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 org.omg.CORBA.INTERNAL;

import java.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;

public class Solution {
    static boolean test = false;

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() throws FileNotFoundException {

            InputStream inputStream = test ? new FileInputStream("/Users/aj/code/HackerRank/input.txt") : System.in;
            br = new BufferedReader(new
                    InputStreamReader(inputStream));//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;
        }
    }

    public static int gcd(int a,int b){
        if(a==0 || b==0) return a+b;
        else return gcd(b,a%b);
    }

    public static void main(String[] args) throws FileNotFoundException {
        FastReader in = new FastReader();
        int n = in.nextInt();
        int[] arr=new int[n];
        int cnt1=0;
        for(int i=0;i<n;i++) {
            arr[i] = in.nextInt();
            if(arr[i]==1)
                cnt1++;
        }
        if(cnt1>0)
            System.out.println(n-cnt1);
        else{
            boolean found=false;
            int dist=2001;
            for(int L=0;L<n-1;L++) {
                int gc=arr[L];
                for(int R=L+1;R<n;R++) {
                    gc=gcd(gc,arr[R]);
                    if(gc==1){
                        if((R-L)<dist)
                            dist=R-L;
                        found=true;
                        break;
                    }
                }
            }
            if(found)
                System.out.println(dist+n-1);
            else
                System.out.println(-1);
        }

    }
}
