$N$ points are placed in the coordinate plane.

Write a program that calculates how many ways we can choose three points so that they form a right triangle with legs parallel to the coordinate axes.

A right triangle has one 90-degree internal angle. The legs of a right triangle are its two shorter sides.

-----Input-----
The first line of input contains the integer $N$ ($3 \le N \le 100000$), the number of points.

Each of the following $N$ lines contains two integers $X$ and $Y$ ($1 \le X, Y \le 100000$), the coordinates of one point.

No pair of points will share the same pair of coordinates.

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

-----Examples-----
Sample Input 1:
3
4 2
2 1
1 3
Sample Output 1:
0

Sample Input 2:
5
1 2
2 1
2 2
2 3
3 2
Sample Output 2:
4

Difficulty: interview

Starter code:

Solutions: