Score : $400$ points

问题描述

我们有 $N$ 个不同的点在二维平面上，编号为 $1,2,\ldots,N$。第 $i$ 个点 $(1 \leq i \leq N)$ 的坐标为 $(x_i,y_i)$。

有多少个矩形的顶点是给定的这些点，并且其边与 $x$-轴或 $y$-轴平行？

以上为通义千问 qwen-max 翻译，仅供参考。

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.

Sample Input 1

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

Sample Output 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 $3$, $4$, $5$, $6$.

Sample Input 2

4
0 1
1 2
2 3
3 4

Sample Output 2

0

Sample Input 3

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

Sample Output 3

1

update @ 2024/3/10 09:38:50