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.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.List;
import java.util.StringTokenizer;

public class D implements Runnable {

	final static boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;

	BufferedReader in;
	PrintWriter out;
	StringTokenizer tok = new StringTokenizer("");

	final static String fileName = "";

	void init() throws IOException {
		if (ONLINE_JUDGE) {
			if (fileName.isEmpty()) {
				in = new BufferedReader(new InputStreamReader(System.in));
				out = new PrintWriter(System.out);
			} else {
				in = new BufferedReader(new FileReader(fileName + ".in"));
				out = new PrintWriter(fileName + ".out");
			}
		} else {
			if (fileName.isEmpty()) {
				in = new BufferedReader(new FileReader("input.txt"));
				out = new PrintWriter("output.txt");
			} else {
				in = new BufferedReader(new FileReader(fileName + ".in"));
				out = new PrintWriter(fileName + ".out");
			}
		}
	}

	public static void main(String[] args) {
		new D().run();
	}

	String readString() throws IOException {
		while (!tok.hasMoreTokens()) {
			tok = new StringTokenizer(in.readLine());
		}
		return tok.nextToken();
	}

	int readInt() throws NumberFormatException, IOException {
		return Integer.parseInt(readString());
	}

	long readLong() throws NumberFormatException, IOException {
		return Long.parseLong(readString());
	}

	int[] readIntArray(int size) throws NumberFormatException, IOException {
		int[] arr = new int[size];
		for (int i = 0; i < size; i++) {
			arr[i] = readInt();
		}
		return arr;
	}

	static long timeIn;

	void time() {
		System.err.println("Time = " + (System.currentTimeMillis() - timeIn));
	}

	@Override
	public void run() {
		try {
			timeIn = System.currentTimeMillis();
			init();
			solve();
			out.close();
			time();
		} catch (IOException e) {
			e.printStackTrace();
			System.exit(-1);
		}
	}

	boolean isPrime(int n) {
		if (n < count) {
			return prime[n];
		}
		for (int i = 2; i * i <= n; i++) {
			if (n % i == 0)
				return false;
		}
		return true;
	}

	boolean[] prime;
	final int count = 100000;

	private void solve() throws IllegalArgumentException, IOException {
		int n = readInt();

		List<Integer> primes = new ArrayList<>();
		prime = new boolean[count];
		Arrays.fill(prime, true);

		for (int i = 2; i < count; i++) {
			if (prime[i]) {
				primes.add(i);
				if (1l * i * i < count) {
					for (int j = i * i; j < count; j += i) {
						prime[j] = false;
					}
				}
			}
		}

		if (isPrime(n)) {
			out.println(1);
			out.println(n);
			return;
		}

		for (int prime : primes) {
			if (prime > n) {
				break;
			} else {
				if (isPrime(n - prime)) {
					out.println(2);
					out.println(prime + " " + (n - prime));
					return;
				}
			}
		}

		n -= 3;
		out.println(3);
		out.print(3 + " ");
		
		for (int prime : primes) {
			if (prime > n) {
				break;
			} else {
				if (isPrime(n - prime)) {
					out.print(prime + " " + (n - prime));
					return;
				}
			}
		}
	}
}