Problem:
Score : 600 points

Problem Statement

There are N dots in a two-dimensional plane. The coordinates of the i-th dot are (x_i, y_i).

We will repeat the following operation as long as possible:

Choose four integers a, b, c, d (a \neq c, b \neq d) such that there are dots at exactly three of the positions (a, b), (a, d), (c, b) and (c, d), and add a dot at the remaining position.

We can prove that we can only do this operation a finite number of times. Find the maximum number of times we can do the operation.

Constraints

1 \leq N \leq 10^5

1 \leq x_i, y_i \leq 10^5

If i \neq j, x_i \neq x_j or y_i \neq y_j.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
:
x_N y_N

Output

Print the maximum number of times we can do the operation.

Sample Input 1

3
1 1
5 1
5 5

Sample Output 1

1

By choosing a = 1, b = 1, c = 5, d = 5, we can add a dot at (1, 5). We cannot do the operation any more, so the maximum number of operations is 1.

Sample Input 2

2
10 10
20 20

Sample Output 2

0

There are only two dots, so we cannot do the operation at all.

Sample Input 3

9
1 1
2 1
3 1
4 1
5 1
1 2
1 3
1 4
1 5

Sample Output 3

16

We can do the operation for all choices of the form a = 1, b = 1, c = i, d = j (2 \leq i,j \leq 5), and no more. Thus, the maximum number of operations is 16.

Solution in Rust (1.42.0) (judge verdict: Accepted)

#![allow(unused_imports)]
#![allow(dead_code)]

use proconio::input;
use proconio::marker::{Bytes, Chars};
use std::collections::*;

fn main() {
    input! {
        n:usize,
        xy:[(usize,usize);n]
    }
    let m = 1e5 as usize;
    //0~1e5:x,1e5~2e5:y
    let mut g = Graph::new(2 * m);
    for (x, y) in xy.iter() {
        let (x, y) = (x - 1, y - 1);
        g.add_undirectional_edge(x, y + m, 1);
    }
    let mut visited = vec![false; 2 * m];
    let mut ans: i64 = 0;
    for i in 0..2 * m {
        if visited[i] {
            continue;
        }
        let mut x_count = 0;
        let mut y_count = 0;
        let mut bfs = VecDeque::new();
        bfs.push_back(i);
        visited[i] = true;
        while let Some(now) = bfs.pop_front() {
            if now < m {
                x_count += 1;
            } else {
                y_count += 1;
            }
            for next in g[now].iter() {
                if visited[next.to] {
                    continue;
                }
                visited[next.to] = true;
                bfs.push_back(next.to);
            }
        }
        ans += x_count * y_count;
    }
    println!("{}", ans - n as i64);
}

#[derive(Debug, Copy, Clone)]
pub struct Edge {
    pub to: usize,
    pub cost: i64,
}
impl Edge {
    pub fn new(to: usize, cost: i64) -> Edge {
        Edge { to: to, cost: cost }
    }
}
pub struct Graph {
    adjacency: Vec<Vec<Edge>>,
}
impl Graph {
    pub fn new(size: usize) -> Self {
        Graph {
            adjacency: vec![vec![]; size],
        }
    }
    pub fn len(&self) -> usize {
        self.adjacency.len()
    }
    pub fn add_directional_edge(&mut self, from: usize, to: usize, cost: i64) {
        self.adjacency[from].push(Edge::new(to, cost));
    }
    pub fn add_undirectional_edge(&mut self, from: usize, to: usize, cost: i64) {
        self.add_directional_edge(from, to, cost);
        self.add_directional_edge(to, from, cost);
    }
}
impl std::ops::Index<usize> for Graph {
    type Output = Vec<Edge>;
    fn index(&self, vertex: usize) -> &Self::Output {
        &self.adjacency[vertex]
    }
}