A12681 | Count The Rectangles

There are $n$ segments drawn on a plane; the $i$ -th segment connects two points ( $x_{i, 1}$ , $y_{i, 1}$ ) and ( $x_{i, 2}$ , $y_{i, 2}$ ). Each segment is non-degenerate, and is either horizontal or vertical — formally, for every $i \in [1, n]$ either $x_{i, 1} = x_{i, 2}$ or $y_{i, 1} = y_{i, 2}$ (but only one of these conditions holds). Only segments of different types may intersect: no pair of horizontal segments shares any common points, and no pair of vertical segments shares any common points.

We say that four segments having indices $h_1$ , $h_2$ , $v_1$ and $v_2$ such that $h_1 < h_2$ and $v_1 < v_2$ form a rectangle if the following conditions hold:

- segments $h_1$ and $h_2$ are horizontal;
- segments $v_1$ and $v_2$ are vertical;
- segment $h_1$ intersects with segment $v_1$ ;
- segment $h_2$ intersects with segment $v_1$ ;
- segment $h_1$ intersects with segment $v_2$ ;
- segment $h_2$ intersects with segment $v_2$ .

Please calculate the number of ways to choose four segments so they form a rectangle. Note that the conditions $h_1 < h_2$ and $v_1 < v_2$ should hold.

The first line contains one integer $n$ ( $1 \le n \le 5000$ ) — the number of segments.

Then $n$ lines follow. The $i$ -th line contains four integers $x_{i, 1}$ , $y_{i, 1}$ , $x_{i, 2}$ and $y_{i, 2}$ denoting the endpoints of the $i$ -th segment. All coordinates of the endpoints are in the range $[-5000, 5000]$ .

It is guaranteed that each segment is non-degenerate and is either horizontal or vertical. Furthermore, if two segments share a common point, one of these segments is horizontal, and another one is vertical.

Print one integer — the number of ways to choose four segments so they form a rectangle.