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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		int N = int.Parse(Console.ReadLine());
		string[] str = Console.ReadLine().Split();
		string[] str2 = Console.ReadLine().Split();
		int[]A = new int[N];
		int[]B = new int[N];
		int[]A2 = new int[N];
		int[]B2 = new int[N];
		int ct = 0;
		for(var i=0;i<N;i++){
			A[i] = int.Parse(str[i]);
			B[i] = int.Parse(str2[i]);
			A2[i] = A[i];
			B2[i] = B[i];
			if(A[i] > B[i]){
              	ct++;
            }
		}
		Array.Sort(A2);
		Array.Sort(B2);
		var C1 = new Dictionary<int,int>();
		var C2 = new Dictionary<int,int>();
		bool flag1 = false;
		for(var i=0;i<N;i++){
			if(C1.ContainsKey(A2[i])){
				flag1 = true;
			}
			if(C2.ContainsKey(B2[i])){
				flag1 = true;
			}
			C1[A2[i]] = i;
			C2[B2[i]] = i;
		}
		string ans = "Yes";
		for(var i=0;i<N;i++){
			if(A2[i]>B2[i]){
				ans = "No";
			}
		}
		bool flag = false;
		for(var i=0;i<N;i++){
			if(C1[A[i]] == 0){
				if(C2[B[i]] == N-1){
				} else {
					//flag = true;
				}
			} else {
				if(C1[A[i]] - C2[B[i]] == 1){
				} else {
					//flag = true;
				}
			}
		}
		if(!flag && ct >= N-1 && !flag1){
			ans = "No";
		}
		Console.WriteLine(ans);
	}
}