Middle European Mathematical Olympiad 2011 Problem T-3

For an integer $n \geq 3$, let $\mathcal{M}$ be the set $\{(x, y) \mid x, y \in \mathbb{Z}, 1 \leq x \leq n, 1 \leq y \leq n\}$ of points in the plane. ($\mathbb{Z}$ is the set of integers.)

What is the maximum possible number of points in a subset $S \subseteq \mathcal{M}$ which does not contain three distinct points being the vertices of a right triangle?