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 A749 {
    public static void main(String q[]){
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        if(n==2 || n==3) {
            System.out.println(1);
            System.out.println(n);
        }else {
            int quo=n/2;
            System.out.println(quo);
            if(n%2==0){
                while (quo!=0) {
                    System.out.print(2 + " ");
                    quo--;
                }
            }else {
                while (quo!=1) {
                    System.out.print(2 + " ");
                    quo--;
                }
                System.out.print(3);
            }
        }
    }
}