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

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