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 collections import defaultdict, deque, Counter
import sys
import heapq
import math

# input = sys.stdin.readline

sys.setrecursionlimit(1000000000)

MIN = -10 ** 9
MOD = 10 ** 9 + 7


def main():
    N = int(input())
    A = [int(a) for a in input().split()]
    B = [int(a) for a in input().split()]
    # A = [
    #     [int(a) for a in input().split()]
    #     for _ in range(N)
    # ]
    for i in range(N):
        if A[i] > B[i]:
            print(-1)
            return
    target = set(i for i, (a, b) in enumerate(zip(A, B)) if a < b)
    q = [i for i in range(N) if B[N - 1 if i == 0 else i - 1] < B[i] and B[i] > B[0 if i == N - 1 else i + 1]]

    result = 0
    while len(q) != 0:
        i = q.pop()
        if i not in target:
            continue

        pre = N - 1 if i == 0 else i - 1
        fwd = 0 if i == N - 1 else i + 1

        if B[pre] < B[i] and B[i] > B[fwd]:
            minus = B[pre] + B[fwd]
            sa = B[i] - max(B[pre], B[fwd])
            kaisu = (1 + sa // minus)
            if B[i] - kaisu * minus < A[i]:
                sa = B[i] - A[i]
                kaisu = sa // minus
                if kaisu == 0:
                    print(-1)
                    return
                B[i] -= kaisu * minus
            else:
                B[i] -= kaisu * minus
            result += kaisu
            if A[i] == B[i]:
                target.remove(i)
            if A[i] > B[i]:
                print(-1)
                return
            q.append(pre)
            q.append(fwd)
    if len(target) != 0:
        print(-1)
    else:
        print(result)


if __name__ == '__main__':
    main()
