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
from heapq import heappush as hpu
from heapq import heappop as hpo
input = sys.stdin.readline
N = int(input())
a = list(map(int, input().split()))
b = list(map(int, input().split()))

base = 10 ** 6
sb = [-(b[i] * base + i) for i in range(N) if a[i] != b[i]]
h = []
for t in sb: hpu(h, t)
res = 0
while len(h):
  v = hpo(h)
  i = -v % base
  v = -v // base
  if v < a[i]:
    print(-1)
    exit(0)
  d = v - a[i]
  x = b[i - 1] + b[(i + 1) % N]
  t = d // x
  if t == 0:
    if v == a[i]: continue
    print(-1)
    exit(0)
  b[i] -= x * (t)
  res += t
  hpu(h, -(b[i] * base + i))
print(res)
