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.*;

public class Main {
	public static void main (String[] args){
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int A [] = new int[N];
		int B [] = new int[N];
		for(int i = 0; i < N; i++) {
			A[i] = sc.nextInt();
		}
		for(int i = 0; i < N; i++) {
			B[i] = sc.nextInt();
		}
		Arrays.sort(A);
		Arrays.sort(B);
		boolean x = true;
		for(int i = 0; i < N; i++) {
			if(A[i] > B[i]) {
				x = false;
				break;
			}	
			else {
				for(int j = 0; j < N-1; j++) {
					if(A[j+1] > B[j]) {
						x = false;
						break;
					}
				}
			}
		}
		if(x == true) {
			System.out.println("Yes");
		}
		else {
			System.out.println("No");
		}
	}
}