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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.Random;
import java.util.StringTokenizer;

public class D
{
	public static final Random RANDOM = new Random(System.currentTimeMillis());
	private BufferedReader bufferedReader;
	private StringTokenizer stringTokenizer;
	private PrintWriter out;

	public D()
	{
		this(new BufferedReader(new InputStreamReader(System.in)));
	}

	public D(BufferedReader bufferedReader)
	{
		this.bufferedReader = bufferedReader;
		this.stringTokenizer = null;
		this.out = new PrintWriter(new BufferedOutputStream(System.out));
	}

	public D(String file) throws FileNotFoundException
	{
		this(new BufferedReader(new InputStreamReader(new FileInputStream(file))));
	}

	private String next() throws IOException
	{
		while ((this.stringTokenizer == null) || (!this.stringTokenizer.hasMoreTokens()))
		{
			this.stringTokenizer = new StringTokenizer(this.bufferedReader.readLine());
		}
		return stringTokenizer.nextToken();
	}

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

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

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

	public String nextLine() throws IOException
	{
		return this.bufferedReader.readLine();
	}

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

	public static void main(String[] args)
	{
		D template = new D();
		try
		{
			template.solve();
		}
		catch (IOException exception)
		{
			exception.printStackTrace();
		}
		template.close();
	}

	public static int convert(int offset, boolean[] sieve, int[] primes, int primesCount)
	{
		for (int index = 0; index < sieve.length; index++)
		{
			if (sieve[index])
			{
				primes[primesCount] = offset + index;
				primesCount += 1;
			}
		}
		return primesCount;
	}

	public static boolean[] generateSieve(int size)
	{
		boolean[] result = new boolean[size];
		for (int index = 0; index < size; index++)
		{
			result[index] = true;
		}
		return result;
	}

	public static int[] generatePrimes(int n)
	{
		int[] primes = new int[(int) (n / Math.log(n) * 2)];
		int primesCount = 0;
		int segmentSize = (int) Math.sqrt(n);
		if (segmentSize * segmentSize < n)
		{
			segmentSize += 1;
		}
		int sqrt4 = (int) Math.sqrt(segmentSize);
		boolean[] sieve = generateSieve(segmentSize);
		sieve[0] = false;
		sieve[1] = false;
		for (int prime = 0; prime <= sqrt4; prime++)
		{
			if (sieve[prime])
			{
				for (int mul = 2; prime * mul < segmentSize; mul++)
				{
					sieve[prime * mul] = false;
				}
			}
		}
		primesCount = convert(0, sieve, primes, primesCount);
		int primesCountSieve = primesCount;
		for (int segment = 1; segment < segmentSize; segment++)
		{
			sieve = generateSieve(segmentSize);
			int offset = segmentSize * segment;
			for (int indexPrime = 0; indexPrime < primesCountSieve; indexPrime++)
			{
				int prime = primes[indexPrime];
				for (int mul = offset / prime; prime * mul - offset < segmentSize; mul++)
				{
					if (prime * mul - offset >= 0)
					{
						sieve[prime * mul - offset] = false;
					}
				}
			}
			primesCount = convert(offset, sieve, primes, primesCount);
		}
		int[] result = new int[primesCount];
		for (int index = 0; index < primesCount; index++)
		{
			result[index] = primes[index];
		}
		return result;
	}

	public static boolean isPrime(int[] primes, int n)
	{
		boolean result = true;
		for (int indexPrime = 0; result && indexPrime < primes.length; indexPrime++)
		{
			if (primes[indexPrime] < n)
			{
				result &= n % primes[indexPrime] != 0;
			}
		}
		return result;
	}

	public static int[] solve(int n)
	{
		int[] result;
		if (n == 3)
		{
			result = new int[]
			{ 3 };
		}
		else
		{
			if (n == 5)
			{
				result = new int[]
				{ 5 };
			}
			else
			{
				result = null;
				int[] primes = generatePrimes((int) (n / Math.log(n) + 1));
				for (int indexPrime0 = 0; result == null && indexPrime0 <primes.length; indexPrime0++)
				{
					int prime0 = primes[indexPrime0];
					for (int indexPrime1 = 0; result == null && indexPrime1 < indexPrime0; indexPrime1++)
					{
						int prime1 = primes[indexPrime1];
						int prime2 = n - prime0 - prime1;
						if (isPrime(primes, prime2))
						{
							result = new int[3];
							result[0] = prime0;
							result[1] = prime1;
							result[2] = prime2;
						}
					}
				}
			}
		}
		return result;
	}

	public void solve() throws IOException
	{
		int n = nextInt();
		int[] primes = solve(n);
		out.println(primes.length);
		for (int prime : primes)
		{
			out.print(prime + " ");
		}
		out.println();
	}
}