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.*;
public class Pride{
    public static long gcd(long a,long b)
    {
        long temp=a;
        while(temp!=0)
        {
            a = temp;
            temp = b%a;
            b = a;
        }
        return a;
    }
    public static void main(String args[])
    {
        Scanner sc = new Scanner(System.in);
        int i,j,n,count=0;
        n = sc.nextInt();
        long arr[] = new long[n];
        for(i=0;i<n;i++)
        {
            arr[i] = sc.nextLong();
        }
        //Arrays.sort(arr);
        //System.out.println(arr[4]);
        for(i=0;i<n;i++)
        {
            if((int)arr[i]==1)
            {
                count++;
            }
        }
        if(count>0)
        {
            System.out.println(n-count);
        }
        else
        {
            for(i=1;i<n;i++)
            {
                for(j=0;j+i<n;j++)
                {
                        arr[j] = gcd(arr[j+1],arr[j]);
                        count++;
                        if((int)arr[j]==1)
                        {
                            System.out.println(i+n-1);
                            break;
                        }
                }
                if((j+i)!=n)
                    break;
            }    
            count = 0;
            for(i=0;i<n;i++)
            {
                if(arr[i]==1)
                {   
                    count++;
                    break;
                }
            }
            if(count==0)
            {
                System.out.println(-1);
            }
        //System.out.println(count);
        }
    }
}