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TOT 1999 Autumn OS5 divide a 8x8 chessboard into 32 rectangles (1x2 or 2x1)

Source:

May 11, 2020
combinatorial geometrycombinatoricsrectangleTiling

Problem Statement

Is it possible to divide a 8×88 \times 8 chessboard into 3232 rectangles, each either 1×21 \times 2 or 2×12 \times 1, and to draw exactly one diagonal on each rectangle such that no two of these diagonals have a common endpoint?
(A Shapovalov)
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