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;

class Program
{
    static void Main()
    {
        int N = int.Parse(Console.ReadLine());
        string[] P = Console.ReadLine().Split(' ');
        string[] Q = Console.ReadLine().Split(' ');
        int pNum = 0;
        int qNum = 0;
        for(int i = 0; i < N - 1; i++)
        {
            int p = int.Parse(P[i]);
            int q = int.Parse(Q[i]);

            pNum += kaijo(N - i - 1) * (p - 1);
            qNum += kaijo(N - i - 1) * (q - 1);


            for (int j = i + 1; j < N; j++)
            {
                int ppp = int.Parse(P[j]);
                int qqq = int.Parse(Q[j]);
                if (p < ppp)
                {
                    P[j] = (ppp - 1).ToString();
                }
                if (q < qqq)
                {
                    Q[j] = (qqq - 1).ToString();
                }
            }
        }

        Console.WriteLine(Math.Abs(pNum - qNum));
    }

    static int kaijo(int a)
    {
        int ret = 1;
        while (a >= 1)
        {
            ret *= a;
            a--;
        }
        return ret;
    }
}