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)

use proconio::fastout;
use proconio::input;
use proconio::marker::Usize1;

#[fastout]
fn main() {
    input!(n: usize, town: [(Usize1, Usize1); n]);

    let mut idx = vec![0; n];
    for i in 0..n {
        idx[town[i].0] = i
    }

    let mut col = vec![0; n];
    let mut siz = vec![0; n];
    let mut cnt = 0;
    let mut min = n + 1;
    for i in 0..n {
        let (_, y) = town[idx[i]];
        if min == n - i {
            cnt += 1;
        }
        min = min.min(y);
        col[idx[i]] = cnt;
        siz[cnt] += 1;
    }

    for i in 0..n {
        println!("{}", siz[col[i]])
    }
}