D - Rectangles

Score : $400$ points

Problem Statement

We have $N$ distinct points on a two-dimensional plane, numbered $1,2,\ldots,N$. Point $i$ $(1 \leq i \leq N)$ has the coordinates $(x_i,y_i)$.

How many rectangles are there whose vertices are among the given points and whose edges are parallel to the $x$- or $y$-axis?

Constraints

• $4 \leq N \leq 2000$
• $0 \leq x_i, y_i \leq 10^9$
• $(x_i,y_i) \neq (x_j,y_j)$ $(i \neq j)$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$x_1$ $y_1$

$x_2$ $y_2$

$\vdots$

$x_N$ $y_N$

Output

Print the answer.

6
0 0
0 1
1 0
1 1
2 0
2 1

3

There are three such rectangles:

the rectangle whose vertices are Points $1$, $2$, $3$, $4$,

the rectangle whose vertices are Points $1$, $2$, $5$, $6$,

and the rectangle whose vertices are Points $3$, $4$, $5$, $6$.

4
0 1
1 2
2 3
3 4

0

7
0 1
1 0
2 0
2 1
2 2
3 0
3 2

1