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.Scanner;
public class a749
{
   public static void main(String args[])
   {
      Scanner hamba = new Scanner(System.in);
      
      int n = hamba.nextInt();
      
      if(n % 2 == 0)
      {
         int result = n/2;
         
         System.out.println(result);
         
         for(int i = 0; i < result; i++)
         {
            System.out.print(2 + " ");
         }System.out.println();
      }
      
      else
      {
         n = n - 3;
         int result = n / 2;
         
         System.out.println(result + 1);
         
         for(int i = 0; i < result; i++)
         {
            System.out.print(2 + " ");
         }
         System.out.print(3);
         System.out.println();
      }
   }
}