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: Wrong Answer)

use std::collections::{BTreeMap, BTreeSet, VecDeque};

fn main() {
    let s = std::io::stdin();
    let mut sc = Scanner { stdin: s.lock() };
    let n: usize = sc.read();
    let mut x: Vec<u64> = vec![];
    let mut y: Vec<u64> = vec![];
    for _ in 0..n {
        x.push(sc.read());
        y.push(sc.read());
    }

    let x_map = x
        .iter()
        .cloned()
        .collect::<BTreeSet<_>>()
        .into_iter()
        .enumerate()
        .map(|(i, x)| (x, i as i64))
        .collect::<BTreeMap<_, _>>();
    let y_map = y
        .iter()
        .cloned()
        .collect::<BTreeSet<_>>()
        .into_iter()
        .enumerate()
        .map(|(i, y)| (y, i as i64))
        .collect::<BTreeMap<_, _>>();

    let x = x
        .into_iter()
        .map(|x| *x_map.get(&x).unwrap())
        .collect::<Vec<_>>();
    let y = y
        .into_iter()
        .map(|y| *y_map.get(&y).unwrap())
        .collect::<Vec<_>>();
    let mut set = (0..n).map(|i| (x[i], y[i])).collect::<BTreeSet<_>>();
    let mut q = VecDeque::new();
    for i in 0..n {
        let x = x[i];
        let y = y[i];
        for dx in (-1)..2 {
            for dy in (-1)..2 {
                let x2 = x + dx;
                let y2 = y + dy;
                if is3(x2, y2, &set) {
                    q.push_back((x2, y2));
                }
            }
        }
    }

    while let Some((x, y)) = q.pop_front() {
        if set.contains(&(x, y)) {
            continue;
        }
        set.insert((x, y));
        for dx in (-1)..2 {
            for dy in (-1)..2 {
                let x2 = x + dx;
                let y2 = y + dy;
                if is3(x2, y2, &set) {
                    q.push_back((x2, y2));
                }
            }
        }
    }
    println!("{}", set.len() - n);
}

fn is3(x: i64, y: i64, set: &BTreeSet<(i64, i64)>) -> bool {
    if set.contains(&(x, y)) {
        return false;
    }
    for (px, py) in vec![(1, -1), (1, 1), (-1, 1), (-1, -1)].into_iter() {
        let mut count = 0;
        for dx in 0..2 {
            for dy in 0..2 {
                let x = x + px * dx;
                let y = y + py * dy;
                if set.contains(&(x, y)) {
                    count += 1;
                }
            }
        }
        if count == 3 {
            return true;
        }
    }
    false
}

pub struct Scanner<R> {
    stdin: R,
}

impl<R: std::io::Read> Scanner<R> {
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .stdin
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}