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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

int main() {
  int N;
  cin >> N;
  
  vector<int> P(N), Q(N);
  for (int i = 0; i < N; i++) {
    cin >> P.at(i);
  }
  for (int i = 0; i < N; i++) {
    cin >> Q.at(i);
  }
  
  vector<int> a(N), b(N);
  for (int i = 0; i < N; i++) {
    a.at(i) = i + 1;
    b.at(i) = i + 1;
  }
  
  int x = 0;
  int y = 0;
  
  
  do {
    bool check = true;
    x++;
    for (int i = 0; i < N; i++) {
      if (a.at(i) != P.at(i)) {
        check = false;
        break;
      }
    }
    if (check) {
      break;
    }
  } while (next_permutation(a.begin(), a.end()));
  
  do {
    bool check = true;
    y++;
    for (int i = 0; i < N; i++) {
      if (b.at(i) != Q.at(i)) {
        check = false;
        break;
      }
    }
    if (check) {
      break;
    }
  } while (next_permutation(b.begin(), b.end()));
  
  cout << abs(x - y) << endl;
  
  return 0;
}