(Challenge) Nanobots

To heal people with virus infections, Ada designed small robots (nanobots) that travel through the bloodstream, scanning all tissues of the body. The nanobots have detected a region of infected cells described by a matrix with $N$ rows (numbered $1$ through $N$ from top to bottom) and $N$ columns (numbered $1$ through $N$ from left to right). For each valid $r$ and $c$, the cell in row $r$ and