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)

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String {
            bytes
                .by_ref()
                .map(|r| r.unwrap() as char)
                .skip_while(|c| c.is_whitespace())
                .take_while(|c| !c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, [ $t:tt ]) => {
        {
            let len = read_value!($next, usize);
            (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        }
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

fn main() {
    input!{
        n: usize,
        mut v: [(usize, usize); n]
    }
    let mut uf: UnionFind<(usize, usize)> = UnionFind::new_points(v.clone());
    v.sort_by_key(|x| x.0);
    for i in 0..n - 1 {
        if v[i].0 == v[i + 1].0 {
            uf.union(v[i].clone(), v[i + 1].clone());
        }
    }
    v.sort_by_key(|x| x.1);
    for i in 0..n - 1 {
        if v[i].1 == v[i + 1].1 {
            uf.union(v[i].clone(), v[i + 1].clone());
        }
    }
    let sets = uf.to_sets();
    let mut ans: usize = 0;
    for (_, s) in sets.iter() {
        let mut xs = HashSet::new();
        let mut ys = HashSet::new();
        for &(x, y) in s {
            xs.insert(x);
            ys.insert(y);
        }
        ans += xs.len() * ys.len();
    }
    println!("{}", ans - n);
}

use std::cmp;
use std::collections::{HashSet, HashMap};

struct UFNode {
    parent: usize,
    rank: usize,
    size: usize
}

struct UnionFind<T> where T: cmp::Eq + std::hash::Hash {
    map: HashMap<T,usize>,
    nodes: Vec<UFNode>,
    next: usize,
    n_unions: usize
}

impl<T: cmp::Eq + std::hash::Hash> UnionFind<T> {
    fn new() -> UnionFind<T> {
        UnionFind{map: HashMap::new(), nodes: Vec::new(), next: 0, n_unions: 0}
    }

    fn new_points(v: Vec<T>) -> UnionFind<T> {
        let mut uf = UnionFind::new();
        for x in v {
            if uf.map.contains_key(&x) {
                continue;
            }
            uf.add_point(x);
        }
        uf
    }

    fn add_point(&mut self, x: T) -> usize {
        let id = self.next;
        self.map.insert(x,id);
        self.nodes.push(UFNode{parent: id, rank: 0, size: 1});
        self.next += 1;
        self.n_unions += 1;
        id
    }

    fn get_id(&self, x: &T) -> Option<usize> {
        self.map.get(x).map(|x| *x)
    }

    fn find(&mut self, id: usize) -> usize {
        let p = self.nodes[id].parent;
        if p == id {
            return id;
        }
        let pr = self.find(p);
        self.nodes[id].parent = pr;
        pr
    }

    fn union(&mut self, x: T, y: T) {
        let idx = self.get_id(&x).unwrap_or_else(|| self.add_point(x));
        let idy = self.get_id(&y).unwrap_or_else(|| self.add_point(y));
        let xp = self.find(idx);
        let yp = self.find(idy);
        if xp == yp {
            return;
        }
        let rx = self.nodes[xp].rank;
        let ry = self.nodes[yp].rank;
        if rx < ry {
            self.nodes[xp].parent = yp;
        } else if rx > ry {
            self.nodes[yp].parent = xp;
        } else {
            self.nodes[yp].parent = xp;
            self.nodes[xp].rank += 1;
        }
        let size = self.nodes[xp].size + self.nodes[yp].size;
        self.nodes[xp].size = size;
        self.nodes[yp].size = size;
        self.n_unions -= 1;
    }

    fn is_same(&mut self, x: &T, y: &T) -> bool {
        let idx = self.get_id(x);
        let idy = self.get_id(y);
        if idx == None || idy == None {
            false
        } else {
            self.find(idx.unwrap()) == self.find(idy.unwrap())
        }
    }

    fn n_points(&self) -> usize {
        self.next
    }

    fn n_unions(&self) -> usize {
        self.n_unions
    }

    fn size(&mut self, x: &T) -> usize {
        let id = self.get_id(x).unwrap();
        let idp = self.find(id);
        self.nodes[idp].size
    }
    fn to_sets(&mut self) -> HashMap<usize,HashSet<T>> where T: Clone {
        let mut map: HashMap<usize, HashSet<T>> = HashMap::new();
        for (k, v) in self.map.clone() {
            let mut s = map.entry(self.find(v)).or_insert_with(HashSet::new);
            s.insert(k);
        }
        map
    }
}