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 MainClass
{
    public static void Main(string[] args)
    {
        var n = int.Parse(Console.ReadLine());
        var p = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        var q = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);

        var a = 0;
        var i = 0;
        perm(n, item =>
        {
            if (eq(p, item))
            {
                a = i;
                return true;
            }
            i++;
            return false;
        });


        var b = 0;
        i = 0;
        perm(n, item =>
        {
            if (eq(q, item))
            {
                b = i;
                return true;
            }
            i++;
            return false;
        });

        Console.WriteLine(Math.Abs(a - b));
    }

    static bool perm(int n, Func<int[], bool> func)
    {
        return _perm(0, new bool[n], new int[n], func);
    }

    static bool _perm(int i, bool[] v, int[] a, Func<int[], bool> pred)
    {
        if (v.Length <= i)
        {
            return pred(a);
        }

        for (int j = 0; j < v.Length; j++)
        {
            if (v[j]) continue;
            v[j] = true;
            a[i] = j + 1;

            if (_perm(i + 1, v, a, pred))
            {
                return true;
            }

            v[j] = false;
        }

        return false;
    }

    static bool eq(int[] x, int[] y)
    {
        for (int i = 0; i < x.Length; i++)
            if (x[i] != y[i])
                return false;

        return true;
    }
}