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