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
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyBufferedReader in = new MyBufferedReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskA {
        public void solve(int testNumber, MyBufferedReader in, PrintWriter out) {
            int n = in.getAnInt();
            int k = n % 2 == 0 ? n / 2 : ((n - 3) / 2 + 1);
            out.println(k);
            int numTwos = n % 2 == 0 ? n / 2 : ((n - 3) / 2);
            int numThrees = k - numTwos;
            for (int i = 0; i < numTwos; i++) {
                out.print(2 + " ");
            }

            for (int i = 0; i < numThrees; i++) {
                out.print(3 + " ");
            }

        }

    }

    static class MyBufferedReader {
        BufferedReader in;

        public MyBufferedReader(InputStream s) {
            this.in = new BufferedReader(new InputStreamReader(s));
        }

        public int getAnInt() {
            int res = -1;
            try {
                res = Integer.parseInt(new StringTokenizer(in.readLine()).nextToken());
            } catch (IOException e) {
                e.printStackTrace();
            }
            return res;
        }

    }
}