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 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
int main(void)
{
  int N,i,j;
  scanf("%d",&N);
  int P[N],Q[N];
  int total_P = 0,total_Q = 0;
  int NK ;
  int ketaCount_P[N]; 
  int ketaCount_Q[N]; 

  NK = KAIJYO(N);
//  printf("aaaa%d\n",NK);

//  printf("debug11 %d\n",N);

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

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


  for(i=0;i<N;i++)
  {
//   printf("qqqq %d ",P[i]);
 //  printf("%d ",Q[i]);
  }
  for(i=0;i<N-1;i++) 
   {
   ketaCount_P[i] = 0;
   ketaCount_Q[i] = 0;

   for(j=i+1;j<N;j++)
    {

      if(P[i]>P[j]) ketaCount_P[i]++;
      if(Q[i]>Q[j]) ketaCount_Q[i]++;
    }
   total_P += ketaCount_P[i]*KAIJYO(N-i-1);
   total_Q += ketaCount_Q[i]*KAIJYO(N-i-1);
   }


  printf("aaa%d  %d\n",total_P,total_Q);
  printf("%d\n",abs(total_P-total_Q));

  return 0;
}

int KAIJYO(int N)
{
 int i=1;
 int count =1;
 for(i=1;i<=N;i++)
 {
  count = count * i;
//  printf("bbb%d\n",count);
}

 return count; 
}