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.Locale;
import java.util.Scanner;

public class Bachgold {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();

        if (n % 2 == 0) {
            System.out.println(n / 2);
            StringBuilder sb = new StringBuilder();
            for (int i = 0; i < n / 2; i++) {
                sb.append("2 ");
            }
            System.out.println(sb.toString().trim());
        }else{
            System.out.println(n / 2);
            StringBuilder sb = new StringBuilder();
            for (int i = 0; i < n / 2 - 1; i++) {
                sb.append("2 ");
            }
            System.out.println(sb.toString() + " 3");
        }

        // 2 => 2
        // 3 => 3
        // 4 => 2 2
        // 5 => 2 3
        // 6 => 2 2 2
        // 7 => 2 2 3

    }
}