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<bits/stdc++.h>
using namespace std;
#define int long long int

int solve(int n,int arr[]){
    int temp[n];
    for(int i=1;i<=n;i++){
        temp[i-1]=i;
    }
    int idx=0;
    do{   
        int flag=0;
        for(int i=0;i<n;i++){
            if(arr[i]!=temp[i]){
                flag=1;
                break;
            }
        }
        if(!flag){
            return idx;
        }
        idx++;
    }
    while(next_permutation(temp,temp+n));
}
int32_t main()
{
    int n;cin>>n;

    int arr1[n],arr2[n];

    for(int i=0;i<n;i++) cin>>arr1[i];
    for(int i=0;i<n;i++) cin>>arr2[i];

    int num1=solve(n,arr1);
    int num2=solve(n,arr2);

    cout<<abs(num1-num2)<<endl;

    return 0;
}