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 ABC150C
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());

            int[] P = ReadInt();
            int[] Q = ReadInt();

            List<int> master = new List<int>();
            for (int i = 0; i < N; i++)
            {
                master.Add(i + 1);
            }

            int countP = int.MaxValue;
            int countQ = int.MaxValue;
            int count = 1;
            foreach (var item in GetPermutation(master))
            {
                bool okp = true;
                bool okq = true;
                for (int i = 0; i < N; i++)
                {
                    if (item[i] != P[i]) { okp = false; }
                    if (item[i] != Q[i]) { okq = false;}
                }

                if (okp && countP > count) countP = count;
                if (okq && countQ > count) countQ = count;
                count++;
            }

            Console.WriteLine(Math.Abs(countP - countQ));
            Console.ReadKey();
        }

        /// <summary>
        /// 順列組み合わせ
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <param name="collection"></param>
        /// <returns></returns>
        public static IEnumerable<T[]> GetPermutation<T>(IEnumerable<T> collection)
        {
            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);

                foreach (var rightside in GetPermutation(unused))
                {
                    yield return selected.Concat(rightside).ToArray();
                }
            }
        }

        static int[] ReadInt()
        {
            int[] ret = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return ret;
        }
        static long[] ReadLong()
        {
            long[] ret = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return ret;
        }
    }
}