convex4gon

Time limit2sMemory limit1024 MB

Summary

Given n points with no three collinear, count the convex quadrilaterals that can be formed from four of them.

Level: Medium5 of 10
Topics: Geometry, Combinatorics, Brute force
Solved: No attempts yet

Problem

There is a point set of $n$ distinct points on the $xy$ -plane ( $0<n<30$ ). Every $x$ - and $y$ -coordinate is an integer whose absolute value is less than $1000$ . No three distinct points in the set lie on the same line. Count the distinct convex quadrilaterals whose vertices are points from the set.

Input

Write a function convex4gon. The parameter L is a list of length $n$ . Each item is a tuple of length 2 holding the x- and y-coordinates of a point, and both coordinates are int objects.

Return value

Return an int object equal to the number of distinct convex quadrilaterals whose vertices are points from the set.

Examples1

Example 1
Input
```
1
0 0
```
Expected output
```
0
```