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

public class BachgoldProblem
{
	public static void main(String[] args) throws IOException 
	{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
            StringTokenizer st = new StringTokenizer(br.readLine());
            
		int n = Integer.parseInt(st.nextToken());
		int numoftwo = 0, numofthree = 0;
		if(n>=3 && n%2 !=0)
		{
		      numoftwo = (n-3)/2;
		      numofthree = 1;
		}
	      else
	            numoftwo = n/2;
		
		System.out.println(numoftwo+numofthree);
		for(int i=1; i<=numoftwo; i++)
		{
		      System.out.print("2"+" ");
            }
            if(n>=3 && n%2 !=0)
                  System.out.print("3");
      }
}