



"""simple docstring"""







class   UpperCamelCase	:




	"""simple docstring"""






	def __init__(     self   ):
			_lowercase				: Optional[Any]     =   [0]
			_lowercase				: List[str]     =   0






	def    lowerCamelCase__					(     self				,UpperCAmelCase_   ):
			_lowercase				: Optional[Any]     =   self.__heap[i]
			while i // 2 > 0:
					if self.__heap[i] > self.__heap[i // 2]:
							_lowercase				: Dict     =   self.__heap[i // 2]
							_lowercase				: Dict     =   temporary
					i //= 2






	def    lowerCamelCase__					(     self				,UpperCAmelCase_   ):
			self.__heap.append(UpperCAmelCase_   )
			self.__size += 1
			self.__swap_up(self.__size   )






	def    lowerCamelCase__					(     self				,UpperCAmelCase_   ):
			while self.__size >= 2 * i:
					if 2 * i + 1 > self.__size:
							_lowercase				: Any     =   2 * i
					else:
							if self.__heap[2 * i] > self.__heap[2 * i + 1]:
									_lowercase				: Optional[Any]     =   2 * i
							else:
									_lowercase				: Optional[Any]     =   2 * i + 1
					_lowercase				: Optional[Any]     =   self.__heap[i]
					if self.__heap[i] < self.__heap[bigger_child]:
							_lowercase				: Any     =   self.__heap[bigger_child]
							_lowercase				: Dict     =   temporary
					_lowercase				: str     =   bigger_child






	def    lowerCamelCase__					(     self   ):
			_lowercase				: Optional[Any]     =   self.__heap[1]
			_lowercase				: str     =   self.__heap[self.__size]
			self.__size -= 1
			self.__heap.pop()
			self.__swap_down(1   )
			return max_value






	@property
	def    lowerCamelCase__					(     self   ):
			return self.__heap[1:]






	def __len__(     self   ):
			return self.__size


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		# create an instance of BinaryHeap
		UpperCAmelCase:  Optional[Any]			     =				BinaryHeap()
		binary_heap.insert(6)
		binary_heap.insert(10)
		binary_heap.insert(15)
		binary_heap.insert(12)
		# pop root(max-values because it is max heap)
		print(binary_heap.pop())  # 15
		print(binary_heap.pop())  # 12
		# get the list and size after operations
		print(binary_heap.get_list)
		print(len(binary_heap))








"""simple docstring"""







import math
from collections.abc import Generator


def  __SCREAMING_SNAKE_CASE (  __UpperCAmelCase      ):
		_lowercase				: Generator     =   (i for i in range(1   ,				(max_n + 1)      ))
		for i in (n for n in numbers if n > 1):
				for j in range(2   ,				__UpperCAmelCase      ):
						if (i % j) == 0:
								break
				else:
						yield i


def  __SCREAMING_SNAKE_CASE (  __UpperCAmelCase      ):
		_lowercase				: Generator     =   (i for i in range(1   ,				(max_n + 1)      ))
		for i in (n for n in numbers if n > 1):
				# only need to check for factors up to sqrt(i)
				_lowercase				: Union[str, Any]     =   int(math.sqrt(__UpperCAmelCase      )      ) + 1
				for j in range(2   ,				__UpperCAmelCase      ):
						if (i % j) == 0:
								break
				else:
						yield i


def  __SCREAMING_SNAKE_CASE (  __UpperCAmelCase      ):
		_lowercase				: Generator     =   (i for i in range(1   ,				(max_n + 1)   ,				2      ))
		# It's useless to test even numbers as they will not be prime
		if max_n > 2:
				yield 2  # Because 2 will not be tested, it's necessary to yield it now
		for i in (n for n in numbers if n > 1):
				_lowercase				: str     =   int(math.sqrt(__UpperCAmelCase      )      ) + 1
				for j in range(3   ,				__UpperCAmelCase   ,				2      ):
						# As we removed the even numbers, we don't need them now
						if (i % j) == 0:
								break
				else:
						yield i


def  __SCREAMING_SNAKE_CASE (  ):
		from timeit import timeit

		_lowercase				: Tuple     =   """from __main__ import slow_primes, primes, fast_primes"""
		print(timeit("""slow_primes(1_000_000_000_000)"""   ,				setup=__UpperCAmelCase   ,				number=1000000      )      )
		print(timeit("""primes(1_000_000_000_000)"""   ,				setup=__UpperCAmelCase   ,				number=1000000      )      )
		print(timeit("""fast_primes(1_000_000_000_000)"""   ,				setup=__UpperCAmelCase   ,				number=1000000      )      )


if __name__ == "__main__":
		UpperCAmelCase:  int			     =				int(input("""Calculate primes up to:\n>> """).strip())
		for ret in primes(number):
				print(ret)
		benchmark()



