21767_L-Shapes

Let's say that two line segments of non-zero length form an L-shape if they are at a 90^° angle to each other and one endpoint of one segment coincides with one endpoint of the other.

There are N line segments on a plane. The segments are numbered from 1 to N. Count the number of distinct pairs of segments that form L-shapes. Two pairs are considered distinct if they contain segments with different numbers.

The first line of the input line contains the integer N (1 ≤ N ≤ 5000). Each of the following N lines describes one segment and contains four integers x₁, y₁, x₂, y₂ (-10000 ≤ x₁, y₁, x₂, y₂ ≤ 10000), where (x₁, y₁) and (x₂, y₂) are endpoints of the segment. It may be assumed that for each segment x₁ ≠ x₂ or y₁ ≠ y₂.

The output file should contain a single integer, the total number of distinct pairs of line segments forming L-shapes.

7
0 4 0 7
4 4 1 6
1 6 -3 0
4 4 0 4
0 0 0 4
0 0 0 2
0 4 4 4

5

In the example the L-shapes are formed by the following pairs of segments: (1, 4), (1, 7), (2, 3), (4, 5), (5, 7). Note that the segments 4 and 7 coincide, but the pairs (1, 4) and (1, 7), for example, are still considered distinct.