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.*;

public class Main {
	public static void main(String args[])
	{
		Scanner sc = new Scanner(System.in);
		//ArrayList<Integer> al = new ArrayList<Integer>();
		
		int an = sc.nextInt();
		System.out.println(an/2);
		if(an % 2 == 0)
		{
			for(int i=0;i<an/2;i++)
			{
				System.out.print("2 ");
			}
		}
		else
		{
			for(int i=0;i<(an/2-1);i++)
			{
				System.out.print("2 ");
			}
			System.out.println("3");
		}
	}
}