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.math.BigInteger;
public class SumPrime{
	public static void main(String[] args){
		Scanner s=new Scanner(System.in);
		int n=s.nextInt();
		if(n==2){System.out.printf("1\n2");}
		else if(n==3){System.out.printf("1\n3");}
		else{
			System.out.println(n/2);
			for(int i=1;i<n/2;i++) System.out.print("2 ");
			if(n%2==0) System.out.println("2");
			else System.out.println("3");
		}
	}
}