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 D {

    static int[] primes;

    static PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));

    public static void main(String[] args) throws Exception {
        primes = calculatePrimeNumbers(1_000_000);

        InputReader in = new InputReader();
        int N = in.nextInt();

        if (Arrays.binarySearch(primes, N) >= 0)
            printSolution(1, N);

        int prime1 = N - 1;
        while (true) {
            if (checkPrime(prime1))
                break;
            prime1--;
        }

        int needNow = N - prime1;
        if (checkPrime(needNow))
            printSolution(2, prime1, needNow);


        int indxCeil = ceilIndex(primes, needNow);

        for (int i = 0; i < indxCeil; i++)
            if (Arrays.binarySearch(primes, needNow - primes[i]) >= 0)
                printSolution(3, prime1, primes[i], needNow - primes[i]);

        throw new IllegalStateException("No solution");
    }

    private static void printSolution(int num, int... nums) {
        out.println(num);
        out.print(nums[0]);
        if (num > 1) {
            out.write(' ');
            out.print(nums[1]);

            if (num > 2) {
                out.write(' ');
                out.print(nums[2]);
            }
        }
        out.write('\n');
        out.close();
        System.exit(0);
    }

    private static boolean checkPrime(int x) {
        if (x < primes[primes.length - 1])
            return Arrays.binarySearch(primes, x) >= 0;

        for (int i = 0; primes[i] * primes[i] <= x; i++) {
            if (x % primes[i] == 0)
                return false;
        }

        return true;
    }

    private static int ceilIndex(int A[], int key) {
        int l = -1;
        int r = A.length - 1;
        int m;

        while (r - l > 1) {
            m = l + (r - l) / 2;
            if (A[m] > key)
                r = m;
            else if (A[m] < key)
                l = m;
            else {
                while (A[m + 1] == key)
                    m++;
                return m + 1;
            }
        }

        return r;
    }

    private static int[] calculatePrimeNumbers(int upTo) {
        boolean[] primes = new boolean[upTo + 1];

        for (int i = 3; i < primes.length; i += 2) {
            primes[i] = true;
        }


        for (int i = 3; i * i < primes.length; i += 2) {
            if (primes[i]) {
                int idx = i * i;
                while (idx < primes.length) {
                    primes[idx] = false;
                    idx += i;
                }
            }
        }
        int primeCount = 1; // 2
        for (int i = 3; i < primes.length; i += 2) {
            if (primes[i])
                primeCount++;
        }

        int[] primeNumbers = new int[primeCount];

        primeNumbers[0] = 2;
        int idx = 1;

        for (int i = 3; i < primes.length; i += 2) {
            if (primes[i])
                primeNumbers[idx++] = i;
        }

        return primeNumbers;
    }

}

class InputReader {

    private InputStream stream;
    private byte[] buf = new byte[2048];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;

    public InputReader() {
        this.stream = System.in;
    }

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

    public InputReader(SpaceCharFilter filter) {
        this.stream = System.in;
        this.filter = filter;
    }

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

    public int read() {
        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 char nextChar() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        return (char) c;
    }

    public int nextDigit() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        return c - '0';
    }

    public int nextInt() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        boolean negative = false;
        if (c == '-') {
            negative = true;
            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 negative ? -res : res;
    }

    public int nextUnsignedInt() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int res = 0;
        do {
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res;
    }

    public final long nextLong() {
        int c = read();
        while (isSpaceChar(c)) {
            c = read();
        }
        boolean negative = false;
        if (c == '-') {
            negative = true;
            c = read();
        }
        long res = 0;
        do {
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return negative ? -res : res;
    }

    public final long nextUnsignedLong() {
        int c = read();
        while (isSpaceChar(c)) {
            c = read();
        }
        long res = 0;
        do {
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res;
    }

    public double nextDouble() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        long 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 (!(c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1 || c == '.'));

        if (c != '.') {
            return res * sgn;
        }
        c = read();

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

        return res * sgn + aft / (1.0 * len);
    }

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

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

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

    public String next() {
        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 char[] nextChars() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));

        char[] chars = new char[res.length()];
        res.getChars(0, chars.length, chars, 0);
        return chars;
    }

    public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
    }
}