Chess Colouring

You are given an $N \times N$ chessboard where all squares are initially white. Determine the number of ways to color exactly $\lfloor \frac{N^2}{2} \rfloor$ squares black such that no two black squares share a side. *Two ways of coloring are considered different if there exists at least one square that is colored differently between them.* ### Input - The first line of input will contain a sin