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 Bachgold_Problem {
    static boolean prime(int a){
        int f=0;
        
        int m=a/2;
        if(a==0||a==1)
        {
            return false;
        }
        else
        {
            
            for(int i=2;i<=m;i++)
            {
                if(a%i==0)
                {
                    f++;
                    break;
                }
            }
            if(f==0){return true;}
            else return false;
        }       
    }   
    public static void main(String[] args) {
       Scanner in = new Scanner(System.in);
       int n=in.nextInt();
       int s[]=new int [100000];
       int z=0;
       int t=2;
        for(int i=n;i>=0;i--)
         {
             if(prime(t)==true)
             {
             if(n%t==0)
             {
                 int m=n/t;
                 for(int k=0;k<m;k++)
                 {
                     s[z]=t;
                     z++;
                     n=n-t;
                 }
                 t++;
             }
             else if(n==3)
             {
                 s[z]=3;
                 z++;
                 break;
             }
             else 
             {      
                 s[z]=t;
                 z++;
                 n=n-t;
                 t=2;
             }
             }
         }
       System.out.println(z);
       for(int j=0;j<z;j++)
           {
               System.out.print(s[j]+" ");
           }
    }   
}