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:
//package com.turtle.bone;

import java.util.Scanner;

public class AK749 {
	public static Scanner cin = new Scanner(System.in);	
	
	public String ak749(int n){
		StringBuffer res=new StringBuffer();
		int resno=n/2;
		int[] resarr=new int[resno];
		if(n%2==0){
			for(int i=0;i<resno;i++){
				resarr[i]=2;
			}
		}else{
			for(int i=0;i<resno-1;i++){
				resarr[i]=2;
			}
			resarr[resno-1]=3;
		}
		res.append(resno).append(System.getProperty("line.separator"));
		for(int i=0;i<resno;i++){
			res.append(resarr[i]+" ");
		}
		
		return res.toString();
	}
	
	public static void main(String[] args) {
		while(cin.hasNext()){
			int n=cin.nextInt();
			
			String res=new AK749().ak749(n);
			
			System.out.println(res);
			
		}
	}

}