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 Java (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;
import java.io.*;
import java.nio.charset.StandardCharsets;

public class Main {

	public static void main(String[] args) throws IOException {
		InputStreamReader reader = new InputStreamReader(System.in, StandardCharsets.UTF_8);
		BufferedReader in = new BufferedReader(reader);
		Main ins = new Main(in);
		ins.calc();
		ins.showResult();
	}

	int N;
	int[] x, y;
	List<Tuple> list;
	Map<Integer, Integer> counts;

	static class Tuple {
		int id, x, y, gid;
		Set<Integer> conns;

		Tuple(int id, int x, int y) {
			this.gid = -1;
			this.id = id;
			this.x = x;
			this.y = y;
			this.conns = new HashSet<>();
		}

	}

	Main(BufferedReader in) throws IOException {
		N = Integer.parseInt(in.readLine());
		x = new int[N];
		y = new int[N];
		for (int i = 0; i < N; ++i) {
			String[] tokens = in.readLine().split(" ");
			x[i] = Integer.parseInt(tokens[0]);
			y[i] = Integer.parseInt(tokens[1]);
		}
		list = new ArrayList<>(N);
		for (int i = 0; i < N; ++i) {
			list.add(new Tuple(i, x[i], y[i]));
		}
		Collections.sort(list, new Comparator<Tuple>() {
			@Override
			public int compare(Tuple o1, Tuple o2) {
				return Integer.compare(o1.x, o2.x);
			}
		});
	}

	void mark(int id, int gid, int parent) {
		list.get(id).gid = gid;
		for (Integer conn : list.get(id).conns) {
			if (conn != parent) {
				mark(conn, gid, id);
			}
		}
	}

	void update(Tuple tuple, Deque<Tuple> deque) {
		List<Tuple> list = new ArrayList<>();
		while (!deque.isEmpty() && deque.peek().y < tuple.y) {
			list.add(deque.poll());
		}

		// tupleとlistの各要素間にedgeを張る
		for (Tuple elem : list) {
			tuple.conns.add(elem.id);
			elem.conns.add(tuple.id);
		}
		if (list.isEmpty()) {
			deque.addFirst(tuple);
		} else {
			deque.addFirst(list.get(0));
		}
	}

	void calc() {
		Deque<Tuple> deque = new ArrayDeque<>();
		deque.add(list.get(0));
		for (int i = 1; i < list.size(); ++i) {
			update(list.get(i), deque);
		}

		Collections.sort(list, new Comparator<Tuple>() {
			@Override
			public int compare(Tuple o1, Tuple o2) {
				return Integer.compare(o1.id, o2.id);
			}
		});

		// gidをmarkする
		int gid = 0;
		for (int i = 0; i < list.size(); ++i) {
			if (list.get(i).gid < 0) {
				mark(i, gid, -1);
				++gid;
			}
		}

		counts = new HashMap<>();
		for (int i = 0; i < list.size(); ++i) {
			int g = list.get(i).gid;
			if (counts.containsKey(g)) {
				counts.put(g, counts.get(g) + 1);
			} else {
				counts.put(g, 1);
			}
		}

	}

	void showResult() {
		for (int i = 0; i < list.size(); ++i) {
			System.out.println(counts.get(list.get(i).gid));
		}
	}
}