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.*;
import java.lang.*;
import java.io.*;

public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
        Scanner sc = new Scanner(System.in);
	    int n = sc.nextInt();
	    if ((n & 1) == 0)
	    {
	        System.out.println (n / 2);
	        for (int i = 0; i < n / 2; i++)
	            System.out.print ("2 ");
	    }
	    else
	    {
	        System.out.println ((n - 1) / 2);
	        for (int i = 1; i < n / 2; i++)
	            System.out.print ("2 ");
	        System.out.print ("3");
	    }
	}
}