Empty Quadrilaterals

A quadrilateral is a polygon with exactly four distinct corners and four distinct sides, without any crossing between its sides. In this problem, you are given a set $P$ of $n$ points in the plane, no three of which are collinear. Count the quadrilaterals whose corners are members of $P$ and whose interior contains no other points of $P$.

For example, if $P$ has five points as shown in the left figure, there are nine distinct quadrilaterals whose corners are members of $P$. Only one of them contains a point of $P$ in its interior, as shown in the right figure. The answer is therefore $8$.

The first line contains an integer $n$ ($1 \le n \le 300$), the number of points in $P$. Each of the following $n$ lines contains two integers, the coordinates of one point in $P$. Every coordinate is between $-10^9$ and $10^9$, inclusive. No three points in $P$ are collinear.

Print one line containing a single integer: the number of quadrilaterals whose corners are members of $P$ and whose interior contains no other points of $P$.