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.*;
import java.io.*;

public class Codeforces{
	
    public static void main(String[] args) throws IOException{
		
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		
		long n = Long.parseLong(br.readLine());
		
		long ans = 0;
		
		long temp = n;
		
		while(n % 2 != 0){
			n -= 3;
			ans++;
		}
		
		long two = (temp - 3 * ans) / 2;
		
		System.out.println(ans + two);
		
		for(int i = 0; i < two; i++)
			System.out.print(2 + " ");
		
		for(int i = 0; i < ans; i++)
			System.out.print(3 + " ");
		
		br.close();
    }
	
}