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)

use petgraph::unionfind::*;
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;
#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
#[allow(unused_imports)]
use std::f64::consts::*;

#[allow(unused)]
const INF: usize = std::usize::MAX / 4;
#[allow(unused)]
const M: usize = 1000000007;

fn main() {
    input! {
        n: usize,
        xy: [(usize, usize); n],
    }

    let mut x_points = HashMap::new();
    let mut y_points = HashMap::new();
    for i in 0..n {
        let (xi, yi) = xy[i];
        x_points.entry(xi).or_insert(vec![]).push(i);
        y_points.entry(yi).or_insert(vec![]).push(i);
    }
    // eprintln!("{:?}", x_points);
    // eprintln!("{:?}", y_points);

    let mut components = UnionFind::new(n);
    for i in 0..n {
        let (xi, yi) = xy[i];
        if x_points[&xi].len() > 1 && y_points[&yi].len() > 1 {
            // eprintln!("{} {}", xi, yi);
            for &j in &x_points[&xi] {
                components.union(i, j);
            }
            for &j in &y_points[&yi] {
                components.union(i, j);
            }
        }
    }

    let mut points = vec![vec![]; n];
    for i in 0..n {
        points[components.find(i)].push(i);
    }
    let mut result = 0usize;
    for i in 0..n {
        if points[i].len() > 2 {
            let mut xs = HashSet::new();
            let mut ys = HashSet::new();
            for &i in &points[i] {
                let (xi, yi) = xy[i];
                xs.insert(xi);
                ys.insert(yi);
            }
            result += xs.len() * ys.len() - points[i].len();
        }
    }
    println!("{}", result);
}