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
def main():
    N=int(input())
    A=list(map(int, input().split()))
    B=list(map(int, input().split()))

    count = 0
    prev_count = -1
    while count!=prev_count:
        prev_count = count
        for i in range(N):
            d = B[i-1 if i>=1 else N-1] + B[i+1 if i<N-1 else 0]
            c = (B[i]-A[i]) // d
            B[i] -= d * c
            count += c

    if A == B:
        print(count)
    else:
        print(-1)

if __name__ == '__main__':
    main()