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.Scanner;

public class numbertwo {

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();
        int ans = n / 2;
        System.out.println(ans);
        if(n % 2 == 0){

            while(n > 0){
                System.out.print("2 ");
                n -= 2;
            }
            System.out.println();
        }
        else if(n == 3){
            System.out.println("3");
        }
        else{
            while(n > 3){
                System.out.print("2 ");
                n -= 2;
            }
            System.out.println("3");
        }

    }


}