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 <unordered_map>
#include <unordered_set>
#include <algorithm>
#include <iostream>
#include <iostream>
#include <fstream>
#include <numeric>
#include <cstring>
#include <cassert>
#include <string>
#include <vector>
#include <queue>
#include <deque>
#include <cmath>
#include <set>
#include <map>
#include <functional>
#include <bitset>
#include <iomanip>
#include <stack>
#include <list>
using namespace std;
#define ll           long long
#define all(v)       (v).begin() , (v).end()
#define vi           vector <ll>
#define vii          vector <pair<ll,ll>>
#define ii           pair<ll,ll>
#define sz(v)	     ((int)((v).size()))
#define lp(i,a,b)    for(int i=a;i<b;i++)
#define pb           push_back
#define pf           push_front
#define F            first
#define S            second
#define endl         "\n"
#define IOS          ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
const double PI = 3.14159265358979323846;
const ll inf=2e9,MOD=998244353,MAX=1e2+2;

int main() {
#ifndef ONLINE_JUDGE
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
#endif
    IOS;
    int n;
    cin>>n;
    vector<int>a(n),b(n),c(n);
    lp(i,0,n)
        cin>>a[i],c[i]=i+1;
    lp(i,0,n)
        cin>>b[i];
    int cnt=1,x=0,y=0;
    do{
        if(c==a)
            x=cnt;
        if(c==b)
            y=cnt;
        cnt++;
    }while(next_permutation(all(c)));
    cout<<abs(x-y);
}