Overlapping Line Segments

You are given N line segments. Two segments are considered overlapping if they share a portion with positive length, not just one point. Equivalently, the set of points contained in both segments must be infinite. If only their endpoints touch, they are not overlapping.

Count the number of unordered pairs of distinct segments that overlap.

N is between 1 and 100,000 inclusive.

The first line contains the integer N. Each of the next N lines contains four integers x1 y1 x2 y2, the coordinates of the two endpoints of one segment.

Every coordinate is an integer between 0 and 1,000,000 inclusive. The two endpoints of a segment are never the same point.

Print the number of unordered pairs of distinct segments that overlap.