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
N = int(input())
B = list(map(int, input().split()))
A = list(map(int, input().split()))
eq = [0] * N

i = 0
ans = 0
eq_flag = 0
while True:
    if A[i] < B[i]:
        ans = -1
        break
    elif A[i] == B[i]:
        i = (i + 1) % N
        if eq[i] == 0:
            eq_flag += 1
            eq[i] = 1
    else:
        if A[i] > A[(i-1) % N] and A[i] > A[(i + 1) % N]:
            A0 = A[(i-1)%N]
            A1 = A[i]
            A2 = A[(i+1)%N]
            temp = (A1 - B[i]) // (A0 + A2)
            if temp == 0:
                ans = -1
                break
            A[i] -= temp * (A0 + A2)
            ans += temp
            i = (i - 1) % N
        else:
            i = (i + 1) % N
    if eq_flag == N:
        break

print(ans)
