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 ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            int[] p = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
            int[] q = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
            int[] arr = new int[n];
            for (int i = 0; i < n; i++)
            {
                arr[i] = i + 1;
            }

            var perms = GeneratePermutation<int>(arr);
            
            int pIndex = perms.FindIndex(e => {
                for (int i = 0; i < e.Length; i++)
                {
                    if (e[i] != p[i])
                    {
                        return false;
                    }
                }
                return true;
            }) + 1;
            int qIndex = perms.FindIndex(e => {
                for (int i = 0; i < e.Length; i++)
                {
                    if (e[i] != q[i])
                    {
                        return false;
                    }
                }
                return true;
            }) + 1;
            Console.WriteLine(Math.Abs(pIndex - qIndex));
        
        }

        static List<T[]> GeneratePermutation<T>(params T[] array) where T : IComparable
        {
            var a = new List<T>(array).ToArray();
            var res = new List<T[]>();
            res.Add(new List<T>(a).ToArray());
            var n = a.Length;
            var next = true;
            while (next)
            {
                next = false;

                int i;
                for (i = n - 2; i >= 0; i--)
                {
                    if (a[i].CompareTo(a[i + 1]) < 0)
                        break;
                }
                if (i < 0)
                    break;

                var j = n;
                do
                {
                    j--;
                } while (a[i].CompareTo(a[j]) > 0);

                if (a[i].CompareTo(a[j]) < 0)
                {
                    var tmp = a[i];
                    a[i] = a[j];
                    a[j] = tmp;
                    Array.Reverse(a, i + 1, n - i - 1);
                    res.Add(new List<T>(a).ToArray());
                    next = true;
                }
            }
            return res;
        }
    }
}