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.*;
import java.lang.*;

public class q1 {
    public static FScanner sc;
    public static PrintWriter out;
    public static void main(String[] args) {
        sc=new FScanner();
        out=new PrintWriter(new BufferedOutputStream(System.out));
        StringBuilder sb = new StringBuilder();
        int counter = 0;
        int n = sc.nextInt();
        while(n > 0) {
            if (n % 2 == 1) {
                n -= 3;
                sb.append(3 + " ");
            }
            else if(n % 2 == 0) {
                n -= 2;
                sb.append(2 + " ");
            }
            ++counter;
        }
        out.println(counter);
        out.println(sb);




        out.close();
    }

    //-----------------------------------------------------HERE---------------------------------------------------------



    //------------------------------------------------------------------------------------------------------------------

    //scanner
    public static class FScanner {
        BufferedReader br;
        StringTokenizer st;

        public FScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}