OpenKattis
Kattis Set 11 - Computational Geometry + Misc 2

#### Start

2021-03-29 05:00 AKDT

## Kattis Set 11 - Computational Geometry + Misc 2

#### End

2021-04-05 01:30 AKDT
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# Problem EDejavu

$N$ 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 $N$ ($3 \le N \le 100\, 000$), the number of points.

Each of the following $N$ lines contains two integers $X$ and $Y$ ($1 \le X, Y \le 100\, 000$), the coordinates of one point.

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

## Output

Output the number of triangles.

Sample Input 1 Sample Output 1
3
4 2
2 1
1 3

0

Sample Input 2 Sample Output 2
5
1 2
2 1
2 2
2 3
3 2

4

Sample Input 3 Sample Output 3
6
10 10
20 10
10 20
20 20
30 20
30 30

8