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.math.BigInteger;
import java.util.Scanner;

public class Pride {
	public static void main (String [] args) {
		int ones=0;
		int gcd=0;
		int steps=0;
		boolean hasOne=false;
		Scanner  s = new Scanner(System.in);
		int y=s.nextInt();
		s.nextLine();
		String x=s.nextLine();
	    String array1[]=x.split("\\s+");
	    
	 
	    	for(int i=0;i<y;i++) {
	    	    if(array1[i].equals("1")) {
	    	    	ones++;
	    	    	hasOne=true;
	    	    }
		    }
	    	if(hasOne) {
	    	System.out.print(y-ones);
	    	return ;
	    	}
	    
	    for(int i=0;i<y-1;i++) {
	    if(gcdThing((int)Double.parseDouble(array1[i]),(int)Double.parseDouble(array1[i+1]))==1) {
	    	
	    	System.out.print(y);
	    	return;
	    }
	    
	    }
	   
	    
	    for(int i=0;i<y-1;i++) {
	    
	    	if(array1[i+1].equals(array1[i])==false) {
	    		gcd=gcdThing((int)Double.parseDouble(array1[i]),(int)Double.parseDouble(array1[i+1]));
	    		 
	    		if(i !=y-2) {
	    		if(gcdThing(gcd,(int)Double.parseDouble(array1[i+2]))==1) {
	    			array1[i+1]=Integer.toString(gcd);
	    			
	    			steps=steps+2;
	    			System.out.print(y-1+steps);
	    			return;
	    		
	    		}
	    		}
	    		if(i !=0) {
	    		if(gcdThing(gcd,(int)Double.parseDouble(array1[i-1]))==1) {
	    			array1[i]=Integer.toString(gcd);
	    			steps=steps+2;
	    			System.out.print(y-1+steps);
	    			return;
	    		}
	    		}
	    		if(gcd==Double.parseDouble(array1[i])) {
		    		array1[i+1]=array1[i];
		    		steps++;
		    		
		    	}
	    		else if(gcd==Double.parseDouble(array1[i+1])) {
		    		array1[i]=array1[i+1];
		    		steps++;
		    		
		    	}
	    		else {
	    			steps++;
	    			
	    			array1[i+1]=Integer.toString(gcd);
	    			
	    		}
	    	}
	    }
	    
	    System.out.print(-1);
	}
	
	
	private static int gcdThing(int a, int b) {
	    BigInteger b1 = BigInteger.valueOf(a);
	    BigInteger b2 = BigInteger.valueOf(b);
	    BigInteger gcd = b1.gcd(b2);
	    return gcd.intValue();
	}
}
