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.io.*;
import java.util.*;
import java.math.*;
public class pride
{
    static int get(int a,int b)
    {
        if(b==0)
        return a;
        else
        {
            return get(b,a%b);
        }
    }
    public static void main(String args[])throws IOException
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        int n=Integer.parseInt(br.readLine());
        String s[]=br.readLine().split(" ");
        int arr[]=new int[n];int count=0;
        for(int i=0;i<n;i++)
        {
            arr[i]=Integer.parseInt(s[i]);
            if(arr[i]==1)
            count++;
        }
        if(count>0)
        {
            System.out.println(n-count);
        }
        else
        {
            int gcd=arr[0];
            for(int i=1;i<n;i++)
            {
                gcd=get(gcd,arr[i]);
            }
            if(gcd>1)
            System.out.println("-1");
            else
            {
                int min=n+1;
                for(int i=0;i<n;i++)
                {
                    int g=arr[i],c=0,f=0;
                    for(int j=i+1;j<n;j++)
                    {
                        g=get(g,arr[j]);
                        c++;
                        if(g==1)
                        {
                            f=1;
                            break;
                        }
                    }
                    if(f==1)
                    min=(int)Math.min(min,c);
                }
                System.out.println(min+n-1);
                //System.out.println(min);
            }
        }
    }
}