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())
c = []
l = []

for i in range(n):
    l.append(tuple(map(int, input().split())))
    
s = set(l.copy())
l.sort()

if n < 3:
    print(0)
else:
    ct = 0
    for i in range(n-2):
        for j in range(i+1, n-1):
            ap = n-j-1
            
            pta = l[i]
            ptb = l[j]
            
            rs = l[j][1]-l[i][1]
            rn = l[j][0]-l[i][0]
            g = math.gcd(rs, rn)
            rs //= g
            rn //= g
            
            x = l[j][0]+rn
            y = l[j][1]+rs
            
            while x <= 100 and y <= 100:
                if (x, y) in s:
                    ap -= 1
                x += rn
                y += rs
                
            ct += ap
#             print(i, j, ap, ct)
            
    print(ct)