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 C (GCC 9.2.1) (judge verdict: Runtime Error)

#include<stdio.h>
int main(void){
  int n = 1, s[n][2], count;
  
  scanf("%d", &n);
  
  for(int i = 0; i < n; i++)
    scanf("%d %d", &s[i][0], &s[i][1]);
  
  for(int i = 0; i < n; i++){
    count = 1;
    	for(int j = i + 1; j != i; j = (j+1) % n){
    		if(i < j && (s[i][0] < s[j][0] && s[i][1] < s[j][1]))
       			count++;
    		else if(i > j && (s[i][0] > s[j][0] && s[i][1] > s[j][1]))
       			count++;
  			}
    	printf("%d", count);
    }
       
    return 0;
}