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 heapq
import os
import sys

if os.getenv("LOCAL"):
    sys.stdin = open("_in.txt", "r")

sys.setrecursionlimit(10 ** 9)
INF = float("inf")
IINF = 10 ** 18
MOD = 10 ** 9 + 7
# MOD = 998244353


N = int(sys.stdin.buffer.readline())
A = list(map(int, sys.stdin.buffer.readline().split()))
B = list(map(int, sys.stdin.buffer.readline().split()))


# 逆から貪欲に操作可能
def solve():
    heap = [(-b, i) for i, b in enumerate(B)]
    heapq.heapify(heap)
    ret = 0
    while heap:
        b, i = heapq.heappop(heap)
        b *= -1
        a = A[i]
        if b < a:
            return -1
        if b == a:
            continue
        step = B[(i - 1) % N] + B[(i + 1) % N]
        if (b - a) // step == 0:
            return -1
        cnt = (b - a) // step
        ret += cnt
        b -= cnt * step
        B[i] = b
        heapq.heappush(heap, (-b, i))
    return ret


ans = solve()
print(ans)
