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

n=int(input())
arr1=list(map(int,input().split()))
arr2=list(map(int,input().split()))
q=[]
for i in range(n):
  if arr2[i]!=arr1[i]:
    heapq.heappush(q,(-arr2[i],i))
cnt=0
while q:
  val,pos=heapq.heappop(q)
  val*=-1
  diff=arr2[pos-1]+arr2[(pos+1)%n]
  move=(val-arr1[pos])//diff
  if move==0:
    break
  cnt+=move
  tmp=arr2[pos]-diff*move
  arr2[pos]=tmp
  if tmp!=arr1[pos]:
    heapq.heappush(q,(-tmp,pos))
for i in range(n):
  if arr1[i]!=arr2[i]:
    print(-1)
    break
else:
  print(cnt)