CF1146H Satanic Panic

Description

You are given a set of $ n $ points in a 2D plane. No three points are collinear. A pentagram is a set of $ 5 $ points $ A,B,C,D,E $ that can be arranged as follows. ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF1146H/f942ae06c7e29cb9bc6462315be09bb7d5b4c362.png) Note the length of the line segments don't matter, only that those particular intersections exist. Count the number of ways to choose $ 5 $ points from the given set that form a pentagram.

Input Format

N/A

Output Format

N/A

Explanation/Hint

A picture of the first sample: ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF1146H/ecb5db206846ce3b41c177fcaeaebe0ee2b1bb2a.png) A picture of the second sample: ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF1146H/4f7f38f01a0904403461b302f8dc7d443ccc0e93.png) A picture of the third sample: ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF1146H/d922b8e812b7b67b3a0bbbb474a47be87ee53781.png)