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:
//package adhoc; 
import java.io.*;
import java.util.*;
public class ex6 {
	public static void main(String[] args) throws IOException {
		 
		 Scanner sc = new Scanner(System.in);  
		 
		 int n = sc.nextInt(); 
		 System.out.println(n/2);
		 
		 if (n % 2 == 0) {
			 while (n/2 > 0) {
				 System.out.printf("2 "); 
				 n -= 2;
			 }		 
		
		 }
		 else {
			 while (n/2 - 1 > 0) {
				 System.out.printf("2 "); 
				 n -= 2;
			 }
			 System.out.printf("3");
		 }
		 
		 
		
		 }
		 
		 
		 

}