RU-ALLRUSSIAN 1978 Problem 14

$\mathrm{n} > 3$ is an integer. Let S be the set of lattice points (a, b) with $0\leq \mathrm{a},\mathrm{b}< \mathrm{n}$ . Show that we can choose n points of S so that no three chosen points are collinear and no four chosen points from a parallelogram.