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: Runtime Error)

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

public class Main {
    public static void main(String args[]){
        Scanner stdIn = new Scanner(System.in);
        int n = stdIn.nextInt();
        int a[] = new int[n];
        int b[] = new int[n];
        String s[] = new String[n];
        String k[] = new String[n];
        int sum = 0;
        boolean flag = true;
        
        for(int i = 0; i < n; i++){
            a[i] = stdIn.nextInt();
            s[i] = "";
            s[i] += a[i];
        }
        
        for(int i = 0; i < n; i++){
            b[i] = stdIn.nextInt();
            s[i] += b[i];
        }
        
        Arrays.sort(a);
        Arrays.sort(b);
        Arrays.sort(s);
        
        for(int i = 0; i < n; i++){
            k[i] = "";
            k[i] += a[i];
            k[i] += b[i];
            if(a[i] > b[i]){
                flag = false;
                break;
            }
        }
        
        if(flag){
            boolean flag2 = false;
            int numa = 0;
            int numb = 0;
            
            while(numa < n && numb < n){
                long num1 = Integer.parseInt(s[numa]);
                long num2 = Integer.parseInt(k[numb]);
                
                if(num1 == num2){
                    sum++;
                }else if(num1 > num2){
                    numb++;
                }else{
                    numa++;
                }
                
                if(sum == 1){
                    flag2 = true;
                    break;
                }
                
            }
                
            if(!flag2){
                flag = false;
            }
            
        }
        
        
        
        if(flag){
            System.out.println("Yes");
        }else{
            System.out.println("No");
        }
    }
}