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.Linq;
using System.Collections.Generic;
using static System.Math;
using System;

public static class Permi
{
    public static IEnumerable<IEnumerable<T>> Perm<T>(this IEnumerable<T> items, int? k = null)
    {
        if (k == null) k = items.Count();
        if (k == 0) yield return Enumerable.Empty<T>();
        else
        {
            var i = 0;
            foreach (var x in items)
            {
                var xs = items.Where((_, index) => i != index);
                foreach (var c in Perm(xs, k - 1))
                    yield return c.Before(x);
                i++;
            }
        }
    }
    public static IEnumerable<T> Before<T>(this IEnumerable<T> items, T first)
    {
        yield return first;
        foreach (var i in items) yield return i;
    }
}

public class Hello
{
    public static void Main()
    {
        var n = int.Parse(Console.ReadLine().Trim());
        var p = Console.ReadLine().Trim().Replace(" ", "");
        var q = Console.ReadLine().Trim().Replace(" ", "");
        getAns(n, p, q);
    }
    static void getAns(int n, string p, string q)
    {
        var alist = new List<string>();
        var a = Enumerable.Range(1, n).Perm();
        foreach (var x in a)
        {
            var t = "";
            foreach (var y in x) t += y.ToString();
            alist.Add(t);
        }
        alist.Sort();
        Console.WriteLine(Abs(alist.FindIndex(x => x == p) - alist.FindIndex(x => x == q)));
    }
}