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 abc150_c
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = GetInt();
            var P = string.Join("", GetStrList());
            var Q = string.Join("", GetStrList());

            var p = Permutation.Enumerate<int>(Enumerable.Range(1, N), N, false).Select(x => string.Join("", x)).OrderBy(x => x).ToList();

            Console.WriteLine(Math.Abs(p.IndexOf(P) - p.IndexOf(Q)));
        }

        public static string GetStr() => Console.ReadLine();
        public static int GetInt() => int.Parse(Console.ReadLine());
        public static long GetLong() => long.Parse(Console.ReadLine());
        public static double GetDouble() => double.Parse(Console.ReadLine());
        public static decimal GetDecimal() => decimal.Parse(Console.ReadLine());

        public static List<string> GetStrList() => Console.ReadLine().Split(' ').ToList();
        public static List<int> GetIntList() => Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToList();
        public static List<long> GetLongList() => Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToList();
        public static List<double> GetDoubleList() => Console.ReadLine().Split(' ').Select(x => double.Parse(x)).ToList();
        public static List<decimal> GetDecimalList() => Console.ReadLine().Split(' ').Select(x => decimal.Parse(x)).ToList();

        /// <summary>
        /// 順列生成クラス
        /// </summary>
        public static class Permutation
        {
            /// <summary>
            /// 順列生成
            /// </summary>
            /// <typeparam name="T"></typeparam>
            /// <param name="items">選択対象</param>
            /// <param name="k">選択数</param>
            /// <param name="withRepetition">重複を許すかフラグ</param>
            /// <returns></returns>
            public static IEnumerable<T[]> Enumerate<T>(IEnumerable<T> items, int k, bool withRepetition)
            {
                if (k == 1)
                {
                    foreach (var item in items)
                    {
                        yield return new T[] { item };
                    }
                    yield break;
                }
                foreach (var item in items)
                {
                    var leftside = new T[] { item };
                    var unused = withRepetition ? items : items.Except(leftside);
                    foreach (var rightside in Enumerate(unused, k - 1, withRepetition))
                    {
                        yield return leftside.Concat(rightside).ToArray();
                    }
                }
            }

            internal static IEnumerable<object[]> Enumerate(string v1, int v2)
            {
                throw new NotImplementedException();
            }
        }

    }
}