#D9825. Satanic Panic
Satanic Panic
Satanic Panic
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.
Input
The first line contains an integer n (5 ≤ n ≤ 300) — the number of points.
Each of the next n lines contains two integers x_i, y_i (-10^6 ≤ x_i,y_i ≤ 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.
Examples
Input
5 0 0 0 2 2 0 2 2 1 3
Output
1
Input
5 0 0 4 0 0 4 4 4 2 3
Output
0
Input
10 841746 527518 595261 331297 -946901 129987 670374 -140388 -684770 309555 -302589 415564 -387435 613331 -624940 -95922 945847 -199224 24636 -565799
Output
85
Note
A picture of the first sample: A picture of the second sample: A picture of the third sample:
inputFormat
Input
The first line contains an integer n (5 ≤ n ≤ 300) — the number of points.
Each of the next n lines contains two integers x_i, y_i (-10^6 ≤ x_i,y_i ≤ 10^6) — the coordinates of the i-th point. It is guaranteed that no three points are collinear.
outputFormat
Output
Print a single integer, the number of sets of 5 points that form a pentagram.
Examples
Input
5 0 0 0 2 2 0 2 2 1 3
Output
1
Input
5 0 0 4 0 0 4 4 4 2 3
Output
0
Input
10 841746 527518 595261 331297 -946901 129987 670374 -140388 -684770 309555 -302589 415564 -387435 613331 -624940 -95922 945847 -199224 24636 -565799
Output
85
Note
A picture of the first sample: A picture of the second sample: A picture of the third sample:
样例
5
0 0
4 0
0 4
4 4
2 3
0