How many squares?

Time limit1sMemory limit256 MB

Summary

Count quadruples of the given infinite lines that form the four sides of a square.

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

Problem

A quiz in a web advertisement asks how many squares a picture holds. To improve your odds of winning, you decide to write a program that counts the answer. To keep the task simple, assume the picture holds only infinite lines, not segments.

Count how many squares the lines in the picture form.

Four lines $\ell_1$ , $\ell_2$ , $\ell_3$ , $\ell_4$ form a square when all three conditions below hold.

$\ell_1$ and $\ell_3$ are parallel.
$\ell_2$ and $\ell_4$ are perpendicular to $\ell_1$ and $\ell_3$ , so $\ell_2$ and $\ell_4$ are parallel to each other.
The distance between $\ell_1$ and $\ell_3$ equals the distance between $\ell_2$ and $\ell_4$ .

The order in which you pick the four lines does not matter, so a square made of the same four lines counts once.

Input

The first line contains the number of lines $n$ . ( $1 \le n \le 2000$ )

Each of the next $n$ lines describes one line with four integers $x_1$ , $y_1$ , $x_2$ , $y_2$ . That line passes through the points $(x_1, y_1)$ and $(x_2, y_2)$ . All four integers have absolute value at most $10000$ .

The two points describing a line are different, and the $n$ lines are all different from each other.

Output

Print the number of squares formed by the given lines as a single integer on one line.

Examples2

Example 1

Input

Expected output

Example 2
Input
```
4
0 0 0 1
1 0 1 5
0 0 1 0
0 1 5 1
```
Expected output
```
1
```