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.*;
import java.lang.*;
import java.lang.reflect.Array;
import java.math.*;
import java.util.stream.Collectors;
public class JavaApplication1 {
 
    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) throws IOException {

   BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
    StringBuffer bw=new StringBuffer();
     int ll=Integer.parseInt(bf.readLine());
     int count=(ll/2);
   
     bw.append(count+"\n");
     if(ll%2==1){count--;}
     for(int i=0;i<count;i++){bw.append("2 ");}
     if(ll%2==1){bw.append("3");}
  
        System.out.print(bw);
    }
   
 
}