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;

public class Bachgold_Problem {
	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int x = Integer.parseInt(br.readLine());
		int n2 = 0;
		int n3 = 0;
		if (x % 2 == 0) {
			n2 = x / 2;
		} else {
			n2 = x / 2 - 1;
			n3 = 1;
		}
		int resN = n2 + n3;
		StringBuilder res = new StringBuilder();
		while (n2 > 0) {
			res.append(2);
			res.append(' ');
			n2--;

		}
		while (n3 > 0) {
			res.append(3);
			n3--;
		}
		System.out.println(resN);
		System.out.println(res);

	}

}