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:
//package codeforces.r388;

import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

/**
 * Created by shaolin on 4/11/16.
 */
public class BachgoldProblem {
    static Scanner scanner;

    public static void main(String[] args) {
        scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        boolean odd = false;
        int count = 0;
        if(n%2!=0) {
            n -= 3;
            count++;
            odd = true;
        }
        count += n/2;
        int i = 0;
        System.out.println(count);
        if(odd) {
            i++;
            System.out.print(3+" ");
        }
        for (;  i<count ; i++) {
            System.out.print(2+" ");
        }
        System.out.println();
    }
}