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 <iostream>

using namespace std;
long long a[200010],b[200010],c[200010],cnt = 0;
int main(){
	int i,n;
	cin >> n;
	for(i=0;i<n;i++){
		cin >> a[i];
	}
	for(i=0;i<n;i++){
		cin >> b[i];
	}
	int k = 0;
	while(k<300){
		k++;
		for(i=0;i<n;i++){
			int l = i - 1,r = i + 1;
			if(l<0) l += n;
			if(r>=n) r -= n;
			long long x = b[l] + b[r];
			if(b[i]%x>=a[i]){
				c[i] = b[i]%(b[l] + b[r]);
				cnt += b[i]/(b[l] + b[r]);
			}else{
				if(b[i] < a[i]){
					cout << -1 << endl;
					return 0;
				}
				if((b[i] - a[i])%(b[l] + b[r])==0){
					c[i] = a[i];
					cnt += (b[i] - a[i])/(b[l] + b[r]);
				}
			}
		}
		bool flag = true;
		for(i=0;i<n;i++){
			b[i] = c[i];
			if(a[i]!=b[i]){
				flag = false;
			}
		}
		if(flag){
			cout << cnt << endl;
			return 0;
		}
	}
	cout << -1 << endl;
}