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 com.company;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class bachgold_problem {
    public static void main(String[] args) throws IOException {
        BufferedReader input = new BufferedReader(new InputStreamReader(System.in));

        int n = Integer.parseInt(input.readLine());

        int k = n/2;
        System.out.println(k + " ");


        if (n%2 == 0) {
            while (k-- > 0) {
                System.out.print("2 ");
            }
        }
        else {
            while (k-- > 1) {
                System.out.print("2 ");
            }
            System.out.print("3");
        }

        System.out.println("");

    }
}