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.Diagnostics;
using System.Linq;

internal static class CR
{
    public static string Get() { return Console.ReadLine(); }
    public static IEnumerable<string> GetTexts() { return Console.ReadLine().Split(' '); }
    public static int GetInteger() { return int.Parse(Console.ReadLine()); }
    public static IEnumerable<int> GetIntegers() { return Console.ReadLine().Split(' ').Select(x => int.Parse(x)); }
}

namespace AtCoderBeginnerContest
{
    internal class Program
    {
        public static int N { get; private set; }
        public static List<int> P { get; private set; }
        public static List<int> Q { get; private set; }

        private static void Main() { var r = GetResult(); Debug.WriteLine(r); Console.WriteLine(r); }

        private static object GetResult()
        {
            N = CR.GetInteger();
            P = CR.GetIntegers().ToList();
            Q = CR.GetIntegers().ToList();

            var a = GetOrder(N, P);
            var b = GetOrder(N, Q);

            return Math.Abs(a - b);
        }

        private static int GetOrder(int n, List<int> p)
        {
            var sum = 0;
            for (int i = 0; i < n; i++)
            {
                var x = GetX(p, i);
                sum += x * Factorial(n - (i + 1));
            }
            return sum;
        }

        private static int GetX(List<int> p, int i)
        {
            var main = p[i];
            var before = Enumerable.Range(0, i).Select(x => p[x]).ToList();
            var after = i == N - 1
                ? new List<int>()
                : Enumerable.Range(i + 1, N - (i + 1)).Select(j => p[j]).ToList();

            return after.Count(x => x < main && !before.Contains(x));
        }

        public static int Factorial(int n)
        {
            if (n == 0) return 1;
            return n * Factorial(n - 1);
        }
    }
}