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.Scanner;

public class Shashank
{
    public static int gcd(int a, int b)
    {
        if (a == 0 || b == 0)
           return 0;

        if (a == b)
            return a;

        if (a > b)
            return gcd(a-b, b);
            
        return gcd(a, b-a);
    }
    
    public static void main(String []args)
    {
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        
        int[] array = new int[n];
        for(int i = 0; i < n; i++)
            array[i] = scan.nextInt();
        
        int[] gcd = new int[n];
        System.arraycopy(array, 0, gcd, 0, array.length);
        int[] newgcd;
        
        int count1 = 0; 
        for(int i = 0; i < n; i++)
            if(array[i] == 1)
                count1++;
                
        if(count1 > 0)
            System.out.println(n - count1);
        else
        {
            int i;
main:       for(i = 0; i < n; i++)
            {
                newgcd = new int[n - i - 1];
                for(int j = 0; j < n - i - 1; j++)
                {
                    newgcd[j] = gcd(gcd[j], gcd[j + 1]);
                    if(newgcd[j] == 1)
                        break main;
                }
                gcd = new int[n - i - 1];
                System.arraycopy(newgcd, 0, gcd, 0, n - i - 1);
            }
            
            if(i == n)
                System.out.println(-1);
            else
                System.out.println(i + n);
        }
    }
}