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;

/*
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/**
 *
 * @author Ярослав
 */
public class R749 {
    public static void main(String[] args) {
        new A();
    }
    
    public static class A{

        public A() {
            Scanner sc=new Scanner(System.in);
            int n=sc.nextInt();
            System.out.println(n/2);
            for(int i=0;i<n/2-1;i++){
                System.out.println(2);
            }
            if(n%2>0) System.out.println(3);
            else System.out.println(2);
            
        }
    }
}