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.util.ArrayList;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.List;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.util.Collections;
import java.io.PrintWriter;
import java.io.Writer;
import java.io.FileReader;
import java.io.IOException;
import java.util.StringTokenizer;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Agostinho Junior (junior94)
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		TaskD solver = new TaskD();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskD {

	public void solve(int testNumber, InputReader in, OutputWriter out) {
		int n = in.readInt();

		int[] primes = XMath.getPrimes((int) 1e4);
		ArrayList<Integer> list = new ArrayList<>();

		if (XMath.isPrime(n)) {
			out.println(1);
			out.println(n);
			return;
		}
		
		int num = n;
		while (num >= 3 && list.size() < primes.length) {
			if (XMath.isPrime(num)) {
				list.add(num);
			}
			num--;
		}

		Collections.reverse(list);

		for (int i = 0; i < primes.length && primes[i] < n; i++) {
			for (int j = i; j < primes.length && primes[i] + primes[j] < n; j++) {
				if (Collections.binarySearch(list, n - (primes[i] + primes[j])) > -1) {
					out.println(3);
					out.printfln("%d %d %d", primes[i], primes[j], n - (primes[i] + primes[j]));
					return;
				}
			}
		}
		}

	}

class InputReader {
	private BufferedReader input;
	private StringTokenizer line = new StringTokenizer("");

	public InputReader(InputStream in) {input = new BufferedReader(new InputStreamReader(in));
	}

	public void fill() {
		try {
			if(!line.hasMoreTokens()) line = new StringTokenizer(input.readLine());
		} catch(IOException io) { io.printStackTrace(); System.exit(0);}
	}

	public int readInt() {
		fill();
		return Integer.parseInt(line.nextToken());
	}

}

class OutputWriter {
	private PrintWriter output;

	public OutputWriter(OutputStream out) {
		output = new PrintWriter(out);
	}

	public void printfln(String format, Object... o) {
		output.printf(format + "\n", o);
	}
	public void println(Object o) {
		output.println(o);
	}

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

class XMath {

	public static boolean isPrime(int n) {
		int max = (int)Math.sqrt(n);
		for (int i = 2; i <= max; i++) {
			if (n % i == 0) {
				return false;
			}
		}
		return n > 1;
	}

	public static int[] getPrimes(int N) {
		boolean[] isComposite = new boolean[N + 1];

		int max = (int)Math.sqrt(N);

		for (int i = 2; i <= max; i++) if (!isComposite[i]) {
			for (int j = i * 2; j <= N; j += i) {
				isComposite[j] = true;
			}
		}

		ArrayList<Integer> list = new ArrayList<>();

		for (int i = 2; i <= N; i++) {
			if (!isComposite[i]) {
				list.add(i);
			}
		}

		return XList.toIntArray(list);
	}
}

class XList {
	public static int[] toIntArray(List<Integer> list) {
		int[] ans = new int[list.size()];
		for (int i = 0; i < list.size(); i++) {
			ans[i] = list.get(i);
		}
		return ans;
	}

}