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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
int fact(int x){
  if(x==0) return 1;
  else return x*fact(x-1);
}
int main() {
  int a,b;
  a=1;
  b=1;
  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];
  for(int i=0;i<N;i++){
    int x=P[i];
    int y=Q[i];
    for(int j=0;j<=i;j++){
      if(x>P[j]) x--;
      if(y>Q[j]) y--;
    }
    a+=(x-1)*fact(N-1-i);
    b+=(y-1)*fact(N-1-i);
  }
  cout<<abs(a-b)<<endl;
}