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
import heapq

def main():
    n=int(input())
    a=list(map(int,input().split()))
    b=list(map(int,input().split()))

    h=[]
    for i in range(n):
        if b[i]>a[i]:
            heapq.heappush(h,(b[i]*-1,i))

    loop=0
    idx=0
    while(1):
    #print(b)
        if not h:
            break
        buf,idx=heapq.heappop(h)
        buf=-1*buf

        x=(buf-a[idx])//(b[(idx-1)%n]+b[(idx+1)%n])
        buf-=x*(b[(idx-1)%n]+b[(idx+1)%n])
        loop+=x
        b[idx]=buf
        if x==0:
            #print(b)
            print(-1)
            sys.exit()
        elif buf>a[idx]:
            heapq.heappush(h,(buf*-1,idx))

    print(loop)

if __name__ == '__main__':
    main()