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.*;
import java.util.*;

public class MikeGcd 
{
	static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader()
        {
            br = new BufferedReader(new
                     InputStreamReader(System.in));
        }
 
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt()
        {
            return Integer.parseInt(next());
        }
 
        long nextLong()
        {
            return Long.parseLong(next());
        }
 
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
 
        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
	
	public static void main(String[] args) 
	{
		FastReader reader = new FastReader();
		int i, j, totalNumbers = reader.nextInt();
		
		int[] array = new int[totalNumbers+1];
		for (i=0; i<totalNumbers; i++)
			array[i] = reader.nextInt();
		
		array[totalNumbers] = 0;
		
		long finalAnswer = gcd (array[0], array[1]);
		for (i=2; i<totalNumbers; i++)
			finalAnswer = gcd (finalAnswer, array[i]);

		System.out.println ("YES");
		
		if (finalAnswer > 1)
			System.out.println (0);
		else
		{
			int answer=0, count=0;
			for (i=0; i<=totalNumbers; i++)
			{
				if (array[i]%2 == 0)
				{
					answer += count/2 + 2*(count%2);
					count = 0;
				}
				else
					count++;
			}
			
			System.out.println (answer);
		}
	}
	
	static long gcd(long a, long b) 
	{
		  long r;
		  
		  while(b!=0)
		  {
		    r = a % b;
		    a = b;
		    b = r;
		  }
		  
		  return a;
	}
}
