#P1146H. Satanic Panic
-
ID: 4707
Type: RemoteJudge
4000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: (None)
Uploaded By:
Hydro
Tags> Satanic Panic
No submission language available for this problem.
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. 
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.
The first line contains an integer $n$ ($5 \leq n \leq 300$) — the number of points.
Each of the next $n$ lines contains two integers $x_i, y_i$ ($-10^6 \leq x_i,y_i \leq 10^6$) — the coordinates of the $i$-th point. It is guaranteed that no three points are collinear.
Print a single integer, the number of sets of $5$ points that form a pentagram.
Input
The first line contains an integer $n$ ($5 \leq n \leq 300$) — the number of points.
Each of the next $n$ lines contains two integers $x_i, y_i$ ($-10^6 \leq x_i,y_i \leq 10^6$) — the coordinates of the $i$-th point. It is guaranteed that no three points are collinear.
Output
Print a single integer, the number of sets of $5$ points that form a pentagram.
Samples
5
0 0
0 2
2 0
2 2
1 3
1
5
0 0
4 0
0 4
4 4
2 3
0
10
841746 527518
595261 331297
-946901 129987
670374 -140388
-684770 309555
-302589 415564
-387435 613331
-624940 -95922
945847 -199224
24636 -565799
85
Note
A picture of the first sample: 
A picture of the second sample: 
A picture of the third sample: 