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

namespace AtCoder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            new Program().Solve(new ConsoleInput(Console.In, ' '));
        }

        public void Solve(ConsoleInput cin)
        {
            int N = cin.ReadInt;
            int[] P = cin.ReadIntArray(N);
            int[] Q = cin.ReadIntArray(N);
            var Nlist = AllPermutation(Enumerable.Range(1, N).ToArray());
            int[][] Narray=Nlist.ToArray();
            int A = 0;
            int B = 0;
            for(int i=0;i<Factorial(N);i++)
            {
                bool flag = false;
                int[] arr = Narray[i];
                for(int j=0;j<N;j++)
                {
                    if (arr[j] != P[j])
                    {
                        flag = true;
                    }
                    
                }
                if (flag == false)
                {
                    A = i + 1;
                }
            }
            for (int i = 0; i < Factorial(N); i++)
            {
                bool flag = false;
                int[] arr = Narray[i];
                for (int j = 0; j < N; j++)
                {
                    if (arr[j] != Q[j])
                    {
                        flag = true;
                    }

                }
                if (flag == false)
                {
                    B = i + 1;
                }
            }
            WriteLine(Abs(A - B));

        }

        int Factorial(int n)
        {
            if (n == 0)
                return 1;
            return n * Factorial(n - 1);
        }


        static List<T[]> AllPermutation<T>(params T[] array) where T : IComparable
        {
            var a = new List<T>(array).ToArray();
            var res = new List<T[]>();
            res.Add(new List<T>(a).ToArray());
            var n = a.Length;
            var next = true;
            while (next)
            {
                next = false;

                // 1
                int i;
                for (i = n - 2; i >= 0; i--)
                {
                    if (a[i].CompareTo(a[i + 1]) < 0) break;
                }
                // 2
                if (i < 0) break;

                // 3
                var j = n;
                do
                {
                    j--;
                } while (a[i].CompareTo(a[j]) > 0);

                if (a[i].CompareTo(a[j]) < 0)
                {
                    // 4
                    var tmp = a[i];
                    a[i] = a[j];
                    a[j] = tmp;
                    Array.Reverse(a, i + 1, n - i - 1);
                    res.Add(new List<T>(a).ToArray());
                    next = true;
                }
            }
            return res;
        }

    }
            


    public class ConsoleInput
    {
        private readonly System.IO.TextReader _stream;
        private char _separator = ' ';
        private Queue<string> inputStream;
        public ConsoleInput(System.IO.TextReader stream, char separator = ' ')
        {
            this._separator = separator;
            this._stream = stream;
            inputStream = new Queue<string>();
        }
        public string Read
        {
            get
            {
                if (inputStream.Count != 0) return inputStream.Dequeue();
                string[] tmp = _stream.ReadLine().Split(_separator);
                for (int i = 0; i < tmp.Length; ++i)
                    inputStream.Enqueue(tmp[i]);
                return inputStream.Dequeue();
            }
        }
        public string ReadLine { get { return _stream.ReadLine(); } }
        public int ReadInt { get { return int.Parse(Read); } }
        public long ReadLong { get { return long.Parse(Read); } }
        public double ReadDouble { get { return double.Parse(Read); } }
        public string[] ReadStrArray(long N) { var ret = new string[N]; for (long i = 0; i < N; ++i) ret[i] = Read; return ret; }
        public int[] ReadIntArray(long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt; return ret; }
        public long[] ReadLongArray(long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong; return ret; }
        public double[] ReadDoubleArray(long N) { var ret = new double[N]; for (long i = 0; i < N; ++i) ret[i] = ReadDouble; return ret; }
    }
}