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;

public class Main1 {

	public static void main(String[] args) {
		
		int i = 0;
		int rr;
		int p = 2;
		
		Scanner sc = new Scanner(System.in);
		int x = sc.nextInt();
		
		int r = x;
		
		
		int countforfirstline = 0;
		String output = "";
		//x/2
		
		//countforfirstline++;
		//output = output+"2 ";
		
		int times = x/2;
		
		
		
		if (x%2 != 0)
		{
			output = repeat("2 ", times-1);
			countforfirstline = x/2 -1;
			countforfirstline++;
			output = output+"3 ";
		}
		else
		{
			countforfirstline = x/2;
			output = repeat("2 ", times);
		}
		
		System.out.println(countforfirstline);
		System.out.println(output);

		

	}
	
	public static String repeat(String str, int times) {
        return new String(new char[times]).replace("\0", str);
    }
	
	

}