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