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.StringTokenizer;
import java.util.Collections;
import java.util.Collection;
import java.util.Set;
import java.util.HashSet;
import java.util.Map;
import java.util.HashMap;
import java.util.Arrays;
import java.util.ArrayList;
import java.util.Queue;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Stack;
import java.util.Vector;
import java.util.Hashtable;
import java.util.Iterator;

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.FileReader;

import java.math.BigInteger;

public class Main
{

	static PrintWriter writer;
	static StringTokenizer sz;
	static BufferedReader reader;

	public static void main(String[] args)
	throws Exception
	{
		declare();

		int num = readInt();

		if (isPrime(num))
		{
			writer.print(1 + "\n" + num);
		}
		else
		if (isPrime(num - 2))
		{
			writer.print(2 + "\n" + 2 + " " + (num - 2));
		}
		else
		{
			writer.println(3);
			writer.print(3+" ");
			num -= 3;

			for (int i=3;;i += 2)
			{
				if (isPrime(i) && isPrime(num - i))
				{
					writer.print(i + " " + (num - i));
					break;
				}
			}

		}

		close();
	}

	private static boolean isPrime(int num)
	{

		if (num % 2 == 0)
			return false;

		for (int i=3;i * i <= num;i += 2)
			if (num % i == 0)
				return false;

		return true;
	}

	private static class Pair implements Comparable<Pair>
	{
		int first,second;

		public Pair(int f, int s)
		{
			first = f;
			second = s;
		}

		public Pair(Pair p)
		{
			first = p.first;
			second = p.second;
		}

		@Override
		public int compareTo(Main.Pair p1)
		{

			if (first == p1.first)
				return  second - p1.second;
			return first - p1.first;

		}

		@Override
		public String toString()
		{
			return first + " " + second + "\n";
		}
	}

	private static String readString()
	throws IOException
	{
		if (sz.hasMoreTokens())
			return sz.nextToken();
		return reader.readLine();
	}

	private static void readLine()
	throws IOException
	{
		sz = new StringTokenizer(reader.readLine());
	}

	private static int readInt()
	throws IOException
	{
		if (sz.hasMoreTokens())
			return Integer.parseInt(sz.nextToken());
		return Integer.parseInt(reader.readLine());
	}

	private static long readLong()
	throws IOException
	{
		if (sz.hasMoreTokens())
			return Long.parseLong(sz.nextToken());
		return Long.parseLong(reader.readLine());
	}

	private static void declare()
	{
		writer = new PrintWriter(System.out);
		reader = new BufferedReader(
			new InputStreamReader(System.in));
		sz = new StringTokenizer("");
	}

	private static void declareFile()
	throws IOException
	{
		writer = new PrintWriter("output.txt");
		reader = new BufferedReader(
			new FileReader("input.txt"));
		sz = new StringTokenizer("");
	}

	private static void close()
	throws IOException
	{
		reader.close();
		writer.flush();
		writer.close();
	}
}