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;

/**
 *
 * @author abhishekraj
 */
public class CodeforcesBatchgold {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int sum=0,cnt=0;
        int n= sc.nextInt();
         if((n&1)==0)
         {
             for(int i=0;i<n;i++)
             {
                if(sum==n)
                 {
                     break;
                 }
                 sum=sum+2;
                 cnt++;
                 
             }
         }
         else{
              for(int i=0;i<n;i++) 
              {
                  if(sum+3==n)
                  {
                      break;
                  }
                  sum=sum+2;
                  cnt++;
                  
              }
         }
         
         if((n&1)==0)
         {
             System.out.println(cnt);
             for(int i=0;i<cnt;i++)
             {
                 System.out.print(2+" ");
             }
         }
         else{
             
             System.out.println(cnt+1);
             for(int i=0;i<cnt;i++)
             {
                 System.out.print(2+" ");
             }
             System.out.print(3);
         }
        
    }
    
}