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.*;

public class main {

    public static void main(String[] args) {
        // write your code here
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        if (n % 2 == 0) {
            System.out.println(n/2);
            for (int i = 0; i < n/2; i++) {
                System.out.print(2 + " ");
            }
        }
        else {
            System.out.println((n-1)/2);
            for (int i = 0; i < ((n-1)/2)-1; i++) {
                System.out.print(2 + " ");
            }
            System.out.print(3);
        }
    }
}