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.text.*;
import java.util.*;
import java.io.*;

public class Codeforces0 {

		public static void main(String [] args) throws IOException
		{


			Scanner sc = new Scanner(System.in);

			int n = sc.nextInt();
			int tows = 0 , threes = 0;
			if((n % 2) % 3 == 0)
			{
				tows = n / 2;
				n = n % 2;

				threes = n / 3;
				n = n % 3;

			}
			else if((n % 2) % 3 == 1 )
			{
				tows = n / 2 - 1;
				n = n % 2;

				threes = n / 3 +1;
				n = n % 3;

			}
			



			System.out.println(tows+threes);

			for(int i = 0 ; i < tows ; i++)
			{
				System.out.print(2 + " ");
			}

			for(int i = 0 ; i < threes ; i++)
			{
				System.out.print(3 + " ");
			}





		}

}