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 ConsoleApp15
{
    class Class292
    {
        static int N;
        static void Main()
        {
            N = int.Parse(Console.ReadLine());
            var P = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            var Q = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            Console.WriteLine(Math.Abs(Order(P)-Order(Q)));
        }

        static int Order(int[] A)
        {
            var e = Enumerable.Range(1, N).ToList();
            int sum = 0;
            for(int i = 1; i <= N; i++)
            {
                int count = 0;
                foreach(int j in e)
                {
                    if (A[i-1] == j)
                    {
                        sum +=count*Bikkuri(N-i);
                        break;
                    }
                    count++;
                }
                e.Remove(A[i-1]);
            }
            return sum;
        }
        static int Bikkuri(int n)
        {
            int ans = 1;
            for (int i = 1; i <= n; i++)
                ans *= i;
            return ans;
        }
    }
}