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
def main():
  import sys
  _int = int
  n = _int(input())
  a = [_int(e) for e in input().split()]
  b = [_int(e) for e in input().split()]
  result = 0
  q = [i for i in range(n) if b[i] != a[i]]
  while len(q) != 0:
    nq = []
    c = 0
    for i in q:
      if i == 0 or i == n - 1:
        j = b[(n + i - 1) % n] + b[(n + i + 1) % n]
      else:
        j = b[i - 1] + b[i + 1]
      if j > b[i] - a[i]:
        nq.append(i)
        continue
      c += 1
      k = (b[i] - a[i]) // j
      result += k
      b[i] -= j * k
      if a[i] != b[i]:
        nq.append(i)
    if c == 0 and len(nq) != 0:
      print(-1)
      sys.exit()
    q = nq
  print(result)
main()