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:
// http://codeforces.com/contest/749/problem/A
import java.io.PrintStream;
import java.util.Scanner;

public class Main {
	//
	public static Scanner in = new Scanner(System.in);
	public static PrintStream out = new PrintStream(System.out);
	//
	public static void main(String... args) {
		int number = in.nextInt();
		StringBuilder sb = new StringBuilder("");
		int n = 0;
		while (number > 3) {
			n++;
			number -= 2;
			sb = sb.append(" 2");
		}
		String string = (n+1) +"\n" + number + sb.toString();
		System.out.println(string);
	}
}