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.Linq;
using System.Collections.Generic;

namespace Algorithm
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var P = string.Join("", Console.ReadLine().Split().Select(int.Parse).ToArray());
            var Q = string.Join("", Console.ReadLine().Split().Select(int.Parse).ToArray());

            var array = Enumerable.Range(1, N).ToArray();
            int a = 0, b = 0, count = 0;
            do
            {
                count++;
                if (P == string.Join("", array)) a = count;
                if (Q == string.Join("", array)) b = count;
            } while (NextPermutation(array)) ;

            Console.WriteLine(Math.Abs(a - b));
        }

        public static void Swap<T>(ref T one, ref T two)
        {
            var temp = one;
            one = two;
            two = temp;
        }

        public static bool NextPermutation<T>(T[] array, int index, int length, Comparison<T> comp)
        {
            if (length <= 1) return false;
            for (int i = length - 1; i > 0; i--)
            {
                int k = i - 1;
                if (comp(array[k], array[i]) < 0)
                {
                    int j = Array.FindLastIndex(array, delegate (T x) { return comp(array[k], x) < 0; });
                    Swap(ref array[k], ref array[j]);
                    Array.Reverse(array, i, length - i);
                    return true;
                }
            }
            Array.Reverse(array, index, length);
            return false;
        }
        public static bool NextPermutation<T>(T[] array) where T : IComparable
        {
            return NextPermutation(array, 0, array.Length, Comparer<T>.Default.Compare);
        }
    }
}