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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        AReachableTowns solver = new AReachableTowns();
        solver.solve(1, in, out);
        out.close();
    }

    static class AReachableTowns {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int N = in.nextInt();
            pair[] a = new pair[N + 1];
            for (int i = 1; i <= N; i++) {
                int x = in.nextInt();
                int y = in.nextInt();
                pair p = new pair(x, y);
                a[i] = p;
            }
            for (int i = 1; i <= N; i++) {
                int c = 0;
                for (int j = 1; j <= N; j++) {
                    if ((a[i].x <= a[j].x && a[i].y <= a[j].y) || (a[i].x >= a[j].x && a[i].y >= a[j].y))
                        c++;

                }
                out.println(c);
            }

        }

    }

    static class pair {
        int x;
        int y;

        pair(int x, int y) {
            this.x = x;
            this.y = y;
        }

    }
}