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.Linq;

public class AtCoder_150_C
{
    public static void Main()
    {
        //var exStdIn = new System.IO.StreamReader( "input.txt" );
        //System.Console.SetIn( exStdIn );

        int num = int.Parse(Console.ReadLine());
        int[] p = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
        int[] q = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();

        int pIndex = 0;
        int qIndex = 0;

        bool[] pChecked = new bool[num + 1];
        bool[] qChecked = new bool[num + 1];

        for (int i = 0; i < num; i++)
        {
            pChecked[p[i]] = true;
            int pCurrentIndex = 0;
            for (int j = 1; j < p[i]; j++)
            {
                if (pChecked[j] == false) pCurrentIndex++;
            }
            int pGap = 1;
            for (int j = 1; j < num - i; j++)
            {
                pGap *= j;
            }
            pIndex += pGap * pCurrentIndex;

            qChecked[q[i]] = true;
            int qCurrentIndex = 0;
            for (int j = 1; j < q[i]; j++)
            {
                if (qChecked[j] == false) qCurrentIndex++;
            }
            int qGap = 1;
            for (int j = 1; j < num - i; j++)
            {
                qGap *= j;
            }
            qIndex += qGap * qCurrentIndex;
        }

        Console.WriteLine(Math.Abs(pIndex - qIndex));
    }
}