




'''simple docstring'''






class 		a__    :





							'''simple docstring'''






							def __init__(		self ,   lowerCamelCase_ ,   lowerCamelCase_=None ,   lowerCamelCase_=None       )	->							List[Any]:
														lowerCAmelCase__	       =     data
														lowerCAmelCase__	       =     previous
														lowerCAmelCase__	       =     next_node







							def __str__(		self       )	->							str:
														return F"""{self.data}"""







							def   __SCREAMING_SNAKE_CASE							(		self       )	->							int:
														return self.data







							def   __SCREAMING_SNAKE_CASE							(		self       )	->							Any:
														return self.next







							def   __SCREAMING_SNAKE_CASE							(		self       )	->							Optional[Any]:
														return self.previous




class 		a__    :





							'''simple docstring'''






							def __init__(		self ,   lowerCamelCase_       )	->							str:
														lowerCAmelCase__	       =     head







							def __iter__(		self       )	->							Any:
														return self







							def   __SCREAMING_SNAKE_CASE							(		self       )	->							str:
														if not self.current:
																					raise StopIteration
														else:
																					lowerCAmelCase__	       =     self.current.get_data()
																					lowerCAmelCase__	       =     self.current.get_next()
																					return value




class 		a__    :





							'''simple docstring'''






							def __init__(		self       )	->							Dict:
														lowerCAmelCase__	       =     None  # First node in list
														lowerCAmelCase__	       =     None  # Last node in list







							def __str__(		self       )	->							List[Any]:
														lowerCAmelCase__	       =     self.head
														lowerCAmelCase__	       =     []
														while current is not None:
																					nodes.append(current.get_data()       )
																					lowerCAmelCase__	       =     current.get_next()
														return " ".join(str(_SCREAMING_SNAKE_CASE       ) for node in nodes       )







							def __contains__(		self ,   lowerCamelCase_       )	->							Optional[int]:
														lowerCAmelCase__	       =     self.head
														while current:
																					if current.get_data() == value:
																												return True
																					lowerCAmelCase__	       =     current.get_next()
														return False







							def __iter__(		self       )	->							int:
														return LinkedListIterator(self.head       )







							def   __SCREAMING_SNAKE_CASE							(		self       )	->							Any:
														if self.head:
																					return self.head.get_data()
														return None







							def   __SCREAMING_SNAKE_CASE							(		self       )	->							List[str]:
														if self.tail:
																					return self.tail.get_data()
														return None







							def   __SCREAMING_SNAKE_CASE							(		self ,   lowerCamelCase_       )	->							None:
														if self.head is None:
																					lowerCAmelCase__	       =     node
																					lowerCAmelCase__	       =     node
														else:
																					self.insert_before_node(self.head ,   _SCREAMING_SNAKE_CASE       )







							def   __SCREAMING_SNAKE_CASE							(		self ,   lowerCamelCase_       )	->							None:
														if self.head is None:
																					self.set_head(_SCREAMING_SNAKE_CASE       )
														else:
																					self.insert_after_node(self.tail ,   _SCREAMING_SNAKE_CASE       )







							def   __SCREAMING_SNAKE_CASE							(		self ,   lowerCamelCase_       )	->							None:
														lowerCAmelCase__	       =     Node(_SCREAMING_SNAKE_CASE       )
														if self.head is None:
																					self.set_head(_SCREAMING_SNAKE_CASE       )
														else:
																					self.set_tail(_SCREAMING_SNAKE_CASE       )







							def   __SCREAMING_SNAKE_CASE							(		self ,   lowerCamelCase_ ,   lowerCamelCase_       )	->							None:
														lowerCAmelCase__	       =     node
														lowerCAmelCase__	       =     node.previous

														if node.get_previous() is None:
																					lowerCAmelCase__	       =     node_to_insert
														else:
																					lowerCAmelCase__	       =     node_to_insert

														lowerCAmelCase__	       =     node_to_insert







							def   __SCREAMING_SNAKE_CASE							(		self ,   lowerCamelCase_ ,   lowerCamelCase_       )	->							None:
														lowerCAmelCase__	       =     node
														lowerCAmelCase__	       =     node.next

														if node.get_next() is None:
																					lowerCAmelCase__	       =     node_to_insert
														else:
																					lowerCAmelCase__	       =     node_to_insert

														lowerCAmelCase__	       =     node_to_insert







							def   __SCREAMING_SNAKE_CASE							(		self ,   lowerCamelCase_ ,   lowerCamelCase_       )	->							None:
														lowerCAmelCase__	       =     1
														lowerCAmelCase__	       =     Node(_SCREAMING_SNAKE_CASE       )
														lowerCAmelCase__	       =     self.head
														while node:
																					if current_position == position:
																												self.insert_before_node(_SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE       )
																												return
																					current_position += 1
																					lowerCAmelCase__	       =     node.next
														self.insert_after_node(self.tail ,   _SCREAMING_SNAKE_CASE       )







							def   __SCREAMING_SNAKE_CASE							(		self ,   lowerCamelCase_       )	->							Node:
														lowerCAmelCase__	       =     self.head
														while node:
																					if node.get_data() == item:
																												return node
																					lowerCAmelCase__	       =     node.get_next()
														raise Exception('''Node not found'''       )







							def   __SCREAMING_SNAKE_CASE							(		self ,   lowerCamelCase_       )	->							Optional[int]:
														if (node := self.get_node(_SCREAMING_SNAKE_CASE       )) is not None:
																					if node == self.head:
																												lowerCAmelCase__	       =     self.head.get_next()

																					if node == self.tail:
																												lowerCAmelCase__	       =     self.tail.get_previous()

																					self.remove_node_pointers(_SCREAMING_SNAKE_CASE       )







							@staticmethod
							def   __SCREAMING_SNAKE_CASE							(		lowerCamelCase_       )	->							None:
														if node.get_next():
																					lowerCAmelCase__	       =     node.previous

														if node.get_previous():
																					lowerCAmelCase__	       =     node.next

														lowerCAmelCase__	       =     None
														lowerCAmelCase__	       =     None







							def   __SCREAMING_SNAKE_CASE							(		self       )	->							Any:
														return self.head is None


def  _snake_case       (					)						->   None:
							pass


if __name__ == "__main__":
		import doctest

		doctest.testmod()



'''simple docstring'''






from __future__ import annotations




class 		a__    :





							'''simple docstring'''






							def __init__(		self ,   lowerCamelCase_       )	->							None:
														lowerCAmelCase__	       =     order

														# a_{0} ... a_{k}
														lowerCAmelCase__	       =     [1.0] + [0.0] * order
														# b_{0} ... b_{k}
														lowerCAmelCase__	       =     [1.0] + [0.0] * order

														# x[n-1] ... x[n-k]
														lowerCAmelCase__	       =     [0.0] * self.order
														# y[n-1] ... y[n-k]
														lowerCAmelCase__	       =     [0.0] * self.order







							def   __SCREAMING_SNAKE_CASE							(		self ,   lowerCamelCase_ ,   lowerCamelCase_       )	->							None:
														if len(lowerCamelCase_       ) < self.order:
																					lowerCAmelCase__	       =     [1.0, *a_coeffs]

														if len(lowerCamelCase_       ) != self.order + 1:
																					lowerCAmelCase__	       =     (
																					    F"""Expected a_coeffs to have {self.order + 1} elements """
																					    F"""for {self.order}-order filter, got {len(lowerCamelCase_       )}"""
																					)
																					raise ValueError(lowerCamelCase_       )

														if len(lowerCamelCase_       ) != self.order + 1:
																					lowerCAmelCase__	       =     (
																					    F"""Expected b_coeffs to have {self.order + 1} elements """
																					    F"""for {self.order}-order filter, got {len(lowerCamelCase_       )}"""
																					)
																					raise ValueError(lowerCamelCase_       )

														lowerCAmelCase__	       =     a_coeffs
														lowerCAmelCase__	       =     b_coeffs







							def   __SCREAMING_SNAKE_CASE							(		self ,   lowerCamelCase_       )	->							float:
														lowerCAmelCase__	       =     0.0

														# Start at index 1 and do index 0 at the end.
														for i in range(1 ,   self.order + 1       ):
																					result += (
																					    self.b_coeffs[i] * self.input_history[i - 1]
																					    - self.a_coeffs[i] * self.output_history[i - 1]
																					)

														lowerCAmelCase__	       =     (result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

														lowerCAmelCase__	       =     self.input_history[:-1]
														lowerCAmelCase__	       =     self.output_history[:-1]

														lowerCAmelCase__	       =     sample
														lowerCAmelCase__	       =     result

														return result