Problem Statement

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.

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.

Constraints

• $3 \leq N \leq 2 \times 10^5$
• $1 \leq A_i, B_i \leq 10^9$
• All values in input are integers.

Sample Input 1

3
1 1 1
13 5 7

Sample Output 1

4

Takahashi can achieve his objective by, for example, performing the following operations:

• Replace the second number with 3.
• Replace the second number with 5.
• Replace the third number with 7.
• Replace the first number with 13.

Sample Input 2

4
1 2 3 4
2 3 4 5

Sample Output 2

-1

Sample Input 3

5
5 6 5 2 1
9817 1108 6890 4343 8704

Sample Output 3

25

见题面 Input 部分

见题面 Output 部分