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 heapify, heappop, heappush

n = int(input())
a = list(map(int, input().split()))
b = list(map(int, input().split()))

q = [(-val, i) for i, val in enumerate(b) if val != a[i]]
heapify(q)

# 3print(q)

cnt = 0

while q:
  bval, i = heappop(q)
  bval = - bval - a[i]
  dv, bval = divmod(bval, b[i - 1] + b[(i + 1) % n])
#   print(dv, bval,i)
  if dv == 0:
    print(-1)
    exit()
  bval += a[i]
  b[i] = bval
  cnt += dv
  if bval != a[i]:
    heappush(q, (- bval, i))
print(cnt)
