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=tuple(map(int,input().split()))
B=list(map(int,input().split()))
from heapq import heappop,heappush
q=[]
a=0
for i,b in enumerate(B):
    heappush(q,(-b,i))
while len(q)>0:
    b,i=heappop(q)
    ba=-b-A[i]
    bb=B[i-1]+B[i+1-N]
    if ba<0:
        a=-1
        break
    elif ba==0:
        continue
    elif -b>bb:
        x,y=divmod(ba,bb)
        if x==0:
            a=-1
            break
        B[i]-=bb*x
        if y>0:
            heappush(q,(-B[i],i))
        a+=x
    else:
        a=-1
        break
print(a)