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
input = sys.stdin.readline
sys.setrecursionlimit(pow(10, 6))
from heapq import heappop, heappush

def main():
    n = int(input())
    a = list(map(int, input().split()))
    b = list(map(int, input().split()))
    hq = []
    for i, _b in enumerate(b):
        heappush(hq, (-_b, i))

    ans = 0
    while len(hq) != 0:
        q = heappop(hq)
        if -q[0] == a[q[1]]:
            # 同じなら何もする必要はない
            continue
        elif -q[0] < a[q[1]]:
            # 増やすことは出来ないので、小さいなら構築不可
            ans = -1
            break

        ac = b[(q[1] - 1) % n] + b[(q[1] + 1) % n]
        if (b[q[1]] - a[q[1]]) // ac == 0:
            # 一致しておらず、さらに減らせないので構築不可
            ans = -1
            break
        else:
            # できる限り減らす
            tmp = (b[q[1]] - a[q[1]]) // ac
            b[q[1]] -= ac * tmp
            ans += tmp
            heappush(hq, (-b[q[1]], q[1]))
    
    print(ans)

if __name__ == '__main__':
    main()
