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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.math.BigInteger;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Pradyumn
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int[] primes = NT.sieveEratosthenes(1000000);
            int n = in.nextInt();
            if (NT.isPrimeMiller(n)) {
                out.println("1\n" + n);
                return;
            }
            for (int i = 0; i < primes.length; ++i) {
                int rem = n - primes[i];
                if (NT.isPrimeMiller(rem)) {
                    out.println("2\n" + primes[i] + " " + rem);
                    return;
                }
                for (int j = 0; j < primes.length; ++j) {
                    rem = n - primes[i] - primes[j];
                    if (NT.isPrimeMiller(rem)) {
                        out.println("3\n" + primes[i] + " " + primes[j] + " " + rem);
                        return;
                    }
                }
            }
            throw new RuntimeException();
        }

    }

    static class NT {
        public static boolean isPrimeMiller(int number) {
            return BigInteger.valueOf(number).isProbablePrime(30);
        }

        public static int[] sieveEratosthenes(int n) {
            if (n <= 32) {
                int[] primes = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31};
                for (int i = 0; i < primes.length; i++) {
                    if (n < primes[i]) {
                        return Arrays.copyOf(primes, i);
                    }
                }
                return primes;
            }

            int u = n + 32;
            double lu = Math.log(u);
            int[] ret = new int[(int) (u / lu + u / lu / lu * 1.5)];
            ret[0] = 2;
            int pos = 1;

            int[] isnp = new int[(n + 1) / 32 / 2 + 1];
            int sup = (n + 1) / 32 / 2 + 1;

            int[] tprimes = {3, 5, 7, 11, 13, 17, 19, 23, 29, 31};
            for (int tp : tprimes) {
                ret[pos++] = tp;
                int[] ptn = new int[tp];
                for (int i = (tp - 3) / 2; i < tp << 5; i += tp)
                    ptn[i >> 5] |= 1 << (i & 31);
                for (int j = 0; j < sup; j += tp) {
                    for (int i = 0; i < tp && i + j < sup; i++) {
                        isnp[j + i] |= ptn[i];
                    }
                }
            }

            // 3,5,7
            // 2x+3=n
            int[] magic = {0, 1, 23, 2, 29, 24, 19, 3, 30, 27, 25, 11, 20, 8, 4, 13, 31, 22, 28, 18, 26, 10, 7, 12, 21, 17,
                    9, 6, 16, 5, 15, 14};
            int h = n / 2;
            for (int i = 0; i < sup; i++) {
                for (int j = ~isnp[i]; j != 0; j &= j - 1) {
                    int pp = i << 5 | magic[(j & -j) * 0x076be629 >>> 27];
                    int p = 2 * pp + 3;
                    if (p > n)
                        break;
                    ret[pos++] = p;
                    if ((long) p * p > n)
                        continue;
                    for (int q = (p * p - 3) / 2; q <= h; q += p)
                        isnp[q >> 5] |= 1 << q;
                }
            }

            return Arrays.copyOf(ret, pos);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar;
        private int pnumChars;

        public InputReader(InputStream var1) {
            this.stream = var1;
        }

        private int pread() {
            if (this.pnumChars == -1) {
                throw new InputMismatchException();
            } else {
                if (this.curChar >= this.pnumChars) {
                    this.curChar = 0;

                    try {
                        this.pnumChars = this.stream.read(this.buf);
                    } catch (IOException var2) {
                        throw new InputMismatchException();
                    }

                    if (this.pnumChars <= 0) {
                        return -1;
                    }
                }

                return this.buf[this.curChar++];
            }
        }

        public int nextInt() {
            int var1;
            for (var1 = this.pread(); this.isSpaceChar(var1); var1 = this.pread()) {
                ;
            }

            byte var2 = 1;
            if (var1 == 45) {
                var2 = -1;
                var1 = this.pread();
            }

            int var3 = 0;

            do {
                if (var1 == 44) {
                    var1 = this.pread();
                }

                if (var1 < 48 || var1 > 57) {
                    throw new InputMismatchException();
                }

                var3 *= 10;
                var3 += var1 - 48;
                var1 = this.pread();
            } while (!this.isSpaceChar(var1));

            return var3 * var2;
        }

        private boolean isSpaceChar(int var1) {
            return var1 == 32 || var1 == 10 || var1 == 13 || var1 == 9 || var1 == -1;
        }

    }
}