You have an array a with length n, you can perform operations. Each operation is like this: choose two adjacent elements from a, say x and y, and replace one of them with gcd(x, y), where gcd denotes the [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor).

What is the minimum number of operations you need to make all of the elements equal to 1?

Input

The first line of the input contains one integer n (1 ≤ n ≤ 2000) — the number of elements in the array.

The second line contains n space separated integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the elements of the array.

Output

Print -1, if it is impossible to turn all numbers to 1. Otherwise, print the minimum number of operations needed to make all numbers equal to 1.

Examples

Input

5
2 2 3 4 6


Output

5


Input

4
2 4 6 8


Output

-1


Input

3
2 6 9


Output

4

Note

In the first sample you can turn all numbers to 1 using the following 5 moves:

  * [2, 2, 3, 4, 6]. 
  * [2, 1, 3, 4, 6]
  * [2, 1, 3, 1, 6]
  * [2, 1, 1, 1, 6]
  * [1, 1, 1, 1, 6]
  * [1, 1, 1, 1, 1]



We can prove that in this case it is not possible to make all numbers one using less than 5 moves.
from fractions import gcd
from functools import reduce

n = int(input())
a = list(map(int, input().split()))


if 1 < reduce(lambda x, y: gcd(x, y), a):
    print(-1)
elif any(map(lambda x: x == 1, a)):
    print(len(list(filter(lambda x: 1 < x, a))))
else:
    l = 0
    r = n
    while 1 < r - l:
        m = (l + r) // 2
        if any(map(lambda x: x == 1, map(lambda i: reduce(lambda x, y: gcd(x, y), a[i: i + m]), range(n - m + 1)))):
            r = m
        else:
            l = m
    print(r + n - 2)
