There are two matrices $A$ and $B$ of size $m\times n$ each filled only by “0”s and “1”s. It is given that along any row or column its elements do not decrease (from left to right and from top to bottom).It is also given that the numbers of “1”s in both matrices are equal and for any $k = 1, . . .$ , $m$ the sum of the elements in the top $k$ rows of the matrix $A$ is no less than that of the matrix $B$. Prove for any $l = 1, . . . $, $n$ the sum of the elements in left $l$ columns of the matrix $A$ is no greater than that of the matrix $B$.