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<stdio.h>
#include<stdlib.h>
int main(){

int N;
scanf("%d",&N);
int P[N],Q[N];
int calc[]={5040,720,120,24,6,2,1,0};

for (int i = 0; i < N; i++){scanf("%d",&P[i]);}
for (int i = 0; i < N; i++){scanf("%d",&Q[i]);}

int check(int sq[])
{
  int ans=0;
  for (int i = 0; i < N; i++)
  {
    int counter=0;
    for (int j = 0;j < i; j++)
    {
      if (sq[j]<sq[i]){counter++;}
    }
    ans += calc[7-(N-1)+i]*(sq[i]-1 - counter);
  }
  return ans;
}

printf("%d",abs(check(P)-check(Q)));

return 0;

}