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 Program {
    public static void main(String[] args) {

        Scanner input = new Scanner(System.in);
        int n = input.nextInt();
        String output = "";

        int total = 0;
        while (!(n == 0)) {

                if(n % 2 == 1 ) {
                    n -= 3;
                    output = add(3, 1);
                    total++;
                }else {
                    int amount = n / 2;
                    output += add(2, amount);
                    n -= amount * 2;
                    total += amount;
                }


        }
        System.out.println(total);
        System.out.println(output);
    }

    public static String add(int prime, int amount) {
        StringBuffer result = new StringBuffer("");
        for( int i=0; i<amount; i++)
            result.append(prime + " ");

        return result.toString();
    }

    public static boolean isPrime(int number) {
        if ( number <= 1)
            return false;

        for( int i=2; i<=(int)Math.sqrt(number); i++) {
            if(number % i == 0 )
                return false;
        }
        return true;
    }


}