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.BufferedReader;
import java.io.InputStreamReader;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

/**
 * <a href="http://codeforces.com/contest/749/problem/A">749A</a>
 */
public class _749A {
    public static void main(String[] args) throws Exception {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.valueOf(reader.readLine());
        int count2 = 0;
        int count3 = 0;
        if (n % 2 == 0) {
            count2 = n / 2;
        } else {
            count2 = n / 2 - 1;
            count3 = 1;
        }
        System.out.println(count2 + count3);
        System.out.println(IntStream.concat(
                IntStream.range(0, count2).map(i -> 2),
                IntStream.range(0, count3).map(i -> 3))
                .boxed()
                .map(Object::toString)
                .collect(Collectors.joining(" "))
        );
    }
}