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.util.Scanner;
import java.util.List;
import java.util.ArrayList; 

public class Main {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int counter = 0;
		List<Integer> primes = new ArrayList<Integer>();
		int tmp = n;
		for (int i = 2; i <= tmp; i++) {
			if(n - i < 0) break;
			while (n - i != 1 && n - i >= 0) {
				counter++;
				n -= i;
				primes.add(i);
			}
		}

		System.out.println(counter);

		for (Integer prime : primes) {
			System.out.print(prime + " ");
		}

		in.close();
	}
}