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# (.NET Core 3.1.201) (judge verdict: Runtime Error)

using System;
using System.Linq;
using static System.Math;

namespace abc126A
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            int[] x = new int[N];
            int[] y = new int[N];
            for (int i = 0; i < N; i++)
            {
                int[] a = Console.ReadLine().Split().Select(int.Parse).ToArray();
                x[i] = a[0];
                y[i] = a[1];
            }
            int[] xi = new int[N * (N-1)];
            int[] yi = new int[N * (N-1)];
            int d = 0;
            for (int i = 0; i < N; i++)
            {
                for (int j = 0; j < N; j++)
                {
                    if (x[j] < x[i] && y[j] < y[i]) { xi[d] = i; yi[d] = j; d++; }
                    if (x[j] > x[i] && y[j] > y[i]) { xi[d] = i; yi[d] = j; d++; }
                }
            }
            int[] vsb = new int[N];
            int[] vsc = new int[N];
            for (int i = 0; i < N; i++)
            {
                int counter = 0;
                int[] vs = new int[xi.Length];
                for (int b = 0; b < N; b++)
                {
                    if (xi[b] == i && yi[b] != xi[b])
                    {
                        counter++;
                    }
                }
                vsb[i] = counter;
                
            }
            for (int i = 0; i < N; i++)
            {
                vsc[i] = vsb[i];
            }
            for (int i = 0; i < N; i++)
            {
                if (vsb[i] > 1)
                {
                    for (int j = 0; j < N; j++)
                    {
                        if (xi[j] == i && yi[j] != xi[j])
                        {
                            int ja = yi[j];
                            vsc[ja]=vsc[ja] + 1;
                        }
                    }
                }
            }
            for (int i = 0; i < N; i++)
            {
                Console.WriteLine(vsc[i]+1);
            }
        }
    } 
}