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)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;
use std::ops::Bound::*;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn main() {
    let n = read::<usize>();
    let mut points = vec![0; n];
    let mut points_indexed = vec![];
    for i in 0..n {
        let v = read_vec::<usize>();
        let (x, y) = (v[0] - 1, v[1] - 1);
        points[x] = y;
        points_indexed.push((x, y));
    }

    let mut found = BTreeSet::new();
    for x in 0..n {
        found.insert((points[x], x));
    }
    let mut used = vec![false; n];
    let mut uft = UnionFindTree::new(n);
    for x in 0..n {
        found.remove(&(points[x], x));
        if used[x] {
            continue;
        }
        let iter = found.range((Excluded((points[x], n)), Unbounded));

        let mut count = 0;
        for num in iter {
            uft.unite(x, num.1);

            if used[num.1] {
                count += 1;
            }
            used[num.1] = true;
            if count > 100 {
                break;
            }
        }
        let iter = found.range((Excluded((points[x], n)), Unbounded));
        let mut count = 0;
        for num in iter.rev() {
            uft.unite(x, num.1);
            if used[num.1] {
                count += 1;
            }
            used[num.1] = true;
            if count > 100 {
                break;
            }
        }
        used[x] = true;
    }

    for i in 0..n {
        println!("{}", uft.get_size(points_indexed[i].0));
    }
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

#[derive(Debug, Clone)]
struct UnionFindTree {
    parent: Vec<isize>,
    size: Vec<usize>,
    height: Vec<u64>,
}

impl UnionFindTree {
    fn new(n: usize) -> UnionFindTree {
        UnionFindTree {
            parent: vec![-1; n],
            size: vec![1usize; n],
            height: vec![0u64; n],
        }
    }

    fn find(&mut self, index: usize) -> usize {
        if self.parent[index] == -1 {
            return index;
        }
        let idx = self.parent[index] as usize;
        let ret = self.find(idx);
        self.parent[index] = ret as isize;
        ret
    }

    fn same(&mut self, x: usize, y: usize) -> bool {
        self.find(x) == self.find(y)
    }

    fn get_size(&mut self, x: usize) -> usize {
        let idx = self.find(x);
        self.size[idx]
    }

    fn unite(&mut self, index0: usize, index1: usize) -> bool {
        let a = self.find(index0);
        let b = self.find(index1);
        if a == b {
            false
        } else {
            if self.height[a] > self.height[b] {
                self.parent[b] = a as isize;
                self.size[a] += self.size[b];
            } else if self.height[a] < self.height[b] {
                self.parent[a] = b as isize;
                self.size[b] += self.size[a];
            } else {
                self.parent[b] = a as isize;
                self.size[a] += self.size[b];
                self.height[a] += 1;
            }
            true
        }
    }
}