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.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedHashMap;
import java.util.Map;
 
/**
 * Built using CHelper plug-in Actual solution is at the top
 */
public class Practice {
 
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        solver.solve(1, in, out);
        out.close();
    }
 
    static class TaskA {
 
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            if(n%2==0){
                out.println(n/2);
                for(int i=0;i<(n/2);i++){
                    out.print(2+" ");
                }
            }
            else{
                n-=3;
                out.println((n/2)+1);
                for(int i=0;i<n/2;i++){
                    out.print(2+" ");
                }
                out.print(3);
            }
        }
    }
 
    public static boolean checkPrime(int n, int p) {
        for (int i = 2; i <= Math.sqrt(n) && i <= p; i++) {
            if (n % i == 0) {
                return false;
            }
        }
        return true;
    }
 
    public static void mergeArrays(int[] arr1, int[] arr2, int n1,
            int n2, int[] arr3) {
        int i = 0, j = 0, k = 0;
        while (i < n1 && j < n2) {
            if (arr1[i] < arr2[j]) {
                arr3[k++] = arr1[i++];
            } else {
                arr3[k++] = arr2[j++];
            }
        }
        while (i < n1) {
            arr3[k++] = arr1[i++];
        }
        while (j < n2) {
            arr3[k++] = arr2[j++];
        }
    }
 
    public long GCD(long a, long b) {
        if (b == 0) {
            return a;
        }
        return GCD(b, a % b);
    }
 
    public static long nCr(int n, int r) {
        return n * (n - 1) / 2;
    }
 
    static class InputReader {
 
        public BufferedReader reader;
        public StringTokenizer tokenizer;
 
        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
 
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
 
        public int nextInt() {
            return Integer.parseInt(next());
        }
 
        public long nextLong() {
            return Long.parseLong(next());
        }
 
        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }
 
}