Even Matrix

Chef has an integer $N$ and he wants to generate a matrix $M$ with $N$ rows (numbered $1$ through $N$) and $N$ columns (numbered $1$ through $N$). He thinks that $M$ would be *delicious* if: - Each element of this matrix is an integer between $1$ and $N^2$ inclusive. - All the elements of the matrix are pairwise distinct. - For each square submatrix containing cells in rows $r$ through $r+a$ an