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 Bachgold {

	public static void main(String[] args) {
	
		Scanner sc = new Scanner(System.in);
		int num = sc.nextInt();
		int pcount,flagOdd=0,i;
		sc.close();
		
		
		if(num%2 == 0)
		{
			pcount = num/2;
		}
		else
		{
			pcount = (num-1)/2;
			flagOdd = 1;
		}
		
		System.out.println(pcount);
		
		for(i=0;i<pcount-1;i++)
			System.out.print("2 ");
		if(flagOdd==1)
			System.out.println("3 ");
		else
			System.out.println("2 ");
		

	}

}