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 as ma

def fu(a,b,c,d):
    if c-a==0:
        return c
    else:
        return ((d-b)/(c-a),(b*c-d*a)/(c-a))

n=int(input())
a=[]
for i in range(n):
    a.append(list(map(int,input().split())))
b={}
for i in range(n):
    for j in range(i+1,n):
        c=fu(a[i][0],a[i][1],a[j][0],a[j][1])
        if c in b.keys():
            b[c]+=1
        else:
            b[c]=1
for i in b:
    b[i]=(1+ma.sqrt(1+8*b[i]))/2
s=n*(n-1)*(n-2)/6
for i in b:
    s-=(b[i]*(b[i]-1)*(b[i]-2))/6
print(int(s))