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 Solution {

    private static void sieve(boolean[] primes) {
        Arrays.fill(primes, true);
        primes[0] = primes[1] = false;

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

    private static boolean isPrime(int n) {
        boolean prime = true;
        for (int i = 2; i <= Math.sqrt(n); i++)
            if (n % i == 0) {
                prime = false;
                break;
            }
        return prime;
    }

    private static void solve(InputReader in, OutputWriter out) {
        int n = in.nextInt();

        if (isPrime(n))
            out.print("1\n" + n);

        else {
            boolean[] primes = new boolean[300];
            sieve(primes);

            int p = 0;
            for (int i = n - 2; i >= 2; i--)
                if (isPrime(i)) {
                    p = i;
                    break;
                }

            n -= p;
            if (primes[n])
                out.print("2\n" + p + " " + n);

            else {
                boolean found = false;
                for (int i = 2; i < primes.length; i++) {
                    for (int j = i; j < primes.length; j++)
                        if (primes[i] && primes[j] && (i + j == n)) {
                            found = true;
                            out.print("3\n" + p + " " + i + " " + j);
                            break;
                        }

                    if (found) break;
                }
            }
        }
    }

    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        OutputWriter out = new OutputWriter(System.out);
        solve(in, out);
        in.close();
        out.close();
    }

    private static class InputReader {
        private BufferedReader br;
        private StringTokenizer st;

        InputReader(InputStream is) {
            br = new BufferedReader(new InputStreamReader(is));
            st = null;
        }

        String nextLine() {
            String line = null;
            try {
                line = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return line;
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                String line = nextLine();
                if (line == null) return null;
                st = new StringTokenizer(line);
            }
            return st.nextToken();
        }

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

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

        double nextDouble() {
            return Double.parseDouble(next());
        }

        void close() {
            try {
                br.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
    }

    private static class OutputWriter {
        BufferedWriter bw;

        OutputWriter(OutputStream os) {
            bw = new BufferedWriter(new OutputStreamWriter(os));
        }

        void print(int i) {
            print(Integer.toString(i));
        }

        void println(int i) {
            println(Integer.toString(i));
        }

        void print(long l) {
            print(Long.toString(l));
        }

        void println(long l) {
            println(Long.toString(l));
        }

        void print(double d) {
            print(Double.toString(d));
        }

        void println(double d) {
            println(Double.toString(d));
        }

        void print(boolean b) {
            print(Boolean.toString(b));
        }

        void println(boolean b) {
            println(Boolean.toString(b));
        }

        void print(char c) {
            try {
                bw.write(c);
            } catch (IOException e) {
                e.printStackTrace();
            }
        }

        void println(char c) {
            println(Character.toString(c));
        }

        void print(String s) {
            try {
                bw.write(s);
            } catch (IOException e) {
                e.printStackTrace();
            }
        }

        void println(String s) {
            print(s);
            print('\n');
        }

        void close() {
            try {
                bw.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
    }
}