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.Scanner;

public class A891 {
    static int gcd(int a,int b){
        if(b>a){
            int temp=a;
            a=b;
            b=temp;
        }
        while(b!=0){
            int temp=b;
            b=a%b;
            a=temp;
        }
        return a;
    }
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n=sc.nextInt();
        int a[]=new int[n];
        for (int i = 0; i < n; i++) {
            a[i]=sc.nextInt();
        }
        boolean cd=true;
        int ans=0,ct=0;
        for(int i=0;i<n;i++){
            if (a[i]==1){
                ct++;
            }
        }
        if(ct==0) {
            for (int j = n - 1; j > 0; j--) {
                for (int i = 0; i < j; i++) {
                    int temp = gcd(a[i], a[i + 1]);
                    if (temp == 1) {
                        cd = false;
                        ans = n + n - 1 - j;
                        break;
                    }
                    a[i] = temp;
                }
                if (!cd) {
                    break;
                }
            }
        }
        else{
            cd =false;
            ans=n-ct;
        }
        if(!cd){
            System.out.println(ans);
        }
        else{
            System.out.println(-1);
        }
    }
}
