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