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: Wrong Answer)

import java.util.Scanner;

public class Main {
    static int fact(int n) {
        if (n == 0)
            return 1;

        return n * fact(n - 1);
    }
    int calculateRank(String s){

        int rank = 1;
        for (int i = 0; i < s.length(); i++) {
            for (int j = i+1 ; j < s.length(); j++) {
                if (s.charAt(i) > s.charAt(j)) {
//                    System.out.println(str.charAt(j));
                    rank = rank + fact(s.length() - (i + 1));
                }
            }
        }
        return rank;
    }

    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);

       int N= sc.nextInt();
        String P=sc.next();
       String Q=sc.next();

        Main obj=new Main();
        
       int j;
       j=obj.calculateRank(P);
       int k;
       k= obj.calculateRank(Q);
       int q=j-k;
       if (q <0)
           q=-1 * q;
        System.out.println(q);

    }
}