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 11.0.6) (judge verdict: Wrong Answer)

import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int A[] = new int[N];
		Point p[] = new Point[N];
		Main main = new Main();
		Map map = new HashMap<>();
		for (int i=0;i<N;i++) {
			Point t = main.new Point();
			t.x= sc.nextInt();
			t.y= sc.nextInt();
			t.num= i;
			p[i] = t;
		}
		Arrays.sort(p,Collections.reverseOrder());
		for (int i=0;i<N;i++) {
			int count =1;
			if (A[p[i].num]==0) {
				for (int j=i+1;j<N;j++) {
					if (p[i].y>p[j].y) {
						count ++;
						A[p[j].num]=i+1;
					}
				}
				map.put(i+1, count);
				A[p[i].num]=i+1;
			}
		}

		for (int i=0;i<N;i++) {
			System.out.println(map.get(A[i]));
		}
	}

	public class Point implements Comparable {
		int x;
		int y;
		int num;
		@Override
		public int compareTo(Object o) {
			Point p = (Point)o;
			if (this.x>p.x) {
				return 1;
			}
			return -1;
		}

	}
}