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.*;
public class Main
{
	public static void main(String[] args) {
		//System.out.println("Hello World");
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		int n1=n;
		int c=1;
		if(n%2==0)
		{
		    System.out.println(n/2);
		    for(int i=0;i<n/2;i++)
		        System.out.print("2 ");
		    System.out.println();
		}
		else
		{
		    while(n1>3)
		    {
		        n1=n1-2;
		        c++;
		    }
		    System.out.println(c);
		    for(int i=1;i<c;i++)
		        System.out.print("2 ");
		    System.out.print("3");
		}
	}
}