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


int ka[] = {1,1,2,6,24,120,720,5040};

int main(){
   int n,i,j,pp=0,qq=0,po,qo;
   scanf("%d", &n);
   int p[n],q[n],pn[n],qn[n];
   for(i=0;i<n;i++){
   	scanf("%d ", &p[i]);
     pn[i] = i+1;
   }
   for(i=0;i<n;i++){
   	scanf("%d ", &q[i]);
    qn[i] = i+1;
   }
   for(i=0,j=n-1 ; i<n ; i++,j--){
     po = 0; qo =0 ;
     if(i!=0){
      	for(int k=0;k<p[i]-1;k++){
        	if(pn[k]==0){ po++; }
        }
       for(int k=0;k<q[i]-1;k++){
        	if(qn[k]==0){ qo++;}
        }
     }
     //if(i==n-1 && po>0){po--;}
     //if(i==n-1 && qo>0){qo--;}
   	 pp = (p[i]-1-po)*ka[j] + pp;
     qq = (q[i]-1-qo)*ka[j] + qq;
     pn[p[i]-1]=0;
     qn[q[i]-1]=0;
     //printf("%d %d\n",  po,qo);
   }
   printf("%d", abs(qq-pp));
   return 0;
}