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.Numerics;
using System.Text;
using static System.Console;
using static System.Math;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = ReadInt();
            var p = int.Parse(Read().Replace(" ",""));
            var q = int.Parse(Read().Replace(" ",""));

            var x = Enumerable.Range(1, n).ToArray();
            var all = AllPermutation(x);

            var list = new List<int>();
            foreach (var item in all)
            {
                list.Add(int.Parse(string.Join("", item)));
            }
            var p_num = list.BinarySearch(p);
            var q_num = list.BinarySearch(q);

            WriteLine(Abs(p_num - q_num));
        }

        static List<T[]> AllPermutation<T>(params T[] array) where T : IComparable
        {
            var a = new List<T>(array).ToArray();
            var res = new List<T[]>();
            res.Add(new List<T>(a).ToArray());
            var n = a.Length;
            var next = true;
            while (next)
            {
                next = false;

                // 1
                int i;
                for (i = n - 2; i >= 0; i--)
                {
                    if (a[i].CompareTo(a[i + 1]) < 0) break;
                }
                // 2
                if (i < 0) break;

                // 3
                var j = n;
                do
                {
                    j--;
                } while (a[i].CompareTo(a[j]) > 0);

                if (a[i].CompareTo(a[j]) < 0)
                {
                    // 4
                    var tmp = a[i];
                    a[i] = a[j];
                    a[j] = tmp;
                    Array.Reverse(a, i + 1, n - i - 1);
                    res.Add(new List<T>(a).ToArray());
                    next = true;
                }
            }
            return res;
        }
        private static string Read() { return ReadLine(); }
        private static string[] Reads() { return (Read().Split()); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}