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(x) cerr<<#x<<" = "<<x<<"\n"
using namespace std;

const int MAX=19,INF=1e9;
int n,a[2][MAX],f[1<<MAX][55];
bool mark[1<<MAX][55];

int getBit(int x,int k) {
	return (x>>k)&1;
}

int dp(int mask,int maxn) {
	if(mask==(1<<n)-1)
		return 0;
	if(mark[mask][maxn])
		return f[mask][maxn];
	f[mask][maxn]=INF;
	mark[mask][maxn]=true;
	int cnt=__builtin_popcount(mask),cnt0=0;
	for(int i=0;i<n;i++) {
		if(getBit(mask,i)==0&&maxn<=a[cnt%2][i])
			f[mask][maxn]=min(f[mask][maxn],dp(mask+(1<<i),a[cnt%2][i])+cnt0);
		cnt0+=1-getBit(mask,i);
	}
	return f[mask][maxn];
}

int main() {
	ios_base::sync_with_stdio(false);
	// freopen("input","r",stdin);
	cin>>n;
	for(int i=0;i<=1;i++)
		for(int j=0;j<n;j++)
			cin>>a[i][j];
	for(int i=1;i<n;i+=2)
		swap(a[0][i],a[1][i]);
	cout<<(dp(0,0)==INF?-1:dp(0,0));
}