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;

class C
{
	static int[] Read() => Console.ReadLine().Split().Select(int.Parse).ToArray();
	static void Main()
	{
		var n = int.Parse(Console.ReadLine());
		var a = Read();
		var b = Read();

		int i = 0, j = 0, c = 0;
		new Perm<int>().Find(Enumerable.Range(1, n).ToArray(), n, p =>
		{
			++c;
			if (p.SequenceEqual(a)) i = c;
			if (p.SequenceEqual(b)) j = c;
		});
		Console.WriteLine(Math.Abs(i - j));
	}
}

class Perm<T>
{
	T[] v, p;
	bool[] u;
	Action<T[]> act;

	public void Find(T[] _v, int r, Action<T[]> _act)
	{
		v = _v; p = new T[r]; u = new bool[v.Length]; act = _act;
		if (p.Length > 0) Dfs(0); else act(p);
	}

	void Dfs(int i)
	{
		for (int j = 0; j < v.Length; ++j)
		{
			if (u[j]) continue;
			p[i] = v[j];
			u[j] = true;
			if (i + 1 < p.Length) Dfs(i + 1); else act(p);
			u[j] = false;
		}
	}
}