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.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Monitor_16C
{
	public static void main(String[] args) throws IOException
	{
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] arr = new int[n];

		int ones = 0;
		for (int i = 0; i < n; i++)
		{
			arr[i] = sc.nextInt();
			if(arr[i] == 1)
				ones++;
		}

		if(ones > 0)
		{
			System.out.println(n - ones);
		}
		else
		{

			int min = 100000;
			for (int i = 0; i < n; i++)
			{
				int g = arr[i];
				if (g == 1)
					min = Math.min(min, 0);
				for (int j = i + 1; j < n; j++)
				{
					g = gcd(g, arr[j]);
					if (g == 1)
						min = Math.min(min, j - i);
				}
			}
			if (min == 100000)
				System.out.println(-1);
			else
				System.out.println(min + n - 1);
		}

	}

	static int gcd(int x, int y)
	{
		if (x == 0)
			return y;
		return gcd(y % x, x);
	}

	static class Scanner
	{
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s)
		{
			br = new BufferedReader(new InputStreamReader(s));
		}

		public String next() throws IOException
		{
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

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

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

		public String nextLine() throws IOException
		{
			return br.readLine();
		}

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

		public boolean ready() throws IOException
		{
			return br.ready();
		}
	}
}
