Ada Rooks 2

In order to beat AlphaZero, Chef Ada is improving her chess calculation skills. Today, Ada took a big chessboard with $N$ rows (numbered $1$ through $N$) and $N$ columns (numbered $1$ through $N$). Let's denote the square in row $r$ and column $c$ of the chessboard by $(r, c)$. Ada wants to place some rooks on the chessboard in such a way that the following conditions are satisfied: - Each squ