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 mohammad {
    public static void main(String[] args) {
/*        ..................................
                       _oo0oo_
                      o8888888o
                      88" . "88
                      (| ^_^ |)
                      0\  =  /0
                    ___/`---'\___
                  .' \\|     |// '.
                 / \\|||  :  ||M// \
                / _||||| -:- |||||- \
               |   | \\\  -  /// |   |
               | \_|  ''\---/''  |_/ |
               \  .-\__  '-'  ___/-. /
             ___'. .'  /--.--\  `. .'___
          ."" '<  `.___\_<|>_/___.' >' "".
         | | :  `- \`.;`\ _ /`;.`/ - ` : | |
         \  \ `_.   \_ __\ /__ _/   .-` /  /
     =====`-.____`.___ \_____/___.-`___.-'=====
                       `=---=' 	
/*--------------->Mohammad Abohasan<---------------*/
        HashMap<String,String>mp = new HashMap<>();
        Scanner sc = new Scanner (System.in);
        int n = sc.nextInt();
        System.out.println(n/2);
        if(n%2 == 0)
	for (int i = 0; i < (n/2) ; i++)
            System.out.print(2 + " ");
        else{
        for (int i = 0; i < (n/2)-1 ; i++)
            System.out.print(2 + " ");
        System.out.println(3);}
    }
}