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
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.PriorityQueue;

public class Main {
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		Obj[] arr = new Obj[n];
		PriorityQueue<Obj> que = new PriorityQueue<>();
		String[] sa = br.readLine().split(" ");
		String[] sb = br.readLine().split(" ");
		for (int i = 0; i < n; i++) {
			Obj o = new Obj();
			o.i = i;
			o.a = Integer.parseInt(sa[i]);
			o.b = Integer.parseInt(sb[i]);
			arr[i] = o;
			que.add(o);
		}
		br.close();

		long ans = 0;
		while (!que.isEmpty()) {
			Obj o = que.poll();
			int sum = arr[(o.i - 1 + n) % n].b + arr[(o.i + 1) % n].b;
			if (o.a % sum == o.b % sum) {
				ans += (o.b - o.a) / sum;
				o.b = o.a;
			} else {
				int ng = o.b / sum + 1;
				int ok = 0;
				while (ng - ok > 1) {
					int mid = (ng + ok) / 2;
					if (o.a <= o.b - sum * mid) {
						ok = mid;
					} else {
						ng = mid;
					}
				}
				if (ok == 0) {
					System.out.println(-1);
					return;
				}
				ans += ok;
				o.b = o.b - sum * ok;
				que.add(o);
			}
		}
		System.out.println(ans);
	}

	static class Obj implements Comparable<Obj> {
		int i, a, b;

		@Override
		public int compareTo(Obj o) {
			return o.b - b;
		}
	}
}
