IMO 1974 Problem 4

Consider decompositions of an $8\times 8$ chessboard into $p$ non-overlapping rectangles subject to the following conditions: (i) Each rectangle has as many white squares as black squares. (ii) If $a_i$ is the number of white squares in the $i$ -th rectangle, then $a_1<a_2<\ldots <a_p$ . Find the maximum value of $p$ for which such a decomposition is possible. For this value of $p$ , determine all possible sequences $a_1,a_2,\ldots ,a_p$ .