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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Globalization;
using System.Linq;
using System.Runtime.InteropServices.ComTypes;
using System.Text;
using System.Threading;

class Program
{
    static void Main(string[] args)
    {
        var a = int.Parse(Console.ReadLine());
        string one = Console.ReadLine().Replace(" ", "");
        string two = Console.ReadLine().Replace(" ", "");
        int count = 0;
        int oneVal = 0;
        int twoVal = 0;
        List<int> list = new List<int>();
        for (int i = 1; i <= a; i++) list.Add(i);
        var perm = new Permutation();
        foreach (var n in perm.Enumerate(list))
        {
            string s = "";
            foreach (var x in n) {
                s += x;
            }
            count++;
            if (s.Equals(one)) oneVal = count;
            if (s.Equals(two)) twoVal = count;
        }
        Console.WriteLine(Math.Abs(oneVal - twoVal));
    }

    public class Permutation
    {
        public IEnumerable<T[]> Enumerate<T>(IEnumerable<T> items)
        {
            return _GetPermutations<T>(new List<T>(), items.ToList());
        }

        private IEnumerable<T[]> _GetPermutations<T>(IEnumerable<T> perm, IEnumerable<T> items)
        {
            if (items.Count() == 0)
            {
                yield return perm.ToArray();
            }
            else
            {
                foreach (var item in items)
                {
                    var result = _GetPermutations<T>(perm.Concat(new T[] { item }),
                                                        items.Where(x => x.Equals(item) == false)
                                    );
                    foreach (var xs in result)
                        yield return xs.ToArray();
                }
            }
        }
    }

}