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 pair<long long, long long> P;
#define override_rep(i, l, r, mes, ...) mes
#define rep1(i, n) for (int i = 0; i < n; i++)
#define rep2(i, l, r) for (int i = l; i < r; i++)
#define rep(...) override_rep(__VA_ARGS__, rep2, rep1)(__VA_ARGS__)
#define int long long
signed main(signed argc, char* argv[]) {
	cin.tie(nullptr);
	ios::sync_with_stdio(false);
	int n;
	cin>>n;
	int a,b;
	vector<int> p(n),q(n),memo(n);
	rep(i,n){
	    memo[i]=i+1;
	    cin>>p[i];
	}
	rep(i,n)cin>>q[i];
	int cnt=1;
	do{
	    bool b_a=true,b_b=true;
	    rep(i,n){
	        if(p[i]!=memo[i])b_a=false;
	        if(q[i]!=memo[i])b_b=false;
	    }
	    if(b_a)a=cnt;
	    if(b_b)b=cnt;
	    cnt++;
	}while(next_permutation(memo.begin(),memo.end()));
	cout<<abs(a-b)<<endl;
}