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.math.BigInteger;
import java.util.*;
import java.util.concurrent.ArrayBlockingQueue;

import sun.security.provider.certpath.OCSP.RevocationStatus;

public class D
{
	String line;
	StringTokenizer inputParser;
	BufferedReader is;
	FileInputStream fstream;
	DataInputStream in;
	
	void openInput(String file)
	{

		if(file==null)is = new BufferedReader(new InputStreamReader(System.in));//stdin
		else
		{
			try{
		
				
			fstream = new FileInputStream(file);
			in = new DataInputStream(fstream);
			is = new BufferedReader(new InputStreamReader(in));
			}catch(Exception e)
			{
				System.err.println(e);
			}
		}

	}
	
	void readNextLine()
	{
		try {
			line = is.readLine();
			if(line!=null)inputParser = new StringTokenizer(line, " ");
			//System.err.println("Input: " + line);
		} catch (IOException e) {
			System.err.println("Unexpected IO ERROR: " + e);
		}	
		
	}
	
	int NextInt()
	{
		String n = inputParser.nextToken();
		int val = Integer.parseInt(n);
		
		//System.out.println("I read this number: " + val);
		return val;
	}
	
	long NextLong()
    {
            String n = inputParser.nextToken();
            
            long val = Long.parseLong(n);
            
            return val;
    }
	
	String NextString()
	{
		String n = inputParser.nextToken();
		return n;
	}
	
	void closeInput()
	{
		try {
			is.close();
		} catch (IOException e) {
			System.err.println("Unexpected IO ERROR: " + e);
		}
			
	}
	
	
	public static void main(String [] argv)
	{
		String filePath=null;
		if(argv.length>0)filePath=argv[0];
		new D(filePath);
	}

	public D(String inputFile)
	{
		openInput(inputFile);
		//readNextLine();
		int T=1;//NextInt();
		StringBuilder sb = new StringBuilder();
		
		ArrayList <Integer> primes = new ArrayList<Integer>();
		
		boolean [] p = new boolean[1000001];
		
		for(int i=0; i<1000001; i++)
			p[i]=true;
		
		for(int i=2; i<1000001; i++)
		{
			if(p[i])
			{
				primes.add(i);
				for(int j=i*2; j<1000001; j+=i)
					p[j]=false;
			}
		}
		
		for(int t=1; t<=T; t++)
		{
			readNextLine();
			int N=NextInt();
			ArrayList <Integer> r = new ArrayList<Integer>();
			BigInteger b = new BigInteger(""+N);
			if(b.isProbablePrime(50))
			{
				r.add(N);
			}
			else
			{
				out:for(int x:primes)
				{
					int rest=N-x;
					if(new BigInteger(rest+"").isProbablePrime(50))
					{
						r.add(x);
						r.add(rest);
						break;
					}
					for(int y:primes)
					{
						int r2=N-x-y;
						if(new BigInteger(r2+"").isProbablePrime(50))
						{
							r.add(x);
							r.add(y);
							r.add(r2);
							break out;
						}
					}
				}
			}
			sb.append(r.size()+"\n");
			for(int x:r)
				sb.append(x+" ");
		}
		System.out.print(sb);
		
		closeInput();		
	}

}