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.awt.geom.Line2D;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.StreamCorruptedException;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashSet;
import java.util.Hashtable;
import java.util.InputMismatchException;
import java.util.Scanner;
import java.util.Stack;
import java.util.TreeSet;


public class q4
{
    public static void main(String[] args) {
        new q4().solve();
    }
    
    public q4()
    {
        in=new FasterScanner();
        out=new PrintWriter(System.out);
    }

    FasterScanner in;
    PrintWriter out;
 
    //long mod=1000000007L ;
   
    public void solve()
    {
    	ArrayList<Integer> prime=new ArrayList<Integer>();
    	boolean[] arr=new boolean[(int)Math.sqrt(1e9)+2];
    	for(int i=2;i<arr.length;i++)
    	{
    		if(!arr[i])
    		{
    			prime.add(i);
    			for(int j=i*i;j<arr.length && j>=0;j+=i)
    			{
    				arr[j]=true;
    			}
    		}
    	}
    	//System.out.println(prime);
    	int n=in.nextInt();
    	
    	int[] ans=new int[3];
    	int c=1;
    	
    	if(n%2==1)
    	{
    		ans[0]=3;
    		n-=3;
    	}
    	else
    	{
    		ans[0]=2;
    		n-=2;
    	}
    	if(n==0)
    	{
    		System.out.println(c);
    		for(int i=0;i<c;i++)
    		{
    			System.out.print(ans[i]+" ");
    		}
    		return;
    	}
    	int x;
    	l:
    	for(int i=0;i<prime.size();i++)
    	{
    		int temp=prime.get(i);
    		 x=n-temp;
    		//System.out.println(n+" "+x);
    		if(x==0)
    		{
    			ans[c++]=temp;
    			System.out.println(c);
        		for(int k=0;k<c;k++)
        		{
        			System.out.print(ans[k]+" ");
        		}
        		return;
    		}
    		for(int xx:prime)
    		{
    			if(x==xx)
    			{
    				break;
    			}
    			if(x%xx==0)
    			{
    				continue l;
    			}
    		}
    		ans[c++]=temp;
    		ans[c++]=x;
    		System.out.println(c);
    		for(int k=0;k<c;k++)
    		{
    			System.out.print(ans[k]+" ");
    		}
    		return;
    	}
    	
        out.close();
    }
    
       
    public static class FasterScanner {
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = System.in.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public String nextString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int[] nextIntArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }

        public long[] nextLongArray(int n) {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }
    }
}