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.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

/**
 * Created by Юля on 18.09.2015.
 */
public class SolverD {
    public static void main(String[] args) throws IOException {
        new SolverD().run();
    }

    BufferedReader br;
    PrintWriter pw;
    StringTokenizer tokenizer;

    public String nextToken() throws IOException {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(br.readLine());
        }
        return tokenizer.nextToken();
    }

    public int nextInt() throws IOException, NumberFormatException {
        return Integer.parseInt(nextToken());
    }

    public long nextLong() throws IOException, NumberFormatException {
        return Long.parseLong(nextToken());
    }

    public double nextDouble() throws IOException, NumberFormatException {
        return Double.parseDouble(nextToken());
    }

    public void run() throws IOException {
//        br = new BufferedReader(new FileReader("input.txt"));
//        pw = new PrintWriter("output.txt");
        br = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(new OutputStreamWriter(System.out));

        solve();

        pw.flush();
        pw.close();
    }

    List<Integer> primes=new ArrayList<Integer>();

    private void solve() throws IOException {
        primes.add(2);
        primes.add(3);
        primes.add(5);
        int n=nextInt();
        if (n<=7) {
            pw.println(1);
            pw.println(n);
            return;
        }
        for (int i=7; i<35000; i++) {
            if (isPrime(i)){
                primes.add(i);
            }
        }
        int[] result=new int[3];
        if (n<35000) {
            result[0]=3;
            n-=3;
        } else {
            int num=n-4;
            while (!isPrime(num)){
                num--;
            }
            result[0]=num;
            n-=num;
        }
        for (int num=2; num<n; num++) {
            if (isPrime(num) && isPrime(n-num)){
                pw.println(3);
                pw.print(result[0]+" "+num+" "+(n-num));
                return;
            }
        }
    }

    boolean isPrime(int num) {
        int sqrt = (int) Math.sqrt(num);
        boolean isPrime = true;
        for (int j=0; primes.get(j)<=sqrt && isPrime; j++) {
            if (num%primes.get(j)==0){
                isPrime=false;
            }
        }
        return isPrime;
    }
}