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.
inp = input();
data = inp.split()
n = int(data[0]);
m = int(data[1]);
start = 1
end = n
ans = n
while(start <= end):
    mid = int((start + end) / 2);
    ds = n;
    print(mid, ds)
    if(mid > m):
        ds = ds - ((((mid - m) * (mid - m + 1))/2)) + mid - m
    if(ds - mid <= 0):
        end = mid - 1;
        ans = mid;
    else:
        start = mid + 1
print(ans)
