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())
def totaltriangle(n):
         return ((n)*(n-1)*(n-2))//6
points=[]
ans=totaltriangle(n)
for i in range(n):
         points.append(list(map(int,input().split())))
for i in range(n):
         dct={}
         for j in range(i+1,n):
                  a=points[i][1]-points[j][1]
                  b=points[i][0]-points[j][0]
                  x=math.gcd(a,b)
                  a//=x
                  b//=x
                  s=str(a)+"/"+str(b)
                  if s in dct:
                           dct[s]+=1
                  else:
                           dct[s]=1
         for i in dct:
                  ans-=totaltriangle(dct[i]+1)
         #print(dct)
print(ans)