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 BahGold {

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

	}