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 sys
reader = (s.rstrip() for s in sys.stdin)
input = reader.__next__

def unable():
    print(-1)
    exit()

n = int(input())
a = list(map(int, input().split()))
b = list(map(int, input().split()))

from heapq import heappush, heappop
h = []
base = 10**6
for i in range(n):
    if a[i]>b[i]:
        unable()
    else:
        heappush(h, -(b[i]*base+i))

ans = 0
while h:
    k = heappop(h)
    i = -k%base
    cnt, mod = divmod(b[i]-a[i],b[i-1]+b[(i+1)%n])
    if cnt == 0:
        if mod != 0:
            unable()
    else:
        ans += cnt
        b[i] = a[i]+mod
        heappush(h, -(b[i]*base+i))
print(ans)
