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
q = []
heapq.heapify(q)

n = int(input())
As = list(map(int, input().split()))
Bs = list(map(int, input().split()))

zeros = [False]*n
Cs = [Bs[(i-1)%n]+Bs[(i+1)%n] for i in range(n)]
# Dが大きい順に操作していく
for i, (b,c,a) in enumerate(zip(Bs,Cs,As)):
    d = b-(c+a) 
    if d < 0: continue
    heapq.heappush(q,(-d,i))

cnt = 0
while len(q) > 0:
    d,i = heapq.heappop(q)
    # 自分と周りの影響を更新
    cnt_ = (Bs[i%n]-As[i%n]) // Cs[i%n]
    Bs[i%n] -= cnt_*Cs[i%n]    
    Cs[(i-1)%n] = Bs[(i-2)%n]+Bs[i%n]
    Cs[(i+1)%n] = Bs[(i+2)%n]+Bs[i%n]
    # 周りとの差
    d_m = Bs[(i-1)%n]-Cs[(i-1)%n]-As[(i-1)%n] 
    d_p = Bs[(i+1)%n]-Cs[(i+1)%n]-As[(i+1)%n]
    if d_m >= 0:
        heapq.heappush(q,(-d_m,i-1))
    if d_p >= 0:
        heapq.heappush(q,(-d_p,i+1))
    cnt += cnt_

if As == Bs:
    print(cnt)
else:
    print(-1)
    
