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 asdf {
	public static void main (String args[]){
		Scanner sc = new Scanner(System.in);
		int a = sc.nextInt();
		int b = 0;
		int d = 0;
		int p = 0;
		int[]c = new int[a/2+1];		
		if(a%2==0){
			d = a/2;
			for(int i = 0;i<a/2;i++){
				c[i]=2;
			}
		}
		else{
			d = a/2;
			for(int i = 0;i<a/2;i++){
				c[i]=2;
			}
			c[a/2-1]=c[a/2-1]+1;
		}
		System.out.println(d);
		for(int i = 0;i<d;i++){
		System.out.print(c[i]+" ");
		}
}
	}