Doraemon

Doraemon has a matrix with $N$ rows (numbered $1$ through $N$) and $M$ columns (numbered $1$ through $M$). Let's denote the element in row $i$ and column $j$ by $A_{i,j}$. Next, let's define a sub-row of a row $r$ as a sequence $A_{r, x}, A_{r, x+1}, \ldots, A_{r, y}$ for some $x$ and $y$ ($1 \le x \le y \le M$) and a sub-column of a column $c$ by $A_{x, c}, A_{x+1, c}, \ldots, A_{y, c}$ for some