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;

class Program
{
    static void Main(string[] args)
    {
        var _N = int.Parse(Console.ReadLine());
        var _P = int.Parse(Console.ReadLine().Replace(" ",""));
        var _Q = int.Parse(Console.ReadLine().Replace(" ", ""));

        var baseStr = string.Empty;
        for(var i = 1; i <= _N; i++)
        {
            baseStr += i.ToString();
        }
        var total = new List<string>();
        CreateList(baseStr, total);
        var sorted = new SortedList<int, string>();
        foreach(var str in total)
        {
            sorted.Add(int.Parse(str), str);
        }
        var a = sorted.IndexOfKey(_P);
        var b = sorted.IndexOfKey(_Q);
        Console.WriteLine(Math.Abs(a - b));
    }

    static void CreateList(string baseStr, List<string> total, string create = "")
    {
        if(baseStr.Length == 1)
        {
            total.Add(create + baseStr);
        }
        else
        {
            for (var i = 0; i < baseStr.Length; i++)
            {
                var newCreate = create + baseStr[i];
                var newBaseStr = baseStr.Remove(i, 1);
                CreateList(newBaseStr, total, newCreate);
            }
        }
    }
}