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: Accepted)

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

namespace TaskC
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = Convert.ToInt32(Console.ReadLine());
            int[] A = System.Console.ReadLine().Split().Select(x => Convert.ToInt32(x)).ToArray();
            int[] B = System.Console.ReadLine().Split().Select(x => Convert.ToInt32(x)).ToArray();
            IDictionary<int, int> upper_bound = new Dictionary<int, int>();
            IDictionary<int, int> lower_bound = new Dictionary<int, int>();

            int[][] c_A = Enumerable.Range(0, n).Select(x => new [] { A[x], x }).ToArray();
            int[][] c_B = Enumerable.Range(0, n).Select(x => new [] { B[x], x }).ToArray();

            Func<int[], int[], int> cmp = (x, y) =>
            {
                return x[0] - y[0];
            };

            Array.Sort(c_A, (x, y) => x[0] - y[0]);
            Array.Sort(c_B, (x, y) => x[0] - y[0]);

            for(int i = 0; i < n; ++i)
            {
                if(c_A[i][0] > c_B[i][0])
                {
                    System.Console.WriteLine("No");
                    return;
                }
            }
            
            for(int i = 0; i < n - 1; ++i)
                if(c_A[i + 1][0] <= c_B[i][0])
                {
                    System.Console.WriteLine("Yes");
                    return;
                }

            int[] pos = new int[n];
            for(int i = 0; i < n; ++i)
                pos[c_A[i][1]] = c_B[i][1];
            
            int cycles = 0;
            HashSet<int> mrk = new HashSet<int>();
            for(int i = 0; i < n; ++i)
            {
                if(mrk.Contains(i))
                    continue;
                ++cycles;   
                int x = pos[i];
                while(x != i)
                {
                    mrk.Add(x);
                    x = pos[x];
                }
            }
            if(cycles > 1)
                System.Console.WriteLine("Yes");
            else
                System.Console.WriteLine("No");
        }
    }
}