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.*;

import java.math.*;
import java.security.*;
import java.text.*;
import java.util.*;
import java.util.concurrent.*;
import java.util.regex.*;
public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
	    int k = sc.nextInt();
	    if(k % 2 == 0) {
	    	System.out.println(k/2);
	    	for(int i = 0; i < k/2;i++) {
		    	System.out.print(2 + " ");	    	
	    	}
	    	System.out.println();
	    }else {
	    	System.out.println(k/2);
	    	for(int i = 0; i < (k/2)-1;i++) {
		    	System.out.print(2 + " ");	    	
	    	}
	    	System.out.println(3);
	    }
	    
	    
		

	}
	public static String reverse(String a) {
		char[] b = a.toCharArray();
		String c = "";
		for(int i = b.length-1; i >= 0 ;i--) {
			c+=b[i];
		}
		return c;
	}
	public static int min(int a, int b,int c) {
		if(a <b && a <c) {
			return a;
		}
		if(b <a && b <c) {
			return b;
		}
		return c;
	}
}