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.Linq;
using System.Collections.Generic;
using System.Text.RegularExpressions;

namespace ACLContest1
{
    class Program
    {
        static void Main(string[] args)
        {
            // 課題A - Reachable Towns(2020/9/20)

            int item = int.Parse(Console.ReadLine());
            //sring[] result;

            List<string[]> iptList = new List<string[]>();
            int x = 0, y = 0, tmpX = 0, tmpY = 0;
            int ptnCnt = 0;
            int[] result = new int[item];

            //for (int i = 1; i <= item; i++)
            //{
            //    for (int j = 1; j <= item; j++)
            //    {

            //        if (i * j < item) ptnCnt++;
            //        else break;
            //    }
            //}



            //var valueDict = new Dictionary<string, int>();

            for (int i = 0; i < item; i++)
            {
                //iptList.Add(Console.ReadLine().Split(' '));
                iptList.Add(Console.ReadLine().Split(' '));

            }


            for(int i= 0; i< item; i++)
            {
               
                x = int.Parse(iptList[i].GetValue(0).ToString());
                y = int.Parse(iptList[i].GetValue(1).ToString());
                result[i]++;

                for (int j = 0; j < item; j++)
                {
                    if (i == j) break;

                    tmpX = int.Parse(iptList[j].GetValue(0).ToString());
                    tmpY = int.Parse(iptList[j].GetValue(1).ToString());

                    if (x > tmpX && y > tmpY)
                    {
                        result[i]++;
                        result[j]++;
                        continue;
                    }
                        
                    if (x < tmpX && y < tmpY)
                    {
                        result[i]++;
                        result[j]++;
                    }
                        
                }
               
                

            }


            for (int i = 0; i < item; i++)
            {
                Console.WriteLine(result[i]);

            }

                //Console.WriteLine(ptnCnt);


                //if(getStr.Equals("s")) Console.Write(str + "es");
                //else Console.Write(str + "s");
        }
    }
}