Vanya and Triangles

题面翻译

求平面上n个点中三个点两两相连形成面积不为0的三角形的个数.

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.

样例 #1

样例输入 #1

4
0 0
1 1
2 0
2 2

样例输出 #1

3

样例 #2

样例输入 #2

3
0 0
1 1
2 0

样例输出 #2

1

样例 #3

样例输入 #3

1
1 1

样例输出 #3

0

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.