26104번 - Empty Quadrilaterals 다국어

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, and asked to count the number of all quadrilaterals whose corners are members of the set $P$ and whose interior contains no other points in $P$.

For example, assume that $P$ 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 $P$, while only one of them contains a point of $P$ 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 $8$ as the correct answer.

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

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 $P$ and whose interior contains no other points in $P$.