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 (1.15.1) (judge verdict: Accepted)

use std::collections::HashMap;
use std::collections::HashSet;

use std::io::*;
use std::str::FromStr;
#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn main() {
    let n = read::<usize>();
    let mut ps = vec![vec![0, 0]; n];
    let mut sort_ps: Vec<HashMap<i64, Vec<usize>>> = vec![HashMap::new(); 2];
    for i in 0..n {
        let x = read::<i64>();
        let y = read::<i64>();
        ps[i] = vec![x, y];
        sort_ps[0].entry(x).or_insert(vec![]).push(i);
        sort_ps[1].entry(y).or_insert(vec![]).push(i);
    }
    let mut used = vec![false; n];
    let mut ans = 0;
    for i in 0..n {
        if used[i] {
            continue;
        }
        used[i] = true;
        let mut que = vec![(0, ps[i][0]), (1, ps[i][1])];
        let mut visit: HashSet<(usize, i64)> = HashSet::new();
        visit.insert((0, ps[i][0]));
        visit.insert((1, ps[i][1]));
        let mut cnts = vec![1, 1];
        while let Some((dir, pos)) = que.pop() {
            for &index in sort_ps[dir][&pos].iter() {
                used[index] = true;
                let ndir = dir ^ 1;
                let npos = ps[index][ndir];
                if visit.contains(&(ndir, npos)) {
                    continue;
                }
                // println!("{} {}", ndir, npos);
                visit.insert((ndir, npos));
                cnts[ndir] += 1;
                que.push((ndir, npos));
            }
        }
        // println!("{:?}", cnts);
        ans += cnts[0] * cnts[1];
    }
    ans -= n;
    println!("{}", ans);
}