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;
struct node{
	int x,y;
	bool operator <(const node s)const{
		return x>s.x;
	}
}b[1000010];
int a[1000010],c[1000010];
int main(){
	int n;cin>>n;
	for(int i=0;i<n;i++)cin>>a[i];
	for(int i=1;i<=n;i++){
		cin>>b[i].x;c[i-1]=b[i].x;
		b[i].y=i-1;
	}
	sort(b+1,b+n+1);long long ans=0;
	bool fla=1;
	while(fla){
		fla=0;
		for(int i=1;i<=n;i++){
			int pl=b[i].y;
			int L=c[(pl+1)%n],R=c[(pl+n-1)%n];
			if(c[pl]-a[pl]>=L+R)fla=1;
			ans+=(c[pl]-a[pl])/(L+R);
			c[pl]-=(c[pl]-a[pl])/(L+R)*(L+R);
		}
	}
	for(int i=0;i<n;i++)if(a[i]!=c[i])return puts("-1"),0;
	cout<<ans;
	return 0;
}
