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;
public class Numbers	{
	public static void main(String args[])	{
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int count=0;
		if(n==2)
			System.out.println("1\n2");
		else if(n==3)
			System.out.println("1\n3");
		else {
			if(n%2==0)	{
				System.out.println(n/2);
				for(int i=0;i<n/2;i++)	
					System.out.print("2 ");
			}
			else {
				System.out.println((1+(n-3)/2));
				System.out.print("3 ");
				for(int i=0;i<(n-3)/2;i++)
					System.out.print("2 ");
			}
		}
	}
}