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();
		long[] A = new long[n];
		long[] B = new long[n];
		for(int i = 0; i < n; i++){
			A[i] = sc.nextInt();
		}
		PriorityQueue<Pair> q = new PriorityQueue<>();
		for(int i = 0; i < n; i++){
			B[i] = sc.nextInt();
			q.add(new Pair(i, B[i]));
		}
		long res = 0;
		while(!q.isEmpty()){
			Pair p = q.remove();
			int u = p.ind;
			if(B[u] == A[u]) continue;
			long sides = B[(u+1)%n] + B[(u+n-1)%n];
			if(sides >= B[u]){
				System.out.println("-1"); return;
			}
			long newb = B[u] % sides;
			if(newb <= A[u]){
				if((A[u] - newb) % sides == 0){
					res += (B[u] - A[u]) / sides;
					B[u] = A[u];
				}
				else{
					System.out.println("-1"); return;
				}
			}
			else{
				res += (B[u] - newb) / sides;
				B[u] = newb;
				q.add(new Pair(u, B[u]));
			}
		}
		System.out.println(res);
	}
	static class Pair implements Comparable<Pair>{
		int ind; long val;
		public Pair(int ind, long val){
			this.ind = ind; this.val = val;
		}
		@Override
		public int compareTo(Pair p) {
			if(val < p.val) return 1;
			else if(val > p.val) return -1;
			else return 0;
		}
		public String toString(){
			return ind+" "+val;
		}
	}

}
