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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
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.Queue;
import java.util.Scanner;
import java.util.Set;
import java.util.Stack;
import java.util.*;


 
 
public class ck {

	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 char[][] arr;
	

	
//	static int[][] dir = {{-1,0},{0,1},{1,0},{0,-1}};

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

//	static int arr[][];
//	static int arr[];
//	static char[][] arr;
//	static int[][] visited;
//  static int c;
//	static int d[];
//	static int arr[][];
//	static ArrayList<Integer> arr[];
	static ArrayList<Integer> comp[];
	
	//static int c;
	static int parent[];
	static int nodes;
	static int ans = 0;
	
	public static void main(String[] args) throws NumberFormatException, IOException{
		//InputReader(System.in);
		//pw = new PrintWriter(System.out);
		
		Scanner in = new Scanner(System.in);
		
//		int t = in.nextInt();
//		in.nextLine();
//		
//		for(int j = 0;j<t;j++){

    	int n = in.nextInt();
    	in.nextLine();
    	
    	int a = n;
    	
    	ArrayList<Integer> list = new ArrayList();
    	while(a > 1 && !isPrime(a)){
    		a--;
    	}
    	
    	list.add(a);
    	
    	int c = n-a;
    	int f = 0;
    	for(int j = 2;j<c;j++){
    		if(isPrime(j) && c-j>1 && isPrime(c-j)){
    			list.add(j);
    			list.add(c-j);
    			f = 1;
    			break;
    		}
    	}
    	
    	if(f == 0){
    		if(isPrime(c)){
    			list.add(c);
    		}
    		System.out.println(list.size());
    		for(int i = 0;i<list.size();i++){
    			System.out.print(list.get(i) + " ");
    		}
    		
    	}else{
    		System.out.println(list.size());
    		
    		for(int i = 0;i<list.size();i++){
    			System.out.print(list.get(i) + " ");
    		}
    	}
		
			
}
	
public static void ddfs(int n,int m,int i,int j,char arr[][],int visited[][],int dir[][],int store[][],int ans){
		
		if(visited[i][j] == 1){
			return;
		}
		
		
		//System.out.println(i + " " + j + " " + arr[i][j]);
		if(arr[i][j] == '*'){
			ans++;
			return;
		}
		
		visited[i][j] = 1;
		store[i][j] = ans;
		int x = i;
		int y = j;
		
		for(int p = 0;p<4;p++){
			
			i = x + dir[p][0];
			j = y + dir[p][1];
			
			if(i < 0 || i >= n|| j < 0 || j >=m){
				
			}else{
				dfs(n,m,i,j,arr,visited,dir);
			}
			
		}
		
		
	}
	
	
	public static void dfs(int n,int m,int i,int j,char arr[][],int visited[][],int dir[][]){
		
		if(visited[i][j] == 1){
			return;
		}
		
		
		//System.out.println(i + " " + j + " " + arr[i][j]);
		if(arr[i][j] == '*'){
			ans++;
			return;
		}
		
		visited[i][j] = 1;
		int x = i;
		int y = j;
		
		for(int p = 0;p<4;p++){
			
			i = x + dir[p][0];
			j = y + dir[p][1];
			
			if(i < 0 || i >= n|| j < 0 || j >=m){
				
			}else{
				dfs(n,m,i,j,arr,visited,dir);
			}
			
		}
		
		
	}
	
	

//	
//	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 union(int a,int b){
		a = find(a);
		b = find(b);
		
		parent[a] = b;
		return;
	}
	
	public static int find(int i){
		if(i == parent[i]){
			return i;
		}
		
		parent[i] = find(parent[i]);
		return parent[i];
	}
	
//	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;
	}
	
	
	
	public static void Range(int[] numbers, int target) {
	    if (numbers == null)
	        return;

	    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;
	    }

	    if (startIndex != -1 && endIndex != -1){
	        for(int i=0; i+startIndex<=endIndex;i++){
	            if(i>0)
	                System.out.print(',');
	            System.out.print(i+startIndex);
	        }
	    }
	}
	
	 // union code starts	
	
	 private static void initialize( int Arr[ ],int size[], int N)
	    {
	        for(int i = 0;i<N;i++)
	        {
	        	Arr[ i ] = i ;
	        	size[ i ] = 1;
	        }
	    }
	 
	 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);
	     
	        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 Arr[],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;
	    }
	 
	 
	 // 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 Node{
	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{
			return 0;
			
			
		}
		
		
	}
}