There are N positive integers arranged in a circle.

Now, the i-th number is A_i. Takahashi wants the i-th number to be B_i. For this objective, he will repeatedly perform the following operation:

* Choose an integer i such that 1 \leq i \leq N.
* Let a, b, c be the (i-1)-th, i-th, and (i+1)-th numbers, respectively. Replace the i-th number with a+b+c.



Here the 0-th number is the N-th number, and the (N+1)-th number is the 1-st number.

Determine if Takahashi can achieve his objective. If the answer is yes, find the minimum number of operations required.

Constraints

* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i, B_i \leq 10^9
* 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

Print the minimum number of operations required, or `-1` if the objective cannot be achieved.

Examples

Input

3
1 1 1
13 5 7


Output

4


Input

4
1 2 3 4
2 3 4 5


Output

-1


Input

5
5 6 5 2 1
9817 1108 6890 4343 8704


Output

25
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 2e5+5;

int n,a[N],b[N];
ll ans;
priority_queue<pair<int,int>>q;

int main(){
	cin>>n;
	for(int i=1;i<=n;++i)cin>>a[i];
	for(int i=1;i<=n;++i)cin>>b[i];
	for(int i=1;i<=n;++i)q.push(make_pair(b[i],i));
	while(!q.empty()){
		int x=q.top().second;q.pop();
		int l=x==1?n:x-1,r=x==n?1:x+1;
		int w=b[x]-a[x];
		if(w==0)continue;
		if(w<(b[l]+b[r])){
			puts("-1");
			return 0;
		}
		b[x]-=w/(b[l]+b[r])*(b[l]+b[r]);
		ans+=w/(b[l]+b[r]);
		q.push(make_pair(b[x],x));
	}
	cout<<ans<<endl;
} 