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
sys.setrecursionlimit(100000)

def getN():
    return int(input())
def getList():
    return list(map(int, input().split()))
import math

n = getN()

anums = getList()
bnums = getList()
ans = 0
okay = [0 for i in range(n)]
update = True
while(update):
    update = False
    for i in range(n):
        if not okay[i]:
            if i == n - 1:
                j = 0
            else:
                j = i + 1
            h = i - 1
            a,b,c, tgt = bnums[h], bnums[i], bnums[j], anums[i]
            # print(a,b,c)
            if b > max(a, c):
                if tgt > b:
                    print(-1)
                    sys.exit()
                if tgt != b:
                    dec = math.ceil((b - (max(a, c, tgt)) ) / (a+c))
                    bnums[i] -= dec * (a+c)
                    ans += dec
                    update = True
                    if anums[i] == bnums[i]:
                        okay[i] = 1
    # print(coll, anums, bnums)

print(ans)