Problem: Bachgold problem is very easy to formulate. Given a positive integer n represent it as a sum of maximum possible number of prime numbers. One can prove that such representation exists for any integer greater than 1.

Recall that integer k is called prime if it is greater than 1 and has exactly two positive integer divisors — 1 and k. 

Input

The only line of the input contains a single integer n (2 ≤ n ≤ 100 000).

Output

The first line of the output contains a single integer k — maximum possible number of primes in representation.

The second line should contain k primes with their sum equal to n. You can print them in any order. If there are several optimal solution, print any of them.

Examples

Input

5


Output

2
2 3


Input

6


Output

3
2 2 2

Solution (in JAVA):

Solution:
import java.io.PrintWriter;
import java.util.Scanner;

public class BachgoldProblem {

	void solve(Scanner s, PrintWriter out) {
		int N = s.nextInt();
		out.println(N / 2);
		while (N > 3) {
			out.print(2 + " ");
			N -= 2;
		}
		out.println(N);
	}

	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		new BachgoldProblem().solve(s, out);
		out.close();
		s.close();
	}

}