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.File;
import java.io.IOException;
import java.util.Scanner;

public class P749A {

	static boolean isServer = System.getProperty("os.name").trim().equalsIgnoreCase("Windows 10") ? false : true;

	public static void main(String[] args) throws IOException {
		Scanner sc;
		if (isServer) {
			sc = new Scanner(System.in);
		} else {
			File file = new File("C:\\cptest\\input.txt");
			sc = new Scanner(file);
		}
		int n = sc.nextInt();
		sc.close();

		if (n % 2 == 0) {
			System.out.println(n/2);
			for (int i = 0; i < n/2; i++) {
				System.out.print("2 ");
			}
			System.out.println();
			return;
		} else {
			int k = n-3;
			System.out.println(k/2+1);
			for (int j = 0; j < k/2; j++) {
				System.out.print("2 ");
			}
			System.out.println("3");
		}

	}

}