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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;

public class CF_Bachgold_Problem {
	public static void main(String[] args) throws IOException {
		InputStreamReader in = new InputStreamReader(System.in);
		BufferedReader br = new BufferedReader(in);
		int s = Integer.parseInt(br.readLine());
		 
		ArrayList<Integer> ar = new ArrayList<>();
		int c= 2;
		int sum= 0;
		while(sum!=s)
		{
			if(sum+c<=s)
			{
				sum+=c;
			}else
			{
				sum-=c;
				c=3;
				ar.remove(ar.size()-1);
				sum+=c;
			}
			ar.add(c);
		}
		System.out.println(ar.size());
		for(int v:ar)
		{
			System.out.print(v+" ");
		}
				

	}

}