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:
/**
 *
 * @author aditya
 */
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;
 
public class BachGold {
 
	public static void main(String[] args) {
            FastScanner fs=new FastScanner();
            int T=1;
            PrintWriter out=new PrintWriter(System.out);
            for (int tt=0; tt<T; tt++) {
                int n=fs.nextInt();
                int res = n/2;
                if(n==2||n==3){
                    System.out.println(1);
                    System.out.println(n);
                    break;
                }
                out.print(res+"\n");
                if(n%2==0){
                    for(int i=1;i<=res;i++){
                        out.print(2+" ");
                    }
                    out.print("\n");
                }else{
                    for(int i=1;i<res;i++){
                        out.print(2+" ");
                    }
                    out.print(3+"\n");
                }
                
            }
            out.close();
	}
	
	static class FastScanner {
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            StringTokenizer st=new StringTokenizer("");
            public String next() {
            while (!st.hasMoreElements())
		try {
                    st=new StringTokenizer(br.readLine());
		} catch (IOException e) {
                    e.printStackTrace();
		}
		return st.nextToken();
            }
		
            int[] readArray(int n) {
            int[] a=new int[n]; 
            for (int i=0; i<n; i++) a[i]=nextInt();
		return a;
            }
            int nextInt () {
                return Integer.parseInt(next());
            }
	}
 
}