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.PriorityQueue;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner scn = new Scanner(System.in);
		int N = scn.nextInt();
		long[] A = new long[N], B = new long[N];
		PriorityQueue<Pair> PQ = new PriorityQueue<Pair>();
		for(int i = 0;i < N;i++) {
			A[i] = scn.nextLong();
		}
		for(int i = 0;i < N;i++) {
			B[i] = scn.nextLong();
			if(B[i] != A[i]) {
				PQ.add(new Pair(i,B[i]));
			}
		}
		boolean can = true;
		long ans = 0;
		while(!PQ.isEmpty()) {
			Pair p = PQ.poll();
			int num = p.num;
			int numb = (num-1+N)%N;
			int numf = (num+1)%N;

			if(B[num] - A[num] < B[numb] + B[numf]) {
				can = false;
				break;
			}

			long t = (B[num] - A[num])/(B[numb] + B[numf]);

			B[num] -= (B[numb] + B[numf])*t;
			ans+=t;
			if(B[num] != A[num]) {
				PQ.add(new Pair(num,B[num]));
			}

		}
		System.out.println((can)?ans:-1);


	}

}

class Pair implements Comparable<Pair>{
	long val;
	int num;
	public Pair(int num, long val) {
		this.num = num;
		this.val = val;
	}
	@Override
	public int compareTo(Pair o) {
		if(this.val < o.val)return 1;
		if(this.val > o.val)return -1;
		return 0;
	}
}

