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.PrintWriter;
import java.util.*;

public class test5 {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		PrintWriter w = new PrintWriter(System.out);
		int x = sc.nextInt();
		StringBuilder r = new StringBuilder();
		int c = 0;
		if (x % 2 == 1) {
			x = x - 3;
			r.append("3 ");
			c++;
		}

		while (x != 0) {
			x = x - 2;
			r.append("2 ");
			c++;
		}

		w.println(c);
		w.print(r);
		w.flush();
		w.close();
		
	}

}