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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;

public class Main {

    public static List<Integer> PRIMES = new ArrayList<>();
    
    public static void main(String[] args) throws Exception {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        InputReader inputReader = new InputReader(in);
        PrintWriter out = new PrintWriter(System.out);

        int n = inputReader.getNextInt();

        for(int i = 2; i < 35000; i++) {
            if(isPrime(i)) {
                PRIMES.add(i);
            }
        }

        if(isPrime(n)) {
            out.println(1);
            out.println(n);
        } else {
            if(isPrime(n-2)) {
                out.println(2);
                out.println((n-2) + " 2");
            } else {
                for (int i : PRIMES) {
                    if ((n - i) % 2 == 0 && isPrime((n - i) / 2)) {
                        out.println(3);
                        out.println(i + " " + ((n - i) / 2) + " " + ((n - i) / 2));
                        break;
                    }
                }
            }
        }

        in.close();
        out.close();
    }

    public static boolean isPrime(int x) {
        if(x < 2) {
            return false;
        }
        for(int j: PRIMES) {
            if(j * j > x) {
                break;
            }
            if(x % j == 0) {
                return false;
            }
        }
        return true;
    }

    public static class InputReader {

        static final String SEPARATOR = " ";

        String[] split;
        int head = 0;
        BufferedReader in;

        public InputReader(BufferedReader in) {
            this.in = in;
        }

        private void fillBuffer() throws IOException {
            if(split == null || head >= split.length) {
                head = 0;
                split = in.readLine().split(SEPARATOR);
            }
        }

        public String getNextToken() throws IOException {
            fillBuffer();
            return split[head++];

        }

        public int getNextInt() throws IOException {
            return Integer.parseInt(getNextToken());
        }

        public long getNextLong() throws IOException {
            return Long.parseLong(getNextToken());
        }
    }

    public static <T> String arrayToString(T[] arr) {
        StringBuilder stringBuilder = new StringBuilder();
        for(T x: arr) {
            stringBuilder.append(x + " ");
        }
        return stringBuilder.toString();
    }

}