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.Arrays;
import java.util.Scanner;

public class NewClass2 {

    public static void main(String[] args) {

        Scanner ob = new Scanner(System.in);
      int n=ob.nextInt();
      if(n%2==0)
      {
          System.out.println(n/2);
          for(int i=0;i<(n/2);i++)
          {
              System.out.print(2+" ");
          }
      }
      else
      {
          System.out.println((int)Math.floor(n*(1.0)/2));
          for(int i=0;i<((n/2)-1);i++)
          {
              System.out.print(2+" ");
          }
          System.out.println(3);
      } 
        }
    }