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.Scanner;
public class Main {
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);

		int n=sc.nextInt();
		int[] x=new int[n];
		int[] y=new int[n];
		for(int i=0;i<=n-1;i++) {
			x[i]=sc.nextInt();
			y[i]=sc.nextInt();
		}
		int cnt=1;
		for(int i=0;i<n;i++) {
			for(int j=0;j<n;j++) {
				if((x[i]<x[j]&&y[i]<y[j])||(x[i]>x[j]&&y[i]>y[j])) {
					cnt++;
					}
				}
			System.out.println(cnt);
		}
		sc.close();
		}
	}