Empty Quadrilaterals

문제

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 $PP$ of $nn$ points in the plane, no three of which are collinear, and asked to count the number of all quadrilaterals whose corners are members of the set $PP$ and whose interior contains no other points in $PP$.

For example, assume that $PP$ consists of five points as shown in the left of the figure above. There are nine distinct quadrilaterals in total whose corners are members of $PP$, while only one of them contains a point of $PP$ in its interior, as in the right of the figure above. Therefore, there are exactly eight quadrilaterals satisfying the condition and your program must print out $88$ as the correct answer.

입력

Your program is to read from standard input. The input starts with a line containing an integer $nn$ (1 ≤ n ≤ 300), where $nn$ denotes the number of points in the set $PP$. In the following $nn$ lines, each line consists of two integers, ranging from $-{10}^9-10^9$ to ${10}^{9}10^9$, representing the coordinates of a point in $PP$. There are no three points in $PP$ that are collinear.

출력

Your program is to write to standard output. Print exactly one line consisting of a single integer that represents the number of quadrilaterals whose corners are members of the set $PP$ and whose interior contains no other points in $PP$.