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.
// package Mathematical;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Pride {
    public static int gcd(int a,int b){
        if(b==0){
            return a;
        }
        return gcd(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 line[]=br.readLine().split(" ");
        int a[]=new int[n];
        int m=0;
        for(int i=0;i<n;i++){
            a[i]=Integer.parseInt(line[i]);
            if(a[i]==1){
                m++;
            }
        }
        int min=n;
        for(int i=0;i<n;i++){
            int temp=a[i];
            for(int j=i;j<n;j++){
                temp=gcd(temp,a[j]);
                if(temp==1){
//                    System.out.println(i+" "+j);
                    min=Math.min(j-i,min);
                    break;
                }
            }
        }
        if(min==n)
        System.out.println("-1");
        else{
            if(m==0)
            System.out.println(min+n-1);
            else{
                System.out.println(n-m);
            }
        }
    }
}
