Minimum value of special tables

Consider an $N \times M$ binary matrix $A$, i.e. a grid consisting of $N$ rows numbered $1$ to $N$ from top to bottom and $M$ columns numbered $1$ to $M$ from left to right, whose cells take the value $0$ or $1$. Let $(i, j)$ denote the cell on the $i$-th row and $j$-th column. The matrix is said to be *special* if for **every** cell $(i, j)$, the following condition holds simultaneously: - $A_{i