BG-MO 1974 Problem 4

Find the maximal count of shapes that can be placed over a chessboard with size $8\times8$ in such a way that no three shapes are not on two squares, lying next to each other by diagonal parallel $A1-H8$ ( $A1$ is the lowest-bottom left corner of the chessboard, $H8$ is the highest-upper right corner of the chessboard).

V. Chukanov