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.util.*;
import java.io.*;
import java.math.BigInteger;

public class Main {
	static int[] prines;

	public static void main(String[] args) throws IOException {
		lenbuf = is.read(inbuf);
		int n = ni();
		prines = generatePrimes(Math.min(n, 34000));
		int length = prines.length;
		if (check(prines, n)) {
			System.out.println(1);
			System.out.println(n);
		} else if (check(prines, n - 2)) {
			System.out.println(2);
			System.out.println(n - 2 + " " + 2);
		} else {
			for (int i = 0; i < length; ++i) {
				for (int j = 0; j < length; ++j) {
					int t = n - prines[i] - prines[j];
					if (check(prines, t) && t >= 2) {
						System.out.println(3);
						System.out.println(t + " " + prines[i] + " "
								+ prines[j]);
						return;
					}
				}
			}
		}

	}

	public static boolean check(int[] primes, int n) {
		for (int i = 0; i < prines.length; ++i) {
			if (prines[i] == n) {
				return true;
			}
			if (n % primes[i] == 0) {
				return false;
			}
		}
		return true;
	}

	public static int[] generatePrimes(int n) {
		boolean[] prime = new boolean[n + 1];
		Arrays.fill(prime, 2, n + 1, true);
		for (int i = 2; i * i <= n; i++)
			if (prime[i])
				for (int j = i * i; j <= n; j += i)
					prime[j] = false;
		int[] primes = new int[n + 1];
		int cnt = 0;
		for (int i = 0; i < prime.length; i++)
			if (prime[i])
				primes[cnt++] = i;

		return Arrays.copyOf(primes, cnt);
	}

	static InputStream is = System.in;
	static byte[] inbuf = new byte[1 << 23];
	static int lenbuf = 0, ptrbuf = 0;

	static int readByte() {

		if (ptrbuf >= lenbuf) {
			return -1;
		}

		return inbuf[ptrbuf++];
	}

	static boolean hasNext() {
		int t = skip();

		if (t == -1) {
			return false;
		}
		ptrbuf--;
		return true;
	}

	static boolean isSpaceChar(int c) {
		return !(c >= 33 && c <= 126);
	}

	static int skip() {
		int b;
		while ((b = readByte()) != -1 && isSpaceChar(b))
			;
		return b;
	}

	static double nd() {
		return Double.parseDouble(ns());
	}

	static char nc() {
		return (char) skip();
	}

	static String ns() {
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while (!(isSpaceChar(b))) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	static char[] ns(int n) {
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while (p < n && !(isSpaceChar(b))) {
			buf[p++] = (char) b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}

	static char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for (int i = 0; i < n; i++)
			map[i] = ns(m);
		return map;
	}

	static int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = ni();
		return a;
	}

	static int ni() {
		int num = 0, b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	static long nl() {
		long num = 0;
		int b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
}

class Edge implements Comparable<Edge> {
	int t;
	long cost;

	public Edge(int t, long cost) {
		this.t = t;
		this.cost = cost;
	}

	@Override
	public int compareTo(Edge other) {
		return Long.compare(this.cost, other.cost);
	}
}