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