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 ABachgoldProblem {

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