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.*;
import java.util.*;
import java.text.*; 

public class Main {
	public static long gcd(long a, long b) { 
        if (a == 0) 
            return b; 
          
        return gcd(b%a, a); 
    } 
	public static void main (String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String st[] = br.readLine().split(" ");
		int n=Integer.parseInt(st[0]);
		long input[]=new long[n];
		st=br.readLine().split(" ");
		int count=0;

		for(int i=0;i<n;i++){
			input[i]=Long.parseLong(st[i]);
			if(input[i]==1)count++;
		}
		if(count>0){
			System.out.println(n-count);
			return;
		}
		long ans=Integer.MAX_VALUE;

		for(int i=0;i<n;i++){
			long g=0;
			for(int j=i+1;j<n;j++){
				if(g==0)
				g=gcd(input[i],input[j]);
				else
				g=gcd(g,input[j]);

				if(g==1){
					ans=Math.min(ans,j-i);
					break;
				}				
			}
		}
		if(ans==Integer.MAX_VALUE){
			System.out.println(-1);
		}
		else{
			System.out.println(ans+n-1);
		}
    }
}
