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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class C
{
	static PrintWriter out = new PrintWriter(
			new BufferedOutputStream(System.out));
	static MyScanner sc = new MyScanner(System.in);
	static StringBuilder output = new StringBuilder();

	public static void main(String... args)
	{
		int n = sc.nextInt();
		
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
		{
			a[i] = sc.nextInt();
		}
		
		int gcd = gcd(a);
		
		if (gcd > 1)
		{
			output.append("YES\n0");
			eOP();
		}
		if (gcd < 1)
		{
			output.append("NO");
			eOP();
		}
		
		int act = 0;
		boolean[] light = new boolean[n];
		for (int i = 0; i < n; i++)
		{
			if (a[i] % 2 == 1)
			{
				light[i] = true;
			}
		}
		
		for (int i = 0; i < n - 1; i++)
		{
			if (light[i])
			{
				act++;
				light[i] ^= light[i + 1];
				light[i + 1] = light[i];
				i--;
			}
		}
		
		if (light[n - 1])
		{
			act += 2;
		}
		
		output.append("YES\n");
		output.append(act);

		eOP();
	}
	
	public static int gcd(int... vals)
	{
		int result = 0;
		
		for (int val : vals)
		{
			result = gcd(result, val, 0);
		}
		
		return result;
	}

	private static int gcd(int val0, int val1, int key)
	{
		while(val1 != 0)
		{
			int temp = val0 % val1;
			val0 = val1;
			val1 = temp;
		}
		return val0;
	}
	

	
	private static void eOP()
	{
		System.out.println(output);
		System.exit(0);
	}
	
	/**
	 * Flatfoot's Scanner with slight modifications.
	 * 
	 * @author <a href="http://codeforces.com/profile/Flatfoot">Flatfoot</a>
	 * @see <a href="http://codeforces.com/blog/entry/7018">Source</a>
	 */
	private static class MyScanner
	{
		BufferedReader br;
		StringTokenizer st;

		MyScanner(InputStream in)
		{
			this.br = new BufferedReader(new InputStreamReader(in));
		}

		String next()
		{
			while (this.st == null || !this.st.hasMoreElements())
			{
				try
				{
					this.st = new StringTokenizer(this.br.readLine());
				}
				catch (IOException e)
				{
					e.printStackTrace();
				}
			}
			return this.st.nextToken();
		}

		int nextInt()
		{
			return Integer.parseInt(this.next());
		}

		long nextLong()
		{
			return Long.parseLong(this.next());
		}

		double nextDouble()
		{
			return Double.parseDouble(this.next());
		}

		/**
		 * This method has been modified to be a bit more similar to Scanner's
		 * 
		 * @author <a href=
		 *         "http://codeforces.com/profile/Flatfoot">Flatfoot</a>,
		 *         <a href=
		 *         "http://codeforces.com/profile/JasonBaby">JasonBaby</a>
		 */
		String nextLine()
		{
			if (this.st == null || !this.st.hasMoreElements())
			{
				String str = "";
				try
				{
					str = this.br.readLine();
				}
				catch (IOException e)
				{
					e.printStackTrace();
				}
				return str;
			}
			else
			{
				StringBuilder str = new StringBuilder();
				while (this.st.hasMoreElements())
				{
					str.append(this.st.nextToken());
					str.append(" ");
				}
				str.deleteCharAt(str.length() - 1);
				return str.toString();
			}
		}

	}
}
