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
from heapq import heapify, heappush, heappop


def solve(N: int, A: "List[int]", B: "List[int]"):

    lh = []
    for i, b in enumerate(B):
        heappush(lh, (-b, i))

    count = 0
    while lh:
        b, i = heappop(lh)
        a, b = A[i], B[i]
        c = B[i-1]+B[(i+1) % N]
        if b > a and b >= c:
            d, m = divmod(b-a, c)
            if d == 0:
                break
            count += d
            B[i] = a+m
            if m != 0:
                heappush(lh, (-B[i], i))

    if A != B:
        count = -1

    print(count)
    return


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()
