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: Runtime Error)

using System;
using System.Linq;
using System.Collections.Generic;
using System.Numerics;

class ProgramC
    {
        static void Main(string[] args)
        {
            string input = Console.ReadLine();
            long n = long.Parse(input);

            long[] a = new long [n];
            long[] b = new long[n];
            long[] a_order = new long [n];
            long sum = 1;

            string[] input_a = Console.ReadLine().Split();
            string[] input_b = Console.ReadLine().Split();


            for(long i = 0;i < n;i++)
            {
                a[i] = long.Parse(input_a[i]);
                b[i] = long.Parse(input_b[i]); 
                a_order[i] = a[i];
            }

            Array.Sort(a_order);
            Array.Sort(b);

            for(long i = 0;i < n;i++)
            {
                if(a_order[i] > b[i])
                {
                    Console.WriteLine("No");
                    return;
                } 
            }

            long p = 0;
            long count = 0;
            do
            {
               p = a_order[p]-1;
               count++;
            }while(p != 0);

            if(count == n)
            {
                for(long i = 1;i < n;i++)
                {
                    if(a_order[i] <= b[i - 1])
                    {
                        Console.WriteLine("Yes");
                        return;
                    } 

                }

                Console.WriteLine("No");
                return;
            }

            
            Console.WriteLine("Yes");

        }
    }