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 hq
mod = 10**9+7
def l(): #intのlist
    return list(map(int,input().split()))
def m(): #複数文字
    return map(int,input().split())
def onem(): #Nとかの取得
    return int(input())

def onon():
    n = onem()

    a = l()

    b = l()

    t = []

    for i in range(n):
        if b[i] != a[i]:
            hq.heappush(t,(-b[i],i))
    co = 0
    while t:
        k = hq.heappop(t)
        k = (-k[0],k[1])
        q,w = divmod(k[0] - a[k[1]], b[(k[1] - 1) % n] + b[(k[1] + 1) % n])
        co += q
        if q == 0:
            return -1
        w = a[k[1]] + w
        b[k[1]] = w
        if b[k[1]] != a[k[1]]:
            hq.heappush(t,(-w,k[1]))
    return co
print(onon())