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.Text;
using System.Threading.Tasks;

namespace ABC150
{
    class C
    {
        static void Main(string[] args)
        {
            int ans = 0;
            int a = 0, b = 0;
            int n = int.Parse(Console.ReadLine());
            int[] p = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int[] q = Console.ReadLine().Split().Select(int.Parse).ToArray();
            for (int i = 0; i < n; i++)
            {
                a += (p[0]-1)*Fanc2(n-i-1);
                p = Func1(p);
            }
            for (int i = 0; i < n; i++)
            {
                b += (q[0] - 1) * Fanc2(n-i-1);
                q = Func1(q);
            }
            Console.WriteLine(a > b ? a - b : b - a);
        }
        static int[] Func1(int[] a)
        {
            if (a.Length == 1) { return new int[1]{ 1 }; }
            int h = a[0];
            int[] ret = new int[a.Length - 1];
            for (int i = 0; i < a.Length-1; i++)
            {
                ret[i] = a[i + 1] > h ? a[i + 1] - 1 : a[i + 1];
            }
            return ret;
        }
        static int Fanc2(int n)
        {
            if (n == 0) { return 1; }
            return Fanc2(n - 1) * n;
        }
    }
}