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 primeSum {
public static void  main(String[] args)
{
	Scanner scan=new Scanner(System.in);
	int originalNumber = scan.nextInt();
	ArrayList <Integer> numbers = new ArrayList<Integer>();
	long count = 0;
	if(originalNumber%2==1)
	{
		numbers.add(3);
		originalNumber-=3;
		count++;
		
	}
	while (originalNumber>0)
	{
		numbers.add(2);
		count++;
		originalNumber-=2;
	}
	System.out.println(count);
	for(int i : numbers)
	{
		System.out.print(i+" ");
	}
}
}