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Problem J
Pravokutni
$N$ 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.
| Sample Input 1 | Sample Output 1 |
|---|---|
3 4 2 2 1 1 3 |
1 |
| Sample Input 2 | Sample Output 2 |
|---|---|
4 5 0 2 6 8 6 5 7 |
0 |
| Sample Input 3 | Sample Output 3 |
|---|---|
5 -1 1 -1 0 0 0 1 0 1 1 |
7 |