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.io.PrintWriter;
import java.util.*;


public class BachgoldProblem {
	
	public static void main(String[] args) throws IOException {
		
		PrintWriter pw = new PrintWriter(System.out);
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		ArrayList<Integer> prime = new ArrayList<>();
		
		while(n>1) {
			
			if(n==3) {
				prime.add(3);
				n-=3;
				break;
			}
			prime.add(2);
			n-=2;
		}
		pw.println(prime.size());
		
		for(int i =0; i< prime.size(); i++) {
			pw.print(prime.get(i) + " ");
		}
		pw.close();
		
	}

}