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 PYTHON3):

Solution:
import math
import itertools

def is_prime(n):
	if n < 2:
		return False
	elif n == 2:
		return True
	elif n % 2 == 0:
		return False
	for div in range(2, math.ceil(math.sqrt(n))):
		if n % div == 0:
			return False
	return True

def generate_infinite_primes():
	for num in itertools.count():
		if is_prime(num):
			yield num

def maximum_possible(n):
	arr = []
	primes = generate_infinite_primes()
	prime = next(primes)
	while n:
		if n - prime > 1 or n - prime == 0:
			arr.append(prime)
			n -= prime
		else:
			prime = next(primes)
	return arr

if __name__ == '__main__':
	res = maximum_possible(int(input()))
	print(len(res))
	print(*res)