KöMaL 2022 B5242

Let $m$ and $n$ denote arbitrary positive integers. Consider those lattice points $(x;y)$ in the Cartesian coordinate plane for which $1\le x\le m$ and $1\le y\le n$. What is the maximum possible number of points that can be selected out of these $mn$ lattice points such that no four points selected should form a non-degenerate parallelogram?