Mike has a sequence A = [a1, a2, ..., an] of length n. He considers the sequence B = [b1, b2, ..., bn] beautiful if the gcd of all its elements is bigger than 1, i.e. <image>. 

Mike wants to change his sequence in order to make it beautiful. In one move he can choose an index i (1 ≤ i < n), delete numbers ai, ai + 1 and put numbers ai - ai + 1, ai + ai + 1 in their place instead, in this order. He wants perform as few operations as possible. Find the minimal number of operations to make sequence A beautiful if it's possible, or tell him that it is impossible to do so.

<image> is the biggest non-negative number d such that d divides bi for every i (1 ≤ i ≤ n).

Input

The first line contains a single integer n (2 ≤ n ≤ 100 000) — length of sequence A.

The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 109) — elements of sequence A.

Output

Output on the first line "YES" (without quotes) if it is possible to make sequence A beautiful by performing operations described above, and "NO" (without quotes) otherwise.

If the answer was "YES", output the minimal number of moves needed to make sequence A beautiful.

Examples

Input

2
1 1


Output

YES
1


Input

3
6 2 4


Output

YES
0


Input

2
1 3


Output

YES
1

Note

In the first example you can simply make one move to obtain sequence [0, 2] with <image>.

In the second example the gcd of the sequence is already greater than 1. 
import java.io.BufferedReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.PrintStream;
import java.util.HashMap;
import java.util.Map;
import java.util.StringTokenizer;

/*
 public class _798C {

 }

 */

public class _798C
{
	public void solve() throws FileNotFoundException
	{
		InputStream inputStream = System.in;

		InputHelper inputHelper = new InputHelper(inputStream);

		PrintStream out = System.out;

		// actual solution
		int n = inputHelper.readInteger();

		int[] a = new int[n];

		for (int i = 0; i < n; i++)
		{
			a[i] = inputHelper.readInteger();
		}

		int gcd = a[0];

		for (int i = 1; i < n; i++)
		{
			gcd = gcd(a[i], gcd);
		}

		if (gcd > 1)
		{
			System.out.println("YES");
			System.out.println("0");
			return;
		}

		int os = 0;
		int ans = 0;
		for (int i = 0; i < n; i++)
		{
			if (a[i] % 2 == 1)
			{
				os++;
			}
			else
			{
				if (os > 0)
				{
					if (os % 2 == 0)
					{
						ans += (os / 2);
					}
					else
					{
						ans += ((os / 2) + 2);
					}

					os = 0;
				}
			}
		}

		if (os > 0)
		{
			if (os % 2 == 0)
			{
				ans += (os / 2);
			}
			else
			{
				ans += ((os / 2) + 2);
			}

			os = 0;
		}

		System.out.println("YES");
		System.out.println(ans);
		// end here
	}

	int gcd(int a, int b)
	{
		if (b == 0)
			return a;
		else
			return gcd(b, a % b);
	}

	public static void main(String[] args) throws FileNotFoundException
	{
		(new _798C()).solve();
	}

	class InputHelper
	{
		StringTokenizer tokenizer = null;
		private BufferedReader bufferedReader;

		public InputHelper(InputStream inputStream)
		{
			InputStreamReader inputStreamReader = new InputStreamReader(
					inputStream);
			bufferedReader = new BufferedReader(inputStreamReader, 16384);
		}

		public String read()
		{
			while (tokenizer == null || !tokenizer.hasMoreTokens())
			{
				try
				{
					String line = bufferedReader.readLine();
					if (line == null)
					{
						return null;
					}
					tokenizer = new StringTokenizer(line);
				}
				catch (IOException e)
				{
					e.printStackTrace();
				}
			}

			return tokenizer.nextToken();
		}

		public Integer readInteger()
		{
			return Integer.parseInt(read());
		}

		public Long readLong()
		{
			return Long.parseLong(read());
		}
	}
}