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 abc{

public static void main(String[] args){
	Scanner sc=new Scanner(System.in);
	int x=sc.nextInt();
	ArrayList<Integer> numbers= new ArrayList<Integer>();

	if(x%2==0){
		for(int i=0;x/2>i;i=i+1){
			numbers.add(2);
		}}else{for(int i=0;(x/2)-1>i;i=i+1){
			numbers.add(2);
		}
		numbers.add(3);
		}
		System.out.println(numbers.size());
		for(int i=0;i<numbers.size();i=i+1){
			System.out.print(numbers.get(i)+" ");
		}

	}

}