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.*;
import java.io.*;
public class A
{
    public static void main(String [] args)
    {
        Scanner s=new Scanner(System.in);
        int t=1;
        while(t-->0)
        {
            int n=s.nextInt();
            int c=n/2;
            if(n==2)
            {
                System.out.println(1);
                System.out.print(2);
            }else
            if(n==3)
            {
               System.out.println(1);
               System.out.print(3); 
            }else
            if(n%2!=0)
            {
                System.out.println(c);
                for(int i=0;i<c-1;i++)
                System.out.print(2+" ");
                System.out.print(3);  
            }
            else
            {
               System.out.println(c);
               for(int i=0;i<c;i++)
               System.out.print(2+" ");
            }
        }
    }
}