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
import heapq as hp


def main():
    N = int(input())
    A = list(map(int, input().split()))
    B = list(map(int, input().split()))

    q = []
    for i, b in enumerate(B):
        hp.heappush(q, (-b, i))

    c = 0
    while q:
        #print(q)
        _, ind = hp.heappop(q)
        b = B[ind]
        if ind == N-1:
            s = B[ind-1]+B[0]
        else:
            s = B[ind-1]+B[ind+1]
        #print(b, s)
        if (b-A[ind])%s == 0:
            B[ind] = A[ind]
            c += (b-A[ind])//s
        elif b%s <= A[ind] or b < s:
            c = -1
            break
        else:
            c += b//s
            B[ind] = b%s
            hp.heappush(q, (-B[ind], ind))

    print(c)

if __name__ == "__main__":
    main()