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

public class A749A {
    public static void main(String[] args) throws IOException {

        A749A a = new A749A();
        a.solve();
    }

    public void solve() throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedOutputStream bos = new BufferedOutputStream(new BufferedOutputStream(System.out));

        String input = br.readLine();
        int n = Integer.parseInt(input);
        int n2 = n / 2;

        bos.write((n2+"\n").getBytes());

        for( int i=0; i<n2-1; i++)
            bos.write((2+" ").getBytes());

        if( n % 2 == 0)
            bos.write("2".getBytes());
        else
            bos.write("3".getBytes());

        bos.flush();
    }
}