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:

/**
 *
 * @author meashish
 */
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStreamWriter;
import java.io.PrintStream;
import java.io.Serializable;
import java.util.HashSet;
import java.util.InputMismatchException;

public class Main {

    InputReader in;
    Printer out;

    static long MOD = 1000000007;

    int p[] = new int[10000001];

    private void start() throws Exception {
        p[0] = p[1] = 1;
        for (int i = 2; i * i < 10000000; i++) {
            if (p[i] == 0) {
                for (int j = 2; i * j <= 10000000; j++) {
                    p[i * j] = 1;
                }
            }

        }

        HashSet<Integer> set = new HashSet<>();

        for (int i = 0; i <= 1000; i++) {
            if (p[i] == 0) {
                set.add(i);
            }
        }

        int n = in.nextInt();

        if (n == 2 || n == 3 || n == 5 || n == 7) {
            out.println("1\n" + n);
        } else if (n == 4) {
            out.println("2\n 2 2");
        } else if (n == 6) {
            out.println("3\n 2 2 2");
        } else if (n == 8) {
            out.println("2\n 3 5");
        } else if (n == 9) {
            out.println("3\n 3 3 3");
        } else if (n == 10) {
            out.println("3\n 2 3 5");
        } else if (n == 11) {
            out.println("3\n 2 2 7");
        } else if (n == 12) {
            out.println("2\n 5 7");
        } else if (n == 13) {
            out.println("1\n 13");
        } else if (n == 14) {
            out.println("2\n 2 11");
        } else if (n == 15) {
            out.println("2\n 2 13");
        } else {
            out.println(3);
            n -= 3;

            for (int i = 2; i <= 10000; i++) {
                if (isPrime(i) && isPrime(n - i)) {
                    out.println(3 + " " + i + " " + (n - i));
                    break;
                }
            }
        }

        out.flush();
    }

    boolean isPrime(int a) {
        if (a == 1) {
            return false;
        }
        if (a == 2 || a == 3) {
            return true;
        }
        
        for (int i = 2; i <= a / i; i++) {
            if ((a % i) == 0) {
                return false;
            }
        }
        
        return true;
    }

    long pow(long x, long n) {
        if (n <= 0) {
            return 1;
        }

        long y = pow(x, n / 2);

        if ((n & 1) == 0) {
            return (y * y) % MOD;
        } else {
            return (((y * y) % MOD) * x) % MOD;
        }
    }

    public static void main(String[] args) throws Exception {
        InputReader in;
        PrintStream out;

        //in = new InputReader(new FileInputStream(new File("in.txt")));
        //out = new PrintStream("out.txt");
        in = new InputReader(System.in);
        out = System.out;

        Main main = new Main();

        main.in = in;
        main.out = new Printer(out);

        main.start();
    }

    private static class InputReader {

        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

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

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

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

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

        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E') {
                    return res * Math.pow(10, nextInt());
                }
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E') {
                        return res * Math.pow(10, nextInt());
                    }
                    if (c < '0' || c > '9') {
                        throw new InputMismatchException();
                    }
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

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

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

        public String next() {
            return nextString();
        }

        public interface SpaceCharFilter {

            public boolean isSpaceChar(int ch);
        }
    }

    private static class Printer {

        PrintStream out;
        StringBuilder buffer = new StringBuilder();
        boolean autoFlush;

        public Printer(PrintStream out) {
            this.out = out;
        }

        public Printer(PrintStream out, boolean autoFlush) {
            this.out = out;
            this.autoFlush = autoFlush;
        }

        public void println() {
            buffer.append("\n");

            if (autoFlush) {
                flush();
            }
        }

        public void println(int n) {
            println(Integer.toString(n));
        }

        public void println(long n) {
            println(Long.toString(n));
        }

        public void println(double n) {
            println(Double.toString(n));
        }

        public void println(float n) {
            println(Float.toString(n));
        }

        public void println(boolean n) {
            println(Boolean.toString(n));
        }

        public void println(char n) {
            println(Character.toString(n));
        }

        public void println(byte n) {
            println(Byte.toString(n));
        }

        public void println(short n) {
            println(Short.toString(n));
        }

        public void println(Object o) {
            println(o.toString());
        }

        public void println(String s) {
            buffer.append(s).append("\n");

            if (autoFlush) {
                flush();
            }
        }

        public void print(String s) {
            buffer.append(s);

            if (autoFlush) {
                flush();
            }
        }

        public void flush() {
            try {
                BufferedWriter log = new BufferedWriter(new OutputStreamWriter(out));
                log.write(buffer.toString());

                log.flush();
                buffer = new StringBuilder();
            } catch (Exception e) {
                e.printStackTrace();
            }
        }
    }

    private class Pair<K, V> implements Serializable {

        private K key;

        public K getKey() {
            return key;
        }
        private V value;

        public V getValue() {
            return value;
        }

        public Pair(K key, V value) {
            this.key = key;
            this.value = value;
        }

        @Override
        public String toString() {
            return key + "=" + value;
        }

        @Override
        public int hashCode() {
            return key.hashCode() * 13 + (value == null ? 0 : value.hashCode());
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) {
                return true;
            }
            if (o instanceof Pair) {
                Pair pair = (Pair) o;
                if (key != null ? !key.equals(pair.key) : pair.key != null) {
                    return false;
                }
                if (value != null ? !value.equals(pair.value) : pair.value != null) {
                    return false;
                }
                return true;
            }
            return false;
        }
    }

}