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,x[200000],y[200000],k[200000];
  scanf("%d",&n);
  for(int i=1;i<=n;i++){
    scanf("%d %d",&x[i],&y[i]);
    k[i]=1;
  }


  for(int i=1;i<=n;i++){
    for(int j=1;j<=n;j++){
      if((x[i]<x[j])&&(y[i]<y[j])){
        k[i]++;
        //printf("%d<%d&&%d<%d\n",x[i],x[j],y[i],y[j]);
      }
      if((x[i]>x[j])&&(y[i]>y[j])){
        k[i]++;
        //printf("%d>%d&&%d>%d\n",x[i],x[j],y[i],y[j]);
      }
    }
  }
  for(int i=1;i<=n;i++){
    printf("%d\n",k[i]);
  }
}