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:
/**
 *   Author: Ridam Nagar
 *   Date: 21 January 2019
 *   Time: 23:02:09
**/
/* 
package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
         
    
          
      
    public static void main (String[] args) throws java.lang.Exception
    { 
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        if(n%2==0){
            System.out.println(n/2);
            for(int i=0;i<n/2;i++){
                System.out.println(2);
            }
        }else{
            n=n-3;
            System.out.println(n/2+1);
            System.out.print(3+" ");
            for(int i=0;i<n/2;i++){
                System.out.print(2+" ");
            }
        }
   
}
}