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 Bachgold {

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

}