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H. Satanic Panic

time limit per test

4 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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 $$$n$$$ ($$$5 \leq n \leq 300$$$) — 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.

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:

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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