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;
class Program
{
	static void Main(string[] args)
	{
		int N = int.Parse(Console.ReadLine());
		string[] str = Console.ReadLine().Split();
		string[] str2 = Console.ReadLine().Split();
		int[]A = new int[N];
		int[]B = new int[N];
		for(var i=0;i<N;i++){
			A[i] = int.Parse(str[i]);
			B[i] = int.Parse(str2[i]);
		}
		int a1 = 0;
		int ac = 1;
		for(var i=N-2;i>=0;i--){
			int ct = A[i];
			for(var j=i-1;j>=0;j--){
				if(A[j]<A[i]){
					ct--;
				}
			}
			a1 += ct * ac;
			ac *= N-i;
		}
		int b1 = 0;
		ac = 1;
		for(var i=N-2;i>=0;i--){
			int ct = B[i];
			for(var j=i-1;j>=0;j--){
				if(B[j]<B[i]){
					ct--;
				}
			}
			b1 += ct * ac;
			ac *= N-i;
		}
		Console.WriteLine(Math.Abs(a1-b1));
	}
}