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.*;
import java.util.*;

public class Main
{
	void solve(Scanner in, PrintWriter out)
	{
		int n = in.nextInt();
		int arr[] = new int[n/2];
		int count = 0;
		while (n>0)
		{
			if (n>3 || n==2)
			{
				n-=2;
				arr[count] = 2;
			}
			else if (n==3)
			{
				n-=3;
				arr[count] = 3;
			}
			count++;
		}
		out.println(count);
		for (int i = 0; i < count; i++)
		{
			out.print(arr[i]+" ");
		}
	}
	
	void run()
	{
		try (Scanner in = new Scanner(System.in); PrintWriter out = new PrintWriter(System.out)) 
		{
			solve(in,out);
		}
	}
	
	public static void main(String args[])
	{
		new Main().run();
	}
}