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.InputStreamReader;
import java.util.StringTokenizer;

public class Hemose {

	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		StringTokenizer st = new StringTokenizer(br.readLine());
		int[]a= new int[n];
		int ones=0;
		for(int i =0;i<n;i++){
			a[i]=Integer.parseInt(st.nextToken());
			if(a[i]==1)ones++;
		}
		int ans= n+1;
		for(int i =0;i<n;i++){
			int x=a[i];
			for(int j=i+1;j<n;j++){
				if(gcd(x,a[j])==1){
					ans=Math.min(ans, j-i);
				}
				x=gcd(x,a[j]);
			}
		}
		if(n==1){
			if(a[0]==1){
				System.out.println(0);
			}
			else System.out.println(-1);
			return;
		}
		if(ans==n+1){
			System.out.println(-1);
		}
		else{
			System.out.println(n+ans-1-ones);
		}
	}
	static int gcd(int a,int b){
		if(a==0)return b;
		return gcd(b%a,a);
	}
}
