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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collection;
import java.util.Collections;

public class p23 {
public static void main(String[] args) throws IOException {
	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	PrintWriter out = new PrintWriter(System.out);
	int a = Integer.parseInt(br.readLine());
	int c = 0;
	ArrayList<Integer> arr = new ArrayList<>();
	while(a>=2) {
		if(a==3) {
			arr.add(3);
			a -=3;
			c++;
		}else {
			arr.add(2);
			a -=2;
			c++;
		}
	}
	out.println(c);
	for(int x : arr)
		out.print(x+" ");
	out.flush();
}
}