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.*;

public class a {
	public static void main(String[]args) {
		Scanner sc= new Scanner(System.in);
		int a=sc.nextInt();
		int c=0;
		StringBuilder num=new StringBuilder();
		if (a%2==0) {
			while(a>0) {
				a-=2;
				c++;
				num.append("2"+" ");
				
			}
		}else {
			c++;
			num.append("3"+" ");
		
			while(a>3) {
				a-=2;
				c++;
				num.append("2"+" ");
			}
		}
		System.out.println(c);
		System.out.println(num);
	}


}