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
import heapq as h
n = int(input())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
e6 = 10**6
q = [-b[i]*e6-i for i in range(n)]
h.heapify(q)
cnt = 0
while q:
  w = -h.heappop(q)
  v,i = w//e6, w%e6
  u = b[(i-1)%n] + b[(i+1)%n]
  if v < u or a[i] == v: continue
  elif a[i] > v: print(-1); exit(0)
  t = (v-a[i])//u
  if not t: print(-1); exit(0)
  cnt += t
  b[i] -= t*u
  if b[i] > a[i]:
    h.heappush(q,-b[i]*e6-i)
print(cnt if a==b else -1)