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.
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*<sub class="lower-index">*i*</sub>, *y*<sub class="lower-index">*i*</sub> ( - 100 ≤ *x*<sub class="lower-index">*i*</sub>, *y*<sub class="lower-index">*i*</sub> ≤ 100) — the coordinates of the *i*-th point. It is guaranteed that no two given points coincide.
import math

n = int(input())
ans = (n*(n-1)*(n-2))//6

arr = []

for _ in range(n):
    a,b = map(int,input().split())
    arr.append((a,b))

cnt = 0

for i in range(n):
    d = dict()
    for j in range(i+1,n):
        dx = arr[j][0]-arr[i][0]
        dy = arr[j][1]-arr[j][0]
        slope = math.atan2(dy,dx)
        d[slope] = d.get(slope,0)+1
    for slope in d:
        cnt+= d[slope] * (d[slope]-1) //2
print(ans-cnt)
