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.IOException;
import java.io.InputStreamReader;

public class BachgoldProblem {
    public static void main(final String[] args) throws IOException {
        final BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in)); 
        int n, k, count2, count3;
        n = Integer.parseInt(bufferedReader.readLine());
        k = count2 = count3  = 0;
        while(n > 0) {
            if(n >= 3 && n % 2 == 1) {
                ++count3;
                ++k;
                n -= 3;
            }
            while(n >= 2 && n%2 == 0) {
                ++count2;
                n -= 2;
                ++k;
            }
        }
        System.out.println(k);
        while(count2-- > 0) System.out.print(2 + " ");
        while(count3-- > 0) System.out.print(3 + " ");   
    }   
}