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.io.*;
import java.util.StringTokenizer;

public class Main {

    private static class Scanner{
        BufferedReader reader;
        StringTokenizer tokenizer;

        Scanner() throws IOException {
            reader=new BufferedReader(new InputStreamReader(System.in));
        }

        String nextLine() throws IOException{
            return reader.readLine();
        }

        String next() throws IOException {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                String line = reader.readLine();
                if (line == null) return null;
                tokenizer = new StringTokenizer(line);
            }
            return tokenizer.nextToken();
        }

        int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        short nextShort() throws IOException{
            return Short.parseShort(next());
        }

        char nextChar() throws IOException{
            return (char)reader.read();
        }

        float nextFloat() throws IOException{
            return Float.parseFloat(next());
        }

        long nextLong() throws IOException{
            return Long.parseLong(next());
        }
    }

    private static PrintWriter out;
    private static Scanner in;

    public static void main(String[] args) throws IOException {
        in = new Scanner();
        out = new PrintWriter(new OutputStreamWriter(System.out));
        solve();
        out.flush();
    }

    private static void solve() throws IOException {
        int n=in.nextInt();
        out.println(n/2);
        if (n%2==0){
            for (int i=0; i<n/2; i++){
                out.print(2);
                out.print(' ');
            }
        } else {
            for (int i=0; i<(n-3)/2; i++){
                out.print(2);
                out.print(' ');
            }
            out.print(3);
        }
    }



}