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.PrintWriter;
import java.util.Scanner;

/**
 *
 * @author Ali_Jaber
 */
public class BachgoldProblem {
    static Scanner in = new Scanner(System.in);
    static PrintWriter out = new PrintWriter(System.out);
    public static void main(String[] args) {
        int n = in.nextInt();
        
            out.println(n/2);
                    if(n % 2 == 0)
            for (int i = 0; i < n/2; i++) {
                 out.print("2 ");
        }
                    else{
                        for (int i = 0; i < n/2-1; i++) {
                 out.print("2 ");
        }
                         out.println("3");
                    }
                   
        out.flush();
}
}