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.*;
public class Day2 {
	public static void main(String[] args) throws IOException {
		BufferedReader br= new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out = new PrintWriter(System.out);
		int n= Integer.parseInt(br.readLine());
		if(n%2==0) {
			out.println((n/2)+" ");
			for(int i=0;i<n/2;i++)
				out.print(2+" ");
		}
		else {
			out.println((n-3)/2+1);
			out.print(3+" ");
			for(int i=0;i<(n-3)/2;i++) {
				out.print(2+" ");
		}
		
	}
		out.flush();
		out.close();
	}
}