Nemotron-IMO-Bench 2026 C33

Let $n\geq 2$ be an integer and let $C_n$ be the set of points in the plane with coordinates in $\{1,2,\ldots, n\}$. Let $S$ be a subset of $C_n$ such that any point of $C_n$ lies on a line determined by two points of $S$. Prove that $|S|\geq (n/4)^{2/3}$.