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: Accepted)

#include<stdio.h>
#include<math.h>
#include<stdlib.h>

int main(){
  int n,i,p[9],q[9],tmp=1,kai[8];
  char s[51];
  scanf("%d",&n);
  for(i=0;i<n;i++){
    scanf("%d",&p[i]);
  }
  for(i=0;i<n;i++){
    scanf("%d",&q[i]);
  }

  for(i=1;i<=7;i++){
    tmp*=i;
    switch (i)
    {
    case 1:
      kai[1]=tmp;
      break;
    case 2:
      kai[2]=tmp;
    case 3:
      kai[3]=tmp;
      break;
    case 4:
      kai[4]=tmp;
      break;
    case 5:
      kai[5]=tmp;
      break;
    case 6:
      kai[6]=tmp;
      break;
    case 7:
      kai[7]=tmp;
      break;
  }
  }

  int sump=0,sumq=0;

  for(i=0;i<n;i++){
    int pp=p[i];
    for(int j=0;j<i;j++){
      if(p[i]>p[j]) pp--;
    }
    sump+=(pp-1)*kai[n-i-1];
  }

  for(i=0;i<n;i++){
    int qq=q[i];
    for(int j=0;j<i;j++){
      if(q[i]>q[j]) qq--;
    }
    sumq+=(qq-1)*kai[n-i-1];
  }
  printf("%d",abs(sump-sumq));
  return 0;
}