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;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Threading.Tasks;

namespace AtCorder
{
	public class Program
	{
		static void Main(string[] args)
		{
			var cin = new Scanner2();
			int n = cin.Int();
			int[] p = cin.ArrayInt(n);
			int[] q = cin.ArrayInt(n);

			int[] ar = new int[n];
			for (int i = 0; i < n; i++) {
				ar[i] = i + 1;
			}

			var all = Permutation<int>.All(ar).ToArray();
			int m = all.Count();

			int pi = -1;
			int qi = -1;
			for (int i = 0; i < m; i++) {
				if (pi < 0){
					bool ok = true;
					for (int j = 0; j < n; j++) {
						if (p[j] != all[i][j]) {
							ok = false;
							break;
						}
					}

					if (ok) {
						pi = i;
					}
				}

				if (qi < 0) {
					bool ok = true;
					for (int j = 0; j < n; j++) {
						if (q[j] != all[i][j]) {
							ok = false;
							break;
						}
					}

					if (ok) {
						qi = i;
					}
				}
			}

			Console.WriteLine(Math.Abs(pi - qi));
		}
	}

	static class Permutation<T>
	{
		private static void Search(List<T[]> perms, Stack<T> stack, T[] a)
		{
			int N = a.Length;
			if (N == 0) {
				perms.Add(stack.Reverse().ToArray());
			} else {
				var b = new T[N - 1];
				Array.Copy(a, 1, b, 0, N - 1);
				for (int i = 0; i < a.Length; ++i) {
					stack.Push(a[i]);
					Search(perms, stack, b);
					if (i < b.Length) { b[i] = a[i]; }
					stack.Pop();
				}
			}
		}
		public static IEnumerable<T[]> All(IEnumerable<T> src)
		{
			var perms = new List<T[]>();
			Search(perms, new Stack<T>(), src.ToArray());
			return perms;
		}
	}

	public class Scanner2
	{
		private readonly char[] delimiter_ = new char[] { ' ' };
		private readonly string filePath_;
		private string[] buf_;
		private int index_;
		Func<string> reader_;

		public Scanner2(string file = "")
		{
			if (string.IsNullOrWhiteSpace(file)) {
				reader_ = Console.ReadLine;
			} else {
				filePath_ = file;
				var fs = new StreamReader(file);
				reader_ = fs.ReadLine;
			}
			buf_ = new string[0];
			index_ = 0;
		}

		public string Next()
		{
			if (index_ < buf_.Length) {
				return buf_[index_++];
			}

			string st = reader_();
			while (st == "") {
				st = reader_();
			}

			buf_ = st.Split(delimiter_, StringSplitOptions.RemoveEmptyEntries);
			if (buf_.Length == 0) {
				return Next();
			}

			index_ = 0;
			return buf_[index_++];
		}

		public int Int() => int.Parse(Next());
		public long Long() => long.Parse(Next());
		public double Double() => double.Parse(Next());

		public int[] ArrayInt(int N, int add = 0)
		{
			int[] Array = new int[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Int() + add;
			}
			return Array;
		}

		public long[] ArrayLong(int N, long add = 0)
		{
			long[] Array = new long[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Long() + add;
			}
			return Array;
		}

		public double[] ArrayDouble(int N, double add = 0)
		{
			double[] Array = new double[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Double() + add;
			}
			return Array;
		}

		public void Save(string text)
		{
			if (string.IsNullOrWhiteSpace(filePath_)) {
				return;
			}

			File.WriteAllText(filePath_ + "_output.txt", text);
		}
	}
}