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 CodeForce {
        public static void main(String[] args) 
        {
            Scanner scan = new Scanner(System.in);
            int n = scan.nextInt();
            int w=0;
            int x = 0;
            if(n%2==0)
            {
                System.out.println(n/2);
                while(n/2>x)
                {
                    System.out.print(2+" ");
                    x++;
                }
            }
            else
            {
                x = 0;
                w = n - 3;
                w = w/2;
                System.out.println(w+1);
                while(w>=x)
                {
                    if(w>x)
                    {
                        System.out.print(2+" ");
                    }
                    else
                    {
                        System.out.print(3);
                    }
                    x++;
                }
            }
        }
}