Points and Convex Hulls

**New constraints are not updated in the translations.** You are given $N$ distinct points on a two-dimensional plane. It is guaranteed that no three of them are collinear. Let's call a subset of these points *compact* if the [convex hull](https://en.wikipedia.org/wiki/Convex_hull) of this subset has exactly four vertices. Find the number of compact non-empty subsets of the given points. Since