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.ArrayList;
import java.util.Scanner;

public class Main {


    public static void count(int input){
       ArrayList<Integer> result = new ArrayList<>();
        int two = input/2;
        for(int i=0; i<two; i++){
            result.add(2);
        }
        int remainder = input - two*2;

        if(isPrime(remainder) == true){
            if(remainder!= 0)
            result.add(remainder);
        }
        else {
            int temp = remainder + 2;
            result.remove(two-1);
            if(isPrime(temp) == true)
                result.add(temp);
        }

        System.out.println(result.size());
        for (Integer i:result) {
            System.out.print(i +" ");
        }



    }
    public static boolean isPrime(int n) {
        int i;
        if(n==1)
            return false;
            else {

            for (i = 2; i <= Math.sqrt(n); i++) {
                if (n % i == 0) {
                    return false;
                }
            }
            return true;
        }
    }



    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        count(scanner.nextInt());



    }
}