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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {

	static int[] fact = new int[9];


	public static void main(String[] args) {
		fact[1] = 1;
		for(int i = 2; i <= 8; i++)
			fact[i] = fact[i-1] * i;

		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] p = new int[n];
		for(int i = 0; i < n; i++)
			p[i] = sc.nextInt();

		int[] q = new int[n];
		for(int i = 0; i < n; i++)
			q[i] = sc.nextInt();

		int ans = Math.abs(getPosi(p) - getPosi(q));
		System.out.println(ans);
        return;
    }

	static private int getPosi(int[] x) {

			int l = x.length;
			int p = 1;

			for(int i = 0; i < l; i++) {
				p += fact[l-i-1] * (x[i]-1);
				for(int j = i+1; j < l; j++) {
					if(x[j] > x[i])
						x[j]--;
				}
			}
		return p;

	}

}