Problem:
Score : 300 points

Problem Statement

There are N cities on a 2D plane. The coordinate of the i-th city is (x_i, y_i). Here (x_1, x_2, \dots, x_N) and (y_1, y_2, \dots, y_N) are both permuations of (1, 2, \dots, N).

For each k = 1,2,\dots,N, find the answer to the following question:

Rng is in City k.
Rng can perform the following move arbitrarily many times:

move to another city that has a smaller x-coordinate and a smaller y-coordinate, or a larger x-coordinate and a larger y-coordinate, than the city he is currently in.

How many cities (including City k) are reachable from City k?

Constraints

1 \leq N \leq 200,000

(x_1, x_2, \dots, x_N) is a permutation of (1, 2, \dots, N).

(y_1, y_2, \dots, y_N) is a permutation of (1, 2, \dots, N).

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
x_2 y_2
:
x_N y_N

Output

Print N lines. In i-th line print the answer to the question when k = i.

Sample Input 1

4
1 4
2 3
3 1
4 2

Sample Output 1

1
1
2
2

Rng can reach City 4 from City 3, or conversely City 3 from City 4.

Sample Input 2

7
6 4
4 3
3 5
7 1
2 7
5 2
1 6

Sample Output 2

3
3
1
1
2
3
2

Solution in Rust (1.42.0) (judge verdict: Accepted)

macro_rules! read_line_to_tuple {
    ( $( $t:ty ),* ) => {{
        let mut input = String::new();
        std::io::stdin().read_line(&mut input).unwrap();
        let mut iter = input.split_whitespace();
        ( $( iter.next().unwrap().parse::<$t>().unwrap() ),* )
    }};
}

struct Dsu {
    n: usize,
    parent_or_size: Vec<usize>,
}

impl Dsu {
    fn new(n: usize) -> Dsu {
        Dsu { n, parent_or_size: vec![!1; n] }
    }

    fn merge(&mut self, a: usize, b: usize) -> usize {
        let (mut x, mut y) = (self.leader(a), self.leader(b));
        if x == y { return x; }
        if !self.parent_or_size[x] < !self.parent_or_size[y] {
            std::mem::swap(&mut x, &mut y);
        }
        self.parent_or_size[x] -= !self.parent_or_size[y];
        self.parent_or_size[y] = x;
        x
    }

    fn leader(&mut self, a: usize) -> usize {
        if self.parent_or_size[a] >= self.n { return a; }
        self.parent_or_size[a] = self.leader(self.parent_or_size[a]);
        self.parent_or_size[a]
    }

    fn size(&mut self, a: usize) -> usize {
        let x = self.leader(a);
        !self.parent_or_size[x]
    }
}

use std::collections::BTreeSet;

fn main() {
    let n = read_line_to_tuple!(usize);

    let mut v = Vec::with_capacity(n);
    for i in 0..n {
        let (x, y) = read_line_to_tuple!(usize, usize);
        v.push((x, y, i));
    }

    let mut dsu = Dsu::new(n);

    v.sort();
    let mut set = BTreeSet::new();
    for i in 0..n {
        if let Some(&(_, j)) = set.range(..(v[i].1, n)).next() {
            dsu.merge(i, j);
        }
        set.insert((v[i].1, i));
    }
    
    let mut set = BTreeSet::new();
    for i in (0..n).rev() {
        if let Some(&(_, j)) = set.range((v[i].1, 0)..).next() {
            dsu.merge(i, j);
        }
        set.insert((v[i].1, i));
    }

    let mut ans = vec![0; n];
    for i in 0..n {
        ans[v[i].2] = i;
    }

    println!(
        "{}",
        ans.iter()
            .map(|&i| dsu.size(i).to_string())
            .collect::<Vec<_>>()
            .join("\n")
    );
}