Brilli the ant sees a square $n \times n$matrix consisting of only $0$'s and $1$s. He is given the task of finding the largest $1$square space( the largest square submatrix consisting of only $1$'s) . For example if he was given the below table, the shaded area would be the largest square area:

Unfortunately Brilli is given a matrix of much larger size. Being the competent programmer that he is, he divides the problem into subproblems and comes up with a brilliant dynamic programming solution.

His dynamic programming solution considers the subproblem $S[i,j]$. $S[i,j]$being the side length of the largest $1$square space whose bottom-right corner is at $i,j$.

Once he solves the problem, his table has the following values:

$S[15][15] = 4$ $S[16][14] = 10$ $S[15][14] = 12$

Given that there is a 1 at [16][15], what is the value of $S[16][15]$?