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;
typedef long long ll;

int main(){
	int n; cin >> n; int a[n], b[n], ds = 0;
	for(int i=0; i<n; i++) cin >>a[i];
	for(int i=0; i<n; i++) {
		cin >> b[i]; ds += a[i] == b[i];
	}
	ll an = 0; bool update = true;
  while (ds != n && update) {
		update = false;
		for(int j=0; j<n; j++){
			int p = b[(j+n-1)%n] + b[(j+1)%n];
			//cout << j << " " << p << " " << b[j] << " " << b[j] - p << " " << update<< endl;
			if (b[j] - p >= a[j]) {
				int c = (b[j] - a[j]) / p;
				b[j] -= p * c; an+=c;
				if (a[j] == b[j]) ds++;
				update = true;
			}
		}
	}
	if (ds != n) cout << "-1" << endl;
	else cout << an << endl;
}