Numbers on a Circle

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

inputFormat

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

outputFormat

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

样例

5
5 6 5 2 1
9817 1108 6890 4343 8704

25