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.Scanner;

/**
 * Created by sanjayyepuri on 12/29/16.
 */
public class A {
    public static void main(String[] args){
        Scanner in = new Scanner(System.in);
        int N = in.nextInt();

        System.out.println(N/2);
        for(int i = 0; i < N/2-1; ++i){
            System.out.print("2 ");
        }
        if(N%2 == 0) System.out.println(2);
        else System.out.println(3);

    }
}