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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;

fn main() {
    input! {
        n: usize,
        mut p: [(i64, i64); n],
    }
    let mut uf = kyopro_lib::unionfind::UnionFind::new(n);
    use std::collections::BTreeMap;
    let mut x = BTreeMap::new();
    let mut y = BTreeMap::new();
    for i in 0..n {
        match (x.get(&p[i].0), y.get(&p[i].1)) {
            (None, None) => {
                x.insert(p[i].0, i);
                y.insert(p[i].1, i);
            }
            (Some(j), None) => {
                uf.unite(i, *j);
                y.insert(p[i].1, *j);
            }
            (None, Some(j)) => {
                uf.unite(i, *j);
                x.insert(p[i].0, *j);
            }
            (Some(j), Some(k)) => {
                uf.unite(i, *j);
                uf.unite(*j, *k);
            }
        }
    }
    use std::collections::BTreeSet;
    let mut g = BTreeMap::new();
    for i in 0..n {
        if uf.size(i) > 2 {
            let r = g
                .entry(uf.root(i))
                .or_insert((BTreeSet::new(), BTreeSet::new(), 0));
            (r.0).insert(p[i].0);
            (r.1).insert(p[i].1);
            r.2 += 1;
        }
    }

    let mut res = 0;
    for (_, (x, y, c)) in g {
        res += x.len() * y.len() - c;
    }
    println!("{}", res);
}
*/

fn main() {
    let exe = "/tmp/binA9EFDA85";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";