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
#!/usr/bin/env python3
import sys
import heapq


def solve(N: int, A: "List[int]", B: "List[int]"):
    diff = [(p[0] - p[1], i) for i, p in enumerate(zip(A, B))]
    heapq.heapify(diff)
    # print(diff)
    count = 0
    while True:
        d, i = heapq.heappop(diff)

        if d == 0:
            break

        x = B[(i+1)%N] + B[i-1]
        n = -d // x
        if n <= 0:
            print(-1)
            return
        d += n * x
        B[i] -= n * x


        heapq.heappush(diff, (d, i))
        count += n
    print(count)
    return


# Generated by 1.1.4 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    A = [ int(next(tokens)) for _ in range(N) ]  # type: "List[int]"
    B = [ int(next(tokens)) for _ in range(N) ]  # type: "List[int]"
    solve(N, A, B)

if __name__ == '__main__':
    main()
