Consider a partition of an 8X8 chessboard info p rectangles whose interiors are disjoint such that each rectangle contains an equal number of white and black cells. assume that a1 < a2​ < ... <ap, where ai denotes the number of white cells in the ith rectangle. find the maximal p for which such a partition is possible and for that p determine all possible corresponding sequences a1 ,a2,​ ...,ap.