Count Squares

Time limit1sMemory limit128 MB

Summary

Given up to 2000 distinct integer points, count how many squares have all four vertices among them, including tilted squares.

Level: Medium6 of 10
Topics: Geometry, Hash map, Math
Solved: No attempts yet

Problem

You are given a set of points with integer coordinates $(x_i, y_i)$ for $i = 1 \ldots N$ . Count the number of squares whose four vertices are all among these points. A square may be tilted; its sides need not be parallel to the axes.

Input

The input starts with the integer $N$ , followed by $N$ pairs of integers $x_i$ $y_i$ . Values are separated by spaces or newlines.

Output

Output a single integer: the number of squares found.

Constraints

$-10^4 \le x_i, y_i \le 10^4$ , $1 \le N \le 2000$ .
All points in the input are distinct.

Examples2

Example 1
Input
```
4 0 0 4 3 -3 4 1 7
```
Expected output
```
1
```

Example 2

Input

9
1 1  1 2  1 3  
2 1  2 2  2 3  
3 1  3 2  3 3

Expected output