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.*;
public class Car {
public static void main (String [] args) {
	Scanner sc = new Scanner(System.in);
	int n = sc.nextInt();
	int k, a;
	System.out.println(n / 2);
	if (n % 2 == 0) {
		for (int i = 1; i <= n / 2; i++)
			System.out.print(2 + " ");
	}
	else {
		for (int j = 1; j <= (n - 3) / 2; j++)
			System.out.print(2 + " ");
		System.out.print(3 + " ");
	}
	}	
}