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 proconio::input;
use std::collections::HashSet;

pub struct UnionFind {
    n: usize,
    par: Vec<usize>,
    rank: Vec<usize>
}

impl UnionFind {

    pub fn new(n:usize) -> UnionFind {
        UnionFind{
            n:n,
            par:(0..n).map(|i|i).collect(),
            rank:vec![0;n],
        }
    }

    pub fn size(&self) -> usize {self.n}

    pub fn find(&mut self,v:usize) -> usize {
        if self.par[v] == v {
            v
        }
        else {
            let p = self.find(self.par[v]);
            self.par[v] = p;
            p
        }
    }

    pub fn unite(&mut self,a:usize,b:usize){
        let a = self.find(a);
        let b = self.find(b);
        if a==b {
            return
        }
        else {
            if self.rank[a]<self.rank[b] {
                self.par[a] = b;
            }
            else {
                if self.rank[a]==self.rank[b] {
                    self.rank[a] += 1;
                }
                self.par[b] = a;
            }
        }
    }

    pub fn is_same(&mut self,a:usize,b:usize) -> bool {
        self.find(a)==self.find(b)
    }

}

const SZ:usize = 100001;
fn main() {
    input! {
        n:usize,
        xy:[(usize,usize);n]
    };

    let mut xid = vec![Vec::new();SZ];
    let mut yid = vec![Vec::new();SZ];
    for (i,&(x,y)) in xy.iter().enumerate() {
        xid[x].push(i);
        yid[y].push(i);
    }

    let mut uf = UnionFind::new(n);

    for i in 0..SZ {
        if xid[i].len()>0 {
            let p = xid[i][0];
            for &e in &xid[i] {
                uf.unite(p,e);
            }
        }
        if yid[i].len()>0 {
            let p = yid[i][0];
            for &e in &yid[i] {
                uf.unite(p,e);
            }
        }
    }

    let mut ids = vec![Vec::new();n];
    for i in 0..n {
        ids[uf.find(i)].push(i);
    }

    let mut ans = 0;
    for i in 0..n {
        let mut xs = HashSet::new();
        let mut ys = HashSet::new();
        for &id in &ids[i] {
            xs.insert(xy[id].0);
            ys.insert(xy[id].1);
        }
        ans+=(xs.len() as i64)*(ys.len() as i64);
    }

    println!("{}",ans-(n as i64));

}