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: Wrong Answer)

#include <stdio.h>

int main(){
  int N,m;
  scanf("%d",&N);
  int x[N],y[N],buf[N],ret[N];
  for(int i = 0;i<N;i++){
	scanf("%d %d",&x[i],&y[i]);
    ret[i] = 0;
  }
  for(int i = 0;i<N;i++){
    if(ret[i]>0){
      //printf("@1:%d,i=%d\n",ret[i],i);
    }else{
      m = 1;
      buf[0] = i;
      //printf("@1:%d,i=%d\n",ret[i],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])){
          //printf("i=%d,j=%d\n",i,j);
          if(i<j){
            buf[m++] = j;
          }
        }
      }
      for(int j = 0;j<m;j++){
        ret[buf[j]] = m;
      }
      //printf("@2:%d\n",ret[i]);
    }
  }
  //printf("###########\n");
  for(int i = 0;i<N;i++){
	printf("%d\n",ret[i]);
  }
  return 0;
}