# Problem 459: Flipping game
The flipping game is a two player game played on a N by N square board.
Each square contains a disk with one side white and one side black. The
game starts with all disks showing their white side. A turn consists of
flipping all disks in a rectangle with the following properties: the
upper right corner of the rectangle contains a white disk the rectangle
width is a perfect square (1, 4, 9, 16, ...) the rectangle height is a
triangular number (1, 3, 6, 10, ...) Players alternate turns. A player
wins by turning the grid all black. Let W(N) be the number of winning
moves for the first player on a N by N board with all disks white,
assuming perfect play. W(1) = 1, W(2) = 0, W(5) = 8 and W(102) = 31395.
For N=5, the first player's eight winning first moves are: Find W(106).