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<stdlib.h>
#include<math.h>
//#include<strint.h>

int fact(int n){
  if(n==0){
    return 1;
  }
  else return n*fact(n-1);
}

int surv(int arr[],int n){
  int kazu=0;
  int i;
  for(i=0;i<n;i++){
    if(arr[i]==1){
      kazu++;
    }
  }
  return kazu;
}

int main(void)
{
  int n;
  scanf("%d",&n);
  int p[n],q[n],pi[n],qi[n];
  int i,j;
  int pno=0,qno=0;
  for(i=0;i<n;i++){
    scanf("%d",&p[i]);
    pi[i]=1;//一が存在する；
  }
  for(i=0;i<n;i++){
    scanf("%d",&q[i]);
    qi[i]=1;
  }
  for(i=0;i<n;i++){
    pno=pno+surv(pi,p[i])*fact(n-i-1);
    pi[p[i]-1]=0;
    //printf("fact=%d\n",fact(n-i-1));
    //printf("surv=%d\n",surv(pi,p[i]));
  }
  //printf("pno=%d\n",pno);
  for(i=0;i<n;i++){
    qno=qno+surv(qi,q[i])*fact(n-i-1);
    qi[q[i]-1]=0;
    //printf("fact=%d\n",fact(n-i-1));
    //printf("surv=%d\n",surv(qi,q[i]));
  }
    //printf("qno=%d\n",qno);

  if(qno>pno){
    printf("%d",qno-pno);
    return 0;
  }
  else{
    printf("%d",pno-qno);
  }





  return 0;
}