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.util.*;
import java.math.*;
import java.io.*;
public class Luck{
	public static InputReader sc;
    public static PrintWriter out;
    public static final long MOD = (long) (1e9 + 7);
    static int n;
    static int m;
    static int q;
    public static void main(String[] args){
    	sc=new InputReader(System.in);	
    	out=new PrintWriter(System.out);
    	int[] sieve=new int[400];
    	for(int i=2;i<sieve.length;i++){
    		if(sieve[i]==0){
    			for(int j=2;j*i<sieve.length;j++){
    				sieve[j*i]=1;
    			}
    		}
    	}
    	int n=sc.nextInt();
    	if(n==3){
    		out.println(1);
    		out.println(3);
    	}
    	else{
    		int p1=-1;
        	for(int i=n-2;i>=2;i--){
        		int flag=0;
        		for(int j=2;j<=Math.sqrt(i);j++){
        			if(i%j==0){
        				flag=1;
        				break;
        			}
        		}
        		if(flag==0){
        			p1=n-i;
        			if(p1==0){
        				out.println(1);
        				out.println(n);
        				break;
        			}
        			else if(sieve[p1]==0){
        				out.println(2);
        				out.println(i+" "+p1);
        				break;
        			}
        			else{
        				int temp=0;
            			for(int j=2;j<p1;j++){
            				if(sieve[j]==0 && sieve[p1-j]==0){
            					out.println(3);
            					out.println(i+" "+j+" "+(p1-j));
            					temp=1;
            					break;
            				}
            			}
            			if(temp==1){
            				break;
            			}
        			}
        		}
        	}
    	}
    	out.close();
    }
   
    static class Pair{
    	int x;
    	int y;
    	Pair(){
    		this.x=-1;
    		this.y=-1;
    	}
    	Pair(int profit,int val){
    		this.x=profit;
    		this.y=val;
    	}
    	public static Comparator<Pair> Val=new Comparator<Pair>(){
    		public int compare(Pair p1,Pair p2){
    			if(p1.x==p2.y){
    				return p1.y-p2.y;
    			}
    			return (int)p1.x-(int)p2.x;
    		}
    	};
    	public int hashCode() {
    		final int prime = 31;
    		int result = 1;
    		result = prime * result + x;
    		result = prime * result + x;
    		return result;
    	}
    	public boolean equals(Object obj){
    		if (this == obj)
    	        return true;
    	    if (!(obj instanceof Pair)) {
    	        return false;
    	    }
    	 
    	    Pair p = (Pair) obj;
    	    if(p.x!=this.x){
    	    	return false;
    	    }
    	    else if(p.y!=p.y){
    	    	return false;
    	    }
    	    return true;
    	}
    }
    static class DisjointSet{
    	int n;
    	int[] par;
    	int[] rank;
    	DisjointSet(int n){
    		this.n=n;
    		this.par=new int[n];
    		this.rank=new int[n];
    		makeSet();
    	}
    	void makeSet(){
    		for(int i=1;i<n;i++){
    			par[i]=i;
    			rank[i]=1;
    		}
    	}
    	void union(int x,int y){
    		int parX=parent(x);
    		int parY=parent(y);
    		if(parX!=parY){
    			if(rank[parX]>=rank[parY]){
    				rank[parX]+=rank[parY];
    				rank[parY]=0;
    				par[parY]=parX;
    			}
    			else{
    				rank[parY]+=rank[parX];
    				rank[parX]=0;
    				par[parX]=parY;
    			}
    		}
    	}
    	int parent(int c){
    		int i=c;
    		while(i!=par[i]){
    			i=par[i];
    		}
    		return i;
    	}
    }
    static int gcd(int a,int b){
    	if(b==0){
    		return a;
    	}
    	return gcd(b,a%b);
    	
    }
    static int lcm(int a,int b){
    	int g;
    	if(a<b){
    		g=gcd(b,a);
    	}
    	else{
    		g=gcd(a,b);
    	}
    	return (a*b)/g;
    }
    static long bigmod ( long a, long p, long m ) {
        long res = 1 % m, x = a % m;
        while ( p>0 ) {
            if ( (p & 1)==1 ) res = ( res * x ) % m;
            x = ( x * x ) % m; p >>= 1;
        }
        return res;
    }
    static boolean isPrime(int n){
    	 if (n == 2)
    	        return true;
    	    for (long i = 2; i * i <= n; i++) {
    	        if (n % i == 0)
    	            return false;
    	    }
    	    return true;
    }
    
    static void shuffle(int[] A){
    	for(int i=A.length-1;i>0;i--){
    		int j=(int)(Math.random()*(i+1));
    		int temp=A[j];
    		A[j]=A[i];
    		A[i]=temp;
    	}
    }
    
//	public static class Node implements Comparable<Node>{
//	    int u;
//	    int v;
//	    public Node(){
//	    	;
//	    }
//	    public Node (int u, int v) {
//	    	this.u = u;
//	        this.v = v;
//	    }
//	    
//	    public void print() {
//	        out.println(v + " " + u + " ");
//	    }
//	   
//	    public int compareTo(Node n1){
//	    	return this.u-n1.u;
//	    }
//	}
	public static long pow(long base,long exp,long mod){
		if(exp==0){
			return 1;
		}
		if(exp==1){
			return base;
		}
		long temp=exp/2;
		long val=pow(base,temp,mod);
		long result=val*val;
		result=(result%mod);
		long AND=exp&1;
		if(AND==1){
			result*=base;
			result=(result%mod);
		}
		return result;
	}
	public static BigInteger pow(BigInteger base, BigInteger exp) {
	    if(exp.equals(new BigInteger(String.valueOf(0)))){
	        return new BigInteger(String.valueOf(1));
	    }    
	    if(exp.equals(new BigInteger(String.valueOf(1))))
	        return base;
	    BigInteger temp=exp.divide(new BigInteger(String.valueOf(2)));
	    BigInteger val = pow(base, temp);
	    BigInteger result = val.multiply(val);
	    result=result.remainder(new BigInteger(String.valueOf(MOD)));
	    BigInteger AND=exp.and(new BigInteger(String.valueOf(1)));
	    if(AND.equals(new BigInteger(String.valueOf(1)))){
	        result = result.multiply(base);
	        result=result.remainder(new BigInteger(String.valueOf(MOD)));
	    }    
	    return result;
	}
	    
	static class InputReader {

	    private InputStream stream;
	    private byte[] buf = new byte[8192];
	    private int curChar, snumChars;
	    private SpaceCharFilter filter;

	    public InputReader(InputStream stream) {
	        this.stream = stream;
	    }

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

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

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

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

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

	    public boolean isSpaceChar(int c) {
	        if (filter != null)
	            return filter.isSpaceChar(c);
	        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	    }

	    public interface SpaceCharFilter {
	        public boolean isSpaceChar(int ch);
	    }
	}

}