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.*;
import java.util.stream.IntStream;

public class Solution
{
    public static void main(String[] args)
    {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        List<Integer> list = new ArrayList<Integer>();

        if (n % 2 == 0)
        {
            int num = n / 2;
            for(int i=0; i<num; i++)
                list.add(2);
        }
        else
        {
            int num = n / 2;
            for(int i=0; i<num-1; i++)
                list.add(2);
            list.add(3);
        }



        System.out.println(list.size());
        for(int i=0; i<list.size(); i++) System.out.print(list.get(i)+" ");
    }
}