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;

namespace AtCoderConsole
{
    class Program
    {
        static void Main(string[] args)
        {
            //入力
            int N = int.Parse(Console.ReadLine());
            var dataList = new List<int[]>();
            for (int i = 0; i < N; i++)
            {
                // スペース区切りの整数の入力
                string[] input = Console.ReadLine().Split(' ');
                var data = new int[4];
                data[0] = i;
                data[1] = int.Parse(input[0]);
                data[2] = int.Parse(input[1]);
                dataList.Add(data);
            }

            //計算
            foreach (var ansData in dataList)
            {
                if(ansData[3] != 0)
                {
                    Console.WriteLine(ansData[3]);
                    continue;
                }

                var candList = new List<int[]>();
                //数える
                candList.AddRange(dataList.Where(val => val[1] < ansData[1] && val[2] < ansData[2]));
                candList.AddRange(dataList.Where(val => val[1] > ansData[1] && val[2] > ansData[2]));

                var answerNum = candList.Count() + 1;
                foreach(var cand in candList)
                {
                    var condNum = dataList.Where(val => val[1] < cand[1] && val[2] < cand[2]).Count() +
                        dataList.Where(val => val[1] > cand[1] && val[2] > cand[2]).Count() + 1;
                    if(condNum > answerNum)
                    {
                        answerNum = condNum;
                    }
                }
                candList.ForEach(val => val[3] = answerNum);

                Console.WriteLine(answerNum);
            }
        }
    }
}