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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author AMR
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA1 solver = new TaskA1();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskA1 {
        public void solve(int testNumber, FastReader in, PrintWriter out) {
            int n = in.nextInt();
            int cnt = 0;
            boolean containsThree = false;
            if (n % 2 == 0) {
                cnt = n / 2;
            } else {
                cnt = n / 2 - 1;
                containsThree = true;
            }
            if (containsThree) {
                out.println(cnt + 1);
                for (int i = 0; i < cnt; i++) out.print("2 ");
                out.println("3");
            } else {
                out.println(cnt);
                for (int i = 0; i < cnt; i++) out.println("2 ");
            }
        }

    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader(InputStream inputStream) {
            br = new BufferedReader(new InputStreamReader(inputStream));
            st = null;
        }

        public String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

    }
}