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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {

    public static void main(String[] args) throws IOException {
        BufferedReader input = new BufferedReader(new InputStreamReader(System.in));
        String in = input.readLine();
        long number = Long.parseLong(in);
        System.out.println(number/2);
        if(number % 2 == 0)
        {
            for (int i = 0; i < number/2; i++) {
                System.out.print("2 ");
            }
        }else
        {
            for (int i = 0; i < (number-3) / 2+1 ; i++) {
                if(i == (number-3) / 2 )
                    System.out.print("3");
                else
                    System.out.print("2 ");
            }
        }


    }
}