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)]
#![allow(non_snake_case, unused)]

use std::cmp::*;
use std::collections::*;
use std::ops::*;

// https://atcoder.jp/contests/hokudai-hitachi2019-1/submissions/10518254 より

macro_rules! eprint {
    ($($t:tt)*) => {{
        use ::std::io::Write;
        let _ = write!(::std::io::stderr(), $($t)*);
    }};
}
macro_rules! eprintln {
    () => { eprintln!(""); };
    ($($t:tt)*) => {{
        use ::std::io::Write;
        let _ = writeln!(::std::io::stderr(), $($t)*);
    }};
}
macro_rules! dbg {
    ($v:expr) => {{
        let val = $v;
        eprintln!("[{}:{}] {} = {:?}", file!(), line!(), stringify!($v), val);
        val
    }}
}

macro_rules! mat {
    ($($e:expr),*) => { Vec::from(vec![$($e),*]) };
    ($($e:expr,)*) => { Vec::from(vec![$($e),*]) };
    ($e:expr; $d:expr) => { Vec::from(vec![$e; $d]) };
    ($e:expr; $d:expr $(; $ds:expr)+) => { Vec::from(vec![mat![$e $(; $ds)*]; $d]) };
}

macro_rules! ok {
    ($a:ident$([$i:expr])*.$f:ident()$(@$t:ident)*) => {
        $a$([$i])*.$f($($t),*)
    };
    ($a:ident$([$i:expr])*.$f:ident($e:expr$(,$es:expr)*)$(@$t:ident)*) => { {
        let t = $e;
        ok!($a$([$i])*.$f($($es),*)$(@$t)*@t)
    } };
}

pub fn readln() -> String {
    let mut line = String::new();
    ::std::io::stdin().read_line(&mut line).unwrap_or_else(|e| panic!("{}", e));
    line
}

macro_rules! read {
    ($($t:tt),*; $n:expr) => {{
        let stdin = ::std::io::stdin();
        let ret = ::std::io::BufRead::lines(stdin.lock()).take($n).map(|line| {
            let line = line.unwrap();
            let mut it = line.split_whitespace();
            _read!(it; $($t),*)
        }).collect::<Vec<_>>();
        ret
    }};
    ($($t:tt),*) => {{
        let line = readln();
        let mut it = line.split_whitespace();
        _read!(it; $($t),*)
    }};
}

macro_rules! _read {
    ($it:ident; [char]) => {
        _read!($it; String).chars().collect::<Vec<_>>()
    };
    ($it:ident; [u8]) => {
        Vec::from(_read!($it; String).into_bytes())
    };
    ($it:ident; usize1) => {
        $it.next().unwrap_or_else(|| panic!("input mismatch")).parse::<usize>().unwrap_or_else(|e| panic!("{}", e)) - 1
    };
    ($it:ident; [usize1]) => {
        $it.map(|s| s.parse::<usize>().unwrap_or_else(|e| panic!("{}", e)) - 1).collect::<Vec<_>>()
    };
    ($it:ident; [$t:ty]) => {
        $it.map(|s| s.parse::<$t>().unwrap_or_else(|e| panic!("{}", e))).collect::<Vec<_>>()
    };
    ($it:ident; $t:ty) => {
        $it.next().unwrap_or_else(|| panic!("input mismatch")).parse::<$t>().unwrap_or_else(|e| panic!("{}", e))
    };
    ($it:ident; $($t:tt),+) => {
        ($(_read!($it; $t)),*)
    };
}


pub fn main() {
    let _ = ::std::thread::Builder::new().name("run".to_string()).stack_size(32 * 1024 * 1024).spawn(run).unwrap().join();
}

const MOD: i64 = 998244353;
// const MOD: usize = 1_000_000_007;
const INF: i64 = std::i64::MAX/2;

fn solve() {
    let n = read!(usize);
    let xy = read!(usize,usize;n);
    let mut v = vec![];
    for (i,&(x,y)) in xy.iter().enumerate() {
        v.push((y,x,i));
    }
    v.sort();
    let mut id = vec![0;n];
    let mut set = BTreeSet::new();
    for &(y,x,i) in &v {
        set.insert((x,i));
    }
    let mut idx = 1;
    for (z,&(y,x,i)) in v.iter().enumerate() {
        set.remove(&(x,i));
        idx = max(idx,z+1);
        if id[i]==0 {
            id[i] = x;
        }
        for j in idx..n {
            if set.len()==0 {
                break;
            }
            let (nx,ni) = *set.iter().last().unwrap();
            if nx > x {
                set.remove(&(v[idx].1,v[idx].2));
                id[v[idx].2] = id[i];
                idx += 1;
            }
            else {
                break;
            }
        }
    }
    let mut count = vec![0;n+1];
    for &i in &id {
        count[i] += 1;
    }
    for i in 0..n {
        println!("{}",count[id[i]]);
    }
}

fn run() {
    let stack_size = 104_857_600; // 100 MB
    let thd = std::thread::Builder::new().stack_size(stack_size);
    solve();
}