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.*;
import java.util.stream.Collectors;
public class main_class {
    static Scanner sc=new Scanner(System.in);
    public static void main(String[] args) {
        int n = sc.nextInt();
        String ans = "";
        int count = 0;
        if(n%2==0) {

            while(n>0) {
                n=n-2;
                ans=ans+Integer.toString(2);
                count++;

            }
            ans.trim();
            System.out.println(count);
           for(String x:ans.split("")) {
               System.out.print(x+" ");
           }

            return;
        }
        else {
            while(n-1>0) {
                n = n - 2;
                ans = ans + Integer.toString(2);
                count++;
            }
           ans=new StringBuilder(ans).deleteCharAt(ans.length()-1).toString();
            ans=ans+'3';
            ans.trim();
            System.out.println(count);
            for(String x:ans.split("")) {
                System.out.print(x+" ");
            }
            return;
        }
    }

}