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.Scanner;
import java.util.Arrays;
import java.util.ArrayList;

public class BachgoldProblem {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int counter =0;
		ArrayList<Integer> arr = new ArrayList();
		while (n>=2){
			if (n==3){
				arr.add(3);
				n -=3;
				counter++;
				break;
			}
			else {
				arr.add(2);
				n -=2;
				counter ++;}
		}
		System.out.println(counter);
		StringBuilder sb = new StringBuilder();
		for(Integer x : arr)
			sb.append(x+" ");
		System.out.println(sb);

	}

}