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 Main{
     public static void main(String ... string){
          Scanner sc = new Scanner(System.in); 
          int n = sc.nextInt(); 
          System.out.println(n/2);
          while(n > 3){
               System.out.print(2 + " "); 
               n -= 2; 
          }
          System.out.print(n); 
     }
}