Problem Description

Given $n$ points on a plane, calculate how many distinct right-angled triangles can be formed such that their vertices are among the given points and the legs of the right angle are parallel to the coordinate axes.

Two right-angled triangles are considered different if and only if they have at least one different vertex.

Input Format

The first line of input contains an integer $n$, representing the number of points.

The next $n$ lines each contain two integers, representing the coordinates of a point.

Output Format

Output the number of right-angled triangles.

Sample Input and Output

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

Sample Input #3

6
10 10
20 10
10 20
20 20
30 20
30 30

Sample Output #3

8

Notes

Data Size and Constraints

• For $40\%$ of the data, $n < 100$;
• For $70\%$ of the data, $n < 10^4$;
• For $100\%$ of the data, $3 \le n \le 10^5$, and the coordinates are between $1$ and $10^5$, with no two points having the same coordinates.

Notes

This problem is translated from COCI2007-2008 CONTEST #3 T4 DEJAVU.

见题面 Input 部分

见题面 Output 部分