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.io.*;
import java.util.*;
public class Solution{
    
    static boolean[] primes;
    
    public static void main(String[] args) throws Exception{
        Scanner s = new Scanner(System.in);
        int num = s.nextInt();
        
        int count = num/2;
        System.out.println(count);
        
        if(num%2 == 0){
            for(int i=0; i<num/2; i++){
                System.out.print(2 + " ");
            }
        }
        else{
            int sum = 0;
            for(int j=0 ;j<num/2 - 1; j++){
                System.out.print(2 + " ");
                sum += 2;
            }
            System.out.print(num-sum);
        }
      
    }
}