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.util.*;
import java.io.*;
public class Main{
   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()); 
        }
        String nextLine(){
            String sr = "";
            try{
                sr = br.readLine();
            }
               catch(IOException e){
                    e.printStackTrace();
                }
                return sr;
        }
    }
    public static void main(String args[])throws Exception{
         FastReader ft = new FastReader();
         BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
             int n = ft.nextInt();
            if((n&1)==0)
            {
                out.write((n/2)+"\n");
                for(int i = 0;i< n/2;i++)
                out.write("2 ");
            }
            else{
                out.write((n/2)+"\n");
                for(int i = 1;i< n/2;i++)
                out.write("2 ");
                 out.write("3 "); 
            }
            out.write("\n");
         out.flush();
        }}