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.Scanner;

public class BachgoldProblem {
	
	public static void main(String [] args)
	{
		Scanner reader = new Scanner(System.in);
		
		int k = reader.nextInt();
		
		if(k % 2 == 0)
		{
			System.out.println(k/2);
			for(int i = 1; i <= k/2; i++)
				System.out.print(2 + " ");		
		}
						
		else
		{
			int count = 0;
			String str = "";
			while(k % 2 != 0)
			{
				count++;
				k -= 3;
				str += "3 ";
			}
			System.out.println(count + k/2);
			System.out.print(str);
			for(int i = 1; i <= k/2; i++)
				System.out.print(2 + " ");
		}
		
		
	}
	

}