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: Wrong Answer)

import java.util.*;
import java.io.*;
public class Main {
    public static void main(String[] args) throws Exception{
        
        Scanner sc = new Scanner(System.in);
        int tests;
       
     tests = sc.nextInt();
        int[][] A = new int[tests][2];
      int x=0;
      int y=0;
      int count=0;
      while(count<tests){
        if(sc.hasNextInt()){
         x = sc.nextInt();
        }
         if(sc.hasNextInt()){
      y = sc.nextInt();
         }
        A[count][0] =x;
          A[count][1] =y;
        
        count++;
      }
      

      
      for(int i=0;i<tests;i++){
       int c=1;
        for(int j=0;j<tests;j++){
          if( (A[i][0] > A[j][0] && A[i][1] > A[j][1] ) ||
              (A[i][0] < A[j][0] && A[i][1] < A[j][1] )){
             c++;
          }
        
        }
         System.out.println(c);
      }
      
       
    
     
         
       
       
        
  }
}