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 ABC150C
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            var p = Console.ReadLine().Replace(" ", "");
            var q = Console.ReadLine().Replace(" ", "");

            var num = new int[] { 1, 2, 3, 4, 5, 6, 7, 8 }.Take(n).ToArray();

            var pp = Get(num, 0, p, "");
            var qq = Get(num, 0, q, "");

            Console.WriteLine(Math.Abs(pp - qq));
        }

        static int Get(int[] num, int cnt, string target, string now)
        {
            if (!num.Any())
            {
                if (target == now)
                {
                    return -(cnt + 1);
                }
                else
                {
                    return cnt + 1;
                }
            }

            for (int i = 0; i < num.Length; i++)
            {
                cnt = Get(num.Where(x => x != num[i]).ToArray(), cnt, target, now + num[i]);
                if (cnt < 0) break;
            }

            return cnt;
        }
    }
}