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 <vector>
#include <iostream>
using namespace std;
int main() {
	cin.tie(0);
	ios_base::sync_with_stdio(false);
	int N;
	cin >> N;
	vector<long long> A(N), B(N);
	for (int i = 0; i < N; ++i) cin >> A[i];
	for (int i = 0; i < N; ++i) cin >> B[i];
	bool ok = true;
	for (int i = 0; i < N; ++i) {
		if (A[i] > B[i]) ok = false;
	}
	long long ans = 0;
	while (A != B && ok) {
		vector<long long> preb = B;
		for (int i = 0; i < N; ++i) {
			if (B[(i + 1) % N] < B[i] && B[(i + N - 1) % N] < B[i]) {
				long long delta = (B[(i + 1) % N] + B[(i + N - 1) % N]);
				long long dl = (B[i] - A[i]) / delta;
				B[i] -= delta * dl;
				ans += dl;
			}
		}
		if (preb == B) ok = false;
	}
	cout << (ok ? ans : -1) << endl;
	return 0;
}