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 heapq import heappush,heappop
import sys
input=sys.stdin.readline

N=int(input())
A=list(map(int,input().split()))
B=list(map(int,input().split()))
lst=[]
for i in range(N):
    heappush(lst,(-B[i],i))

count=0
while lst:
    h,i=heappop(lst)
    h=-h
    x,z=B[i-1],B[(i+1)%N]
    kkk=x+z
    if (h-A[i])%kkk==0:
        count+=(h-A[i])//kkk
        B[i]=A[i]
        continue
    elif kkk>=h:
        print(-1)
        sys.exit()
    else:
        count+=h//kkk
        h=h%kkk
        B[i]=h    
        if A[i]>h:
            print(-1)
            sys.exit()
        heappush(lst,(-h,i))

if A==B:
    print(count)
else:
    print(-1)