




'''simple docstring'''


from collections.abc import Callable

class     A					:







					def __init__(						self :						List[Any]							,    lowerCAmelCase_ :						Callable | None = None      )    ->							None:


												"""simple docstring"""


												_a			  =       []
												# Stores indexes of each item for supporting updates and deletion.
												_a			  =       {}
												# Stores current size of heap.
												_a			  =       0
												# Stores function used to evaluate the score of an item on which basis ordering
												# will be done.
												_a			  =       key or (lambda lowerCAmelCase_      : x)







					def      __lowerCAmelCase    (						self :						Tuple							,    lowerCAmelCase_ :						int      )    ->							int | None:


												"""simple docstring"""


												return int((i - 1) / 2      ) if i > 0 else None







					def      __lowerCAmelCase    (						self :						Tuple							,    lowerCAmelCase_ :						int      )    ->							int | None:


												"""simple docstring"""


												_a			  =       int(2 * i + 1      )
												return left if 0 < left < self.size else None







					def      __lowerCAmelCase    (						self :						List[str]							,    lowerCAmelCase_ :						int      )    ->							int | None:


												"""simple docstring"""


												_a			  =       int(2 * i + 2      )
												return right if 0 < right < self.size else None







					def      __lowerCAmelCase    (						self :						List[str]							,    lowerCAmelCase_ :						int							,    lowerCAmelCase_ :						int      )    ->							None:


												"""simple docstring"""


												_a  ,							_a			  =       (
												    self.pos_map[self.arr[j][0]],
												    self.pos_map[self.arr[i][0]],
												)
												# Then swap the items in the list.
												_a  ,							_a			  =       self.arr[j], self.arr[i]







					def      __lowerCAmelCase    (						self :						str							,    lowerCAmelCase_ :						int							,    lowerCAmelCase_ :						int      )    ->							bool:


												"""simple docstring"""


												return self.arr[i][1] < self.arr[j][1]







					def      __lowerCAmelCase    (						self :						Optional[int]							,    lowerCAmelCase_ :						int      )    ->							int:


												"""simple docstring"""


												_a			  =       self._left(lowerCAmelCase_      )
												_a			  =       self._right(lowerCAmelCase_      )
												_a			  =       i

												if left is not None and not self._cmp(lowerCAmelCase_							,    lowerCAmelCase_      ):
																			_a			  =       left
												if right is not None and not self._cmp(lowerCAmelCase_							,    lowerCAmelCase_      ):
																			_a			  =       right

												return valid_parent







					def      __lowerCAmelCase    (						self :						str							,    lowerCAmelCase_ :						int      )    ->							None:


												"""simple docstring"""


												_a			  =       self._parent(lowerCAmelCase_      )
												while parent is not None and not self._cmp(lowerCAmelCase_							,    lowerCAmelCase_      ):
																			self._swap(lowerCAmelCase_							,    lowerCAmelCase_      )
																			_a  ,							_a			  =       parent, self._parent(lowerCAmelCase_      )







					def      __lowerCAmelCase    (						self :						Union[str, Any]							,    lowerCAmelCase_ :						int      )    ->							None:


												"""simple docstring"""


												_a			  =       self._get_valid_parent(lowerCAmelCase_      )
												while valid_parent != index:
																			self._swap(lowerCAmelCase_							,    lowerCAmelCase_      )
																			_a  ,							_a			  =       valid_parent, self._get_valid_parent(lowerCAmelCase_      )







					def      __lowerCAmelCase    (						self :						List[str]							,    lowerCAmelCase_ :						int							,    lowerCAmelCase_ :						int      )    ->							None:


												"""simple docstring"""


												if item not in self.pos_map:
																			return
												_a			  =       self.pos_map[item]
												_a			  =       [item, self.key(lowerCAmelCase_      )]
												# Make sure heap is right in both up and down direction.
												# Ideally only one of them will make any change.
												self._heapify_up(lowerCAmelCase_      )
												self._heapify_down(lowerCAmelCase_      )







					def      __lowerCAmelCase    (						self :						Any							,    lowerCAmelCase_ :						int      )    ->							None:


												"""simple docstring"""


												if item not in self.pos_map:
																			return
												_a			  =       self.pos_map[item]
												del self.pos_map[item]
												_a			  =       self.arr[self.size - 1]
												_a			  =       index
												self.size -= 1
												# Make sure heap is right in both up and down direction. Ideally only one
												# of them will make any change- so no performance loss in calling both.
												if self.size > index:
																			self._heapify_up(lowerCAmelCase_      )
																			self._heapify_down(lowerCAmelCase_      )







					def      __lowerCAmelCase    (						self :						Any							,    lowerCAmelCase_ :						int							,    lowerCAmelCase_ :						int      )    ->							None:


												"""simple docstring"""


												_a			  =       len(self.arr      )
												if arr_len == self.size:
																			self.arr.append([item, self.key(lowerCAmelCase_      )]      )
												else:
																			_a			  =       [item, self.key(lowerCAmelCase_      )]
												_a			  =       self.size
												self.size += 1
												self._heapify_up(self.size - 1      )







					def      __lowerCAmelCase    (						self :						int      )    ->							tuple | None:


												"""simple docstring"""


												return self.arr[0] if self.size else None







					def      __lowerCAmelCase    (						self :						Union[str, Any]      )    ->							tuple | None:


												"""simple docstring"""


												_a			  =       self.get_top()
												if top_item_tuple:
																			self.delete_item(top_item_tuple[0]      )
												return top_item_tuple



def 	snake_case_					():





							'''simple docstring'''






if __name__ == "__main__":
				import doctest

				doctest.testmod()







'''simple docstring'''


from ..utils import DummyObject, requires_backends

class     A					(	metaclass=_a					):
							lowercase_           =       ['torch', 'torchsde']







							def __init__(						self :						Optional[Any]							,    *lowerCAmelCase_ :						Any							,    **lowerCAmelCase_ :						Tuple      )    ->							Dict:


														"""simple docstring"""


														requires_backends(self							,    ['''torch''', '''torchsde''']      )







							@classmethod
							def      __lowerCAmelCase    (						cls :						Dict							,    *lowerCAmelCase_ :						Optional[int]							,    **lowerCAmelCase_ :						Optional[Any]      )    ->							int:


														"""simple docstring"""


														requires_backends(cls							,    ['''torch''', '''torchsde''']      )







							@classmethod
							def      __lowerCAmelCase    (						cls :						List[str]							,    *lowerCAmelCase_ :						str							,    **lowerCAmelCase_ :						Optional[Any]      )    ->							Any:


														"""simple docstring"""


														requires_backends(cls							,    ['''torch''', '''torchsde''']      )

