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.io.*;
import java.util.*;

public class A{

	public static void main (String[] args) throws Exception{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		int ans = 0;
		int twos = 0;
		int threes = 0;
		if(n % 2 == 0){
			ans = n / 2;
			twos = ans;
		}
		else{
			threes++;
			n -= 3;
			ans = (n / 2) + 1;
			twos = n / 2;
		}
		System.out.println(ans);
		for(int i = 0; i < twos; i++)
			System.out.print(2 + " ");
		for(int i = 0; i < threes; i++)
			System.out.print(3 + " ");
		br.close();
	}
}