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.
import java.util.*;
public class Solution
{
    public static void main(String arg[])
    {
        Scanner io=new Scanner(System.in);
        int n=io.nextInt();
        ArrayList<Integer> arr=new ArrayList<>();
        for(int i=0;i<n;i++)
            arr.add(io.nextInt());
        if(arr.contains(1))
        {
            System.out.println(arr.size()-Collections.frequency(arr,1));
            System.exit(0);
        }
        int res=Integer.MAX_VALUE,gcd;
        for(int i=0;i<n;i++)
        {
            int xx=arr.get(i);
            for(int j=i+1;j<n;j++)
            {
                xx=gcdf(Math.max(xx,arr.get(j)),Math.min(xx,arr.get(j)));
                if(xx==1)
                {
                    res=Math.min(res,j-i);
                }
            }
        }
        if(res==Integer.MAX_VALUE)
            System.out.println("-1");
        else
            System.out.println(n-1+res);

    }
    public static int gcdf(int a,int b)
    {
        if(b==0)
            return a;
        else 
            return gcdf(b,a%b);
    }
}
