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;

int main(){
	ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
	int n;
	cin >> n;
	vector<int> a(n), b(n);
	for(int i = 0; i < n; i++) cin >> b[i];
	for(int i = 0; i < n; i++) cin >> a[i];
	vector<int> x;
	for(int i = 0; i < n; i++){
		x.push_back(i);
	}
	long long num = 0;
	int s = 0;
	while(s < (int)x.size()){
		int i = x[s];
		s += 1;
		int j = (i + n - 1) % n;
		int k = (i + 1) % n;
		if(a[i] - b[i] >= a[j] + a[k]){
			int v = (a[i] - b[i]) / (a[j] + a[k]);
			a[i] -= (a[j] + a[k]) * v;
			x.push_back(j);
			x.push_back(k);
			num += v;
		}
	}
	for(int i = 0; i < n; i++){
		if(a[i] != b[i]){
			cout << -1 << '\n';
			return 0;
		}
	}
	cout << num << '\n';
}