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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
 
typedef long long ll;
typedef pair<int,int> P;

int main(){
	int n;
	cin>>n;
	vector<int>p(n),q(n),tmp1(n);
	for(int i=0;i<n;i++){
		cin>>p[i];
		tmp1[i]=p[i];
	}
	for(int i=0;i<n;i++){
		cin>>q[i];
	}
	sort(tmp1.begin(),tmp1.end());
	int ans1=0,ans2=0,res=0;
	bool ok1=true,ok2=true;
	do{
		res++;
		for(int i=0;i<n;i++){
			if(tmp1[i]!=p[i])ok1=false;
			if(tmp1[i]!=q[i])ok2=false;
		}
		if(ok1)ans1=res;
		if(ok2)ans2=res;
		ok1=true,ok2=true;
	}while(next_permutation(tmp1.begin(),tmp1.end()));
	cout<<abs(ans2-ans1)<<endl;
	return 0;
}