Greedy Students

Rafid is teaching his students plane geometry. Today they are talking about convex polygons. A [convex polygon](https://en.wikipedia.org/wiki/Convex_polygon) is a simple non-degenerate polygon such that each of its internal angles is strictly smaller than $180^\circ$. Rafid drew $N$ points (numbered $1$ through $N$) on a blackboard (a two-dimensional plane) and told each student to choose some of