Problem: Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes.

More formally, you are given an odd numer n. Find a set of numbers pi (1 ≤ i ≤ k), such that

  1. 1 ≤ k ≤ 3
  2. pi is a prime
  3. <image>



The numbers pi do not necessarily have to be distinct. It is guaranteed that at least one possible solution exists.

Input

The single line contains an odd number n (3 ≤ n < 109).

Output

In the first line print k (1 ≤ k ≤ 3), showing how many numbers are in the representation you found.

In the second line print numbers pi in any order. If there are multiple possible solutions, you can print any of them.

Examples

Input

27


Output

3
5 11 11

Note

A prime is an integer strictly larger than one that is divisible only by one and by itself.

Solution (in JAVA):

Solution:
import java.io.*;
import java.io.PrintWriter;
import java.util.*;
import java.io.InputStream;
import java.io.DataInputStream;
 
 
 public class Main
{ 
   // static{ System.out.println("hello");}
	    static InputStream inputStream = System.in;
        static OutputStream outputStream = System.out;
        static FastReader scn = new FastReader(inputStream);
        static PrintWriter out = new PrintWriter(outputStream);
        static boolean chk(int n)
        {  if (n==1) return false; if(n==2) return true;
           for(int i=2; i<=(int)Math.sqrt(n);i++) if (n%i==0) return false;    
            return true;
        }    
         public static void main(String[] args) throws IOException
       { int n=scn.ni(); 
          if (chk(n)) {out.println(1); out.print(n); }
          else if (chk(n-2)) {out.println(2); out.println(2+" "+(n-2));}
          else 
           {   out.println(3);  out.print(3+" ");
             n-=3;
             int a=n/2; int b=n/2;
             while(true)
             {
                 if (chk(a) && chk(b))
                 { out.print(a+" "+b); break; }
                 a-=1; b+=1;
             } 
            }    
         out.close();
        }    
                    
         
}


  class num implements Comparator<num>
    {
        
        public int ff;
        public int ss;
   
        num()
        {
            
        }
        num(int x,int y)
        {
            this.ff = x;
            this.ss =y;
       
        }
        public int getff()
        {
        return ff;
        }
        public int getss()
        {
        return ss;
        }
       public boolean equals(Object n1)
        {num n=(num)n1;
        if (this.ff==n.ff && this.ss==n.ss) return true;
        else return false;
            
            
        }
       public int compare(num n1,num n2)
        {  if (n1.ff!=n2.ff) return n1.ff-n2.ff;
            else return n1.ss-n2.ss;
            
            
        }    
        
    }

class FastReader
{
 
    public InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;
 
    public FastReader(InputStream stream)
    {
        this.stream = stream;
    }
 
    public int read()
    {
        if (numChars == -1)
        {
            throw new InputMismatchException ();
        }
        if (curChar >= numChars)
        {
            curChar = 0;
            try
            {
                numChars = stream.read (buf);
            } catch (IOException e)
            {
                throw new InputMismatchException ();
            }
            if (numChars <= 0)
            {
                return -1;
            }
        }
        return buf[curChar++];
    }
    
 public char nc()
    {
        int c = read ();
        while (isSpaceChar (c))
            c = read ();
        return (char) c;
    }
    
    public int ni()
    {
        int c = read ();
        while (isSpaceChar (c))
            c = read ();
        int sgn = 1;
        if (c == '-')
        {
            sgn = -1;
            c = read ();
        }
        int res = 0;
        do
        {
            if (c < '0' || c > '9')
            {
 
                
            }
            res *= 10;
            res += c - '0';
            c = read ();
        } while (!isSpaceChar (c));
        return res * sgn;
    }
 
    public long nl()
    {
        int c = read ();
        while (isSpaceChar (c))
            c = read ();
        int sgn = 1;
        if (c == '-')
        {
            sgn = -1;
            c = read ();
        }
        long res = 0;
        do
        {
            if (c < '0' || c > '9')
            {
                throw new InputMismatchException ();
            }
            res *= 10;
            res += c - '0';
            c = read ();
        } while (!isSpaceChar (c));
        return res * sgn;
    }
 
    public String ns()
    {
        int c = read ();
        while (isSpaceChar (c))
            c = read ();
        StringBuilder res = new StringBuilder ();
        do
        {
            res.appendCodePoint (c);
            c = read ();
        } while (!isSpaceChar (c));
        return res.toString ();
    }
 
    public boolean isSpaceChar(int c)
    {
        if (filter != null)
        {
            return filter.isSpaceChar (c);
        }
        return isWhitespace (c);
    }
 
    public static boolean isWhitespace(int c)
    {
        return c==' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }
 
    public String next()
    {
        return ns ();
    }
 
    public interface SpaceCharFilter
    {
        public boolean isSpaceChar(int ch);
    }
}