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 <= N <= 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
5
-1 1
-1 0
0 0
1 0
1 1
output
7

input
4
5 0
2 6
8 6
5 7

output
0