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.lang.*;
import java.io.*;
import java.io.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.Scanner; 
import java.util.StringTokenizer;

import javax.lang.model.util.ElementScanner6; 

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
    
    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    
    }
    static long power(long x,long y) 
    { 
        long temp; 
        if( y == 0) 
            return 1; 
        temp = power(x, y/2);  
          
        if (y%2 == 0) 
            return temp*temp; 
        else
        { 
            if(y > 0) 
                return x * temp * temp; 
            else
                return (temp * temp) / x; 
        } 
    }
    static long gcd(long a, long b)
    {
        if(b==0)
        {
            return a;
        }
        else
        return gcd(b,a%b);
    }  
     
public static void main(String args[])
{
    Scanner sc=new Scanner(System.in);
    int n=sc.nextInt();
    long a[]=new long[n];
    
    for( int i=0;i<n;i++)
    {
        a[i]=sc.nextLong();
    }
    long gcd_arr=a[0];
    int count=0;
    for( int i=0;i<n;i++)
    {
        if(a[i]==1)
        {
            count++;
        }
        gcd_arr=gcd(Math.max(gcd_arr,a[i]),Math.min(gcd_arr,a[i]));
    }
    if(count==1)
    {
        System.out.println(n-1);
    }
    else if( count>1)
    {
        System.out.println(n-count);
    }
    else
    {
        long min=1000000009;
        for( int i=0;i<n;i++)
        {
            long value=a[i];
            for( int j=i;j>=0;j--)
            {
                value=gcd(Math.max(value,a[j]),Math.min(value,a[j]));
                if(value==1)
                {
                    min=Math.min(min,(i-j));
                }
            }value=a[i];
            for( int j=i;j<n;j++)
            {
                value=gcd(Math.max(value,a[j]),Math.min(value,a[j]));
                if(value==1)
                {
                    min=Math.min(min,(j-i));
                }
            }
        }
        if(gcd_arr!=1)
        {
            System.out.println(-1);
        }
        else
        System.out.println(min+n-1);
    }
}
}

class myComparator implements Comparator<Long>
{
    public int compare(Long a,Long b)
    {
        if(b>a)
        return 1;
        else if(a>b)
        return -1;
        else
        return 0;

    }
}