18888번 - New Year and Castle Construction 다국어

문제

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

In a 2-dimension plane, you have 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,ドル no three distinct points lie on a single line. For a point $p \in s,ドル we can protect this point by building a castle. A castle is a simple quadrilateral (polygon with 4ドル$ vertices) that strictly encloses the point $p$ (i.e. the point $p$ is strictly inside a quadrilateral).

Kiwon is interested in the number of 4ドル$-point subsets of $s$ that can be used to build a castle protecting $p$. Note that, 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ドル$-point subsets that can enclose the point $p$. Please compute the sum of $f(p)$ for all points $p \in s$.

입력

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

In the next $n$ lines, two integers $x_i$ and $y_i$ ($-10^9 \le x_i, y_i \le 10^9$) denoting the position of points are given.

It is guaranteed that all points are distinct, and there are no three collinear points.

출력

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

제한

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