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;
import java.util.function.Function;
import java.util.stream.Collectors;
import java.util.stream.Stream;

/**
 * Created by shunter on 12/24/16.
 */
public class z749a {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);

        int n = in.nextInt();

        Stream<String> numbers = Stream.generate(() -> "2").limit(n / 2 - 1);
        numbers = Stream.concat(numbers, Stream.of(Integer.toString(2 + n % 2)));

        System.out.println(n / 2);
        System.out.println(numbers.collect(Collectors.joining(" ")));

    }
}