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.*;
import java.io.*;

  

public class Main
{   public static int gcd(int a,int b)
    {
        if(b==0)
            return a;
        else return gcd(b,a%b);
    }
    public static void main(String args[])
    {
         InputStream in=System.in;
       //  OutputStream out=System.out;
        FastScanner fs=new FastScanner(in);
        PrintWriter out=new PrintWriter(System.out);
        
         int n=fs.nextInt();
        int arr[]=new int[n];
        int one=0;
       // out.println(gcd(42,35));
        
        arr[0]=fs.nextInt();
        if(arr[0]==1)
            one++;
        int gd=arr[0];
        for(int i=1;i<n;i++)
        {
        arr[i]=fs.nextInt();
    gd=gcd(gd,arr[i]);
        if(arr[i]==1)
            one++;

        }

        if(one==0&&gd==1&&n>1)
        {
            int tem[]=new int[n];

        int diff=n;
          int j=0;
          int tr=0;
          int ans=0;
        for(int i=0;i<n-1;i++)
        {    tem[i]=gcd(arr[i],arr[i+1]);
                if(tem[i]==1)
                    tr=1;
}
        tem[n-1]=arr[n-1];
        //for(int i=0;i<n;i++)
        //    out.println(tem[i]);

if(tr==0)
{
 LOOP:     for( j=2;j<=n;j++)
      {
        for(int i=0;i<n-1;i++)
           {
            tem[i]=gcd(tem[i],tem[i+1]);
            if(tem[i]==1)
                break LOOP;
           }
       }
       if(j!=n)
         ans=j+n-1;

}
else
      ans=n;

            out.println(ans);
        
    }
    else if(one>0)
        out.println(n-one);
      
    else 
        out.println("-1");
     out.close();
    //   for(int i=0;i<n;i++)
      // System.out.println(arr[i]); 
    
    }

   static    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        FastScanner(InputStream f) {
            try {
                br = new BufferedReader(new InputStreamReader(f));
            } catch (Exception e) {
                e.printStackTrace();
            }
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        
    }


}