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.*;
import java.math.*;
 
 
import static java.lang.Math.*;
import static java.util.Arrays.*;
import static java.util.Collections.*;
 
 
public class Main{ 
 
 
    static long mod=1000000007;
    static int dx[]={1,-1,0,0};
    static int dy[]={0,0,1,-1};
    // static int dx[]={1,-1,0,0,1,1,-1,-1};
    // static int dy[]={0,0,1,-1,1,-1,1,-1};
    // PriorityQueue<Integer> que = new PriorityQueue<Integer>(); 
    //HashMap<Integer,Integer> map = new HashMap<Integer,Integer>();
 
    public  static void main(String[] args)   throws Exception, IOException{
     
        
        Reader sc = new Reader(System.in);
        PrintWriter out=new PrintWriter(System.out);
     
        int n=sc.nextInt();
        // char c[][] = new char[h][w];
        long a[] = new long [n];
        int one = 0; 
        for (int i=0; i<n; i++ ) {
            a[i] = sc.nextLong();
            if(a[i]==1)one++;
        }
        int ans = 0;
        if(n==1){
            if(a[0]>1)ans = -1;
        }
        else {int c=0; ans=-1;
        lp: for (int t=1;  t<=n-1; t++) {
                for (int i=0;  i<n-t; i++) {
                    a[i] = gcd(a[i],a[i+1]);
                    if(a[i]==1){ans = t + n - 1;  break lp;}
                }
                // db(a);
            }
            if(one>0)ans=n-one;
        }
        out.println(ans);
        out.flush();
    }

    static long gcd(long a, long b){
        if(min(a,b) == 0)return max(a,b);
        return gcd(max(a,b) % min(a,b),min(a,b));
    }
     
    static void db(Object... os){
     
        System.err.println(Arrays.deepToString(os));
     
    }
     
    static boolean validpos(int x,int y,int r, int c){
        
        return x<r && 0<=x && y<c && 0<=y;
        
    }
     
    static boolean bit(long x,int k){
        // weather k-th bit (from right) be one or zero
        return  ( 0 < ( (x>>k) & 1 )  )  ? true:false;
    }    
}
 
class XY {
    int x,y,d;
    XY(int x, int y, int d) {
        this.x=x;
        this.y=y;
        this.d=d;
    } 
}
 
class P implements Comparable<P>{
    int x,y;
    P(int x, int y) {
        this.x=x;
        this.y=y;
    } 
      
    public int compareTo(P p){
        return -x + p.x;//des
    } 
}
 
class Reader
{ 
    private BufferedReader x;
    private StringTokenizer st;
    
    public Reader(InputStream in)
    {
        x = new BufferedReader(new InputStreamReader(in));
        st = null;
    }
    public String nextString() throws IOException
    {
        while( st==null || !st.hasMoreTokens() )
            st = new StringTokenizer(x.readLine());
        return st.nextToken();
    }
    public int nextInt() throws IOException
    {
        return Integer.parseInt(nextString());
    }
    public long nextLong() throws IOException
    {
        return Long.parseLong(nextString());
    }
    public double nextDouble() throws IOException
    {
        return Double.parseDouble(nextString());
    }
}