






from __future__ import annotations





def 						A_					(						lowercase_			)				->bool:







 """simple docstring"""

 SCREAMING_SNAKE_CASE				    =		42
 SCREAMING_SNAKE_CASE				    =		list(lowercase_			)
 SCREAMING_SNAKE_CASE    ,   SCREAMING_SNAKE_CASE				    =		_vector[:-1], int(_vector[-1]			)
 SCREAMING_SNAKE_CASE				    =		[int(lowercase_			) for digit in __vector]

 vector.reverse()
 for i, digit in enumerate(lowercase_			):
  if i & 1 == 0:
   SCREAMING_SNAKE_CASE				    =		digit * 2
   if doubled > 9:
    doubled -= 9
   check_digit += doubled
  else:
   check_digit += digit

 return check_digit % 1_0 == 0


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      assert is_luhn("79927398713")
      assert not is_luhn("79927398714")









class 				lowerCAmelCase__	:







					def __init__(							self   :  Union[str, Any]):
											A__						:				Optional[int]         =			[0]
											A__						:				Any         =			0







					def 			_lowercase      (							self   :  Optional[int]      ,		_A   :  int):
											A__						:				Optional[Any]         =			self.__heap[i]
											while i // 2 > 0:
																	if self.__heap[i] > self.__heap[i // 2]:
																							A__						:				Union[str, Any]         =			self.__heap[i // 2]
																							A__						:				List[str]         =			temporary
																	i //= 2







					def 			_lowercase      (							self   :  Union[str, Any]      ,		_A   :  int):
											self.__heap.append(_A)
											self.__size += 1
											self.__swap_up(self.__size)







					def 			_lowercase      (							self   :  Any      ,		_A   :  int):
											while self.__size >= 2 * i:
																	if 2 * i + 1 > self.__size:
																							A__						:				str         =			2 * i
																	else:
																							if self.__heap[2 * i] > self.__heap[2 * i + 1]:
																													A__						:				Tuple         =			2 * i
																							else:
																													A__						:				Tuple         =			2 * i + 1
																	A__						:				Any         =			self.__heap[i]
																	if self.__heap[i] < self.__heap[bigger_child]:
																							A__						:				List[str]         =			self.__heap[bigger_child]
																							A__						:				Tuple         =			temporary
																	A__						:				Tuple         =			bigger_child







					def 			_lowercase      (							self   :  int):
											A__						:				str         =			self.__heap[1]
											A__						:				Tuple         =			self.__heap[self.__size]
											self.__size -= 1
											self.__heap.pop()
											self.__swap_down(1)
											return max_value







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







					def __len__(							self   :  Union[str, Any]):
											return self.__size


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		# create an instance of BinaryHeap
		snake_case     :    List[Any]						=    BinaryHeap()
		binary_heap.insert(6)
		binary_heap.insert(1_0)
		binary_heap.insert(1_5)
		binary_heap.insert(1_2)
		# 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))