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.Text;
using System.Text.RegularExpressions;

namespace AtCoder
{
	public class ABC
	{
		static readonly int mod = 1000000007;  // 10^9+7

		static void Main(string[] args)
		{
			Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });


			int n = int.Parse(Console.ReadLine());
			//string s = Console.ReadLine();
			//long x = long.Parse(Console.ReadLine());
			int[] p = Console.ReadLine().Split().Select(int.Parse).ToArray();
			int[] q = Console.ReadLine().Split().Select(int.Parse).ToArray();
			//long[] vs = Console.ReadLine().Split().Select(long.Parse).ToArray();
			int st = 0, en = 0;
			for (int i = 1, j = 1; i <= n; i++, j *= 10) {
				st = st * 10 + i;
				en = en + i * j;
				px = px * 10 + p[i - 1];
				qx = qx * 10 + q[i - 1];
			}
			saiki(n, 0, 0, new bool[n]);
			Console.WriteLine(Math.Abs(a - b));


			Console.Out.Flush();
		}

		static int px = 0;
		static int qx = 0;
		static int a = 0;
		static int b = 0;

		static int saiki(int n, int m, int c, bool[] f)
		{
			if (n == 0) {
				c++;
				if (px == m) { a = c; }
				if (qx == m) { b = c; }
				//System.Diagnostics.Debug.WriteLine($"{c} {m}");
				return c;
			}
			for (int i = 1; i <= f.Length; i++) {
				if (!f[i - 1]) {
					f[i - 1] = true;
					c = saiki(n - 1, m * 10 + i, c, f);
					f[i - 1] = false;
				}
			}
			return c;
		}

	}
}