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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.*;

public class practiceJAVA{
    public static void main(String[] args) throws IOException {
        Reader.init(System.in);
        int n =Reader.nextInt();
        int a[]=new int[n];
        int b[]= new int[n];
        int ar[]=new int[n];
        for(int i=0;i<n;i++){
            ar[i]=Reader.nextInt();
        }
        int count=0;
        for(int i=0;i<n;i++) {
            if (ar[i] == 1) {
                count++;
            }
            b[i] = ar[i];
        }

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

        for(int i=1;i<n;i++){
            for(int j=i;j<n;j++){
                a[j]=gcd(b[j-1],ar[j]);
                if(a[j]==1){
                    System.out.println(n-1+i);
                    return;
                }
            }
            for(int j=i;j<n;j++){
                b[j]=a[j];
            }
        }
        System.out.println(-1);

    } // main end

    static int gcd(int a, int b){
        if(b==0){
            return a;
        }
        return gcd(b,a%b);
    }
} // class end


class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    static void init(InputStream input) {
        reader = new BufferedReader(
                new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            tokenizer = new StringTokenizer(
                    reader.readLine() );
        }
        return tokenizer.nextToken();
    }
    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }
    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
    static long nextLong() throws IOException {
        return Long.parseLong( next() );
    }
}