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TOT 1999 Autumn OJ5 divide a 6x6 chessboard into 18 rectangles (1x2 or 2x1)

Source:

May 11, 2020
rectanglecombinatorial geometrycombinatoricsTiling

Problem Statement

Is it possible to divide a 6×66 \times 6 chessboard into 1818 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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