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.lang.*;
import java.util.*;
public class  pr3
{
static class FastScanner {
InputStreamReader is;
BufferedReader br;
StringTokenizer st;
public FastScanner() {
is = new InputStreamReader(System.in);
br = new BufferedReader(is);
}
String next() throws Exception {
while (st == null || !st.hasMoreElements())
st = new StringTokenizer(br.readLine());
return st.nextToken();
}
int nextInt() throws Exception {
return Integer.parseInt(next());
}
long nextLong() throws Exception {
return Long.parseLong(next());
}
int[] readArray(int num) throws Exception {
int arr[]=new int[num];
for(int i=0;i<num;i++)
arr[i]=nextInt();
return arr;
}
String nextLine() throws Exception {
return br.readLine();
}
}
 public static boolean power_of_two(int a)
{
  if((a&(a-1))==0)
{
 return true;
}
return false;
}
static boolean PS(double x)
{
if (x >= 0) {
double i= Math.sqrt(x);
if(i%1!=0)
{
return false;
}
return ((i * i) == x);
}
return false;
}
public static int[] ia(int n)
{
    int ar[]=new int[n];
    return ar;
}
public static long[] la(int n)
{
    long ar[]=new long[n];
    return ar;
}
public static void print(int ans,int t)
{
    System.out.println("Case"+" "+"#"+t+":"+" "+ans);
}
//****   M A I N      C O D E     ****
 
public static void main(String args[]) throws java.lang.Exception
{
FastScanner sc=new FastScanner();
int n=sc.nextInt();
long ar[]=new long[n+1];
int count=0;
for(int i=1;i<=n;i++)
{
    ar[i]=sc.nextInt();
    if(ar[i]==1)
    {
        count++;
    }
}
if(count>0)
{
    System.out.println(n-count);
    return;
}

long min=Integer.MAX_VALUE;
for(int i=1;i<n;i++)
{
    long gcd=ar[i];
    for(int j=i+1;j<=n;j++)
    {
     gcd=gcd(ar[j],gcd);
        if(gcd==1)
        {
min=Math.min(min,j-i);
break;
        }
    }
   
}
    if(min==Integer.MAX_VALUE)
    {
        System.out.println(-1);
    }
    else{
        System.out.println(min+n-1);
    }
}
public static long gcd(long a, long b)
{
    if(a==0)
    {
        return b;
    }
    return gcd(b%a,a);
}
}