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 a[222222], b[222222];
int main() {
	int n;
	cin >> n;
	for (int i = 0; i < n; i++)
		scanf("%d", a + i);
	for (int i = 0; i < n; i++)
		scanf("%d", b + i);
	priority_queue<pair<int, int>> q;
	for (int i = 0; i < n; i++) {
		if (b[i] < a[i]) {
			cout << -1 << endl;
			return 0;
		}
		q.emplace(b[i] - a[i], i);
	}
	long c = 0;
	for (;;) {
		auto r = q.top();
		q.pop();
		if (!r.first) break;
		int m = r.second;
		int z = (b[m] - a[m]) / (b[(m + n - 1) % n] + b[(m + 1) % n]);
		c += z;
		if (!z) {
			cout << -1 << endl;
			return 0;
		}
		b[m] -= z * (b[(m + n - 1) % n] + b[(m + 1) % n]);
		q.emplace(b[m] - a[m], m);
	}
	cout << c << endl;
	return 0;
}
