Problem: We have N cards numbered 1, 2, ..., N. Card i (1 \leq i \leq N) has an integer A_i written in red ink on one side and an integer B_i written in blue ink on the other side. Initially, these cards are arranged from left to right in the order from Card 1 to Card N, with the red numbers facing up.

Determine whether it is possible to have a non-decreasing sequence facing up from left to right (that is, for each i (1 \leq i \leq N - 1), the integer facing up on the (i+1)-th card from the left is not less than the integer facing up on the i-th card from the left) by repeating the operation below. If the answer is yes, find the minimum number of operations required to achieve it.

* Choose an integer i (1 \leq i \leq N - 1). Swap the i-th and (i+1)-th cards from the left, then flip these two cards.

Constraints

* 1 \leq N \leq 18
* 1 \leq A_i, B_i \leq 50 (1 \leq i \leq N)
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 ... A_N
B_1 B_2 ... B_N


Output

If it is impossible to have a non-decreasing sequence, print `-1`. If it is possible, print the minimum number of operations required to achieve it.

Examples

Input

3
3 4 3
3 2 3


Output

1


Input

2
2 1
1 2


Output

-1


Input

4
1 2 3 4
5 6 7 8


Output

0


Input

5
28 15 22 43 31
20 22 43 33 32


Output

-1


Input

5
4 46 6 38 43
33 15 18 27 37


Output

3

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#define DB double
#define LL long long

#define MST(a,b) memset((a),(b),sizeof(a))
#define MRK() cout<<"Mark"<<endl;
#define WRT(x) cout<<#x<<" = "<<(x)<<endl;

#define MAXN 210000
#define MAXM 410000
#define MOD 998244353
#define INF 0x3f3f3f3f
#define LLINF 0x3f3f3f3f3f3f3f3f
#define EPS 1e-5

#define _ 0
using namespace std;

int n;
int a[MAXN][2];

void init()
{
	cin>>n;
	for (int i=0;i<n;i++)
		cin>>a[i][0];
	for (int i=0;i<n;i++)
		cin>>a[i][1];
}

void work()
{
	int ans=INF;
	for (int mask=0;mask<(1<<n);mask++)
	{
		vector<int> tmp;
		bool f=true;
		for (int i=0;i<n;i++)
		{
			f^=(mask>>i)&1;
			tmp.push_back(a[i][(mask>>i)&1]);
		}
		if (!f)
			continue;
		sort(tmp.begin(),tmp.end());
		int cnt=0;
		for (int i=0;i<n;i++)
			for (int j=0;j<n;j++)
				if (a[i][(mask>>i)&1]==tmp[j] && (((i-j)&1)==((mask>>i)&1)))
				{
					cnt++;
					tmp[j]=-i;
					break;
				}
		if (cnt!=n)
			continue;
		int cnt1=0;
		for (int i=0;i<n;i++)
			for (int j=i+1;j<n;j++)
				if (tmp[i]<tmp[j])
					cnt1++;
		ans=min(ans,cnt1);
	}
	if (ans==INF)
		cout<<-1;
	else
		cout<<ans;
}

int main()
{
	init();
	work();
	return ~~(0^_^0);
}