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)

#![allow(unused_imports, non_snake_case)]
use proconio::{
    input, fastout,
    marker::{Chars, Bytes, Usize1}
};

struct UnionFind {
    size: usize,
    pos: Vec<isize>,
}
impl UnionFind {
    fn new(n: usize) -> Self {
        let size = n;
        let pos = vec![-1; n + 1];
        UnionFind { size, pos }
    }
    fn find(&mut self, x: usize) -> usize {
        if self.pos[x] < 0 {
            x
        } else {
            let v = self.pos[x] as usize;
            self.pos[x] = self.find(v) as isize;
            self.pos[x] as usize
        }
    }
    fn unite(&mut self, x: usize, y: usize) -> Result<(), ()> {
        let mut x = self.find(x);
        let mut y = self.find(y);
        if x == y {
            return Err(());
        };
        if self.pos[x] > self.pos[y] {
            std::mem::swap(&mut x, &mut y);
        }
        self.pos[x] += self.pos[y];
        self.pos[y] = x as isize;
        Ok(())
    }
    fn same(&mut self, x: usize, y: usize) -> bool {
        self.find(x) == self.find(y)
    }
    fn size(&mut self, x: usize) -> usize {
        let x = self.find(x);
        -self.pos[x] as usize
    }
}


#[fastout]
fn main() {
    input!{
        N: usize,
        l:[(Usize1, Usize1); N]
    }
    let mut g = vec![0; N];
    for &(x, y) in &l {
        g[x] = y;
    }
    let mut stack = vec![];
    let mut uf = UnionFind::new(N);
    for x in 0..N {
        let y = g[x];
        if stack.is_empty() {
            stack.push(x);
            continue;
        } else {
            let m = stack.len();
            if g[stack[m-1]] > y {
                stack.push(x);
                continue;
            }
            for idx in (0..m).rev() {
                if g[stack[idx]] < y {
                    uf.unite(stack[idx], x).ok();
                    if idx < m - 1 {
                        stack[idx] = stack[idx+1];
                        stack.pop();
                    }
                } else {
                    break;
                }
            }
        }
    }
    for &(x, _) in &l {
        println!("{}", uf.size(x));
    }
}