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 BachgoldProblem{
  public static void main(String[] args){
    Scanner gd = new Scanner(System.in);
    int num = gd.nextInt();
    int temp;
    if(num%2==0){
      System.out.println(num/2);
      for(int i=0;i<(num/2);i++){
        System.out.printf("2 ");
      }
      System.out.println();
    }
    else{
      temp = ((num/2)-1);
      System.out.println(num/2);
      for(int i=0;i<temp;i++){
        System.out.printf("2 ");
      }
      System.out.println("3");
    }
  }
}