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.*;
import java.io.*;

public class Main
{
	static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(new
                     InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }

	public static void main (String[] args)
	{
		FastReader reader = new FastReader();
		int totalElements = reader.nextInt();
		int[] array = new int[totalElements];
		int[][] matrix = new int[totalElements][totalElements];
		int count = 0;

		for (int i=0; i<totalElements; i++)
		{
			array[i] = reader.nextInt();
			matrix[i][i] = array[i];

			if (array[i] == 1)
				count++;
		}

		int low = Integer.MAX_VALUE;
		for (int i=0; i<totalElements; i++)
		{
			for (int j=i+1; j<totalElements; j++)
			{
				matrix[i][j] = gcdExtended (matrix[i][j-1], array[j], 1, 1);

				if (matrix[i][j] == 1)
				{
					if (j-i < low)
						low = j-i;
				}
			}
		}

		if (low == Integer.MAX_VALUE && count == 0)
				System.out.println (-1);
		else if (count == 0)
			System.out.println (low + totalElements - 1);
		else
			System.out.println (totalElements - count);
	}

	static int gcdExtended(int a, int b, int x, int y)
	{
			// Base Case
			if (a == 0)
			{
					x = 0;
					y = 1;
					return b;
			}

			int x1=1, y1=1; // To store results of recursive call
			int gcd = gcdExtended(b%a, a, x1, y1);

			// Update x and y using results of recursive
			// call
			x = y1 - (b/a) * x1;
			y = x1;

			return gcd;
	}
}
