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;

bool check(vector<int> v, vector<int> w){
  for(int i=0; i<v.size(); i++){
    if(v[i]!=w[i]) return false;
  }
  return true;
}
int main(){
  int N;
  cin >> N;
  vector<int> P(N);
  vector<int> Q(N);
  for(int i=0; i<N; i++){
    cin >> P[i];
  }
  for(int i=0; i<N; i++){
    cin >> Q[i];
  }
  
  vector<int> per(N);
  for(int i=0; i<N; i++){
    per[i]=i+1;
  }
  int a,b;
  int now=1;
  do{
    if(check(per,P)) a=now;
    if(check(per,Q)) b=now;
    now++;
  }while(next_permutation(per.begin(), per.end()));
  int ans=abs(a-b);
  cout << ans <<endl;
}