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

class Program
{
    static void Main(string[] args)
    {
        // 入力
        int n = int.Parse(Console.ReadLine());
        int[] p = Console.ReadLine().Split().Select(int.Parse).ToArray();
        int[] q = Console.ReadLine().Split().Select(int.Parse).ToArray();

        var k1 = "";
        var k2 = "";
        for (int i = 0; i < n; i++)
        {
            k1 += p[i];
            k2 += q[i];

        }

        var dic = new Dictionary<int, int>() { };
        var count = 0;

        var src = new List<string>() { };
        for (int i = 0; i < n; i++)
        {
            src.Add((i+1).ToString());
        }

        foreach (var permutation in Permutations(src, n))
        {
            var tmp = string.Join("", permutation);
            dic.Add(int.Parse(tmp), count);
            count++;
        }

        var ans= Math.Abs(dic[int.Parse(k1)] - dic[int.Parse(k2)]);
        Console.WriteLine(ans);
    }


    static List<List<T>> Permutations<T>(List<T> src, int n)
    {
        // nは1以上かつsrcの長さよりも短い必要がある。
        int len = src.Count;
        if (!(0 < n && n <= len))
        {
            throw new ArgumentOutOfRangeException();
        }

        var permutations = new List<List<T>>();
        var queue = new Queue<List<int>>(Enumerable.Range(0, len).Select(i => new List<int>() { i }));
        while (queue.Any())
        {
            var indexes = queue.Dequeue();

            if (indexes.Count == n)
            {
                permutations.Add(indexes.Select(index => src[index]).ToList());
                continue;
            }

            for (int index = 0; index < len; index++)
            {
                if (indexes.Contains(index))
                {
                    continue;
                }

                var newIndexes = new List<int>(indexes);
                newIndexes.Add(index);
                queue.Enqueue(newIndexes);
            }
        }

        return permutations;
    }
}