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.Arrays;
import java.util.Scanner;

public class problem1372A25 {
    private static Scanner sc=new Scanner(System.in);

    public static void main(String[] args) {
//        int t=sc.nextInt();
//        while(t>0) {

           int n=sc.nextInt();
           if(n%2==0)
           {
               int q=n/2;
               System.out.println(q);
               for(int i=1;i<q;i++)
                   System.out.print(2+" ");
               System.out.print(2);
           }
           else
           {int q=n/2;
               System.out.println(q);
               for (int i = 1; i <q ; i++)
                   System.out.print(2+" ");
               System.out.println(3);
           }



      //  System.out.print(arr[n-1][n-1]);




//            t--;
//        }
    }
}