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 AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            //[summary]C - Count Order
            int N = int.Parse(Console.ReadLine());
            var numbers = Enumerable.Range(1, N).ToList();

            var lib = new Library.Combination();
            var combis = lib.AllCombinations<int>(numbers, N, true);

            var dic = new Dictionary<string, int>();
            int i = 1;

            foreach(var c in combis)
            {
                var s = String.Join(" ", c);
                dic.Add(s, i);
                i++;
            }

            var P = Console.ReadLine();
            var Q = Console.ReadLine();

            int ans = Math.Abs(dic[P] - dic[Q]);
            Console.WriteLine(ans);
        }
    }
}

namespace Library
{
    class Combination
    {
        public IEnumerable<List<T>> AllCombinations<T>(List<T> source, int n,
                                                       bool isAllowDupication = false)
        {
            //[summary]異なる要素から、n個を選ぶ組み合わせを列挙する
            //"isAllowDupication"を"true"にすると、重複を許可する
            //(重複を許可して、nを要素数と同じにすると、順列を列挙する)

            if (n == 1)
            {
                foreach (var s in source)
                {
                    yield return new List<T> { s };
                }

                yield break;
            }
            else
            {
                for (int i = 0; i < source.Count; i++)
                {
                    List<T> clone;

                    if (isAllowDupication)
                    {
                        //重複を許可する場合は、その要素のみを削除
                        clone = new List<T>(source);
                        clone.RemoveAt(i);
                    }
                    else
                    {
                        //重複を許可しない場合は、自分よりも前の要素はすべて削除
                        clone = new List<T>(source.Skip(i + 1));
                    }

                    //再帰処理
                    var items = AllCombinations(clone, n - 1, isAllowDupication);

                    foreach (var item in items)
                    {
                        item.Insert(0, source[i]);
                        yield return item;
                    }
                }
            }
        }

        public int CountCombinations(int n, int r)
        {
            //[summary]組み合わせの数 nCr を計算
            //(n種類の中から、r種類を選ぶ)
            int ans = 1;

            for (int i = 1; i <= r; i++)
            {
                ans = ans * (n - i + 1) / i;
            }

            return ans;
        }
    }
}