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.

Input

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.

Output

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

Note

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.