CF552D.Vanya and Triangles

普及/提高-

通过率：0%

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题目描述

Vanya got bored and he painted $n$ distinct points on the plane. After that he connected all the points pairwise and saw that as a result many triangles were formed with vertices in the painted points. He asks you to count the number of the formed triangles with the non-zero area.

输入格式

The first line contains integer $n$ ( $1<=n<=2000$ ) — the number of the points painted on the plane.

Next $n$ lines contain two integers each $x_{i},y_{i}$ ( $-100<=x_{i},y_{i}<=100$ ) — the coordinates of the $i$ -th point. It is guaranteed that no two given points coincide.

输出格式

In the first line print an integer — the number of triangles with the non-zero area among the painted points.

输入输出样例

输入#1
```
4
0 0
1 1
2 0
2 2
```
输出#1
```
3
```
输入#2
```
3
0 0
1 1
2 0
```
输出#2
```
1
```
输入#3
```
1
1 1
```
输出#3
```
0
```

说明/提示

Note to the first sample test. There are $3$ triangles formed: $(0,0)-(1,1)-(2,0)$ ; $(0,0)-(2,2)-(2,0)$ ; $(1,1)-(2,2)-(2,0)$ .

Note to the second sample test. There is $1$ triangle formed: $(0,0)-(1,1)-(2,0)$ .

Note to the third sample test. A single point doesn't form a single triangle.

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