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
#input = sys.stdin.readline
import heapq
def main():
    N = int( input())
    A = list( map( int, input().split()))
    B = list( map( int, input().split()))
    C = [(-B[i],i) for i in range(N)]
    heapq.heapify(C)
    ans = 0
    check = 0
    while check < N:
        a,i = heapq.heappop(C)
        a *= -1

        if B[i] == A[i]:
            check += 1
            continue
        cnt = (B[i] - A[i])//(B[i-1] + B[(i+1)%N])
        if cnt == 0:
            print(-1)
            return
        ans += cnt        
        a -= (B[i-1] + B[(i+1)%N])*cnt
        B[i] = a
        if B[i] == A[i]:
            check += 1
        elif B[i] > A[i]:
            heapq.heappush(C, (-a, i))
        else:
            print(-1)
            return

    print(ans)
        
if __name__ == '__main__':
    main()
