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.Text;

namespace AtCoder
{
  class Program
  {
    internal class Town : IComparable
    {
      internal int X, Y, G = 200001;
      internal Town(int x, int y)
      {
        this.X = x;
        this.Y = y;
      }
      public int CompareTo(object o)
      {
        Town t = o as Town;
        return (this.X + this.Y).CompareTo(t.X + t.Y);
      }
    }
    static void Main(string[] args)
    {
      int N = int.Parse(Console.ReadLine());
      List<Town> ts = new List<Town>();
      List<Town> sorted = new List<Town>();
      for(int i = 0; i < N; i++)
      {
        string[] ss = Console.ReadLine().Split(' ');
        int x = int.Parse(ss[0]);
        int y = int.Parse(ss[1]);
        Town t = new Town(x, y);
        ts.Add(t);
        sorted.Add(t);
      }
      sorted.Sort();

      for(int i = 0; i < N; i++)
      {
        Town t = sorted[i];
        if(t.G < 200001)
          continue;

        t.G = i;
        if(NewMethod(sorted, i, t))
          continue;

        if(NewMethod1(N, sorted, i, t))
          continue;
      }
      int[] gs = new int[N];
      for(int i = 0; i < N; i++)
        gs[ts[i].G]++;

      for(int i = 0; i < N; i++)
        Console.WriteLine(gs[ts[i].G]);

      Console.ReadLine();

    }

    private static bool NewMethod1(int N, List<Town> sorted, int i, Town t)
    {
      for(int j = i + 1; j < N; j++)
        if(sorted[j].X > t.X && sorted[j].Y > t.Y)
        {
          t.G = sorted[j].G = Math.Min(t.G, sorted[j].G);
          return true;
        }
      return false;
    }

    private static bool NewMethod(List<Town> sorted, int i, Town t)
    {
      for(int j = 0; j < i; j++)
        if(sorted[j].X < t.X && sorted[j].Y < t.Y)
        {
          t.G = sorted[j].G = Math.Min(t.G, sorted[j].G);
          return true;
        }

      return false;
    }
  }
}