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>
#define forn(i,b) for(int i=0 ; i< b ;i++)
#define for1(i,b) for(int i=1 ; i<=b ;i++)
#define reps(i,a,b) for(int i=a ; i< b.length() ;i++)
typedef long long ll;
#define MOD 1000000007

using namespace std;

bool checkArraysEqual(int tab[],int tab2[],int dim) {
  for(int i=0; i<dim ; i++){
    if(tab[i]!=tab2[i]) return 0;
  }
  return 1;
}

int main()
{

  int n,p,q,pos1=0,pos2=0;
  int tab[9],tabb[9],tab3[9];
  int i=1;
  cin>>n;
  for(int i=0;i<n;i++){ cin>>tab[i]; tab3[i]=tab[i]; }
  for(int i=0;i<n;i++){ cin>>tabb[i];  }
  sort(tab3,tab3+n);

  do{
    if(checkArraysEqual(tab,tab3,n)==1)  pos1=i;
    if(checkArraysEqual(tabb,tab3,n)==1) pos2=i;
    i++;
  }while(next_permutation(tab3,tab3+n));

  cout<<abs(pos2-pos1);

  return 0 ;
}