Watchmen

题意翻译

给出 $n$ 对坐标 $(x_i,y_i)$。求问曼哈顿距离和欧氏距离相等的坐标组 $(i,j)$（$1\leq i<j\leq n$）有多少对？ $1\leq n\leq 2\times 10^5,|x_i|,|y_i|\leq 10^9$。

题目描述

Watchmen are in a danger and Doctor Manhattan together with his friend Daniel Dreiberg should warn them as soon as possible. There are $ n $ watchmen on a plane, the $ i $ -th watchman is located at point $ (x_{i},y_{i}) $ . They need to arrange a plan, but there are some difficulties on their way. As you know, Doctor Manhattan considers the distance between watchmen $ i $ and $ j $ to be $ |x_{i}-x_{j}|+|y_{i}-y_{j}| $ . Daniel, as an ordinary person, calculates the distance using the formula . The success of the operation relies on the number of pairs $ (i,j) $ ( $ 1<=i&lt;j<=n $ ), such that the distance between watchman $ i $ and watchmen $ j $ calculated by Doctor Manhattan is equal to the distance between them calculated by Daniel. You were asked to compute the number of such pairs.

输入输出格式

输入格式

The first line of the input contains the single integer $ n $ ( $ 1<=n<=200000 $ ) — the number of watchmen. Each of the following $ n $ lines contains two integers $ x_{i} $ and $ y_{i} $ ( $ |x_{i}|,|y_{i}|<=10^{9} $ ). Some positions may coincide.

输出格式

Print the number of pairs of watchmen such that the distance between them calculated by Doctor Manhattan is equal to the distance calculated by Daniel.

输入输出样例

输入样例 #1

3
1 1
7 5
1 5

输出样例 #1

2

输入样例 #2

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

输出样例 #2

11

说明

In the first sample, the distance between watchman $ 1 $ and watchman $ 2 $ is equal to $ |1-7|+|1-5|=10 $ for Doctor Manhattan and  for Daniel. For pairs $ (1,1) $ , $ (1,5) $ and $ (7,5) $ , $ (1,5) $ Doctor Manhattan and Daniel will calculate the same distances.

题意翻译

给出 $n$ 对坐标 $(x_i,y_i)$。求问曼哈顿距离和欧氏距离相等的坐标组 $(i,j)$（$1\leq i<j\leq n$）有多少对？ $1\leq n\leq 2\times 10^5,|x_i|,|y_i|\leq 10^9$。