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.*;

public class Main {

    static List<String> z;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] p = new int[n];
        int[] q = new int[n];
        Arrays.setAll(p, i -> sc.nextInt());
        Arrays.setAll(q, i -> sc.nextInt());

        z = new ArrayList<>();
        String s = "";
        String pa = "";
        String qb = "";
        for (int i = 1; i <= n; i++) {
            s += i;
        }
        for (int i = 0; i < n; i++) {
            pa += p[i];
            qb += q[i];
        }
        permutation(s,"");
        int a = 0;
        int b = 0;
        for(int i = 0; i < z.size(); i++) {
            if (z.get(i).equals(pa)) a = i;
            if (z.get(i).equals(qb)) b = i;
        }
        System.out.println(Math.abs(a-b));
    }

    public static void permutation(String q, String ans){
        if(q.length() <= 1) {
            z.add(ans + q);
        }
        else {
            for (int i = 0; i < q.length(); i++) {
                permutation(q.substring(0, i) + q.substring(i + 1),
                ans + q.charAt(i));
            }
        }
    }

}