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.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder_solve
{
    class Program
    {
        public const ulong mod = 1000000007;

        static void Main(string[] args)
        {
            var n = Input();
            var p = Input3();
            var q = Input3();
            var a = 0;
            var b = 0;
            int cnt = 1;
            var array = new int[n];
            for(int i = 1; i <= n; i++)
            {
                array[i - 1] = i;
            }
            
           foreach( var item in GetAllPermutation(array))
            {
                for(int j = 0; j < n; j++)
                {
                    if (p[j] != item[j]) break;
                    if (j == n - 1) a = cnt;
                }
                for (int k = 0; k < n; k++)
                {
                    if (q[k] != item[k]) break;
                    if (k == n - 1) b = cnt;
                }


                cnt++;
            }

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



            

        }

        static public long Input()
        {
            return long.Parse(Console.ReadLine());
        }

        static public string[] Input2()
        {
            return Console.ReadLine().Split();
        }
        
        static public long[] Input3()
        {
            string[] data = Console.ReadLine().Split();
            long[] res = new long[data.LongLength];
            for(long i = 0; i < data.LongLength; i++)
            {
                res[i] = long.Parse(data[i]);
            }
            return res;
        }
        public static long Choose(long n, long a)
        {
            long x = 1;
            long y = 1;
            for (long i = 0; i < a; i++)
            {
                x *= n - i;
                y *= i + 1;
            }
            return x / y;
        }

        public static long Gcd(long a, long b)
        {
            long x = Math.Max(a, b);
            long y = Math.Min(a, b);
            if (x % y == 0) return y;
            else return Gcd(y, x % y);
        }

        static List<int[]> GetAllPermutation(int N)
        {
            var res = new List<int[]>();
            var array = Enumerable.Range(0, N).ToArray();
            do
            {
                var copy = new int[N];
                array.CopyTo(copy, 0);
                res.Add(copy);
            } while (NextPermutation(array));

            return res;
        }

        static bool NextPermutation(int[] array)
        {
            var size = array.Length;
            var ok = false;

            //array[i]<array[i+1]を満たす最大のiを求める
            int i = size - 2;
            for (; 0 <= i; i--)
            {
                if (array[i] < array[i + 1])
                {
                    ok = true;
                    break;
                }
            }

            //全ての要素が降順の場合、NextPermutationは存在しない
            if (ok == false) return false;

            //array[i]<array[j]を満たす最大のjを求める
            int j = size - 1;
            for (; ; j--)
            {
                if (array[i] < array[j]) break;
            }

            //iとjの要素をswapする
            var tmp = array[i];
            array[i] = array[j];
            array[j] = tmp;

            //i以降の要素を反転させる
            Array.Reverse(array, i + 1, size - (i + 1));

            return true;
        }

        //配列arrayを引数として渡し,辞書順がarray以上の順列をすべて返す
        static List<int[]> GetAllPermutation(int[] array)
        {
            var size = array.Length;
            var res = new List<int[]>();
            do
            {
                var copy = new int[size];
                array.CopyTo(copy, 0);
                res.Add(copy);
            } while (NextPermutation(array));

            return res;
        }



    }
}