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;

/**
 * Created by sreps on 12/19/2016.
 */
public class CF388A {
    public static void main(String[] args) throws IOException {
            BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
            Integer T = Integer.parseInt(br.readLine());

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