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 heappop as hpp, heappush as hp

readline = sys.stdin.readline
N = int(readline())
A = list(map(int, readline().split()))
B = list(map(int, readline().split()))

geta = 10**6        
Q = [-(B[i]*geta+i) for i in range(N)] + [0]
Q.sort()

ans = 0
cnt = 0
inf = 10**9+7
while cnt < N:
    b, idx = divmod(-hpp(Q), geta)
    a = A[idx]
    if b < a:
        ans = -1
        break
    bside = B[(idx+1)%N] + B[(idx-1)%N]
    kb = 1+(b-bside)//bside
    ka = (b-a)//bside
    k = min(ka, kb)
    B[idx] -= k*bside
    ans += k
    if B[idx] == a:
        cnt += 1
    elif k == 0:
        ans = -1
        break
    else:
        hp(Q, -(B[idx]*geta+idx))
print(ans)