We represent the checkerboard by using a two$-$dimensional integer array $+4[0$m$-1,0.$m$-11,$ where m is a power of two. For example, the value of m can be $2,4,8,16,32,......$ Suppose that, in the two$-$dimensional array $4,$ the missing cell is set to O and the other cells are initialized to $-1.$