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;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;

public static class P
{
    public static void Main()
    {
        int n = int.Parse(Console.ReadLine());
        var p = Console.ReadLine().Split().Select(int.Parse).ToArray();
        var q = Console.ReadLine().Split().Select(int.Parse).ToArray();
        var a = Enumerable.Range(1, n).ToArray();
        int ctr = 0;
        var pind = ctr;
        var qind = ctr;
        foreach (var perm in Permutations(a))
        {
            if (p.Zip(perm, (x, y) => x == y).All(x => x)) pind = ctr;
            if (q.Zip(perm, (x, y) => x == y).All(x => x)) qind = ctr;
            ctr++;
        }
        Console.WriteLine(Abs(pind - qind));
    }


    static IEnumerable<T[]> Permutations<T>(T[] array) where T : IComparable<T>
    {
        int index = 0;
        yield return array;
        while (true)
        {
            for (int i = array.Length - 1; i > 0; i--)
            {
                if (array[i - 1].CompareTo(array[i]) >= 0) continue;
                int j = Array.FindLastIndex(array, x => array[i - 1].CompareTo(x) < 0);
                T tmp = array[i - 1]; array[i - 1] = array[j]; array[j] = tmp;
                Array.Reverse(array, i, array.Length - i);
                yield return array;
                goto end;
            }
            Array.Reverse(array, index, array.Length);
            yield break;
            end:;
        }
    }
}