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
N = int(input())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
import heapq
que = []
for i, b in enumerate(B):
    heapq.heappush(que, (-b, i))
flag = True
ans = 0
while que:
    b, i = heapq.heappop(que)
    b = -b
    if b == A[i]:
        continue
    a, c = B[(i-1)%N], B[(i+1)%N]
    if b-A[i]<a+c:
        flag = False
        break
    r = (b-A[i])//(a+c)
    b-=(a+c)*r
    B[i] = b
    ans+=r
    if b!=A[i]:
        heapq.heappush(que, (-b, i))
if flag:
    print(ans)
else:
    print(-1)