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
from heapq import *

input = sys.stdin.readline

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

dif = [x-y for (x,y) in zip(A,B)]
difh = []
for i, d in enumerate(dif):
	heappush(difh, (d,i))

ans = 0
while difh[0][0]!=0:
	tv, ti = difh[0]
	if ti==0:
		ll, rr = B[-1], B[1]
	elif ti==N-1:
		ll, rr = B[N-2], B[0]
	else:
		ll, rr = B[ti-1], B[ti+1]

	plus = int((-tv)/(ll+rr))
	if plus==0:
		ans=-1
		break
	else:
		tv += (ll+rr)*plus
		ans += plus
		B[ti] = A[ti]-tv
		heappushpop(difh, (tv, ti))

print(ans)