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 ####
import sys
import math
from collections import defaultdict

#### 設定 ####
sys.setrecursionlimit(10**7)
def input():
    return sys.stdin.readline()[:-1]


#### 読み込み ####
def I(): return int(input())
def II(): return map(int, input().split())
def III(): return list(map(int, input().split()))
def Line(N):
    read_all = [tuple(map(int, input().split())) for _ in range(N)]
    return map(list,zip(*read_all))

#################

import heapq

N = I()
A = III()
B = III()

x = []
for i,b in enumerate(B):
    heapq.heappush(x,(-b,i))

counter = 0

while x:
    temp = heapq.heappop(x)
    i = temp[1]
    b = -temp[0]
    a = B[(i-1)%N]
    c = B[(i+1)%N]
    if b == A[i]:
        continue
    elif b<A[i]:
        print(-1)
        exit()
    else:
        d,m = divmod(b-A[i],a+c)
        if d==0:
            print(-1)
            exit()
        elif m == 0:
            B[i] = A[i]
            counter += d
        else:
            B[i] = A[i]+m
            heapq.heappush(x,(-B[i],i))
            counter += d

print(counter)