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.PrintWriter;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int n = sc.nextInt();

        if (n == 2) {
            out.println(1);
            out.println(2);
            out.flush();
        }
        if (n == 3) {
            out.println(1);
            out.println(3);
            out.flush();
        }
        if ((n % 2 == 0) & (n != 2)) {
            out.println(n/2);
            out.flush();
            for (int i = 2; i <= n; i = i + 2) {
                out.print("2 ");
                out.flush();
            }
        }
        if ((n % 2 == 1) & (n != 3)) {
            out.println(n/2);
            out.flush();
            out.print("3 ");
            out.flush();
            for (int i = 4; i <= n; i = i + 2) {
                out.print("2 ");
                out.flush();
            }
        }   
    }
}