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
from heapq import *

N = int(input())
A = [int(a) for a in input().split()]
B = [int(a) for a in input().split()]

h = []
for i in range(N):
    heappush(h, -((B[i]<<18)+i))

ans = 0
while h:
    a = -heappop(h)
    b = a>>18
    i = a%(1<<18)
    if b == A[i]:
        continue
    k = - (-(B[i] - max(B[i-1], B[(i+1)%N], A[i])) // (B[i-1] + B[(i+1)%N]))
    if k <= 0:
        print("-1")
        break
    B[i] -= (B[i-1] + B[(i+1)%N]) * k
    heappush(h, -((B[i]<<18)+i))
    ans += k
else:
    print(ans)
