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 ConsoleApp
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var P = int.Parse(Console.ReadLine().Split().Aggregate((s, t) => s += t));
            var Q = int.Parse(Console.ReadLine().Split().Aggregate((s, t) => s += t));

            var baseArray = Enumerable.Range(1, N).ToArray();
            var list = new List<int>();
            SetList(0, N, baseArray, new int[N], list);
            var dict = list.Select((s, i) => new { Key = s, Value = i }).ToDictionary(s => s.Key, s => s.Value);

            Console.WriteLine(Math.Abs(dict[P] - dict[Q]));
        }

        static void SetList(int i, int N, int[] baseArray, int[] array, List<int> list)
        {
            if (i == N)
            {
                list.Add(int.Parse(array.Select(s => s.ToString()).Aggregate((s, t) => s += t)));
                return;
            }

            foreach (var j in baseArray.Except(array))
            {
                var copy = Copy(array);
                copy[i] = j;
                SetList(i + 1, N, baseArray, copy, list);
            }
        }

        static int[] Copy(int[] x)
        {
            var ret = new int[x.Length];
            Array.Copy(x, ret, x.Length);
            return ret;
        }
    }
}