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.*;
import java.io.*;
public class Task {
public static void main(String args[]) throws  IOException {
         assign();
              int t=1,cn=1;
              while(t--!=0){
                int n=int_v(read());
                int[] x=int_arr();
                int res=2000000,c=0,ff=x[0];
                for(int o:x){ff=gcd(ff,o);}
                for(int i=0;i<n;i++){
                    if(x[i]==1)c++;
                    int tmp=x[i];
                    for(int j=i;j<n;j++){
                        tmp=gcd(tmp,x[j]);
                        if(tmp==1) {res=Math.min(res,j-i);break;}
                    }
                }
                if(ff!=1){out.write("-1");}
                else{
                    if(c!=0){out.write(Math.min(n-c,n-1+res)+"");}
                    else{out.write(n-1+res+"");}
                }
            }
            out.flush();
               
            }

static BufferedReader s1;
static BufferedWriter out;
static String read() throws IOException{String line="";while(line.length()==0){line=s1.readLine();continue;}return line;}
static int int_v (String s1){return Integer.parseInt(s1);}
static long long_v(String s1){return Long.parseLong(s1);}
static int[] int_arr() throws IOException{String[] a=read().split(" ");int[] b=new int[a.length];for(int i=0;i<a.length;i++){b[i]=int_v(a[i]);}return b;}
static long[] long_arr() throws IOException{String[] a=read().split(" ");long[] b=new long[a.length];for(int i=0;i<a.length;i++){b[i]=long_v(a[i]);}return b;}
static void assign(){s1=new BufferedReader(new InputStreamReader(System.in));out=new BufferedWriter(new OutputStreamWriter(System.out));}
static int gcd(int a,int b){if(b==0){return a;}return gcd(b,a%b);}

           
}