


'''simple docstring'''
class 					_A						:



   '''simple docstring'''






   def __init__(	self	:					List[Any]						)->	Tuple:
          snake_case__					:	Optional[Any]          =					[0]
          snake_case__					:	Dict          =					0




   def   __lowerCAmelCase						(	self	:					List[Any]					, lowerCamelCase	:					int						)->	int:
          snake_case__					:	Union[str, Any]          =					self.__heap[i]
          while i // 2 > 0:
                 if self.__heap[i] > self.__heap[i // 2]:
                        snake_case__					:	int          =					self.__heap[i // 2]
                        snake_case__					:	Optional[int]          =					temporary
                 i //= 2




   def   __lowerCAmelCase						(	self	:					Optional[int]					, lowerCamelCase	:					int						)->	int:
          self.__heap.append(lowerCamelCase						)
          self.__size += 1
          self.__swap_up(self.__size						)




   def   __lowerCAmelCase						(	self	:					Optional[int]					, lowerCamelCase	:					int						)->	Union[str, Any]:
          while self.__size >= 2 * i:
                 if 2 * i + 1 > self.__size:
                        snake_case__					:	str          =					2 * i
                 else:
                        if self.__heap[2 * i] > self.__heap[2 * i + 1]:
                               snake_case__					:	Optional[int]          =					2 * i
                        else:
                               snake_case__					:	Optional[Any]          =					2 * i + 1
                 snake_case__					:	Optional[int]          =					self.__heap[i]
                 if self.__heap[i] < self.__heap[bigger_child]:
                        snake_case__					:	Any          =					self.__heap[bigger_child]
                        snake_case__					:	int          =					temporary
                 snake_case__					:	str          =					bigger_child




   def   __lowerCAmelCase						(	self	:					Union[str, Any]						)->	Union[str, Any]:
          snake_case__					:	List[Any]          =					self.__heap[1]
          snake_case__					:	Dict          =					self.__heap[self.__size]
          self.__size -= 1
          self.__heap.pop()
          self.__swap_down(1						)
          return max_value




   @property
   def   __lowerCAmelCase						(	self	:					List[str]						)->	int:
          return self.__heap[1:]




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


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     # create an instance of BinaryHeap
     lowerCAmelCase__  =     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))











from functools import lru_cache







@lru_cache
def      A__				(       SCREAMING_SNAKE_CASE__)  ->       int:
  if not isinstance(SCREAMING_SNAKE_CASE__   ,   SCREAMING_SNAKE_CASE__):
    raise TypeError("""k must be an integer.""")
  if k < 0:
    raise ValueError("""k integer must be greater or equal to zero.""")
  if k == 0:
    return 0
  elif k == 1:
    return 1
  else:
    return fibonacci(k - 1) + fibonacci(k - 2)







def      A__				(       SCREAMING_SNAKE_CASE__   ,   SCREAMING_SNAKE_CASE__)  ->       int:
  __snake_case:		str					    =		len(SCREAMING_SNAKE_CASE__)
  # Find m such that F_m >= n where F_i is the i_th fibonacci number.
  __snake_case:		Optional[int]					    =		0
  while True:
    if fibonacci(SCREAMING_SNAKE_CASE__) >= len_list:
      __snake_case:		str					    =		i
      break
    i += 1
  __snake_case:		Tuple					    =		0
  while fibb_k > 0:
    __snake_case:		str					    =		min(
        offset + fibonacci(fibb_k - 1)   ,   len_list - 1)  # Prevent out of range
    __snake_case:		List[Any]					    =		arr[index_k]
    if item_k_1 == val:
      return index_k
    elif val < item_k_1:
      fibb_k -= 1
    elif val > item_k_1:
      offset += fibonacci(fibb_k - 1)
      fibb_k -= 2
  else:
    return -1


if __name__ == "__main__":
      import doctest

      doctest.testmod()






