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.*;
import java.lang.*;
 
public class Rextester{
    static int gcd(int a,int b){
        if(a%b==0){
            return b;
        }
        return gcd(b,a%b);
    }
    static int gcd(int[] array,int low,int high){
        int x = array[low];
        for(int i=low+1;i<=high;i++){
            x = gcd(x,array[i]);
        }
        return x;
    }
    public static void main(String[] args)throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = new Integer(br.readLine());
        StringTokenizer st = new StringTokenizer(br.readLine());
        br.close();
        int[] array = new int[n];
        boolean flag=false;
        for(int i=0;i<n;i++){
            array[i]=new Integer(st.nextToken());
            if(array[i]==1){
                flag=true;
            }
        }
        if(flag){
            int count  = 0;
            for(int i=0;i<n;i++){
                if(array[i]!=1){
                    count++;
                }
            }
            System.out.println(count);
            return;
        }
        if(gcd(array,0,n-1)>1){
            System.out.println("-1");
            return;
        }
        int x = Integer.MAX_VALUE;
        for(int i=0;i<n;i++){
            for(int j=i+1;j<n;j++){
                if(gcd(array[i],array[j])==1){
                    x=Math.min(j-i+1,x);
                }
            }
        }
        if(x==Integer.MAX_VALUE){
            x=3;
        }
        System.out.println(n-x+2*(x-1));
    }
}