Problem: Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes.

More formally, you are given an odd numer n. Find a set of numbers pi (1 ≤ i ≤ k), such that

  1. 1 ≤ k ≤ 3
  2. pi is a prime
  3. <image>



The numbers pi do not necessarily have to be distinct. It is guaranteed that at least one possible solution exists.

Input

The single line contains an odd number n (3 ≤ n < 109).

Output

In the first line print k (1 ≤ k ≤ 3), showing how many numbers are in the representation you found.

In the second line print numbers pi in any order. If there are multiple possible solutions, you can print any of them.

Examples

Input

27


Output

3
5 11 11

Note

A prime is an integer strictly larger than one that is divisible only by one and by itself.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class ProblemD {
    private static List<Integer> primes = new ArrayList<Integer>();

    public static void main(String[] args) {
        InputReader in = new InputReader();
        PrintWriter out = new PrintWriter(System.out);

        new ProblemD().solve(in, out);

        out.close();
    }

    public void solve(InputReader in, PrintWriter out) {
        int n = in.nextInt();

        if (isPrime(n)) {
            out.println(1);
            out.print(n);

            return;
        }

        int k = (n + 1) / 2;

        for (int i = 3; i <= k; i++) {
            if (isPrime(i)) {
                int t = (n - i) / 2;

                if (isPrime(t)) {
                    out.println(3);
                    out.print(i + " " + t + " " + t);
                    return;
                }
            }
        }
    }

    public static boolean isPrime(int n) {
        if (primes.contains(n)) {
            return true;
        }

        if (n == 2) {
            return true;
        }

        if (n <= 1 || n % 2 == 0) {
            return false;
        }

        for (int i = 3; i * i <= n; i += 2) {
            if (n % i == 0) {
                return false;
            }
        }

        primes.add(n);

        return true;
    }

    static class InputReader {
        public BufferedReader br;
        public StringTokenizer st;

        public InputReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

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

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

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

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}