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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Runtime.InteropServices.ComTypes;

namespace ConsoleApp2
{
    class Program
    {
        static void Main()
        {
            int count =0;
            var list = new List<int[]>();
            while (true)
            { 
                
                string line = Console.ReadLine();
                // 読み込める文字列が無くなった
                if (line == null)
                {                 
                    break;
                }

                //初回はスキップ
                if (count==0)
                {
                    count++;
                    continue;
                }

                var a = new int[] { line[0], line[2] };
                list.Add(a);

                count++;
            }

            for (int i = 0; i < list.Count(); i++)
            {
                int point = 1;
                foreach (var item in list)
                {
                    if ((list[i][0] > item[0] && list[i][1] > item[1])||(list[i][0] < item[0] && list[i][1] < item[1]))
                    {
                        point++;
                    }
                }
                Console.WriteLine(point);

            }
           

        }
    }
}