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;

namespace AC
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = ReadInt();
            var P = ReadArrayInt();
            var Q = ReadArrayInt();

            var PN = Factorial(N);
            var QN = Factorial(N);

            var Pst = new List<int>();
            for (int i = 1; i <= N; i++) Pst.Add(i);
            Pst.Reverse();
            var Qst = new List<int>(Pst);
            var Pm = 0L;
            var Qm = 0L;

            for (int i = 0; i < N - 1; i++)
            {
                var chk = P[i];
                var idx = 0;
                for (int j = 0; j < Pst.Count(); j++)
                {
                    if (Pst[j] == chk)
                    {
                        idx = j;
                        break;
                    }
                }
                PN /= Pst.Count();
                Pm += PN * (idx + 1);
                Pst.RemoveAt(idx);
            }
            for (int i = 0; i < N - 1; i++)
            {
                var chk = Q[i];
                var idx = 0;
                for (int j = 0; j < Qst.Count(); j++)
                {
                    if (Qst[j] == chk)
                    {
                        idx = j;
                        break;
                    }
                }
                QN /= Qst.Count();
                Qm += QN * (idx + 1);
                Qst.RemoveAt(idx);
            }

            Console.WriteLine(Math.Abs(Pm - Qm));
            Console.ReadKey();
        }

        static long Factorial(long num) { if (num == 0) return 1L; return num * Factorial(num - 1); }

        static string Read() { return Console.ReadLine(); }
        static int ReadInt() { return int.Parse(Read()); }
        static long ReadLong() { return long.Parse(Read()); }
        static int[] ReadArrayInt() { return Read().Split(' ').Select(s => int.Parse(s)).ToArray(); }
        static long[] ReadArrayLong() { return Read().Split(' ').Select(s => long.Parse(s)).ToArray(); }
    }
}