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.*;
/*
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/**
 *
 * @author Vishwa Raval
 */
public class BachgoldProblem {
    public static int Calculation(int n){
        if (2<=n && n<=100000){
            int count = n/2;
            System.out.println(count);
            if (n%2==1){
                System.out.print("3 ");
                n=n-3;
            }
            while (n>0){
                System.out.print("2 ");
                n=n-2;
            }
        }
        return 0;
    }
    public static void main(String[] args) {
        Scanner input=new Scanner (System.in);
        int n=input.nextInt();
        
        Calculation(n);
    }
}