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.
/**
 * DA-IICT
 * Author : Savaliya Sagar
 */
import java.io.*;
import java.math.*;
import java.util.*;

import static java.util.Arrays.fill;
import static java.lang.Math.*;
import static java.util.Arrays.sort;
import static java.util.Collections.sort;

public class C891
{
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni();
		int a[] = new int[n];
		int flag = 0;
		for(int i=0;i<n;i++)
		{
			a[i] = ni();
			if(a[i]==1)
				flag++;
		}
		
		if(flag!=0) {
			out.println(n-flag);
			return;
		}
		
		int  min = Integer.MAX_VALUE;
		for(int i=0;i<n;i++) {
			int g = a[i];
			for(int j=i;j<n;j++) {
				g = (int) gcd(g,a[j]);
				if(g==1) {
					min = min(min,j-i+1);
					break;
				}
			}
		}
		if(min==Integer.MAX_VALUE)
			out.println(-1);
		else
			out.println(n-1+min-1);
	}
	
	long gcd(long n1, long n2)
	{
		long r;
		while (n2 != 0)
		{
			r = n1 % n2;
			n1 = n2;
			n2 = r;
		}
		return n1;
	}
	
	void run() throws Exception
	{
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		if (!INPUT.isEmpty())
			tr(System.currentTimeMillis() - s + "ms");
	}
	
	public static void main(String[] args) throws Exception
	{
		new Thread(null, new Runnable()
		{
			public void run()
			{
				try
				{
					new C891().run();
				} catch (Exception e)
				{
					e.printStackTrace();
				}
			}
		}, "1", 1 << 26).start();
	}
	
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if (lenbuf == -1)
			throw new InputMismatchException();
		if (ptrbuf >= lenbuf)
		{
			ptrbuf = 0;
			try
			{
				lenbuf = is.read(inbuf);
			} catch (IOException e)
			{
				throw new InputMismatchException();
			}
			if (lenbuf <= 0)
				return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c)
	{
		return !(c >= 33 && c <= 126);
	}
	
	private int skip()
	{
		int b;
		while ((b = readByte()) != -1 && isSpaceChar(b))
			;
		return b;
	}
	
	private double nd()
	{
		return Double.parseDouble(ns());
	}
	
	private char nc()
	{
		return (char) skip();
	}
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while (!(isSpaceChar(b)))
		{ // when nextLine, (isSpaceChar(b) && b !=
			// ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while (p < n && !(isSpaceChar(b)))
		{
			buf[p++] = (char) b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for (int i = 0; i < n; i++)
			map[i] = ns(m);
		return map;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-')
		{
			minus = true;
			b = readByte();
		}
		
		while (true)
		{
			if (b >= '0' && b <= '9')
			{
				num = num * 10 + (b - '0');
			} else
			{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-')
		{
			minus = true;
			b = readByte();
		}
		
		while (true)
		{
			if (b >= '0' && b <= '9')
			{
				num = num * 10 + (b - '0');
			} else
			{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private void tr(Object... o)
	{
		System.out.println(Arrays.deepToString(o));
	}
}
