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.*;
import static java.lang.Math.*;
import java.math.BigInteger;

public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		
		// 入力
		int n = sc.nextInt();
		int[][] a = new int[n][2];
		int[] b = new int[n];
		for(int i = 0; i < n; i++){
		    a[i][0] = i;
		    a[i][1] = sc.nextInt();
		}
		for(int i = 0; i < n; i++){
		    b[i] = sc.nextInt();
		}
		Arrays.sort(a, (s, t) -> Integer.compare(s[1], t[1]));
		Arrays.sort(b);
		
		// 計算
		String result = "";
		int[] chk = new int[n];
		Arrays.fill(chk, -1);
		for(int i = 0; i < n; i++){
		    if(a[i][1] > b[i]){
		        result = "No";
		        System.out.println(result);
		        return;
		    }
		    if(i < n-1 && a[i+1][1] <= b[i]) result = "Yes";
		    if(a[i][0] == i) result = "Yes";
		    if(chk[i] == a[i][0]) result = "Yes";
		    chk[a[i][0]] = i;
		}
		
		// 出力
		System.out.println(result);
	}
}