 666 != 24, drop this branch.\n     |- Try 644 - 22 = 622. Evaluate 622 != 24, drop this branch.\n     |- Try 644 * 22 = 14168. 14168 exceeds the maximum intermediate result, drop this branch.\n     |- Try 644 \/ 22 = 29.3. 29.3 is a decimal, drop this branch.\n    |- Try 640 - 4 = 636. Add 636 to the number set. Current number set: [636, 22], target: 24, just two numbers left.\n     |- Try 636 + 22 = 658. Evaluate 658 != 24, drop this branch.\n     |- Try 636 - 22 = 614. Evaluate 614 != 24, drop this branch.\n     |- Try 636 * 22 = 13992. 13992 exceeds the maximum intermediate result, drop this branch.\n     |- Try 636 \/ 22 = 28.9. 28.9 is a decimal, drop this branch.\n    |- Try 640 * 4 = 2560. 2560 exceeds the maximum intermediate result, drop this branch.\n    |- Try 640 \/ 4 = 160. Add 160 to the number set. Current number set: [160, 22], target: 24, just two numbers left.\n     |- Try 160 + 22 = 182. Evaluate 182 != 24, drop this branch.\n     |- Try 160 - 22 = 138. Evaluate 138 != 24, drop this branch.\n     |- Try 160 * 22 = 3520. 3520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 160 \/ 22 = 7.3. 7.3 is a decimal, drop this branch.\n   |- Pick two numbers (22, 4) (numbers left: [640]). Try possible operations.\n    |- Try 22 + 4 = 26. Add 26 to the number set. Current number set: [26, 640], target: 24, just two numbers left.\n     |- Try 640 + 26 = 666. Evaluate 666 != 24, drop this branch.\n     |- Try 640 - 26 = 614. Evaluate 614 != 24, drop this branch.\n     |- Try 640 * 26 = 16640. 16640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 640 \/ 26 = 24.6. 24.6 is a decimal, drop this branch.\n    |- Try 22 - 4 = 18. Add 18 to the number set. Current number set: [18, 640], target: 24, just two numbers left.\n     |- Try 640 + 18 = 658. Evaluate 658 != 24, drop this branch.\n     |- Try 640 - 18 = 622. Evaluate 622 != 24, drop this branch.\n     |- Try 640 * 18 = 11520. 11520 exceeds the maximum intermediate result, drop this branch.\n     |- Try 640 \/ 18 = 35.6. 35.6 is a decimal, drop this branch.\n    |- Try 22 * 4 = 88. Add 88 to the number set. Current number set: [88, 640], target: 24, just two numbers left.\n     |- Try 640 + 88 = 728. Evaluate 728 != 24, drop this branch.\n     |- Try 640 - 88 = 552. Evaluate 552 != 24, drop this branch.\n     |- Try 640 * 88 = 56320. 56320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 640 \/ 88 = 7.3. 7.3 is a decimal, drop this branch.\n    |- Try 22 \/ 4 = 5.5. 5.5 is a decimal, drop this branch.\n  |- Try 32 \/ 20 = 1.6. 1.6 is a decimal, drop this branch.\n |- Pick two numbers (20, 22) (numbers left: [32, 4]). Try possible operations.\n  |- Try 22 + 20 = 42. Add 42 to the number set. Current number set: [42, 32, 4], target: 24. Options for choosing two numbers: [(42, 32), (42, 4), (32, 4)].\n   |- Pick two numbers (42, 32) (numbers left: [4]). Try possible operations.\n    |- Try 42 + 32 = 74. Add 74 to the number set. Current number set: [74, 4], target: 24, just two numbers left.\n     |- Try 74 + 4 = 78. Evaluate 78 != 24, drop this branch.\n     |- Try 74 - 4 = 70. Evaluate 70 != 24, drop this branch.\n     |- Try 74 * 4 = 296. Evaluate 296 != 24, drop this branch.\n     |- Try 74 \/ 4 = 18.5. 18.5 is a decimal, drop this branch.\n    |- Try 42 - 32 = 10. Add 10 to the number set. Current number set: [10, 4], target: 24, just two numbers left.\n     |- Try 10 + 4 = 14. Evaluate 14 != 24, drop this branch.\n     |- Try 10 - 4 = 6. Evaluate 6 != 24, drop this branch.\n     |- Try 10 * 4 = 40. Evaluate 40 != 24, drop this branch.\n     |- Try 10 \/ 4 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 42 * 32 = 1344. Add 1344 to the number set. Current number set: [1344, 4], target: 24, just two numbers left.\n     |- Try 1344 + 4 = 1348. Evaluate 1348 != 24, drop this branch.\n     |- Try 1344 - 4 = 1340. Evaluate 1340 != 24, drop this branch.\n     |- Try 1344 * 4 = 5376. 5376 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1344 \/ 4 = 336. Evaluate 336 != 24, drop this branch.\n    |- Try 42 \/ 32 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (42, 4) (numbers left: [32]). Try possible operations.\n    |- Try 42 + 4 = 46. Add 46 to the number set. Current number set: [46, 32], target: 24, just two numbers left.\n     |- Try 46 + 32 = 78. Evaluate 78 != 24, drop this branch.\n     |- Try 46 - 32 = 14. Evaluate 14 != 24, drop this branch.\n     |- Try 46 * 32 = 1472. Evaluate 1472 != 24, drop this branch.\n     |- Try 46 \/ 32 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 42 - 4 = 38. Add 38 to the number set. Current number set: [38, 32], target: 24, just two numbers left.\n     |- Try 38 + 32 = 70. Evaluate 70 != 24, drop this branch.\n     |- Try 38 - 32 = 6. Evaluate 6 != 24, drop this branch.\n     |- Try 38 * 32 = 1216. Evaluate 1216 != 24, drop this branch.\n     |- Try 38 \/ 32 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 42 * 4 = 168. Add 168 to the number set. Current number set: [168, 32], target: 24, just two numbers left.\n     |- Try 168 + 32 = 200. Evaluate 200 != 24, drop this branch.\n     |- Try 168 - 32 = 136. Evaluate 136 != 24, drop this branch.\n     |- Try 168 * 32 = 5376. 5376 exceeds the maximum intermediate result, drop this branch.\n     |- Try 168 \/ 32 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 42 \/ 4 = 10.5. 10.5 is a decimal, drop this branch.\n   |- Pick two numbers (32, 4) (numbers left: [42]). Try possible operations.\n    |- Try 32 + 4 = 36. Add 36 to the number set. Current number set: [36, 42], target: 24, just two numbers left.\n     |- Try 42 + 36 = 78. Evaluate 78 != 24, drop this branch.\n     |- Try 42 - 36 = 6. Evaluate 6 != 24, drop this branch.\n     |- Try 42 * 36 = 1512. Evaluate 1512 != 24, drop this branch.\n     |- Try 42 \/ 36 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 32 - 4 = 28. Add 28 to the number set. Current number set: [28, 42], target: 24, just two numbers left.\n     |- Try 42 + 28 = 70. Evaluate 70 != 24, drop this branch.\n     |- Try 42 - 28 = 14. Evaluate 14 != 24, drop this branch.\n     |- Try 42 * 28 = 1176. Evaluate 1176 != 24, drop this branch.\n     |- Try 42 \/ 28 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 32 * 4 = 128. Add 128 to the number set. Current number set: [128, 42], target: 24, just two numbers left.\n     |- Try 128 + 42 = 170. Evaluate 170 != 24, drop this branch.\n     |- Try 128 - 42 = 86. Evaluate 86 != 24, drop this branch.\n     |- Try 128 * 42 = 5376. 5376 exceeds the maximum intermediate result, drop this branch.\n     |- Try 128 \/ 42 = 3.0. 3.0 is a decimal, drop this branch.\n    |- Try 32 \/ 4 = 8. Add 8 to the number set. Current number set: [8, 42], target: 24, just two numbers left.\n     |- Try 42 + 8 = 50. Evaluate 50 != 24, drop this branch.\n     |- Try 42 - 8 = 34. Evaluate 34 != 24, drop this branch.\n     |- Try 42 * 8 = 336. Evaluate 336 != 24, drop this branch.\n     |- Try 42 \/ 8 = 5.2. 5.2 is a decimal, drop this branch.\n  |- Try 22 - 20 = 2. Add 2 to the number set. Current number set: [2, 32, 4], target: 24. Options for choosing two numbers: [(2, 32), (2, 4), (32, 4)].\n   |- Pick two numbers (2, 32) (numbers left: [4]). Try possible operations.\n    |- Try 32 + 2 = 34. Add 34 to the number set. Current number set: [34, 4], target: 24, just two numbers left.\n     |- Try 34 + 4 = 38. Evaluate 38 != 24, drop this branch.\n     |- Try 34 - 4 = 30. Evaluate 30 != 24, drop this branch.\n     |- Try 34 * 4 = 136. Evaluate 136 != 24, drop this branch.\n     |- Try 34 \/ 4 = 8.5. 8.5 is a decimal, drop this branch.\n    |- Try 32 - 2 = 30. Add 30 to the number set. Current number set: [30, 4], target: 24, just two numbers left.\n     |- Try 30 + 4 = 34. Evaluate 34 != 24, drop this branch.\n     |- Try 30 - 4 = 26. Evaluate 26 != 24, drop this branch.\n     |- Try 30 * 4 = 120. Evaluate 120 != 24, drop this branch.\n     |- Try 30 \/ 4 = 7.5. 7.5 is a decimal, drop this branch.\n    |- Try 32 * 2 = 64. Add 64 to the number set. Current number set: [64, 4], target: 24, just two numbers left.\n     |- Try 64 + 4 = 68. Evaluate 68 != 24, drop this branch.\n     |- Try 64 - 4 = 60. Evaluate 60 != 24, drop this branch.\n     |- Try 64 * 4 = 256. Evaluate 256 != 24, drop this branch.\n     |- Try 64 \/ 4 = 16. Evaluate 16 != 24, drop this branch.\n    |- Try 32 \/ 2 = 16. Add 16 to the number set. Current number set: [16, 4], target: 24, just two numbers left.\n     |- Try 16 + 4 = 20. Evaluate 20 != 24, drop this branch.\n     |- Try 16 - 4 = 12. Evaluate 12 != 24, drop this branch.\n     |- Try 16 * 4 = 64. Evaluate 64 != 24, drop this branch.\n     |- Try 16 \/ 4 = 4. Evaluate 4 != 24, drop this branch.\n   |- Pick two numbers (2, 4) (numbers left: [32]). Try possible operations.\n    |- Try 4 + 2 = 6. Add 6 to the number set. Current number set: [6, 32], target: 24, just two numbers left.\n     |- Try 32 + 6 = 38. Evaluate 38 != 24, drop this branch.\n     |- Try 32 - 6 = 26. Evaluate 26 != 24, drop this branch.\n     |- Try 32 * 6 = 192. Evaluate 192 != 24, drop this branch.\n     |- Try 32 \/ 6 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 4 - 2 = 2. Add 2 to the number set. Current number set: [2, 32], target: 24, just two numbers left.\n     |- Try 32 + 2 = 34. Evaluate 34 != 24, drop this branch.\n     |- Try 32 - 2 = 30. Evaluate 30 != 24, drop this branch.\n     |- Try 32 * 2 = 64. Evaluate 64 != 24, drop this branch.\n     |- Try 32 \/ 2 = 16. Evaluate 16 != 24, drop this branch.\n    |- Try 4 * 2 = 8. Add 8 to the number set. Current number set: [8, 32], target: 24, just two numbers left.\n     |- Try 32 + 8 = 40. Evaluate 40 != 24, drop this branch.\n     |- Try 32 - 8 = 24. Evaluate 24 == 24, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 32 - 8 = 24\nThe step before: 4 * 2 = 8\nThe first step: 22 - 20 = 2\n\nOutput the solution in the required format:\n<Solution>\n22 - 20 = 2\n4 * 2 = 8\n32 - 8 = 24\n<\/Solution>\n","item":{"nums":[20,32,22,4],"solution":["22 - 20 = 2","4 * 2 = 8","32 - 8 = 24"],"target":24}}
+{"instance_id":"countdown_8k_186","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [13, 1, 32, 2]\nTarget: 45","reference_output":"# Search Procedure\nInitial number set: [13, 1, 32, 2], target: 45. Options for choosing two numbers: [(13, 1), (13, 32), (13, 2), (1, 32), (1, 2), (32, 2)].\n |- Pick two numbers (13, 1) (numbers left: [32, 2]). Try possible operations.\n  |- Try 13 + 1 = 14. Add 14 to the number set. Current number set: [14, 32, 2], target: 45. Options for choosing two numbers: [(14, 32), (14, 2), (32, 2)].\n   |- Pick two numbers (14, 32) (numbers left: [2]). Try possible operations.\n    |- Try 32 + 14 = 46. Add 46 to the number set. Current number set: [46, 2], target: 45, just two numbers left.\n     |- Try 46 + 2 = 48. Evaluate 48 != 45, drop this branch.\n     |- Try 46 - 2 = 44. Evaluate 44 != 45, drop this branch.\n     |- Try 46 * 2 = 92. Evaluate 92 != 45, drop this branch.\n     |- Try 46 \/ 2 = 23. Evaluate 23 != 45, drop this branch.\n    |- Try 32 - 14 = 18. Add 18 to the number set. Current number set: [18, 2], target: 45, just two numbers left.\n     |- Try 18 + 2 = 20. Evaluate 20 != 45, drop this branch.\n     |- Try 18 - 2 = 16. Evaluate 16 != 45, drop this branch.\n     |- Try 18 * 2 = 36. Evaluate 36 != 45, drop this branch.\n     |- Try 18 \/ 2 = 9. Evaluate 9 != 45, drop this branch.\n    |- Try 32 * 14 = 448. Add 448 to the number set. Current number set: [448, 2], target: 45, just two numbers left.\n     |- Try 448 + 2 = 450. Evaluate 450 != 45, drop this branch.\n     |- Try 448 - 2 = 446. Evaluate 446 != 45, drop this branch.\n     |- Try 448 * 2 = 896. Evaluate 896 != 45, drop this branch.\n     |- Try 448 \/ 2 = 224. Evaluate 224 != 45, drop this branch.\n    |- Try 32 \/ 14 = 2.3. 2.3 is a decimal, drop this branch.\n   |- Pick two numbers (14, 2) (numbers left: [32]). Try possible operations.\n    |- Try 14 + 2 = 16. Add 16 to the number set. Current number set: [16, 32], target: 45, just two numbers left.\n     |- Try 32 + 16 = 48. Evaluate 48 != 45, drop this branch.\n     |- Try 32 - 16 = 16. Evaluate 16 != 45, drop this branch.\n     |- Try 32 * 16 = 512. Evaluate 512 != 45, drop this branch.\n     |- Try 32 \/ 16 = 2. Evaluate 2 != 45, drop this branch.\n    |- Try 14 - 2 = 12. Add 12 to the number set. Current number set: [12, 32], target: 45, just two numbers left.\n     |- Try 32 + 12 = 44. Evaluate 44 != 45, drop this branch.\n     |- Try 32 - 12 = 20. Evaluate 20 != 45, drop this branch.\n     |- Try 32 * 12 = 384. Evaluate 384 != 45, drop this branch.\n     |- Try 32 \/ 12 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 14 * 2 = 28. Add 28 to the number set. Current number set: [28, 32], target: 45, just two numbers left.\n     |- Try 32 + 28 = 60. Evaluate 60 != 45, drop this branch.\n     |- Try 32 - 28 = 4. Evaluate 4 != 45, drop this branch.\n     |- Try 32 * 28 = 896. Evaluate 896 != 45, drop this branch.\n     |- Try 32 \/ 28 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 14 \/ 2 = 7. Add 7 to the number set. Current number set: [7, 32], target: 45, just two numbers left.\n     |- Try 32 + 7 = 39. Evaluate 39 != 45, drop this branch.\n     |- Try 32 - 7 = 25. Evaluate 25 != 45, drop this branch.\n     |- Try 32 * 7 = 224. Evaluate 224 != 45, drop this branch.\n     |- Try 32 \/ 7 = 4.6. 4.6 is a decimal, drop this branch.\n   |- Pick two numbers (32, 2) (numbers left: [14]). Try possible operations.\n    |- Try 32 + 2 = 34. Add 34 to the number set. Current number set: [34, 14], target: 45, just two numbers left.\n     |- Try 34 + 14 = 48. Evaluate 48 != 45, drop this branch.\n     |- Try 34 - 14 = 20. Evaluate 20 != 45, drop this branch.\n     |- Try 34 * 14 = 476. Evaluate 476 != 45, drop this branch.\n     |- Try 34 \/ 14 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 32 - 2 = 30. Add 30 to the number set. Current number set: [30, 14], target: 45, just two numbers left.\n     |- Try 30 + 14 = 44. Evaluate 44 != 45, drop this branch.\n     |- Try 30 - 14 = 16. Evaluate 16 != 45, drop this branch.\n     |- Try 30 * 14 = 420. Evaluate 420 != 45, drop this branch.\n     |- Try 30 \/ 14 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 32 * 2 = 64. Add 64 to the number set. Current number set: [64, 14], target: 45, just two numbers left.\n     |- Try 64 + 14 = 78. Evaluate 78 != 45, drop this branch.\n     |- Try 64 - 14 = 50. Evaluate 50 != 45, drop this branch.\n     |- Try 64 * 14 = 896. Evaluate 896 != 45, drop this branch.\n     |- Try 64 \/ 14 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 32 \/ 2 = 16. Add 16 to the number set. Current number set: [16, 14], target: 45, just two numbers left.\n     |- Try 16 + 14 = 30. Evaluate 30 != 45, drop this branch.\n     |- Try 16 - 14 = 2. Evaluate 2 != 45, drop this branch.\n     |- Try 16 * 14 = 224. Evaluate 224 != 45, drop this branch.\n     |- Try 16 \/ 14 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 13 - 1 = 12. Add 12 to the number set. Current number set: [12, 32, 2], target: 45. Options for choosing two numbers: [(12, 32), (12, 2), (32, 2)].\n   |- Pick two numbers (12, 32) (numbers left: [2]). Try possible operations.\n    |- Try 32 + 12 = 44. Add 44 to the number set. Current number set: [44, 2], target: 45, just two numbers left.\n     |- Try 44 + 2 = 46. Evaluate 46 != 45, drop this branch.\n     |- Try 44 - 2 = 42. Evaluate 42 != 45, drop this branch.\n     |- Try 44 * 2 = 88. Evaluate 88 != 45, drop this branch.\n     |- Try 44 \/ 2 = 22. Evaluate 22 != 45, drop this branch.\n    |- Try 32 - 12 = 20. Add 20 to the number set. Current number set: [20, 2], target: 45, just two numbers left.\n     |- Try 20 + 2 = 22. Evaluate 22 != 45, drop this branch.\n     |- Try 20 - 2 = 18. Evaluate 18 != 45, drop this branch.\n     |- Try 20 * 2 = 40. Evaluate 40 != 45, drop this branch.\n     |- Try 20 \/ 2 = 10. Evaluate 10 != 45, drop this branch.\n    |- Try 32 * 12 = 384. Add 384 to the number set. Current number set: [384, 2], target: 45, just two numbers left.\n     |- Try 384 + 2 = 386. Evaluate 386 != 45, drop this branch.\n     |- Try 384 - 2 = 382. Evaluate 382 != 45, drop this branch.\n     |- Try 384 * 2 = 768. Evaluate 768 != 45, drop this branch.\n     |- Try 384 \/ 2 = 192. Evaluate 192 != 45, drop this branch.\n    |- Try 32 \/ 12 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (12, 2) (numbers left: [32]). Try possible operations.\n    |- Try 12 + 2 = 14. Add 14 to the number set. Current number set: [14, 32], target: 45, just two numbers left.\n     |- Try 32 + 14 = 46. Evaluate 46 != 45, drop this branch.\n     |- Try 32 - 14 = 18. Evaluate 18 != 45, drop this branch.\n     |- Try 32 * 14 = 448. Evaluate 448 != 45, drop this branch.\n     |- Try 32 \/ 14 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 12 - 2 = 10. Add 10 to the number set. Current number set: [10, 32], target: 45, just two numbers left.\n     |- Try 32 + 10 = 42. Evaluate 42 != 45, drop this branch.\n     |- Try 32 - 10 = 22. Evaluate 22 != 45, drop this branch.\n     |- Try 32 * 10 = 320. Evaluate 320 != 45, drop this branch.\n     |- Try 32 \/ 10 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 12 * 2 = 24. Add 24 to the number set. Current number set: [24, 32], target: 45, just two numbers left.\n     |- Try 32 + 24 = 56. Evaluate 56 != 45, drop this branch.\n     |- Try 32 - 24 = 8. Evaluate 8 != 45, drop this branch.\n     |- Try 32 * 24 = 768. Evaluate 768 != 45, drop this branch.\n     |- Try 32 \/ 24 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 12 \/ 2 = 6. Add 6 to the number set. Current number set: [6, 32], target: 45, just two numbers left.\n     |- Try 32 + 6 = 38. Evaluate 38 != 45, drop this branch.\n     |- Try 32 - 6 = 26. Evaluate 26 != 45, drop this branch.\n     |- Try 32 * 6 = 192. Evaluate 192 != 45, drop this branch.\n     |- Try 32 \/ 6 = 5.3. 5.3 is a decimal, drop this branch.\n   |- Pick two numbers (32, 2) (numbers left: [12]). Try possible operations.\n    |- Try 32 + 2 = 34. Add 34 to the number set. Current number set: [34, 12], target: 45, just two numbers left.\n     |- Try 34 + 12 = 46. Evaluate 46 != 45, drop this branch.\n     |- Try 34 - 12 = 22. Evaluate 22 != 45, drop this branch.\n     |- Try 34 * 12 = 408. Evaluate 408 != 45, drop this branch.\n     |- Try 34 \/ 12 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 32 - 2 = 30. Add 30 to the number set. Current number set: [30, 12], target: 45, just two numbers left.\n     |- Try 30 + 12 = 42. Evaluate 42 != 45, drop this branch.\n     |- Try 30 - 12 = 18. Evaluate 18 != 45, drop this branch.\n     |- Try 30 * 12 = 360. Evaluate 360 != 45, drop this branch.\n     |- Try 30 \/ 12 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 32 * 2 = 64. Add 64 to the number set. Current number set: [64, 12], target: 45, just two numbers left.\n     |- Try 64 + 12 = 76. Evaluate 76 != 45, drop this branch.\n     |- Try 64 - 12 = 52. Evaluate 52 != 45, drop this branch.\n     |- Try 64 * 12 = 768. Evaluate 768 != 45, drop this branch.\n     |- Try 64 \/ 12 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 32 \/ 2 = 16. Add 16 to the number set. Current number set: [16, 12], target: 45, just two numbers left.\n     |- Try 16 + 12 = 28. Evaluate 28 != 45, drop this branch.\n     |- Try 16 - 12 = 4. Evaluate 4 != 45, drop this branch.\n     |- Try 16 * 12 = 192. Evaluate 192 != 45, drop this branch.\n     |- Try 16 \/ 12 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 13 * 1 = 13. Add 13 to the number set. Current number set: [13, 32, 2], target: 45. Options for choosing two numbers: [(13, 32), (13, 2), (32, 2)].\n   |- Pick two numbers (13, 32) (numbers left: [2]). Try possible operations.\n    |- Try 32 + 13 = 45. Add 45 to the number set. Current number set: [45, 2], target: 45, just two numbers left.\n     |- Try 45 + 2 = 47. Evaluate 47 != 45, drop this branch.\n     |- Try 45 - 2 = 43. Evaluate 43 != 45, drop this branch.\n     |- Try 45 * 2 = 90. Evaluate 90 != 45, drop this branch.\n     |- Try 45 \/ 2 = 22.5. 22.5 is a decimal, drop this branch.\n    |- Try 32 - 13 = 19. Add 19 to the number set. Current number set: [19, 2], target: 45, just two numbers left.\n     |- Try 19 + 2 = 21. Evaluate 21 != 45, drop this branch.\n     |- Try 19 - 2 = 17. Evaluate 17 != 45, drop this branch.\n     |- Try 19 * 2 = 38. Evaluate 38 != 45, drop this branch.\n     |- Try 19 \/ 2 = 9.5. 9.5 is a decimal, drop this branch.\n    |- Try 32 * 13 = 416. Add 416 to the number set. Current number set: [416, 2], target: 45, just two numbers left.\n     |- Try 416 + 2 = 418. Evaluate 418 != 45, drop this branch.\n     |- Try 416 - 2 = 414. Evaluate 414 != 45, drop this branch.\n     |- Try 416 * 2 = 832. Evaluate 832 != 45, drop this branch.\n     |- Try 416 \/ 2 = 208. Evaluate 208 != 45, drop this branch.\n    |- Try 32 \/ 13 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (13, 2) (numbers left: [32]). Try possible operations.\n    |- Try 13 + 2 = 15. Add 15 to the number set. Current number set: [15, 32], target: 45, just two numbers left.\n     |- Try 32 + 15 = 47. Evaluate 47 != 45, drop this branch.\n     |- Try 32 - 15 = 17. Evaluate 17 != 45, drop this branch.\n     |- Try 32 * 15 = 480. Evaluate 480 != 45, drop this branch.\n     |- Try 32 \/ 15 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 13 - 2 = 11. Add 11 to the number set. Current number set: [11, 32], target: 45, just two numbers left.\n     |- Try 32 + 11 = 43. Evaluate 43 != 45, drop this branch.\n     |- Try 32 - 11 = 21. Evaluate 21 != 45, drop this branch.\n     |- Try 32 * 11 = 352. Evaluate 352 != 45, drop this branch.\n     |- Try 32 \/ 11 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 13 * 2 = 26. Add 26 to the number set. Current number set: [26, 32], target: 45, just two numbers left.\n     |- Try 32 + 26 = 58. Evaluate 58 != 45, drop this branch.\n     |- Try 32 - 26 = 6. Evaluate 6 != 45, drop this branch.\n     |- Try 32 * 26 = 832. Evaluate 832 != 45, drop this branch.\n     |- Try 32 \/ 26 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 13 \/ 2 = 6.5. 6.5 is a decimal, drop this branch.\n   |- Pick two numbers (32, 2) (numbers left: [13]). Try possible operations.\n    |- Try 32 + 2 = 34. Add 34 to the number set. Current number set: [34, 13], target: 45, just two numbers left.\n     |- Try 34 + 13 = 47. Evaluate 47 != 45, drop this branch.\n     |- Try 34 - 13 = 21. Evaluate 21 != 45, drop this branch.\n     |- Try 34 * 13 = 442. Evaluate 442 != 45, drop this branch.\n     |- Try 34 \/ 13 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 32 - 2 = 30. Add 30 to the number set. Current number set: [30, 13], target: 45, just two numbers left.\n     |- Try 30 + 13 = 43. Evaluate 43 != 45, drop this branch.\n     |- Try 30 - 13 = 17. Evaluate 17 != 45, drop this branch.\n     |- Try 30 * 13 = 390. Evaluate 390 != 45, drop this branch.\n     |- Try 30 \/ 13 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 32 * 2 = 64. Add 64 to the number set. Current number set: [64, 13], target: 45, just two numbers left.\n     |- Try 64 + 13 = 77. Evaluate 77 != 45, drop this branch.\n     |- Try 64 - 13 = 51. Evaluate 51 != 45, drop this branch.\n     |- Try 64 * 13 = 832. Evaluate 832 != 45, drop this branch.\n     |- Try 64 \/ 13 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 32 \/ 2 = 16. Add 16 to the number set. Current number set: [16, 13], target: 45, just two numbers left.\n     |- Try 16 + 13 = 29. Evaluate 29 != 45, drop this branch.\n     |- Try 16 - 13 = 3. Evaluate 3 != 45, drop this branch.\n     |- Try 16 * 13 = 208. Evaluate 208 != 45, drop this branch.\n     |- Try 16 \/ 13 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 13 \/ 1 = 13. Add 13 to the number set. Current number set: [13, 32, 2], target: 45. Options for choosing two numbers: [(13, 32), (13, 2), (32, 2)].\n   |- Pick two numbers (13, 32) (numbers left: [2]). Try possible operations.\n    |- Try 32 + 13 = 45. Add 45 to the number set. Current number set: [45, 2], target: 45, just two numbers left.\n     |- Try 45 + 2 = 47. Evaluate 47 != 45, drop this branch.\n     |- Try 45 - 2 = 43. Evaluate 43 != 45, drop this branch.\n     |- Try 45 * 2 = 90. Evaluate 90 != 45, drop this branch.\n     |- Try 45 \/ 2 = 22.5. 22.5 is a decimal, drop this branch.\n    |- Try 32 - 13 = 19. Add 19 to the number set. Current number set: [19, 2], target: 45, just two numbers left.\n     |- Try 19 + 2 = 21. Evaluate 21 != 45, drop this branch.\n     |- Try 19 - 2 = 17. Evaluate 17 != 45, drop this branch.\n     |- Try 19 * 2 = 38. Evaluate 38 != 45, drop this branch.\n     |- Try 19 \/ 2 = 9.5. 9.5 is a decimal, drop this branch.\n    |- Try 32 * 13 = 416. Add 416 to the number set. Current number set: [416, 2], target: 45, just two numbers left.\n     |- Try 416 + 2 = 418. Evaluate 418 != 45, drop this branch.\n     |- Try 416 - 2 = 414. Evaluate 414 != 45, drop this branch.\n     |- Try 416 * 2 = 832. Evaluate 832 != 45, drop this branch.\n     |- Try 416 \/ 2 = 208. Evaluate 208 != 45, drop this branch.\n    |- Try 32 \/ 13 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (13, 2) (numbers left: [32]). Try possible operations.\n    |- Try 13 + 2 = 15. Add 15 to the number set. Current number set: [15, 32], target: 45, just two numbers left.\n     |- Try 32 + 15 = 47. Evaluate 47 != 45, drop this branch.\n     |- Try 32 - 15 = 17. Evaluate 17 != 45, drop this branch.\n     |- Try 32 * 15 = 480. Evaluate 480 != 45, drop this branch.\n     |- Try 32 \/ 15 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 13 - 2 = 11. Add 11 to the number set. Current number set: [11, 32], target: 45, just two numbers left.\n     |- Try 32 + 11 = 43. Evaluate 43 != 45, drop this branch.\n     |- Try 32 - 11 = 21. Evaluate 21 != 45, drop this branch.\n     |- Try 32 * 11 = 352. Evaluate 352 != 45, drop this branch.\n     |- Try 32 \/ 11 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 13 * 2 = 26. Add 26 to the number set. Current number set: [26, 32], target: 45, just two numbers left.\n     |- Try 32 + 26 = 58. Evaluate 58 != 45, drop this branch.\n     |- Try 32 - 26 = 6. Evaluate 6 != 45, drop this branch.\n     |- Try 32 * 26 = 832. Evaluate 832 != 45, drop this branch.\n     |- Try 32 \/ 26 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 13 \/ 2 = 6.5. 6.5 is a decimal, drop this branch.\n   |- Pick two numbers (32, 2) (numbers left: [13]). Try possible operations.\n    |- Try 32 + 2 = 34. Add 34 to the number set. Current number set: [34, 13], target: 45, just two numbers left.\n     |- Try 34 + 13 = 47. Evaluate 47 != 45, drop this branch.\n     |- Try 34 - 13 = 21. Evaluate 21 != 45, drop this branch.\n     |- Try 34 * 13 = 442. Evaluate 442 != 45, drop this branch.\n     |- Try 34 \/ 13 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 32 - 2 = 30. Add 30 to the number set. Current number set: [30, 13], target: 45, just two numbers left.\n     |- Try 30 + 13 = 43. Evaluate 43 != 45, drop this branch.\n     |- Try 30 - 13 = 17. Evaluate 17 != 45, drop this branch.\n     |- Try 30 * 13 = 390. Evaluate 390 != 45, drop this branch.\n     |- Try 30 \/ 13 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 32 * 2 = 64. Add 64 to the number set. Current number set: [64, 13], target: 45, just two numbers left.\n     |- Try 64 + 13 = 77. Evaluate 77 != 45, drop this branch.\n     |- Try 64 - 13 = 51. Evaluate 51 != 45, drop this branch.\n     |- Try 64 * 13 = 832. Evaluate 832 != 45, drop this branch.\n     |- Try 64 \/ 13 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 32 \/ 2 = 16. Add 16 to the number set. Current number set: [16, 13], target: 45, just two numbers left.\n     |- Try 16 + 13 = 29. Evaluate 29 != 45, drop this branch.\n     |- Try 16 - 13 = 3. Evaluate 3 != 45, drop this branch.\n     |- Try 16 * 13 = 208. Evaluate 208 != 45, drop this branch.\n     |- Try 16 \/ 13 = 1.2. 1.2 is a decimal, drop this branch.\n |- Pick two numbers (13, 32) (numbers left: [1, 2]). Try possible operations.\n  |- Try 32 + 13 = 45. Add 45 to the number set. Current number set: [45, 1, 2], target: 45. Options for choosing two numbers: [(45, 1), (45, 2), (1, 2)].\n   |- Pick two numbers (45, 1) (numbers left: [2]). Try possible operations.\n    |- Try 45 + 1 = 46. Add 46 to the number set. Current number set: [46, 2], target: 45, just two numbers left.\n     |- Try 46 + 2 = 48. Evaluate 48 != 45, drop this branch.\n     |- Try 46 - 2 = 44. Evaluate 44 != 45, drop this branch.\n     |- Try 46 * 2 = 92. Evaluate 92 != 45, drop this branch.\n     |- Try 46 \/ 2 = 23. Evaluate 23 != 45, drop this branch.\n    |- Try 45 - 1 = 44. Add 44 to the number set. Current number set: [44, 2], target: 45, just two numbers left.\n     |- Try 44 + 2 = 46. Evaluate 46 != 45, drop this branch.\n     |- Try 44 - 2 = 42. Evaluate 42 != 45, drop this branch.\n     |- Try 44 * 2 = 88. Evaluate 88 != 45, drop this branch.\n     |- Try 44 \/ 2 = 22. Evaluate 22 != 45, drop this branch.\n    |- Try 45 * 1 = 45. Add 45 to the number set. Current number set: [45, 2], target: 45, just two numbers left.\n     |- Try 45 + 2 = 47. Evaluate 47 != 45, drop this branch.\n     |- Try 45 - 2 = 43. Evaluate 43 != 45, drop this branch.\n     |- Try 45 * 2 = 90. Evaluate 90 != 45, drop this branch.\n     |- Try 45 \/ 2 = 22.5. 22.5 is a decimal, drop this branch.\n    |- Try 45 \/ 1 = 45. Add 45 to the number set. Current number set: [45, 2], target: 45, just two numbers left.\n     |- Try 45 + 2 = 47. Evaluate 47 != 45, drop this branch.\n     |- Try 45 - 2 = 43. Evaluate 43 != 45, drop this branch.\n     |- Try 45 * 2 = 90. Evaluate 90 != 45, drop this branch.\n     |- Try 45 \/ 2 = 22.5. 22.5 is a decimal, drop this branch.\n   |- Pick two numbers (45, 2) (numbers left: [1]). Try possible operations.\n    |- Try 45 + 2 = 47. Add 47 to the number set. Current number set: [47, 1], target: 45, just two numbers left.\n     |- Try 47 + 1 = 48. Evaluate 48 != 45, drop this branch.\n     |- Try 47 - 1 = 46. Evaluate 46 != 45, drop this branch.\n     |- Try 47 * 1 = 47. Evaluate 47 != 45, drop this branch.\n     |- Try 47 \/ 1 = 47. Evaluate 47 != 45, drop this branch.\n    |- Try 45 - 2 = 43. Add 43 to the number set. Current number set: [43, 1], target: 45, just two numbers left.\n     |- Try 43 + 1 = 44. Evaluate 44 != 45, drop this branch.\n     |- Try 43 - 1 = 42. Evaluate 42 != 45, drop this branch.\n     |- Try 43 * 1 = 43. Evaluate 43 != 45, drop this branch.\n     |- Try 43 \/ 1 = 43. Evaluate 43 != 45, drop this branch.\n    |- Try 45 * 2 = 90. Add 90 to the number set. Current number set: [90, 1], target: 45, just two numbers left.\n     |- Try 90 + 1 = 91. Evaluate 91 != 45, drop this branch.\n     |- Try 90 - 1 = 89. Evaluate 89 != 45, drop this branch.\n     |- Try 90 * 1 = 90. Evaluate 90 != 45, drop this branch.\n     |- Try 90 \/ 1 = 90. Evaluate 90 != 45, drop this branch.\n    |- Try 45 \/ 2 = 22.5. 22.5 is a decimal, drop this branch.\n   |- Pick two numbers (1, 2) (numbers left: [45]). Try possible operations.\n    |- Try 2 + 1 = 3. Add 3 to the number set. Current number set: [3, 45], target: 45, just two numbers left.\n     |- Try 45 + 3 = 48. Evaluate 48 != 45, drop this branch.\n     |- Try 45 - 3 = 42. Evaluate 42 != 45, drop this branch.\n     |- Try 45 * 3 = 135. Evaluate 135 != 45, drop this branch.\n     |- Try 45 \/ 3 = 15. Evaluate 15 != 45, drop this branch.\n    |- Try 2 - 1 = 1. Add 1 to the number set. Current number set: [1, 45], target: 45, just two numbers left.\n     |- Try 45 + 1 = 46. Evaluate 46 != 45, drop this branch.\n     |- Try 45 - 1 = 44. Evaluate 44 != 45, drop this branch.\n     |- Try 45 * 1 = 45. Evaluate 45 == 45, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 45 * 1 = 45\nThe step before: 2 - 1 = 1\nThe first step: 32 + 13 = 45\n\nOutput the solution in the required format:\n<Solution>\n32 + 13 = 45\n2 - 1 = 1\n45 * 1 = 45\n<\/Solution>\n","item":{"nums":[13,1,32,2],"solution":["32 + 13 = 45","2 - 1 = 1","45 * 1 = 45"],"target":45}}
+{"instance_id":"countdown_8k_187","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [15, 44, 13, 17]\nTarget: 10","reference_output":"# Search Procedure\nInitial number set: [15, 44, 13, 17], target: 10. Options for choosing two numbers: [(15, 44), (15, 13), (15, 17), (44, 13), (44, 17), (13, 17)].\n |- Pick two numbers (15, 44) (numbers left: [13, 17]). Try possible operations.\n  |- Try 44 + 15 = 59. Add 59 to the number set. Current number set: [59, 13, 17], target: 10. Options for choosing two numbers: [(59, 13), (59, 17), (13, 17)].\n   |- Pick two numbers (59, 13) (numbers left: [17]). Try possible operations.\n    |- Try 59 + 13 = 72. Add 72 to the number set. Current number set: [72, 17], target: 10, just two numbers left.\n     |- Try 72 + 17 = 89. Evaluate 89 != 10, drop this branch.\n     |- Try 72 - 17 = 55. Evaluate 55 != 10, drop this branch.\n     |- Try 72 * 17 = 1224. Evaluate 1224 != 10, drop this branch.\n     |- Try 72 \/ 17 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 59 - 13 = 46. Add 46 to the number set. Current number set: [46, 17], target: 10, just two numbers left.\n     |- Try 46 + 17 = 63. Evaluate 63 != 10, drop this branch.\n     |- Try 46 - 17 = 29. Evaluate 29 != 10, drop this branch.\n     |- Try 46 * 17 = 782. Evaluate 782 != 10, drop this branch.\n     |- Try 46 \/ 17 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 59 * 13 = 767. Add 767 to the number set. Current number set: [767, 17], target: 10, just two numbers left.\n     |- Try 767 + 17 = 784. Evaluate 784 != 10, drop this branch.\n     |- Try 767 - 17 = 750. Evaluate 750 != 10, drop this branch.\n     |- Try 767 * 17 = 13039. 13039 exceeds the maximum intermediate result, drop this branch.\n     |- Try 767 \/ 17 = 45.1. 45.1 is a decimal, drop this branch.\n    |- Try 59 \/ 13 = 4.5. 4.5 is a decimal, drop this branch.\n   |- Pick two numbers (59, 17) (numbers left: [13]). Try possible operations.\n    |- Try 59 + 17 = 76. Add 76 to the number set. Current number set: [76, 13], target: 10, just two numbers left.\n     |- Try 76 + 13 = 89. Evaluate 89 != 10, drop this branch.\n     |- Try 76 - 13 = 63. Evaluate 63 != 10, drop this branch.\n     |- Try 76 * 13 = 988. Evaluate 988 != 10, drop this branch.\n     |- Try 76 \/ 13 = 5.8. 5.8 is a decimal, drop this branch.\n    |- Try 59 - 17 = 42. Add 42 to the number set. Current number set: [42, 13], target: 10, just two numbers left.\n     |- Try 42 + 13 = 55. Evaluate 55 != 10, drop this branch.\n     |- Try 42 - 13 = 29. Evaluate 29 != 10, drop this branch.\n     |- Try 42 * 13 = 546. Evaluate 546 != 10, drop this branch.\n     |- Try 42 \/ 13 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 59 * 17 = 1003. Add 1003 to the number set. Current number set: [1003, 13], target: 10, just two numbers left.\n     |- Try 1003 + 13 = 1016. Evaluate 1016 != 10, drop this branch.\n     |- Try 1003 - 13 = 990. Evaluate 990 != 10, drop this branch.\n     |- Try 1003 * 13 = 13039. 13039 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1003 \/ 13 = 77.2. 77.2 is a decimal, drop this branch.\n    |- Try 59 \/ 17 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (13, 17) (numbers left: [59]). Try possible operations.\n    |- Try 17 + 13 = 30. Add 30 to the number set. Current number set: [30, 59], target: 10, just two numbers left.\n     |- Try 59 + 30 = 89. Evaluate 89 != 10, drop this branch.\n     |- Try 59 - 30 = 29. Evaluate 29 != 10, drop this branch.\n     |- Try 59 * 30 = 1770. Evaluate 1770 != 10, drop this branch.\n     |- Try 59 \/ 30 = 2.0. 2.0 is a decimal, drop this branch.\n    |- Try 17 - 13 = 4. Add 4 to the number set. Current number set: [4, 59], target: 10, just two numbers left.\n     |- Try 59 + 4 = 63. Evaluate 63 != 10, drop this branch.\n     |- Try 59 - 4 = 55. Evaluate 55 != 10, drop this branch.\n     |- Try 59 * 4 = 236. Evaluate 236 != 10, drop this branch.\n     |- Try 59 \/ 4 = 14.8. 14.8 is a decimal, drop this branch.\n    |- Try 17 * 13 = 221. Add 221 to the number set. Current number set: [221, 59], target: 10, just two numbers left.\n     |- Try 221 + 59 = 280. Evaluate 280 != 10, drop this branch.\n     |- Try 221 - 59 = 162. Evaluate 162 != 10, drop this branch.\n     |- Try 221 * 59 = 13039. 13039 exceeds the maximum intermediate result, drop this branch.\n     |- Try 221 \/ 59 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 17 \/ 13 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 44 - 15 = 29. Add 29 to the number set. Current number set: [29, 13, 17], target: 10. Options for choosing two numbers: [(29, 13), (29, 17), (13, 17)].\n   |- Pick two numbers (29, 13) (numbers left: [17]). Try possible operations.\n    |- Try 29 + 13 = 42. Add 42 to the number set. Current number set: [42, 17], target: 10, just two numbers left.\n     |- Try 42 + 17 = 59. Evaluate 59 != 10, drop this branch.\n     |- Try 42 - 17 = 25. Evaluate 25 != 10, drop this branch.\n     |- Try 42 * 17 = 714. Evaluate 714 != 10, drop this branch.\n     |- Try 42 \/ 17 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 29 - 13 = 16. Add 16 to the number set. Current number set: [16, 17], target: 10, just two numbers left.\n     |- Try 17 + 16 = 33. Evaluate 33 != 10, drop this branch.\n     |- Try 17 - 16 = 1. Evaluate 1 != 10, drop this branch.\n     |- Try 17 * 16 = 272. Evaluate 272 != 10, drop this branch.\n     |- Try 17 \/ 16 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 29 * 13 = 377. Add 377 to the number set. Current number set: [377, 17], target: 10, just two numbers left.\n     |- Try 377 + 17 = 394. Evaluate 394 != 10, drop this branch.\n     |- Try 377 - 17 = 360. Evaluate 360 != 10, drop this branch.\n     |- Try 377 * 17 = 6409. 6409 exceeds the maximum intermediate result, drop this branch.\n     |- Try 377 \/ 17 = 22.2. 22.2 is a decimal, drop this branch.\n    |- Try 29 \/ 13 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (29, 17) (numbers left: [13]). Try possible operations.\n    |- Try 29 + 17 = 46. Add 46 to the number set. Current number set: [46, 13], target: 10, just two numbers left.\n     |- Try 46 + 13 = 59. Evaluate 59 != 10, drop this branch.\n     |- Try 46 - 13 = 33. Evaluate 33 != 10, drop this branch.\n     |- Try 46 * 13 = 598. Evaluate 598 != 10, drop this branch.\n     |- Try 46 \/ 13 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 29 - 17 = 12. Add 12 to the number set. Current number set: [12, 13], target: 10, just two numbers left.\n     |- Try 13 + 12 = 25. Evaluate 25 != 10, drop this branch.\n     |- Try 13 - 12 = 1. Evaluate 1 != 10, drop this branch.\n     |- Try 13 * 12 = 156. Evaluate 156 != 10, drop this branch.\n     |- Try 13 \/ 12 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 29 * 17 = 493. Add 493 to the number set. Current number set: [493, 13], target: 10, just two numbers left.\n     |- Try 493 + 13 = 506. Evaluate 506 != 10, drop this branch.\n     |- Try 493 - 13 = 480. Evaluate 480 != 10, drop this branch.\n     |- Try 493 * 13 = 6409. 6409 exceeds the maximum intermediate result, drop this branch.\n     |- Try 493 \/ 13 = 37.9. 37.9 is a decimal, drop this branch.\n    |- Try 29 \/ 17 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (13, 17) (numbers left: [29]). Try possible operations.\n    |- Try 17 + 13 = 30. Add 30 to the number set. Current number set: [30, 29], target: 10, just two numbers left.\n     |- Try 30 + 29 = 59. Evaluate 59 != 10, drop this branch.\n     |- Try 30 - 29 = 1. Evaluate 1 != 10, drop this branch.\n     |- Try 30 * 29 = 870. Evaluate 870 != 10, drop this branch.\n     |- Try 30 \/ 29 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 17 - 13 = 4. Add 4 to the number set. Current number set: [4, 29], target: 10, just two numbers left.\n     |- Try 29 + 4 = 33. Evaluate 33 != 10, drop this branch.\n     |- Try 29 - 4 = 25. Evaluate 25 != 10, drop this branch.\n     |- Try 29 * 4 = 116. Evaluate 116 != 10, drop this branch.\n     |- Try 29 \/ 4 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 17 * 13 = 221. Add 221 to the number set. Current number set: [221, 29], target: 10, just two numbers left.\n     |- Try 221 + 29 = 250. Evaluate 250 != 10, drop this branch.\n     |- Try 221 - 29 = 192. Evaluate 192 != 10, drop this branch.\n     |- Try 221 * 29 = 6409. 6409 exceeds the maximum intermediate result, drop this branch.\n     |- Try 221 \/ 29 = 7.6. 7.6 is a decimal, drop this branch.\n    |- Try 17 \/ 13 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 44 * 15 = 660. Add 660 to the number set. Current number set: [660, 13, 17], target: 10. Options for choosing two numbers: [(660, 13), (660, 17), (13, 17)].\n   |- Pick two numbers (660, 13) (numbers left: [17]). Try possible operations.\n    |- Try 660 + 13 = 673. Add 673 to the number set. Current number set: [673, 17], target: 10, just two numbers left.\n     |- Try 673 + 17 = 690. Evaluate 690 != 10, drop this branch.\n     |- Try 673 - 17 = 656. Evaluate 656 != 10, drop this branch.\n     |- Try 673 * 17 = 11441. 11441 exceeds the maximum intermediate result, drop this branch.\n     |- Try 673 \/ 17 = 39.6. 39.6 is a decimal, drop this branch.\n    |- Try 660 - 13 = 647. Add 647 to the number set. Current number set: [647, 17], target: 10, just two numbers left.\n     |- Try 647 + 17 = 664. Evaluate 664 != 10, drop this branch.\n     |- Try 647 - 17 = 630. Evaluate 630 != 10, drop this branch.\n     |- Try 647 * 17 = 10999. 10999 exceeds the maximum intermediate result, drop this branch.\n     |- Try 647 \/ 17 = 38.1. 38.1 is a decimal, drop this branch.\n    |- Try 660 * 13 = 8580. 8580 exceeds the maximum intermediate result, drop this branch.\n    |- Try 660 \/ 13 = 50.8. 50.8 is a decimal, drop this branch.\n   |- Pick two numbers (660, 17) (numbers left: [13]). Try possible operations.\n    |- Try 660 + 17 = 677. Add 677 to the number set. Current number set: [677, 13], target: 10, just two numbers left.\n     |- Try 677 + 13 = 690. Evaluate 690 != 10, drop this branch.\n     |- Try 677 - 13 = 664. Evaluate 664 != 10, drop this branch.\n     |- Try 677 * 13 = 8801. 8801 exceeds the maximum intermediate result, drop this branch.\n     |- Try 677 \/ 13 = 52.1. 52.1 is a decimal, drop this branch.\n    |- Try 660 - 17 = 643. Add 643 to the number set. Current number set: [643, 13], target: 10, just two numbers left.\n     |- Try 643 + 13 = 656. Evaluate 656 != 10, drop this branch.\n     |- Try 643 - 13 = 630. Evaluate 630 != 10, drop this branch.\n     |- Try 643 * 13 = 8359. 8359 exceeds the maximum intermediate result, drop this branch.\n     |- Try 643 \/ 13 = 49.5. 49.5 is a decimal, drop this branch.\n    |- Try 660 * 17 = 11220. 11220 exceeds the maximum intermediate result, drop this branch.\n    |- Try 660 \/ 17 = 38.8. 38.8 is a decimal, drop this branch.\n   |- Pick two numbers (13, 17) (numbers left: [660]). Try possible operations.\n    |- Try 17 + 13 = 30. Add 30 to the number set. Current number set: [30, 660], target: 10, just two numbers left.\n     |- Try 660 + 30 = 690. Evaluate 690 != 10, drop this branch.\n     |- Try 660 - 30 = 630. Evaluate 630 != 10, drop this branch.\n     |- Try 660 * 30 = 19800. 19800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 660 \/ 30 = 22. Evaluate 22 != 10, drop this branch.\n    |- Try 17 - 13 = 4. Add 4 to the number set. Current number set: [4, 660], target: 10, just two numbers left.\n     |- Try 660 + 4 = 664. Evaluate 664 != 10, drop this branch.\n     |- Try 660 - 4 = 656. Evaluate 656 != 10, drop this branch.\n     |- Try 660 * 4 = 2640. 2640 exceeds the maximum intermediate result, drop this branch.\n     |- Try 660 \/ 4 = 165. Evaluate 165 != 10, drop this branch.\n    |- Try 17 * 13 = 221. Add 221 to the number set. Current number set: [221, 660], target: 10, just two numbers left.\n     |- Try 660 + 221 = 881. Evaluate 881 != 10, drop this branch.\n     |- Try 660 - 221 = 439. Evaluate 439 != 10, drop this branch.\n     |- Try 660 * 221 = 145860. 145860 exceeds the maximum intermediate result, drop this branch.\n     |- Try 660 \/ 221 = 3.0. 3.0 is a decimal, drop this branch.\n    |- Try 17 \/ 13 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 44 \/ 15 = 2.9. 2.9 is a decimal, drop this branch.\n |- Pick two numbers (15, 13) (numbers left: [44, 17]). Try possible operations.\n  |- Try 15 + 13 = 28. Add 28 to the number set. Current number set: [28, 44, 17], target: 10. Options for choosing two numbers: [(28, 44), (28, 17), (44, 17)].\n   |- Pick two numbers (28, 44) (numbers left: [17]). Try possible operations.\n    |- Try 44 + 28 = 72. Add 72 to the number set. Current number set: [72, 17], target: 10, just two numbers left.\n     |- Try 72 + 17 = 89. Evaluate 89 != 10, drop this branch.\n     |- Try 72 - 17 = 55. Evaluate 55 != 10, drop this branch.\n     |- Try 72 * 17 = 1224. Evaluate 1224 != 10, drop this branch.\n     |- Try 72 \/ 17 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 44 - 28 = 16. Add 16 to the number set. Current number set: [16, 17], target: 10, just two numbers left.\n     |- Try 17 + 16 = 33. Evaluate 33 != 10, drop this branch.\n     |- Try 17 - 16 = 1. Evaluate 1 != 10, drop this branch.\n     |- Try 17 * 16 = 272. Evaluate 272 != 10, drop this branch.\n     |- Try 17 \/ 16 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 44 * 28 = 1232. Add 1232 to the number set. Current number set: [1232, 17], target: 10, just two numbers left.\n     |- Try 1232 + 17 = 1249. Evaluate 1249 != 10, drop this branch.\n     |- Try 1232 - 17 = 1215. Evaluate 1215 != 10, drop this branch.\n     |- Try 1232 * 17 = 20944. 20944 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1232 \/ 17 = 72.5. 72.5 is a decimal, drop this branch.\n    |- Try 44 \/ 28 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (28, 17) (numbers left: [44]). Try possible operations.\n    |- Try 28 + 17 = 45. Add 45 to the number set. Current number set: [45, 44], target: 10, just two numbers left.\n     |- Try 45 + 44 = 89. Evaluate 89 != 10, drop this branch.\n     |- Try 45 - 44 = 1. Evaluate 1 != 10, drop this branch.\n     |- Try 45 * 44 = 1980. Evaluate 1980 != 10, drop this branch.\n     |- Try 45 \/ 44 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 28 - 17 = 11. Add 11 to the number set. Current number set: [11, 44], target: 10, just two numbers left.\n     |- Try 44 + 11 = 55. Evaluate 55 != 10, drop this branch.\n     |- Try 44 - 11 = 33. Evaluate 33 != 10, drop this branch.\n     |- Try 44 * 11 = 484. Evaluate 484 != 10, drop this branch.\n     |- Try 44 \/ 11 = 4. Evaluate 4 != 10, drop this branch.\n    |- Try 28 * 17 = 476. Add 476 to the number set. Current number set: [476, 44], target: 10, just two numbers left.\n     |- Try 476 + 44 = 520. Evaluate 520 != 10, drop this branch.\n     |- Try 476 - 44 = 432. Evaluate 432 != 10, drop this branch.\n     |- Try 476 * 44 = 20944. 20944 exceeds the maximum intermediate result, drop this branch.\n     |- Try 476 \/ 44 = 10.8. 10.8 is a decimal, drop this branch.\n    |- Try 28 \/ 17 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (44, 17) (numbers left: [28]). Try possible operations.\n    |- Try 44 + 17 = 61. Add 61 to the number set. Current number set: [61, 28], target: 10, just two numbers left.\n     |- Try 61 + 28 = 89. Evaluate 89 != 10, drop this branch.\n     |- Try 61 - 28 = 33. Evaluate 33 != 10, drop this branch.\n     |- Try 61 * 28 = 1708. Evaluate 1708 != 10, drop this branch.\n     |- Try 61 \/ 28 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 44 - 17 = 27. Add 27 to the number set. Current number set: [27, 28], target: 10, just two numbers left.\n     |- Try 28 + 27 = 55. Evaluate 55 != 10, drop this branch.\n     |- Try 28 - 27 = 1. Evaluate 1 != 10, drop this branch.\n     |- Try 28 * 27 = 756. Evaluate 756 != 10, drop this branch.\n     |- Try 28 \/ 27 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 44 * 17 = 748. Add 748 to the number set. Current number set: [748, 28], target: 10, just two numbers left.\n     |- Try 748 + 28 = 776. Evaluate 776 != 10, drop this branch.\n     |- Try 748 - 28 = 720. Evaluate 720 != 10, drop this branch.\n     |- Try 748 * 28 = 20944. 20944 exceeds the maximum intermediate result, drop this branch.\n     |- Try 748 \/ 28 = 26.7. 26.7 is a decimal, drop this branch.\n    |- Try 44 \/ 17 = 2.6. 2.6 is a decimal, drop this branch.\n  |- Try 15 - 13 = 2. Add 2 to the number set. Current number set: [2, 44, 17], target: 10. Options for choosing two numbers: [(2, 44), (2, 17), (44, 17)].\n   |- Pick two numbers (2, 44) (numbers left: [17]). Try possible operations.\n    |- Try 44 + 2 = 46. Add 46 to the number set. Current number set: [46, 17], target: 10, just two numbers left.\n     |- Try 46 + 17 = 63. Evaluate 63 != 10, drop this branch.\n     |- Try 46 - 17 = 29. Evaluate 29 != 10, drop this branch.\n     |- Try 46 * 17 = 782. Evaluate 782 != 10, drop this branch.\n     |- Try 46 \/ 17 = 2.7. 2.7 is a decimal, drop this branch.\n    |- Try 44 - 2 = 42. Add 42 to the number set. Current number set: [42, 17], target: 10, just two numbers left.\n     |- Try 42 + 17 = 59. Evaluate 59 != 10, drop this branch.\n     |- Try 42 - 17 = 25. Evaluate 25 != 10, drop this branch.\n     |- Try 42 * 17 = 714. Evaluate 714 != 10, drop this branch.\n     |- Try 42 \/ 17 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 44 * 2 = 88. Add 88 to the number set. Current number set: [88, 17], target: 10, just two numbers left.\n     |- Try 88 + 17 = 105. Evaluate 105 != 10, drop this branch.\n     |- Try 88 - 17 = 71. Evaluate 71 != 10, drop this branch.\n     |- Try 88 * 17 = 1496. Evaluate 1496 != 10, drop this branch.\n     |- Try 88 \/ 17 = 5.2. 5.2 is a decimal, drop this branch.\n    |- Try 44 \/ 2 = 22. Add 22 to the number set. Current number set: [22, 17], target: 10, just two numbers left.\n     |- Try 22 + 17 = 39. Evaluate 39 != 10, drop this branch.\n     |- Try 22 - 17 = 5. Evaluate 5 != 10, drop this branch.\n     |- Try 22 * 17 = 374. Evaluate 374 != 10, drop this branch.\n     |- Try 22 \/ 17 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (2, 17) (numbers left: [44]). Try possible operations.\n    |- Try 17 + 2 = 19. Add 19 to the number set. Current number set: [19, 44], target: 10, just two numbers left.\n     |- Try 44 + 19 = 63. Evaluate 63 != 10, drop this branch.\n     |- Try 44 - 19 = 25. Evaluate 25 != 10, drop this branch.\n     |- Try 44 * 19 = 836. Evaluate 836 != 10, drop this branch.\n     |- Try 44 \/ 19 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 17 - 2 = 15. Add 15 to the number set. Current number set: [15, 44], target: 10, just two numbers left.\n     |- Try 44 + 15 = 59. Evaluate 59 != 10, drop this branch.\n     |- Try 44 - 15 = 29. Evaluate 29 != 10, drop this branch.\n     |- Try 44 * 15 = 660. Evaluate 660 != 10, drop this branch.\n     |- Try 44 \/ 15 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 17 * 2 = 34. Add 34 to the number set. Current number set: [34, 44], target: 10, just two numbers left.\n     |- Try 44 + 34 = 78. Evaluate 78 != 10, drop this branch.\n     |- Try 44 - 34 = 10. Evaluate 10 == 10, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 44 - 34 = 10\nThe step before: 17 * 2 = 34\nThe first step: 15 - 13 = 2\n\nOutput the solution in the required format:\n<Solution>\n15 - 13 = 2\n17 * 2 = 34\n44 - 34 = 10\n<\/Solution>\n","item":{"nums":[15,44,13,17],"solution":["15 - 13 = 2","17 * 2 = 34","44 - 34 = 10"],"target":10}}
+{"instance_id":"countdown_8k_188","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [15, 8, 49, 49]\nTarget: 41","reference_output":"# Search Procedure\nInitial number set: [15, 8, 49, 49], target: 41. Options for choosing two numbers: [(15, 8), (15, 49), (15, 49), (8, 49), (8, 49), (49, 49)].\n |- Pick two numbers (15, 8) (numbers left: [49, 49]). Try possible operations.\n  |- Try 15 + 8 = 23. Add 23 to the number set. Current number set: [23, 49, 49], target: 41. Options for choosing two numbers: [(23, 49), (23, 49), (49, 49)].\n   |- Pick two numbers (23, 49) (numbers left: [49]). Try possible operations.\n    |- Try 49 + 23 = 72. Add 72 to the number set. Current number set: [72, 49], target: 41, just two numbers left.\n     |- Try 72 + 49 = 121. Evaluate 121 != 41, drop this branch.\n     |- Try 72 - 49 = 23. Evaluate 23 != 41, drop this branch.\n     |- Try 72 * 49 = 3528. 3528 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 49 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 49 - 23 = 26. Add 26 to the number set. Current number set: [26, 49], target: 41, just two numbers left.\n     |- Try 49 + 26 = 75. Evaluate 75 != 41, drop this branch.\n     |- Try 49 - 26 = 23. Evaluate 23 != 41, drop this branch.\n     |- Try 49 * 26 = 1274. Evaluate 1274 != 41, drop this branch.\n     |- Try 49 \/ 26 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 49 * 23 = 1127. Add 1127 to the number set. Current number set: [1127, 49], target: 41, just two numbers left.\n     |- Try 1127 + 49 = 1176. Evaluate 1176 != 41, drop this branch.\n     |- Try 1127 - 49 = 1078. Evaluate 1078 != 41, drop this branch.\n     |- Try 1127 * 49 = 55223. 55223 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1127 \/ 49 = 23. Evaluate 23 != 41, drop this branch.\n    |- Try 49 \/ 23 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (23, 49) (numbers left: [49]). Try possible operations.\n    |- Try 49 + 23 = 72. Add 72 to the number set. Current number set: [72, 49], target: 41, just two numbers left.\n     |- Try 72 + 49 = 121. Evaluate 121 != 41, drop this branch.\n     |- Try 72 - 49 = 23. Evaluate 23 != 41, drop this branch.\n     |- Try 72 * 49 = 3528. 3528 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 49 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 49 - 23 = 26. Add 26 to the number set. Current number set: [26, 49], target: 41, just two numbers left.\n     |- Try 49 + 26 = 75. Evaluate 75 != 41, drop this branch.\n     |- Try 49 - 26 = 23. Evaluate 23 != 41, drop this branch.\n     |- Try 49 * 26 = 1274. Evaluate 1274 != 41, drop this branch.\n     |- Try 49 \/ 26 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 49 * 23 = 1127. Add 1127 to the number set. Current number set: [1127, 49], target: 41, just two numbers left.\n     |- Try 1127 + 49 = 1176. Evaluate 1176 != 41, drop this branch.\n     |- Try 1127 - 49 = 1078. Evaluate 1078 != 41, drop this branch.\n     |- Try 1127 * 49 = 55223. 55223 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1127 \/ 49 = 23. Evaluate 23 != 41, drop this branch.\n    |- Try 49 \/ 23 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (49, 49) (numbers left: [23]). Try possible operations.\n    |- Try 49 + 49 = 98. Add 98 to the number set. Current number set: [98, 23], target: 41, just two numbers left.\n     |- Try 98 + 23 = 121. Evaluate 121 != 41, drop this branch.\n     |- Try 98 - 23 = 75. Evaluate 75 != 41, drop this branch.\n     |- Try 98 * 23 = 2254. 2254 exceeds the maximum intermediate result, drop this branch.\n     |- Try 98 \/ 23 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 49 - 49 = 0. Add 0 to the number set. Current number set: [0, 23], target: 41, just two numbers left.\n     |- Try 23 + 0 = 23. Evaluate 23 != 41, drop this branch.\n     |- Try 23 - 0 = 23. Evaluate 23 != 41, drop this branch.\n     |- Try 23 * 0 = 0. Evaluate 0 != 41, drop this branch.\n     |- Try 23 \/ 0 (invalid operation). drop this branch.\n    |- Try 49 * 49 = 2401. 2401 exceeds the maximum intermediate result, drop this branch.\n    |- Try 49 \/ 49 = 1. Add 1 to the number set. Current number set: [1, 23], target: 41, just two numbers left.\n     |- Try 23 + 1 = 24. Evaluate 24 != 41, drop this branch.\n     |- Try 23 - 1 = 22. Evaluate 22 != 41, drop this branch.\n     |- Try 23 * 1 = 23. Evaluate 23 != 41, drop this branch.\n     |- Try 23 \/ 1 = 23. Evaluate 23 != 41, drop this branch.\n  |- Try 15 - 8 = 7. Add 7 to the number set. Current number set: [7, 49, 49], target: 41. Options for choosing two numbers: [(7, 49), (7, 49), (49, 49)].\n   |- Pick two numbers (7, 49) (numbers left: [49]). Try possible operations.\n    |- Try 49 + 7 = 56. Add 56 to the number set. Current number set: [56, 49], target: 41, just two numbers left.\n     |- Try 56 + 49 = 105. Evaluate 105 != 41, drop this branch.\n     |- Try 56 - 49 = 7. Evaluate 7 != 41, drop this branch.\n     |- Try 56 * 49 = 2744. 2744 exceeds the maximum intermediate result, drop this branch.\n     |- Try 56 \/ 49 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 49 - 7 = 42. Add 42 to the number set. Current number set: [42, 49], target: 41, just two numbers left.\n     |- Try 49 + 42 = 91. Evaluate 91 != 41, drop this branch.\n     |- Try 49 - 42 = 7. Evaluate 7 != 41, drop this branch.\n     |- Try 49 * 42 = 2058. 2058 exceeds the maximum intermediate result, drop this branch.\n     |- Try 49 \/ 42 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 49 * 7 = 343. Add 343 to the number set. Current number set: [343, 49], target: 41, just two numbers left.\n     |- Try 343 + 49 = 392. Evaluate 392 != 41, drop this branch.\n     |- Try 343 - 49 = 294. Evaluate 294 != 41, drop this branch.\n     |- Try 343 * 49 = 16807. 16807 exceeds the maximum intermediate result, drop this branch.\n     |- Try 343 \/ 49 = 7. Evaluate 7 != 41, drop this branch.\n    |- Try 49 \/ 7 = 7. Add 7 to the number set. Current number set: [7, 49], target: 41, just two numbers left.\n     |- Try 49 + 7 = 56. Evaluate 56 != 41, drop this branch.\n     |- Try 49 - 7 = 42. Evaluate 42 != 41, drop this branch.\n     |- Try 49 * 7 = 343. Evaluate 343 != 41, drop this branch.\n     |- Try 49 \/ 7 = 7. Evaluate 7 != 41, drop this branch.\n   |- Pick two numbers (7, 49) (numbers left: [49]). Try possible operations.\n    |- Try 49 + 7 = 56. Add 56 to the number set. Current number set: [56, 49], target: 41, just two numbers left.\n     |- Try 56 + 49 = 105. Evaluate 105 != 41, drop this branch.\n     |- Try 56 - 49 = 7. Evaluate 7 != 41, drop this branch.\n     |- Try 56 * 49 = 2744. 2744 exceeds the maximum intermediate result, drop this branch.\n     |- Try 56 \/ 49 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 49 - 7 = 42. Add 42 to the number set. Current number set: [42, 49], target: 41, just two numbers left.\n     |- Try 49 + 42 = 91. Evaluate 91 != 41, drop this branch.\n     |- Try 49 - 42 = 7. Evaluate 7 != 41, drop this branch.\n     |- Try 49 * 42 = 2058. 2058 exceeds the maximum intermediate result, drop this branch.\n     |- Try 49 \/ 42 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 49 * 7 = 343. Add 343 to the number set. Current number set: [343, 49], target: 41, just two numbers left.\n     |- Try 343 + 49 = 392. Evaluate 392 != 41, drop this branch.\n     |- Try 343 - 49 = 294. Evaluate 294 != 41, drop this branch.\n     |- Try 343 * 49 = 16807. 16807 exceeds the maximum intermediate result, drop this branch.\n     |- Try 343 \/ 49 = 7. Evaluate 7 != 41, drop this branch.\n    |- Try 49 \/ 7 = 7. Add 7 to the number set. Current number set: [7, 49], target: 41, just two numbers left.\n     |- Try 49 + 7 = 56. Evaluate 56 != 41, drop this branch.\n     |- Try 49 - 7 = 42. Evaluate 42 != 41, drop this branch.\n     |- Try 49 * 7 = 343. Evaluate 343 != 41, drop this branch.\n     |- Try 49 \/ 7 = 7. Evaluate 7 != 41, drop this branch.\n   |- Pick two numbers (49, 49) (numbers left: [7]). Try possible operations.\n    |- Try 49 + 49 = 98. Add 98 to the number set. Current number set: [98, 7], target: 41, just two numbers left.\n     |- Try 98 + 7 = 105. Evaluate 105 != 41, drop this branch.\n     |- Try 98 - 7 = 91. Evaluate 91 != 41, drop this branch.\n     |- Try 98 * 7 = 686. Evaluate 686 != 41, drop this branch.\n     |- Try 98 \/ 7 = 14. Evaluate 14 != 41, drop this branch.\n    |- Try 49 - 49 = 0. Add 0 to the number set. Current number set: [0, 7], target: 41, just two numbers left.\n     |- Try 7 + 0 = 7. Evaluate 7 != 41, drop this branch.\n     |- Try 7 - 0 = 7. Evaluate 7 != 41, drop this branch.\n     |- Try 7 * 0 = 0. Evaluate 0 != 41, drop this branch.\n     |- Try 7 \/ 0 (invalid operation). drop this branch.\n    |- Try 49 * 49 = 2401. 2401 exceeds the maximum intermediate result, drop this branch.\n    |- Try 49 \/ 49 = 1. Add 1 to the number set. Current number set: [1, 7], target: 41, just two numbers left.\n     |- Try 7 + 1 = 8. Evaluate 8 != 41, drop this branch.\n     |- Try 7 - 1 = 6. Evaluate 6 != 41, drop this branch.\n     |- Try 7 * 1 = 7. Evaluate 7 != 41, drop this branch.\n     |- Try 7 \/ 1 = 7. Evaluate 7 != 41, drop this branch.\n  |- Try 15 * 8 = 120. Add 120 to the number set. Current number set: [120, 49, 49], target: 41. Options for choosing two numbers: [(120, 49), (120, 49), (49, 49)].\n   |- Pick two numbers (120, 49) (numbers left: [49]). Try possible operations.\n    |- Try 120 + 49 = 169. Add 169 to the number set. Current number set: [169, 49], target: 41, just two numbers left.\n     |- Try 169 + 49 = 218. Evaluate 218 != 41, drop this branch.\n     |- Try 169 - 49 = 120. Evaluate 120 != 41, drop this branch.\n     |- Try 169 * 49 = 8281. 8281 exceeds the maximum intermediate result, drop this branch.\n     |- Try 169 \/ 49 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 120 - 49 = 71. Add 71 to the number set. Current number set: [71, 49], target: 41, just two numbers left.\n     |- Try 71 + 49 = 120. Evaluate 120 != 41, drop this branch.\n     |- Try 71 - 49 = 22. Evaluate 22 != 41, drop this branch.\n     |- Try 71 * 49 = 3479. 3479 exceeds the maximum intermediate result, drop this branch.\n     |- Try 71 \/ 49 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 120 * 49 = 5880. 5880 exceeds the maximum intermediate result, drop this branch.\n    |- Try 120 \/ 49 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (120, 49) (numbers left: [49]). Try possible operations.\n    |- Try 120 + 49 = 169. Add 169 to the number set. Current number set: [169, 49], target: 41, just two numbers left.\n     |- Try 169 + 49 = 218. Evaluate 218 != 41, drop this branch.\n     |- Try 169 - 49 = 120. Evaluate 120 != 41, drop this branch.\n     |- Try 169 * 49 = 8281. 8281 exceeds the maximum intermediate result, drop this branch.\n     |- Try 169 \/ 49 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 120 - 49 = 71. Add 71 to the number set. Current number set: [71, 49], target: 41, just two numbers left.\n     |- Try 71 + 49 = 120. Evaluate 120 != 41, drop this branch.\n     |- Try 71 - 49 = 22. Evaluate 22 != 41, drop this branch.\n     |- Try 71 * 49 = 3479. 3479 exceeds the maximum intermediate result, drop this branch.\n     |- Try 71 \/ 49 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 120 * 49 = 5880. 5880 exceeds the maximum intermediate result, drop this branch.\n    |- Try 120 \/ 49 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (49, 49) (numbers left: [120]). Try possible operations.\n    |- Try 49 + 49 = 98. Add 98 to the number set. Current number set: [98, 120], target: 41, just two numbers left.\n     |- Try 120 + 98 = 218. Evaluate 218 != 41, drop this branch.\n     |- Try 120 - 98 = 22. Evaluate 22 != 41, drop this branch.\n     |- Try 120 * 98 = 11760. 11760 exceeds the maximum intermediate result, drop this branch.\n     |- Try 120 \/ 98 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 49 - 49 = 0. Add 0 to the number set. Current number set: [0, 120], target: 41, just two numbers left.\n     |- Try 120 + 0 = 120. Evaluate 120 != 41, drop this branch.\n     |- Try 120 - 0 = 120. Evaluate 120 != 41, drop this branch.\n     |- Try 120 * 0 = 0. Evaluate 0 != 41, drop this branch.\n     |- Try 120 \/ 0 (invalid operation). drop this branch.\n    |- Try 49 * 49 = 2401. 2401 exceeds the maximum intermediate result, drop this branch.\n    |- Try 49 \/ 49 = 1. Add 1 to the number set. Current number set: [1, 120], target: 41, just two numbers left.\n     |- Try 120 + 1 = 121. Evaluate 121 != 41, drop this branch.\n     |- Try 120 - 1 = 119. Evaluate 119 != 41, drop this branch.\n     |- Try 120 * 1 = 120. Evaluate 120 != 41, drop this branch.\n     |- Try 120 \/ 1 = 120. Evaluate 120 != 41, drop this branch.\n  |- Try 15 \/ 8 = 1.9. 1.9 is a decimal, drop this branch.\n |- Pick two numbers (15, 49) (numbers left: [8, 49]). Try possible operations.\n  |- Try 49 + 15 = 64. Add 64 to the number set. Current number set: [64, 8, 49], target: 41. Options for choosing two numbers: [(64, 8), (64, 49), (8, 49)].\n   |- Pick two numbers (64, 8) (numbers left: [49]). Try possible operations.\n    |- Try 64 + 8 = 72. Add 72 to the number set. Current number set: [72, 49], target: 41, just two numbers left.\n     |- Try 72 + 49 = 121. Evaluate 121 != 41, drop this branch.\n     |- Try 72 - 49 = 23. Evaluate 23 != 41, drop this branch.\n     |- Try 72 * 49 = 3528. 3528 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 49 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 64 - 8 = 56. Add 56 to the number set. Current number set: [56, 49], target: 41, just two numbers left.\n     |- Try 56 + 49 = 105. Evaluate 105 != 41, drop this branch.\n     |- Try 56 - 49 = 7. Evaluate 7 != 41, drop this branch.\n     |- Try 56 * 49 = 2744. 2744 exceeds the maximum intermediate result, drop this branch.\n     |- Try 56 \/ 49 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 64 * 8 = 512. Add 512 to the number set. Current number set: [512, 49], target: 41, just two numbers left.\n     |- Try 512 + 49 = 561. Evaluate 561 != 41, drop this branch.\n     |- Try 512 - 49 = 463. Evaluate 463 != 41, drop this branch.\n     |- Try 512 * 49 = 25088. 25088 exceeds the maximum intermediate result, drop this branch.\n     |- Try 512 \/ 49 = 10.4. 10.4 is a decimal, drop this branch.\n    |- Try 64 \/ 8 = 8. Add 8 to the number set. Current number set: [8, 49], target: 41, just two numbers left.\n     |- Try 49 + 8 = 57. Evaluate 57 != 41, drop this branch.\n     |- Try 49 - 8 = 41. Evaluate 41 == 41, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 49 - 8 = 41\nThe step before: 64 \/ 8 = 8\nThe first step: 49 + 15 = 64\n\nOutput the solution in the required format:\n<Solution>\n49 + 15 = 64\n64 \/ 8 = 8\n49 - 8 = 41\n<\/Solution>\n","item":{"nums":[15,8,49,49],"solution":["49 + 15 = 64","64 \/ 8 = 8","49 - 8 = 41"],"target":41}}
+{"instance_id":"countdown_8k_189","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [31, 21, 20, 33]\nTarget: 18","reference_output":"# Search Procedure\nInitial number set: [31, 21, 20, 33], target: 18. Options for choosing two numbers: [(31, 21), (31, 20), (31, 33), (21, 20), (21, 33), (20, 33)].\n |- Pick two numbers (31, 21) (numbers left: [20, 33]). Try possible operations.\n  |- Try 31 + 21 = 52. Add 52 to the number set. Current number set: [52, 20, 33], target: 18. Options for choosing two numbers: [(52, 20), (52, 33), (20, 33)].\n   |- Pick two numbers (52, 20) (numbers left: [33]). Try possible operations.\n    |- Try 52 + 20 = 72. Add 72 to the number set. Current number set: [72, 33], target: 18, just two numbers left.\n     |- Try 72 + 33 = 105. Evaluate 105 != 18, drop this branch.\n     |- Try 72 - 33 = 39. Evaluate 39 != 18, drop this branch.\n     |- Try 72 * 33 = 2376. 2376 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 33 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 52 - 20 = 32. Add 32 to the number set. Current number set: [32, 33], target: 18, just two numbers left.\n     |- Try 33 + 32 = 65. Evaluate 65 != 18, drop this branch.\n     |- Try 33 - 32 = 1. Evaluate 1 != 18, drop this branch.\n     |- Try 33 * 32 = 1056. Evaluate 1056 != 18, drop this branch.\n     |- Try 33 \/ 32 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 52 * 20 = 1040. Add 1040 to the number set. Current number set: [1040, 33], target: 18, just two numbers left.\n     |- Try 1040 + 33 = 1073. Evaluate 1073 != 18, drop this branch.\n     |- Try 1040 - 33 = 1007. Evaluate 1007 != 18, drop this branch.\n     |- Try 1040 * 33 = 34320. 34320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1040 \/ 33 = 31.5. 31.5 is a decimal, drop this branch.\n    |- Try 52 \/ 20 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (52, 33) (numbers left: [20]). Try possible operations.\n    |- Try 52 + 33 = 85. Add 85 to the number set. Current number set: [85, 20], target: 18, just two numbers left.\n     |- Try 85 + 20 = 105. Evaluate 105 != 18, drop this branch.\n     |- Try 85 - 20 = 65. Evaluate 65 != 18, drop this branch.\n     |- Try 85 * 20 = 1700. Evaluate 1700 != 18, drop this branch.\n     |- Try 85 \/ 20 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 52 - 33 = 19. Add 19 to the number set. Current number set: [19, 20], target: 18, just two numbers left.\n     |- Try 20 + 19 = 39. Evaluate 39 != 18, drop this branch.\n     |- Try 20 - 19 = 1. Evaluate 1 != 18, drop this branch.\n     |- Try 20 * 19 = 380. Evaluate 380 != 18, drop this branch.\n     |- Try 20 \/ 19 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 52 * 33 = 1716. Add 1716 to the number set. Current number set: [1716, 20], target: 18, just two numbers left.\n     |- Try 1716 + 20 = 1736. Evaluate 1736 != 18, drop this branch.\n     |- Try 1716 - 20 = 1696. Evaluate 1696 != 18, drop this branch.\n     |- Try 1716 * 20 = 34320. 34320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1716 \/ 20 = 85.8. 85.8 is a decimal, drop this branch.\n    |- Try 52 \/ 33 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (20, 33) (numbers left: [52]). Try possible operations.\n    |- Try 33 + 20 = 53. Add 53 to the number set. Current number set: [53, 52], target: 18, just two numbers left.\n     |- Try 53 + 52 = 105. Evaluate 105 != 18, drop this branch.\n     |- Try 53 - 52 = 1. Evaluate 1 != 18, drop this branch.\n     |- Try 53 * 52 = 2756. 2756 exceeds the maximum intermediate result, drop this branch.\n     |- Try 53 \/ 52 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 33 - 20 = 13. Add 13 to the number set. Current number set: [13, 52], target: 18, just two numbers left.\n     |- Try 52 + 13 = 65. Evaluate 65 != 18, drop this branch.\n     |- Try 52 - 13 = 39. Evaluate 39 != 18, drop this branch.\n     |- Try 52 * 13 = 676. Evaluate 676 != 18, drop this branch.\n     |- Try 52 \/ 13 = 4. Evaluate 4 != 18, drop this branch.\n    |- Try 33 * 20 = 660. Add 660 to the number set. Current number set: [660, 52], target: 18, just two numbers left.\n     |- Try 660 + 52 = 712. Evaluate 712 != 18, drop this branch.\n     |- Try 660 - 52 = 608. Evaluate 608 != 18, drop this branch.\n     |- Try 660 * 52 = 34320. 34320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 660 \/ 52 = 12.7. 12.7 is a decimal, drop this branch.\n    |- Try 33 \/ 20 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 31 - 21 = 10. Add 10 to the number set. Current number set: [10, 20, 33], target: 18. Options for choosing two numbers: [(10, 20), (10, 33), (20, 33)].\n   |- Pick two numbers (10, 20) (numbers left: [33]). Try possible operations.\n    |- Try 20 + 10 = 30. Add 30 to the number set. Current number set: [30, 33], target: 18, just two numbers left.\n     |- Try 33 + 30 = 63. Evaluate 63 != 18, drop this branch.\n     |- Try 33 - 30 = 3. Evaluate 3 != 18, drop this branch.\n     |- Try 33 * 30 = 990. Evaluate 990 != 18, drop this branch.\n     |- Try 33 \/ 30 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 20 - 10 = 10. Add 10 to the number set. Current number set: [10, 33], target: 18, just two numbers left.\n     |- Try 33 + 10 = 43. Evaluate 43 != 18, drop this branch.\n     |- Try 33 - 10 = 23. Evaluate 23 != 18, drop this branch.\n     |- Try 33 * 10 = 330. Evaluate 330 != 18, drop this branch.\n     |- Try 33 \/ 10 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 20 * 10 = 200. Add 200 to the number set. Current number set: [200, 33], target: 18, just two numbers left.\n     |- Try 200 + 33 = 233. Evaluate 233 != 18, drop this branch.\n     |- Try 200 - 33 = 167. Evaluate 167 != 18, drop this branch.\n     |- Try 200 * 33 = 6600. 6600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 200 \/ 33 = 6.1. 6.1 is a decimal, drop this branch.\n    |- Try 20 \/ 10 = 2. Add 2 to the number set. Current number set: [2, 33], target: 18, just two numbers left.\n     |- Try 33 + 2 = 35. Evaluate 35 != 18, drop this branch.\n     |- Try 33 - 2 = 31. Evaluate 31 != 18, drop this branch.\n     |- Try 33 * 2 = 66. Evaluate 66 != 18, drop this branch.\n     |- Try 33 \/ 2 = 16.5. 16.5 is a decimal, drop this branch.\n   |- Pick two numbers (10, 33) (numbers left: [20]). Try possible operations.\n    |- Try 33 + 10 = 43. Add 43 to the number set. Current number set: [43, 20], target: 18, just two numbers left.\n     |- Try 43 + 20 = 63. Evaluate 63 != 18, drop this branch.\n     |- Try 43 - 20 = 23. Evaluate 23 != 18, drop this branch.\n     |- Try 43 * 20 = 860. Evaluate 860 != 18, drop this branch.\n     |- Try 43 \/ 20 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 33 - 10 = 23. Add 23 to the number set. Current number set: [23, 20], target: 18, just two numbers left.\n     |- Try 23 + 20 = 43. Evaluate 43 != 18, drop this branch.\n     |- Try 23 - 20 = 3. Evaluate 3 != 18, drop this branch.\n     |- Try 23 * 20 = 460. Evaluate 460 != 18, drop this branch.\n     |- Try 23 \/ 20 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 33 * 10 = 330. Add 330 to the number set. Current number set: [330, 20], target: 18, just two numbers left.\n     |- Try 330 + 20 = 350. Evaluate 350 != 18, drop this branch.\n     |- Try 330 - 20 = 310. Evaluate 310 != 18, drop this branch.\n     |- Try 330 * 20 = 6600. 6600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 330 \/ 20 = 16.5. 16.5 is a decimal, drop this branch.\n    |- Try 33 \/ 10 = 3.3. 3.3 is a decimal, drop this branch.\n   |- Pick two numbers (20, 33) (numbers left: [10]). Try possible operations.\n    |- Try 33 + 20 = 53. Add 53 to the number set. Current number set: [53, 10], target: 18, just two numbers left.\n     |- Try 53 + 10 = 63. Evaluate 63 != 18, drop this branch.\n     |- Try 53 - 10 = 43. Evaluate 43 != 18, drop this branch.\n     |- Try 53 * 10 = 530. Evaluate 530 != 18, drop this branch.\n     |- Try 53 \/ 10 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 33 - 20 = 13. Add 13 to the number set. Current number set: [13, 10], target: 18, just two numbers left.\n     |- Try 13 + 10 = 23. Evaluate 23 != 18, drop this branch.\n     |- Try 13 - 10 = 3. Evaluate 3 != 18, drop this branch.\n     |- Try 13 * 10 = 130. Evaluate 130 != 18, drop this branch.\n     |- Try 13 \/ 10 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 33 * 20 = 660. Add 660 to the number set. Current number set: [660, 10], target: 18, just two numbers left.\n     |- Try 660 + 10 = 670. Evaluate 670 != 18, drop this branch.\n     |- Try 660 - 10 = 650. Evaluate 650 != 18, drop this branch.\n     |- Try 660 * 10 = 6600. 6600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 660 \/ 10 = 66. Evaluate 66 != 18, drop this branch.\n    |- Try 33 \/ 20 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 31 * 21 = 651. Add 651 to the number set. Current number set: [651, 20, 33], target: 18. Options for choosing two numbers: [(651, 20), (651, 33), (20, 33)].\n   |- Pick two numbers (651, 20) (numbers left: [33]). Try possible operations.\n    |- Try 651 + 20 = 671. Add 671 to the number set. Current number set: [671, 33], target: 18, just two numbers left.\n     |- Try 671 + 33 = 704. Evaluate 704 != 18, drop this branch.\n     |- Try 671 - 33 = 638. Evaluate 638 != 18, drop this branch.\n     |- Try 671 * 33 = 22143. 22143 exceeds the maximum intermediate result, drop this branch.\n     |- Try 671 \/ 33 = 20.3. 20.3 is a decimal, drop this branch.\n    |- Try 651 - 20 = 631. Add 631 to the number set. Current number set: [631, 33], target: 18, just two numbers left.\n     |- Try 631 + 33 = 664. Evaluate 664 != 18, drop this branch.\n     |- Try 631 - 33 = 598. Evaluate 598 != 18, drop this branch.\n     |- Try 631 * 33 = 20823. 20823 exceeds the maximum intermediate result, drop this branch.\n     |- Try 631 \/ 33 = 19.1. 19.1 is a decimal, drop this branch.\n    |- Try 651 * 20 = 13020. 13020 exceeds the maximum intermediate result, drop this branch.\n    |- Try 651 \/ 20 = 32.5. 32.5 is a decimal, drop this branch.\n   |- Pick two numbers (651, 33) (numbers left: [20]). Try possible operations.\n    |- Try 651 + 33 = 684. Add 684 to the number set. Current number set: [684, 20], target: 18, just two numbers left.\n     |- Try 684 + 20 = 704. Evaluate 704 != 18, drop this branch.\n     |- Try 684 - 20 = 664. Evaluate 664 != 18, drop this branch.\n     |- Try 684 * 20 = 13680. 13680 exceeds the maximum intermediate result, drop this branch.\n     |- Try 684 \/ 20 = 34.2. 34.2 is a decimal, drop this branch.\n    |- Try 651 - 33 = 618. Add 618 to the number set. Current number set: [618, 20], target: 18, just two numbers left.\n     |- Try 618 + 20 = 638. Evaluate 638 != 18, drop this branch.\n     |- Try 618 - 20 = 598. Evaluate 598 != 18, drop this branch.\n     |- Try 618 * 20 = 12360. 12360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 618 \/ 20 = 30.9. 30.9 is a decimal, drop this branch.\n    |- Try 651 * 33 = 21483. 21483 exceeds the maximum intermediate result, drop this branch.\n    |- Try 651 \/ 33 = 19.7. 19.7 is a decimal, drop this branch.\n   |- Pick two numbers (20, 33) (numbers left: [651]). Try possible operations.\n    |- Try 33 + 20 = 53. Add 53 to the number set. Current number set: [53, 651], target: 18, just two numbers left.\n     |- Try 651 + 53 = 704. Evaluate 704 != 18, drop this branch.\n     |- Try 651 - 53 = 598. Evaluate 598 != 18, drop this branch.\n     |- Try 651 * 53 = 34503. 34503 exceeds the maximum intermediate result, drop this branch.\n     |- Try 651 \/ 53 = 12.3. 12.3 is a decimal, drop this branch.\n    |- Try 33 - 20 = 13. Add 13 to the number set. Current number set: [13, 651], target: 18, just two numbers left.\n     |- Try 651 + 13 = 664. Evaluate 664 != 18, drop this branch.\n     |- Try 651 - 13 = 638. Evaluate 638 != 18, drop this branch.\n     |- Try 651 * 13 = 8463. 8463 exceeds the maximum intermediate result, drop this branch.\n     |- Try 651 \/ 13 = 50.1. 50.1 is a decimal, drop this branch.\n    |- Try 33 * 20 = 660. Add 660 to the number set. Current number set: [660, 651], target: 18, just two numbers left.\n     |- Try 660 + 651 = 1311. Evaluate 1311 != 18, drop this branch.\n     |- Try 660 - 651 = 9. Evaluate 9 != 18, drop this branch.\n     |- Try 660 * 651 = 429660. 429660 exceeds the maximum intermediate result, drop this branch.\n     |- Try 660 \/ 651 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 33 \/ 20 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 31 \/ 21 = 1.5. 1.5 is a decimal, drop this branch.\n |- Pick two numbers (31, 20) (numbers left: [21, 33]). Try possible operations.\n  |- Try 31 + 20 = 51. Add 51 to the number set. Current number set: [51, 21, 33], target: 18. Options for choosing two numbers: [(51, 21), (51, 33), (21, 33)].\n   |- Pick two numbers (51, 21) (numbers left: [33]). Try possible operations.\n    |- Try 51 + 21 = 72. Add 72 to the number set. Current number set: [72, 33], target: 18, just two numbers left.\n     |- Try 72 + 33 = 105. Evaluate 105 != 18, drop this branch.\n     |- Try 72 - 33 = 39. Evaluate 39 != 18, drop this branch.\n     |- Try 72 * 33 = 2376. 2376 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 33 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 51 - 21 = 30. Add 30 to the number set. Current number set: [30, 33], target: 18, just two numbers left.\n     |- Try 33 + 30 = 63. Evaluate 63 != 18, drop this branch.\n     |- Try 33 - 30 = 3. Evaluate 3 != 18, drop this branch.\n     |- Try 33 * 30 = 990. Evaluate 990 != 18, drop this branch.\n     |- Try 33 \/ 30 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 51 * 21 = 1071. Add 1071 to the number set. Current number set: [1071, 33], target: 18, just two numbers left.\n     |- Try 1071 + 33 = 1104. Evaluate 1104 != 18, drop this branch.\n     |- Try 1071 - 33 = 1038. Evaluate 1038 != 18, drop this branch.\n     |- Try 1071 * 33 = 35343. 35343 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1071 \/ 33 = 32.5. 32.5 is a decimal, drop this branch.\n    |- Try 51 \/ 21 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (51, 33) (numbers left: [21]). Try possible operations.\n    |- Try 51 + 33 = 84. Add 84 to the number set. Current number set: [84, 21], target: 18, just two numbers left.\n     |- Try 84 + 21 = 105. Evaluate 105 != 18, drop this branch.\n     |- Try 84 - 21 = 63. Evaluate 63 != 18, drop this branch.\n     |- Try 84 * 21 = 1764. Evaluate 1764 != 18, drop this branch.\n     |- Try 84 \/ 21 = 4. Evaluate 4 != 18, drop this branch.\n    |- Try 51 - 33 = 18. Add 18 to the number set. Current number set: [18, 21], target: 18, just two numbers left.\n     |- Try 21 + 18 = 39. Evaluate 39 != 18, drop this branch.\n     |- Try 21 - 18 = 3. Evaluate 3 != 18, drop this branch.\n     |- Try 21 * 18 = 378. Evaluate 378 != 18, drop this branch.\n     |- Try 21 \/ 18 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 51 * 33 = 1683. Add 1683 to the number set. Current number set: [1683, 21], target: 18, just two numbers left.\n     |- Try 1683 + 21 = 1704. Evaluate 1704 != 18, drop this branch.\n     |- Try 1683 - 21 = 1662. Evaluate 1662 != 18, drop this branch.\n     |- Try 1683 * 21 = 35343. 35343 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1683 \/ 21 = 80.1. 80.1 is a decimal, drop this branch.\n    |- Try 51 \/ 33 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (21, 33) (numbers left: [51]). Try possible operations.\n    |- Try 33 + 21 = 54. Add 54 to the number set. Current number set: [54, 51], target: 18, just two numbers left.\n     |- Try 54 + 51 = 105. Evaluate 105 != 18, drop this branch.\n     |- Try 54 - 51 = 3. Evaluate 3 != 18, drop this branch.\n     |- Try 54 * 51 = 2754. 2754 exceeds the maximum intermediate result, drop this branch.\n     |- Try 54 \/ 51 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 33 - 21 = 12. Add 12 to the number set. Current number set: [12, 51], target: 18, just two numbers left.\n     |- Try 51 + 12 = 63. Evaluate 63 != 18, drop this branch.\n     |- Try 51 - 12 = 39. Evaluate 39 != 18, drop this branch.\n     |- Try 51 * 12 = 612. Evaluate 612 != 18, drop this branch.\n     |- Try 51 \/ 12 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 33 * 21 = 693. Add 693 to the number set. Current number set: [693, 51], target: 18, just two numbers left.\n     |- Try 693 + 51 = 744. Evaluate 744 != 18, drop this branch.\n     |- Try 693 - 51 = 642. Evaluate 642 != 18, drop this branch.\n     |- Try 693 * 51 = 35343. 35343 exceeds the maximum intermediate result, drop this branch.\n     |- Try 693 \/ 51 = 13.6. 13.6 is a decimal, drop this branch.\n    |- Try 33 \/ 21 = 1.6. 1.6 is a decimal, drop this branch.\n  |- Try 31 - 20 = 11. Add 11 to the number set. Current number set: [11, 21, 33], target: 18. Options for choosing two numbers: [(11, 21), (11, 33), (21, 33)].\n   |- Pick two numbers (11, 21) (numbers left: [33]). Try possible operations.\n    |- Try 21 + 11 = 32. Add 32 to the number set. Current number set: [32, 33], target: 18, just two numbers left.\n     |- Try 33 + 32 = 65. Evaluate 65 != 18, drop this branch.\n     |- Try 33 - 32 = 1. Evaluate 1 != 18, drop this branch.\n     |- Try 33 * 32 = 1056. Evaluate 1056 != 18, drop this branch.\n     |- Try 33 \/ 32 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 21 - 11 = 10. Add 10 to the number set. Current number set: [10, 33], target: 18, just two numbers left.\n     |- Try 33 + 10 = 43. Evaluate 43 != 18, drop this branch.\n     |- Try 33 - 10 = 23. Evaluate 23 != 18, drop this branch.\n     |- Try 33 * 10 = 330. Evaluate 330 != 18, drop this branch.\n     |- Try 33 \/ 10 = 3.3. 3.3 is a decimal, drop this branch.\n    |- Try 21 * 11 = 231. Add 231 to the number set. Current number set: [231, 33], target: 18, just two numbers left.\n     |- Try 231 + 33 = 264. Evaluate 264 != 18, drop this branch.\n     |- Try 231 - 33 = 198. Evaluate 198 != 18, drop this branch.\n     |- Try 231 * 33 = 7623. 7623 exceeds the maximum intermediate result, drop this branch.\n     |- Try 231 \/ 33 = 7. Evaluate 7 != 18, drop this branch.\n    |- Try 21 \/ 11 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (11, 33) (numbers left: [21]). Try possible operations.\n    |- Try 33 + 11 = 44. Add 44 to the number set. Current number set: [44, 21], target: 18, just two numbers left.\n     |- Try 44 + 21 = 65. Evaluate 65 != 18, drop this branch.\n     |- Try 44 - 21 = 23. Evaluate 23 != 18, drop this branch.\n     |- Try 44 * 21 = 924. Evaluate 924 != 18, drop this branch.\n     |- Try 44 \/ 21 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 33 - 11 = 22. Add 22 to the number set. Current number set: [22, 21], target: 18, just two numbers left.\n     |- Try 22 + 21 = 43. Evaluate 43 != 18, drop this branch.\n     |- Try 22 - 21 = 1. Evaluate 1 != 18, drop this branch.\n     |- Try 22 * 21 = 462. Evaluate 462 != 18, drop this branch.\n     |- Try 22 \/ 21 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 33 * 11 = 363. Add 363 to the number set. Current number set: [363, 21], target: 18, just two numbers left.\n     |- Try 363 + 21 = 384. Evaluate 384 != 18, drop this branch.\n     |- Try 363 - 21 = 342. Evaluate 342 != 18, drop this branch.\n     |- Try 363 * 21 = 7623. 7623 exceeds the maximum intermediate result, drop this branch.\n     |- Try 363 \/ 21 = 17.3. 17.3 is a decimal, drop this branch.\n    |- Try 33 \/ 11 = 3. Add 3 to the number set. Current number set: [3, 21], target: 18, just two numbers left.\n     |- Try 21 + 3 = 24. Evaluate 24 != 18, drop this branch.\n     |- Try 21 - 3 = 18. Evaluate 18 == 18, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 21 - 3 = 18\nThe step before: 33 \/ 11 = 3\nThe first step: 31 - 20 = 11\n\nOutput the solution in the required format:\n<Solution>\n31 - 20 = 11\n33 \/ 11 = 3\n21 - 3 = 18\n<\/Solution>\n","item":{"nums":[31,21,20,33],"solution":["31 - 20 = 11","33 \/ 11 = 3","21 - 3 = 18"],"target":18}}
+{"instance_id":"countdown_8k_190","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [7, 3, 24, 2]\nTarget: 11","reference_output":"# Search Procedure\nInitial number set: [7, 3, 24, 2], target: 11. Options for choosing two numbers: [(7, 3), (7, 24), (7, 2), (3, 24), (3, 2), (24, 2)].\n |- Pick two numbers (7, 3) (numbers left: [24, 2]). Try possible operations.\n  |- Try 7 + 3 = 10. Add 10 to the number set. Current number set: [10, 24, 2], target: 11. Options for choosing two numbers: [(10, 24), (10, 2), (24, 2)].\n   |- Pick two numbers (10, 24) (numbers left: [2]). Try possible operations.\n    |- Try 24 + 10 = 34. Add 34 to the number set. Current number set: [34, 2], target: 11, just two numbers left.\n     |- Try 34 + 2 = 36. Evaluate 36 != 11, drop this branch.\n     |- Try 34 - 2 = 32. Evaluate 32 != 11, drop this branch.\n     |- Try 34 * 2 = 68. Evaluate 68 != 11, drop this branch.\n     |- Try 34 \/ 2 = 17. Evaluate 17 != 11, drop this branch.\n    |- Try 24 - 10 = 14. Add 14 to the number set. Current number set: [14, 2], target: 11, just two numbers left.\n     |- Try 14 + 2 = 16. Evaluate 16 != 11, drop this branch.\n     |- Try 14 - 2 = 12. Evaluate 12 != 11, drop this branch.\n     |- Try 14 * 2 = 28. Evaluate 28 != 11, drop this branch.\n     |- Try 14 \/ 2 = 7. Evaluate 7 != 11, drop this branch.\n    |- Try 24 * 10 = 240. Add 240 to the number set. Current number set: [240, 2], target: 11, just two numbers left.\n     |- Try 240 + 2 = 242. Evaluate 242 != 11, drop this branch.\n     |- Try 240 - 2 = 238. Evaluate 238 != 11, drop this branch.\n     |- Try 240 * 2 = 480. Evaluate 480 != 11, drop this branch.\n     |- Try 240 \/ 2 = 120. Evaluate 120 != 11, drop this branch.\n    |- Try 24 \/ 10 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (10, 2) (numbers left: [24]). Try possible operations.\n    |- Try 10 + 2 = 12. Add 12 to the number set. Current number set: [12, 24], target: 11, just two numbers left.\n     |- Try 24 + 12 = 36. Evaluate 36 != 11, drop this branch.\n     |- Try 24 - 12 = 12. Evaluate 12 != 11, drop this branch.\n     |- Try 24 * 12 = 288. Evaluate 288 != 11, drop this branch.\n     |- Try 24 \/ 12 = 2. Evaluate 2 != 11, drop this branch.\n    |- Try 10 - 2 = 8. Add 8 to the number set. Current number set: [8, 24], target: 11, just two numbers left.\n     |- Try 24 + 8 = 32. Evaluate 32 != 11, drop this branch.\n     |- Try 24 - 8 = 16. Evaluate 16 != 11, drop this branch.\n     |- Try 24 * 8 = 192. Evaluate 192 != 11, drop this branch.\n     |- Try 24 \/ 8 = 3. Evaluate 3 != 11, drop this branch.\n    |- Try 10 * 2 = 20. Add 20 to the number set. Current number set: [20, 24], target: 11, just two numbers left.\n     |- Try 24 + 20 = 44. Evaluate 44 != 11, drop this branch.\n     |- Try 24 - 20 = 4. Evaluate 4 != 11, drop this branch.\n     |- Try 24 * 20 = 480. Evaluate 480 != 11, drop this branch.\n     |- Try 24 \/ 20 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 10 \/ 2 = 5. Add 5 to the number set. Current number set: [5, 24], target: 11, just two numbers left.\n     |- Try 24 + 5 = 29. Evaluate 29 != 11, drop this branch.\n     |- Try 24 - 5 = 19. Evaluate 19 != 11, drop this branch.\n     |- Try 24 * 5 = 120. Evaluate 120 != 11, drop this branch.\n     |- Try 24 \/ 5 = 4.8. 4.8 is a decimal, drop this branch.\n   |- Pick two numbers (24, 2) (numbers left: [10]). Try possible operations.\n    |- Try 24 + 2 = 26. Add 26 to the number set. Current number set: [26, 10], target: 11, just two numbers left.\n     |- Try 26 + 10 = 36. Evaluate 36 != 11, drop this branch.\n     |- Try 26 - 10 = 16. Evaluate 16 != 11, drop this branch.\n     |- Try 26 * 10 = 260. Evaluate 260 != 11, drop this branch.\n     |- Try 26 \/ 10 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 24 - 2 = 22. Add 22 to the number set. Current number set: [22, 10], target: 11, just two numbers left.\n     |- Try 22 + 10 = 32. Evaluate 32 != 11, drop this branch.\n     |- Try 22 - 10 = 12. Evaluate 12 != 11, drop this branch.\n     |- Try 22 * 10 = 220. Evaluate 220 != 11, drop this branch.\n     |- Try 22 \/ 10 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 24 * 2 = 48. Add 48 to the number set. Current number set: [48, 10], target: 11, just two numbers left.\n     |- Try 48 + 10 = 58. Evaluate 58 != 11, drop this branch.\n     |- Try 48 - 10 = 38. Evaluate 38 != 11, drop this branch.\n     |- Try 48 * 10 = 480. Evaluate 480 != 11, drop this branch.\n     |- Try 48 \/ 10 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 24 \/ 2 = 12. Add 12 to the number set. Current number set: [12, 10], target: 11, just two numbers left.\n     |- Try 12 + 10 = 22. Evaluate 22 != 11, drop this branch.\n     |- Try 12 - 10 = 2. Evaluate 2 != 11, drop this branch.\n     |- Try 12 * 10 = 120. Evaluate 120 != 11, drop this branch.\n     |- Try 12 \/ 10 = 1.2. 1.2 is a decimal, drop this branch.\n  |- Try 7 - 3 = 4. Add 4 to the number set. Current number set: [4, 24, 2], target: 11. Options for choosing two numbers: [(4, 24), (4, 2), (24, 2)].\n   |- Pick two numbers (4, 24) (numbers left: [2]). Try possible operations.\n    |- Try 24 + 4 = 28. Add 28 to the number set. Current number set: [28, 2], target: 11, just two numbers left.\n     |- Try 28 + 2 = 30. Evaluate 30 != 11, drop this branch.\n     |- Try 28 - 2 = 26. Evaluate 26 != 11, drop this branch.\n     |- Try 28 * 2 = 56. Evaluate 56 != 11, drop this branch.\n     |- Try 28 \/ 2 = 14. Evaluate 14 != 11, drop this branch.\n    |- Try 24 - 4 = 20. Add 20 to the number set. Current number set: [20, 2], target: 11, just two numbers left.\n     |- Try 20 + 2 = 22. Evaluate 22 != 11, drop this branch.\n     |- Try 20 - 2 = 18. Evaluate 18 != 11, drop this branch.\n     |- Try 20 * 2 = 40. Evaluate 40 != 11, drop this branch.\n     |- Try 20 \/ 2 = 10. Evaluate 10 != 11, drop this branch.\n    |- Try 24 * 4 = 96. Add 96 to the number set. Current number set: [96, 2], target: 11, just two numbers left.\n     |- Try 96 + 2 = 98. Evaluate 98 != 11, drop this branch.\n     |- Try 96 - 2 = 94. Evaluate 94 != 11, drop this branch.\n     |- Try 96 * 2 = 192. Evaluate 192 != 11, drop this branch.\n     |- Try 96 \/ 2 = 48. Evaluate 48 != 11, drop this branch.\n    |- Try 24 \/ 4 = 6. Add 6 to the number set. Current number set: [6, 2], target: 11, just two numbers left.\n     |- Try 6 + 2 = 8. Evaluate 8 != 11, drop this branch.\n     |- Try 6 - 2 = 4. Evaluate 4 != 11, drop this branch.\n     |- Try 6 * 2 = 12. Evaluate 12 != 11, drop this branch.\n     |- Try 6 \/ 2 = 3. Evaluate 3 != 11, drop this branch.\n   |- Pick two numbers (4, 2) (numbers left: [24]). Try possible operations.\n    |- Try 4 + 2 = 6. Add 6 to the number set. Current number set: [6, 24], target: 11, just two numbers left.\n     |- Try 24 + 6 = 30. Evaluate 30 != 11, drop this branch.\n     |- Try 24 - 6 = 18. Evaluate 18 != 11, drop this branch.\n     |- Try 24 * 6 = 144. Evaluate 144 != 11, drop this branch.\n     |- Try 24 \/ 6 = 4. Evaluate 4 != 11, drop this branch.\n    |- Try 4 - 2 = 2. Add 2 to the number set. Current number set: [2, 24], target: 11, just two numbers left.\n     |- Try 24 + 2 = 26. Evaluate 26 != 11, drop this branch.\n     |- Try 24 - 2 = 22. Evaluate 22 != 11, drop this branch.\n     |- Try 24 * 2 = 48. Evaluate 48 != 11, drop this branch.\n     |- Try 24 \/ 2 = 12. Evaluate 12 != 11, drop this branch.\n    |- Try 4 * 2 = 8. Add 8 to the number set. Current number set: [8, 24], target: 11, just two numbers left.\n     |- Try 24 + 8 = 32. Evaluate 32 != 11, drop this branch.\n     |- Try 24 - 8 = 16. Evaluate 16 != 11, drop this branch.\n     |- Try 24 * 8 = 192. Evaluate 192 != 11, drop this branch.\n     |- Try 24 \/ 8 = 3. Evaluate 3 != 11, drop this branch.\n    |- Try 4 \/ 2 = 2. Add 2 to the number set. Current number set: [2, 24], target: 11, just two numbers left.\n     |- Try 24 + 2 = 26. Evaluate 26 != 11, drop this branch.\n     |- Try 24 - 2 = 22. Evaluate 22 != 11, drop this branch.\n     |- Try 24 * 2 = 48. Evaluate 48 != 11, drop this branch.\n     |- Try 24 \/ 2 = 12. Evaluate 12 != 11, drop this branch.\n   |- Pick two numbers (24, 2) (numbers left: [4]). Try possible operations.\n    |- Try 24 + 2 = 26. Add 26 to the number set. Current number set: [26, 4], target: 11, just two numbers left.\n     |- Try 26 + 4 = 30. Evaluate 30 != 11, drop this branch.\n     |- Try 26 - 4 = 22. Evaluate 22 != 11, drop this branch.\n     |- Try 26 * 4 = 104. Evaluate 104 != 11, drop this branch.\n     |- Try 26 \/ 4 = 6.5. 6.5 is a decimal, drop this branch.\n    |- Try 24 - 2 = 22. Add 22 to the number set. Current number set: [22, 4], target: 11, just two numbers left.\n     |- Try 22 + 4 = 26. Evaluate 26 != 11, drop this branch.\n     |- Try 22 - 4 = 18. Evaluate 18 != 11, drop this branch.\n     |- Try 22 * 4 = 88. Evaluate 88 != 11, drop this branch.\n     |- Try 22 \/ 4 = 5.5. 5.5 is a decimal, drop this branch.\n    |- Try 24 * 2 = 48. Add 48 to the number set. Current number set: [48, 4], target: 11, just two numbers left.\n     |- Try 48 + 4 = 52. Evaluate 52 != 11, drop this branch.\n     |- Try 48 - 4 = 44. Evaluate 44 != 11, drop this branch.\n     |- Try 48 * 4 = 192. Evaluate 192 != 11, drop this branch.\n     |- Try 48 \/ 4 = 12. Evaluate 12 != 11, drop this branch.\n    |- Try 24 \/ 2 = 12. Add 12 to the number set. Current number set: [12, 4], target: 11, just two numbers left.\n     |- Try 12 + 4 = 16. Evaluate 16 != 11, drop this branch.\n     |- Try 12 - 4 = 8. Evaluate 8 != 11, drop this branch.\n     |- Try 12 * 4 = 48. Evaluate 48 != 11, drop this branch.\n     |- Try 12 \/ 4 = 3. Evaluate 3 != 11, drop this branch.\n  |- Try 7 * 3 = 21. Add 21 to the number set. Current number set: [21, 24, 2], target: 11. Options for choosing two numbers: [(21, 24), (21, 2), (24, 2)].\n   |- Pick two numbers (21, 24) (numbers left: [2]). Try possible operations.\n    |- Try 24 + 21 = 45. Add 45 to the number set. Current number set: [45, 2], target: 11, just two numbers left.\n     |- Try 45 + 2 = 47. Evaluate 47 != 11, drop this branch.\n     |- Try 45 - 2 = 43. Evaluate 43 != 11, drop this branch.\n     |- Try 45 * 2 = 90. Evaluate 90 != 11, drop this branch.\n     |- Try 45 \/ 2 = 22.5. 22.5 is a decimal, drop this branch.\n    |- Try 24 - 21 = 3. Add 3 to the number set. Current number set: [3, 2], target: 11, just two numbers left.\n     |- Try 3 + 2 = 5. Evaluate 5 != 11, drop this branch.\n     |- Try 3 - 2 = 1. Evaluate 1 != 11, drop this branch.\n     |- Try 3 * 2 = 6. Evaluate 6 != 11, drop this branch.\n     |- Try 3 \/ 2 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 24 * 21 = 504. Add 504 to the number set. Current number set: [504, 2], target: 11, just two numbers left.\n     |- Try 504 + 2 = 506. Evaluate 506 != 11, drop this branch.\n     |- Try 504 - 2 = 502. Evaluate 502 != 11, drop this branch.\n     |- Try 504 * 2 = 1008. Evaluate 1008 != 11, drop this branch.\n     |- Try 504 \/ 2 = 252. Evaluate 252 != 11, drop this branch.\n    |- Try 24 \/ 21 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (21, 2) (numbers left: [24]). Try possible operations.\n    |- Try 21 + 2 = 23. Add 23 to the number set. Current number set: [23, 24], target: 11, just two numbers left.\n     |- Try 24 + 23 = 47. Evaluate 47 != 11, drop this branch.\n     |- Try 24 - 23 = 1. Evaluate 1 != 11, drop this branch.\n     |- Try 24 * 23 = 552. Evaluate 552 != 11, drop this branch.\n     |- Try 24 \/ 23 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 21 - 2 = 19. Add 19 to the number set. Current number set: [19, 24], target: 11, just two numbers left.\n     |- Try 24 + 19 = 43. Evaluate 43 != 11, drop this branch.\n     |- Try 24 - 19 = 5. Evaluate 5 != 11, drop this branch.\n     |- Try 24 * 19 = 456. Evaluate 456 != 11, drop this branch.\n     |- Try 24 \/ 19 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 21 * 2 = 42. Add 42 to the number set. Current number set: [42, 24], target: 11, just two numbers left.\n     |- Try 42 + 24 = 66. Evaluate 66 != 11, drop this branch.\n     |- Try 42 - 24 = 18. Evaluate 18 != 11, drop this branch.\n     |- Try 42 * 24 = 1008. Evaluate 1008 != 11, drop this branch.\n     |- Try 42 \/ 24 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 21 \/ 2 = 10.5. 10.5 is a decimal, drop this branch.\n   |- Pick two numbers (24, 2) (numbers left: [21]). Try possible operations.\n    |- Try 24 + 2 = 26. Add 26 to the number set. Current number set: [26, 21], target: 11, just two numbers left.\n     |- Try 26 + 21 = 47. Evaluate 47 != 11, drop this branch.\n     |- Try 26 - 21 = 5. Evaluate 5 != 11, drop this branch.\n     |- Try 26 * 21 = 546. Evaluate 546 != 11, drop this branch.\n     |- Try 26 \/ 21 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 24 - 2 = 22. Add 22 to the number set. Current number set: [22, 21], target: 11, just two numbers left.\n     |- Try 22 + 21 = 43. Evaluate 43 != 11, drop this branch.\n     |- Try 22 - 21 = 1. Evaluate 1 != 11, drop this branch.\n     |- Try 22 * 21 = 462. Evaluate 462 != 11, drop this branch.\n     |- Try 22 \/ 21 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 24 * 2 = 48. Add 48 to the number set. Current number set: [48, 21], target: 11, just two numbers left.\n     |- Try 48 + 21 = 69. Evaluate 69 != 11, drop this branch.\n     |- Try 48 - 21 = 27. Evaluate 27 != 11, drop this branch.\n     |- Try 48 * 21 = 1008. Evaluate 1008 != 11, drop this branch.\n     |- Try 48 \/ 21 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 24 \/ 2 = 12. Add 12 to the number set. Current number set: [12, 21], target: 11, just two numbers left.\n     |- Try 21 + 12 = 33. Evaluate 33 != 11, drop this branch.\n     |- Try 21 - 12 = 9. Evaluate 9 != 11, drop this branch.\n     |- Try 21 * 12 = 252. Evaluate 252 != 11, drop this branch.\n     |- Try 21 \/ 12 = 1.8. 1.8 is a decimal, drop this branch.\n  |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n |- Pick two numbers (7, 24) (numbers left: [3, 2]). Try possible operations.\n  |- Try 24 + 7 = 31. Add 31 to the number set. Current number set: [31, 3, 2], target: 11. Options for choosing two numbers: [(31, 3), (31, 2), (3, 2)].\n   |- Pick two numbers (31, 3) (numbers left: [2]). Try possible operations.\n    |- Try 31 + 3 = 34. Add 34 to the number set. Current number set: [34, 2], target: 11, just two numbers left.\n     |- Try 34 + 2 = 36. Evaluate 36 != 11, drop this branch.\n     |- Try 34 - 2 = 32. Evaluate 32 != 11, drop this branch.\n     |- Try 34 * 2 = 68. Evaluate 68 != 11, drop this branch.\n     |- Try 34 \/ 2 = 17. Evaluate 17 != 11, drop this branch.\n    |- Try 31 - 3 = 28. Add 28 to the number set. Current number set: [28, 2], target: 11, just two numbers left.\n     |- Try 28 + 2 = 30. Evaluate 30 != 11, drop this branch.\n     |- Try 28 - 2 = 26. Evaluate 26 != 11, drop this branch.\n     |- Try 28 * 2 = 56. Evaluate 56 != 11, drop this branch.\n     |- Try 28 \/ 2 = 14. Evaluate 14 != 11, drop this branch.\n    |- Try 31 * 3 = 93. Add 93 to the number set. Current number set: [93, 2], target: 11, just two numbers left.\n     |- Try 93 + 2 = 95. Evaluate 95 != 11, drop this branch.\n     |- Try 93 - 2 = 91. Evaluate 91 != 11, drop this branch.\n     |- Try 93 * 2 = 186. Evaluate 186 != 11, drop this branch.\n     |- Try 93 \/ 2 = 46.5. 46.5 is a decimal, drop this branch.\n    |- Try 31 \/ 3 = 10.3. 10.3 is a decimal, drop this branch.\n   |- Pick two numbers (31, 2) (numbers left: [3]). Try possible operations.\n    |- Try 31 + 2 = 33. Add 33 to the number set. Current number set: [33, 3], target: 11, just two numbers left.\n     |- Try 33 + 3 = 36. Evaluate 36 != 11, drop this branch.\n     |- Try 33 - 3 = 30. Evaluate 30 != 11, drop this branch.\n     |- Try 33 * 3 = 99. Evaluate 99 != 11, drop this branch.\n     |- Try 33 \/ 3 = 11. Evaluate 11 == 11, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 33 \/ 3 = 11\nThe step before: 31 + 2 = 33\nThe first step: 24 + 7 = 31\n\nOutput the solution in the required format:\n<Solution>\n24 + 7 = 31\n31 + 2 = 33\n33 \/ 3 = 11\n<\/Solution>\n","item":{"nums":[7,3,24,2],"solution":["24 + 7 = 31","31 + 2 = 33","33 \/ 3 = 11"],"target":11}}
+{"instance_id":"countdown_8k_191","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [6, 12, 29, 3]\nTarget: 30","reference_output":"# Search Procedure\nInitial number set: [6, 12, 29, 3], target: 30. Options for choosing two numbers: [(6, 12), (6, 29), (6, 3), (12, 29), (12, 3), (29, 3)].\n |- Pick two numbers (6, 12) (numbers left: [29, 3]). Try possible operations.\n  |- Try 12 + 6 = 18. Add 18 to the number set. Current number set: [18, 29, 3], target: 30. Options for choosing two numbers: [(18, 29), (18, 3), (29, 3)].\n   |- Pick two numbers (18, 29) (numbers left: [3]). Try possible operations.\n    |- Try 29 + 18 = 47. Add 47 to the number set. Current number set: [47, 3], target: 30, just two numbers left.\n     |- Try 47 + 3 = 50. Evaluate 50 != 30, drop this branch.\n     |- Try 47 - 3 = 44. Evaluate 44 != 30, drop this branch.\n     |- Try 47 * 3 = 141. Evaluate 141 != 30, drop this branch.\n     |- Try 47 \/ 3 = 15.7. 15.7 is a decimal, drop this branch.\n    |- Try 29 - 18 = 11. Add 11 to the number set. Current number set: [11, 3], target: 30, just two numbers left.\n     |- Try 11 + 3 = 14. Evaluate 14 != 30, drop this branch.\n     |- Try 11 - 3 = 8. Evaluate 8 != 30, drop this branch.\n     |- Try 11 * 3 = 33. Evaluate 33 != 30, drop this branch.\n     |- Try 11 \/ 3 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 29 * 18 = 522. Add 522 to the number set. Current number set: [522, 3], target: 30, just two numbers left.\n     |- Try 522 + 3 = 525. Evaluate 525 != 30, drop this branch.\n     |- Try 522 - 3 = 519. Evaluate 519 != 30, drop this branch.\n     |- Try 522 * 3 = 1566. Evaluate 1566 != 30, drop this branch.\n     |- Try 522 \/ 3 = 174. Evaluate 174 != 30, drop this branch.\n    |- Try 29 \/ 18 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (18, 3) (numbers left: [29]). Try possible operations.\n    |- Try 18 + 3 = 21. Add 21 to the number set. Current number set: [21, 29], target: 30, just two numbers left.\n     |- Try 29 + 21 = 50. Evaluate 50 != 30, drop this branch.\n     |- Try 29 - 21 = 8. Evaluate 8 != 30, drop this branch.\n     |- Try 29 * 21 = 609. Evaluate 609 != 30, drop this branch.\n     |- Try 29 \/ 21 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 18 - 3 = 15. Add 15 to the number set. Current number set: [15, 29], target: 30, just two numbers left.\n     |- Try 29 + 15 = 44. Evaluate 44 != 30, drop this branch.\n     |- Try 29 - 15 = 14. Evaluate 14 != 30, drop this branch.\n     |- Try 29 * 15 = 435. Evaluate 435 != 30, drop this branch.\n     |- Try 29 \/ 15 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 18 * 3 = 54. Add 54 to the number set. Current number set: [54, 29], target: 30, just two numbers left.\n     |- Try 54 + 29 = 83. Evaluate 83 != 30, drop this branch.\n     |- Try 54 - 29 = 25. Evaluate 25 != 30, drop this branch.\n     |- Try 54 * 29 = 1566. Evaluate 1566 != 30, drop this branch.\n     |- Try 54 \/ 29 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 18 \/ 3 = 6. Add 6 to the number set. Current number set: [6, 29], target: 30, just two numbers left.\n     |- Try 29 + 6 = 35. Evaluate 35 != 30, drop this branch.\n     |- Try 29 - 6 = 23. Evaluate 23 != 30, drop this branch.\n     |- Try 29 * 6 = 174. Evaluate 174 != 30, drop this branch.\n     |- Try 29 \/ 6 = 4.8. 4.8 is a decimal, drop this branch.\n   |- Pick two numbers (29, 3) (numbers left: [18]). Try possible operations.\n    |- Try 29 + 3 = 32. Add 32 to the number set. Current number set: [32, 18], target: 30, just two numbers left.\n     |- Try 32 + 18 = 50. Evaluate 50 != 30, drop this branch.\n     |- Try 32 - 18 = 14. Evaluate 14 != 30, drop this branch.\n     |- Try 32 * 18 = 576. Evaluate 576 != 30, drop this branch.\n     |- Try 32 \/ 18 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 29 - 3 = 26. Add 26 to the number set. Current number set: [26, 18], target: 30, just two numbers left.\n     |- Try 26 + 18 = 44. Evaluate 44 != 30, drop this branch.\n     |- Try 26 - 18 = 8. Evaluate 8 != 30, drop this branch.\n     |- Try 26 * 18 = 468. Evaluate 468 != 30, drop this branch.\n     |- Try 26 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 29 * 3 = 87. Add 87 to the number set. Current number set: [87, 18], target: 30, just two numbers left.\n     |- Try 87 + 18 = 105. Evaluate 105 != 30, drop this branch.\n     |- Try 87 - 18 = 69. Evaluate 69 != 30, drop this branch.\n     |- Try 87 * 18 = 1566. Evaluate 1566 != 30, drop this branch.\n     |- Try 87 \/ 18 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 29 \/ 3 = 9.7. 9.7 is a decimal, drop this branch.\n  |- Try 12 - 6 = 6. Add 6 to the number set. Current number set: [6, 29, 3], target: 30. Options for choosing two numbers: [(6, 29), (6, 3), (29, 3)].\n   |- Pick two numbers (6, 29) (numbers left: [3]). Try possible operations.\n    |- Try 29 + 6 = 35. Add 35 to the number set. Current number set: [35, 3], target: 30, just two numbers left.\n     |- Try 35 + 3 = 38. Evaluate 38 != 30, drop this branch.\n     |- Try 35 - 3 = 32. Evaluate 32 != 30, drop this branch.\n     |- Try 35 * 3 = 105. Evaluate 105 != 30, drop this branch.\n     |- Try 35 \/ 3 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 29 - 6 = 23. Add 23 to the number set. Current number set: [23, 3], target: 30, just two numbers left.\n     |- Try 23 + 3 = 26. Evaluate 26 != 30, drop this branch.\n     |- Try 23 - 3 = 20. Evaluate 20 != 30, drop this branch.\n     |- Try 23 * 3 = 69. Evaluate 69 != 30, drop this branch.\n     |- Try 23 \/ 3 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 29 * 6 = 174. Add 174 to the number set. Current number set: [174, 3], target: 30, just two numbers left.\n     |- Try 174 + 3 = 177. Evaluate 177 != 30, drop this branch.\n     |- Try 174 - 3 = 171. Evaluate 171 != 30, drop this branch.\n     |- Try 174 * 3 = 522. Evaluate 522 != 30, drop this branch.\n     |- Try 174 \/ 3 = 58. Evaluate 58 != 30, drop this branch.\n    |- Try 29 \/ 6 = 4.8. 4.8 is a decimal, drop this branch.\n   |- Pick two numbers (6, 3) (numbers left: [29]). Try possible operations.\n    |- Try 6 + 3 = 9. Add 9 to the number set. Current number set: [9, 29], target: 30, just two numbers left.\n     |- Try 29 + 9 = 38. Evaluate 38 != 30, drop this branch.\n     |- Try 29 - 9 = 20. Evaluate 20 != 30, drop this branch.\n     |- Try 29 * 9 = 261. Evaluate 261 != 30, drop this branch.\n     |- Try 29 \/ 9 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 6 - 3 = 3. Add 3 to the number set. Current number set: [3, 29], target: 30, just two numbers left.\n     |- Try 29 + 3 = 32. Evaluate 32 != 30, drop this branch.\n     |- Try 29 - 3 = 26. Evaluate 26 != 30, drop this branch.\n     |- Try 29 * 3 = 87. Evaluate 87 != 30, drop this branch.\n     |- Try 29 \/ 3 = 9.7. 9.7 is a decimal, drop this branch.\n    |- Try 6 * 3 = 18. Add 18 to the number set. Current number set: [18, 29], target: 30, just two numbers left.\n     |- Try 29 + 18 = 47. Evaluate 47 != 30, drop this branch.\n     |- Try 29 - 18 = 11. Evaluate 11 != 30, drop this branch.\n     |- Try 29 * 18 = 522. Evaluate 522 != 30, drop this branch.\n     |- Try 29 \/ 18 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 6 \/ 3 = 2. Add 2 to the number set. Current number set: [2, 29], target: 30, just two numbers left.\n     |- Try 29 + 2 = 31. Evaluate 31 != 30, drop this branch.\n     |- Try 29 - 2 = 27. Evaluate 27 != 30, drop this branch.\n     |- Try 29 * 2 = 58. Evaluate 58 != 30, drop this branch.\n     |- Try 29 \/ 2 = 14.5. 14.5 is a decimal, drop this branch.\n   |- Pick two numbers (29, 3) (numbers left: [6]). Try possible operations.\n    |- Try 29 + 3 = 32. Add 32 to the number set. Current number set: [32, 6], target: 30, just two numbers left.\n     |- Try 32 + 6 = 38. Evaluate 38 != 30, drop this branch.\n     |- Try 32 - 6 = 26. Evaluate 26 != 30, drop this branch.\n     |- Try 32 * 6 = 192. Evaluate 192 != 30, drop this branch.\n     |- Try 32 \/ 6 = 5.3. 5.3 is a decimal, drop this branch.\n    |- Try 29 - 3 = 26. Add 26 to the number set. Current number set: [26, 6], target: 30, just two numbers left.\n     |- Try 26 + 6 = 32. Evaluate 32 != 30, drop this branch.\n     |- Try 26 - 6 = 20. Evaluate 20 != 30, drop this branch.\n     |- Try 26 * 6 = 156. Evaluate 156 != 30, drop this branch.\n     |- Try 26 \/ 6 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 29 * 3 = 87. Add 87 to the number set. Current number set: [87, 6], target: 30, just two numbers left.\n     |- Try 87 + 6 = 93. Evaluate 93 != 30, drop this branch.\n     |- Try 87 - 6 = 81. Evaluate 81 != 30, drop this branch.\n     |- Try 87 * 6 = 522. Evaluate 522 != 30, drop this branch.\n     |- Try 87 \/ 6 = 14.5. 14.5 is a decimal, drop this branch.\n    |- Try 29 \/ 3 = 9.7. 9.7 is a decimal, drop this branch.\n  |- Try 12 * 6 = 72. Add 72 to the number set. Current number set: [72, 29, 3], target: 30. Options for choosing two numbers: [(72, 29), (72, 3), (29, 3)].\n   |- Pick two numbers (72, 29) (numbers left: [3]). Try possible operations.\n    |- Try 72 + 29 = 101. Add 101 to the number set. Current number set: [101, 3], target: 30, just two numbers left.\n     |- Try 101 + 3 = 104. Evaluate 104 != 30, drop this branch.\n     |- Try 101 - 3 = 98. Evaluate 98 != 30, drop this branch.\n     |- Try 101 * 3 = 303. Evaluate 303 != 30, drop this branch.\n     |- Try 101 \/ 3 = 33.7. 33.7 is a decimal, drop this branch.\n    |- Try 72 - 29 = 43. Add 43 to the number set. Current number set: [43, 3], target: 30, just two numbers left.\n     |- Try 43 + 3 = 46. Evaluate 46 != 30, drop this branch.\n     |- Try 43 - 3 = 40. Evaluate 40 != 30, drop this branch.\n     |- Try 43 * 3 = 129. Evaluate 129 != 30, drop this branch.\n     |- Try 43 \/ 3 = 14.3. 14.3 is a decimal, drop this branch.\n    |- Try 72 * 29 = 2088. 2088 exceeds the maximum intermediate result, drop this branch.\n    |- Try 72 \/ 29 = 2.5. 2.5 is a decimal, drop this branch.\n   |- Pick two numbers (72, 3) (numbers left: [29]). Try possible operations.\n    |- Try 72 + 3 = 75. Add 75 to the number set. Current number set: [75, 29], target: 30, just two numbers left.\n     |- Try 75 + 29 = 104. Evaluate 104 != 30, drop this branch.\n     |- Try 75 - 29 = 46. Evaluate 46 != 30, drop this branch.\n     |- Try 75 * 29 = 2175. 2175 exceeds the maximum intermediate result, drop this branch.\n     |- Try 75 \/ 29 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 72 - 3 = 69. Add 69 to the number set. Current number set: [69, 29], target: 30, just two numbers left.\n     |- Try 69 + 29 = 98. Evaluate 98 != 30, drop this branch.\n     |- Try 69 - 29 = 40. Evaluate 40 != 30, drop this branch.\n     |- Try 69 * 29 = 2001. 2001 exceeds the maximum intermediate result, drop this branch.\n     |- Try 69 \/ 29 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 72 * 3 = 216. Add 216 to the number set. Current number set: [216, 29], target: 30, just two numbers left.\n     |- Try 216 + 29 = 245. Evaluate 245 != 30, drop this branch.\n     |- Try 216 - 29 = 187. Evaluate 187 != 30, drop this branch.\n     |- Try 216 * 29 = 6264. 6264 exceeds the maximum intermediate result, drop this branch.\n     |- Try 216 \/ 29 = 7.4. 7.4 is a decimal, drop this branch.\n    |- Try 72 \/ 3 = 24. Add 24 to the number set. Current number set: [24, 29], target: 30, just two numbers left.\n     |- Try 29 + 24 = 53. Evaluate 53 != 30, drop this branch.\n     |- Try 29 - 24 = 5. Evaluate 5 != 30, drop this branch.\n     |- Try 29 * 24 = 696. Evaluate 696 != 30, drop this branch.\n     |- Try 29 \/ 24 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (29, 3) (numbers left: [72]). Try possible operations.\n    |- Try 29 + 3 = 32. Add 32 to the number set. Current number set: [32, 72], target: 30, just two numbers left.\n     |- Try 72 + 32 = 104. Evaluate 104 != 30, drop this branch.\n     |- Try 72 - 32 = 40. Evaluate 40 != 30, drop this branch.\n     |- Try 72 * 32 = 2304. 2304 exceeds the maximum intermediate result, drop this branch.\n     |- Try 72 \/ 32 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 29 - 3 = 26. Add 26 to the number set. Current number set: [26, 72], target: 30, just two numbers left.\n     |- Try 72 + 26 = 98. Evaluate 98 != 30, drop this branch.\n     |- Try 72 - 26 = 46. Evaluate 46 != 30, drop this branch.\n     |- Try 72 * 26 = 1872. Evaluate 1872 != 30, drop this branch.\n     |- Try 72 \/ 26 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 29 * 3 = 87. Add 87 to the number set. Current number set: [87, 72], target: 30, just two numbers left.\n     |- Try 87 + 72 = 159. Evaluate 159 != 30, drop this branch.\n     |- Try 87 - 72 = 15. Evaluate 15 != 30, drop this branch.\n     |- Try 87 * 72 = 6264. 6264 exceeds the maximum intermediate result, drop this branch.\n     |- Try 87 \/ 72 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 29 \/ 3 = 9.7. 9.7 is a decimal, drop this branch.\n  |- Try 12 \/ 6 = 2. Add 2 to the number set. Current number set: [2, 29, 3], target: 30. Options for choosing two numbers: [(2, 29), (2, 3), (29, 3)].\n   |- Pick two numbers (2, 29) (numbers left: [3]). Try possible operations.\n    |- Try 29 + 2 = 31. Add 31 to the number set. Current number set: [31, 3], target: 30, just two numbers left.\n     |- Try 31 + 3 = 34. Evaluate 34 != 30, drop this branch.\n     |- Try 31 - 3 = 28. Evaluate 28 != 30, drop this branch.\n     |- Try 31 * 3 = 93. Evaluate 93 != 30, drop this branch.\n     |- Try 31 \/ 3 = 10.3. 10.3 is a decimal, drop this branch.\n    |- Try 29 - 2 = 27. Add 27 to the number set. Current number set: [27, 3], target: 30, just two numbers left.\n     |- Try 27 + 3 = 30. Evaluate 30 == 30, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 27 + 3 = 30\nThe step before: 29 - 2 = 27\nThe first step: 12 \/ 6 = 2\n\nOutput the solution in the required format:\n<Solution>\n12 \/ 6 = 2\n29 - 2 = 27\n27 + 3 = 30\n<\/Solution>\n","item":{"nums":[6,12,29,3],"solution":["12 \/ 6 = 2","29 - 2 = 27","27 + 3 = 30"],"target":30}}
+{"instance_id":"countdown_8k_192","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [1, 14, 41, 24]\nTarget: 21","reference_output":"# Search Procedure\nInitial number set: [1, 14, 41, 24], target: 21. Options for choosing two numbers: [(1, 14), (1, 41), (1, 24), (14, 41), (14, 24), (41, 24)].\n |- Pick two numbers (1, 14) (numbers left: [41, 24]). Try possible operations.\n  |- Try 14 + 1 = 15. Add 15 to the number set. Current number set: [15, 41, 24], target: 21. Options for choosing two numbers: [(15, 41), (15, 24), (41, 24)].\n   |- Pick two numbers (15, 41) (numbers left: [24]). Try possible operations.\n    |- Try 41 + 15 = 56. Add 56 to the number set. Current number set: [56, 24], target: 21, just two numbers left.\n     |- Try 56 + 24 = 80. Evaluate 80 != 21, drop this branch.\n     |- Try 56 - 24 = 32. Evaluate 32 != 21, drop this branch.\n     |- Try 56 * 24 = 1344. Evaluate 1344 != 21, drop this branch.\n     |- Try 56 \/ 24 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 41 - 15 = 26. Add 26 to the number set. Current number set: [26, 24], target: 21, just two numbers left.\n     |- Try 26 + 24 = 50. Evaluate 50 != 21, drop this branch.\n     |- Try 26 - 24 = 2. Evaluate 2 != 21, drop this branch.\n     |- Try 26 * 24 = 624. Evaluate 624 != 21, drop this branch.\n     |- Try 26 \/ 24 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 41 * 15 = 615. Add 615 to the number set. Current number set: [615, 24], target: 21, just two numbers left.\n     |- Try 615 + 24 = 639. Evaluate 639 != 21, drop this branch.\n     |- Try 615 - 24 = 591. Evaluate 591 != 21, drop this branch.\n     |- Try 615 * 24 = 14760. 14760 exceeds the maximum intermediate result, drop this branch.\n     |- Try 615 \/ 24 = 25.6. 25.6 is a decimal, drop this branch.\n    |- Try 41 \/ 15 = 2.7. 2.7 is a decimal, drop this branch.\n   |- Pick two numbers (15, 24) (numbers left: [41]). Try possible operations.\n    |- Try 24 + 15 = 39. Add 39 to the number set. Current number set: [39, 41], target: 21, just two numbers left.\n     |- Try 41 + 39 = 80. Evaluate 80 != 21, drop this branch.\n     |- Try 41 - 39 = 2. Evaluate 2 != 21, drop this branch.\n     |- Try 41 * 39 = 1599. Evaluate 1599 != 21, drop this branch.\n     |- Try 41 \/ 39 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 24 - 15 = 9. Add 9 to the number set. Current number set: [9, 41], target: 21, just two numbers left.\n     |- Try 41 + 9 = 50. Evaluate 50 != 21, drop this branch.\n     |- Try 41 - 9 = 32. Evaluate 32 != 21, drop this branch.\n     |- Try 41 * 9 = 369. Evaluate 369 != 21, drop this branch.\n     |- Try 41 \/ 9 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 24 * 15 = 360. Add 360 to the number set. Current number set: [360, 41], target: 21, just two numbers left.\n     |- Try 360 + 41 = 401. Evaluate 401 != 21, drop this branch.\n     |- Try 360 - 41 = 319. Evaluate 319 != 21, drop this branch.\n     |- Try 360 * 41 = 14760. 14760 exceeds the maximum intermediate result, drop this branch.\n     |- Try 360 \/ 41 = 8.8. 8.8 is a decimal, drop this branch.\n    |- Try 24 \/ 15 = 1.6. 1.6 is a decimal, drop this branch.\n   |- Pick two numbers (41, 24) (numbers left: [15]). Try possible operations.\n    |- Try 41 + 24 = 65. Add 65 to the number set. Current number set: [65, 15], target: 21, just two numbers left.\n     |- Try 65 + 15 = 80. Evaluate 80 != 21, drop this branch.\n     |- Try 65 - 15 = 50. Evaluate 50 != 21, drop this branch.\n     |- Try 65 * 15 = 975. Evaluate 975 != 21, drop this branch.\n     |- Try 65 \/ 15 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 41 - 24 = 17. Add 17 to the number set. Current number set: [17, 15], target: 21, just two numbers left.\n     |- Try 17 + 15 = 32. Evaluate 32 != 21, drop this branch.\n     |- Try 17 - 15 = 2. Evaluate 2 != 21, drop this branch.\n     |- Try 17 * 15 = 255. Evaluate 255 != 21, drop this branch.\n     |- Try 17 \/ 15 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 41 * 24 = 984. Add 984 to the number set. Current number set: [984, 15], target: 21, just two numbers left.\n     |- Try 984 + 15 = 999. Evaluate 999 != 21, drop this branch.\n     |- Try 984 - 15 = 969. Evaluate 969 != 21, drop this branch.\n     |- Try 984 * 15 = 14760. 14760 exceeds the maximum intermediate result, drop this branch.\n     |- Try 984 \/ 15 = 65.6. 65.6 is a decimal, drop this branch.\n    |- Try 41 \/ 24 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 14 - 1 = 13. Add 13 to the number set. Current number set: [13, 41, 24], target: 21. Options for choosing two numbers: [(13, 41), (13, 24), (41, 24)].\n   |- Pick two numbers (13, 41) (numbers left: [24]). Try possible operations.\n    |- Try 41 + 13 = 54. Add 54 to the number set. Current number set: [54, 24], target: 21, just two numbers left.\n     |- Try 54 + 24 = 78. Evaluate 78 != 21, drop this branch.\n     |- Try 54 - 24 = 30. Evaluate 30 != 21, drop this branch.\n     |- Try 54 * 24 = 1296. Evaluate 1296 != 21, drop this branch.\n     |- Try 54 \/ 24 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 41 - 13 = 28. Add 28 to the number set. Current number set: [28, 24], target: 21, just two numbers left.\n     |- Try 28 + 24 = 52. Evaluate 52 != 21, drop this branch.\n     |- Try 28 - 24 = 4. Evaluate 4 != 21, drop this branch.\n     |- Try 28 * 24 = 672. Evaluate 672 != 21, drop this branch.\n     |- Try 28 \/ 24 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 41 * 13 = 533. Add 533 to the number set. Current number set: [533, 24], target: 21, just two numbers left.\n     |- Try 533 + 24 = 557. Evaluate 557 != 21, drop this branch.\n     |- Try 533 - 24 = 509. Evaluate 509 != 21, drop this branch.\n     |- Try 533 * 24 = 12792. 12792 exceeds the maximum intermediate result, drop this branch.\n     |- Try 533 \/ 24 = 22.2. 22.2 is a decimal, drop this branch.\n    |- Try 41 \/ 13 = 3.2. 3.2 is a decimal, drop this branch.\n   |- Pick two numbers (13, 24) (numbers left: [41]). Try possible operations.\n    |- Try 24 + 13 = 37. Add 37 to the number set. Current number set: [37, 41], target: 21, just two numbers left.\n     |- Try 41 + 37 = 78. Evaluate 78 != 21, drop this branch.\n     |- Try 41 - 37 = 4. Evaluate 4 != 21, drop this branch.\n     |- Try 41 * 37 = 1517. Evaluate 1517 != 21, drop this branch.\n     |- Try 41 \/ 37 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 24 - 13 = 11. Add 11 to the number set. Current number set: [11, 41], target: 21, just two numbers left.\n     |- Try 41 + 11 = 52. Evaluate 52 != 21, drop this branch.\n     |- Try 41 - 11 = 30. Evaluate 30 != 21, drop this branch.\n     |- Try 41 * 11 = 451. Evaluate 451 != 21, drop this branch.\n     |- Try 41 \/ 11 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 24 * 13 = 312. Add 312 to the number set. Current number set: [312, 41], target: 21, just two numbers left.\n     |- Try 312 + 41 = 353. Evaluate 353 != 21, drop this branch.\n     |- Try 312 - 41 = 271. Evaluate 271 != 21, drop this branch.\n     |- Try 312 * 41 = 12792. 12792 exceeds the maximum intermediate result, drop this branch.\n     |- Try 312 \/ 41 = 7.6. 7.6 is a decimal, drop this branch.\n    |- Try 24 \/ 13 = 1.8. 1.8 is a decimal, drop this branch.\n   |- Pick two numbers (41, 24) (numbers left: [13]). Try possible operations.\n    |- Try 41 + 24 = 65. Add 65 to the number set. Current number set: [65, 13], target: 21, just two numbers left.\n     |- Try 65 + 13 = 78. Evaluate 78 != 21, drop this branch.\n     |- Try 65 - 13 = 52. Evaluate 52 != 21, drop this branch.\n     |- Try 65 * 13 = 845. Evaluate 845 != 21, drop this branch.\n     |- Try 65 \/ 13 = 5. Evaluate 5 != 21, drop this branch.\n    |- Try 41 - 24 = 17. Add 17 to the number set. Current number set: [17, 13], target: 21, just two numbers left.\n     |- Try 17 + 13 = 30. Evaluate 30 != 21, drop this branch.\n     |- Try 17 - 13 = 4. Evaluate 4 != 21, drop this branch.\n     |- Try 17 * 13 = 221. Evaluate 221 != 21, drop this branch.\n     |- Try 17 \/ 13 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 41 * 24 = 984. Add 984 to the number set. Current number set: [984, 13], target: 21, just two numbers left.\n     |- Try 984 + 13 = 997. Evaluate 997 != 21, drop this branch.\n     |- Try 984 - 13 = 971. Evaluate 971 != 21, drop this branch.\n     |- Try 984 * 13 = 12792. 12792 exceeds the maximum intermediate result, drop this branch.\n     |- Try 984 \/ 13 = 75.7. 75.7 is a decimal, drop this branch.\n    |- Try 41 \/ 24 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 14 * 1 = 14. Add 14 to the number set. Current number set: [14, 41, 24], target: 21. Options for choosing two numbers: [(14, 41), (14, 24), (41, 24)].\n   |- Pick two numbers (14, 41) (numbers left: [24]). Try possible operations.\n    |- Try 41 + 14 = 55. Add 55 to the number set. Current number set: [55, 24], target: 21, just two numbers left.\n     |- Try 55 + 24 = 79. Evaluate 79 != 21, drop this branch.\n     |- Try 55 - 24 = 31. Evaluate 31 != 21, drop this branch.\n     |- Try 55 * 24 = 1320. Evaluate 1320 != 21, drop this branch.\n     |- Try 55 \/ 24 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 41 - 14 = 27. Add 27 to the number set. Current number set: [27, 24], target: 21, just two numbers left.\n     |- Try 27 + 24 = 51. Evaluate 51 != 21, drop this branch.\n     |- Try 27 - 24 = 3. Evaluate 3 != 21, drop this branch.\n     |- Try 27 * 24 = 648. Evaluate 648 != 21, drop this branch.\n     |- Try 27 \/ 24 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 41 * 14 = 574. Add 574 to the number set. Current number set: [574, 24], target: 21, just two numbers left.\n     |- Try 574 + 24 = 598. Evaluate 598 != 21, drop this branch.\n     |- Try 574 - 24 = 550. Evaluate 550 != 21, drop this branch.\n     |- Try 574 * 24 = 13776. 13776 exceeds the maximum intermediate result, drop this branch.\n     |- Try 574 \/ 24 = 23.9. 23.9 is a decimal, drop this branch.\n    |- Try 41 \/ 14 = 2.9. 2.9 is a decimal, drop this branch.\n   |- Pick two numbers (14, 24) (numbers left: [41]). Try possible operations.\n    |- Try 24 + 14 = 38. Add 38 to the number set. Current number set: [38, 41], target: 21, just two numbers left.\n     |- Try 41 + 38 = 79. Evaluate 79 != 21, drop this branch.\n     |- Try 41 - 38 = 3. Evaluate 3 != 21, drop this branch.\n     |- Try 41 * 38 = 1558. Evaluate 1558 != 21, drop this branch.\n     |- Try 41 \/ 38 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 24 - 14 = 10. Add 10 to the number set. Current number set: [10, 41], target: 21, just two numbers left.\n     |- Try 41 + 10 = 51. Evaluate 51 != 21, drop this branch.\n     |- Try 41 - 10 = 31. Evaluate 31 != 21, drop this branch.\n     |- Try 41 * 10 = 410. Evaluate 410 != 21, drop this branch.\n     |- Try 41 \/ 10 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 24 * 14 = 336. Add 336 to the number set. Current number set: [336, 41], target: 21, just two numbers left.\n     |- Try 336 + 41 = 377. Evaluate 377 != 21, drop this branch.\n     |- Try 336 - 41 = 295. Evaluate 295 != 21, drop this branch.\n     |- Try 336 * 41 = 13776. 13776 exceeds the maximum intermediate result, drop this branch.\n     |- Try 336 \/ 41 = 8.2. 8.2 is a decimal, drop this branch.\n    |- Try 24 \/ 14 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (41, 24) (numbers left: [14]). Try possible operations.\n    |- Try 41 + 24 = 65. Add 65 to the number set. Current number set: [65, 14], target: 21, just two numbers left.\n     |- Try 65 + 14 = 79. Evaluate 79 != 21, drop this branch.\n     |- Try 65 - 14 = 51. Evaluate 51 != 21, drop this branch.\n     |- Try 65 * 14 = 910. Evaluate 910 != 21, drop this branch.\n     |- Try 65 \/ 14 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 41 - 24 = 17. Add 17 to the number set. Current number set: [17, 14], target: 21, just two numbers left.\n     |- Try 17 + 14 = 31. Evaluate 31 != 21, drop this branch.\n     |- Try 17 - 14 = 3. Evaluate 3 != 21, drop this branch.\n     |- Try 17 * 14 = 238. Evaluate 238 != 21, drop this branch.\n     |- Try 17 \/ 14 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 41 * 24 = 984. Add 984 to the number set. Current number set: [984, 14], target: 21, just two numbers left.\n     |- Try 984 + 14 = 998. Evaluate 998 != 21, drop this branch.\n     |- Try 984 - 14 = 970. Evaluate 970 != 21, drop this branch.\n     |- Try 984 * 14 = 13776. 13776 exceeds the maximum intermediate result, drop this branch.\n     |- Try 984 \/ 14 = 70.3. 70.3 is a decimal, drop this branch.\n    |- Try 41 \/ 24 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 14 \/ 1 = 14. Add 14 to the number set. Current number set: [14, 41, 24], target: 21. Options for choosing two numbers: [(14, 41), (14, 24), (41, 24)].\n   |- Pick two numbers (14, 41) (numbers left: [24]). Try possible operations.\n    |- Try 41 + 14 = 55. Add 55 to the number set. Current number set: [55, 24], target: 21, just two numbers left.\n     |- Try 55 + 24 = 79. Evaluate 79 != 21, drop this branch.\n     |- Try 55 - 24 = 31. Evaluate 31 != 21, drop this branch.\n     |- Try 55 * 24 = 1320. Evaluate 1320 != 21, drop this branch.\n     |- Try 55 \/ 24 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 41 - 14 = 27. Add 27 to the number set. Current number set: [27, 24], target: 21, just two numbers left.\n     |- Try 27 + 24 = 51. Evaluate 51 != 21, drop this branch.\n     |- Try 27 - 24 = 3. Evaluate 3 != 21, drop this branch.\n     |- Try 27 * 24 = 648. Evaluate 648 != 21, drop this branch.\n     |- Try 27 \/ 24 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 41 * 14 = 574. Add 574 to the number set. Current number set: [574, 24], target: 21, just two numbers left.\n     |- Try 574 + 24 = 598. Evaluate 598 != 21, drop this branch.\n     |- Try 574 - 24 = 550. Evaluate 550 != 21, drop this branch.\n     |- Try 574 * 24 = 13776. 13776 exceeds the maximum intermediate result, drop this branch.\n     |- Try 574 \/ 24 = 23.9. 23.9 is a decimal, drop this branch.\n    |- Try 41 \/ 14 = 2.9. 2.9 is a decimal, drop this branch.\n   |- Pick two numbers (14, 24) (numbers left: [41]). Try possible operations.\n    |- Try 24 + 14 = 38. Add 38 to the number set. Current number set: [38, 41], target: 21, just two numbers left.\n     |- Try 41 + 38 = 79. Evaluate 79 != 21, drop this branch.\n     |- Try 41 - 38 = 3. Evaluate 3 != 21, drop this branch.\n     |- Try 41 * 38 = 1558. Evaluate 1558 != 21, drop this branch.\n     |- Try 41 \/ 38 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 24 - 14 = 10. Add 10 to the number set. Current number set: [10, 41], target: 21, just two numbers left.\n     |- Try 41 + 10 = 51. Evaluate 51 != 21, drop this branch.\n     |- Try 41 - 10 = 31. Evaluate 31 != 21, drop this branch.\n     |- Try 41 * 10 = 410. Evaluate 410 != 21, drop this branch.\n     |- Try 41 \/ 10 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 24 * 14 = 336. Add 336 to the number set. Current number set: [336, 41], target: 21, just two numbers left.\n     |- Try 336 + 41 = 377. Evaluate 377 != 21, drop this branch.\n     |- Try 336 - 41 = 295. Evaluate 295 != 21, drop this branch.\n     |- Try 336 * 41 = 13776. 13776 exceeds the maximum intermediate result, drop this branch.\n     |- Try 336 \/ 41 = 8.2. 8.2 is a decimal, drop this branch.\n    |- Try 24 \/ 14 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (41, 24) (numbers left: [14]). Try possible operations.\n    |- Try 41 + 24 = 65. Add 65 to the number set. Current number set: [65, 14], target: 21, just two numbers left.\n     |- Try 65 + 14 = 79. Evaluate 79 != 21, drop this branch.\n     |- Try 65 - 14 = 51. Evaluate 51 != 21, drop this branch.\n     |- Try 65 * 14 = 910. Evaluate 910 != 21, drop this branch.\n     |- Try 65 \/ 14 = 4.6. 4.6 is a decimal, drop this branch.\n    |- Try 41 - 24 = 17. Add 17 to the number set. Current number set: [17, 14], target: 21, just two numbers left.\n     |- Try 17 + 14 = 31. Evaluate 31 != 21, drop this branch.\n     |- Try 17 - 14 = 3. Evaluate 3 != 21, drop this branch.\n     |- Try 17 * 14 = 238. Evaluate 238 != 21, drop this branch.\n     |- Try 17 \/ 14 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 41 * 24 = 984. Add 984 to the number set. Current number set: [984, 14], target: 21, just two numbers left.\n     |- Try 984 + 14 = 998. Evaluate 998 != 21, drop this branch.\n     |- Try 984 - 14 = 970. Evaluate 970 != 21, drop this branch.\n     |- Try 984 * 14 = 13776. 13776 exceeds the maximum intermediate result, drop this branch.\n     |- Try 984 \/ 14 = 70.3. 70.3 is a decimal, drop this branch.\n    |- Try 41 \/ 24 = 1.7. 1.7 is a decimal, drop this branch.\n |- Pick two numbers (1, 41) (numbers left: [14, 24]). Try possible operations.\n  |- Try 41 + 1 = 42. Add 42 to the number set. Current number set: [42, 14, 24], target: 21. Options for choosing two numbers: [(42, 14), (42, 24), (14, 24)].\n   |- Pick two numbers (42, 14) (numbers left: [24]). Try possible operations.\n    |- Try 42 + 14 = 56. Add 56 to the number set. Current number set: [56, 24], target: 21, just two numbers left.\n     |- Try 56 + 24 = 80. Evaluate 80 != 21, drop this branch.\n     |- Try 56 - 24 = 32. Evaluate 32 != 21, drop this branch.\n     |- Try 56 * 24 = 1344. Evaluate 1344 != 21, drop this branch.\n     |- Try 56 \/ 24 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 42 - 14 = 28. Add 28 to the number set. Current number set: [28, 24], target: 21, just two numbers left.\n     |- Try 28 + 24 = 52. Evaluate 52 != 21, drop this branch.\n     |- Try 28 - 24 = 4. Evaluate 4 != 21, drop this branch.\n     |- Try 28 * 24 = 672. Evaluate 672 != 21, drop this branch.\n     |- Try 28 \/ 24 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 42 * 14 = 588. Add 588 to the number set. Current number set: [588, 24], target: 21, just two numbers left.\n     |- Try 588 + 24 = 612. Evaluate 612 != 21, drop this branch.\n     |- Try 588 - 24 = 564. Evaluate 564 != 21, drop this branch.\n     |- Try 588 * 24 = 14112. 14112 exceeds the maximum intermediate result, drop this branch.\n     |- Try 588 \/ 24 = 24.5. 24.5 is a decimal, drop this branch.\n    |- Try 42 \/ 14 = 3. Add 3 to the number set. Current number set: [3, 24], target: 21, just two numbers left.\n     |- Try 24 + 3 = 27. Evaluate 27 != 21, drop this branch.\n     |- Try 24 - 3 = 21. Evaluate 21 == 21, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 24 - 3 = 21\nThe step before: 42 \/ 14 = 3\nThe first step: 41 + 1 = 42\n\nOutput the solution in the required format:\n<Solution>\n41 + 1 = 42\n42 \/ 14 = 3\n24 - 3 = 21\n<\/Solution>\n","item":{"nums":[1,14,41,24],"solution":["41 + 1 = 42","42 \/ 14 = 3","24 - 3 = 21"],"target":21}}
+{"instance_id":"countdown_8k_193","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [30, 35, 12, 49]\nTarget: 30","reference_output":"# Search Procedure\nInitial number set: [30, 35, 12, 49], target: 30. Options for choosing two numbers: [(30, 35), (30, 12), (30, 49), (35, 12), (35, 49), (12, 49)].\n |- Pick two numbers (30, 35) (numbers left: [12, 49]). Try possible operations.\n  |- Try 35 + 30 = 65. Add 65 to the number set. Current number set: [65, 12, 49], target: 30. Options for choosing two numbers: [(65, 12), (65, 49), (12, 49)].\n   |- Pick two numbers (65, 12) (numbers left: [49]). Try possible operations.\n    |- Try 65 + 12 = 77. Add 77 to the number set. Current number set: [77, 49], target: 30, just two numbers left.\n     |- Try 77 + 49 = 126. Evaluate 126 != 30, drop this branch.\n     |- Try 77 - 49 = 28. Evaluate 28 != 30, drop this branch.\n     |- Try 77 * 49 = 3773. 3773 exceeds the maximum intermediate result, drop this branch.\n     |- Try 77 \/ 49 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 65 - 12 = 53. Add 53 to the number set. Current number set: [53, 49], target: 30, just two numbers left.\n     |- Try 53 + 49 = 102. Evaluate 102 != 30, drop this branch.\n     |- Try 53 - 49 = 4. Evaluate 4 != 30, drop this branch.\n     |- Try 53 * 49 = 2597. 2597 exceeds the maximum intermediate result, drop this branch.\n     |- Try 53 \/ 49 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 65 * 12 = 780. Add 780 to the number set. Current number set: [780, 49], target: 30, just two numbers left.\n     |- Try 780 + 49 = 829. Evaluate 829 != 30, drop this branch.\n     |- Try 780 - 49 = 731. Evaluate 731 != 30, drop this branch.\n     |- Try 780 * 49 = 38220. 38220 exceeds the maximum intermediate result, drop this branch.\n     |- Try 780 \/ 49 = 15.9. 15.9 is a decimal, drop this branch.\n    |- Try 65 \/ 12 = 5.4. 5.4 is a decimal, drop this branch.\n   |- Pick two numbers (65, 49) (numbers left: [12]). Try possible operations.\n    |- Try 65 + 49 = 114. Add 114 to the number set. Current number set: [114, 12], target: 30, just two numbers left.\n     |- Try 114 + 12 = 126. Evaluate 126 != 30, drop this branch.\n     |- Try 114 - 12 = 102. Evaluate 102 != 30, drop this branch.\n     |- Try 114 * 12 = 1368. Evaluate 1368 != 30, drop this branch.\n     |- Try 114 \/ 12 = 9.5. 9.5 is a decimal, drop this branch.\n    |- Try 65 - 49 = 16. Add 16 to the number set. Current number set: [16, 12], target: 30, just two numbers left.\n     |- Try 16 + 12 = 28. Evaluate 28 != 30, drop this branch.\n     |- Try 16 - 12 = 4. Evaluate 4 != 30, drop this branch.\n     |- Try 16 * 12 = 192. Evaluate 192 != 30, drop this branch.\n     |- Try 16 \/ 12 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 65 * 49 = 3185. 3185 exceeds the maximum intermediate result, drop this branch.\n    |- Try 65 \/ 49 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (12, 49) (numbers left: [65]). Try possible operations.\n    |- Try 49 + 12 = 61. Add 61 to the number set. Current number set: [61, 65], target: 30, just two numbers left.\n     |- Try 65 + 61 = 126. Evaluate 126 != 30, drop this branch.\n     |- Try 65 - 61 = 4. Evaluate 4 != 30, drop this branch.\n     |- Try 65 * 61 = 3965. 3965 exceeds the maximum intermediate result, drop this branch.\n     |- Try 65 \/ 61 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 49 - 12 = 37. Add 37 to the number set. Current number set: [37, 65], target: 30, just two numbers left.\n     |- Try 65 + 37 = 102. Evaluate 102 != 30, drop this branch.\n     |- Try 65 - 37 = 28. Evaluate 28 != 30, drop this branch.\n     |- Try 65 * 37 = 2405. 2405 exceeds the maximum intermediate result, drop this branch.\n     |- Try 65 \/ 37 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 49 * 12 = 588. Add 588 to the number set. Current number set: [588, 65], target: 30, just two numbers left.\n     |- Try 588 + 65 = 653. Evaluate 653 != 30, drop this branch.\n     |- Try 588 - 65 = 523. Evaluate 523 != 30, drop this branch.\n     |- Try 588 * 65 = 38220. 38220 exceeds the maximum intermediate result, drop this branch.\n     |- Try 588 \/ 65 = 9.0. 9.0 is a decimal, drop this branch.\n    |- Try 49 \/ 12 = 4.1. 4.1 is a decimal, drop this branch.\n  |- Try 35 - 30 = 5. Add 5 to the number set. Current number set: [5, 12, 49], target: 30. Options for choosing two numbers: [(5, 12), (5, 49), (12, 49)].\n   |- Pick two numbers (5, 12) (numbers left: [49]). Try possible operations.\n    |- Try 12 + 5 = 17. Add 17 to the number set. Current number set: [17, 49], target: 30, just two numbers left.\n     |- Try 49 + 17 = 66. Evaluate 66 != 30, drop this branch.\n     |- Try 49 - 17 = 32. Evaluate 32 != 30, drop this branch.\n     |- Try 49 * 17 = 833. Evaluate 833 != 30, drop this branch.\n     |- Try 49 \/ 17 = 2.9. 2.9 is a decimal, drop this branch.\n    |- Try 12 - 5 = 7. Add 7 to the number set. Current number set: [7, 49], target: 30, just two numbers left.\n     |- Try 49 + 7 = 56. Evaluate 56 != 30, drop this branch.\n     |- Try 49 - 7 = 42. Evaluate 42 != 30, drop this branch.\n     |- Try 49 * 7 = 343. Evaluate 343 != 30, drop this branch.\n     |- Try 49 \/ 7 = 7. Evaluate 7 != 30, drop this branch.\n    |- Try 12 * 5 = 60. Add 60 to the number set. Current number set: [60, 49], target: 30, just two numbers left.\n     |- Try 60 + 49 = 109. Evaluate 109 != 30, drop this branch.\n     |- Try 60 - 49 = 11. Evaluate 11 != 30, drop this branch.\n     |- Try 60 * 49 = 2940. 2940 exceeds the maximum intermediate result, drop this branch.\n     |- Try 60 \/ 49 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 12 \/ 5 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (5, 49) (numbers left: [12]). Try possible operations.\n    |- Try 49 + 5 = 54. Add 54 to the number set. Current number set: [54, 12], target: 30, just two numbers left.\n     |- Try 54 + 12 = 66. Evaluate 66 != 30, drop this branch.\n     |- Try 54 - 12 = 42. Evaluate 42 != 30, drop this branch.\n     |- Try 54 * 12 = 648. Evaluate 648 != 30, drop this branch.\n     |- Try 54 \/ 12 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 49 - 5 = 44. Add 44 to the number set. Current number set: [44, 12], target: 30, just two numbers left.\n     |- Try 44 + 12 = 56. Evaluate 56 != 30, drop this branch.\n     |- Try 44 - 12 = 32. Evaluate 32 != 30, drop this branch.\n     |- Try 44 * 12 = 528. Evaluate 528 != 30, drop this branch.\n     |- Try 44 \/ 12 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 49 * 5 = 245. Add 245 to the number set. Current number set: [245, 12], target: 30, just two numbers left.\n     |- Try 245 + 12 = 257. Evaluate 257 != 30, drop this branch.\n     |- Try 245 - 12 = 233. Evaluate 233 != 30, drop this branch.\n     |- Try 245 * 12 = 2940. 2940 exceeds the maximum intermediate result, drop this branch.\n     |- Try 245 \/ 12 = 20.4. 20.4 is a decimal, drop this branch.\n    |- Try 49 \/ 5 = 9.8. 9.8 is a decimal, drop this branch.\n   |- Pick two numbers (12, 49) (numbers left: [5]). Try possible operations.\n    |- Try 49 + 12 = 61. Add 61 to the number set. Current number set: [61, 5], target: 30, just two numbers left.\n     |- Try 61 + 5 = 66. Evaluate 66 != 30, drop this branch.\n     |- Try 61 - 5 = 56. Evaluate 56 != 30, drop this branch.\n     |- Try 61 * 5 = 305. Evaluate 305 != 30, drop this branch.\n     |- Try 61 \/ 5 = 12.2. 12.2 is a decimal, drop this branch.\n    |- Try 49 - 12 = 37. Add 37 to the number set. Current number set: [37, 5], target: 30, just two numbers left.\n     |- Try 37 + 5 = 42. Evaluate 42 != 30, drop this branch.\n     |- Try 37 - 5 = 32. Evaluate 32 != 30, drop this branch.\n     |- Try 37 * 5 = 185. Evaluate 185 != 30, drop this branch.\n     |- Try 37 \/ 5 = 7.4. 7.4 is a decimal, drop this branch.\n    |- Try 49 * 12 = 588. Add 588 to the number set. Current number set: [588, 5], target: 30, just two numbers left.\n     |- Try 588 + 5 = 593. Evaluate 593 != 30, drop this branch.\n     |- Try 588 - 5 = 583. Evaluate 583 != 30, drop this branch.\n     |- Try 588 * 5 = 2940. 2940 exceeds the maximum intermediate result, drop this branch.\n     |- Try 588 \/ 5 = 117.6. 117.6 is a decimal, drop this branch.\n    |- Try 49 \/ 12 = 4.1. 4.1 is a decimal, drop this branch.\n  |- Try 35 * 30 = 1050. Add 1050 to the number set. Current number set: [1050, 12, 49], target: 30. Options for choosing two numbers: [(1050, 12), (1050, 49), (12, 49)].\n   |- Pick two numbers (1050, 12) (numbers left: [49]). Try possible operations.\n    |- Try 1050 + 12 = 1062. Add 1062 to the number set. Current number set: [1062, 49], target: 30, just two numbers left.\n     |- Try 1062 + 49 = 1111. Evaluate 1111 != 30, drop this branch.\n     |- Try 1062 - 49 = 1013. Evaluate 1013 != 30, drop this branch.\n     |- Try 1062 * 49 = 52038. 52038 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1062 \/ 49 = 21.7. 21.7 is a decimal, drop this branch.\n    |- Try 1050 - 12 = 1038. Add 1038 to the number set. Current number set: [1038, 49], target: 30, just two numbers left.\n     |- Try 1038 + 49 = 1087. Evaluate 1087 != 30, drop this branch.\n     |- Try 1038 - 49 = 989. Evaluate 989 != 30, drop this branch.\n     |- Try 1038 * 49 = 50862. 50862 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1038 \/ 49 = 21.2. 21.2 is a decimal, drop this branch.\n    |- Try 1050 * 12 = 12600. 12600 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1050 \/ 12 = 87.5. 87.5 is a decimal, drop this branch.\n   |- Pick two numbers (1050, 49) (numbers left: [12]). Try possible operations.\n    |- Try 1050 + 49 = 1099. Add 1099 to the number set. Current number set: [1099, 12], target: 30, just two numbers left.\n     |- Try 1099 + 12 = 1111. Evaluate 1111 != 30, drop this branch.\n     |- Try 1099 - 12 = 1087. Evaluate 1087 != 30, drop this branch.\n     |- Try 1099 * 12 = 13188. 13188 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1099 \/ 12 = 91.6. 91.6 is a decimal, drop this branch.\n    |- Try 1050 - 49 = 1001. Add 1001 to the number set. Current number set: [1001, 12], target: 30, just two numbers left.\n     |- Try 1001 + 12 = 1013. Evaluate 1013 != 30, drop this branch.\n     |- Try 1001 - 12 = 989. Evaluate 989 != 30, drop this branch.\n     |- Try 1001 * 12 = 12012. 12012 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1001 \/ 12 = 83.4. 83.4 is a decimal, drop this branch.\n    |- Try 1050 * 49 = 51450. 51450 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1050 \/ 49 = 21.4. 21.4 is a decimal, drop this branch.\n   |- Pick two numbers (12, 49) (numbers left: [1050]). Try possible operations.\n    |- Try 49 + 12 = 61. Add 61 to the number set. Current number set: [61, 1050], target: 30, just two numbers left.\n     |- Try 1050 + 61 = 1111. Evaluate 1111 != 30, drop this branch.\n     |- Try 1050 - 61 = 989. Evaluate 989 != 30, drop this branch.\n     |- Try 1050 * 61 = 64050. 64050 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1050 \/ 61 = 17.2. 17.2 is a decimal, drop this branch.\n    |- Try 49 - 12 = 37. Add 37 to the number set. Current number set: [37, 1050], target: 30, just two numbers left.\n     |- Try 1050 + 37 = 1087. Evaluate 1087 != 30, drop this branch.\n     |- Try 1050 - 37 = 1013. Evaluate 1013 != 30, drop this branch.\n     |- Try 1050 * 37 = 38850. 38850 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1050 \/ 37 = 28.4. 28.4 is a decimal, drop this branch.\n    |- Try 49 * 12 = 588. Add 588 to the number set. Current number set: [588, 1050], target: 30, just two numbers left.\n     |- Try 1050 + 588 = 1638. Evaluate 1638 != 30, drop this branch.\n     |- Try 1050 - 588 = 462. Evaluate 462 != 30, drop this branch.\n     |- Try 1050 * 588 = 617400. 617400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1050 \/ 588 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 49 \/ 12 = 4.1. 4.1 is a decimal, drop this branch.\n  |- Try 35 \/ 30 = 1.2. 1.2 is a decimal, drop this branch.\n |- Pick two numbers (30, 12) (numbers left: [35, 49]). Try possible operations.\n  |- Try 30 + 12 = 42. Add 42 to the number set. Current number set: [42, 35, 49], target: 30. Options for choosing two numbers: [(42, 35), (42, 49), (35, 49)].\n   |- Pick two numbers (42, 35) (numbers left: [49]). Try possible operations.\n    |- Try 42 + 35 = 77. Add 77 to the number set. Current number set: [77, 49], target: 30, just two numbers left.\n     |- Try 77 + 49 = 126. Evaluate 126 != 30, drop this branch.\n     |- Try 77 - 49 = 28. Evaluate 28 != 30, drop this branch.\n     |- Try 77 * 49 = 3773. 3773 exceeds the maximum intermediate result, drop this branch.\n     |- Try 77 \/ 49 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 42 - 35 = 7. Add 7 to the number set. Current number set: [7, 49], target: 30, just two numbers left.\n     |- Try 49 + 7 = 56. Evaluate 56 != 30, drop this branch.\n     |- Try 49 - 7 = 42. Evaluate 42 != 30, drop this branch.\n     |- Try 49 * 7 = 343. Evaluate 343 != 30, drop this branch.\n     |- Try 49 \/ 7 = 7. Evaluate 7 != 30, drop this branch.\n    |- Try 42 * 35 = 1470. Add 1470 to the number set. Current number set: [1470, 49], target: 30, just two numbers left.\n     |- Try 1470 + 49 = 1519. Evaluate 1519 != 30, drop this branch.\n     |- Try 1470 - 49 = 1421. Evaluate 1421 != 30, drop this branch.\n     |- Try 1470 * 49 = 72030. 72030 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1470 \/ 49 = 30. Evaluate 30 == 30, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 1470 \/ 49 = 30\nThe step before: 42 * 35 = 1470\nThe first step: 30 + 12 = 42\n\nOutput the solution in the required format:\n<Solution>\n30 + 12 = 42\n42 * 35 = 1470\n1470 \/ 49 = 30\n<\/Solution>\n","item":{"nums":[30,35,12,49],"solution":["30 + 12 = 42","42 * 35 = 1470","1470 \/ 49 = 30"],"target":30}}
+{"instance_id":"countdown_8k_194","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [15, 5, 40, 19]\nTarget: 30","reference_output":"# Search Procedure\nInitial number set: [15, 5, 40, 19], target: 30. Options for choosing two numbers: [(15, 5), (15, 40), (15, 19), (5, 40), (5, 19), (40, 19)].\n |- Pick two numbers (15, 5) (numbers left: [40, 19]). Try possible operations.\n  |- Try 15 + 5 = 20. Add 20 to the number set. Current number set: [20, 40, 19], target: 30. Options for choosing two numbers: [(20, 40), (20, 19), (40, 19)].\n   |- Pick two numbers (20, 40) (numbers left: [19]). Try possible operations.\n    |- Try 40 + 20 = 60. Add 60 to the number set. Current number set: [60, 19], target: 30, just two numbers left.\n     |- Try 60 + 19 = 79. Evaluate 79 != 30, drop this branch.\n     |- Try 60 - 19 = 41. Evaluate 41 != 30, drop this branch.\n     |- Try 60 * 19 = 1140. Evaluate 1140 != 30, drop this branch.\n     |- Try 60 \/ 19 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 40 - 20 = 20. Add 20 to the number set. Current number set: [20, 19], target: 30, just two numbers left.\n     |- Try 20 + 19 = 39. Evaluate 39 != 30, drop this branch.\n     |- Try 20 - 19 = 1. Evaluate 1 != 30, drop this branch.\n     |- Try 20 * 19 = 380. Evaluate 380 != 30, drop this branch.\n     |- Try 20 \/ 19 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 40 * 20 = 800. Add 800 to the number set. Current number set: [800, 19], target: 30, just two numbers left.\n     |- Try 800 + 19 = 819. Evaluate 819 != 30, drop this branch.\n     |- Try 800 - 19 = 781. Evaluate 781 != 30, drop this branch.\n     |- Try 800 * 19 = 15200. 15200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 800 \/ 19 = 42.1. 42.1 is a decimal, drop this branch.\n    |- Try 40 \/ 20 = 2. Add 2 to the number set. Current number set: [2, 19], target: 30, just two numbers left.\n     |- Try 19 + 2 = 21. Evaluate 21 != 30, drop this branch.\n     |- Try 19 - 2 = 17. Evaluate 17 != 30, drop this branch.\n     |- Try 19 * 2 = 38. Evaluate 38 != 30, drop this branch.\n     |- Try 19 \/ 2 = 9.5. 9.5 is a decimal, drop this branch.\n   |- Pick two numbers (20, 19) (numbers left: [40]). Try possible operations.\n    |- Try 20 + 19 = 39. Add 39 to the number set. Current number set: [39, 40], target: 30, just two numbers left.\n     |- Try 40 + 39 = 79. Evaluate 79 != 30, drop this branch.\n     |- Try 40 - 39 = 1. Evaluate 1 != 30, drop this branch.\n     |- Try 40 * 39 = 1560. Evaluate 1560 != 30, drop this branch.\n     |- Try 40 \/ 39 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 20 - 19 = 1. Add 1 to the number set. Current number set: [1, 40], target: 30, just two numbers left.\n     |- Try 40 + 1 = 41. Evaluate 41 != 30, drop this branch.\n     |- Try 40 - 1 = 39. Evaluate 39 != 30, drop this branch.\n     |- Try 40 * 1 = 40. Evaluate 40 != 30, drop this branch.\n     |- Try 40 \/ 1 = 40. Evaluate 40 != 30, drop this branch.\n    |- Try 20 * 19 = 380. Add 380 to the number set. Current number set: [380, 40], target: 30, just two numbers left.\n     |- Try 380 + 40 = 420. Evaluate 420 != 30, drop this branch.\n     |- Try 380 - 40 = 340. Evaluate 340 != 30, drop this branch.\n     |- Try 380 * 40 = 15200. 15200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 380 \/ 40 = 9.5. 9.5 is a decimal, drop this branch.\n    |- Try 20 \/ 19 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (40, 19) (numbers left: [20]). Try possible operations.\n    |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 20], target: 30, just two numbers left.\n     |- Try 59 + 20 = 79. Evaluate 79 != 30, drop this branch.\n     |- Try 59 - 20 = 39. Evaluate 39 != 30, drop this branch.\n     |- Try 59 * 20 = 1180. Evaluate 1180 != 30, drop this branch.\n     |- Try 59 \/ 20 = 3.0. 3.0 is a decimal, drop this branch.\n    |- Try 40 - 19 = 21. Add 21 to the number set. Current number set: [21, 20], target: 30, just two numbers left.\n     |- Try 21 + 20 = 41. Evaluate 41 != 30, drop this branch.\n     |- Try 21 - 20 = 1. Evaluate 1 != 30, drop this branch.\n     |- Try 21 * 20 = 420. Evaluate 420 != 30, drop this branch.\n     |- Try 21 \/ 20 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 40 * 19 = 760. Add 760 to the number set. Current number set: [760, 20], target: 30, just two numbers left.\n     |- Try 760 + 20 = 780. Evaluate 780 != 30, drop this branch.\n     |- Try 760 - 20 = 740. Evaluate 740 != 30, drop this branch.\n     |- Try 760 * 20 = 15200. 15200 exceeds the maximum intermediate result, drop this branch.\n     |- Try 760 \/ 20 = 38. Evaluate 38 != 30, drop this branch.\n    |- Try 40 \/ 19 = 2.1. 2.1 is a decimal, drop this branch.\n  |- Try 15 - 5 = 10. Add 10 to the number set. Current number set: [10, 40, 19], target: 30. Options for choosing two numbers: [(10, 40), (10, 19), (40, 19)].\n   |- Pick two numbers (10, 40) (numbers left: [19]). Try possible operations.\n    |- Try 40 + 10 = 50. Add 50 to the number set. Current number set: [50, 19], target: 30, just two numbers left.\n     |- Try 50 + 19 = 69. Evaluate 69 != 30, drop this branch.\n     |- Try 50 - 19 = 31. Evaluate 31 != 30, drop this branch.\n     |- Try 50 * 19 = 950. Evaluate 950 != 30, drop this branch.\n     |- Try 50 \/ 19 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 40 - 10 = 30. Add 30 to the number set. Current number set: [30, 19], target: 30, just two numbers left.\n     |- Try 30 + 19 = 49. Evaluate 49 != 30, drop this branch.\n     |- Try 30 - 19 = 11. Evaluate 11 != 30, drop this branch.\n     |- Try 30 * 19 = 570. Evaluate 570 != 30, drop this branch.\n     |- Try 30 \/ 19 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 40 * 10 = 400. Add 400 to the number set. Current number set: [400, 19], target: 30, just two numbers left.\n     |- Try 400 + 19 = 419. Evaluate 419 != 30, drop this branch.\n     |- Try 400 - 19 = 381. Evaluate 381 != 30, drop this branch.\n     |- Try 400 * 19 = 7600. 7600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 400 \/ 19 = 21.1. 21.1 is a decimal, drop this branch.\n    |- Try 40 \/ 10 = 4. Add 4 to the number set. Current number set: [4, 19], target: 30, just two numbers left.\n     |- Try 19 + 4 = 23. Evaluate 23 != 30, drop this branch.\n     |- Try 19 - 4 = 15. Evaluate 15 != 30, drop this branch.\n     |- Try 19 * 4 = 76. Evaluate 76 != 30, drop this branch.\n     |- Try 19 \/ 4 = 4.8. 4.8 is a decimal, drop this branch.\n   |- Pick two numbers (10, 19) (numbers left: [40]). Try possible operations.\n    |- Try 19 + 10 = 29. Add 29 to the number set. Current number set: [29, 40], target: 30, just two numbers left.\n     |- Try 40 + 29 = 69. Evaluate 69 != 30, drop this branch.\n     |- Try 40 - 29 = 11. Evaluate 11 != 30, drop this branch.\n     |- Try 40 * 29 = 1160. Evaluate 1160 != 30, drop this branch.\n     |- Try 40 \/ 29 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 19 - 10 = 9. Add 9 to the number set. Current number set: [9, 40], target: 30, just two numbers left.\n     |- Try 40 + 9 = 49. Evaluate 49 != 30, drop this branch.\n     |- Try 40 - 9 = 31. Evaluate 31 != 30, drop this branch.\n     |- Try 40 * 9 = 360. Evaluate 360 != 30, drop this branch.\n     |- Try 40 \/ 9 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 19 * 10 = 190. Add 190 to the number set. Current number set: [190, 40], target: 30, just two numbers left.\n     |- Try 190 + 40 = 230. Evaluate 230 != 30, drop this branch.\n     |- Try 190 - 40 = 150. Evaluate 150 != 30, drop this branch.\n     |- Try 190 * 40 = 7600. 7600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 190 \/ 40 = 4.8. 4.8 is a decimal, drop this branch.\n    |- Try 19 \/ 10 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (40, 19) (numbers left: [10]). Try possible operations.\n    |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 10], target: 30, just two numbers left.\n     |- Try 59 + 10 = 69. Evaluate 69 != 30, drop this branch.\n     |- Try 59 - 10 = 49. Evaluate 49 != 30, drop this branch.\n     |- Try 59 * 10 = 590. Evaluate 590 != 30, drop this branch.\n     |- Try 59 \/ 10 = 5.9. 5.9 is a decimal, drop this branch.\n    |- Try 40 - 19 = 21. Add 21 to the number set. Current number set: [21, 10], target: 30, just two numbers left.\n     |- Try 21 + 10 = 31. Evaluate 31 != 30, drop this branch.\n     |- Try 21 - 10 = 11. Evaluate 11 != 30, drop this branch.\n     |- Try 21 * 10 = 210. Evaluate 210 != 30, drop this branch.\n     |- Try 21 \/ 10 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 40 * 19 = 760. Add 760 to the number set. Current number set: [760, 10], target: 30, just two numbers left.\n     |- Try 760 + 10 = 770. Evaluate 770 != 30, drop this branch.\n     |- Try 760 - 10 = 750. Evaluate 750 != 30, drop this branch.\n     |- Try 760 * 10 = 7600. 7600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 760 \/ 10 = 76. Evaluate 76 != 30, drop this branch.\n    |- Try 40 \/ 19 = 2.1. 2.1 is a decimal, drop this branch.\n  |- Try 15 * 5 = 75. Add 75 to the number set. Current number set: [75, 40, 19], target: 30. Options for choosing two numbers: [(75, 40), (75, 19), (40, 19)].\n   |- Pick two numbers (75, 40) (numbers left: [19]). Try possible operations.\n    |- Try 75 + 40 = 115. Add 115 to the number set. Current number set: [115, 19], target: 30, just two numbers left.\n     |- Try 115 + 19 = 134. Evaluate 134 != 30, drop this branch.\n     |- Try 115 - 19 = 96. Evaluate 96 != 30, drop this branch.\n     |- Try 115 * 19 = 2185. 2185 exceeds the maximum intermediate result, drop this branch.\n     |- Try 115 \/ 19 = 6.1. 6.1 is a decimal, drop this branch.\n    |- Try 75 - 40 = 35. Add 35 to the number set. Current number set: [35, 19], target: 30, just two numbers left.\n     |- Try 35 + 19 = 54. Evaluate 54 != 30, drop this branch.\n     |- Try 35 - 19 = 16. Evaluate 16 != 30, drop this branch.\n     |- Try 35 * 19 = 665. Evaluate 665 != 30, drop this branch.\n     |- Try 35 \/ 19 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 75 * 40 = 3000. 3000 exceeds the maximum intermediate result, drop this branch.\n    |- Try 75 \/ 40 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (75, 19) (numbers left: [40]). Try possible operations.\n    |- Try 75 + 19 = 94. Add 94 to the number set. Current number set: [94, 40], target: 30, just two numbers left.\n     |- Try 94 + 40 = 134. Evaluate 134 != 30, drop this branch.\n     |- Try 94 - 40 = 54. Evaluate 54 != 30, drop this branch.\n     |- Try 94 * 40 = 3760. 3760 exceeds the maximum intermediate result, drop this branch.\n     |- Try 94 \/ 40 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 75 - 19 = 56. Add 56 to the number set. Current number set: [56, 40], target: 30, just two numbers left.\n     |- Try 56 + 40 = 96. Evaluate 96 != 30, drop this branch.\n     |- Try 56 - 40 = 16. Evaluate 16 != 30, drop this branch.\n     |- Try 56 * 40 = 2240. 2240 exceeds the maximum intermediate result, drop this branch.\n     |- Try 56 \/ 40 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 75 * 19 = 1425. Add 1425 to the number set. Current number set: [1425, 40], target: 30, just two numbers left.\n     |- Try 1425 + 40 = 1465. Evaluate 1465 != 30, drop this branch.\n     |- Try 1425 - 40 = 1385. Evaluate 1385 != 30, drop this branch.\n     |- Try 1425 * 40 = 57000. 57000 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1425 \/ 40 = 35.6. 35.6 is a decimal, drop this branch.\n    |- Try 75 \/ 19 = 3.9. 3.9 is a decimal, drop this branch.\n   |- Pick two numbers (40, 19) (numbers left: [75]). Try possible operations.\n    |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 75], target: 30, just two numbers left.\n     |- Try 75 + 59 = 134. Evaluate 134 != 30, drop this branch.\n     |- Try 75 - 59 = 16. Evaluate 16 != 30, drop this branch.\n     |- Try 75 * 59 = 4425. 4425 exceeds the maximum intermediate result, drop this branch.\n     |- Try 75 \/ 59 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 40 - 19 = 21. Add 21 to the number set. Current number set: [21, 75], target: 30, just two numbers left.\n     |- Try 75 + 21 = 96. Evaluate 96 != 30, drop this branch.\n     |- Try 75 - 21 = 54. Evaluate 54 != 30, drop this branch.\n     |- Try 75 * 21 = 1575. Evaluate 1575 != 30, drop this branch.\n     |- Try 75 \/ 21 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 40 * 19 = 760. Add 760 to the number set. Current number set: [760, 75], target: 30, just two numbers left.\n     |- Try 760 + 75 = 835. Evaluate 835 != 30, drop this branch.\n     |- Try 760 - 75 = 685. Evaluate 685 != 30, drop this branch.\n     |- Try 760 * 75 = 57000. 57000 exceeds the maximum intermediate result, drop this branch.\n     |- Try 760 \/ 75 = 10.1. 10.1 is a decimal, drop this branch.\n    |- Try 40 \/ 19 = 2.1. 2.1 is a decimal, drop this branch.\n  |- Try 15 \/ 5 = 3. Add 3 to the number set. Current number set: [3, 40, 19], target: 30. Options for choosing two numbers: [(3, 40), (3, 19), (40, 19)].\n   |- Pick two numbers (3, 40) (numbers left: [19]). Try possible operations.\n    |- Try 40 + 3 = 43. Add 43 to the number set. Current number set: [43, 19], target: 30, just two numbers left.\n     |- Try 43 + 19 = 62. Evaluate 62 != 30, drop this branch.\n     |- Try 43 - 19 = 24. Evaluate 24 != 30, drop this branch.\n     |- Try 43 * 19 = 817. Evaluate 817 != 30, drop this branch.\n     |- Try 43 \/ 19 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 40 - 3 = 37. Add 37 to the number set. Current number set: [37, 19], target: 30, just two numbers left.\n     |- Try 37 + 19 = 56. Evaluate 56 != 30, drop this branch.\n     |- Try 37 - 19 = 18. Evaluate 18 != 30, drop this branch.\n     |- Try 37 * 19 = 703. Evaluate 703 != 30, drop this branch.\n     |- Try 37 \/ 19 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 40 * 3 = 120. Add 120 to the number set. Current number set: [120, 19], target: 30, just two numbers left.\n     |- Try 120 + 19 = 139. Evaluate 139 != 30, drop this branch.\n     |- Try 120 - 19 = 101. Evaluate 101 != 30, drop this branch.\n     |- Try 120 * 19 = 2280. 2280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 120 \/ 19 = 6.3. 6.3 is a decimal, drop this branch.\n    |- Try 40 \/ 3 = 13.3. 13.3 is a decimal, drop this branch.\n   |- Pick two numbers (3, 19) (numbers left: [40]). Try possible operations.\n    |- Try 19 + 3 = 22. Add 22 to the number set. Current number set: [22, 40], target: 30, just two numbers left.\n     |- Try 40 + 22 = 62. Evaluate 62 != 30, drop this branch.\n     |- Try 40 - 22 = 18. Evaluate 18 != 30, drop this branch.\n     |- Try 40 * 22 = 880. Evaluate 880 != 30, drop this branch.\n     |- Try 40 \/ 22 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 19 - 3 = 16. Add 16 to the number set. Current number set: [16, 40], target: 30, just two numbers left.\n     |- Try 40 + 16 = 56. Evaluate 56 != 30, drop this branch.\n     |- Try 40 - 16 = 24. Evaluate 24 != 30, drop this branch.\n     |- Try 40 * 16 = 640. Evaluate 640 != 30, drop this branch.\n     |- Try 40 \/ 16 = 2.5. 2.5 is a decimal, drop this branch.\n    |- Try 19 * 3 = 57. Add 57 to the number set. Current number set: [57, 40], target: 30, just two numbers left.\n     |- Try 57 + 40 = 97. Evaluate 97 != 30, drop this branch.\n     |- Try 57 - 40 = 17. Evaluate 17 != 30, drop this branch.\n     |- Try 57 * 40 = 2280. 2280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 57 \/ 40 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 19 \/ 3 = 6.3. 6.3 is a decimal, drop this branch.\n   |- Pick two numbers (40, 19) (numbers left: [3]). Try possible operations.\n    |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 3], target: 30, just two numbers left.\n     |- Try 59 + 3 = 62. Evaluate 62 != 30, drop this branch.\n     |- Try 59 - 3 = 56. Evaluate 56 != 30, drop this branch.\n     |- Try 59 * 3 = 177. Evaluate 177 != 30, drop this branch.\n     |- Try 59 \/ 3 = 19.7. 19.7 is a decimal, drop this branch.\n    |- Try 40 - 19 = 21. Add 21 to the number set. Current number set: [21, 3], target: 30, just two numbers left.\n     |- Try 21 + 3 = 24. Evaluate 24 != 30, drop this branch.\n     |- Try 21 - 3 = 18. Evaluate 18 != 30, drop this branch.\n     |- Try 21 * 3 = 63. Evaluate 63 != 30, drop this branch.\n     |- Try 21 \/ 3 = 7. Evaluate 7 != 30, drop this branch.\n    |- Try 40 * 19 = 760. Add 760 to the number set. Current number set: [760, 3], target: 30, just two numbers left.\n     |- Try 760 + 3 = 763. Evaluate 763 != 30, drop this branch.\n     |- Try 760 - 3 = 757. Evaluate 757 != 30, drop this branch.\n     |- Try 760 * 3 = 2280. 2280 exceeds the maximum intermediate result, drop this branch.\n     |- Try 760 \/ 3 = 253.3. 253.3 is a decimal, drop this branch.\n    |- Try 40 \/ 19 = 2.1. 2.1 is a decimal, drop this branch.\n |- Pick two numbers (15, 40) (numbers left: [5, 19]). Try possible operations.\n  |- Try 40 + 15 = 55. Add 55 to the number set. Current number set: [55, 5, 19], target: 30. Options for choosing two numbers: [(55, 5), (55, 19), (5, 19)].\n   |- Pick two numbers (55, 5) (numbers left: [19]). Try possible operations.\n    |- Try 55 + 5 = 60. Add 60 to the number set. Current number set: [60, 19], target: 30, just two numbers left.\n     |- Try 60 + 19 = 79. Evaluate 79 != 30, drop this branch.\n     |- Try 60 - 19 = 41. Evaluate 41 != 30, drop this branch.\n     |- Try 60 * 19 = 1140. Evaluate 1140 != 30, drop this branch.\n     |- Try 60 \/ 19 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 55 - 5 = 50. Add 50 to the number set. Current number set: [50, 19], target: 30, just two numbers left.\n     |- Try 50 + 19 = 69. Evaluate 69 != 30, drop this branch.\n     |- Try 50 - 19 = 31. Evaluate 31 != 30, drop this branch.\n     |- Try 50 * 19 = 950. Evaluate 950 != 30, drop this branch.\n     |- Try 50 \/ 19 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 55 * 5 = 275. Add 275 to the number set. Current number set: [275, 19], target: 30, just two numbers left.\n     |- Try 275 + 19 = 294. Evaluate 294 != 30, drop this branch.\n     |- Try 275 - 19 = 256. Evaluate 256 != 30, drop this branch.\n     |- Try 275 * 19 = 5225. 5225 exceeds the maximum intermediate result, drop this branch.\n     |- Try 275 \/ 19 = 14.5. 14.5 is a decimal, drop this branch.\n    |- Try 55 \/ 5 = 11. Add 11 to the number set. Current number set: [11, 19], target: 30, just two numbers left.\n     |- Try 19 + 11 = 30. Evaluate 30 == 30, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 19 + 11 = 30\nThe step before: 55 \/ 5 = 11\nThe first step: 40 + 15 = 55\n\nOutput the solution in the required format:\n<Solution>\n40 + 15 = 55\n55 \/ 5 = 11\n19 + 11 = 30\n<\/Solution>\n","item":{"nums":[15,5,40,19],"solution":["40 + 15 = 55","55 \/ 5 = 11","19 + 11 = 30"],"target":30}}
+{"instance_id":"countdown_8k_195","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [17, 26, 3, 43]\nTarget: 34","reference_output":"# Search Procedure\nInitial number set: [17, 26, 3, 43], target: 34. Options for choosing two numbers: [(17, 26), (17, 3), (17, 43), (26, 3), (26, 43), (3, 43)].\n |- Pick two numbers (17, 26) (numbers left: [3, 43]). Try possible operations.\n  |- Try 26 + 17 = 43. Add 43 to the number set. Current number set: [43, 3, 43], target: 34. Options for choosing two numbers: [(43, 3), (43, 43), (3, 43)].\n   |- Pick two numbers (43, 3) (numbers left: [43]). Try possible operations.\n    |- Try 43 + 3 = 46. Add 46 to the number set. Current number set: [46, 43], target: 34, just two numbers left.\n     |- Try 46 + 43 = 89. Evaluate 89 != 34, drop this branch.\n     |- Try 46 - 43 = 3. Evaluate 3 != 34, drop this branch.\n     |- Try 46 * 43 = 1978. Evaluate 1978 != 34, drop this branch.\n     |- Try 46 \/ 43 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 43 - 3 = 40. Add 40 to the number set. Current number set: [40, 43], target: 34, just two numbers left.\n     |- Try 43 + 40 = 83. Evaluate 83 != 34, drop this branch.\n     |- Try 43 - 40 = 3. Evaluate 3 != 34, drop this branch.\n     |- Try 43 * 40 = 1720. Evaluate 1720 != 34, drop this branch.\n     |- Try 43 \/ 40 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 43 * 3 = 129. Add 129 to the number set. Current number set: [129, 43], target: 34, just two numbers left.\n     |- Try 129 + 43 = 172. Evaluate 172 != 34, drop this branch.\n     |- Try 129 - 43 = 86. Evaluate 86 != 34, drop this branch.\n     |- Try 129 * 43 = 5547. 5547 exceeds the maximum intermediate result, drop this branch.\n     |- Try 129 \/ 43 = 3. Evaluate 3 != 34, drop this branch.\n    |- Try 43 \/ 3 = 14.3. 14.3 is a decimal, drop this branch.\n   |- Pick two numbers (43, 43) (numbers left: [3]). Try possible operations.\n    |- Try 43 + 43 = 86. Add 86 to the number set. Current number set: [86, 3], target: 34, just two numbers left.\n     |- Try 86 + 3 = 89. Evaluate 89 != 34, drop this branch.\n     |- Try 86 - 3 = 83. Evaluate 83 != 34, drop this branch.\n     |- Try 86 * 3 = 258. Evaluate 258 != 34, drop this branch.\n     |- Try 86 \/ 3 = 28.7. 28.7 is a decimal, drop this branch.\n    |- Try 43 - 43 = 0. Add 0 to the number set. Current number set: [0, 3], target: 34, just two numbers left.\n     |- Try 3 + 0 = 3. Evaluate 3 != 34, drop this branch.\n     |- Try 3 - 0 = 3. Evaluate 3 != 34, drop this branch.\n     |- Try 3 * 0 = 0. Evaluate 0 != 34, drop this branch.\n     |- Try 3 \/ 0 (invalid operation). drop this branch.\n    |- Try 43 * 43 = 1849. Add 1849 to the number set. Current number set: [1849, 3], target: 34, just two numbers left.\n     |- Try 1849 + 3 = 1852. Evaluate 1852 != 34, drop this branch.\n     |- Try 1849 - 3 = 1846. Evaluate 1846 != 34, drop this branch.\n     |- Try 1849 * 3 = 5547. 5547 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1849 \/ 3 = 616.3. 616.3 is a decimal, drop this branch.\n    |- Try 43 \/ 43 = 1. Add 1 to the number set. Current number set: [1, 3], target: 34, just two numbers left.\n     |- Try 3 + 1 = 4. Evaluate 4 != 34, drop this branch.\n     |- Try 3 - 1 = 2. Evaluate 2 != 34, drop this branch.\n     |- Try 3 * 1 = 3. Evaluate 3 != 34, drop this branch.\n     |- Try 3 \/ 1 = 3. Evaluate 3 != 34, drop this branch.\n   |- Pick two numbers (3, 43) (numbers left: [43]). Try possible operations.\n    |- Try 43 + 3 = 46. Add 46 to the number set. Current number set: [46, 43], target: 34, just two numbers left.\n     |- Try 46 + 43 = 89. Evaluate 89 != 34, drop this branch.\n     |- Try 46 - 43 = 3. Evaluate 3 != 34, drop this branch.\n     |- Try 46 * 43 = 1978. Evaluate 1978 != 34, drop this branch.\n     |- Try 46 \/ 43 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 43 - 3 = 40. Add 40 to the number set. Current number set: [40, 43], target: 34, just two numbers left.\n     |- Try 43 + 40 = 83. Evaluate 83 != 34, drop this branch.\n     |- Try 43 - 40 = 3. Evaluate 3 != 34, drop this branch.\n     |- Try 43 * 40 = 1720. Evaluate 1720 != 34, drop this branch.\n     |- Try 43 \/ 40 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 43 * 3 = 129. Add 129 to the number set. Current number set: [129, 43], target: 34, just two numbers left.\n     |- Try 129 + 43 = 172. Evaluate 172 != 34, drop this branch.\n     |- Try 129 - 43 = 86. Evaluate 86 != 34, drop this branch.\n     |- Try 129 * 43 = 5547. 5547 exceeds the maximum intermediate result, drop this branch.\n     |- Try 129 \/ 43 = 3. Evaluate 3 != 34, drop this branch.\n    |- Try 43 \/ 3 = 14.3. 14.3 is a decimal, drop this branch.\n  |- Try 26 - 17 = 9. Add 9 to the number set. Current number set: [9, 3, 43], target: 34. Options for choosing two numbers: [(9, 3), (9, 43), (3, 43)].\n   |- Pick two numbers (9, 3) (numbers left: [43]). Try possible operations.\n    |- Try 9 + 3 = 12. Add 12 to the number set. Current number set: [12, 43], target: 34, just two numbers left.\n     |- Try 43 + 12 = 55. Evaluate 55 != 34, drop this branch.\n     |- Try 43 - 12 = 31. Evaluate 31 != 34, drop this branch.\n     |- Try 43 * 12 = 516. Evaluate 516 != 34, drop this branch.\n     |- Try 43 \/ 12 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 9 - 3 = 6. Add 6 to the number set. Current number set: [6, 43], target: 34, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 34, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 34, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 34, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 9 * 3 = 27. Add 27 to the number set. Current number set: [27, 43], target: 34, just two numbers left.\n     |- Try 43 + 27 = 70. Evaluate 70 != 34, drop this branch.\n     |- Try 43 - 27 = 16. Evaluate 16 != 34, drop this branch.\n     |- Try 43 * 27 = 1161. Evaluate 1161 != 34, drop this branch.\n     |- Try 43 \/ 27 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 9 \/ 3 = 3. Add 3 to the number set. Current number set: [3, 43], target: 34, just two numbers left.\n     |- Try 43 + 3 = 46. Evaluate 46 != 34, drop this branch.\n     |- Try 43 - 3 = 40. Evaluate 40 != 34, drop this branch.\n     |- Try 43 * 3 = 129. Evaluate 129 != 34, drop this branch.\n     |- Try 43 \/ 3 = 14.3. 14.3 is a decimal, drop this branch.\n   |- Pick two numbers (9, 43) (numbers left: [3]). Try possible operations.\n    |- Try 43 + 9 = 52. Add 52 to the number set. Current number set: [52, 3], target: 34, just two numbers left.\n     |- Try 52 + 3 = 55. Evaluate 55 != 34, drop this branch.\n     |- Try 52 - 3 = 49. Evaluate 49 != 34, drop this branch.\n     |- Try 52 * 3 = 156. Evaluate 156 != 34, drop this branch.\n     |- Try 52 \/ 3 = 17.3. 17.3 is a decimal, drop this branch.\n    |- Try 43 - 9 = 34. Add 34 to the number set. Current number set: [34, 3], target: 34, just two numbers left.\n     |- Try 34 + 3 = 37. Evaluate 37 != 34, drop this branch.\n     |- Try 34 - 3 = 31. Evaluate 31 != 34, drop this branch.\n     |- Try 34 * 3 = 102. Evaluate 102 != 34, drop this branch.\n     |- Try 34 \/ 3 = 11.3. 11.3 is a decimal, drop this branch.\n    |- Try 43 * 9 = 387. Add 387 to the number set. Current number set: [387, 3], target: 34, just two numbers left.\n     |- Try 387 + 3 = 390. Evaluate 390 != 34, drop this branch.\n     |- Try 387 - 3 = 384. Evaluate 384 != 34, drop this branch.\n     |- Try 387 * 3 = 1161. Evaluate 1161 != 34, drop this branch.\n     |- Try 387 \/ 3 = 129. Evaluate 129 != 34, drop this branch.\n    |- Try 43 \/ 9 = 4.8. 4.8 is a decimal, drop this branch.\n   |- Pick two numbers (3, 43) (numbers left: [9]). Try possible operations.\n    |- Try 43 + 3 = 46. Add 46 to the number set. Current number set: [46, 9], target: 34, just two numbers left.\n     |- Try 46 + 9 = 55. Evaluate 55 != 34, drop this branch.\n     |- Try 46 - 9 = 37. Evaluate 37 != 34, drop this branch.\n     |- Try 46 * 9 = 414. Evaluate 414 != 34, drop this branch.\n     |- Try 46 \/ 9 = 5.1. 5.1 is a decimal, drop this branch.\n    |- Try 43 - 3 = 40. Add 40 to the number set. Current number set: [40, 9], target: 34, just two numbers left.\n     |- Try 40 + 9 = 49. Evaluate 49 != 34, drop this branch.\n     |- Try 40 - 9 = 31. Evaluate 31 != 34, drop this branch.\n     |- Try 40 * 9 = 360. Evaluate 360 != 34, drop this branch.\n     |- Try 40 \/ 9 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 43 * 3 = 129. Add 129 to the number set. Current number set: [129, 9], target: 34, just two numbers left.\n     |- Try 129 + 9 = 138. Evaluate 138 != 34, drop this branch.\n     |- Try 129 - 9 = 120. Evaluate 120 != 34, drop this branch.\n     |- Try 129 * 9 = 1161. Evaluate 1161 != 34, drop this branch.\n     |- Try 129 \/ 9 = 14.3. 14.3 is a decimal, drop this branch.\n    |- Try 43 \/ 3 = 14.3. 14.3 is a decimal, drop this branch.\n  |- Try 26 * 17 = 442. Add 442 to the number set. Current number set: [442, 3, 43], target: 34. Options for choosing two numbers: [(442, 3), (442, 43), (3, 43)].\n   |- Pick two numbers (442, 3) (numbers left: [43]). Try possible operations.\n    |- Try 442 + 3 = 445. Add 445 to the number set. Current number set: [445, 43], target: 34, just two numbers left.\n     |- Try 445 + 43 = 488. Evaluate 488 != 34, drop this branch.\n     |- Try 445 - 43 = 402. Evaluate 402 != 34, drop this branch.\n     |- Try 445 * 43 = 19135. 19135 exceeds the maximum intermediate result, drop this branch.\n     |- Try 445 \/ 43 = 10.3. 10.3 is a decimal, drop this branch.\n    |- Try 442 - 3 = 439. Add 439 to the number set. Current number set: [439, 43], target: 34, just two numbers left.\n     |- Try 439 + 43 = 482. Evaluate 482 != 34, drop this branch.\n     |- Try 439 - 43 = 396. Evaluate 396 != 34, drop this branch.\n     |- Try 439 * 43 = 18877. 18877 exceeds the maximum intermediate result, drop this branch.\n     |- Try 439 \/ 43 = 10.2. 10.2 is a decimal, drop this branch.\n    |- Try 442 * 3 = 1326. Add 1326 to the number set. Current number set: [1326, 43], target: 34, just two numbers left.\n     |- Try 1326 + 43 = 1369. Evaluate 1369 != 34, drop this branch.\n     |- Try 1326 - 43 = 1283. Evaluate 1283 != 34, drop this branch.\n     |- Try 1326 * 43 = 57018. 57018 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1326 \/ 43 = 30.8. 30.8 is a decimal, drop this branch.\n    |- Try 442 \/ 3 = 147.3. 147.3 is a decimal, drop this branch.\n   |- Pick two numbers (442, 43) (numbers left: [3]). Try possible operations.\n    |- Try 442 + 43 = 485. Add 485 to the number set. Current number set: [485, 3], target: 34, just two numbers left.\n     |- Try 485 + 3 = 488. Evaluate 488 != 34, drop this branch.\n     |- Try 485 - 3 = 482. Evaluate 482 != 34, drop this branch.\n     |- Try 485 * 3 = 1455. Evaluate 1455 != 34, drop this branch.\n     |- Try 485 \/ 3 = 161.7. 161.7 is a decimal, drop this branch.\n    |- Try 442 - 43 = 399. Add 399 to the number set. Current number set: [399, 3], target: 34, just two numbers left.\n     |- Try 399 + 3 = 402. Evaluate 402 != 34, drop this branch.\n     |- Try 399 - 3 = 396. Evaluate 396 != 34, drop this branch.\n     |- Try 399 * 3 = 1197. Evaluate 1197 != 34, drop this branch.\n     |- Try 399 \/ 3 = 133. Evaluate 133 != 34, drop this branch.\n    |- Try 442 * 43 = 19006. 19006 exceeds the maximum intermediate result, drop this branch.\n    |- Try 442 \/ 43 = 10.3. 10.3 is a decimal, drop this branch.\n   |- Pick two numbers (3, 43) (numbers left: [442]). Try possible operations.\n    |- Try 43 + 3 = 46. Add 46 to the number set. Current number set: [46, 442], target: 34, just two numbers left.\n     |- Try 442 + 46 = 488. Evaluate 488 != 34, drop this branch.\n     |- Try 442 - 46 = 396. Evaluate 396 != 34, drop this branch.\n     |- Try 442 * 46 = 20332. 20332 exceeds the maximum intermediate result, drop this branch.\n     |- Try 442 \/ 46 = 9.6. 9.6 is a decimal, drop this branch.\n    |- Try 43 - 3 = 40. Add 40 to the number set. Current number set: [40, 442], target: 34, just two numbers left.\n     |- Try 442 + 40 = 482. Evaluate 482 != 34, drop this branch.\n     |- Try 442 - 40 = 402. Evaluate 402 != 34, drop this branch.\n     |- Try 442 * 40 = 17680. 17680 exceeds the maximum intermediate result, drop this branch.\n     |- Try 442 \/ 40 = 11.1. 11.1 is a decimal, drop this branch.\n    |- Try 43 * 3 = 129. Add 129 to the number set. Current number set: [129, 442], target: 34, just two numbers left.\n     |- Try 442 + 129 = 571. Evaluate 571 != 34, drop this branch.\n     |- Try 442 - 129 = 313. Evaluate 313 != 34, drop this branch.\n     |- Try 442 * 129 = 57018. 57018 exceeds the maximum intermediate result, drop this branch.\n     |- Try 442 \/ 129 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 43 \/ 3 = 14.3. 14.3 is a decimal, drop this branch.\n  |- Try 26 \/ 17 = 1.5. 1.5 is a decimal, drop this branch.\n |- Pick two numbers (17, 3) (numbers left: [26, 43]). Try possible operations.\n  |- Try 17 + 3 = 20. Add 20 to the number set. Current number set: [20, 26, 43], target: 34. Options for choosing two numbers: [(20, 26), (20, 43), (26, 43)].\n   |- Pick two numbers (20, 26) (numbers left: [43]). Try possible operations.\n    |- Try 26 + 20 = 46. Add 46 to the number set. Current number set: [46, 43], target: 34, just two numbers left.\n     |- Try 46 + 43 = 89. Evaluate 89 != 34, drop this branch.\n     |- Try 46 - 43 = 3. Evaluate 3 != 34, drop this branch.\n     |- Try 46 * 43 = 1978. Evaluate 1978 != 34, drop this branch.\n     |- Try 46 \/ 43 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 26 - 20 = 6. Add 6 to the number set. Current number set: [6, 43], target: 34, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 34, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 34, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 34, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 26 * 20 = 520. Add 520 to the number set. Current number set: [520, 43], target: 34, just two numbers left.\n     |- Try 520 + 43 = 563. Evaluate 563 != 34, drop this branch.\n     |- Try 520 - 43 = 477. Evaluate 477 != 34, drop this branch.\n     |- Try 520 * 43 = 22360. 22360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 520 \/ 43 = 12.1. 12.1 is a decimal, drop this branch.\n    |- Try 26 \/ 20 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (20, 43) (numbers left: [26]). Try possible operations.\n    |- Try 43 + 20 = 63. Add 63 to the number set. Current number set: [63, 26], target: 34, just two numbers left.\n     |- Try 63 + 26 = 89. Evaluate 89 != 34, drop this branch.\n     |- Try 63 - 26 = 37. Evaluate 37 != 34, drop this branch.\n     |- Try 63 * 26 = 1638. Evaluate 1638 != 34, drop this branch.\n     |- Try 63 \/ 26 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 43 - 20 = 23. Add 23 to the number set. Current number set: [23, 26], target: 34, just two numbers left.\n     |- Try 26 + 23 = 49. Evaluate 49 != 34, drop this branch.\n     |- Try 26 - 23 = 3. Evaluate 3 != 34, drop this branch.\n     |- Try 26 * 23 = 598. Evaluate 598 != 34, drop this branch.\n     |- Try 26 \/ 23 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 43 * 20 = 860. Add 860 to the number set. Current number set: [860, 26], target: 34, just two numbers left.\n     |- Try 860 + 26 = 886. Evaluate 886 != 34, drop this branch.\n     |- Try 860 - 26 = 834. Evaluate 834 != 34, drop this branch.\n     |- Try 860 * 26 = 22360. 22360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 860 \/ 26 = 33.1. 33.1 is a decimal, drop this branch.\n    |- Try 43 \/ 20 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (26, 43) (numbers left: [20]). Try possible operations.\n    |- Try 43 + 26 = 69. Add 69 to the number set. Current number set: [69, 20], target: 34, just two numbers left.\n     |- Try 69 + 20 = 89. Evaluate 89 != 34, drop this branch.\n     |- Try 69 - 20 = 49. Evaluate 49 != 34, drop this branch.\n     |- Try 69 * 20 = 1380. Evaluate 1380 != 34, drop this branch.\n     |- Try 69 \/ 20 = 3.5. 3.5 is a decimal, drop this branch.\n    |- Try 43 - 26 = 17. Add 17 to the number set. Current number set: [17, 20], target: 34, just two numbers left.\n     |- Try 20 + 17 = 37. Evaluate 37 != 34, drop this branch.\n     |- Try 20 - 17 = 3. Evaluate 3 != 34, drop this branch.\n     |- Try 20 * 17 = 340. Evaluate 340 != 34, drop this branch.\n     |- Try 20 \/ 17 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 43 * 26 = 1118. Add 1118 to the number set. Current number set: [1118, 20], target: 34, just two numbers left.\n     |- Try 1118 + 20 = 1138. Evaluate 1138 != 34, drop this branch.\n     |- Try 1118 - 20 = 1098. Evaluate 1098 != 34, drop this branch.\n     |- Try 1118 * 20 = 22360. 22360 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1118 \/ 20 = 55.9. 55.9 is a decimal, drop this branch.\n    |- Try 43 \/ 26 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 17 - 3 = 14. Add 14 to the number set. Current number set: [14, 26, 43], target: 34. Options for choosing two numbers: [(14, 26), (14, 43), (26, 43)].\n   |- Pick two numbers (14, 26) (numbers left: [43]). Try possible operations.\n    |- Try 26 + 14 = 40. Add 40 to the number set. Current number set: [40, 43], target: 34, just two numbers left.\n     |- Try 43 + 40 = 83. Evaluate 83 != 34, drop this branch.\n     |- Try 43 - 40 = 3. Evaluate 3 != 34, drop this branch.\n     |- Try 43 * 40 = 1720. Evaluate 1720 != 34, drop this branch.\n     |- Try 43 \/ 40 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 26 - 14 = 12. Add 12 to the number set. Current number set: [12, 43], target: 34, just two numbers left.\n     |- Try 43 + 12 = 55. Evaluate 55 != 34, drop this branch.\n     |- Try 43 - 12 = 31. Evaluate 31 != 34, drop this branch.\n     |- Try 43 * 12 = 516. Evaluate 516 != 34, drop this branch.\n     |- Try 43 \/ 12 = 3.6. 3.6 is a decimal, drop this branch.\n    |- Try 26 * 14 = 364. Add 364 to the number set. Current number set: [364, 43], target: 34, just two numbers left.\n     |- Try 364 + 43 = 407. Evaluate 407 != 34, drop this branch.\n     |- Try 364 - 43 = 321. Evaluate 321 != 34, drop this branch.\n     |- Try 364 * 43 = 15652. 15652 exceeds the maximum intermediate result, drop this branch.\n     |- Try 364 \/ 43 = 8.5. 8.5 is a decimal, drop this branch.\n    |- Try 26 \/ 14 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (14, 43) (numbers left: [26]). Try possible operations.\n    |- Try 43 + 14 = 57. Add 57 to the number set. Current number set: [57, 26], target: 34, just two numbers left.\n     |- Try 57 + 26 = 83. Evaluate 83 != 34, drop this branch.\n     |- Try 57 - 26 = 31. Evaluate 31 != 34, drop this branch.\n     |- Try 57 * 26 = 1482. Evaluate 1482 != 34, drop this branch.\n     |- Try 57 \/ 26 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 43 - 14 = 29. Add 29 to the number set. Current number set: [29, 26], target: 34, just two numbers left.\n     |- Try 29 + 26 = 55. Evaluate 55 != 34, drop this branch.\n     |- Try 29 - 26 = 3. Evaluate 3 != 34, drop this branch.\n     |- Try 29 * 26 = 754. Evaluate 754 != 34, drop this branch.\n     |- Try 29 \/ 26 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 43 * 14 = 602. Add 602 to the number set. Current number set: [602, 26], target: 34, just two numbers left.\n     |- Try 602 + 26 = 628. Evaluate 628 != 34, drop this branch.\n     |- Try 602 - 26 = 576. Evaluate 576 != 34, drop this branch.\n     |- Try 602 * 26 = 15652. 15652 exceeds the maximum intermediate result, drop this branch.\n     |- Try 602 \/ 26 = 23.2. 23.2 is a decimal, drop this branch.\n    |- Try 43 \/ 14 = 3.1. 3.1 is a decimal, drop this branch.\n   |- Pick two numbers (26, 43) (numbers left: [14]). Try possible operations.\n    |- Try 43 + 26 = 69. Add 69 to the number set. Current number set: [69, 14], target: 34, just two numbers left.\n     |- Try 69 + 14 = 83. Evaluate 83 != 34, drop this branch.\n     |- Try 69 - 14 = 55. Evaluate 55 != 34, drop this branch.\n     |- Try 69 * 14 = 966. Evaluate 966 != 34, drop this branch.\n     |- Try 69 \/ 14 = 4.9. 4.9 is a decimal, drop this branch.\n    |- Try 43 - 26 = 17. Add 17 to the number set. Current number set: [17, 14], target: 34, just two numbers left.\n     |- Try 17 + 14 = 31. Evaluate 31 != 34, drop this branch.\n     |- Try 17 - 14 = 3. Evaluate 3 != 34, drop this branch.\n     |- Try 17 * 14 = 238. Evaluate 238 != 34, drop this branch.\n     |- Try 17 \/ 14 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 43 * 26 = 1118. Add 1118 to the number set. Current number set: [1118, 14], target: 34, just two numbers left.\n     |- Try 1118 + 14 = 1132. Evaluate 1132 != 34, drop this branch.\n     |- Try 1118 - 14 = 1104. Evaluate 1104 != 34, drop this branch.\n     |- Try 1118 * 14 = 15652. 15652 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1118 \/ 14 = 79.9. 79.9 is a decimal, drop this branch.\n    |- Try 43 \/ 26 = 1.7. 1.7 is a decimal, drop this branch.\n  |- Try 17 * 3 = 51. Add 51 to the number set. Current number set: [51, 26, 43], target: 34. Options for choosing two numbers: [(51, 26), (51, 43), (26, 43)].\n   |- Pick two numbers (51, 26) (numbers left: [43]). Try possible operations.\n    |- Try 51 + 26 = 77. Add 77 to the number set. Current number set: [77, 43], target: 34, just two numbers left.\n     |- Try 77 + 43 = 120. Evaluate 120 != 34, drop this branch.\n     |- Try 77 - 43 = 34. Evaluate 34 == 34, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 77 - 43 = 34\nThe step before: 51 + 26 = 77\nThe first step: 17 * 3 = 51\n\nOutput the solution in the required format:\n<Solution>\n17 * 3 = 51\n51 + 26 = 77\n77 - 43 = 34\n<\/Solution>\n","item":{"nums":[17,26,3,43],"solution":["17 * 3 = 51","51 + 26 = 77","77 - 43 = 34"],"target":34}}
+{"instance_id":"countdown_8k_196","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [42, 25, 36, 33]\nTarget: 48","reference_output":"# Search Procedure\nInitial number set: [42, 25, 36, 33], target: 48. Options for choosing two numbers: [(42, 25), (42, 36), (42, 33), (25, 36), (25, 33), (36, 33)].\n |- Pick two numbers (42, 25) (numbers left: [36, 33]). Try possible operations.\n  |- Try 42 + 25 = 67. Add 67 to the number set. Current number set: [67, 36, 33], target: 48. Options for choosing two numbers: [(67, 36), (67, 33), (36, 33)].\n   |- Pick two numbers (67, 36) (numbers left: [33]). Try possible operations.\n    |- Try 67 + 36 = 103. Add 103 to the number set. Current number set: [103, 33], target: 48, just two numbers left.\n     |- Try 103 + 33 = 136. Evaluate 136 != 48, drop this branch.\n     |- Try 103 - 33 = 70. Evaluate 70 != 48, drop this branch.\n     |- Try 103 * 33 = 3399. 3399 exceeds the maximum intermediate result, drop this branch.\n     |- Try 103 \/ 33 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 67 - 36 = 31. Add 31 to the number set. Current number set: [31, 33], target: 48, just two numbers left.\n     |- Try 33 + 31 = 64. Evaluate 64 != 48, drop this branch.\n     |- Try 33 - 31 = 2. Evaluate 2 != 48, drop this branch.\n     |- Try 33 * 31 = 1023. Evaluate 1023 != 48, drop this branch.\n     |- Try 33 \/ 31 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 67 * 36 = 2412. 2412 exceeds the maximum intermediate result, drop this branch.\n    |- Try 67 \/ 36 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (67, 33) (numbers left: [36]). Try possible operations.\n    |- Try 67 + 33 = 100. Add 100 to the number set. Current number set: [100, 36], target: 48, just two numbers left.\n     |- Try 100 + 36 = 136. Evaluate 136 != 48, drop this branch.\n     |- Try 100 - 36 = 64. Evaluate 64 != 48, drop this branch.\n     |- Try 100 * 36 = 3600. 3600 exceeds the maximum intermediate result, drop this branch.\n     |- Try 100 \/ 36 = 2.8. 2.8 is a decimal, drop this branch.\n    |- Try 67 - 33 = 34. Add 34 to the number set. Current number set: [34, 36], target: 48, just two numbers left.\n     |- Try 36 + 34 = 70. Evaluate 70 != 48, drop this branch.\n     |- Try 36 - 34 = 2. Evaluate 2 != 48, drop this branch.\n     |- Try 36 * 34 = 1224. Evaluate 1224 != 48, drop this branch.\n     |- Try 36 \/ 34 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 67 * 33 = 2211. 2211 exceeds the maximum intermediate result, drop this branch.\n    |- Try 67 \/ 33 = 2.0. 2.0 is a decimal, drop this branch.\n   |- Pick two numbers (36, 33) (numbers left: [67]). Try possible operations.\n    |- Try 36 + 33 = 69. Add 69 to the number set. Current number set: [69, 67], target: 48, just two numbers left.\n     |- Try 69 + 67 = 136. Evaluate 136 != 48, drop this branch.\n     |- Try 69 - 67 = 2. Evaluate 2 != 48, drop this branch.\n     |- Try 69 * 67 = 4623. 4623 exceeds the maximum intermediate result, drop this branch.\n     |- Try 69 \/ 67 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 36 - 33 = 3. Add 3 to the number set. Current number set: [3, 67], target: 48, just two numbers left.\n     |- Try 67 + 3 = 70. Evaluate 70 != 48, drop this branch.\n     |- Try 67 - 3 = 64. Evaluate 64 != 48, drop this branch.\n     |- Try 67 * 3 = 201. Evaluate 201 != 48, drop this branch.\n     |- Try 67 \/ 3 = 22.3. 22.3 is a decimal, drop this branch.\n    |- Try 36 * 33 = 1188. Add 1188 to the number set. Current number set: [1188, 67], target: 48, just two numbers left.\n     |- Try 1188 + 67 = 1255. Evaluate 1255 != 48, drop this branch.\n     |- Try 1188 - 67 = 1121. Evaluate 1121 != 48, drop this branch.\n     |- Try 1188 * 67 = 79596. 79596 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1188 \/ 67 = 17.7. 17.7 is a decimal, drop this branch.\n    |- Try 36 \/ 33 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 42 - 25 = 17. Add 17 to the number set. Current number set: [17, 36, 33], target: 48. Options for choosing two numbers: [(17, 36), (17, 33), (36, 33)].\n   |- Pick two numbers (17, 36) (numbers left: [33]). Try possible operations.\n    |- Try 36 + 17 = 53. Add 53 to the number set. Current number set: [53, 33], target: 48, just two numbers left.\n     |- Try 53 + 33 = 86. Evaluate 86 != 48, drop this branch.\n     |- Try 53 - 33 = 20. Evaluate 20 != 48, drop this branch.\n     |- Try 53 * 33 = 1749. Evaluate 1749 != 48, drop this branch.\n     |- Try 53 \/ 33 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 36 - 17 = 19. Add 19 to the number set. Current number set: [19, 33], target: 48, just two numbers left.\n     |- Try 33 + 19 = 52. Evaluate 52 != 48, drop this branch.\n     |- Try 33 - 19 = 14. Evaluate 14 != 48, drop this branch.\n     |- Try 33 * 19 = 627. Evaluate 627 != 48, drop this branch.\n     |- Try 33 \/ 19 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 36 * 17 = 612. Add 612 to the number set. Current number set: [612, 33], target: 48, just two numbers left.\n     |- Try 612 + 33 = 645. Evaluate 645 != 48, drop this branch.\n     |- Try 612 - 33 = 579. Evaluate 579 != 48, drop this branch.\n     |- Try 612 * 33 = 20196. 20196 exceeds the maximum intermediate result, drop this branch.\n     |- Try 612 \/ 33 = 18.5. 18.5 is a decimal, drop this branch.\n    |- Try 36 \/ 17 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (17, 33) (numbers left: [36]). Try possible operations.\n    |- Try 33 + 17 = 50. Add 50 to the number set. Current number set: [50, 36], target: 48, just two numbers left.\n     |- Try 50 + 36 = 86. Evaluate 86 != 48, drop this branch.\n     |- Try 50 - 36 = 14. Evaluate 14 != 48, drop this branch.\n     |- Try 50 * 36 = 1800. Evaluate 1800 != 48, drop this branch.\n     |- Try 50 \/ 36 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 33 - 17 = 16. Add 16 to the number set. Current number set: [16, 36], target: 48, just two numbers left.\n     |- Try 36 + 16 = 52. Evaluate 52 != 48, drop this branch.\n     |- Try 36 - 16 = 20. Evaluate 20 != 48, drop this branch.\n     |- Try 36 * 16 = 576. Evaluate 576 != 48, drop this branch.\n     |- Try 36 \/ 16 = 2.2. 2.2 is a decimal, drop this branch.\n    |- Try 33 * 17 = 561. Add 561 to the number set. Current number set: [561, 36], target: 48, just two numbers left.\n     |- Try 561 + 36 = 597. Evaluate 597 != 48, drop this branch.\n     |- Try 561 - 36 = 525. Evaluate 525 != 48, drop this branch.\n     |- Try 561 * 36 = 20196. 20196 exceeds the maximum intermediate result, drop this branch.\n     |- Try 561 \/ 36 = 15.6. 15.6 is a decimal, drop this branch.\n    |- Try 33 \/ 17 = 1.9. 1.9 is a decimal, drop this branch.\n   |- Pick two numbers (36, 33) (numbers left: [17]). Try possible operations.\n    |- Try 36 + 33 = 69. Add 69 to the number set. Current number set: [69, 17], target: 48, just two numbers left.\n     |- Try 69 + 17 = 86. Evaluate 86 != 48, drop this branch.\n     |- Try 69 - 17 = 52. Evaluate 52 != 48, drop this branch.\n     |- Try 69 * 17 = 1173. Evaluate 1173 != 48, drop this branch.\n     |- Try 69 \/ 17 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 36 - 33 = 3. Add 3 to the number set. Current number set: [3, 17], target: 48, just two numbers left.\n     |- Try 17 + 3 = 20. Evaluate 20 != 48, drop this branch.\n     |- Try 17 - 3 = 14. Evaluate 14 != 48, drop this branch.\n     |- Try 17 * 3 = 51. Evaluate 51 != 48, drop this branch.\n     |- Try 17 \/ 3 = 5.7. 5.7 is a decimal, drop this branch.\n    |- Try 36 * 33 = 1188. Add 1188 to the number set. Current number set: [1188, 17], target: 48, just two numbers left.\n     |- Try 1188 + 17 = 1205. Evaluate 1205 != 48, drop this branch.\n     |- Try 1188 - 17 = 1171. Evaluate 1171 != 48, drop this branch.\n     |- Try 1188 * 17 = 20196. 20196 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1188 \/ 17 = 69.9. 69.9 is a decimal, drop this branch.\n    |- Try 36 \/ 33 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 42 * 25 = 1050. Add 1050 to the number set. Current number set: [1050, 36, 33], target: 48. Options for choosing two numbers: [(1050, 36), (1050, 33), (36, 33)].\n   |- Pick two numbers (1050, 36) (numbers left: [33]). Try possible operations.\n    |- Try 1050 + 36 = 1086. Add 1086 to the number set. Current number set: [1086, 33], target: 48, just two numbers left.\n     |- Try 1086 + 33 = 1119. Evaluate 1119 != 48, drop this branch.\n     |- Try 1086 - 33 = 1053. Evaluate 1053 != 48, drop this branch.\n     |- Try 1086 * 33 = 35838. 35838 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1086 \/ 33 = 32.9. 32.9 is a decimal, drop this branch.\n    |- Try 1050 - 36 = 1014. Add 1014 to the number set. Current number set: [1014, 33], target: 48, just two numbers left.\n     |- Try 1014 + 33 = 1047. Evaluate 1047 != 48, drop this branch.\n     |- Try 1014 - 33 = 981. Evaluate 981 != 48, drop this branch.\n     |- Try 1014 * 33 = 33462. 33462 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1014 \/ 33 = 30.7. 30.7 is a decimal, drop this branch.\n    |- Try 1050 * 36 = 37800. 37800 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1050 \/ 36 = 29.2. 29.2 is a decimal, drop this branch.\n   |- Pick two numbers (1050, 33) (numbers left: [36]). Try possible operations.\n    |- Try 1050 + 33 = 1083. Add 1083 to the number set. Current number set: [1083, 36], target: 48, just two numbers left.\n     |- Try 1083 + 36 = 1119. Evaluate 1119 != 48, drop this branch.\n     |- Try 1083 - 36 = 1047. Evaluate 1047 != 48, drop this branch.\n     |- Try 1083 * 36 = 38988. 38988 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1083 \/ 36 = 30.1. 30.1 is a decimal, drop this branch.\n    |- Try 1050 - 33 = 1017. Add 1017 to the number set. Current number set: [1017, 36], target: 48, just two numbers left.\n     |- Try 1017 + 36 = 1053. Evaluate 1053 != 48, drop this branch.\n     |- Try 1017 - 36 = 981. Evaluate 981 != 48, drop this branch.\n     |- Try 1017 * 36 = 36612. 36612 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1017 \/ 36 = 28.2. 28.2 is a decimal, drop this branch.\n    |- Try 1050 * 33 = 34650. 34650 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1050 \/ 33 = 31.8. 31.8 is a decimal, drop this branch.\n   |- Pick two numbers (36, 33) (numbers left: [1050]). Try possible operations.\n    |- Try 36 + 33 = 69. Add 69 to the number set. Current number set: [69, 1050], target: 48, just two numbers left.\n     |- Try 1050 + 69 = 1119. Evaluate 1119 != 48, drop this branch.\n     |- Try 1050 - 69 = 981. Evaluate 981 != 48, drop this branch.\n     |- Try 1050 * 69 = 72450. 72450 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1050 \/ 69 = 15.2. 15.2 is a decimal, drop this branch.\n    |- Try 36 - 33 = 3. Add 3 to the number set. Current number set: [3, 1050], target: 48, just two numbers left.\n     |- Try 1050 + 3 = 1053. Evaluate 1053 != 48, drop this branch.\n     |- Try 1050 - 3 = 1047. Evaluate 1047 != 48, drop this branch.\n     |- Try 1050 * 3 = 3150. 3150 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1050 \/ 3 = 350. Evaluate 350 != 48, drop this branch.\n    |- Try 36 * 33 = 1188. Add 1188 to the number set. Current number set: [1188, 1050], target: 48, just two numbers left.\n     |- Try 1188 + 1050 = 2238. 2238 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1188 - 1050 = 138. Evaluate 138 != 48, drop this branch.\n     |- Try 1188 * 1050 = 1247400. 1247400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1188 \/ 1050 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 36 \/ 33 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 42 \/ 25 = 1.7. 1.7 is a decimal, drop this branch.\n |- Pick two numbers (42, 36) (numbers left: [25, 33]). Try possible operations.\n  |- Try 42 + 36 = 78. Add 78 to the number set. Current number set: [78, 25, 33], target: 48. Options for choosing two numbers: [(78, 25), (78, 33), (25, 33)].\n   |- Pick two numbers (78, 25) (numbers left: [33]). Try possible operations.\n    |- Try 78 + 25 = 103. Add 103 to the number set. Current number set: [103, 33], target: 48, just two numbers left.\n     |- Try 103 + 33 = 136. Evaluate 136 != 48, drop this branch.\n     |- Try 103 - 33 = 70. Evaluate 70 != 48, drop this branch.\n     |- Try 103 * 33 = 3399. 3399 exceeds the maximum intermediate result, drop this branch.\n     |- Try 103 \/ 33 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 78 - 25 = 53. Add 53 to the number set. Current number set: [53, 33], target: 48, just two numbers left.\n     |- Try 53 + 33 = 86. Evaluate 86 != 48, drop this branch.\n     |- Try 53 - 33 = 20. Evaluate 20 != 48, drop this branch.\n     |- Try 53 * 33 = 1749. Evaluate 1749 != 48, drop this branch.\n     |- Try 53 \/ 33 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 78 * 25 = 1950. Add 1950 to the number set. Current number set: [1950, 33], target: 48, just two numbers left.\n     |- Try 1950 + 33 = 1983. Evaluate 1983 != 48, drop this branch.\n     |- Try 1950 - 33 = 1917. Evaluate 1917 != 48, drop this branch.\n     |- Try 1950 * 33 = 64350. 64350 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1950 \/ 33 = 59.1. 59.1 is a decimal, drop this branch.\n    |- Try 78 \/ 25 = 3.1. 3.1 is a decimal, drop this branch.\n   |- Pick two numbers (78, 33) (numbers left: [25]). Try possible operations.\n    |- Try 78 + 33 = 111. Add 111 to the number set. Current number set: [111, 25], target: 48, just two numbers left.\n     |- Try 111 + 25 = 136. Evaluate 136 != 48, drop this branch.\n     |- Try 111 - 25 = 86. Evaluate 86 != 48, drop this branch.\n     |- Try 111 * 25 = 2775. 2775 exceeds the maximum intermediate result, drop this branch.\n     |- Try 111 \/ 25 = 4.4. 4.4 is a decimal, drop this branch.\n    |- Try 78 - 33 = 45. Add 45 to the number set. Current number set: [45, 25], target: 48, just two numbers left.\n     |- Try 45 + 25 = 70. Evaluate 70 != 48, drop this branch.\n     |- Try 45 - 25 = 20. Evaluate 20 != 48, drop this branch.\n     |- Try 45 * 25 = 1125. Evaluate 1125 != 48, drop this branch.\n     |- Try 45 \/ 25 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 78 * 33 = 2574. 2574 exceeds the maximum intermediate result, drop this branch.\n    |- Try 78 \/ 33 = 2.4. 2.4 is a decimal, drop this branch.\n   |- Pick two numbers (25, 33) (numbers left: [78]). Try possible operations.\n    |- Try 33 + 25 = 58. Add 58 to the number set. Current number set: [58, 78], target: 48, just two numbers left.\n     |- Try 78 + 58 = 136. Evaluate 136 != 48, drop this branch.\n     |- Try 78 - 58 = 20. Evaluate 20 != 48, drop this branch.\n     |- Try 78 * 58 = 4524. 4524 exceeds the maximum intermediate result, drop this branch.\n     |- Try 78 \/ 58 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 33 - 25 = 8. Add 8 to the number set. Current number set: [8, 78], target: 48, just two numbers left.\n     |- Try 78 + 8 = 86. Evaluate 86 != 48, drop this branch.\n     |- Try 78 - 8 = 70. Evaluate 70 != 48, drop this branch.\n     |- Try 78 * 8 = 624. Evaluate 624 != 48, drop this branch.\n     |- Try 78 \/ 8 = 9.8. 9.8 is a decimal, drop this branch.\n    |- Try 33 * 25 = 825. Add 825 to the number set. Current number set: [825, 78], target: 48, just two numbers left.\n     |- Try 825 + 78 = 903. Evaluate 903 != 48, drop this branch.\n     |- Try 825 - 78 = 747. Evaluate 747 != 48, drop this branch.\n     |- Try 825 * 78 = 64350. 64350 exceeds the maximum intermediate result, drop this branch.\n     |- Try 825 \/ 78 = 10.6. 10.6 is a decimal, drop this branch.\n    |- Try 33 \/ 25 = 1.3. 1.3 is a decimal, drop this branch.\n  |- Try 42 - 36 = 6. Add 6 to the number set. Current number set: [6, 25, 33], target: 48. Options for choosing two numbers: [(6, 25), (6, 33), (25, 33)].\n   |- Pick two numbers (6, 25) (numbers left: [33]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 33], target: 48, just two numbers left.\n     |- Try 33 + 31 = 64. Evaluate 64 != 48, drop this branch.\n     |- Try 33 - 31 = 2. Evaluate 2 != 48, drop this branch.\n     |- Try 33 * 31 = 1023. Evaluate 1023 != 48, drop this branch.\n     |- Try 33 \/ 31 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 33], target: 48, just two numbers left.\n     |- Try 33 + 19 = 52. Evaluate 52 != 48, drop this branch.\n     |- Try 33 - 19 = 14. Evaluate 14 != 48, drop this branch.\n     |- Try 33 * 19 = 627. Evaluate 627 != 48, drop this branch.\n     |- Try 33 \/ 19 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 33], target: 48, just two numbers left.\n     |- Try 150 + 33 = 183. Evaluate 183 != 48, drop this branch.\n     |- Try 150 - 33 = 117. Evaluate 117 != 48, drop this branch.\n     |- Try 150 * 33 = 4950. 4950 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 33 = 4.5. 4.5 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (6, 33) (numbers left: [25]). Try possible operations.\n    |- Try 33 + 6 = 39. Add 39 to the number set. Current number set: [39, 25], target: 48, just two numbers left.\n     |- Try 39 + 25 = 64. Evaluate 64 != 48, drop this branch.\n     |- Try 39 - 25 = 14. Evaluate 14 != 48, drop this branch.\n     |- Try 39 * 25 = 975. Evaluate 975 != 48, drop this branch.\n     |- Try 39 \/ 25 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 33 - 6 = 27. Add 27 to the number set. Current number set: [27, 25], target: 48, just two numbers left.\n     |- Try 27 + 25 = 52. Evaluate 52 != 48, drop this branch.\n     |- Try 27 - 25 = 2. Evaluate 2 != 48, drop this branch.\n     |- Try 27 * 25 = 675. Evaluate 675 != 48, drop this branch.\n     |- Try 27 \/ 25 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 33 * 6 = 198. Add 198 to the number set. Current number set: [198, 25], target: 48, just two numbers left.\n     |- Try 198 + 25 = 223. Evaluate 223 != 48, drop this branch.\n     |- Try 198 - 25 = 173. Evaluate 173 != 48, drop this branch.\n     |- Try 198 * 25 = 4950. 4950 exceeds the maximum intermediate result, drop this branch.\n     |- Try 198 \/ 25 = 7.9. 7.9 is a decimal, drop this branch.\n    |- Try 33 \/ 6 = 5.5. 5.5 is a decimal, drop this branch.\n   |- Pick two numbers (25, 33) (numbers left: [6]). Try possible operations.\n    |- Try 33 + 25 = 58. Add 58 to the number set. Current number set: [58, 6], target: 48, just two numbers left.\n     |- Try 58 + 6 = 64. Evaluate 64 != 48, drop this branch.\n     |- Try 58 - 6 = 52. Evaluate 52 != 48, drop this branch.\n     |- Try 58 * 6 = 348. Evaluate 348 != 48, drop this branch.\n     |- Try 58 \/ 6 = 9.7. 9.7 is a decimal, drop this branch.\n    |- Try 33 - 25 = 8. Add 8 to the number set. Current number set: [8, 6], target: 48, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 48, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 48, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 == 48, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 8 * 6 = 48\nThe step before: 33 - 25 = 8\nThe first step: 42 - 36 = 6\n\nOutput the solution in the required format:\n<Solution>\n42 - 36 = 6\n33 - 25 = 8\n8 * 6 = 48\n<\/Solution>\n","item":{"nums":[42,25,36,33],"solution":["42 - 36 = 6","33 - 25 = 8","8 * 6 = 48"],"target":48}}
+{"instance_id":"countdown_8k_197","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [46, 29, 44, 19]\nTarget: 24","reference_output":"# Search Procedure\nInitial number set: [46, 29, 44, 19], target: 24. Options for choosing two numbers: [(46, 29), (46, 44), (46, 19), (29, 44), (29, 19), (44, 19)].\n |- Pick two numbers (46, 29) (numbers left: [44, 19]). Try possible operations.\n  |- Try 46 + 29 = 75. Add 75 to the number set. Current number set: [75, 44, 19], target: 24. Options for choosing two numbers: [(75, 44), (75, 19), (44, 19)].\n   |- Pick two numbers (75, 44) (numbers left: [19]). Try possible operations.\n    |- Try 75 + 44 = 119. Add 119 to the number set. Current number set: [119, 19], target: 24, just two numbers left.\n     |- Try 119 + 19 = 138. Evaluate 138 != 24, drop this branch.\n     |- Try 119 - 19 = 100. Evaluate 100 != 24, drop this branch.\n     |- Try 119 * 19 = 2261. 2261 exceeds the maximum intermediate result, drop this branch.\n     |- Try 119 \/ 19 = 6.3. 6.3 is a decimal, drop this branch.\n    |- Try 75 - 44 = 31. Add 31 to the number set. Current number set: [31, 19], target: 24, just two numbers left.\n     |- Try 31 + 19 = 50. Evaluate 50 != 24, drop this branch.\n     |- Try 31 - 19 = 12. Evaluate 12 != 24, drop this branch.\n     |- Try 31 * 19 = 589. Evaluate 589 != 24, drop this branch.\n     |- Try 31 \/ 19 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 75 * 44 = 3300. 3300 exceeds the maximum intermediate result, drop this branch.\n    |- Try 75 \/ 44 = 1.7. 1.7 is a decimal, drop this branch.\n   |- Pick two numbers (75, 19) (numbers left: [44]). Try possible operations.\n    |- Try 75 + 19 = 94. Add 94 to the number set. Current number set: [94, 44], target: 24, just two numbers left.\n     |- Try 94 + 44 = 138. Evaluate 138 != 24, drop this branch.\n     |- Try 94 - 44 = 50. Evaluate 50 != 24, drop this branch.\n     |- Try 94 * 44 = 4136. 4136 exceeds the maximum intermediate result, drop this branch.\n     |- Try 94 \/ 44 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 75 - 19 = 56. Add 56 to the number set. Current number set: [56, 44], target: 24, just two numbers left.\n     |- Try 56 + 44 = 100. Evaluate 100 != 24, drop this branch.\n     |- Try 56 - 44 = 12. Evaluate 12 != 24, drop this branch.\n     |- Try 56 * 44 = 2464. 2464 exceeds the maximum intermediate result, drop this branch.\n     |- Try 56 \/ 44 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 75 * 19 = 1425. Add 1425 to the number set. Current number set: [1425, 44], target: 24, just two numbers left.\n     |- Try 1425 + 44 = 1469. Evaluate 1469 != 24, drop this branch.\n     |- Try 1425 - 44 = 1381. Evaluate 1381 != 24, drop this branch.\n     |- Try 1425 * 44 = 62700. 62700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1425 \/ 44 = 32.4. 32.4 is a decimal, drop this branch.\n    |- Try 75 \/ 19 = 3.9. 3.9 is a decimal, drop this branch.\n   |- Pick two numbers (44, 19) (numbers left: [75]). Try possible operations.\n    |- Try 44 + 19 = 63. Add 63 to the number set. Current number set: [63, 75], target: 24, just two numbers left.\n     |- Try 75 + 63 = 138. Evaluate 138 != 24, drop this branch.\n     |- Try 75 - 63 = 12. Evaluate 12 != 24, drop this branch.\n     |- Try 75 * 63 = 4725. 4725 exceeds the maximum intermediate result, drop this branch.\n     |- Try 75 \/ 63 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 44 - 19 = 25. Add 25 to the number set. Current number set: [25, 75], target: 24, just two numbers left.\n     |- Try 75 + 25 = 100. Evaluate 100 != 24, drop this branch.\n     |- Try 75 - 25 = 50. Evaluate 50 != 24, drop this branch.\n     |- Try 75 * 25 = 1875. Evaluate 1875 != 24, drop this branch.\n     |- Try 75 \/ 25 = 3. Evaluate 3 != 24, drop this branch.\n    |- Try 44 * 19 = 836. Add 836 to the number set. Current number set: [836, 75], target: 24, just two numbers left.\n     |- Try 836 + 75 = 911. Evaluate 911 != 24, drop this branch.\n     |- Try 836 - 75 = 761. Evaluate 761 != 24, drop this branch.\n     |- Try 836 * 75 = 62700. 62700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 836 \/ 75 = 11.1. 11.1 is a decimal, drop this branch.\n    |- Try 44 \/ 19 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 46 - 29 = 17. Add 17 to the number set. Current number set: [17, 44, 19], target: 24. Options for choosing two numbers: [(17, 44), (17, 19), (44, 19)].\n   |- Pick two numbers (17, 44) (numbers left: [19]). Try possible operations.\n    |- Try 44 + 17 = 61. Add 61 to the number set. Current number set: [61, 19], target: 24, just two numbers left.\n     |- Try 61 + 19 = 80. Evaluate 80 != 24, drop this branch.\n     |- Try 61 - 19 = 42. Evaluate 42 != 24, drop this branch.\n     |- Try 61 * 19 = 1159. Evaluate 1159 != 24, drop this branch.\n     |- Try 61 \/ 19 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 44 - 17 = 27. Add 27 to the number set. Current number set: [27, 19], target: 24, just two numbers left.\n     |- Try 27 + 19 = 46. Evaluate 46 != 24, drop this branch.\n     |- Try 27 - 19 = 8. Evaluate 8 != 24, drop this branch.\n     |- Try 27 * 19 = 513. Evaluate 513 != 24, drop this branch.\n     |- Try 27 \/ 19 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 44 * 17 = 748. Add 748 to the number set. Current number set: [748, 19], target: 24, just two numbers left.\n     |- Try 748 + 19 = 767. Evaluate 767 != 24, drop this branch.\n     |- Try 748 - 19 = 729. Evaluate 729 != 24, drop this branch.\n     |- Try 748 * 19 = 14212. 14212 exceeds the maximum intermediate result, drop this branch.\n     |- Try 748 \/ 19 = 39.4. 39.4 is a decimal, drop this branch.\n    |- Try 44 \/ 17 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (17, 19) (numbers left: [44]). Try possible operations.\n    |- Try 19 + 17 = 36. Add 36 to the number set. Current number set: [36, 44], target: 24, just two numbers left.\n     |- Try 44 + 36 = 80. Evaluate 80 != 24, drop this branch.\n     |- Try 44 - 36 = 8. Evaluate 8 != 24, drop this branch.\n     |- Try 44 * 36 = 1584. Evaluate 1584 != 24, drop this branch.\n     |- Try 44 \/ 36 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 19 - 17 = 2. Add 2 to the number set. Current number set: [2, 44], target: 24, just two numbers left.\n     |- Try 44 + 2 = 46. Evaluate 46 != 24, drop this branch.\n     |- Try 44 - 2 = 42. Evaluate 42 != 24, drop this branch.\n     |- Try 44 * 2 = 88. Evaluate 88 != 24, drop this branch.\n     |- Try 44 \/ 2 = 22. Evaluate 22 != 24, drop this branch.\n    |- Try 19 * 17 = 323. Add 323 to the number set. Current number set: [323, 44], target: 24, just two numbers left.\n     |- Try 323 + 44 = 367. Evaluate 367 != 24, drop this branch.\n     |- Try 323 - 44 = 279. Evaluate 279 != 24, drop this branch.\n     |- Try 323 * 44 = 14212. 14212 exceeds the maximum intermediate result, drop this branch.\n     |- Try 323 \/ 44 = 7.3. 7.3 is a decimal, drop this branch.\n    |- Try 19 \/ 17 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (44, 19) (numbers left: [17]). Try possible operations.\n    |- Try 44 + 19 = 63. Add 63 to the number set. Current number set: [63, 17], target: 24, just two numbers left.\n     |- Try 63 + 17 = 80. Evaluate 80 != 24, drop this branch.\n     |- Try 63 - 17 = 46. Evaluate 46 != 24, drop this branch.\n     |- Try 63 * 17 = 1071. Evaluate 1071 != 24, drop this branch.\n     |- Try 63 \/ 17 = 3.7. 3.7 is a decimal, drop this branch.\n    |- Try 44 - 19 = 25. Add 25 to the number set. Current number set: [25, 17], target: 24, just two numbers left.\n     |- Try 25 + 17 = 42. Evaluate 42 != 24, drop this branch.\n     |- Try 25 - 17 = 8. Evaluate 8 != 24, drop this branch.\n     |- Try 25 * 17 = 425. Evaluate 425 != 24, drop this branch.\n     |- Try 25 \/ 17 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 44 * 19 = 836. Add 836 to the number set. Current number set: [836, 17], target: 24, just two numbers left.\n     |- Try 836 + 17 = 853. Evaluate 853 != 24, drop this branch.\n     |- Try 836 - 17 = 819. Evaluate 819 != 24, drop this branch.\n     |- Try 836 * 17 = 14212. 14212 exceeds the maximum intermediate result, drop this branch.\n     |- Try 836 \/ 17 = 49.2. 49.2 is a decimal, drop this branch.\n    |- Try 44 \/ 19 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 46 * 29 = 1334. Add 1334 to the number set. Current number set: [1334, 44, 19], target: 24. Options for choosing two numbers: [(1334, 44), (1334, 19), (44, 19)].\n   |- Pick two numbers (1334, 44) (numbers left: [19]). Try possible operations.\n    |- Try 1334 + 44 = 1378. Add 1378 to the number set. Current number set: [1378, 19], target: 24, just two numbers left.\n     |- Try 1378 + 19 = 1397. Evaluate 1397 != 24, drop this branch.\n     |- Try 1378 - 19 = 1359. Evaluate 1359 != 24, drop this branch.\n     |- Try 1378 * 19 = 26182. 26182 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1378 \/ 19 = 72.5. 72.5 is a decimal, drop this branch.\n    |- Try 1334 - 44 = 1290. Add 1290 to the number set. Current number set: [1290, 19], target: 24, just two numbers left.\n     |- Try 1290 + 19 = 1309. Evaluate 1309 != 24, drop this branch.\n     |- Try 1290 - 19 = 1271. Evaluate 1271 != 24, drop this branch.\n     |- Try 1290 * 19 = 24510. 24510 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1290 \/ 19 = 67.9. 67.9 is a decimal, drop this branch.\n    |- Try 1334 * 44 = 58696. 58696 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1334 \/ 44 = 30.3. 30.3 is a decimal, drop this branch.\n   |- Pick two numbers (1334, 19) (numbers left: [44]). Try possible operations.\n    |- Try 1334 + 19 = 1353. Add 1353 to the number set. Current number set: [1353, 44], target: 24, just two numbers left.\n     |- Try 1353 + 44 = 1397. Evaluate 1397 != 24, drop this branch.\n     |- Try 1353 - 44 = 1309. Evaluate 1309 != 24, drop this branch.\n     |- Try 1353 * 44 = 59532. 59532 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1353 \/ 44 = 30.8. 30.8 is a decimal, drop this branch.\n    |- Try 1334 - 19 = 1315. Add 1315 to the number set. Current number set: [1315, 44], target: 24, just two numbers left.\n     |- Try 1315 + 44 = 1359. Evaluate 1359 != 24, drop this branch.\n     |- Try 1315 - 44 = 1271. Evaluate 1271 != 24, drop this branch.\n     |- Try 1315 * 44 = 57860. 57860 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1315 \/ 44 = 29.9. 29.9 is a decimal, drop this branch.\n    |- Try 1334 * 19 = 25346. 25346 exceeds the maximum intermediate result, drop this branch.\n    |- Try 1334 \/ 19 = 70.2. 70.2 is a decimal, drop this branch.\n   |- Pick two numbers (44, 19) (numbers left: [1334]). Try possible operations.\n    |- Try 44 + 19 = 63. Add 63 to the number set. Current number set: [63, 1334], target: 24, just two numbers left.\n     |- Try 1334 + 63 = 1397. Evaluate 1397 != 24, drop this branch.\n     |- Try 1334 - 63 = 1271. Evaluate 1271 != 24, drop this branch.\n     |- Try 1334 * 63 = 84042. 84042 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1334 \/ 63 = 21.2. 21.2 is a decimal, drop this branch.\n    |- Try 44 - 19 = 25. Add 25 to the number set. Current number set: [25, 1334], target: 24, just two numbers left.\n     |- Try 1334 + 25 = 1359. Evaluate 1359 != 24, drop this branch.\n     |- Try 1334 - 25 = 1309. Evaluate 1309 != 24, drop this branch.\n     |- Try 1334 * 25 = 33350. 33350 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1334 \/ 25 = 53.4. 53.4 is a decimal, drop this branch.\n    |- Try 44 * 19 = 836. Add 836 to the number set. Current number set: [836, 1334], target: 24, just two numbers left.\n     |- Try 1334 + 836 = 2170. 2170 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1334 - 836 = 498. Evaluate 498 != 24, drop this branch.\n     |- Try 1334 * 836 = 1115224. 1115224 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1334 \/ 836 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 44 \/ 19 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 46 \/ 29 = 1.6. 1.6 is a decimal, drop this branch.\n |- Pick two numbers (46, 44) (numbers left: [29, 19]). Try possible operations.\n  |- Try 46 + 44 = 90. Add 90 to the number set. Current number set: [90, 29, 19], target: 24. Options for choosing two numbers: [(90, 29), (90, 19), (29, 19)].\n   |- Pick two numbers (90, 29) (numbers left: [19]). Try possible operations.\n    |- Try 90 + 29 = 119. Add 119 to the number set. Current number set: [119, 19], target: 24, just two numbers left.\n     |- Try 119 + 19 = 138. Evaluate 138 != 24, drop this branch.\n     |- Try 119 - 19 = 100. Evaluate 100 != 24, drop this branch.\n     |- Try 119 * 19 = 2261. 2261 exceeds the maximum intermediate result, drop this branch.\n     |- Try 119 \/ 19 = 6.3. 6.3 is a decimal, drop this branch.\n    |- Try 90 - 29 = 61. Add 61 to the number set. Current number set: [61, 19], target: 24, just two numbers left.\n     |- Try 61 + 19 = 80. Evaluate 80 != 24, drop this branch.\n     |- Try 61 - 19 = 42. Evaluate 42 != 24, drop this branch.\n     |- Try 61 * 19 = 1159. Evaluate 1159 != 24, drop this branch.\n     |- Try 61 \/ 19 = 3.2. 3.2 is a decimal, drop this branch.\n    |- Try 90 * 29 = 2610. 2610 exceeds the maximum intermediate result, drop this branch.\n    |- Try 90 \/ 29 = 3.1. 3.1 is a decimal, drop this branch.\n   |- Pick two numbers (90, 19) (numbers left: [29]). Try possible operations.\n    |- Try 90 + 19 = 109. Add 109 to the number set. Current number set: [109, 29], target: 24, just two numbers left.\n     |- Try 109 + 29 = 138. Evaluate 138 != 24, drop this branch.\n     |- Try 109 - 29 = 80. Evaluate 80 != 24, drop this branch.\n     |- Try 109 * 29 = 3161. 3161 exceeds the maximum intermediate result, drop this branch.\n     |- Try 109 \/ 29 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 90 - 19 = 71. Add 71 to the number set. Current number set: [71, 29], target: 24, just two numbers left.\n     |- Try 71 + 29 = 100. Evaluate 100 != 24, drop this branch.\n     |- Try 71 - 29 = 42. Evaluate 42 != 24, drop this branch.\n     |- Try 71 * 29 = 2059. 2059 exceeds the maximum intermediate result, drop this branch.\n     |- Try 71 \/ 29 = 2.4. 2.4 is a decimal, drop this branch.\n    |- Try 90 * 19 = 1710. Add 1710 to the number set. Current number set: [1710, 29], target: 24, just two numbers left.\n     |- Try 1710 + 29 = 1739. Evaluate 1739 != 24, drop this branch.\n     |- Try 1710 - 29 = 1681. Evaluate 1681 != 24, drop this branch.\n     |- Try 1710 * 29 = 49590. 49590 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1710 \/ 29 = 59.0. 59.0 is a decimal, drop this branch.\n    |- Try 90 \/ 19 = 4.7. 4.7 is a decimal, drop this branch.\n   |- Pick two numbers (29, 19) (numbers left: [90]). Try possible operations.\n    |- Try 29 + 19 = 48. Add 48 to the number set. Current number set: [48, 90], target: 24, just two numbers left.\n     |- Try 90 + 48 = 138. Evaluate 138 != 24, drop this branch.\n     |- Try 90 - 48 = 42. Evaluate 42 != 24, drop this branch.\n     |- Try 90 * 48 = 4320. 4320 exceeds the maximum intermediate result, drop this branch.\n     |- Try 90 \/ 48 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 29 - 19 = 10. Add 10 to the number set. Current number set: [10, 90], target: 24, just two numbers left.\n     |- Try 90 + 10 = 100. Evaluate 100 != 24, drop this branch.\n     |- Try 90 - 10 = 80. Evaluate 80 != 24, drop this branch.\n     |- Try 90 * 10 = 900. Evaluate 900 != 24, drop this branch.\n     |- Try 90 \/ 10 = 9. Evaluate 9 != 24, drop this branch.\n    |- Try 29 * 19 = 551. Add 551 to the number set. Current number set: [551, 90], target: 24, just two numbers left.\n     |- Try 551 + 90 = 641. Evaluate 641 != 24, drop this branch.\n     |- Try 551 - 90 = 461. Evaluate 461 != 24, drop this branch.\n     |- Try 551 * 90 = 49590. 49590 exceeds the maximum intermediate result, drop this branch.\n     |- Try 551 \/ 90 = 6.1. 6.1 is a decimal, drop this branch.\n    |- Try 29 \/ 19 = 1.5. 1.5 is a decimal, drop this branch.\n  |- Try 46 - 44 = 2. Add 2 to the number set. Current number set: [2, 29, 19], target: 24. Options for choosing two numbers: [(2, 29), (2, 19), (29, 19)].\n   |- Pick two numbers (2, 29) (numbers left: [19]). Try possible operations.\n    |- Try 29 + 2 = 31. Add 31 to the number set. Current number set: [31, 19], target: 24, just two numbers left.\n     |- Try 31 + 19 = 50. Evaluate 50 != 24, drop this branch.\n     |- Try 31 - 19 = 12. Evaluate 12 != 24, drop this branch.\n     |- Try 31 * 19 = 589. Evaluate 589 != 24, drop this branch.\n     |- Try 31 \/ 19 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 29 - 2 = 27. Add 27 to the number set. Current number set: [27, 19], target: 24, just two numbers left.\n     |- Try 27 + 19 = 46. Evaluate 46 != 24, drop this branch.\n     |- Try 27 - 19 = 8. Evaluate 8 != 24, drop this branch.\n     |- Try 27 * 19 = 513. Evaluate 513 != 24, drop this branch.\n     |- Try 27 \/ 19 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 29 * 2 = 58. Add 58 to the number set. Current number set: [58, 19], target: 24, just two numbers left.\n     |- Try 58 + 19 = 77. Evaluate 77 != 24, drop this branch.\n     |- Try 58 - 19 = 39. Evaluate 39 != 24, drop this branch.\n     |- Try 58 * 19 = 1102. Evaluate 1102 != 24, drop this branch.\n     |- Try 58 \/ 19 = 3.1. 3.1 is a decimal, drop this branch.\n    |- Try 29 \/ 2 = 14.5. 14.5 is a decimal, drop this branch.\n   |- Pick two numbers (2, 19) (numbers left: [29]). Try possible operations.\n    |- Try 19 + 2 = 21. Add 21 to the number set. Current number set: [21, 29], target: 24, just two numbers left.\n     |- Try 29 + 21 = 50. Evaluate 50 != 24, drop this branch.\n     |- Try 29 - 21 = 8. Evaluate 8 != 24, drop this branch.\n     |- Try 29 * 21 = 609. Evaluate 609 != 24, drop this branch.\n     |- Try 29 \/ 21 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 19 - 2 = 17. Add 17 to the number set. Current number set: [17, 29], target: 24, just two numbers left.\n     |- Try 29 + 17 = 46. Evaluate 46 != 24, drop this branch.\n     |- Try 29 - 17 = 12. Evaluate 12 != 24, drop this branch.\n     |- Try 29 * 17 = 493. Evaluate 493 != 24, drop this branch.\n     |- Try 29 \/ 17 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 19 * 2 = 38. Add 38 to the number set. Current number set: [38, 29], target: 24, just two numbers left.\n     |- Try 38 + 29 = 67. Evaluate 67 != 24, drop this branch.\n     |- Try 38 - 29 = 9. Evaluate 9 != 24, drop this branch.\n     |- Try 38 * 29 = 1102. Evaluate 1102 != 24, drop this branch.\n     |- Try 38 \/ 29 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 19 \/ 2 = 9.5. 9.5 is a decimal, drop this branch.\n   |- Pick two numbers (29, 19) (numbers left: [2]). Try possible operations.\n    |- Try 29 + 19 = 48. Add 48 to the number set. Current number set: [48, 2], target: 24, just two numbers left.\n     |- Try 48 + 2 = 50. Evaluate 50 != 24, drop this branch.\n     |- Try 48 - 2 = 46. Evaluate 46 != 24, drop this branch.\n     |- Try 48 * 2 = 96. Evaluate 96 != 24, drop this branch.\n     |- Try 48 \/ 2 = 24. Evaluate 24 == 24, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 48 \/ 2 = 24\nThe step before: 29 + 19 = 48\nThe first step: 46 - 44 = 2\n\nOutput the solution in the required format:\n<Solution>\n46 - 44 = 2\n29 + 19 = 48\n48 \/ 2 = 24\n<\/Solution>\n","item":{"nums":[46,29,44,19],"solution":["46 - 44 = 2","29 + 19 = 48","48 \/ 2 = 24"],"target":24}}
+{"instance_id":"countdown_8k_198","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [30, 7, 35, 4]\nTarget: 27","reference_output":"# Search Procedure\nInitial number set: [30, 7, 35, 4], target: 27. Options for choosing two numbers: [(30, 7), (30, 35), (30, 4), (7, 35), (7, 4), (35, 4)].\n |- Pick two numbers (30, 7) (numbers left: [35, 4]). Try possible operations.\n  |- Try 30 + 7 = 37. Add 37 to the number set. Current number set: [37, 35, 4], target: 27. Options for choosing two numbers: [(37, 35), (37, 4), (35, 4)].\n   |- Pick two numbers (37, 35) (numbers left: [4]). Try possible operations.\n    |- Try 37 + 35 = 72. Add 72 to the number set. Current number set: [72, 4], target: 27, just two numbers left.\n     |- Try 72 + 4 = 76. Evaluate 76 != 27, drop this branch.\n     |- Try 72 - 4 = 68. Evaluate 68 != 27, drop this branch.\n     |- Try 72 * 4 = 288. Evaluate 288 != 27, drop this branch.\n     |- Try 72 \/ 4 = 18. Evaluate 18 != 27, drop this branch.\n    |- Try 37 - 35 = 2. Add 2 to the number set. Current number set: [2, 4], target: 27, just two numbers left.\n     |- Try 4 + 2 = 6. Evaluate 6 != 27, drop this branch.\n     |- Try 4 - 2 = 2. Evaluate 2 != 27, drop this branch.\n     |- Try 4 * 2 = 8. Evaluate 8 != 27, drop this branch.\n     |- Try 4 \/ 2 = 2. Evaluate 2 != 27, drop this branch.\n    |- Try 37 * 35 = 1295. Add 1295 to the number set. Current number set: [1295, 4], target: 27, just two numbers left.\n     |- Try 1295 + 4 = 1299. Evaluate 1299 != 27, drop this branch.\n     |- Try 1295 - 4 = 1291. Evaluate 1291 != 27, drop this branch.\n     |- Try 1295 * 4 = 5180. 5180 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1295 \/ 4 = 323.8. 323.8 is a decimal, drop this branch.\n    |- Try 37 \/ 35 = 1.1. 1.1 is a decimal, drop this branch.\n   |- Pick two numbers (37, 4) (numbers left: [35]). Try possible operations.\n    |- Try 37 + 4 = 41. Add 41 to the number set. Current number set: [41, 35], target: 27, just two numbers left.\n     |- Try 41 + 35 = 76. Evaluate 76 != 27, drop this branch.\n     |- Try 41 - 35 = 6. Evaluate 6 != 27, drop this branch.\n     |- Try 41 * 35 = 1435. Evaluate 1435 != 27, drop this branch.\n     |- Try 41 \/ 35 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 37 - 4 = 33. Add 33 to the number set. Current number set: [33, 35], target: 27, just two numbers left.\n     |- Try 35 + 33 = 68. Evaluate 68 != 27, drop this branch.\n     |- Try 35 - 33 = 2. Evaluate 2 != 27, drop this branch.\n     |- Try 35 * 33 = 1155. Evaluate 1155 != 27, drop this branch.\n     |- Try 35 \/ 33 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 37 * 4 = 148. Add 148 to the number set. Current number set: [148, 35], target: 27, just two numbers left.\n     |- Try 148 + 35 = 183. Evaluate 183 != 27, drop this branch.\n     |- Try 148 - 35 = 113. Evaluate 113 != 27, drop this branch.\n     |- Try 148 * 35 = 5180. 5180 exceeds the maximum intermediate result, drop this branch.\n     |- Try 148 \/ 35 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 37 \/ 4 = 9.2. 9.2 is a decimal, drop this branch.\n   |- Pick two numbers (35, 4) (numbers left: [37]). Try possible operations.\n    |- Try 35 + 4 = 39. Add 39 to the number set. Current number set: [39, 37], target: 27, just two numbers left.\n     |- Try 39 + 37 = 76. Evaluate 76 != 27, drop this branch.\n     |- Try 39 - 37 = 2. Evaluate 2 != 27, drop this branch.\n     |- Try 39 * 37 = 1443. Evaluate 1443 != 27, drop this branch.\n     |- Try 39 \/ 37 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 35 - 4 = 31. Add 31 to the number set. Current number set: [31, 37], target: 27, just two numbers left.\n     |- Try 37 + 31 = 68. Evaluate 68 != 27, drop this branch.\n     |- Try 37 - 31 = 6. Evaluate 6 != 27, drop this branch.\n     |- Try 37 * 31 = 1147. Evaluate 1147 != 27, drop this branch.\n     |- Try 37 \/ 31 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 35 * 4 = 140. Add 140 to the number set. Current number set: [140, 37], target: 27, just two numbers left.\n     |- Try 140 + 37 = 177. Evaluate 177 != 27, drop this branch.\n     |- Try 140 - 37 = 103. Evaluate 103 != 27, drop this branch.\n     |- Try 140 * 37 = 5180. 5180 exceeds the maximum intermediate result, drop this branch.\n     |- Try 140 \/ 37 = 3.8. 3.8 is a decimal, drop this branch.\n    |- Try 35 \/ 4 = 8.8. 8.8 is a decimal, drop this branch.\n  |- Try 30 - 7 = 23. Add 23 to the number set. Current number set: [23, 35, 4], target: 27. Options for choosing two numbers: [(23, 35), (23, 4), (35, 4)].\n   |- Pick two numbers (23, 35) (numbers left: [4]). Try possible operations.\n    |- Try 35 + 23 = 58. Add 58 to the number set. Current number set: [58, 4], target: 27, just two numbers left.\n     |- Try 58 + 4 = 62. Evaluate 62 != 27, drop this branch.\n     |- Try 58 - 4 = 54. Evaluate 54 != 27, drop this branch.\n     |- Try 58 * 4 = 232. Evaluate 232 != 27, drop this branch.\n     |- Try 58 \/ 4 = 14.5. 14.5 is a decimal, drop this branch.\n    |- Try 35 - 23 = 12. Add 12 to the number set. Current number set: [12, 4], target: 27, just two numbers left.\n     |- Try 12 + 4 = 16. Evaluate 16 != 27, drop this branch.\n     |- Try 12 - 4 = 8. Evaluate 8 != 27, drop this branch.\n     |- Try 12 * 4 = 48. Evaluate 48 != 27, drop this branch.\n     |- Try 12 \/ 4 = 3. Evaluate 3 != 27, drop this branch.\n    |- Try 35 * 23 = 805. Add 805 to the number set. Current number set: [805, 4], target: 27, just two numbers left.\n     |- Try 805 + 4 = 809. Evaluate 809 != 27, drop this branch.\n     |- Try 805 - 4 = 801. Evaluate 801 != 27, drop this branch.\n     |- Try 805 * 4 = 3220. 3220 exceeds the maximum intermediate result, drop this branch.\n     |- Try 805 \/ 4 = 201.2. 201.2 is a decimal, drop this branch.\n    |- Try 35 \/ 23 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (23, 4) (numbers left: [35]). Try possible operations.\n    |- Try 23 + 4 = 27. Add 27 to the number set. Current number set: [27, 35], target: 27, just two numbers left.\n     |- Try 35 + 27 = 62. Evaluate 62 != 27, drop this branch.\n     |- Try 35 - 27 = 8. Evaluate 8 != 27, drop this branch.\n     |- Try 35 * 27 = 945. Evaluate 945 != 27, drop this branch.\n     |- Try 35 \/ 27 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 23 - 4 = 19. Add 19 to the number set. Current number set: [19, 35], target: 27, just two numbers left.\n     |- Try 35 + 19 = 54. Evaluate 54 != 27, drop this branch.\n     |- Try 35 - 19 = 16. Evaluate 16 != 27, drop this branch.\n     |- Try 35 * 19 = 665. Evaluate 665 != 27, drop this branch.\n     |- Try 35 \/ 19 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 23 * 4 = 92. Add 92 to the number set. Current number set: [92, 35], target: 27, just two numbers left.\n     |- Try 92 + 35 = 127. Evaluate 127 != 27, drop this branch.\n     |- Try 92 - 35 = 57. Evaluate 57 != 27, drop this branch.\n     |- Try 92 * 35 = 3220. 3220 exceeds the maximum intermediate result, drop this branch.\n     |- Try 92 \/ 35 = 2.6. 2.6 is a decimal, drop this branch.\n    |- Try 23 \/ 4 = 5.8. 5.8 is a decimal, drop this branch.\n   |- Pick two numbers (35, 4) (numbers left: [23]). Try possible operations.\n    |- Try 35 + 4 = 39. Add 39 to the number set. Current number set: [39, 23], target: 27, just two numbers left.\n     |- Try 39 + 23 = 62. Evaluate 62 != 27, drop this branch.\n     |- Try 39 - 23 = 16. Evaluate 16 != 27, drop this branch.\n     |- Try 39 * 23 = 897. Evaluate 897 != 27, drop this branch.\n     |- Try 39 \/ 23 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 35 - 4 = 31. Add 31 to the number set. Current number set: [31, 23], target: 27, just two numbers left.\n     |- Try 31 + 23 = 54. Evaluate 54 != 27, drop this branch.\n     |- Try 31 - 23 = 8. Evaluate 8 != 27, drop this branch.\n     |- Try 31 * 23 = 713. Evaluate 713 != 27, drop this branch.\n     |- Try 31 \/ 23 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 35 * 4 = 140. Add 140 to the number set. Current number set: [140, 23], target: 27, just two numbers left.\n     |- Try 140 + 23 = 163. Evaluate 163 != 27, drop this branch.\n     |- Try 140 - 23 = 117. Evaluate 117 != 27, drop this branch.\n     |- Try 140 * 23 = 3220. 3220 exceeds the maximum intermediate result, drop this branch.\n     |- Try 140 \/ 23 = 6.1. 6.1 is a decimal, drop this branch.\n    |- Try 35 \/ 4 = 8.8. 8.8 is a decimal, drop this branch.\n  |- Try 30 * 7 = 210. Add 210 to the number set. Current number set: [210, 35, 4], target: 27. Options for choosing two numbers: [(210, 35), (210, 4), (35, 4)].\n   |- Pick two numbers (210, 35) (numbers left: [4]). Try possible operations.\n    |- Try 210 + 35 = 245. Add 245 to the number set. Current number set: [245, 4], target: 27, just two numbers left.\n     |- Try 245 + 4 = 249. Evaluate 249 != 27, drop this branch.\n     |- Try 245 - 4 = 241. Evaluate 241 != 27, drop this branch.\n     |- Try 245 * 4 = 980. Evaluate 980 != 27, drop this branch.\n     |- Try 245 \/ 4 = 61.2. 61.2 is a decimal, drop this branch.\n    |- Try 210 - 35 = 175. Add 175 to the number set. Current number set: [175, 4], target: 27, just two numbers left.\n     |- Try 175 + 4 = 179. Evaluate 179 != 27, drop this branch.\n     |- Try 175 - 4 = 171. Evaluate 171 != 27, drop this branch.\n     |- Try 175 * 4 = 700. Evaluate 700 != 27, drop this branch.\n     |- Try 175 \/ 4 = 43.8. 43.8 is a decimal, drop this branch.\n    |- Try 210 * 35 = 7350. 7350 exceeds the maximum intermediate result, drop this branch.\n    |- Try 210 \/ 35 = 6. Add 6 to the number set. Current number set: [6, 4], target: 27, just two numbers left.\n     |- Try 6 + 4 = 10. Evaluate 10 != 27, drop this branch.\n     |- Try 6 - 4 = 2. Evaluate 2 != 27, drop this branch.\n     |- Try 6 * 4 = 24. Evaluate 24 != 27, drop this branch.\n     |- Try 6 \/ 4 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (210, 4) (numbers left: [35]). Try possible operations.\n    |- Try 210 + 4 = 214. Add 214 to the number set. Current number set: [214, 35], target: 27, just two numbers left.\n     |- Try 214 + 35 = 249. Evaluate 249 != 27, drop this branch.\n     |- Try 214 - 35 = 179. Evaluate 179 != 27, drop this branch.\n     |- Try 214 * 35 = 7490. 7490 exceeds the maximum intermediate result, drop this branch.\n     |- Try 214 \/ 35 = 6.1. 6.1 is a decimal, drop this branch.\n    |- Try 210 - 4 = 206. Add 206 to the number set. Current number set: [206, 35], target: 27, just two numbers left.\n     |- Try 206 + 35 = 241. Evaluate 241 != 27, drop this branch.\n     |- Try 206 - 35 = 171. Evaluate 171 != 27, drop this branch.\n     |- Try 206 * 35 = 7210. 7210 exceeds the maximum intermediate result, drop this branch.\n     |- Try 206 \/ 35 = 5.9. 5.9 is a decimal, drop this branch.\n    |- Try 210 * 4 = 840. Add 840 to the number set. Current number set: [840, 35], target: 27, just two numbers left.\n     |- Try 840 + 35 = 875. Evaluate 875 != 27, drop this branch.\n     |- Try 840 - 35 = 805. Evaluate 805 != 27, drop this branch.\n     |- Try 840 * 35 = 29400. 29400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 840 \/ 35 = 24. Evaluate 24 != 27, drop this branch.\n    |- Try 210 \/ 4 = 52.5. 52.5 is a decimal, drop this branch.\n   |- Pick two numbers (35, 4) (numbers left: [210]). Try possible operations.\n    |- Try 35 + 4 = 39. Add 39 to the number set. Current number set: [39, 210], target: 27, just two numbers left.\n     |- Try 210 + 39 = 249. Evaluate 249 != 27, drop this branch.\n     |- Try 210 - 39 = 171. Evaluate 171 != 27, drop this branch.\n     |- Try 210 * 39 = 8190. 8190 exceeds the maximum intermediate result, drop this branch.\n     |- Try 210 \/ 39 = 5.4. 5.4 is a decimal, drop this branch.\n    |- Try 35 - 4 = 31. Add 31 to the number set. Current number set: [31, 210], target: 27, just two numbers left.\n     |- Try 210 + 31 = 241. Evaluate 241 != 27, drop this branch.\n     |- Try 210 - 31 = 179. Evaluate 179 != 27, drop this branch.\n     |- Try 210 * 31 = 6510. 6510 exceeds the maximum intermediate result, drop this branch.\n     |- Try 210 \/ 31 = 6.8. 6.8 is a decimal, drop this branch.\n    |- Try 35 * 4 = 140. Add 140 to the number set. Current number set: [140, 210], target: 27, just two numbers left.\n     |- Try 210 + 140 = 350. Evaluate 350 != 27, drop this branch.\n     |- Try 210 - 140 = 70. Evaluate 70 != 27, drop this branch.\n     |- Try 210 * 140 = 29400. 29400 exceeds the maximum intermediate result, drop this branch.\n     |- Try 210 \/ 140 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 35 \/ 4 = 8.8. 8.8 is a decimal, drop this branch.\n  |- Try 30 \/ 7 = 4.3. 4.3 is a decimal, drop this branch.\n |- Pick two numbers (30, 35) (numbers left: [7, 4]). Try possible operations.\n  |- Try 35 + 30 = 65. Add 65 to the number set. Current number set: [65, 7, 4], target: 27. Options for choosing two numbers: [(65, 7), (65, 4), (7, 4)].\n   |- Pick two numbers (65, 7) (numbers left: [4]). Try possible operations.\n    |- Try 65 + 7 = 72. Add 72 to the number set. Current number set: [72, 4], target: 27, just two numbers left.\n     |- Try 72 + 4 = 76. Evaluate 76 != 27, drop this branch.\n     |- Try 72 - 4 = 68. Evaluate 68 != 27, drop this branch.\n     |- Try 72 * 4 = 288. Evaluate 288 != 27, drop this branch.\n     |- Try 72 \/ 4 = 18. Evaluate 18 != 27, drop this branch.\n    |- Try 65 - 7 = 58. Add 58 to the number set. Current number set: [58, 4], target: 27, just two numbers left.\n     |- Try 58 + 4 = 62. Evaluate 62 != 27, drop this branch.\n     |- Try 58 - 4 = 54. Evaluate 54 != 27, drop this branch.\n     |- Try 58 * 4 = 232. Evaluate 232 != 27, drop this branch.\n     |- Try 58 \/ 4 = 14.5. 14.5 is a decimal, drop this branch.\n    |- Try 65 * 7 = 455. Add 455 to the number set. Current number set: [455, 4], target: 27, just two numbers left.\n     |- Try 455 + 4 = 459. Evaluate 459 != 27, drop this branch.\n     |- Try 455 - 4 = 451. Evaluate 451 != 27, drop this branch.\n     |- Try 455 * 4 = 1820. Evaluate 1820 != 27, drop this branch.\n     |- Try 455 \/ 4 = 113.8. 113.8 is a decimal, drop this branch.\n    |- Try 65 \/ 7 = 9.3. 9.3 is a decimal, drop this branch.\n   |- Pick two numbers (65, 4) (numbers left: [7]). Try possible operations.\n    |- Try 65 + 4 = 69. Add 69 to the number set. Current number set: [69, 7], target: 27, just two numbers left.\n     |- Try 69 + 7 = 76. Evaluate 76 != 27, drop this branch.\n     |- Try 69 - 7 = 62. Evaluate 62 != 27, drop this branch.\n     |- Try 69 * 7 = 483. Evaluate 483 != 27, drop this branch.\n     |- Try 69 \/ 7 = 9.9. 9.9 is a decimal, drop this branch.\n    |- Try 65 - 4 = 61. Add 61 to the number set. Current number set: [61, 7], target: 27, just two numbers left.\n     |- Try 61 + 7 = 68. Evaluate 68 != 27, drop this branch.\n     |- Try 61 - 7 = 54. Evaluate 54 != 27, drop this branch.\n     |- Try 61 * 7 = 427. Evaluate 427 != 27, drop this branch.\n     |- Try 61 \/ 7 = 8.7. 8.7 is a decimal, drop this branch.\n    |- Try 65 * 4 = 260. Add 260 to the number set. Current number set: [260, 7], target: 27, just two numbers left.\n     |- Try 260 + 7 = 267. Evaluate 267 != 27, drop this branch.\n     |- Try 260 - 7 = 253. Evaluate 253 != 27, drop this branch.\n     |- Try 260 * 7 = 1820. Evaluate 1820 != 27, drop this branch.\n     |- Try 260 \/ 7 = 37.1. 37.1 is a decimal, drop this branch.\n    |- Try 65 \/ 4 = 16.2. 16.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 4) (numbers left: [65]). Try possible operations.\n    |- Try 7 + 4 = 11. Add 11 to the number set. Current number set: [11, 65], target: 27, just two numbers left.\n     |- Try 65 + 11 = 76. Evaluate 76 != 27, drop this branch.\n     |- Try 65 - 11 = 54. Evaluate 54 != 27, drop this branch.\n     |- Try 65 * 11 = 715. Evaluate 715 != 27, drop this branch.\n     |- Try 65 \/ 11 = 5.9. 5.9 is a decimal, drop this branch.\n    |- Try 7 - 4 = 3. Add 3 to the number set. Current number set: [3, 65], target: 27, just two numbers left.\n     |- Try 65 + 3 = 68. Evaluate 68 != 27, drop this branch.\n     |- Try 65 - 3 = 62. Evaluate 62 != 27, drop this branch.\n     |- Try 65 * 3 = 195. Evaluate 195 != 27, drop this branch.\n     |- Try 65 \/ 3 = 21.7. 21.7 is a decimal, drop this branch.\n    |- Try 7 * 4 = 28. Add 28 to the number set. Current number set: [28, 65], target: 27, just two numbers left.\n     |- Try 65 + 28 = 93. Evaluate 93 != 27, drop this branch.\n     |- Try 65 - 28 = 37. Evaluate 37 != 27, drop this branch.\n     |- Try 65 * 28 = 1820. Evaluate 1820 != 27, drop this branch.\n     |- Try 65 \/ 28 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 4 = 1.8. 1.8 is a decimal, drop this branch.\n  |- Try 35 - 30 = 5. Add 5 to the number set. Current number set: [5, 7, 4], target: 27. Options for choosing two numbers: [(5, 7), (5, 4), (7, 4)].\n   |- Pick two numbers (5, 7) (numbers left: [4]). Try possible operations.\n    |- Try 7 + 5 = 12. Add 12 to the number set. Current number set: [12, 4], target: 27, just two numbers left.\n     |- Try 12 + 4 = 16. Evaluate 16 != 27, drop this branch.\n     |- Try 12 - 4 = 8. Evaluate 8 != 27, drop this branch.\n     |- Try 12 * 4 = 48. Evaluate 48 != 27, drop this branch.\n     |- Try 12 \/ 4 = 3. Evaluate 3 != 27, drop this branch.\n    |- Try 7 - 5 = 2. Add 2 to the number set. Current number set: [2, 4], target: 27, just two numbers left.\n     |- Try 4 + 2 = 6. Evaluate 6 != 27, drop this branch.\n     |- Try 4 - 2 = 2. Evaluate 2 != 27, drop this branch.\n     |- Try 4 * 2 = 8. Evaluate 8 != 27, drop this branch.\n     |- Try 4 \/ 2 = 2. Evaluate 2 != 27, drop this branch.\n    |- Try 7 * 5 = 35. Add 35 to the number set. Current number set: [35, 4], target: 27, just two numbers left.\n     |- Try 35 + 4 = 39. Evaluate 39 != 27, drop this branch.\n     |- Try 35 - 4 = 31. Evaluate 31 != 27, drop this branch.\n     |- Try 35 * 4 = 140. Evaluate 140 != 27, drop this branch.\n     |- Try 35 \/ 4 = 8.8. 8.8 is a decimal, drop this branch.\n    |- Try 7 \/ 5 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (5, 4) (numbers left: [7]). Try possible operations.\n    |- Try 5 + 4 = 9. Add 9 to the number set. Current number set: [9, 7], target: 27, just two numbers left.\n     |- Try 9 + 7 = 16. Evaluate 16 != 27, drop this branch.\n     |- Try 9 - 7 = 2. Evaluate 2 != 27, drop this branch.\n     |- Try 9 * 7 = 63. Evaluate 63 != 27, drop this branch.\n     |- Try 9 \/ 7 = 1.3. 1.3 is a decimal, drop this branch.\n    |- Try 5 - 4 = 1. Add 1 to the number set. Current number set: [1, 7], target: 27, just two numbers left.\n     |- Try 7 + 1 = 8. Evaluate 8 != 27, drop this branch.\n     |- Try 7 - 1 = 6. Evaluate 6 != 27, drop this branch.\n     |- Try 7 * 1 = 7. Evaluate 7 != 27, drop this branch.\n     |- Try 7 \/ 1 = 7. Evaluate 7 != 27, drop this branch.\n    |- Try 5 * 4 = 20. Add 20 to the number set. Current number set: [20, 7], target: 27, just two numbers left.\n     |- Try 20 + 7 = 27. Evaluate 27 == 27, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 20 + 7 = 27\nThe step before: 5 * 4 = 20\nThe first step: 35 - 30 = 5\n\nOutput the solution in the required format:\n<Solution>\n35 - 30 = 5\n5 * 4 = 20\n20 + 7 = 27\n<\/Solution>\n","item":{"nums":[30,7,35,4],"solution":["35 - 30 = 5","5 * 4 = 20","20 + 7 = 27"],"target":27}}
+{"instance_id":"countdown_8k_199","input_prompt":"[TASK]\nYou will be given four numbers and a target number, your task is to find a way to use all four numbers exactly once, along with the basic operations (+, -, *, \/), to reach the target number.\n\n[RULES]\n- You can use each number exactly once.\n- You can use the four basic operations (+, -, *, \/).\n- The intermediate results must be integers (no decimals allowed).\n- The intermediate results must be positive.\n- The intermediate results will not exceed 2000.\n\n[APPROACH]\nWe will solve the problem by searching. Starting from a given set of four numbers, we will follow this search process:\n- At each state, we will consider all possible number pairs (in order) from the current number set. Choose one pair and apply one of the four basic operations to them to obtain a new number.\n  * If there are still numbers left, we will add the new number to the number set and continue the search.\n  * If we have used all numbers, we will check if the new number is equal to the target number. If it is, we have found the solution. Otherwise, we will backtrack.\n- Suppose the two numbers we choose are a and b (where a >= b). We will try the four options (a + b), (a - b), (a * b), (a \/ b) to obtain the new number. Remember to always use the larger number as the first operand.\n- If the new number is a decimal, or exceeds the maximum intermediate result, we will discard this branch and backtrack.\n- We will continue this process until we reach the target number with four numbers used or exhaust all possible combinations.\n\n[EXAMPLES]\n# Example\nNumbers: [40, 19, 23, 7]\nTarget: 29\n\n# Search Procedure\nInitial number set: [40, 19, 23, 7], target: 29. Options for choosing two numbers: [(40, 19), (40, 23), (40, 7), (19, 23), (19, 7), (23, 7)].\n |- Pick two numbers (40, 19) (numbers left: [23, 7]). Try possible operations.\n  |- Try 40 + 19 = 59. Add 59 to the number set. Current number set: [59, 23, 7], target: 29. Options for choosing two numbers: [(59, 23), (59, 7), (23, 7)].\n   |- Pick two numbers (59, 23) (numbers left: [7]). Try possible operations.\n    |- Try 59 + 23 = 82. Add 82 to the number set. Current number set: [82, 7], target: 29, just two numbers left.\n     |- Try 82 + 7 = 89. Evaluate 89 != 29, drop this branch.\n     |- Try 82 - 7 = 75. Evaluate 75 != 29, drop this branch.\n     |- Try 82 * 7 = 574. Evaluate 574 != 29, drop this branch.\n     |- Try 82 \/ 7 = 11.7. 11.7 is a decimal, drop this branch.\n    |- Try 59 - 23 = 36. Add 36 to the number set. Current number set: [36, 7], target: 29, just two numbers left.\n     |- Try 36 + 7 = 43. Evaluate 43 != 29, drop this branch.\n     |- Try 36 - 7 = 29. Evaluate 29 == 29, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 36 - 7 = 29\nThe step before: 59 - 23 = 36\nThe first step: 40 + 19 = 59\n\nOutput the solution in the required format:\n<Solution>\n40 + 19 = 59\n59 - 23 = 36\n36 - 7 = 29\n<\/Solution>\n\n\n# Example\nNumbers: [9, 16, 6, 18]\nTarget: 12\n\n# Search Procedure\nInitial number set: [9, 16, 6, 18], target: 12. Options for choosing two numbers: [(9, 16), (9, 6), (9, 18), (16, 6), (16, 18), (6, 18)].\n |- Pick two numbers (9, 16) (numbers left: [6, 18]). Try possible operations.\n  |- Try 16 + 9 = 25. Add 25 to the number set. Current number set: [25, 6, 18], target: 12. Options for choosing two numbers: [(25, 6), (25, 18), (6, 18)].\n   |- Pick two numbers (25, 6) (numbers left: [18]). Try possible operations.\n    |- Try 25 + 6 = 31. Add 31 to the number set. Current number set: [31, 18], target: 12, just two numbers left.\n     |- Try 31 + 18 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 31 - 18 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 31 * 18 = 558. Evaluate 558 != 12, drop this branch.\n     |- Try 31 \/ 18 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 25 - 6 = 19. Add 19 to the number set. Current number set: [19, 18], target: 12, just two numbers left.\n     |- Try 19 + 18 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 19 - 18 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 19 * 18 = 342. Evaluate 342 != 12, drop this branch.\n     |- Try 19 \/ 18 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 25 * 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n   |- Pick two numbers (25, 18) (numbers left: [6]). Try possible operations.\n    |- Try 25 + 18 = 43. Add 43 to the number set. Current number set: [43, 6], target: 12, just two numbers left.\n     |- Try 43 + 6 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 43 - 6 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 43 * 6 = 258. Evaluate 258 != 12, drop this branch.\n     |- Try 43 \/ 6 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 25 - 18 = 7. Add 7 to the number set. Current number set: [7, 6], target: 12, just two numbers left.\n     |- Try 7 + 6 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 7 - 6 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 7 * 6 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 25 * 18 = 450. Add 450 to the number set. Current number set: [450, 6], target: 12, just two numbers left.\n     |- Try 450 + 6 = 456. Evaluate 456 != 12, drop this branch.\n     |- Try 450 - 6 = 444. Evaluate 444 != 12, drop this branch.\n     |- Try 450 * 6 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 450 \/ 6 = 75. Evaluate 75 != 12, drop this branch.\n    |- Try 25 \/ 18 = 1.4. 1.4 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [25]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 25], target: 12, just two numbers left.\n     |- Try 25 + 24 = 49. Evaluate 49 != 12, drop this branch.\n     |- Try 25 - 24 = 1. Evaluate 1 != 12, drop this branch.\n     |- Try 25 * 24 = 600. Evaluate 600 != 12, drop this branch.\n     |- Try 25 \/ 24 = 1.0. 1.0 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 25], target: 12, just two numbers left.\n     |- Try 25 + 12 = 37. Evaluate 37 != 12, drop this branch.\n     |- Try 25 - 12 = 13. Evaluate 13 != 12, drop this branch.\n     |- Try 25 * 12 = 300. Evaluate 300 != 12, drop this branch.\n     |- Try 25 \/ 12 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 25], target: 12, just two numbers left.\n     |- Try 108 + 25 = 133. Evaluate 133 != 12, drop this branch.\n     |- Try 108 - 25 = 83. Evaluate 83 != 12, drop this branch.\n     |- Try 108 * 25 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 108 \/ 25 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 25], target: 12, just two numbers left.\n     |- Try 25 + 3 = 28. Evaluate 28 != 12, drop this branch.\n     |- Try 25 - 3 = 22. Evaluate 22 != 12, drop this branch.\n     |- Try 25 * 3 = 75. Evaluate 75 != 12, drop this branch.\n     |- Try 25 \/ 3 = 8.3. 8.3 is a decimal, drop this branch.\n  |- Try 16 - 9 = 7. Add 7 to the number set. Current number set: [7, 6, 18], target: 12. Options for choosing two numbers: [(7, 6), (7, 18), (6, 18)].\n   |- Pick two numbers (7, 6) (numbers left: [18]). Try possible operations.\n    |- Try 7 + 6 = 13. Add 13 to the number set. Current number set: [13, 18], target: 12, just two numbers left.\n     |- Try 18 + 13 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 18 - 13 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 18 * 13 = 234. Evaluate 234 != 12, drop this branch.\n     |- Try 18 \/ 13 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 7 - 6 = 1. Add 1 to the number set. Current number set: [1, 18], target: 12, just two numbers left.\n     |- Try 18 + 1 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 18 - 1 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 18 * 1 = 18. Evaluate 18 != 12, drop this branch.\n     |- Try 18 \/ 1 = 18. Evaluate 18 != 12, drop this branch.\n    |- Try 7 * 6 = 42. Add 42 to the number set. Current number set: [42, 18], target: 12, just two numbers left.\n     |- Try 42 + 18 = 60. Evaluate 60 != 12, drop this branch.\n     |- Try 42 - 18 = 24. Evaluate 24 != 12, drop this branch.\n     |- Try 42 * 18 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 42 \/ 18 = 2.3. 2.3 is a decimal, drop this branch.\n    |- Try 7 \/ 6 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (7, 18) (numbers left: [6]). Try possible operations.\n    |- Try 18 + 7 = 25. Add 25 to the number set. Current number set: [25, 6], target: 12, just two numbers left.\n     |- Try 25 + 6 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 25 - 6 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 25 * 6 = 150. Evaluate 150 != 12, drop this branch.\n     |- Try 25 \/ 6 = 4.2. 4.2 is a decimal, drop this branch.\n    |- Try 18 - 7 = 11. Add 11 to the number set. Current number set: [11, 6], target: 12, just two numbers left.\n     |- Try 11 + 6 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 11 - 6 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 11 * 6 = 66. Evaluate 66 != 12, drop this branch.\n     |- Try 11 \/ 6 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 18 * 7 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 18 \/ 7 = 2.6. 2.6 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [7]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 7], target: 12, just two numbers left.\n     |- Try 24 + 7 = 31. Evaluate 31 != 12, drop this branch.\n     |- Try 24 - 7 = 17. Evaluate 17 != 12, drop this branch.\n     |- Try 24 * 7 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 24 \/ 7 = 3.4. 3.4 is a decimal, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 7], target: 12, just two numbers left.\n     |- Try 12 + 7 = 19. Evaluate 19 != 12, drop this branch.\n     |- Try 12 - 7 = 5. Evaluate 5 != 12, drop this branch.\n     |- Try 12 * 7 = 84. Evaluate 84 != 12, drop this branch.\n     |- Try 12 \/ 7 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 18 * 6 = 108. Add 108 to the number set. Current number set: [108, 7], target: 12, just two numbers left.\n     |- Try 108 + 7 = 115. Evaluate 115 != 12, drop this branch.\n     |- Try 108 - 7 = 101. Evaluate 101 != 12, drop this branch.\n     |- Try 108 * 7 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 108 \/ 7 = 15.4. 15.4 is a decimal, drop this branch.\n    |- Try 18 \/ 6 = 3. Add 3 to the number set. Current number set: [3, 7], target: 12, just two numbers left.\n     |- Try 7 + 3 = 10. Evaluate 10 != 12, drop this branch.\n     |- Try 7 - 3 = 4. Evaluate 4 != 12, drop this branch.\n     |- Try 7 * 3 = 21. Evaluate 21 != 12, drop this branch.\n     |- Try 7 \/ 3 = 2.3. 2.3 is a decimal, drop this branch.\n  |- Try 16 * 9 = 144. Add 144 to the number set. Current number set: [144, 6, 18], target: 12. Options for choosing two numbers: [(144, 6), (144, 18), (6, 18)].\n   |- Pick two numbers (144, 6) (numbers left: [18]). Try possible operations.\n    |- Try 144 + 6 = 150. Add 150 to the number set. Current number set: [150, 18], target: 12, just two numbers left.\n     |- Try 150 + 18 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 150 - 18 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 150 * 18 = 2700. 2700 exceeds the maximum intermediate result, drop this branch.\n     |- Try 150 \/ 18 = 8.3. 8.3 is a decimal, drop this branch.\n    |- Try 144 - 6 = 138. Add 138 to the number set. Current number set: [138, 18], target: 12, just two numbers left.\n     |- Try 138 + 18 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 138 - 18 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 138 * 18 = 2484. 2484 exceeds the maximum intermediate result, drop this branch.\n     |- Try 138 \/ 18 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 144 * 6 = 864. Add 864 to the number set. Current number set: [864, 18], target: 12, just two numbers left.\n     |- Try 864 + 18 = 882. Evaluate 882 != 12, drop this branch.\n     |- Try 864 - 18 = 846. Evaluate 846 != 12, drop this branch.\n     |- Try 864 * 18 = 15552. 15552 exceeds the maximum intermediate result, drop this branch.\n     |- Try 864 \/ 18 = 48. Evaluate 48 != 12, drop this branch.\n    |- Try 144 \/ 6 = 24. Add 24 to the number set. Current number set: [24, 18], target: 12, just two numbers left.\n     |- Try 24 + 18 = 42. Evaluate 42 != 12, drop this branch.\n     |- Try 24 - 18 = 6. Evaluate 6 != 12, drop this branch.\n     |- Try 24 * 18 = 432. Evaluate 432 != 12, drop this branch.\n     |- Try 24 \/ 18 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (144, 18) (numbers left: [6]). Try possible operations.\n    |- Try 144 + 18 = 162. Add 162 to the number set. Current number set: [162, 6], target: 12, just two numbers left.\n     |- Try 162 + 6 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 162 - 6 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 162 * 6 = 972. Evaluate 972 != 12, drop this branch.\n     |- Try 162 \/ 6 = 27. Evaluate 27 != 12, drop this branch.\n    |- Try 144 - 18 = 126. Add 126 to the number set. Current number set: [126, 6], target: 12, just two numbers left.\n     |- Try 126 + 6 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 126 - 6 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 126 * 6 = 756. Evaluate 756 != 12, drop this branch.\n     |- Try 126 \/ 6 = 21. Evaluate 21 != 12, drop this branch.\n    |- Try 144 * 18 = 2592. 2592 exceeds the maximum intermediate result, drop this branch.\n    |- Try 144 \/ 18 = 8. Add 8 to the number set. Current number set: [8, 6], target: 12, just two numbers left.\n     |- Try 8 + 6 = 14. Evaluate 14 != 12, drop this branch.\n     |- Try 8 - 6 = 2. Evaluate 2 != 12, drop this branch.\n     |- Try 8 * 6 = 48. Evaluate 48 != 12, drop this branch.\n     |- Try 8 \/ 6 = 1.3. 1.3 is a decimal, drop this branch.\n   |- Pick two numbers (6, 18) (numbers left: [144]). Try possible operations.\n    |- Try 18 + 6 = 24. Add 24 to the number set. Current number set: [24, 144], target: 12, just two numbers left.\n     |- Try 144 + 24 = 168. Evaluate 168 != 12, drop this branch.\n     |- Try 144 - 24 = 120. Evaluate 120 != 12, drop this branch.\n     |- Try 144 * 24 = 3456. 3456 exceeds the maximum intermediate result, drop this branch.\n     |- Try 144 \/ 24 = 6. Evaluate 6 != 12, drop this branch.\n    |- Try 18 - 6 = 12. Add 12 to the number set. Current number set: [12, 144], target: 12, just two numbers left.\n     |- Try 144 + 12 = 156. Evaluate 156 != 12, drop this branch.\n     |- Try 144 - 12 = 132. Evaluate 132 != 12, drop this branch.\n     |- Try 144 * 12 = 1728. Evaluate 1728 != 12, drop this branch.\n     |- Try 144 \/ 12 = 12. Evaluate 12 == 12, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 144 \/ 12 = 12\nThe step before: 18 - 6 = 12\nThe first step: 16 * 9 = 144\n\nOutput the solution in the required format:\n<Solution>\n16 * 9 = 144\n18 - 6 = 12\n144 \/ 12 = 12\n<\/Solution>\n\n\n[Problem]\nNow, solve the following problem. Note that:\n- Please carefully read the approach and examples provided above, and follow them to solve the problem.\n- Please ALWAYS include your search procedure (after # Search Procedure). The search procedure should follow the format of the examples provided above.\n- Please mark your answer with <Solution> and <\/Solution> tags. The solution should be a sequence of three equations exactly following the format of the examples above, with no additional text in between.\n\nNumbers: [8, 29, 6, 31]\nTarget: 30","reference_output":"# Search Procedure\nInitial number set: [8, 29, 6, 31], target: 30. Options for choosing two numbers: [(8, 29), (8, 6), (8, 31), (29, 6), (29, 31), (6, 31)].\n |- Pick two numbers (8, 29) (numbers left: [6, 31]). Try possible operations.\n  |- Try 29 + 8 = 37. Add 37 to the number set. Current number set: [37, 6, 31], target: 30. Options for choosing two numbers: [(37, 6), (37, 31), (6, 31)].\n   |- Pick two numbers (37, 6) (numbers left: [31]). Try possible operations.\n    |- Try 37 + 6 = 43. Add 43 to the number set. Current number set: [43, 31], target: 30, just two numbers left.\n     |- Try 43 + 31 = 74. Evaluate 74 != 30, drop this branch.\n     |- Try 43 - 31 = 12. Evaluate 12 != 30, drop this branch.\n     |- Try 43 * 31 = 1333. Evaluate 1333 != 30, drop this branch.\n     |- Try 43 \/ 31 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 37 - 6 = 31. Add 31 to the number set. Current number set: [31, 31], target: 30, just two numbers left.\n     |- Try 31 + 31 = 62. Evaluate 62 != 30, drop this branch.\n     |- Try 31 - 31 = 0. Evaluate 0 != 30, drop this branch.\n     |- Try 31 * 31 = 961. Evaluate 961 != 30, drop this branch.\n     |- Try 31 \/ 31 = 1. Evaluate 1 != 30, drop this branch.\n    |- Try 37 * 6 = 222. Add 222 to the number set. Current number set: [222, 31], target: 30, just two numbers left.\n     |- Try 222 + 31 = 253. Evaluate 253 != 30, drop this branch.\n     |- Try 222 - 31 = 191. Evaluate 191 != 30, drop this branch.\n     |- Try 222 * 31 = 6882. 6882 exceeds the maximum intermediate result, drop this branch.\n     |- Try 222 \/ 31 = 7.2. 7.2 is a decimal, drop this branch.\n    |- Try 37 \/ 6 = 6.2. 6.2 is a decimal, drop this branch.\n   |- Pick two numbers (37, 31) (numbers left: [6]). Try possible operations.\n    |- Try 37 + 31 = 68. Add 68 to the number set. Current number set: [68, 6], target: 30, just two numbers left.\n     |- Try 68 + 6 = 74. Evaluate 74 != 30, drop this branch.\n     |- Try 68 - 6 = 62. Evaluate 62 != 30, drop this branch.\n     |- Try 68 * 6 = 408. Evaluate 408 != 30, drop this branch.\n     |- Try 68 \/ 6 = 11.3. 11.3 is a decimal, drop this branch.\n    |- Try 37 - 31 = 6. Add 6 to the number set. Current number set: [6, 6], target: 30, just two numbers left.\n     |- Try 6 + 6 = 12. Evaluate 12 != 30, drop this branch.\n     |- Try 6 - 6 = 0. Evaluate 0 != 30, drop this branch.\n     |- Try 6 * 6 = 36. Evaluate 36 != 30, drop this branch.\n     |- Try 6 \/ 6 = 1. Evaluate 1 != 30, drop this branch.\n    |- Try 37 * 31 = 1147. Add 1147 to the number set. Current number set: [1147, 6], target: 30, just two numbers left.\n     |- Try 1147 + 6 = 1153. Evaluate 1153 != 30, drop this branch.\n     |- Try 1147 - 6 = 1141. Evaluate 1141 != 30, drop this branch.\n     |- Try 1147 * 6 = 6882. 6882 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1147 \/ 6 = 191.2. 191.2 is a decimal, drop this branch.\n    |- Try 37 \/ 31 = 1.2. 1.2 is a decimal, drop this branch.\n   |- Pick two numbers (6, 31) (numbers left: [37]). Try possible operations.\n    |- Try 31 + 6 = 37. Add 37 to the number set. Current number set: [37, 37], target: 30, just two numbers left.\n     |- Try 37 + 37 = 74. Evaluate 74 != 30, drop this branch.\n     |- Try 37 - 37 = 0. Evaluate 0 != 30, drop this branch.\n     |- Try 37 * 37 = 1369. Evaluate 1369 != 30, drop this branch.\n     |- Try 37 \/ 37 = 1. Evaluate 1 != 30, drop this branch.\n    |- Try 31 - 6 = 25. Add 25 to the number set. Current number set: [25, 37], target: 30, just two numbers left.\n     |- Try 37 + 25 = 62. Evaluate 62 != 30, drop this branch.\n     |- Try 37 - 25 = 12. Evaluate 12 != 30, drop this branch.\n     |- Try 37 * 25 = 925. Evaluate 925 != 30, drop this branch.\n     |- Try 37 \/ 25 = 1.5. 1.5 is a decimal, drop this branch.\n    |- Try 31 * 6 = 186. Add 186 to the number set. Current number set: [186, 37], target: 30, just two numbers left.\n     |- Try 186 + 37 = 223. Evaluate 223 != 30, drop this branch.\n     |- Try 186 - 37 = 149. Evaluate 149 != 30, drop this branch.\n     |- Try 186 * 37 = 6882. 6882 exceeds the maximum intermediate result, drop this branch.\n     |- Try 186 \/ 37 = 5.0. 5.0 is a decimal, drop this branch.\n    |- Try 31 \/ 6 = 5.2. 5.2 is a decimal, drop this branch.\n  |- Try 29 - 8 = 21. Add 21 to the number set. Current number set: [21, 6, 31], target: 30. Options for choosing two numbers: [(21, 6), (21, 31), (6, 31)].\n   |- Pick two numbers (21, 6) (numbers left: [31]). Try possible operations.\n    |- Try 21 + 6 = 27. Add 27 to the number set. Current number set: [27, 31], target: 30, just two numbers left.\n     |- Try 31 + 27 = 58. Evaluate 58 != 30, drop this branch.\n     |- Try 31 - 27 = 4. Evaluate 4 != 30, drop this branch.\n     |- Try 31 * 27 = 837. Evaluate 837 != 30, drop this branch.\n     |- Try 31 \/ 27 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 21 - 6 = 15. Add 15 to the number set. Current number set: [15, 31], target: 30, just two numbers left.\n     |- Try 31 + 15 = 46. Evaluate 46 != 30, drop this branch.\n     |- Try 31 - 15 = 16. Evaluate 16 != 30, drop this branch.\n     |- Try 31 * 15 = 465. Evaluate 465 != 30, drop this branch.\n     |- Try 31 \/ 15 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 21 * 6 = 126. Add 126 to the number set. Current number set: [126, 31], target: 30, just two numbers left.\n     |- Try 126 + 31 = 157. Evaluate 157 != 30, drop this branch.\n     |- Try 126 - 31 = 95. Evaluate 95 != 30, drop this branch.\n     |- Try 126 * 31 = 3906. 3906 exceeds the maximum intermediate result, drop this branch.\n     |- Try 126 \/ 31 = 4.1. 4.1 is a decimal, drop this branch.\n    |- Try 21 \/ 6 = 3.5. 3.5 is a decimal, drop this branch.\n   |- Pick two numbers (21, 31) (numbers left: [6]). Try possible operations.\n    |- Try 31 + 21 = 52. Add 52 to the number set. Current number set: [52, 6], target: 30, just two numbers left.\n     |- Try 52 + 6 = 58. Evaluate 58 != 30, drop this branch.\n     |- Try 52 - 6 = 46. Evaluate 46 != 30, drop this branch.\n     |- Try 52 * 6 = 312. Evaluate 312 != 30, drop this branch.\n     |- Try 52 \/ 6 = 8.7. 8.7 is a decimal, drop this branch.\n    |- Try 31 - 21 = 10. Add 10 to the number set. Current number set: [10, 6], target: 30, just two numbers left.\n     |- Try 10 + 6 = 16. Evaluate 16 != 30, drop this branch.\n     |- Try 10 - 6 = 4. Evaluate 4 != 30, drop this branch.\n     |- Try 10 * 6 = 60. Evaluate 60 != 30, drop this branch.\n     |- Try 10 \/ 6 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 31 * 21 = 651. Add 651 to the number set. Current number set: [651, 6], target: 30, just two numbers left.\n     |- Try 651 + 6 = 657. Evaluate 657 != 30, drop this branch.\n     |- Try 651 - 6 = 645. Evaluate 645 != 30, drop this branch.\n     |- Try 651 * 6 = 3906. 3906 exceeds the maximum intermediate result, drop this branch.\n     |- Try 651 \/ 6 = 108.5. 108.5 is a decimal, drop this branch.\n    |- Try 31 \/ 21 = 1.5. 1.5 is a decimal, drop this branch.\n   |- Pick two numbers (6, 31) (numbers left: [21]). Try possible operations.\n    |- Try 31 + 6 = 37. Add 37 to the number set. Current number set: [37, 21], target: 30, just two numbers left.\n     |- Try 37 + 21 = 58. Evaluate 58 != 30, drop this branch.\n     |- Try 37 - 21 = 16. Evaluate 16 != 30, drop this branch.\n     |- Try 37 * 21 = 777. Evaluate 777 != 30, drop this branch.\n     |- Try 37 \/ 21 = 1.8. 1.8 is a decimal, drop this branch.\n    |- Try 31 - 6 = 25. Add 25 to the number set. Current number set: [25, 21], target: 30, just two numbers left.\n     |- Try 25 + 21 = 46. Evaluate 46 != 30, drop this branch.\n     |- Try 25 - 21 = 4. Evaluate 4 != 30, drop this branch.\n     |- Try 25 * 21 = 525. Evaluate 525 != 30, drop this branch.\n     |- Try 25 \/ 21 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 31 * 6 = 186. Add 186 to the number set. Current number set: [186, 21], target: 30, just two numbers left.\n     |- Try 186 + 21 = 207. Evaluate 207 != 30, drop this branch.\n     |- Try 186 - 21 = 165. Evaluate 165 != 30, drop this branch.\n     |- Try 186 * 21 = 3906. 3906 exceeds the maximum intermediate result, drop this branch.\n     |- Try 186 \/ 21 = 8.9. 8.9 is a decimal, drop this branch.\n    |- Try 31 \/ 6 = 5.2. 5.2 is a decimal, drop this branch.\n  |- Try 29 * 8 = 232. Add 232 to the number set. Current number set: [232, 6, 31], target: 30. Options for choosing two numbers: [(232, 6), (232, 31), (6, 31)].\n   |- Pick two numbers (232, 6) (numbers left: [31]). Try possible operations.\n    |- Try 232 + 6 = 238. Add 238 to the number set. Current number set: [238, 31], target: 30, just two numbers left.\n     |- Try 238 + 31 = 269. Evaluate 269 != 30, drop this branch.\n     |- Try 238 - 31 = 207. Evaluate 207 != 30, drop this branch.\n     |- Try 238 * 31 = 7378. 7378 exceeds the maximum intermediate result, drop this branch.\n     |- Try 238 \/ 31 = 7.7. 7.7 is a decimal, drop this branch.\n    |- Try 232 - 6 = 226. Add 226 to the number set. Current number set: [226, 31], target: 30, just two numbers left.\n     |- Try 226 + 31 = 257. Evaluate 257 != 30, drop this branch.\n     |- Try 226 - 31 = 195. Evaluate 195 != 30, drop this branch.\n     |- Try 226 * 31 = 7006. 7006 exceeds the maximum intermediate result, drop this branch.\n     |- Try 226 \/ 31 = 7.3. 7.3 is a decimal, drop this branch.\n    |- Try 232 * 6 = 1392. Add 1392 to the number set. Current number set: [1392, 31], target: 30, just two numbers left.\n     |- Try 1392 + 31 = 1423. Evaluate 1423 != 30, drop this branch.\n     |- Try 1392 - 31 = 1361. Evaluate 1361 != 30, drop this branch.\n     |- Try 1392 * 31 = 43152. 43152 exceeds the maximum intermediate result, drop this branch.\n     |- Try 1392 \/ 31 = 44.9. 44.9 is a decimal, drop this branch.\n    |- Try 232 \/ 6 = 38.7. 38.7 is a decimal, drop this branch.\n   |- Pick two numbers (232, 31) (numbers left: [6]). Try possible operations.\n    |- Try 232 + 31 = 263. Add 263 to the number set. Current number set: [263, 6], target: 30, just two numbers left.\n     |- Try 263 + 6 = 269. Evaluate 269 != 30, drop this branch.\n     |- Try 263 - 6 = 257. Evaluate 257 != 30, drop this branch.\n     |- Try 263 * 6 = 1578. Evaluate 1578 != 30, drop this branch.\n     |- Try 263 \/ 6 = 43.8. 43.8 is a decimal, drop this branch.\n    |- Try 232 - 31 = 201. Add 201 to the number set. Current number set: [201, 6], target: 30, just two numbers left.\n     |- Try 201 + 6 = 207. Evaluate 207 != 30, drop this branch.\n     |- Try 201 - 6 = 195. Evaluate 195 != 30, drop this branch.\n     |- Try 201 * 6 = 1206. Evaluate 1206 != 30, drop this branch.\n     |- Try 201 \/ 6 = 33.5. 33.5 is a decimal, drop this branch.\n    |- Try 232 * 31 = 7192. 7192 exceeds the maximum intermediate result, drop this branch.\n    |- Try 232 \/ 31 = 7.5. 7.5 is a decimal, drop this branch.\n   |- Pick two numbers (6, 31) (numbers left: [232]). Try possible operations.\n    |- Try 31 + 6 = 37. Add 37 to the number set. Current number set: [37, 232], target: 30, just two numbers left.\n     |- Try 232 + 37 = 269. Evaluate 269 != 30, drop this branch.\n     |- Try 232 - 37 = 195. Evaluate 195 != 30, drop this branch.\n     |- Try 232 * 37 = 8584. 8584 exceeds the maximum intermediate result, drop this branch.\n     |- Try 232 \/ 37 = 6.3. 6.3 is a decimal, drop this branch.\n    |- Try 31 - 6 = 25. Add 25 to the number set. Current number set: [25, 232], target: 30, just two numbers left.\n     |- Try 232 + 25 = 257. Evaluate 257 != 30, drop this branch.\n     |- Try 232 - 25 = 207. Evaluate 207 != 30, drop this branch.\n     |- Try 232 * 25 = 5800. 5800 exceeds the maximum intermediate result, drop this branch.\n     |- Try 232 \/ 25 = 9.3. 9.3 is a decimal, drop this branch.\n    |- Try 31 * 6 = 186. Add 186 to the number set. Current number set: [186, 232], target: 30, just two numbers left.\n     |- Try 232 + 186 = 418. Evaluate 418 != 30, drop this branch.\n     |- Try 232 - 186 = 46. Evaluate 46 != 30, drop this branch.\n     |- Try 232 * 186 = 43152. 43152 exceeds the maximum intermediate result, drop this branch.\n     |- Try 232 \/ 186 = 1.2. 1.2 is a decimal, drop this branch.\n    |- Try 31 \/ 6 = 5.2. 5.2 is a decimal, drop this branch.\n  |- Try 29 \/ 8 = 3.6. 3.6 is a decimal, drop this branch.\n |- Pick two numbers (8, 6) (numbers left: [29, 31]). Try possible operations.\n  |- Try 8 + 6 = 14. Add 14 to the number set. Current number set: [14, 29, 31], target: 30. Options for choosing two numbers: [(14, 29), (14, 31), (29, 31)].\n   |- Pick two numbers (14, 29) (numbers left: [31]). Try possible operations.\n    |- Try 29 + 14 = 43. Add 43 to the number set. Current number set: [43, 31], target: 30, just two numbers left.\n     |- Try 43 + 31 = 74. Evaluate 74 != 30, drop this branch.\n     |- Try 43 - 31 = 12. Evaluate 12 != 30, drop this branch.\n     |- Try 43 * 31 = 1333. Evaluate 1333 != 30, drop this branch.\n     |- Try 43 \/ 31 = 1.4. 1.4 is a decimal, drop this branch.\n    |- Try 29 - 14 = 15. Add 15 to the number set. Current number set: [15, 31], target: 30, just two numbers left.\n     |- Try 31 + 15 = 46. Evaluate 46 != 30, drop this branch.\n     |- Try 31 - 15 = 16. Evaluate 16 != 30, drop this branch.\n     |- Try 31 * 15 = 465. Evaluate 465 != 30, drop this branch.\n     |- Try 31 \/ 15 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 29 * 14 = 406. Add 406 to the number set. Current number set: [406, 31], target: 30, just two numbers left.\n     |- Try 406 + 31 = 437. Evaluate 437 != 30, drop this branch.\n     |- Try 406 - 31 = 375. Evaluate 375 != 30, drop this branch.\n     |- Try 406 * 31 = 12586. 12586 exceeds the maximum intermediate result, drop this branch.\n     |- Try 406 \/ 31 = 13.1. 13.1 is a decimal, drop this branch.\n    |- Try 29 \/ 14 = 2.1. 2.1 is a decimal, drop this branch.\n   |- Pick two numbers (14, 31) (numbers left: [29]). Try possible operations.\n    |- Try 31 + 14 = 45. Add 45 to the number set. Current number set: [45, 29], target: 30, just two numbers left.\n     |- Try 45 + 29 = 74. Evaluate 74 != 30, drop this branch.\n     |- Try 45 - 29 = 16. Evaluate 16 != 30, drop this branch.\n     |- Try 45 * 29 = 1305. Evaluate 1305 != 30, drop this branch.\n     |- Try 45 \/ 29 = 1.6. 1.6 is a decimal, drop this branch.\n    |- Try 31 - 14 = 17. Add 17 to the number set. Current number set: [17, 29], target: 30, just two numbers left.\n     |- Try 29 + 17 = 46. Evaluate 46 != 30, drop this branch.\n     |- Try 29 - 17 = 12. Evaluate 12 != 30, drop this branch.\n     |- Try 29 * 17 = 493. Evaluate 493 != 30, drop this branch.\n     |- Try 29 \/ 17 = 1.7. 1.7 is a decimal, drop this branch.\n    |- Try 31 * 14 = 434. Add 434 to the number set. Current number set: [434, 29], target: 30, just two numbers left.\n     |- Try 434 + 29 = 463. Evaluate 463 != 30, drop this branch.\n     |- Try 434 - 29 = 405. Evaluate 405 != 30, drop this branch.\n     |- Try 434 * 29 = 12586. 12586 exceeds the maximum intermediate result, drop this branch.\n     |- Try 434 \/ 29 = 15.0. 15.0 is a decimal, drop this branch.\n    |- Try 31 \/ 14 = 2.2. 2.2 is a decimal, drop this branch.\n   |- Pick two numbers (29, 31) (numbers left: [14]). Try possible operations.\n    |- Try 31 + 29 = 60. Add 60 to the number set. Current number set: [60, 14], target: 30, just two numbers left.\n     |- Try 60 + 14 = 74. Evaluate 74 != 30, drop this branch.\n     |- Try 60 - 14 = 46. Evaluate 46 != 30, drop this branch.\n     |- Try 60 * 14 = 840. Evaluate 840 != 30, drop this branch.\n     |- Try 60 \/ 14 = 4.3. 4.3 is a decimal, drop this branch.\n    |- Try 31 - 29 = 2. Add 2 to the number set. Current number set: [2, 14], target: 30, just two numbers left.\n     |- Try 14 + 2 = 16. Evaluate 16 != 30, drop this branch.\n     |- Try 14 - 2 = 12. Evaluate 12 != 30, drop this branch.\n     |- Try 14 * 2 = 28. Evaluate 28 != 30, drop this branch.\n     |- Try 14 \/ 2 = 7. Evaluate 7 != 30, drop this branch.\n    |- Try 31 * 29 = 899. Add 899 to the number set. Current number set: [899, 14], target: 30, just two numbers left.\n     |- Try 899 + 14 = 913. Evaluate 913 != 30, drop this branch.\n     |- Try 899 - 14 = 885. Evaluate 885 != 30, drop this branch.\n     |- Try 899 * 14 = 12586. 12586 exceeds the maximum intermediate result, drop this branch.\n     |- Try 899 \/ 14 = 64.2. 64.2 is a decimal, drop this branch.\n    |- Try 31 \/ 29 = 1.1. 1.1 is a decimal, drop this branch.\n  |- Try 8 - 6 = 2. Add 2 to the number set. Current number set: [2, 29, 31], target: 30. Options for choosing two numbers: [(2, 29), (2, 31), (29, 31)].\n   |- Pick two numbers (2, 29) (numbers left: [31]). Try possible operations.\n    |- Try 29 + 2 = 31. Add 31 to the number set. Current number set: [31, 31], target: 30, just two numbers left.\n     |- Try 31 + 31 = 62. Evaluate 62 != 30, drop this branch.\n     |- Try 31 - 31 = 0. Evaluate 0 != 30, drop this branch.\n     |- Try 31 * 31 = 961. Evaluate 961 != 30, drop this branch.\n     |- Try 31 \/ 31 = 1. Evaluate 1 != 30, drop this branch.\n    |- Try 29 - 2 = 27. Add 27 to the number set. Current number set: [27, 31], target: 30, just two numbers left.\n     |- Try 31 + 27 = 58. Evaluate 58 != 30, drop this branch.\n     |- Try 31 - 27 = 4. Evaluate 4 != 30, drop this branch.\n     |- Try 31 * 27 = 837. Evaluate 837 != 30, drop this branch.\n     |- Try 31 \/ 27 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 29 * 2 = 58. Add 58 to the number set. Current number set: [58, 31], target: 30, just two numbers left.\n     |- Try 58 + 31 = 89. Evaluate 89 != 30, drop this branch.\n     |- Try 58 - 31 = 27. Evaluate 27 != 30, drop this branch.\n     |- Try 58 * 31 = 1798. Evaluate 1798 != 30, drop this branch.\n     |- Try 58 \/ 31 = 1.9. 1.9 is a decimal, drop this branch.\n    |- Try 29 \/ 2 = 14.5. 14.5 is a decimal, drop this branch.\n   |- Pick two numbers (2, 31) (numbers left: [29]). Try possible operations.\n    |- Try 31 + 2 = 33. Add 33 to the number set. Current number set: [33, 29], target: 30, just two numbers left.\n     |- Try 33 + 29 = 62. Evaluate 62 != 30, drop this branch.\n     |- Try 33 - 29 = 4. Evaluate 4 != 30, drop this branch.\n     |- Try 33 * 29 = 957. Evaluate 957 != 30, drop this branch.\n     |- Try 33 \/ 29 = 1.1. 1.1 is a decimal, drop this branch.\n    |- Try 31 - 2 = 29. Add 29 to the number set. Current number set: [29, 29], target: 30, just two numbers left.\n     |- Try 29 + 29 = 58. Evaluate 58 != 30, drop this branch.\n     |- Try 29 - 29 = 0. Evaluate 0 != 30, drop this branch.\n     |- Try 29 * 29 = 841. Evaluate 841 != 30, drop this branch.\n     |- Try 29 \/ 29 = 1. Evaluate 1 != 30, drop this branch.\n    |- Try 31 * 2 = 62. Add 62 to the number set. Current number set: [62, 29], target: 30, just two numbers left.\n     |- Try 62 + 29 = 91. Evaluate 91 != 30, drop this branch.\n     |- Try 62 - 29 = 33. Evaluate 33 != 30, drop this branch.\n     |- Try 62 * 29 = 1798. Evaluate 1798 != 30, drop this branch.\n     |- Try 62 \/ 29 = 2.1. 2.1 is a decimal, drop this branch.\n    |- Try 31 \/ 2 = 15.5. 15.5 is a decimal, drop this branch.\n   |- Pick two numbers (29, 31) (numbers left: [2]). Try possible operations.\n    |- Try 31 + 29 = 60. Add 60 to the number set. Current number set: [60, 2], target: 30, just two numbers left.\n     |- Try 60 + 2 = 62. Evaluate 62 != 30, drop this branch.\n     |- Try 60 - 2 = 58. Evaluate 58 != 30, drop this branch.\n     |- Try 60 * 2 = 120. Evaluate 120 != 30, drop this branch.\n     |- Try 60 \/ 2 = 30. Evaluate 30 == 30, target found!\n\nNow we have found the target, let's trace back the solution:\nFinal step: 60 \/ 2 = 30\nThe step before: 31 + 29 = 60\nThe first step: 8 - 6 = 2\n\nOutput the solution in the required format:\n<Solution>\n8 - 6 = 2\n31 + 29 = 60\n60 \/ 2 = 30\n<\/Solution>\n","item":{"nums":[8,29,6,31],"solution":["8 - 6 = 2","31 + 29 = 60","60 \/ 2 = 30"],"target":30}}