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.util.*;

public class Main {
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int[] A = new int[N];
		int[] B = new int[N];
		
		for(int i=0; i<N; i++)
			A[i] = sc.nextInt();
		for(int i=0; i<N; i++)
			B[i] = sc.nextInt();

		long ans = 0;
		boolean update = true;
		while(update) {
			update = false;
			for(int i=0; i<N; i++) {
				if(B[i]<A[i]) {
					update = false;
					break;
				}
				int i0 = (i-1+N)%N;
				int i2 = (i+1)%N;
				if(B[i0] < B[i] && B[i] > B[i2]) {
					int move = (B[i]-A[i])/(B[i0]+B[i2]);
					ans += move;
					B[i] -= move*(B[i0]+B[i2]);
					if(move>0)
						update = true;
				}
			}
		}
		boolean ok = true;
		for(int i=0; i<N; i++) {
			if(A[i]!=B[i]) {
				ok = false;
				break;
			}
		}
		
		System.out.println(ok ? ans : -1);
		sc.close();
	}
}
