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 ct = 0;
		for(var i=0;i<N;i++){
			A[i] = new int[4]{int.Parse(str[i]),-1,int.Parse(str2[i]),-1};
			B[i] = A[i][0];
			if(A[i][0] <= A[i][2]){
				ct++;
			}
		}
		string ans = "Yes";
		if(ct==N){
			ans = "Yes";
		} else {
		Array.Sort(A,(x,y)=>x[0]-y[0]);
      	for(var i=0;i<N;i++){
			A[i][1] = i;
		}
		Array.Sort(A,(x,y)=>x[2]-y[2]);
      	for(var i=0;i<N;i++){
			A[i][3] = i;
		}
		Array.Sort(B);
		for(var i=0;i<N;i++){
			if(B[i]>A[i][2]){
				ans = "No";
			}
		}
		if(ans == "Yes"){
			ans = "No";
			int[]S = new int[N];
			int si = 0;
			for(var i=0;i<N;i++){
				//Console.Error.WriteLine(si+" "+A[si][1]);
				si = A[si][1];
				if(S[si]==1){
					ans = "Yes";
					break;
				} else {
					S[si] = 1;
				}
			}
		}
        }
		Console.WriteLine(ans);
	}
}