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.*;
import java.util.*;
import java.math.*;


public class Main implements Runnable {
    public BufferedReader in;
    public PrintWriter out;
    public StringTokenizer tok;
    
    
    public void solve() throws Exception {
        int n = nextInt();
        if (isPrime(n)) {
            out.println(1);
            out.println(n);
            return;
        }
        for (int i = n - 1; i >= 1; --i) {
            if (isPrime(i)) {
                if (n - i == 2) {
                    out.println(2);
                    out.println(i + " " + (n - i));
                    return;
                } else {
                    for (int j = n - i - 1; j >= 2; --j) {
                        if (isPrime(j) && isPrime(n - i - j)) {
                            out.println(3);
                            out.println(i + " " + j + " " + (n - i - j));
                            return;
                        }
                    }
                }
            }
        }
    }
    
    public boolean isPrime(int n) {
        if (n < 2) {
            return false;
        }
        for (int i = 2; i * i <= n; ++i) {
            if (n % i == 0) {
                return false;
            }
        }
        return true;
    }
    
    public int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

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

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

    public BigInteger nextBigInteger() throws IOException {
        return new BigInteger(next());
    }
    
    public String next() throws IOException {
        while (tok == null || !tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine());
        }
        return tok.nextToken();
    }
    
    public String nextLine() throws IOException {
        tok = new StringTokenizer("");
        return in.readLine();
    }

    public boolean hasNext() throws IOException {
        while (tok == null || !tok.hasMoreTokens()) {
            String s = in.readLine();
            if (s == null) {
                return false;
            }
            tok = new StringTokenizer(s);
        }
        return true;
    }
    
    public static void main(String args[]) {
        new Thread(null, new Main(), "Main", 1 << 28).start();
    }
    
    public void run() {
        try {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(new OutputStreamWriter(System.out));
            //in = new BufferedReader(new FileReader("input.in"));
            //out = new PrintWriter(new FileWriter("output.out"));
            Locale.setDefault(Locale.US);
            solve();
            in.close();
            out.close();
        } catch (Throwable e) {
            e.printStackTrace();
            java.lang.System.exit(1);
        }
    }
}