Problem: Bachgold problem is very easy to formulate. Given a positive integer n represent it as a sum of maximum possible number of prime numbers. One can prove that such representation exists for any integer greater than 1.

Recall that integer k is called prime if it is greater than 1 and has exactly two positive integer divisors — 1 and k. 

Input

The only line of the input contains a single integer n (2 ≤ n ≤ 100 000).

Output

The first line of the output contains a single integer k — maximum possible number of primes in representation.

The second line should contain k primes with their sum equal to n. You can print them in any order. If there are several optimal solution, print any of them.

Examples

Input

5


Output

2
2 3


Input

6


Output

3
2 2 2

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.Comparator;
import java.util.HashSet;
import java.util.Hashtable;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Scanner;
import java.util.StringTokenizer;
 
public class Main
{
    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader()
        {
            br = new BufferedReader(new
                     InputStreamReader(System.in));
        }
 
        public String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        public int nextInt()
        {
            return Integer.parseInt(next());
        }
 
        public long nextLong()
        {
            return Long.parseLong(next());
        }
 
        public double nextDouble()
        {
            return Double.parseDouble(next());
        }
 
        public String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
    public static boolean ve(int [][] matris , int i, int j)
    {
    	
    	for (int k = 0; k < matris.length; k++) {
			for (int k2 = 0; k2 < matris.length; k2++) {
				if(matris[i][k]+ matris[k2][j] == matris[i][j] )
				{
					return true;
				}
			}
		}
    	return false;
    }
    
    static int max = 10000001;
    static int [] pri = new int[max+1];
    public static void sieve()
    {
    	pri[0] = 1;
    	pri[1] = 1;
    	for(int i=2; i <=1000; i++){
    		if(pri[i]!=0){continue;}
    		for(int j=2*i; j<=1000000; j+=i){
    			pri[j] = i;
    		}
    	}
    }
    public static void mos(String a[]){
    	for (String x : a){
    		System.out.print(x+" ");
    	}
    	System.out.println();
    }
   public static boolean isNum(String a){
	   return a.equals("1")||a.equals("2")||a.equals("3")||a.equals("4")||a.equals("5")||a.equals("6")||a.equals("7")||a.equals("8")||a.equals("9")||a.equals("0");
   }
   public static void mos(int a[]){
	  for (int i = 0; i < a.length; i++) {
		System.out.print(a[i]+" ");
	}
	  System.out.println();
   }
    public static void main(String[] args)
    {

    	Scanner sn = new Scanner(System.in);
        int n = sn.nextInt();
        if(n%2==0){
        	System.out.println(n/2);
        	System.out.print("2");
        	for (int i = 0; i < n/2-1; i++) {
        		System.out.print(" ");
				System.out.print("2");
			}
        	System.out.println();
        }
        else if(n==3){
        	System.out.println("1");
        	System.out.println("3");
        }
        else{
        	System.out.println(n/2);
        	System.out.print("2");
        	for (int i = 0; i < n/2-2; i++) {
				System.out.print(" ");
				System.out.print("2");
			}
        	System.out.print(" ");
        	System.out.print(3);
        	System.out.println();
        }
        
        
        
        
        
    }
}