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.math.BigInteger;
import java.util.*;
public class BachgoldProblem {
	public static boolean isPrime(int i) {
		BigInteger b=new BigInteger(String.valueOf(i));
		return b.isProbablePrime(1);
	}

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner s=new Scanner(System.in);
		int c=0,sum=0;
		int n=s.nextInt();
		c=n/2;
		System.out.print(c);
		System.out.println();
		if(n%2==0) {
			for(int i=0;i<c;i++)
				System.out.print(2+" ");
		}
			
		else {
			for(int i=0;i<c-1;i++)
				System.out.print(2+" ");
			System.out.print(3);
		}
		
		
	}

}