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.ArrayList;
import java.util.Scanner;

public class ejerGCD 
{

	static int gcd(int a,int b)
	{
		while (b > 0) {
			int t = a;
			a = b;
			b = t % a;
		}
		return a;
	}
	public static void main(String[] args) throws NumberFormatException, IOException 
	{
		Scanner sc = new Scanner(System.in);
		int nElementos=sc.nextInt();
		int numeros[]=new int[nElementos];
		int cont1=0;
		for (int i = 0; i < nElementos; i++)
		{
			numeros[i]=sc.nextInt();
			if(numeros[i]==1)
				cont1++;
		}

		if(cont1>0)
		{
			System.out.println(nElementos-cont1);
			return;
		}
		else
		{
			int resp=-1;

			for (int i = 0; i < numeros.length; i++) 
			{
				int numeroX=numeros[i];
				for (int j = i; j < numeros.length; j++) 
				{
					numeroX=gcd(numeroX,numeros[j]);
					if(numeroX==1)
					{
						int temp = j - i + nElementos - 1;
						if (temp < resp|| resp < 0) {
							resp = temp;
						}
					}

				}
			}
			
			System.out.println(resp);
		}

		sc.close();
	}

}