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>
#define int long long
using namespace std;
int a[200010],b[200010];
int l[200010],r[200010];
int n;
signed 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++){
		if(a[i]>b[i]){
			puts("-1");
			return 0;
		}
	}
	for(int i=2;i<=n;i++)l[i]=i-1;
	l[1]=n;
	for(int i=1;i<n;i++)r[i]=i+1;
	r[n]=1;
	int step=0;
	while(1){
		bool ok=1,ch=0;
		for(int i=1;i<=n;i++){
			if(a[i]==b[i])continue;
			if(a[i]>b[i]){
				puts("-1");
				return 0;
			}
			ok=0;
			int p=b[l[i]]+b[r[i]];
			if(b[i]-p<a[i])continue;
			step+=(b[i]-a[i])/p;
			b[i]-=(b[i]-a[i])/p*p;
			ch=1;
		}
		if(ok)break;
		if(!ch){
			puts("-1");
			return 0;
		}
	}
	cout<<step<<endl;
	return 0;
}
