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 Bach {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long n = sc.nextLong();
		
		System.out.println((int)n/2);
		for(int i=0; i<n/2; ++i){
			if(i==(int)n/2-1)
				if(n%2==1){
					System.out.printf("%d", 3);
					break;
				}
				else{
					System.out.printf("%d", 2);
					break;
				}
			System.out.printf("%d ", 2);
			
		}
		/*int[] arr = new int[(int)n/2];
		int count = 0;
		while(true){
			arr[count] = 2;
			count++;
			n-=2;
			if(n==3){
				arr[count] = 3;
				count++;
				break;
			}
			if(n==0)
				break;
		}
		System.out.println(count);
		for(int i=0; i<arr.length; ++i)
			System.out.printf("%d ", arr[i]);*/
		sc.close();
	}

}