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 pprint import pprint
import heapq

def solve(n, a, b):
    b_pq = []
    b_rev = {}
    delete = []
    for i, b_i in enumerate(b):
        if b_i == a[i]:
            continue
        heapq.heappush(b_pq, (-1 * b_i, i))

    count = 0
    while b_pq:
        tmp = heapq.heappop(b_pq)
        # pprint(tmp)
        b_i = tmp[0] * -1
        i_b = tmp[1]
        # print(i_b, b_i)
        i_a = (i_b - 1 + n) % n
        i_c = (i_b + 1) % n
        b_cand = b_i
        if b_cand - b[i_a] - b[i_c] < a[i_b]:
            continue

        #while b_cand - b[i_a] - b[i_c] >= a[i_b]:
        #    b_cand = b_cand - b[i_a] - b[i_c]
        #    count += 1
        tmp_count =  (b_cand - a[i_b]) // (b[i_a] + b[i_c])
        b_cand -= (b[i_a] + b[i_c]) * tmp_count
        count += tmp_count

        b[i_b] = b_cand
        if b_cand != a[i_b]:
            heapq.heappush(b_pq, (-1 * b_cand, i_b))
        # print("count: ", count)
        # pprint(b)
         

        if b_cand == a[i_b] and b == a:
            return count
    
    return -1


if __name__ == '__main__':

    n = int(input().strip())
    a = list(map(int, input().strip().split(" ")))
    b = list(map(int, input().strip().split(" ")))
    print(solve(n, a, b))