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.*;

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

}