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 ;
import java.util.*;

public class cf2{
    public static void main(String[] args ){
        Scanner s =new Scanner (System.in);
        int n =s.nextInt();
        int count=0;
        System.out.println(n/2);
        while(n>0){
            //System.out.println(n/2);
            if(n>=2 && n%2==0){
                System.out.print("2"+" ");
                n=n-2;
            }
            else if( n>1 && n%2==1){
                System.out.print("3"+" ");
                n=n-3;
                if(n>=2 && n%2==0){
                    //System.out.print(" ");
                    System.out.print("2"+" ");
                    n=n-2;
                }
            }
        }
        System.exit(0);
    }
}