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.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

public class a {
	public static class node implements Comparable<node> {
		int x;
		int y;

		node(int x, int y) {
			this.x = x;
			this.y = y;
		}

		@Override
		public int compareTo(node o) {
			if (o.x < x)
				return 1;
			else if (o.x > x)
				return -1;
			else if (o.y > y)
				return 1;
			else if (o.y < y)
				return -1;
			return 0;
		}

	}

	public static class point {
		int x;
		int y;

		point(int x, int val) {
			this.x = x;
			this.y = val;
		}

	}

	public static long gcd(long a, long b) {
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}

	public static ArrayList<Integer> prime;

	public static void sieve(int n) {
		boolean vis[] = new boolean[n + 5];
		vis[1] = true;
		vis[0] = true;
		for (int i = 2; i <= n; i++) {
			if (!vis[i]) {
				prime.add(i);
				for (long j = (long) i * (long) i; j <= n; j += i) {
					vis[(int) j] = true;
				}
			}
		}
	}

	public static int tree[][];
	public static boolean end[][];
	public static int counter;

	public static void trie(String a) {
		int st = 0;

		for (int i = 0; i < a.length(); i++) {
			if (tree[a.charAt(i) - 'a'][st] == 0) {
				tree[a.charAt(i) - 'a'][st] = counter++;
			}

			st = tree[a.charAt(i) - 'a'][st];
		}
		end[a.charAt(a.length() - 1) - 'a'][st] = true;

	}

	public static int seg[][];

	public static int get(int s, int e, int p, int from, int to, int seg[]) {
		if (s >= from && e <= to)
			return seg[p];
		if (s > to || e < from)
			return 0;
		int mid = (s + e) / 2;
		int one = get(s, mid, p * 2, from, to, seg);
		int two = get(mid + 1, e, p * 2 + 1, from, to, seg);
		return Math.max(one, two);
	}

	public static long comp(int n, int r) {
		long ans = 1;
		r = Math.min(r, n - r);
		for (int i = 1; i <= r; i++) {
			ans = ans * ((long) n - (long) i + 1L) / (long) i;
		}
		return ans;
	}

	public static ArrayList<Integer> arr[];
	public static boolean vis[];
	public static Stack<Integer> S;

	public static void bfs(int node) {
		for (int i = 0; i < arr[node].size(); i++) {
			int k = arr[node].get(i);
			if (vis[k] == false) {
				vis[k] = true;
				S.push(k);
				bfs(k);
			}
		}
		S.push(node);
	}

	public static void dfs(int node) {

		for (int i = 0; i < arr[node].size(); i++) {
			int k = arr[node].get(i);
			if (vis[k] == false) {
				vis[k] = true;
				dfs(k);
			}
		}
	}

	public static boolean chPrime(int r) {

		for (int i = 2; i * i <= r; i++) {
			if (r % i == 0)
				return false;
		}
		return true;
	}

	public static long mod = (long) Math.pow(10, 9) + 7;

	public static void main(String[] args) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		// BufferedReader in = new BufferedReader(new FileReader("cubes.in"));

		StringBuilder qq = new StringBuilder();
		PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
		// PrintWriter out = new PrintWriter(new FileWriter("out.txt"));

		String y[] = in.readLine().split(" ");
		int n = Integer.parseInt(y[0]);
		prime = new ArrayList();
		sieve(10000000);
		if (chPrime(n)) {
			System.out.println(1);
			System.out.println(n);
			return;
		}
		for (int i = 0; i < prime.size(); i++) {
			int r = n - prime.get(i);

			if (r > 1 && chPrime(r)) {
				System.out.println(2);
				System.out.println(prime.get(i) + " " + r);
				return;
			}

			int r1 = n - 2 * prime.get(i);
			if (r1 > 1 && chPrime(r1)) {
				System.out.println(3);
				System.out.println(prime.get(i) + " " + prime.get(i) + " " + r1);
				return;
			}
			
		}

		out.close();

	}
}