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=[int(i) for i in input().split()]
B=[int(i) for i in input().split()]

from heapq import heappop, heappush
push = lambda x,i: heappush(BB,(-x,i))
BB=[]

for i,b in enumerate(B):
  push(b,i)

ans=0
while BB:
  b,ind=heappop(BB)
  b,ai=-b,A[ind]
  if b<ai:
    ans=-1
    break
  d=B[(ind-1)%n]+B[(ind+1)%n]
  dd=(b-ai)//d
  if dd==0:
    if b==ai:
      continue
    ans=-1
    break
  ans+=dd
  B[ind]-=d*dd
  push(b-d*dd,ind)
  
print(ans)
