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.awt.Point;
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class C {
	
	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		
		int n = sc.nextInt();
		int arr[] = new int[n];
		int ones = 0;
		for(int i = 0; i < n; ++i) if((arr[i] = sc.nextInt()) == 1) ones++;
		
		if(ones > 0)
			out.println(n - ones);
		else
		{
			int min = n + 1;
			for(int i = 0; i < n; ++i)
			{
				int gcd = 0;
				for(int j = i - 1; j >= 0; --j)
				{
					gcd = gcd(arr[j], gcd);
					if(gcd(gcd, arr[i]) == 1)
					{
						min = Math.min(min, i - j);
						break;
					}
				}
				gcd = 0;
				for(int j = i + 1; j < n; ++j)
				{
					gcd = gcd(arr[j], gcd);
					if(gcd(gcd, arr[i]) == 1)
					{
						min = Math.min(min, j - i);
						break;
					}
				}
			}
			
			if(min == n + 1)
				out.println(-1);
			else
				out.println(min + n - 1);
		}
		
		out.flush();
		out.close();
	}
	
	static int gcd(int a, int b) { return b == 0?a:gcd(b, a % b); }

	static class Scanner{
		StringTokenizer st;
		BufferedReader br;

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

		public Scanner(FileReader r){	br = new BufferedReader(r);}

		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();}
	}
}