Problem E. Empty rectangles

Author:A. Baranov   Time limit:1 sec
Input file:Standard input   Memory limit:512 Mb
Output file:Standard output  

Statement

Consider a set of N two-dimensional points represented by their coordinates (Xi, Yi).

It is required to determine the number of all possible rectangles that satisfy the following conditions:

Input format

Input starts with integer N,
followed by 2 × N integers, representing point coordinates: Xi, Yi.

Output format

The output should contain
the number of detected rectangles.

Constraints

All input points are different.

 − 106 ≤ (Xi, Yi) ≤ 106,

4 ≤ N ≤ 105

Sample tests

No. Standard input Standard output
1
12
-35 -17
 43  10
 24 -17
-16 -29
 43  54
-35  40
 43 -29
 24  10
-16  54
-35  10
 43 -17
 24  40
3
2
12
-20 -34
 17  34
-20  40
-10 -20
-43 -17
 19  15
-15  16
  0 -34
-32  19
  0 -12
-13   0
  0  40
0

0.110s 0.022s 13