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 math import gcd

n = int(input())
j = [int(x) for x in input().split(" ")]

def screen(l):
    o = []
    for i in range(len(l)-1):
        c = gcd(l[i],l[i+1])
        if c == 1:
            return 1
        else:
            o.append(c)

    return o


if n == 1:
    if j[0] == 1:
        print(0)
    else:
        print(-1)
else:
    d = j.count(1)
    if d == 0:
        t = j
        for i in range(len(j)-1):
            r = screen(t)
            if r == 1:
                print(i+n)
                break
            else:
                t = r

        if t != 1:
            if len(t) ==1:
                print(-1)
    else:
        print(n-d)
