You are given a 2D plane containing \(N\) distinct integral points in the form of \((X,Y)\). Now a line segment is drawn between each pair of points. Your task is to determine the number of unordered pairs of these line segments that are orthogonal to each other. 

Input format

• First line: \(N\)
• Next \(N\) lines: Two space-separated integers \(X\) and \(Y\) denoting a point on the plane

Output format

Print a single integer that represents the number of quadruples as described in the problem statement

Constraints

\(1 \le N \le 2*10^3\)

\(-2*10^3 \le X,Y \le 2*10^3\)

Subtasks

• For 20 points: \(1 \le N \le 100\)
• For 80 points: Implement the original constraints