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.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Ideone
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		
		if(n%2==0){
			System.out.println(n/2);
			
			for(int i=0; i<n/2; i++){
				System.out.println(2+" ");
				
			}

			
		}
		if(n%2==1){
			n -=3;
			System.out.println(n/2+1);
			for(int i=0 ; i<n/2 ; i++)
          	 System.out.print(2+" ");
    	   System.out.println(3);
			
		}

	}
}