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;
using System.Linq;

public class Solution
{
    public static void Main()
    {
        var N = int.Parse(Console.ReadLine());
        var A = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
        var B = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();

        var orderedA = A.OrderBy(x => x).ToArray();
        var orderedB = B.OrderBy(x => x).ToArray();

        for (int i = 0; i < N; i++)
        {
            if (orderedA[i] > orderedB[i])
            {
                Console.WriteLine("No");
                return;
            }
        }

        var pos = new Dictionary<long, Queue<int>>();
        var order = new int[N];
        for (int i = 0; i < N; i++)
        {
            if (!pos.ContainsKey(A[i]))
            {
                pos[A[i]] = new Queue<int>();
            }
            pos[A[i]].Enqueue(i);
        }
        for (int i = 0; i < N; i++)
        {
            order[i] = pos[orderedA[i]].Dequeue();
        }
        var count = 0;
        var p = 0;
        do
        {
            p = order[p];
            count++;
        } while (p != 0);
        if (count != N)
        {
            Console.WriteLine("Yes");
            return;
        }

        for (int i = 0; i < N - 1; i++)
        {
            if (orderedA[i + 1] <= orderedB[i])
            {
                Console.WriteLine("Yes");
                return;
            }
        }

        Console.WriteLine("No");
    }
}