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.
//https://yymelo.com/codeforces891apride%EF%BC%88%E6%95%B0%E5%AD%A6%EF%BC%89/
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Scanner;
import java.util.ArrayList;
import static java.lang.Math.min;

public class CDF891A{

  private static int gcd(int a, int b){
    return (b==0)?a:gcd(b,a%b);
  }
  public static void main(String[] args) {
    Scanner input = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
    int n = input.nextInt();
    ArrayList a = new ArrayList();
    while(true){
      int cont=0;
      for(int i=0;i<n;i++){
        a.add(input.nextInt());
        if(a.get(i).equals(1)) cont++;
      }
      if(cont>0){
        System.out.println(n - cont);
        break;
      }else{
        int  t = Integer.MAX_VALUE; //Get infinity
        for(int i=0;i<n;i++){
          int cur = 0;
          for(int j=i;j<n;j++){
            if((cur=gcd(cur,(int)a.get(j))) == 1){
              t=min(t,(j-i));
              j=n;
            }
          }
        }
        if(t == Integer.MAX_VALUE){
          System.out.println("-1");
          break;
        }else{
          System.out.println(t+n-1);
          break;
        }
      }
    }
  }
}
