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 9.2.1) (judge verdict: Accepted)

#include <stdio.h>

void dfs(int disit);
int abs(int a);

int n=0,count=0,a=0,b=0;
int P[10]={},Q[10]={},flag[10]={},array[10]={};

int main(void)
{
    scanf("%d",&n);
    for(int i=0;i<n;i++) scanf("%d",&P[i]);
    for(int i=0;i<n;i++) scanf("%d",&Q[i]);
    dfs(0);
    printf("%d",abs(a-b));
    return 0;
}

void dfs(int disit){
    int flaga=1,flagb=1;
    if(disit==n){
        // for(int s=0;s<n;s++) printf("%d",array[s]);
        // printf("\n");
        count+=1;
        for(int j=0;j<n;j++){
            if(P[j]!=array[j]) flaga=0;
            if(Q[j]!=array[j]) flagb=0;
        }
        if(flaga==1) a=count;
        if(flagb==1) b=count;
    } else {
        for(int i=1;i<=n;i++){
            if(flag[i]==0){
                flag[i]=1;
                array[disit]=i;
                dfs(disit+1);
                flag[i]=0;
            }
        }
    }
}

int abs(int a){
    if(a<0) a=(-1)*a;
    return 0;
}