$N$ points are placed in the coordinate plane.

Write a program which calculates in how many ways a right triangle can be formed by three of the given points. A right triangle is one in which one of the angles is $90$ degrees.

-----Input-----
The first line of input contains an integer $N$ ($3 \le N \le 1500$), the number of points.

Each of the following $N$ lines contains the coordinates of one point, two integers separated by a space. The coordinates will be between $-10^9$ and $10^9$.

No two points will be located at the same coordinates.

-----Output-----
Output the number of right triangles.

-----Examples-----
Sample Input 1:
3
4 2
2 1
1 3
Sample Output 1:
1

Sample Input 2:
4
5 0
2 6
8 6
5 7
Sample Output 2:
0

Difficulty: competition

Starter code:

Solutions: