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