New Year and Castle Construction

Kiwon's favorite video game is holding a new year event to motivate its users. The game is about building and defending a castle, and this led Kiwon to think about the following puzzle.

In a 2-dimensional plane, there is a set $s = \{(x_1, y_1), (x_2, y_2), \ldots, (x_n, y_n)\}$ consisting of $n$ distinct points. In the set $s$, no three distinct points lie on a single line. For a point $p \in s$, we can protect this point by building a castle. A castle is a simple quadrilateral (a polygon with $4$ vertices) that strictly encloses the point $p$ (that is, the point $p$ lies strictly inside the quadrilateral).

Kiwon is interested in the number of $4$-point subsets of $s$ that can be used to build a castle protecting $p$. If a single subset can be connected in more than one way to enclose a point, it is counted only once.

Let $f(p)$ be the number of $4$-point subsets that can enclose the point $p$. Compute the sum of $f(p)$ over all points $p \in s$.

The first line contains a single integer $n$ ($5 \le n \le 2\,500$).

The next $n$ lines each contain two integers $x_i$ and $y_i$, the coordinates of a point ($-10^9 \le x_i, y_i \le 10^9$).

All points are distinct, and no three points are collinear.

Print the sum of $f(p)$ over all points $p \in s$.