As long as we move the first index from row to column, rather than from column to row, the intermediate results will require addresses no longer than the length of i.
if ϕ(B) = d, then every configuration in which B appears is balanced: If ϕ(B) = d and B appears in more than one configuration, that is, |config(B)| > 1, it is impossible to copy entries for B between the cells using a matrix of size (2n) d .