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