CMO 2019 Problem 3

Let $m$ and $n$ be positive integers. A $2 m \times 2 n$ grid of squares is coloured in the usual chessboard fashion. Find the number of ways of placing $m n$ counters on the white squares, at most one counter per square, so that no two counters are on white squares that are diagonally adjacent. An example of a way to place the counters when $m=2$ and $n=3$ is shown below.