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.BufferedReader;import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;


public class Bachgold {
    
    static StringTokenizer st;
    static BufferedReader sc;
    static PrintWriter pw;
    
    public static void main(String args[]) throws Exception {
        sc = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(
            System.out)));
        int a = nextInt();
        // int b = nextInt();
        int max=0,n=0;
        if (a%2==0) {
        	n = a/2;
            pw.println(n);
            for (int i=0;i<n;i++)
            	pw.print("2 ");
        }
        else {
        	a = a-3;
        	n = a/2;
        	pw.println(n+1);
        	for (int i=0;i<n;i++)
        		pw.print("2 ");
        	pw.print("3");
        }

        pw.println();
        pw.close();
        
    }
    
    public static boolean istPalindrom(char[] word){
        int i1 = 0;
        int i2 = word.length - 1;
        while (i2 > i1) {
            if (word[i1] != word[i2]) {
                return false;
            }
            ++i1;
            --i2;
        }
        return true;
    }
    
    private static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    private static long nextLong() throws IOException {
        return Long.parseLong(next());
    }

/*  private static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
*/
    private static String next() throws IOException {
        while (st == null || !st.hasMoreTokens())
            st = new StringTokenizer(sc.readLine());
        return st.nextToken();
    }


}