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.io.*;
public class Main {
    static class Scan {
        private byte[] buf=new byte[1024];
        private int index;
        private InputStream in;
        private int total;
        public Scan()
        {
            in=System.in;
        }
        public int scan()throws IOException
        {
            if(total<0)
            throw new InputMismatchException();
            if(index>=total)
            {
                index=0;
                total=in.read(buf);
                if(total<=0)
                return -1;
            }
            return buf[index++];
        }
        public int scanInt()throws IOException
        {
            int integer=0;
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            int neg=1;
            if(n=='-')
            {
                neg=-1;
                n=scan();
            }
            while(!isWhiteSpace(n))
            {
                if(n>='0'&&n<='9')
                {
                    integer*=10;
                    integer+=n-'0';
                    n=scan();
                }
                else throw new InputMismatchException();
            }
            return neg*integer;
        }
        public double scanDouble()throws IOException
        {
            double doub=0;
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            int neg=1;
            if(n=='-')
            {
                neg=-1;
                n=scan();
            }
            while(!isWhiteSpace(n)&&n!='.')
            {
                if(n>='0'&&n<='9')
                {
                    doub*=10;
                    doub+=n-'0';
                    n=scan();
                }
                else throw new InputMismatchException();
            }
            if(n=='.')
            {
                n=scan();
                double temp=1;
                while(!isWhiteSpace(n))
                {
                    if(n>='0'&&n<='9')
                    {
                        temp/=10;
                        doub+=(n-'0')*temp;
                        n=scan();
                    }
                    else throw new InputMismatchException();
                }
            }
            return doub*neg;
        }
        public String scanString()throws IOException
        {
            StringBuilder sb=new StringBuilder();
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            while(!isWhiteSpace(n))
            {
                sb.append((char)n);
                n=scan();
            }
            return sb.toString();
        }
        private boolean isWhiteSpace(int n)
        {
            if(n==' '||n=='\n'||n=='\r'||n=='\t'||n==-1)
            return true;
            return false;
        }
    }
    static int primes[];
    public static void main(String args[]) throws IOException {
        Scan input=new Scan();
        int n=input.scanInt();
        primes=new int[9592];
        sieve(100001);
        if(is_prime(n)) {
            System.out.println(1+"\n"+n);
            return;
        }
        ArrayList<Integer> arrli=new ArrayList<>();
        for(int i=n-2;i>=0;i-=2) {
            if(is_prime(i)) {
                n-=i;
                arrli.add(i);
                break;
            }
        }
        if(is_prime(n)) {
            arrli.add(n);
            n=0;
        }
        for(int i=0;i<primes.length && primes[i]<=n;i++) {
            if(is_prime(n-primes[i])) {
                arrli.add(primes[i]);
                arrli.add(n-primes[i]);
                break;
            }
        }
        System.out.println(arrli.size());
        for(int i=0;i<arrli.size();i++) {
            System.out.print(arrli.get(i)+" ");
        }
    }
    //false for prime number and true for composite number
    public static void sieve(int n) {
        boolean sieve[]=new boolean[n];
        int indx=0;
        for(int i=2;i<n;i++) {
            if(!sieve[i]) {
                primes[indx]=i;
                indx++;
                for(int j=2*i;j<n;j=j+i) {
                    sieve[j]=true;
                }
            }           
        }
//        System.out.println(indx);
    }
    public static boolean is_prime(int n) {
        for(int i=0;i<primes.length && primes[i]<n;i++) {
            if(n%primes[i]==0) {
                return false;
            }
        }
        return true;
    }
}