Geometrija

문제

You are given n points on the plane, such that no three points lie on the same line.

We say that line segments AB and CD cross if they share a point X different from the points A, B, C and D.

Let S be the set of all line segments between pairs of the given points. Find the number of segments in S that don’t cross with any other segment in S.

입력

The first line contains an integer n (3 ≤ n ≤ 1000), the number of points.

The following n lines contain integers x_i and y_i (−10⁹ ≤ x_i, y_i ≤ 10⁹), the coordinates of the points.

출력

Output the requested number of segments.