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[] FACTORIALS = {1, 1, 2, 6, 24, 120, 720, 5040};

  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int max = sc.nextInt();
    int sum1 = permutation(max, sc);
    int sum2 = permutation(max, sc);
    System.out.println(Math.abs(sum1 - sum2));
  }

  private static int permutation(int max, Scanner sc) {
    int ret = 0;
    boolean[] used = new boolean[max + 1];
    for (int i = max; i > 0; i--) {
      int value = sc.nextInt();
      int num = 0;
      for (int j = 1; j <= max; j++) {
        if (value == j) {
          used[j] = true;
          break;
        } else if (used[j]) {
          // do nothing
          continue;
        } else {
          num++;
        }
      }
      ret += FACTORIALS[i - 1] * num;
    }
    return ret;
  }
}