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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class BachGold {
	
	static BufferedReader reader;
	static StringTokenizer tokenizer;

	public static void main(String[] args) throws IOException{
		// TODO Auto-generated method stub throws IOException
		reader=new BufferedReader(new InputStreamReader(System.in));
		tokenizer=new StringTokenizer("");
		int n=nextInt();
		if(n%2==0){
			System.out.println(n/2);
			for(int i=0;i<=n/2-1;i++){
				System.out.print(2+" ");
			}
		}
		else
			{System.out.println(n/2);
			for (int i=0;i<=(n/2)-2;i++)
				{System.out.print(2+" ");}
				System.out.print(3);
			}
	}
	
	static String next() throws IOException{
		while(! tokenizer.hasMoreTokens()){
			tokenizer=new StringTokenizer(reader.readLine());
		}
		return tokenizer.nextToken();
	}
	
	static int nextInt() throws IOException{
		return Integer.parseInt(next());
	}

}