Problem E. Empty rectangles ≡

Statement

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

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

• the vertices of the rectangle must belong to the original set of points,
  and its sides must be parallel to the coordinate axes;
• among the remaining points, none should lie on the border or inside such a rectangle;
• the rectangle must be non-degenerate (have a non-zero area).

Input format

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

Output format

The output should contain
the number of detected rectangles.

Constraints

All input points are different.

 − 10⁶ ≤ (X_i, Y_i) ≤ 10⁶,

4 ≤ N ≤ 10⁵

Sample tests

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

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