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)

#[allow(unused_imports)]
use std::cmp::{Ordering};

#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};

#[allow(unused_imports)]
use std::io::{stdin, stdout, BufWriter, Write};

#[allow(unused_imports)]
use std::iter::FromIterator;

#[allow(unused_macros)]
macro_rules! min {
    ($x: expr) => ($x);
    ($x: expr, $($z: expr),+) => {{
        std::cmp::min($x, min!($($z),*))
    }}
}

#[allow(unused_macros)]
macro_rules! max {
    ($x: expr) => ($x);
    ($x: expr, $($z: expr),+) => {{
        std::cmp::max($x, max!($($z),*))
    }}
}

#[allow(unused_macros)]
macro_rules! get { 
    ([$t: ty]) => { 
        { 
            let mut line = String::new(); 
            stdin().read_line(&mut line).unwrap(); 
            line.split_whitespace().map(|t|t.parse::<$t>().unwrap()).collect::<Vec<_>>()
        }
    };
    ([$t: ty];$n: expr) => {
        (0..$n).map(|_|get!([$t])).collect::<Vec<_>>()
    };
    ($t: ty) => {
        {
            let mut line = String::new();
            stdin().read_line(&mut line).unwrap();
            line.trim().parse::<$t>().unwrap()
        }
    };
    ($($t: ty),*) => {
        { 
            let mut line = String::new();
            stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            ($(iter.next().unwrap().parse::<$t>().unwrap(),)*)
        }
    };
    ($t: ty; $n: expr) => {
        (0..$n).map(|_|get!($t)).collect::<Vec<_>>()
    };
    ($($t: ty),*; $n: expr) => {
        (0..$n).map(|_|get!($($t),*)).collect::<Vec<_>>()
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        #[cfg(debug_assertions)]
        writeln!(&mut std::io::stderr(), concat!("[DEBUG] ", $(stringify!($a), "={:?} "),*), $($a),*).unwrap();
    }
}

const BIG_STACK_SIZE: bool = true;

#[allow(dead_code)]
fn main() {
    use std::thread;
    if BIG_STACK_SIZE {
        thread::Builder::new()
            .stack_size(32 * 1024 * 1024)
            .name("solve".into())
            .spawn(solve)
            .unwrap()
            .join()
            .unwrap();
    } else {
        solve();
    }
}

pub struct UnionFindRank {
    parent: Vec<usize>,
    rank: Vec<usize>,
}
impl UnionFindRank {
#[allow(dead_code)]
    pub fn new(n: usize) -> Self {
        let mut parent = vec![0; n];
        for i in 0..n {
            parent[i] = i;
        }
        UnionFindRank {
            parent: parent,
            rank: vec![0; n],
        }
    }
#[allow(dead_code)]
    pub fn root(&mut self, a: usize) -> usize {
        if self.parent[a] == a {
            a
        } else {
            let tmp = self.parent[a];
            self.parent[a] = self.root(tmp);
            self.parent[a]
        }
    }
#[allow(dead_code)]
    pub fn unite(&mut self, a: usize, b: usize) {
        let a = self.root(a);
        let b = self.root(b);
        if a == b {
            return;
        }
        if self.rank[a] > self.rank[b] {
            self.parent[b] = a;
        } else {
            self.parent[a] = b;
            if self.rank[a] == self.rank[b] {
                self.rank[b] += 1;
            }
        }
    }
#[allow(dead_code)]
    pub fn is_same(&mut self, a: usize, b: usize) -> bool {
        self.root(a) == self.root(b)
    }
}

fn solve() {
    let n = get!(usize);
    let xy = get!(usize, usize; n);

    if n < 3 {
        println!("0");
        return;
    }

    let xmax = 100_001;
    let mut tree = UnionFindRank::new(300_000);
    for &(x,y) in &xy {
        tree.unite(x, y+xmax);
    }
    let mut xmap = BTreeMap::new();
    let mut ymap = BTreeMap::new();
    for i in 0..xmax {
        *xmap.entry(tree.root(i)).or_insert(0usize) += 1;
    } 
    for i in xmax..(2*xmax) {
        *ymap.entry(tree.root(i)).or_insert(0usize) += 1;
    }

    let mut sum = 0usize;
    for i in 0..2*xmax {
        sum += xmap.get(&i).unwrap_or(&0) * ymap.get(&i).unwrap_or(&0);
    }
    println!("{}", sum-n);
}