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: Time Limit Exceeded)

using System.Linq;
using System;

public class UnionFind
{
    private int[] data;
    public UnionFind(int size)
    {
        data = new int[size];
        for (int i = 0; i < size; i++) data[i] = -1;
    }
    public bool Unite(int x, int y)
    {
        x = Root(x);
        y = Root(y);
        if (x != y)
        {
            if (data[y] < data[x])
            {
                var tmp = y;
                y = x;
                x = tmp;
            }
            data[x] += data[y];
            data[y] = x;
        }
        return x != y;
    }
    public bool IsSameGroup(int x, int y) => Root(x) == Root(y);
    public int Root(int x) => data[x] < 0 ? x : data[x] = Root(data[x]);
    public int getMem(int x) => -data[Root(x)];
}


public class P
{
    public int x { get; set; }
    public int y { get; set; }
    public int id { get; set; }
}

public class Hello
{
    public static void Main()
    {
        var n = int.Parse(Console.ReadLine().Trim());
        var ps = new P[n];
        for (int i = 0; i < n; i++)
        {
            string[] line = Console.ReadLine().Trim().Split(' ');
            var x = int.Parse(line[0]);
            var y = int.Parse(line[1]);
            ps[i] = new P { id = i, x = x, y = y };
        }
        getAns(n, ps);
    }
    static void getAns(int n, P[] ps)
    {
        var uf = new UnionFind(n);
        ps = ps.OrderByDescending(x => x.x).ToArray();
        for (int i = 0; i < n - 1; i++)
            for (int j = i + 1; j < n; j++)
                if (ps[i].y > ps[j].y) uf.Unite(ps[i].id, ps[j].id);
        var ans = new int[n];
        for (int i = 0; i < n; i++)
            ans[i] = uf.getMem(i);
        Console.WriteLine(string.Join("\n", ans));
    }
}