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.math.BigInteger;

public class Tests{
	static Scanner in = new Scanner (System.in);
	//static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

	static PrintWriter out = new PrintWriter (System.out);
  

	
	public static void main (String []args) throws IOException,ArithmeticException {
		int n = in.nextInt();
		
		out.println(n/2);
		
		if(n % 2 == 0){
			for(int i = 0 ; i< (n/2) ;  i++){
				out.print(2+" ");
			}
		}else{
			for(int i = 0 ; i< (n/2)-1 ; i++){
				out.print(2+" ");
			}
			out.print(3);
		}
		
		
	
		

	
		 
	    out.flush();
		out.close();
				
	}
	

	
	

}