CF1025F.Disjoint Triangles

A point belongs to a triangle if it lies inside the triangle or on one of its sides. Two triangles are disjoint if there is no point on the plane that belongs to both triangles.

You are given $n$ points on the plane. No two points coincide and no three points are collinear.

Find the number of different ways to choose two disjoint triangles with vertices in the given points. Two ways which differ only in order of triangles or in order of vertices inside triangles are considered equal.

一个点属于某个三角形，当且仅当该点位于该三角形内部或在其某条边上。两个三角形是互不相交的（disjoint），当且仅当平面上不存在同时属于这两个三角形的点。

给定平面上的 $n$ 个点，其中任意两点不重合，且任意三点不共线。

求：从给定点中选取两个互不相交的三角形（每个三角形的顶点均来自给定点）的不同方案数。若两种方案仅在三角形的顺序上不同，或仅在某个三角形内部顶点的顺序上不同，则视为同一种方案。

The first line of the input contains an integer $n$ ($6 \le n \le 2000$) – the number of points.

Each of the next $n$ lines contains two integers $x_i$ and $y_i$ ($|x_i|, |y_i| \le 10^9$) – the coordinates of a point.

No two points coincide and no three points are collinear.

输入的第一行包含一个整数 $n$（$6 \le n \le 2000$）——点的数量。

接下来的 $n$ 行，每行包含两个整数 $x_i$ 和 $y_i$（$|x_i|, |y_i| \le 10^9$）——一个点的坐标。

任意两点不重合，且任意三点不共线。

Print one integer – the number of ways to choose two disjoint triangles.

输出一个整数——选择两个不相交三角形的方案数。

In the first example there are six pairs of disjoint triangles, they are shown on the picture below.

All other pairs of triangles are not disjoint, for example the following pair:

在第一个例子中，共有六对互不相交的三角形，如下图所示：

其余所有三角形对均不互不相交，例如以下这一对：