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 Solution{

    static class FastReader{
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(new
                     InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }

    static long gcd(long a, long b){
        if(b==0)
            return a;
        return gcd(b, a%b);
    }

    public static void main (String[] args) throws Exception{
        FastReader sc = new FastReader();

        int n = sc.nextInt();
        long[] arr = new long[n];

        for(int i=0;i<n;i++)
            arr[i] = sc.nextLong();

        long[][] ggcd = new long[n][n];
        int cnt=0;
        for(int i=0;i<n;i++){
            ggcd[i][i] = arr[i];
            if(ggcd[i][i]==1)
                cnt++;
        }

        if(cnt>0){
            System.out.println(n-cnt);
            return;
        }

        int res = 10000;
        for(int l=1;l<n;l++){
            for(int i=0;i<n-l;i++){
                int j=i+l;
                int k = (int)(j+i)/2;
                ggcd[i][j] = gcd(ggcd[i][k], ggcd[k+1][j]);

                if(ggcd[i][j]==1)
                    res = Math.min(res, l);
            }
        }

        System.out.println( (res==10000)?"-1":(n-1+res) );

    }

}
