Problem:
Score : 600 points

Problem Statement

Given are two integer sequences of N elements each: A_1,...,A_N and B_1,...,B_N.
Determine if it is possible to do the following operation at most N-2 times (possibly zero) so that, for every integer i from 1 to N, A_i \leq B_i holds:

Choose two distinct integers x and y between 1 and N (inclusive), and swap the values of A_x and A_y.

Constraints

2 \leq N \leq 10^5

1 \leq A_i,B_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N
B_1 B_2 ... B_N

Output

If the objective is achievable, print Yes; if it is not, print No.

Sample Input 1

3
1 3 2
1 2 3

Sample Output 1

Yes

We should swap the values of A_2 and A_3.

Sample Input 2

3
1 2 3
2 2 2

Sample Output 2

No

Sample Input 3

6
3 1 2 6 3 4
2 2 8 3 4 3

Sample Output 3

Yes

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Arrays;
import java.util.Scanner;

public class Main {


	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = Integer.parseInt(sc.next());
		Integer[] a = new Integer[n];
		Integer[] a_ = new Integer[n];
		Integer[] b = new Integer[n];
		Integer[] b_ = new Integer[n];



		for (int i = 0; i < n ; i++) {
			a[i] = Integer.parseInt(sc.next());

		}

		for (int i = 0; i < n ; i++) {
			b[i] = Integer.parseInt(sc.next());
		}

		a_ = Arrays.copyOf(a, a.length);
		b_ = Arrays.copyOf(b, b.length);
		
		
		
		Arrays.sort(a);
		Arrays.sort(b);


		String ans = "Yes";
		for (int i = 0; i < n ; i++) {
			if(a[i] > b[i]) {
				ans = "No";
				break;
			}
		}

		
		boolean flag = false;
		for (int i = 0; i < n ; i++) {
				
				if(a_[i] <= b_[i] && b_[i] <= b[i]) {
					flag = true;
				}
		}

		if(!flag) {
			ans = "No";
		}
		
		System.out.println(ans);
	}

}