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 <iostream>
#include <cstring>
#include <algorithm>
#include <functional>
#include <bits/stdc++.h>
#include <cmath>
#include <limits>
#include <numeric>
#include <type_traits>
#include <stdlib.h>
using namespace std;
 
int main () {
  int n;
  cin >> n;
  int t[n];
  for (int h = 0; h<n; h++){
    t[h] = h + 1;
  }
  int p[n];
  int q[n];
  for (int i = 0; i < n; i++){
    cin >> p[i];
  }
  for (int j = 0; j < n; j++){
    cin >> q[j];
  }
  int a = 0;
  int b = 0;
  bool fa = true;
  bool fb = true;
  int m = 1;
  do{
    for (int k=0; k<n; k++){
      if (t[k] != p[k]){
        fa = false;
      }
      if (t[k] != q[k]){
        fb = false;
      }
    }
    if (fa){
      a = m;
    } 
    if (fb) {
      b = m;
    }
    m ++;
    fa = true;
    fb = true;
  }while(next_permutation(t, t+n));
  
  cout << abs(a-b);
  return 0;
}