






"""simple docstring"""


class __a :



  def __init__(self	:		Dict )		->				Dict:
   __A						:							Dict      =						[0]
   __A						:							Any      =						0



  def     A_					(self	:		List[Any]					,      lowercase_	:		int )		->				None:
   __A						:							Any      =						self.__heap[i]
   while i // 2 > 0:
    if self.__heap[i] > self.__heap[i // 2]:
     __A						:							List[str]      =						self.__heap[i // 2]
     __A						:							List[Any]      =						temporary
    i //= 2



  def     A_					(self	:		str					,      lowercase_	:		int )		->				None:
   self.__heap.append(lowercase_ )
   self.__size += 1
   self.__swap_up(self.__size )



  def     A_					(self	:		List[str]					,      lowercase_	:		int )		->				None:
   while self.__size >= 2 * i:
    if 2 * i + 1 > self.__size:
     __A						:							Optional[Any]      =						2 * i
    else:
     if self.__heap[2 * i] > self.__heap[2 * i + 1]:
      __A						:							Dict      =						2 * i
     else:
      __A						:							int      =						2 * i + 1
    __A						:							Tuple      =						self.__heap[i]
    if self.__heap[i] < self.__heap[bigger_child]:
     __A						:							List[str]      =						self.__heap[bigger_child]
     __A						:							List[str]      =						temporary
    __A						:							str      =						bigger_child



  def     A_					(self	:		Dict )		->				int:
   __A						:							str      =						self.__heap[1]
   __A						:							List[str]      =						self.__heap[self.__size]
   self.__size -= 1
   self.__heap.pop()
   self.__swap_down(1 )
   return max_value



  @property
  def     A_					(self	:		str )		->				Dict:
   return self.__heap[1:]



  def __len__(self	:		List[Any] )		->				Tuple:
   return self.__size


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   # create an instance of BinaryHeap
   _UpperCamelCase :    Dict      =			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"""


def 					a			(  UpperCamelCase_				:					int  ,						UpperCamelCase_				:					int  ,						UpperCamelCase_				:					int  ,						UpperCamelCase_				:					int		)	->		int:
 return len_board * len_board_column * row + column




def 					a			(  UpperCamelCase_				:					list[list[str]]  ,						UpperCamelCase_				:					str  ,						UpperCamelCase_				:					int  ,						UpperCamelCase_				:					int  ,						UpperCamelCase_				:					int  ,						UpperCamelCase_				:					set[int]  ,						)	->		bool:

 if board[row][column] != word[word_index]:
  return False

 if word_index == len(UpperCamelCase_		) - 1:
  return True

 __A						:							List[str]      =						[(0, 1), (0, -1), (-1, 0), (1, 0)]
 __A						:							Any      =						len(UpperCamelCase_		)
 __A						:							Union[str, Any]      =						len(board[0]		)
 for direction in traverts_directions:
  __A						:							Any      =						row + direction[0]
  __A						:							List[Any]      =						column + direction[1]
  if not (0 <= next_i < len_board and 0 <= next_j < len_board_column):
   continue

  __A						:							Any      =						get_point_key(UpperCamelCase_  ,						UpperCamelCase_  ,						UpperCamelCase_  ,						UpperCamelCase_		)
  if key in visited_points_set:
   continue

  visited_points_set.add(UpperCamelCase_		)
  if exits_word(UpperCamelCase_  ,						UpperCamelCase_  ,						UpperCamelCase_  ,						UpperCamelCase_  ,						word_index + 1  ,						UpperCamelCase_		):
   return True

  visited_points_set.remove(UpperCamelCase_		)

 return False




def 					a			(  UpperCamelCase_				:					list[list[str]]  ,						UpperCamelCase_				:					str		)	->		bool:
 __A						:							Optional[Any]      =						(
     'The board should be a non empty matrix of single chars strings.'
 )

 __A						:							Dict      =						len(UpperCamelCase_		)
 if not isinstance(UpperCamelCase_  ,						UpperCamelCase_		) or len(UpperCamelCase_		) == 0:
  raise ValueError(UpperCamelCase_		)

 for row in board:
  if not isinstance(UpperCamelCase_  ,						UpperCamelCase_		) or len(UpperCamelCase_		) == 0:
   raise ValueError(UpperCamelCase_		)

  for item in row:
   if not isinstance(UpperCamelCase_  ,						UpperCamelCase_		) or len(UpperCamelCase_		) != 1:
    raise ValueError(UpperCamelCase_		)

    # Validate word
 if not isinstance(UpperCamelCase_  ,						UpperCamelCase_		) or len(UpperCamelCase_		) == 0:
  raise ValueError(
      'The word parameter should be a string of length greater than 0.'		)

 __A						:							List[Any]      =						len(board[0]		)
 for i in range(UpperCamelCase_		):
  for j in range(UpperCamelCase_		):
   if exits_word(
       UpperCamelCase_  ,						UpperCamelCase_  ,						UpperCamelCase_  ,						UpperCamelCase_  ,						0  ,						{get_point_key(UpperCamelCase_  ,						UpperCamelCase_  ,						UpperCamelCase_  ,						UpperCamelCase_		)}		):
    return True

 return False


if __name__ == "__main__":
   import doctest

   doctest.testmod()





