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;
using System.Diagnostics;
using System.IO;
using System.Linq;

namespace MyProject
{
    class Program
    {
        static void Main(string[] args)
        {
#if Local
            var sw = new Stopwatch();
            sw.Start();
            Console.SetIn(new StreamReader("input.in"));
#endif

            var solver = new Solver();
            solver.Solve();
#if Local
            Console.WriteLine($"{sw.ElapsedMilliseconds}ms");
#endif
        }
    }

    class Solver
    {
        public void Solve()
        {
            var N = int.Parse(Console.ReadLine());
            var P = Console.ReadLine().Replace(" ", "");
            var Q = Console.ReadLine().Replace(" ", "");

            var list = Permutation.Enumerate(Enumerable.Range(1, N)).Select(elem1 => new string(elem1.Select(elem2 => elem2.ToString()[0]).ToArray())).ToList();
            var orderP = list.IndexOf(P) + 1;
            var orderQ = list.IndexOf(Q) + 1;
            var answer  = Math.Abs(orderP - orderQ);

            Console.WriteLine(answer);
        }
    }

    public static class Permutation {
        public static IEnumerable<T[]> Enumerate<T>(IEnumerable<T> items)
        {
            if (items.Count() == 1)
            {
                yield return new T[] { items.First() };
                yield break;
            }
            foreach (var item in items)
            {
                var leftside = new T[] { item };
                var unused = items.Except(leftside);
                foreach (var rightside in Enumerate(unused))
                {
                    yield return leftside.Concat(rightside).ToArray();
                }
            }
        }
    }
}