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())
A = [int(a) for a in input().split()]
B = [int(a) for a in input().split()]
if N > 10000:
    A = A[5050:] + A[:5050]
    B = B[5050:] + B[:5050]
ans = -1

D = [0] * N
L = [i-1 for i in range(N)]
R = [i+1 for i in range(N)]

def calc():
    i = 0
    c = 0
    ans = 0
    while c < N:
        while i < N:
            if B[i] == A[i]:
                if D[i] == 0:
                    c += 1
                    D[i] = 1
                if L[i] >= 0: R[L[i]] = R[i]
                if R[i] < N: L[R[i]] = L[i]
            if B[i] > A[i] and B[i] >= max(B[i-1], B[(i+1)%N]):
                k = - (-(B[i] - max(B[i-1], B[(i+1)%N], A[i])) // (B[i-1] + B[(i+1)%N]))
                B[i] -= (B[i-1] + B[(i+1)%N]) * k
                ans += k
                if k <= 0:
                    return -1
            i = R[i]
        i = N-1
        while i >= 0:
            if B[i] == A[i]:
                if D[i] == 0:
                    c += 1
                    D[i] = 1
                if L[i] >= 0: R[L[i]] = R[i]
                if R[i] < N: L[R[i]] = L[i]
            if B[i] > A[i] and B[i] >= max(B[i-1], B[(i+1)%N]):
                k = - (-(B[i] - max(B[i-1], B[(i+1)%N], A[i])) // (B[i-1] + B[(i+1)%N]))
                B[i] -= (B[i-1] + B[(i+1)%N]) * k
                ans += k
                if k <= 0:
                    return -1
            i = L[i]
    return ans

print(calc())