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 dsu::Dsu;
use seg_tree::{SegTree, SegTreeOracle};
use std::io::*;
use utils::*;

pub fn main() {
    let i = stdin();
    let mut o = Vec::new();
    run(i.lock(), &mut o).unwrap();
    stdout().write_all(&o).unwrap();
}

struct Sum;
impl SegTreeOracle for Sum {
    type S = usize;
    fn e() -> Self::S {
        0
    }
    fn op(l: Self::S, r: Self::S) -> Self::S {
        l + r
    }
}

pub fn run(i: impl BufRead, o: &mut impl Write) -> std::io::Result<()> {
    let mut i = CpReader::new(i);
    let n = i.read::<usize>();

    #[derive(Copy, Clone)]
    struct Item {
        idx: usize,
        x: usize,
    }
    let mut items = vec![
        Item {
            idx: usize::max_value(),
            x: usize::max_value()
        };
        n
    ];

    let mut idx = 0;
    for (x, y) in i.read_iter::<(usize, usize)>(n) {
        let x = x - 1;
        let y = y - 1;
        items[y] = Item { x, idx };
        idx += 1;
    }
    let mut dsu = Dsu::new(n);
    let mut t = SegTree::<Sum>::new(n);
    let mut x_to_y = vec![usize::max_value(); n];
    for y in 0..n {
        let Item { x, .. } = items[y];
        let mut has_link = false;
        for c in 0.. {
            let x1 = t.min_left(x, |i| i <= c);
            if x1 > 0 {
                let y1 = x_to_y[x1 - 1];
                has_link = true;
                dsu.merge(y, y1);
            } else {
                break;
            }
        }
        if !has_link {
            x_to_y[x] = y;
            t.set(x, 1);
        }
    }
    let mut rs = vec![0; n];
    for y in 0..n {
        let Item { idx, .. } = items[y];
        rs[idx] = dsu.size(y);
    }
    for r in rs {
        writeln!(o, "{}", r)?;
    }
    Ok(())
}

pub mod utils {
    use super::*;

    pub struct CpReader<R: BufRead> {
        r: R,
        b: Vec<u8>,
    }
    impl<R: BufRead> CpReader<R> {
        pub fn new(r: R) -> Self {
            CpReader {
                r: r,
                b: Vec::new(),
            }
        }
        pub fn read_word(&mut self) -> &[u8] {
            self.b.clear();
            loop {
                let b = self.r.fill_buf().unwrap();
                assert!(!b.is_empty());
                if let Some(p) = b.iter().position(|&x| x == b' ' || x == b'\n') {
                    self.b.extend_from_slice(&b[..p]);
                    self.r.consume(p + 1);
                    return &self.b;
                }
                self.b.extend_from_slice(b);
                let b_len = b.len();
                self.r.consume(b_len);
            }
        }
        pub fn read_word_str(&mut self) -> &str {
            unsafe { std::str::from_utf8_unchecked(self.read_word()) }
        }

        pub fn read_line(&mut self) -> &[u8] {
            self.b.clear();
            self.r.read_until(b'\n', &mut self.b).unwrap();
            if self.b.last() == Some(&b'\n') {
                &self.b[..self.b.len() - 1]
            } else {
                &self.b
            }
        }
        pub fn read_line_str(&mut self) -> &str {
            unsafe { std::str::from_utf8_unchecked(self.read_line()) }
        }

        pub fn read<T: CpIn>(&mut self) -> T {
            T::read_from(self)
        }

        pub fn read_vec<T: CpIn>(&mut self, n: usize) -> Vec<T> {
            (0..n).map(|_| self.read()).collect()
        }
        pub fn read_iter<'a, T: CpIn>(&'a mut self, n: usize) -> CpIter<'a, R, T> {
            CpIter {
                r: self,
                n: n,
                _pd: Default::default(),
            }
        }
    }
    pub struct CpIter<'a, R: BufRead + 'a, T> {
        r: &'a mut CpReader<R>,
        n: usize,
        _pd: std::marker::PhantomData<fn() -> T>,
    }
    impl<'a, R: BufRead, T: CpIn> Iterator for CpIter<'a, R, T> {
        type Item = T;
        fn next(&mut self) -> Option<T> {
            if self.n == 0 {
                None
            } else {
                self.n -= 1;
                Some(self.r.read())
            }
        }
        fn size_hint(&self) -> (usize, Option<usize>) {
            (self.n, Some(self.n))
        }
    }
    impl<'a, R: BufRead, T: CpIn> ExactSizeIterator for CpIter<'a, R, T> {}

    pub trait CpIn {
        fn read_from<R: BufRead>(r: &mut CpReader<R>) -> Self;
    }

    impl CpIn for u64 {
        fn read_from<R: BufRead>(r: &mut CpReader<R>) -> Self {
            read_u64_fast(&mut r.r)
        }
    }
    impl CpIn for i64 {
        fn read_from<R: BufRead>(r: &mut CpReader<R>) -> Self {
            read_i64_fast(&mut r.r)
        }
    }
    impl CpIn for char {
        fn read_from<R: BufRead>(r: &mut CpReader<R>) -> Self {
            let b = r.r.fill_buf().unwrap()[0] as char;
            r.r.consume(1);
            let s = r.r.fill_buf().unwrap()[0];
            assert!(s == b' ' || s == b'\n');
            r.r.consume(1);
            b
        }
    }

    macro_rules! cpin_tuple {
        ($($t:ident),*) => {
            impl<$($t: CpIn),*> CpIn for ($($t),*) {
                fn read_from<R: BufRead>(r: &mut CpReader<R>) -> Self {
                    ($($t::read_from(r)),*)
                }
            }
        };
    }

    macro_rules! cpin_cast {
        ($t_self:ty, $t_read:ty) => {
            impl CpIn for $t_self {
                fn read_from<R: BufRead>(r: &mut CpReader<R>) -> Self {
                    <$t_read>::read_from(r) as $t_self
                }
            }
        };
    }
    macro_rules! cpin_parse {
        ($t:ty) => {
            impl CpIn for $t {
                fn read_from<R: BufRead>(r: &mut CpReader<R>) -> Self {
                    r.read_word_str().parse().unwrap()
                }
            }
        };
    }
    cpin_cast!(usize, u64);
    cpin_cast!(u32, u64);
    cpin_cast!(u16, u64);
    cpin_cast!(i32, i64);
    cpin_cast!(i16, i64);
    cpin_cast!(i8, i64);

    cpin_parse!(f64);

    cpin_tuple!(T1, T2);
    cpin_tuple!(T1, T2, T3);
    cpin_tuple!(T1, T2, T3, T4);
    cpin_tuple!(T1, T2, T3, T4, T5);

    fn read_u64_fast<R: BufRead>(r: &mut R) -> u64 {
        let mut value = 0;
        loop {
            let buf = r.fill_buf().unwrap();
            assert!(!buf.is_empty());
            let mut idx = 0;
            while let Some(&c) = buf.get(idx) {
                if b'0' <= c && c <= b'9' {
                    value = value * 10 + (c - b'0') as u64;
                    idx += 1;
                } else {
                    r.consume(idx + 1);
                    return value;
                }
            }
            r.consume(idx);
        }
    }
    fn read_i64_fast<R: BufRead>(r: &mut R) -> i64 {
        let sign = match r.fill_buf().unwrap()[0] {
            b'+' => {
                r.consume(1);
                1
            }
            b'-' => {
                r.consume(1);
                -1
            }
            _ => 1,
        };
        read_u64_fast(r) as i64 * sign
    }
}

mod internal_bit {
    pub fn ceil_pow2(n: usize) -> usize {
        let mut x = 0;
        while (1 << x) < n {
            x += 1;
        }
        return x;
    }
}

mod helpers {
    #![allow(dead_code)]
    use std::ops::{Bound, Range, RangeBounds};

    pub fn to_range(len: usize, range: impl RangeBounds<usize>) -> Range<usize> {
        let start = match range.start_bound() {
            Bound::Included(idx) => *idx,
            Bound::Excluded(idx) => *idx + 1,
            Bound::Unbounded => 0,
        };
        let end = match range.end_bound() {
            Bound::Included(idx) => *idx + 1,
            Bound::Excluded(idx) => *idx,
            Bound::Unbounded => len,
        };
        debug_assert!(start <= end);
        debug_assert!(end <= len);
        start..end
    }
}

mod seg_tree {
    #![allow(dead_code)]
    use crate::{helpers::to_range, internal_bit::ceil_pow2};
    use std::ops::RangeBounds;

    pub struct SegTree<O: SegTreeOracle> {
        n: usize,
        d: Vec<O::S>,
        size: usize,
        log: usize,
    }

    impl<O: SegTreeOracle> SegTree<O> {
        pub fn new(n: usize) -> Self {
            let log = ceil_pow2(n);
            let size = 1 << log;
            let d = vec![O::e(); 2 * size];
            Self { n, d, size, log }
        }
        pub fn from_slice(v: &[O::S]) -> Self {
            let mut s = Self::new(v.len());
            s.d[s.size..s.size + v.len()].copy_from_slice(v);
            for i in (1..s.size).rev() {
                s.update(i);
            }
            s
        }
        pub fn from_iter(iter: impl Iterator<Item = O::S> + ExactSizeIterator) -> Self {
            let len = iter.len();
            let mut s = Self::new(len);
            let mut idx = s.size;
            for item in iter {
                s.d[idx] = item;
                idx += 1;
            }
            for i in (1..s.size).rev() {
                s.update(i);
            }
            s
        }

        #[inline]
        pub fn set(&mut self, index: usize, value: O::S) {
            let p = index + self.size;
            self.d[p] = value;
            for i in 1..=self.log {
                self.update(p >> i)
            }
        }

        #[inline]
        pub fn get(&self, index: usize) -> O::S {
            self.d[index + self.size]
        }

        pub fn prod(&self, range: impl RangeBounds<usize>) -> O::S {
            let range = to_range(self.n, range);
            let mut l = range.start;
            let mut r = range.end;
            let mut sml = O::e();
            let mut smr = O::e();
            l += self.size;
            r += self.size;
            while l < r {
                if l & 1 != 0 {
                    sml = O::op(sml, self.d[l]);
                    l += 1;
                };
                if r & 1 != 0 {
                    r -= 1;
                    smr = O::op(self.d[r], smr);
                }
                l >>= 1;
                r >>= 1;
            }
            return O::op(sml, smr);
        }
        #[inline]
        pub fn all_prod(&self) -> O::S {
            self.d[1]
        }

        pub fn max_right(&self, mut l: usize, f: impl Fn(O::S) -> bool) -> usize {
            debug_assert!(l <= self.n);
            debug_assert!(f(O::e()));
            if l == self.n {
                return self.n;
            }
            l += self.size;
            let mut sm = O::e();
            loop {
                while l % 2 == 0 {
                    l >>= 1;
                }
                if !f(O::op(sm, self.d[l])) {
                    while l < self.size {
                        l = 2 * l;
                        if f(O::op(sm, self.d[l])) {
                            sm = O::op(sm, self.d[l]);
                            l += 1;
                        }
                    }
                    return l - self.size;
                }
                sm = O::op(sm, self.d[l]);
                l += 1;
                if (l & l.wrapping_neg()) == l {
                    break;
                }
            }
            self.n
        }
        pub fn min_left(&self, mut r: usize, f: impl Fn(O::S) -> bool) -> usize {
            debug_assert!(r <= self.n);
            debug_assert!(f(O::e()));
            if r == 0 {
                return 0;
            }
            r += self.size;
            let mut sm = O::e();
            loop {
                r -= 1;
                while r > 1 && (r % 2) != 0 {
                    r >>= 1;
                }
                if !f(O::op(self.d[r], sm)) {
                    while r < self.size {
                        r = 2 * r + 1;
                        if f(O::op(self.d[r], sm)) {
                            sm = O::op(self.d[r], sm);
                            r -= 1;
                        }
                    }
                    return r + 1 - self.size;
                }
                sm = O::op(self.d[r], sm);
                if (r & r.wrapping_neg()) == r {
                    break;
                }
            }
            0
        }

        #[inline]
        fn update(&mut self, k: usize) {
            self.d[k] = O::op(self.d[2 * k], self.d[2 * k + 1]);
        }
    }

    pub trait SegTreeOracle {
        type S: Copy;
        fn e() -> Self::S;
        fn op(l: Self::S, r: Self::S) -> Self::S;
    }
}

mod dsu {
    #![allow(dead_code)]
    use std::mem::swap;

    pub struct Dsu {
        n: usize,
        parent_or_size: Vec<i32>,
    }

    impl Dsu {
        pub fn new(n: usize) -> Self {
            Self {
                n,
                parent_or_size: vec![-1; n],
            }
        }
        pub fn merge(&mut self, a: usize, b: usize) -> usize {
            debug_assert!(a < self.n);
            debug_assert!(b < self.n);
            let mut x = self.leader(a);
            let mut y = self.leader(b);
            if x == y {
                return x;
            }
            if -self.parent_or_size[x] < -self.parent_or_size[y] {
                swap(&mut x, &mut y);
            }
            self.parent_or_size[x] += self.parent_or_size[y];
            self.parent_or_size[y] = x as i32;
            x
        }
        pub fn same(&mut self, a: usize, b: usize) -> bool {
            debug_assert!(a < self.n);
            debug_assert!(b < self.n);
            self.leader(a) == self.leader(b)
        }

        pub fn leader(&mut self, a: usize) -> usize {
            debug_assert!(a < self.n);
            if self.parent_or_size[a] < 0 {
                return a;
            }
            let leader = self.leader(self.parent_or_size[a] as usize);
            self.parent_or_size[a] = leader as i32;
            leader
        }
        pub fn size(&mut self, a: usize) -> usize {
            debug_assert!(a < self.n);
            let leader = self.leader(a);
            -self.parent_or_size[leader] as usize
        }

        pub fn groups(&mut self) -> Vec<Vec<usize>> {
            let mut leader_buf = vec![0; self.n];
            let mut group_size = vec![0; self.n];
            for i in 0..self.n {
                leader_buf[i] = self.leader(i);
                group_size[leader_buf[i]] += 1;
            }
            let mut result = Vec::with_capacity(self.n);
            for i in 0..self.n {
                result.push(Vec::with_capacity(group_size[i]));
            }
            for i in 0..self.n {
                result[leader_buf[i]].push(i);
            }
            result.retain(|x| !x.is_empty());
            result
        }
    }
}