Garden

Time limit3sMemory limit128 MB

Summary

Count the number of axis-aligned squares whose four corners are all points from a given set.

Level: Medium4 of 10
Topics: Hash map, Geometry, Brute force
Solved: No attempts yet

Problem

Byteen wants to plant a garden next to her house. The garden must be an axis-aligned square, that is, a square whose sides are parallel to the North-South and East-West directions. Each of the square's four corners must coincide with one of the $n$ apple-trees growing nearby.

Byteen inspects every possible location before choosing, and checking one location takes exactly one second. Determine how many valid garden locations there are: the number of axis-aligned squares whose four corners are all apple-trees.

Input

The first line contains the number of apple-trees $n$ ( $1 \le n \le 100\,000$ ). Each of the next $n$ lines contains two space-separated integers $x_i$ and $y_i$ ( $-10^6 \le x_i, y_i \le 10^6$ ), the coordinates of the $i$ -th apple-tree. No two trees share the same coordinates.

Output

Print a single integer: the number of axis-aligned squares (sides parallel to the coordinate axes) whose four corners are all apple-trees.

Examples4

Example 1
Input
```
6
0 0
0 1
1 0
1 1
3 0
3 1
```
Expected output
```
1
```
Example 2
Input
```
4
0 0
0 1
1 0
1 1
```
Expected output
```
1
```
Example 3
Input
```
4
0 0
0 1
2 0
2 1
```
Expected output
```
0
```

Example 4

Input

Expected output