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 learn {
 
  public static void main(String[] args) {

	Scanner sc = new Scanner(System.in);
		
		int t = Integer.parseInt(sc.next());
		int count = 0;
		StringBuilder sb = new StringBuilder();
		
			int times = t/2;
			for (int i = 0; i < times; ++i) {
				sb.append(2);
				sb.append(" ");
			}
			
			if((t & 1) == 1) {
				count = sb.length();
				sb.replace(count-2, count-1, "3 ");
			}
			
			
			System.out.println(sb.length()/2);
			
			System.out.println(sb.toString());

		
  }
}