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.util.*;

public class Main {
    static ArrayList<Integer> primes;
    static boolean[] isPrime;
    public static void sieve(){
        primes = new ArrayList<>();
        int n = 2*100_000 + 1;
        isPrime = new boolean[2*100_000 + 1];
        Arrays.fill(isPrime, true); isPrime[0] = isPrime[1] = false;

        int i = 2;
        for (; i * i < n; i++) {
            if(isPrime[i]){
                primes.add(i);
                for (int j = i*i; j < n; j += i) {
                    isPrime[j] = false;
                }
            }
        }

        for (; i < n; i++) {
            if(isPrime[i]) primes.add(i);
        }
    }

    public static boolean checkPrime(int x){
        for (int i = 0; primes.get(i) * primes.get(i) <= x; i++) {
            if(x % primes.get(i) == 0) return false;
        }
        return true;
    }

    public static void main(String[] args) throws IOException {
        sieve();
        int n = sc.nextInt();
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i <= 300; i++) {
            if(checkPrime(n-i)){
                sb.append((n-i));
                n = i;
                break;
            }
        }

        if(n == 0) {
            pw.println(1);
            pw.println(sb);
            pw.close();
            return;
        }

        if(n == 2){
            pw.println(2);
            pw.println(2 + " " + sb);
            pw.close();
            return;
        }

//        pw.println(isPrime[4-primes.get(0)]);
        for (int i = 0; primes.get(i) <= n/2; i++) {
            if(isPrime[n-primes.get(i)]){
                pw.println(3);
                pw.println(sb + " " +primes.get(i) + " " + (n-primes.get(i)));
                pw.close();
                return;
            }
        }

        pw.close();
    }

    public static void pairSort(Pair[] arr) {
        ArrayList<Pair> l = new ArrayList<>();
        Collections.addAll(l, arr);
        Collections.sort(l);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = l.get(i);
        }
    }
    public static void longSort(long[] arr) {
        ArrayList<Long> l = new ArrayList<>();
        for (long i : arr) l.add(i);
        Collections.sort(l);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = l.get(i);
        }
    }
    public static void intSort(int[] arr) {
        ArrayList<Integer> l = new ArrayList<>();
        for (int i : arr) l.add(i);
        Collections.sort(l);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = l.get(i);
        }
    }

    static class Pair implements Comparable<Pair>{
        long first; long second;
        public Pair(long first, long second){
            this.first = first; this.second = second;
        }
        @Override
        public int compareTo(Pair p2) {
            if(second == p2.second) return (int) (p2.first - first);
            else return (int) (second - p2.second);
        }

        @Override
        public String toString() { return "("+ first + "," + second + ')'; }

    }
    static class Triple implements Comparable<Triple> {
        double x, y, z, sum;

        Triple(double a, double b, double c) { x = a; y = b; z = c; sum = x + y + z; }


        public int compareTo(Triple t)
        {
            if(Math.abs(sum - t.sum) < 1e-9) return x > t.x ? 1 : -1;
            return sum > t.sum ? 1 : -1;
        }
        public String toString()
        {
            return x + " " + y  + " " + z;
        }
    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if (x.charAt(0) == '-') {
                neg = true;
                start++;
            }
            for (int i = start; i < x.length(); i++)
                if (x.charAt(i) == '.') {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                } else {
                    sb.append(x.charAt(i));
                    if (dec)
                        f *= 10;
                }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg ? -1 : 1);
        }

        public boolean ready() throws IOException {
            return br.ready();
        }

        public int[] nextIntArr(int n) throws IOException {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = Integer.parseInt(next());
            }
            return arr;
        }

        public long[] nextLongArr(int n) throws IOException {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = Long.parseLong(next());
            }
            return arr;
        }

    }
    static PrintWriter pw = new PrintWriter(System.out);
    static Scanner sc = new Scanner(System.in);
    static Random random = new Random();
    static final long MOD = 1000000007;
}