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;
import java.lang.Math; 
import java.util.Arrays;

public class pa {
	
	static Scanner sc = new Scanner(System.in);
	
	public static void main(String args[])
	{
		int n,i;
    	n=sc.nextInt();
		System.out.println(n/2);
    	if (n%2==0){
        	for(i=0;i<n/2-1;i++){
            	System.out.println("2 ");
        	}
        	System.out.println("2\n");
    	}	
    	if(n%2==1){
        	for (i=0;i<n/2-1;i++){
            	System.out.println("2 ");
        	}
        	System.out.println("3\n");
    	}
	}
			
}