Let M be a matrix with n rows and m columns that records whether a grid location M(i, j) is noisy (n) or quiet (q). Given M, your task is to design a dynamic programming algorithm to find the size Q of the largest balanced quiet submatrix in M. A submatrix of M with upper left corner at row I and column J is balanced and quiet and of size Q if for all i, j such that I i I + Q 1 and J j J + Q 1, M(i, j) = q