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.*;
public class Main{

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        // TODO code application logic here
        Scanner input = new Scanner(System.in);
        
        int n = input.nextInt();
        
        int result=0;


        if(n%2==0)
        {
         System.out.println(n/2);
         while(result!=n)
         {
           System.out.printf(2+" ");
            result+=2;
        }
        System.out.println();
    }
    else
    {
        System.out.println(n/2);

        while(result!=(n-3))
        {
            System.out.printf(2+" ");
            result+=2;
        }
        System.out.println(3);
    }
     
    } 
}