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.*;
import java.math.*;
 
public class _410div2Q3
{
    public static void main(String[] args) throws IOException
    {
        FastScanner obj = new FastScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
      
      	int n = obj.nextInt();
      	int[] arr = obj.nextIntArray();
		gettheans(arr);
        out.close();
   	}
   	static void gettheans(int[]arr)
   	{
   		int gcd = arr[0];
   		int n = arr.length;
   		for(int i=1;i<n;i++)
   			gcd = gcdFunc(arr[i],gcd);
   		out.println("YES");
   		
   		if(gcd>1){	
   			out.println(0);
   			return;
   		}
   		
   		int ans = 0;
		for(int i=0;i<n-1;i++)
   		{
   			if(arr[i]%2==0 && arr[i+1]%2==0)
   				continue;
   			else if(arr[i]%2==1 && arr[i+1]%2==1)
   			{
   				ans++;
   				arr[i] = 0;
				arr[i+1] = 0;
			}
		}
   		for(int i=0;i<n-1;i++)
   		{
   			if(arr[i]%2==0 && arr[i+1]%2==0)
   				continue;
   			else if(arr[i]%2==1 && arr[i+1]%2==1)
   				ans++;
   			else
   				ans += 2;

			arr[i] = 0;
			arr[i+1] = 0;
		}   	
		out.println(ans);
		return;	
   	}
   
   	public static int gcdFunc(int a, int b)
	{
 	 if(a == 0 || b == 0) return a+b; 
  	return gcdFunc(b,a%b);
	}

   //-----------PrintWriter for faster output---------------------------------
   public static PrintWriter out;
      
   //-----------FastScanner class for faster input----------
   public static class FastScanner {
        BufferedReader br;
        StringTokenizer tokenizer;
 
        public FastScanner() throws IOException {
            br = new BufferedReader(new InputStreamReader(System.in));
            tokenizer = new StringTokenizer(br.readLine().trim());
        }
 
        String next() {
            while (tokenizer == null || !tokenizer.hasMoreElements()) {
                try {
                    tokenizer = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                    }
            }
          return tokenizer.nextToken();
        }
 
        int nextInt() {
            return Integer.parseInt(next());
        }
 
        long nextLong() {
            return Long.parseLong(next());
        }
 
        double nextDouble() {
            return Double.parseDouble(next());
        }
      
        int[] nextIntArray() throws IOException {
            String[] line = br.readLine().trim().split(" ");
            int[] out = new int[line.length];
            
            for (int i = 0; i < line.length; i++) {
                out[i] = Integer.valueOf(line[i]);
            }
            return out;
        }
        
        BigInteger nextBigInteger() throws IOException {
            return new BigInteger(next());
        }
        
        String nextLine(){
            String str = "";
	        try {
	            str = br.readLine();
	        } catch (IOException e) {
	            e.printStackTrace();
	        }
	        return str;
        }

   }
   //--------------------------------------------------------
}