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.*;

public class BachgoldProblem {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		
		if(n == 2) {
			System.out.println(1);
			System.out.println(2);
		}
		else if(n == 3) {
			System.out.println(1);
			System.out.println(3);
		}
		else {
			if(n % 2 == 0) {
				System.out.println(n/2);
				for(int i=0; i<n/2; i++) System.out.print(2 + " ");
			}
			else {
				System.out.println(n/2);
				for(int i=0; i<n/2-1; i++) System.out.print(2 + " ");
				System.out.print(3);
			}
		}
		sc.close();
	}
}