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
def examA():
    S = SI(); N = len(S)
    prev = S[0]; cur = ""
    k = 0; ans = 1
    while(k<N-1):
        k +=1
        cur += S[k]
        if cur==prev:
            continue
        prev = cur
        cur = ""
        ans +=1
    print(ans)
    return

def examB():
    N = I()
    S = SI()
    return

def examC():
    N = I()
    A = LI()
    B = LI()
    ans = 0
    que = []
    for i in range(N):
        heappush(que,(-B[i],i))
    flag = True
    while(que):
        b,i = heappop(que)
        b *=(-1)
        if b == A[i]:
            continue
        a, c = B[(i - 1) % N], B[(i + 1) % N]
        if b - A[i] < a + c:
            flag = False
            break
        r = (b - A[i]) // (a + c)
        b -= (a + c) * r
        B[i] = b
        ans += r
        if b != A[i]:
            heapq.heappush(que, (-b, i))
#    print(que)
#    print(K)
    if flag:
        print(ans)
    else:
        print(-1)
    return

import sys,copy,bisect,itertools,heapq,math
from heapq import heappop,heappush,heapify
from collections import Counter,defaultdict,deque
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))
def LSI(): return list(map(str,sys.stdin.readline().split()))
def LS(): return sys.stdin.readline().split()
def SI(): return sys.stdin.readline().strip()
global mod,mod2,inf
mod = 10**9 + 7
mod2 = 998244353
inf = 10**18

if __name__ == '__main__':
    examC()
