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.
/*
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 * and open the template in the editor.
 */

import java.util.*;

/**
 *
 * @author Bryan AW
 */
public class Codeforces {

    /**
     * @param args the command line arguments
     */
     
    static int GCD(int x, int y){
        
        if (y==0){
            return x;
        }
        else {
            return GCD(y, x%y);
        }
        
    }
     
    public static void main(String[] args){
        
        //Pride
                            
        Scanner sc=new Scanner(System.in);
        
        int n=sc.nextInt();
        
        int cnt=0;
        
        int[] a=new int[n];
        
        for (int i=0;i<n;i++){
            a[i]=sc.nextInt();
            if (a[i]==1){
                cnt++;
            }
        }
        
        int ans=-1;
        
        if (cnt>0){
            ans=n-cnt;
        }
        else {
            int[][] g=new int[n][n];
            for (int i=0;i<n-1;i++){
                g[i][i+1]=GCD(a[i], a[i+1]);
                if (g[i][i+1]==1){
                    ans=n;
                }
            }
            if (ans==-1){
                for (int t=2;t<n;t++){
                    for (int i=0;i<n-t;i++){
                        int gcd=GCD(g[i][i+t-1], a[i+t]);
                        g[i][i+t]=gcd;
                        if (gcd==1){
                            ans=n+t-1;
                            break;
                        }
                    }
                    if (ans!=-1) break;
                }
            }
        }
        
        System.out.println(ans);
        
    }
    
}