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 BachgoldProblem
{
    public static void main(String[] args)
    {
        Scanner scanner = new Scanner(System.in);
        
        int number = scanner.nextInt();
        
        long[] primes = {2, 3, 5, 7, 9};
        long primeIndex = 0;
        long[] answer = new long[50000];
        long count = 0;
        
        while (number > 0)
        {
            if (number - primes[(int) primeIndex] == 1)
            {
                primeIndex++;
            }
            else
            {
                number -= primes[(int) primeIndex];
                answer[(int) count] = primes[(int) primeIndex];
                count++;
            }
        }
        
        System.out.println(count);
        for (long i = 0; i < count; i++)
        {
            System.out.print(answer[(int) i]);
            if (i < count - 1)
            {
                System.out.print(" ");
            }
        }
        scanner.close();
    }
}