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.*;

public class test
{	
    private static Scanner sc = new Scanner(System.in);
	private static String abc[] = {"a","b","c","d","e","f","g","h","i","j","k","l","m","n","o","p","q","r","s","t","u","v","w","x","y","z"};
	
	
	private static int gcd(int a, int b)
	{
		if(b == 0)
		{
			return a;
		}
		else
		{
			return gcd(b, a%b);
		}
	}
	
	public static void main(String[] args)
    {	
		int n = sc.nextInt();
		
		int data[] = new int[2000];
		
		int cnt1 = 0;
		for(int i = 0; i < n; i++)
		{
			data[i] = sc.nextInt();
			if(data[i] == 1)cnt1++;
		}
		
		if(cnt1>0)
		{
			System.out.println(n-cnt1);
			return;
		}
		
		
		int dist = 123456;
		
		for(int i=0;i<n;i++)
		{
			int x = data[i];
			for(int j =i+1;j<n;j++)
			{
				x = gcd(x,data[j]);
				if(x == 1)
				{
					dist = Math.min(dist,j-i);
					break;
				}
			}
		}
		
		if(dist == 123456)
		{
			System.out.println(-1);
			return;
		}
		
		System.out.println(dist + n -1);
		
		
	}
}


/*
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7  8
8  8
9  20

10 18
11 46
12 67
13 69
14 68
15 75
*/






