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
#C問題
N = int(input())
A = list(map(int,input().split()))
B = list(map(int,input().split()))

ans = 0
div = 0
flag = 1
while flag == 1:
    flag = 0
    for i in range(N):
        if B[i]-B[i-1]-B[(i+1)%N] >= A[i]:
            div = (B[i]-A[i])//(B[i-1]+B[(i+1)%N])
            B[i] -= (B[i-1]+B[(i+1)%N])*div
            ans+=div
            flag = 1
            
print(ans if A == B else -1)