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.util.*;
import java.io.*;
public class pt{ 
      
       static int gcd(int a,int b){
                         if(b%a==0) return(a);
                          return gcd(b%a,a);
                   }
      public static void main(String[] args)throws IOException { 
                      PrintWriter out = new PrintWriter(System.out);
                  
                        int n = ni();
                        int g = ni();
                        int ans=0,cnt=0;
                        if((g&1)!=0)cnt++;

                          for(int i=1;i<n;i++){
                                  int x = ni();
                                   g = gcd(g,x);
                                   if((x&1)!=0)cnt++;
                                   else{
                                           ans = ans + cnt/2 + 2*(cnt&1);
                                           cnt=0;
                                   }
                           }
                                 out.println("YES");      
                                     ans = ans + cnt/2 + 2*(cnt&1);
                                if(g>1) out.println("0");
                                else     out.println(ans);

                               out.flush();
                            
    } 
    static FastReader sc=new FastReader(); 
 
      static int ni(){
                 int x = sc.nextInt();
                 return(x);
        }
      static long nl(){
              long x = sc.nextLong();
              return(x);
         }
      static String n(){
                 String str = sc.next();
                     return(str);
       }
     static String ns(){
                 String str = sc.nextLine();
                   return(str);
      }
     static double nd(){
               double d = sc.nextDouble();
                 return(d);
       }
  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; 
        } 
    } 
}