Problem:
Score : 300 points

Problem Statement

We have two permutations P and Q of size N (that is, P and Q are both rearrangements of (1,~2,~...,~N)).

There are N! possible permutations of size N. Among them, let P and Q be the a-th and b-th lexicographically smallest permutations, respectively. Find |a - b|.

Notes

For two sequences X and Y, X is said to be lexicographically smaller than Y if and only if there exists an integer k such that X_i = Y_i~(1 \leq i < k) and X_k < Y_k.

Constraints

2 \leq N \leq 8

P and Q are permutations of size N.

Input

Input is given from Standard Input in the following format:

N
P_1 P_2 ... P_N
Q_1 Q_2 ... Q_N

Output

Print |a - b|.

Sample Input 1

3
1 3 2
3 1 2

Sample Output 1

3

There are 6 permutations of size 3: (1,~2,~3), (1,~3,~2), (2,~1,~3), (2,~3,~1), (3,~1,~2), and (3,~2,~1). Among them, (1,~3,~2) and (3,~1,~2) come 2-nd and 5-th in lexicographical order, so the answer is |2 - 5| = 3.

Sample Input 2

8
7 3 5 4 2 1 6 8
3 8 2 5 4 6 7 1

Sample Output 2

17517

Sample Input 3

3
1 2 3
1 2 3

Sample Output 3

0

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
public class Permutation
{
    public IEnumerable<T[]> Enumerate<T>(IEnumerable<T> items)
    {
        return _GetPermutations<T>(new List<T>(), items.ToList());
    }

    private IEnumerable<T[]> _GetPermutations<T>(IEnumerable<T> perm, IEnumerable<T> items)
    {
        if (items.Count() == 0)
        {
            yield return perm.ToArray();
        }
        else
        {
            foreach (var item in items)
            {
                var result = _GetPermutations<T>(perm.Concat(new T[] { item }),
                                                    items.Where(x => x.Equals(item) == false)
                                );
                foreach (var xs in result)
                    yield return xs.ToArray();
            }
        }
    }
}

class Program
{
    public static void Main()
    {
        int N = int.Parse(Console.ReadLine());
        string[] input = Console.ReadLine().Split();
        string[] input2 = Console.ReadLine().Split();
        int[] A = new int[N];
        int[] B = new int[N];
        int[] temp = new int[N];
        int pattern = 1;
        for (var i = 0; i < N; i++)
        {
            A[i] = int.Parse(input[i]);
            B[i] = int.Parse(input2[i]);
            pattern *= (i + 1);
            temp[i] = i+1;
        }
        int[,] xx = new int[pattern, N];
        // 確認用コード
        var perm = new Permutation();
        int count = 0,a_num=0,b_num=0;
        bool A_flag = true;
        bool B_flag = true;
        foreach (var n in perm.Enumerate(temp))
        {
            A_flag = true;B_flag = true;
            for (int i = 0; i < N; i++)
            {
                xx[count, i] = n[i];
                if (A[i] != n[i]) A_flag = false;
                if (B[i] != n[i]) B_flag = false;
            }
            count++;
            if (A_flag == true) { a_num = count; }
            if (B_flag == true) { b_num = count; }
        }
        Console.WriteLine(Math.Abs(a_num - b_num));
    }
}