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