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.io.PrintWriter;
import java.util.ArrayList;
import java.util.Scanner;

public class ProblemA {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		ArrayList<Integer> list = new ArrayList<>();
		
		while(n > 3) {
			list.add(2);
			n = n - 2;
		}
		
		if(n == 3) {
			list.add(3);
		}
		else list.add(2);
		
		PrintWriter pw = new PrintWriter(System.out);
		pw.println(list.size());
		for(int i = 0; i < list.size(); i++) {
			pw.print(list.get(i) + " ");
		}
		pw.flush();

	}

}