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
import sys
input = sys.stdin.readline

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N = int(input())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
q = []
q = [(-b, i) for i, b in enumerate(B)]
heapq.heapify(q)
ans = 0
N_m1 = N-1
while len(q)>0:
    b, idx = q[0]
    b = -b
    b_p1, b_m1 = B[idx+1 if idx<N_m1 else 0], B[idx-1]
    d = b_p1 + b_m1

    a = A[idx]
    p = min((b-a)//d, (b-b_m1)//d+1, (b-b_p1)//d+1)

    b -= p * d
    B[idx] = b
    ans += p
    if b > a:
        heapq.heapreplace(q, (-b, idx))
        if q[0][1] == idx:
            print(-1)
            exit()
    else:
        heapq.heappop(q)
print(ans)
