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>

int num(int arr[], int n, int used[], int i);
int fact(int n)
{
    int ans;

    if(n==0) return 1;
    ans=n*fact(n-1);

    return ans;
}

int main(void)
{
    int n,p[8],q[8],useda[8]={0},usedb[8]={0},a,b,ans,i;

    scanf("%d",&n);
    for ( i = 0; i < n; i++)
    {
        scanf("%d",p+i);
    }
    for ( i = 0; i < n; i++)
    {
        scanf("%d",q+i);
    }

    a=num(p,n,useda,0);
    b=num(q,n,usedb,0);

    ans=(a-b>0)? a-b:b-a;
    printf("%d",ans);

    return 0;
}

int num(int arr[], int n, int used[], int i)
{
    if(i==n-1) return 0;
    used[arr[i]]=1;
    int now,nokori=arr[i]-1;
    for (int j = 1; j < arr[i]; j++)
    {
        if(used[j]==1) nokori--;
    }
    now=nokori*fact(n-i-1);
    int partial=num(arr,n,used,i+1);
    return now+partial;
}