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


def gcd(a, b):
    if b > 0:
        return gcd(b, a % b)
    else:
        return a


allGcd = array[0]
for elem in array:
    allGcd = gcd(allGcd, elem)

if allGcd > 1:
    print(-1)
else:
    ones = 0
    for elem in array:
        if elem == 1:
            ones += 1

    if ones > 1:
        print(n - ones)
    else:
        res = 2000000000
        for i in range(n):
            tmp = array[i]
            for j in range(i, n):
                tmp = gcd(tmp, array[j])
                if tmp == 1:
                    res = min(res, j-i)
        print(n + res - 1)
