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.*;
    				
    				
    				public class Practice {
    					private static InputStream stream;
    					private static byte[] buf = new byte[1024];
    					private static int curChar;
    					private static int numChars;
    					private static SpaceCharFilter filter;
    					private static PrintWriter pw;
    					private static long mod=1000000009;
    				
    				    public static void main(String[] args) {
    				    	InputReader(System.in);
    						pw = new PrintWriter(System.out); 
    				        new Thread(null ,new Runnable(){
    				           public void run(){
    				               try{
    				                   solve();//This is solution method
    				                   pw.close();
    				               } catch(Exception e){
    				                   e.printStackTrace();
    				               }
    				           }
    				       },"1",1<<26).start();
    				   }
    				    
    				    
    				    
    				    private static void solve() throws NumberFormatException, IOException{
    				    	
     
    				    	long n=nextLong();
    				    	long c=0;
    				    	for(long i=n;;i--){
    				    		if(isPrime(i)){
    				    			pw.print(i+" ");
    				    			c++;
    				    			n-=i;
    				    			break;
    				    		}
    				    	}
    				    	for(int i=2;i<=n;i++){
    				    		if(isPrime(i) && (n-i)==0){
    				    			pw.print(i);
    				    			c++;
    				    			break;
    				    		}
    				    		if(isPrime(i) && isPrime(n-i)){
    				    			pw.print(i+" "+(n-i));
    				    			c+=2;
    				    			break;
    				    		}
    				    	}
    				    	System.out.println(c);
    				    	pw.close();
    				    }
    					public static long pow(long n, long p) {
				    		if(p==0)
				    			return 1;
				    		if(p==1)
				    			return n;
				    		if(p%2==0){
				    			long temp=pow(n, p/2);
				    		return (temp*temp);
				    		}else{
				    			 	long temp=pow(n,p/2);
				    			 	temp=(temp*temp);
				    			 	return(temp*n);
				    			 	
				    		}
				    	}
    				    public static String reverseString(String s) {
    			    		StringBuilder sb = new StringBuilder(s);
    			    		sb.reverse();
    			    		return (sb.toString());
    			    	}
    				    private static BigInteger ncr(int n,int k){
    				    	if (k < 0 || k > n) return BigInteger.ZERO;
    				        if (n-k < k) k = n-k;
    			
    				        BigInteger x = BigInteger.ONE;
    				        for (int i = 1; i <= k; i++) {
    				            x = x.multiply(new BigInteger(""+(n-i+1)));
    				            x = x.divide(new BigInteger(""+i));
    				        }
    			
    				return x;
    				    }
    				    static long fact[];
    				private static void factmod(int n,int mod){
    					fact=new long[n+1];
    					fact[0]=1;
    					for(int i=1;i<=n;i++){
    						fact[i]=i*fact[i-1];
    						//fact[i]%=mod;
    				
    					}
    					
    				}
    				private static long phi(long n){
    					long ans=n;
    					if(n%2==0)
    						ans-=(ans/2);
    					while(n%2==0)
    					{
    						n/=2;
    						
    					}
    					for(int i=3;i*i<=n;i+=2){
    						if(n%i==0){
    						while(n%i==0){
    							n/=i;
    						}
    						ans-=(ans/i);
    						}
    					}
    					if(n>2)
    						ans-=(ans/n);
    					
    					return ans;
    				}
    				static long d,x,y;
    				static long modInverse(long A, long M)
    				{
    				extendedEuclid(A,M);
    				return (x%M+M)%M;    //x may be negative
    				}
    				static void extendedEuclid(long A, long B) {
    				if(B == 0) {
    				d = A;
    				x = 1;
    				y = 0;
    				}
    				else {
    				extendedEuclid(B, A%B);
    				long temp = x;
    				x = y;
    				y = temp - (A/B)*y;
    				}
    				}
    				static boolean prime[];
    				public static void sieve(int n){
    					prime=new boolean[n+1];
    					Arrays.fill(prime, true);
    				for(int i=4;i<=1000000;i+=2)
    					prime[i]=false;
    				
    				for(int i=3;i*i<=1000000;i+=2){
    					if(prime[i]){
    						for(int j=2*i;j<=1000000;j+=i){
    							prime[i]=false;
    						}
    					}
    				}
    					
    				}
    				public static boolean isPrime(long n) {
    					
    					if (n <= 1)
    						return false;
    					if (n <= 3)
    						return true;
    				
    					if (n % 2 == 0 || n % 3 == 0)
    						return false;
    				
    					for (long i = 5; i * i <= n; i = i + 6)
    						if (n % i == 0 || n % (i + 2) == 0)
    							return false;
    				
    					return true;
    				}
    				
    				    public static long pow(long n, long p,long mod) {
    						if(p==0)
    							return 1;
    						if(p==1)
    							return n%mod;
    						if(p%2==0){
    							long temp=pow(n, p/2,mod);
    						return (temp*temp)%mod;
    						}else{
    							 	long temp=pow(n,p/2,mod);
    							 	temp=(temp*temp)%mod;
    							 	return(temp*n)%mod;
    							 	
    						}
    					}
    					public static long gcd(long x, long y) {
    						if (x == 0)
    							return y;
    						else
    							return gcd( y % x,x);
    					}
    					
    					
    					public static void InputReader(InputStream stream1) {
    						stream = stream1;
    					}
    				 
    					private static boolean isWhitespace(int c) {
    						return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    					}
    				 
    					private static boolean isEndOfLine(int c) {
    						return c == '\n' || c == '\r' || c == -1;
    					}
    				 
    					private static int read() {
    						if (numChars == -1)
    							throw new InputMismatchException();
    						if (curChar >= numChars) {
    							curChar = 0;
    							try {
    								numChars = stream.read(buf);
    							} catch (IOException e) {
    								throw new InputMismatchException();
    							}
    							if (numChars <= 0)
    								return -1;
    						}
    						return buf[curChar++];
    					}
    				 
    					private static 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;
    					}
    				 
    					private static 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;
    					}
    				 
    					private static String nextToken() {
    						int c = read();
    						while (isSpaceChar(c))
    							c = read();
    						StringBuilder res = new StringBuilder();
    						do {
    							res.appendCodePoint(c);
    							c = read();
    						} while (!isSpaceChar(c));
    						return res.toString();
    					}
    				 
    					private static 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();
    					}
    				 
    					private static int[] nextIntArray(int n) {
    						int[] arr = new int[n];
    						for (int i = 0; i < n; i++) {
    							arr[i] = nextInt();
    						}
    						return arr;
    					}
    				 
    					private static int[][] next2dArray(int n, int m) {
    						int[][] arr = new int[n][m];
    						for (int i = 0; i < n; i++) {
    							for (int j = 0; j < m; j++) {
    								arr[i][j] = nextInt();
    							}
    						}
    						return arr;
    					}
    					private static char[][] nextCharArray(int n,int m){
    						char [][]c=new char[n][m];
    						for(int i=0;i<n;i++){
    							String s=nextLine();
    							for(int j=0;j<s.length();j++){
    								c[i][j]=s.charAt(j);
    							}
    						}
    						return c;
    					}
    				 
    					private static long[] nextLongArray(int n) {
    						long[] arr = new long[n];
    						for (int i = 0; i < n; i++) {
    							arr[i] = nextLong();
    						}
    						return arr;
    					}
    				 
    					private static void pArray(int[] arr) {
    						for (int i = 0; i < arr.length; i++) {
    							pw.print(arr[i] + " ");
    						}
    						pw.println();
    						return;
    					}
    				 
    					private static void pArray(long[] arr) {
    						for (int i = 0; i < arr.length; i++) {
    							pw.print(arr[i] + " ");
    						}
    						pw.println();
    						return;
    					}
    				 
    					private static void pArray(boolean[] arr) {
    						for (int i = 0; i < arr.length; i++) {
    							pw.print(arr[i] + " ");
    						}
    						pw.println();
    						return;
    					}
    				 
    					private static boolean isSpaceChar(int c) {
    						if (filter != null)
    							return filter.isSpaceChar(c);
    						return isWhitespace(c);
    					}
    				 
    					private interface SpaceCharFilter {
    						public boolean isSpaceChar(int ch);
    					}
    				
    					
    				}	
    				
    				class Pair implements Comparable<Pair>{
    					
    					int city,pop;
    					Pair(int city,int pop){
    						this.city=city;
    						this.pop=pop;
    					}
    					@Override
    					public int compareTo(Pair o) {
    				return pop-o.pop;
    				
    					}
    					public int hashCode() {
    							int hu = (int) (city ^ (city >>> 32));
    							int hv = (int) (pop ^ (pop >>> 32));
    							//int hw = (int) (mass ^ (mass >>> 32));
    							return 31 * hu + hv ;
    						//return 0;
    						}
    						public boolean equals(Object o) {
    							Pair other = (Pair) o;
    							return city == other.city && pop == other.pop;
    						}
    				}