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 Solution {

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

    } else {
      int z = n/2;
      System.out.println(z);
      for(int i=0;i<z-1;i++) {
        System.out.print(2 + " ");

      }
      System.out.print(" 3");
    }
  }

}