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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class PrimeSum {
	// -------------------
	public static final int MOD = (int) (1e9 + 7);
	// ------------------

	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	StringTokenizer st;
	PrintWriter out = new PrintWriter(System.out);

	String next() {
		while (st == null || !st.hasMoreElements()) {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (IOException e) {
				e.printStackTrace();
			}
		}
		return st.nextToken();
	}

	int nextInt() {
		return Integer.parseInt(next());
	}

	long nextLong() {
		return Long.parseLong(next());
	}

	// ------------------
	public static void main(String[] args) {
		PrimeSum ob = new PrimeSum();
		
		ob.run();
	}

	private void run() {
		int n = nextInt();
		if(checkPrime(n)) {
			out.println(1);
			out.println(n);
		}else {
			//Every large odd number (n > 5) is the sum of a prime and the double of a prime
			//Hardy and Littlewood 
			for(int i=2;i<=n-2 && n>2*i;i++) {
				int p1 =i, p2 = n-2*i;
				if(checkPrime(p1) && checkPrime(p2)) {
					out.println(3);
					out.println(p1 +" "+p1+" "+p2);
					break;
				}
			}
		}
		
		out.close();
	}
	
	private boolean checkPrime(int x) {
		if(x<=1) return false;
//		if(x==2 || x==3) return true;
		for(int i=2;i*i<=x;i++) {
			if(x%i==0) return false;
		}
		return true;
	}

}