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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define REP(i,f,n) for(int i=f; i<(n); i++)
int main()
{
  int ans = 0;
  int n;
  vector<int> a,b,c;
  cin >> n;
  REP(i,0,n){
    int inter;
    cin >> inter;
    a.push_back(inter);
    c.push_back(i+1);
  }
  REP(i,0,n){
    int inter;
    cin >> inter;
    b.push_back(inter);
  }

  int cnt=0;
  do{
    int a_co=0, b_co=0;
    cnt++;
    REP(i,0,n){
      if(c[i] == a[i])a_co++;
      if(c[i] == b[i])b_co++;
    }
    if(a_co==n)ans+=cnt;
    if(b_co==n)ans-=cnt;
  }while(next_permutation(c.begin(),c.end()));

  cout << abs(ans) << endl;

  //--debug : end_stoper
  //string end_stoper; cin >> end_stoper;

  return 0;
}