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