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.*;

public class CF749A {
	static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	static PrintWriter pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
	
	public static void main(String[] args) throws IOException {
		int num = Integer.parseInt(br.readLine());
		
		pw.println(num/2);
		pw.print((num%2) + 2);
		
		while(num > 3) {
			pw.print(" 2");
			num -= 2;
		}
		pw.println();
		
		pw.close();
	}
}