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 math
#import numpy as np
import queue
from collections import deque,defaultdict
import heapq
from sys import stdin,setrecursionlimit
#from scipy.sparse.csgraph import dijkstra
#from scipy.sparse import csr_matrix
ipt = stdin.readline
setrecursionlimit(10**7)

def main():
    n = int(ipt())
    a = [int(i) for i in ipt().split()]
    b = [int(i) for i in ipt().split()]
    hq = []
    ans = 0
    for i,bi in enumerate(b):
        if bi > a[i]:
            heapq.heappush(hq,(-bi,i))
    while len(hq) > 0:
        #print(hq,b)
        nbi,i = heapq.heappop(hq)
        if i == n-1:
            bp = b[0]
        else:
            bp = b[i+1]
        bm = b[i-1]
        t = (-a[i]-nbi)//(bm+bp)
        if t == 0:
            print(-1)
            exit()
        b[i] -= (bm+bp)*t
        if b[i] > a[i]:
            heapq.heappush(hq,(-b[i],i))
        ans += t
    print(ans)
    return

if __name__ == '__main__':
    main()
