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.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Main5{
	static int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); }
	public static void main(String[] args) throws Throwable 
	{
		Scanner sc = new Scanner((System.in));
//		Scanner sc = new Scanner("out");
		int n = sc.nextInt();
		int[] arr = new int[n];
		int ones = 0;
		for (int i = 0; i < arr.length; i++) {
			arr[i] = sc.nextInt();
			if(arr[i]==1)ones++;
		}
		int g = arr[0];
		for (int i = 1; i < arr.length; i++) {
			g = gcd(g,arr[i]);
		}
		if(g!=1)
		{
			System.out.println(-1);
			return;
		}
		if(n==1)
		{
			if(arr[0] == 1)
				System.out.println(0);
			else
				System.out.println(-1);
			return;
		}
		int ans = Integer.MAX_VALUE;
		if(ones != 0)
		{
			ans = n - ones;
		}
		else
		{
			for (int i = 0; i < arr.length; i++) {
				int minSegment = arr[i];
				for (int j = i+1; j < arr.length; j++) 
				{
					minSegment = gcd(minSegment, arr[j]);
					if(minSegment == 1)
					{
						ans = Math.min(ans, n - 1 + j-i);
						break;
					}
				}
			}
		}
		
		System.out.println(ans);
	}
	
	static class Scanner 
	{
		StringTokenizer st;
		BufferedReader br;
		public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}
		public Scanner(String s) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(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 String nextLine() throws IOException {return br.readLine();}		
		public long nextLong() throws IOException {return Long.parseLong(next());}		
		public double nextDouble() throws IOException {return Double.parseDouble(next());}	
		public boolean ready() throws IOException {return br.ready();}
	}
}