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
from heapq import heappush, heappop

N = int(input())
A_list = list(map(int, input().split()))
B_list = list(map(int, input().split()))

res = True
res_cnt = 0

h = []
for i in range(N):
    if B_list[i] > A_list[i]:
        heappush(h, (-B_list[i], i))
    elif B_list[i] < A_list[i]:
        res = False

while len(h) > 0 and res:
    _, i = heappop(h)
    a = B_list[(i - 1) % N]
    c = B_list[(i + 1) % N]

    if B_list[i] > max(a, c):
        k1 = (B_list[i] - A_list[i]) // (a + c)
        k2 = (B_list[i] - max(a, c)) // (a + c)
        k = min(k1, k2+1)
        if k == 0:
            res = False
        res_cnt += k
        B_list[i] -= k * (a + c)
        if B_list[i] > A_list[i]:
            heappush(h, (-B_list[i], i))
    else:
        res = False

if __name__ == "__main__":
    if res:
        print(res_cnt)
    else:
        print(-1)
