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.*;


public class CF2D {
    public static String filename = "CF2D".toLowerCase();
    public static int read = 2; //0 - .in/.out; 1 - input.txt/output.txt; 2 - stdin/stdout

    public static void main(String[] argv) throws IOException {
        Task t;
        boolean home = argv.length > 0 && argv[0].equals("test");
        InputStream inputStream;
        OutputStream outputStream;
        if (home) {
            inputStream = new FileInputStream(filename + ".in");
            outputStream = new FileOutputStream(filename + ".out");
        } else {
            switch (CF2D.read) {
                case 0:
                    inputStream = new FileInputStream(filename + ".in");
                    outputStream = new FileOutputStream(filename + ".out");
                    break;
                case 1:
                    inputStream = new FileInputStream("input.txt");
                    outputStream = new FileOutputStream("output.txt");
                    break;
                default:
                    inputStream = System.in;
                    outputStream = System.out;
                    break;

            }

        }
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream, home);


        if (home)
            do {
                long time = System.currentTimeMillis();
                t = new Task();
                t.in = in;
                t.out = out;
                t.run();

                out.writeln();
                out.writeln("=====Time:" + (System.currentTimeMillis() - time));
                out.flush();
            } while (in.toNextTest());
        else {
            t = new Task();
            t.in = in;
            t.out = out;
            t.run();
        }

        out.close();

    }

}
class Task {
    public OutputWriter out;
    public InputReader in;

    boolean isPrime(int n){
        int max = (int) Math.sqrt(n);
        for(int i = 2; i<=max;i++){
            if(n%i==0)
                return false;
        }
        return true;
    }
    public void run() {

        int n = in.nextInt();

        if(isPrime(n))
        {
            out.writeln(1);
            out.writeln(n);
            return;
        }
        int n1 = n;
        while (!isPrime(n1)||(n-n1<7))
            n1--;

        int q = n - n1;
        boolean[] primes = new boolean[q+1];
        primes[0] = primes[1] = false;
        for(int i =2;i < q/2;i++){
            if(!primes[i]){
                int cur = i+i;
                while (cur<=q){
                    primes[cur]=true;
                    cur+=i;
                }
            }
        }
        int a = 2;
        while (primes[q-a]){
            a++;
            while (primes[a])
                a++;

        }

        out.writeln(3);
        out.writeln(n1, " ", a, " ", q-a);
    }


}


/*
===Readers===
 */
class InputReader {

    BufferedReader reader;
    StringTokenizer tokenizer;
    String nextLine;


    public InputReader(InputStream stream) throws IOException {
        reader = new BufferedReader(new InputStreamReader(stream));
        tokenizer = new StringTokenizer("");
        nextLine = reader.readLine();
    }

    public boolean hasNext() {
        while (!tokenizer.hasMoreTokens() && nextLine!=null)
            tokenizer = new StringTokenizer(nextLine());
        return tokenizer.hasMoreTokens() || nextLine!=null;
    }
    public boolean toNextTest(){
        while (hasNext() && !next().equals("=")){}
        return  hasNext();
    }


    public String next() {
        while (!tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(nextLine());

        }

        return tokenizer.nextToken();
    }

    public String nextLine() {
        String oldLine = nextLine;

        try {
            nextLine = reader.readLine();
        } catch (IOException e) {
            throw new RuntimeException();
        }
        return oldLine;
    }

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

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

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

    public int[] nextIntArray(int n) {
        int[] res = new int[n];
        for (int i = 0; i < n; i++)
            res[i] = nextInt();

        return res;
    }

}

class OutputWriter {

    PrintWriter out;


    boolean home;

    public OutputWriter(OutputStream stream, boolean _home) {
        out = new PrintWriter(new BufferedWriter(
                new OutputStreamWriter(stream)));
        home = _home;
    }

    public void write(Object... o) {
        for (Object cur : o)
            out.print(cur);

    }

    public void debug(Object... o) {
        if (home) {

            out.print("==DEBUG:");
            for (Object cur : o)
                out.print(" " + cur);
            out.println();
        }
    }

    public void writeln(Object... o) {
        write(o);
        out.println();
    }

    public void flush() {
        out.flush();
    }

    public void close() {
        out.close();
    }

}