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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
public class LOCaug {
	 public static void main(String args[]) throws NumberFormatException, IOException{
		 BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		 int n=Integer.parseInt(br.readLine());
		 System.out.println(n/2);  
			   for(int i=0;i<(n/2)-1;i++){
				   System.out.print(2+" ");
			   }
			   if(n%2==0)
				   System.out.print(2);  
			   else
				   System.out.print(3); 
	 } 
}