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 with AC Library v1.1) (judge verdict: Time Limit Exceeded)

#include <bits/stdc++.h>
#include <atcoder/all>

using namespace std;
using namespace atcoder;

int main()
{
    int N;
    cin>>N;

    dsu d(N);
    vector<int>qer(N);
    vector<int>b_sort;
    //入力
    for (int i = 0; i < N; i++)
    {
        int x,y;
        cin>>x>>y;
        qer[x-1]=y;
        b_sort.emplace_back(x-1);
    }

    
    for(int i=0;i<N;++i)
    {
        int y = qer[i];
        for(int j=0;j<i;++j)
        {
            if(qer[j]<y)
            {
                d.merge(i,j);
            }
        }
    }

    

    for (auto&&i:b_sort)
    {
        cout<<d.size(i)<<endl;
    }
    
    


    return 0;
}