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,sys
input = sys.stdin.readline

n = int(input())
a = tuple(map(int,input().split()))
b = list(map(int,input().split()))
le = 10**6

tank = []
for i,e in enumerate(b):
    heapq.heappush(tank,-e*le-i)

res = 0
while len(tank):
    p = -heapq.heappop(tank)

    ele = p//le
    ind = p%le

    if ele == a[ind]:
        continue
    elif ele < a[ind]:
        print(-1)
        exit()

    if ind == n-1:
        w = b[ind-1] + b[0]
    elif ind == 0:
        w = b[-1] + b[1]
    else:
        w = b[ind-1] + b[ind+1]
    
    q = (ele-a[ind])//w
    if q == 0:
        print(-1)
        exit()
    res += q
    ele -= q*w
    b[ind] = ele
    heapq.heappush(tank,-ele*le-ind)

print(res)