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.Linq;
using System.Text;
using System.Text.RegularExpressions;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var d = new int[N];
            for (var i = 1; i <= N; i++)
            {
                d[i-1] = i;
            }

            var jyunretsus = GetPermutation(d);

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


            var a = 0;
            var b = 0;
            var cnt = 0;

            foreach(int[] jyunretsu in jyunretsus)
            {
                if (a == 0)
                {
                    bool isEqual = true;

                    for (int i = 0; i < jyunretsu.Length; i++)
                    {
                        if (!jyunretsu[i].Equals(p[i]))
                        {
                            isEqual = false;
                            break;
                        }
                    }

                    if (isEqual) a = cnt + 1;
                }

                if(b == 0)
                {
                    bool isEqual = true;

                    for (int i = 0; i < jyunretsu.Length; i++)
                    {
                        if (!jyunretsu[i].Equals(q[i]))
                        {
                            isEqual = false;
                            break;
                        }
                    }

                    if (isEqual) b = cnt + 1;
                }


                cnt++;
            }

            Console.WriteLine(Math.Abs(a - b));
        }

        public static IEnumerable<T[]> GetPermutation<T>(IEnumerable<T> collection)
        {
            // 未確定要素が一個のみ
            if (collection.Count() == 1)
            {
                yield return new T[] { collection.First() };
            }

            foreach (var item in collection)
            {
                var selected = new T[] { item };
                var unused = collection.Except(selected);

                // 確定した要素以外の組み合わせを再帰で取り出し連結
                foreach (var rightside in GetPermutation(unused))
                {
                    yield return selected.Concat(rightside).ToArray();
                }
            }
        }
    }
}