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:
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import java.util.Scanner;

public class Main
{
	public static void main(String[] args) {
	    Scanner in = new Scanner(System.in);
		int m = in.nextInt();
		int res;
		
		if(m%2 == 0){
		    res = 1;
		    
		} else {
		    res = -1;
		}
		
		if(res == 1) {
		    System.out.println(m/2); 
		    
		    for(int i=1; i<=(int)m/2; i++){
		        System.out.print(2+" ");
		    }
		    
		} else {
		    System.out.println(m/2 ); 
		    
		    for(int i=1; i<(int)m/2; i++){
		        System.out.print(2+" ");
		    }
		    
		    System.out.print(3);
		}
		
	
		   
	}
}