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 test{
    public static void main(String [] args){
        Scanner in=new Scanner(System.in);
        int num=in.nextInt();
        int ans;
        boolean status=false;
        if(num%2==1){
            ans=((num-3)/2)+1;
            System.out.println(ans);
            status=true;
            ans--;
        }else{
            ans=num/2;
            System.out.println(ans);
        }
        for(int i=0;i<ans;i++){
            System.out.print(2+" ");
        }
        if(status==true){
            System.out.println(3);
        }
    }
}