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.List;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.Map.Entry;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;
import java.util.Stack;
import java.util.*;


 
 
public class cool {

	private static InputStream stream;
	private static PrintWriter pw;
	
	
	
//	static int a;
//	static int b;
//	static int f = 0;
	static int n;
	static int m;
//	static int[][] arr;
	//static char[][] arr;
	
	static int Arr[];
	static int tree[];
	
	static int time = 0;
	
	static int[][] dir = {{-1,0},{0,1},{1,0},{0,-1}};

	static int visited[];
	static int visited2[][];
	static Stack<Integer> stack;
	
//	static ArrayList<Integer> ans;

//	static int arr[][];
//	static int arr[];
	static char[][] arr;
	static int[][] pos;
//	static int[][] visited;
//  static int c;
//	static int d[];
//	static int arr[][];
	static ArrayList[] adj;
//	static ArrayList<Integer> ans;
//	static int f;
	static int red[];
	static int black[];
	static int color[];
//	static ArrayList<Integer> comp[];

	static int f = 0;
	static int k = 0;
	static int count = 0;
	static int total = 0;
	static int ini[];
	
	static ArrayList<Node> list;
	static ArrayList<Integer> ind;


	
	public static void main(String[] args){
		//InputReader(System.in);
		pw = new PrintWriter(System.out);
		
		Scanner in = new Scanner(System.in);

		int n = in.nextInt();
		in.nextLine();
		
		if(isPrime(n)){
			pw.println(1);
			pw.println(n);
		}else{
			pw.println(3);
			pw.print(3 + " ");
			n = n-3;
			
			for(int i = 2;i<=n;i++){
				//pw.println(i + " " + (n-i));
				if(isPrime(i) && isPrime(n-i)){
					pw.print(i + " " + (n-i));
					break;
				}
			}
		}
		pw.close();
	}
	
	
	
	
	public static long pow(long n,long p,long m){
        long  result = 1;
         if(p==0)
           return 1;
       if (p==1)
           return n;
       while(p!=0)
       {
           if(p%2==1)
               result *= n;
           if(result>=m)
           result%=m;
           p >>=1;
           n*=n;
           if(n>=m)
           n%=m;
       }
       return result;
       }
	

	
	public static int cs(ArrayList<Integer> arr, int low, int high, int x)
	{
	  int mid;    
	 
	  if(x <= arr.get(low))
	    return low; 
	 
	  if(x > arr.get(high))
	    return -1;  
	 
	 
	  mid = (low + high)/2; 
	 
	  if(arr.get(mid) == x)
	    return mid;
	    
	  else if(arr.get(mid) < x)
	  {
	    if(mid + 1 <= high && x <= arr.get(mid+1))
	      return mid + 1;
	    else
	      return cs(arr, mid+1, high, x);
	  }
	   
	  else
	  {
	    if(mid - 1 >= low && x > arr.get(mid-1))
	      return mid;
	    else    
	      return cs(arr, low, mid - 1, x);
	  }
	}
	
	
	public static int fs(int arr[], int low, int high, int x)
	{
	   
	    if (low > high)
	        return -1;
	 
	    if (x >= arr[high])
	        return high;
	 
	    // Find the middle point
	    int mid = (low+high)/2;
	 
	    // If middle point is floor.
	    if (arr[mid] == x)
	        return mid;
	 
	    // If x lies between mid-1 and mid
	    if (mid > 0 && arr[mid-1] <= x && x < arr[mid])
	        return mid-1;
	 
	    // If x is smaller than mid, floor must be in
	    // left half.
	    if (x < arr[mid])
	        return fs(arr, low, mid-1, x);
	 
	    // If mid-1 is not floor and x is greater than
	    // arr[mid],
	    return fs(arr, mid+1, high, x);
	}
	 

	public static long gcd(long x, long y) {
		if (x == 0)
			return y;
		else
			return gcd( y % x,x);
	}
	
//	public static void dfs(int a,int p){
//		System.out.println(a);
//		if(a > 30000){
//			return;
//		}
//		
//		if(visited[a] == 1){
//			return;
//		}
//		
//		visited[a] = 1;
//		
//		if(ini[a] != 0){
//			count+= ini[a];
//		}
//		
//		int l = a-p;
//		
//		if(visited[a+l-1] == 0){
//			dfs(a+l-1,a);
//		}else if(visited[a+l] == 0){
//			dfs(a+l,a);
//		}else if(visited[a+l+1] == 0){
//			dfs(a+l+1,a);
//		}
//		
//	}
//	
	
	
	
	
	
	public static int prev(int i,boolean[] arr){
		
		while(arr[i]){
			if(i == 0){
				if(arr[i]){
					return -1;
				}else{
					return 0;
				}
				
				
			}
			
			
			i--;
			
		}
		
		return i;
		
		
	}
	
	
	public static int next(int i,boolean[] arr){
		
		
		while(arr[i]){
			if(i == arr.length-1){
				if(arr[i]){
					return -1;
				}else{
					return 0;
				}
			}
			
			i++;
		}
		
		
		return i;
	}
	

	
	private static Map<String, Integer> sortByValue(Map<String, Integer> unsortMap) {

        // 1. Convert Map to List of Map
        LinkedList<Entry<String, Integer>> list =
                new LinkedList<Map.Entry<String, Integer>>(unsortMap.entrySet());

        // 2. Sort list with Collections.sort(), provide a custom Comparator
        //    Try switch the o1 o2 position for a different order
        Collections.sort(list, new Comparator<Map.Entry<String, Integer>>() {
            public int compare(Map.Entry<String, Integer> o1,
                               Map.Entry<String, Integer> o2) {
                return (o1.getValue()).compareTo(o2.getValue());
            }
        });

        // 3. Loop the sorted list and put it into a new insertion order Map LinkedHashMap
        Map<String, Integer> sortedMap = new LinkedHashMap<String, Integer>();
        for (Map.Entry<String, Integer> entry : list) {
            sortedMap.put(entry.getKey(), entry.getValue());
        }

        /*
        //classic iterator example
        for (Iterator<Map.Entry<String, Integer>> it = list.iterator(); it.hasNext(); ) {
            Map.Entry<String, Integer> entry = it.next();
            sortedMap.put(entry.getKey(), entry.getValue());
        }*/


        return sortedMap;
    }

	
	public static ArrayList<Integer> Range(int[] numbers, int target) {
	  

	    int low = 0, high = numbers.length - 1;
	    // get the start index of target number
	    int startIndex = -1;
	    while (low <= high) {
	        int mid = (high - low) / 2 + low;
	        if (numbers[mid] > target) {
	            high = mid - 1;
	        } else if (numbers[mid] == target) {
	            startIndex = mid;
	            high = mid - 1;
	        } else
	            low = mid + 1;
	    }

	    // get the end index of target number
	    int endIndex = -1;
	    low = 0;
	    high = numbers.length - 1;
	    while (low <= high) {
	        int mid = (high - low) / 2 + low;
	        if (numbers[mid] > target) {
	            high = mid - 1;
	        } else if (numbers[mid] == target) {
	            endIndex = mid;
	            low = mid + 1;
	        } else
	            low = mid + 1;
	    }

	    ArrayList<Integer> list = new ArrayList<Integer>();
	    int c = 0;
	    if (startIndex != -1 && endIndex != -1){
	        for(int i = startIndex;i<=endIndex;i++){
	        	list.add(i);
	        }
	    }
	    
	    
	    return list;
	    
	    
	}

	
	
	 private static int root(int Arr[],int i)
	    {
	        while(Arr[ i ] != i)           //chase parent of current element until it reaches root
	        {
	            Arr[ i ] = Arr[ Arr[ i ] ] ; 
	            i = Arr[ i ];
	        }
	        return i;
	    }
	 
	 private static void union(int Arr[],int size[],int A,int B)
	    {
	        int root_A = root(Arr,A);
	        int root_B = root(Arr,B);
	     
	       System.out.println(root_A + " " + root_B);
	        if(root_A != root_B){
	        	 if(size[root_A] < size[root_B ])
	 	        {
	        		 Arr[ root_A ] = Arr[root_B];
	        		 size[root_B] += size[root_A];	 	
	 	        }
	 	        else
	 	        {   	
	 	        	Arr[ root_B ] = Arr[root_A];
	 	        	size[root_A] += size[root_B];	 	   
	 	        }	
	        }
	    }
	 
	 private static boolean find(int A,int B)
	    {
	        if( root(Arr,A)==root(Arr,B) )       //if A and B have the same root, it means that they are connected.
	        return true;
	        else
	        return false;
	    }
	 
	
	


//	
//	public static void bfs(int i){
//		
//		Queue<Integer> q=new LinkedList<Integer>();
//    	q.add(i);
//    	
//    	visited[i] = 1;
//    	c++;
//    	nodes++;
//    	while(!q.isEmpty()){
//    		int top=q.poll();
//    		
//    		Iterator<Integer> it= arr[top].listIterator();
//    		while(it.hasNext()){
//    			int next =it.next();
//    			
//    			if(visited[next] == 0){
//    				nodes++;
//    				visited[next] = 1;
//    				q.add(next);
//    			}
//    		
//    		}
//    	}
//		
//	}
	
	
	
//	public static void dfs(int i){
//		
//		
//		if(visited[i] == 1){
//			return;
//		}
//		
//		visited[i] = 1;
//		con[c].add(i);
//		//System.out.print(i + " ");
//		for(int j = 0;j<arr[i].size();j++){
//			dfs(arr[i].get(j));
//		}
//		
//	}
//	
//	
//	public static void dfss(int i){
//		if(visited[i] == 1){
//			return;
//		}
//		
//		visited[i] = 1;
//		
//		for(int j = 0;j<arr[i].size();j++){
//			dfss(arr[i].get(j));
//		}
//	//	System.out.println(i);
//		stack.push(i);
//	}
//	
//	public static void reverse(){
//		ArrayList[] temp = new ArrayList[n];
//		
//		for(int i = 0;i<n;i++){
//			temp[i] = new ArrayList();
//		}
//		
//		for(int i = 0;i<n;i++){
//			for(int j = 0;j<arr[i].size();j++){
//				temp[arr[i].get(j)].add(i);
//			}
//		}
//		
//		arr = temp;
//		
//	}
//	
//	
	
	
	
	
	
	
	public static boolean isPrime(int n) {
		// Corner cases
		if (n <= 1)
			return false;
		if (n <= 3)
			return true;
 
		// This is checked so that we can skip 
		// middle five numbers in below loop
		if (n % 2 == 0 || n % 3 == 0)
			return false;
 
		for (int i = 5; i * i <= n; i = i + 6)
			if (n % i == 0 || n % (i + 2) == 0)
				return false;
 
		return true;
	}
	
		 
	 // union code starts	
	
	
	 
	 // union code ends
	
	
	 
//	 // Segment tree code begins
//	 
//	 
//	 static void build(int node,int start,int end)
//	 {
//	 if(start==end)
//	 tree[node]=a[start];
//	 else
//	 {
//	 int mid=(start+end)/2;
//	 build(2*node,start,mid);
//	 build(2*node+1,mid+1,end);
//	 if(tree[2*node]<tree[2*node+1])
//	 tree[node]=tree[2*node];
//	 else
//	 tree[node]=tree[2*node+1];
//	 }
//	 }
//	 
//	 
//	 static void update(int node,int start,int end,int idx,int val)
//	 {
//	 if(start==end)
//	 {
//	 a[idx]=val;
//	 tree[node]=val;
//	 }
//	 else
//	 {
//	 int mid=(start+end)/2;
//	 if(idx>=start&&idx<=mid)
//	 update(2*node,start,mid,idx,val);
//	 else
//	 update(2*node+1,mid+1,end,idx,val);
//	 if(tree[2*node]<tree[2*node+1])
//	 tree[node]=tree[2*node];
//	 else
//	 tree[node]=tree[2*node+1];
//	 }
//	 }
//	 
//	 static int query(int node,int start,int end,int l,int r)
//	 {
//	 if(l>end||start>r)
//	 return 100005;
//	 if(l<=start&&r>=end)
//	 return tree[node];
//	 int p1,p2;
//	 int mid=(start+end)/2;
//	 p1=query(2*node,start,mid,l,r);
//	 p2=query(2*node+1,mid+1,end,l,r);
//	 if(p1<p2)
//	 return p1;
//	 else
//	 return p2;
//	 }
//	 
//	 
//	 
//}

}

class Stone implements Comparable<Stone>{
	
	int a;
	int b;
	int c;
	int i;
	
	Stone(int a,int b,int c,int d){
		this.a = a;
		this.b = b;
		this.c = c;
		this.i = d;
	}

	@Override
	public int compareTo(Stone b) {

		if(this.c > b.c){
			return 1;
		}else if(this.c < b.c){
			return -1;
		}else if(this.b > b.b){
			return 1;
		}else if(this.b < b.b){
			return -1;
		}else if(this.a > b.a){
			return 1;
		}else if(this.a < b.a){
			return -1;
		}
		
		return 0;
	}
	

	
	
}


class Node{
	int a;
	int b;
}

class point{
	int a;
	int b;
}


class MyComp2 implements Comparator<Node>{
    
	@Override
	public int compare(Node o1, Node o2) {
		
		if( o1.b > o2.b){
			return 1;
		}else if( o1.b < o2.b){
			return -1;
		}else{
			if(o1.a == o2.a){
				return 0;
			}else if(o1.a > o2.a){
				return 1;
			}else if(o1.a < o2.a){
				return -1;
			}
		}
		
		return 0;
	}
}


class Card implements Comparable<Card>
{
	int a,b;
	public Card(int w,int h)
	{
		this.a=w;
		this.b=h;
		
	}
	public int compareTo(Card that)
	{
		return this.a-that.a;
	}
}