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.*;
import java.lang.*;
import java.io.*;

public final class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner sc = new Scanner(System.in);
		int num = sc.nextInt();
		if(num % 2 == 0) {
			System.out.println(num/2);
			for(int i = 0 ; i < num; i+=2) {
				System.out.print(2 + " ");
			}
		} else {
			System.out.println(num/2);
			for(int i = 3 ; i < num; i+=2) {
				System.out.print(2 + " ");
			}
			System.out.print(3);
		}
	}
}