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.util.Scanner;
public class Bachgold { 
public static void main (String [] args) { 
Scanner scanner = new Scanner (System.in);
int n=scanner.nextInt();
if (n%2==0) {
	System.out.println(n/2);
	for (int i=0;i<n/2;i++) {
	System.out.print(2);
	if (i==n/2-1) break;
	System.out.print(" ");
	}
}
else {
	System.out.println(n/2);
	for (int i=0;i<n/2-1;i++) {
		System.out.print(2 + " ");
		}
	System.out.print(3);
}
scanner.close(); }}