






from collections.abc import Callable




class       snake_case__ :

       '''simple docstring'''



       def __init__(				self      ,    a__ = None     )			->   None:






            '''simple docstring'''





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



       def        __lowercase    (				self      ,    a__     )			->   int | None:






            '''simple docstring'''





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



       def        __lowercase    (				self      ,    a__     )			->   int | None:






            '''simple docstring'''





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



       def        __lowercase    (				self      ,    a__     )			->   int | None:






            '''simple docstring'''





            __snake_case      :Optional[int] 							=    int(2 * i + 2     )
            return right if 0 < right < self.size else None



       def        __lowercase    (				self      ,    a__      ,    a__     )			->   None:






            '''simple docstring'''





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



       def        __lowercase    (				self      ,    a__      ,    a__     )			->   bool:






            '''simple docstring'''





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



       def        __lowercase    (				self      ,    a__     )			->   int:






            '''simple docstring'''





            __snake_case      :int 							=    self._left(a__     )
            __snake_case      :Optional[int] 							=    self._right(a__     )
            __snake_case      :List[Any] 							=    i

            if left is not None and not self._cmp(a__      ,    a__     ):
                 __snake_case      :int 							=    left
            if right is not None and not self._cmp(a__      ,    a__     ):
                 __snake_case      :Tuple 							=    right

            return valid_parent



       def        __lowercase    (				self      ,    a__     )			->   None:






            '''simple docstring'''





            __snake_case      :int 							=    self._parent(a__     )
            while parent is not None and not self._cmp(a__      ,    a__     ):
                 self._swap(a__      ,    a__     )
                 __snake_case							,			__snake_case      :str 							=    parent, self._parent(a__     )



       def        __lowercase    (				self      ,    a__     )			->   None:






            '''simple docstring'''





            __snake_case      :List[Any] 							=    self._get_valid_parent(a__     )
            while valid_parent != index:
                 self._swap(a__      ,    a__     )
                 __snake_case							,			__snake_case      :Optional[int] 							=    valid_parent, self._get_valid_parent(a__     )



       def        __lowercase    (				self      ,    a__      ,    a__     )			->   None:






            '''simple docstring'''





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



       def        __lowercase    (				self      ,    a__     )			->   None:






            '''simple docstring'''





            if item not in self.pos_map:
                 return
            __snake_case      :Dict 							=    self.pos_map[item]
            del self.pos_map[item]
            __snake_case      :Dict 							=    self.arr[self.size - 1]
            __snake_case      :List[str] 							=    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(a__     )
                 self._heapify_down(a__     )



       def        __lowercase    (				self      ,    a__      ,    a__     )			->   None:






            '''simple docstring'''





            __snake_case      :Optional[int] 							=    len(self.arr     )
            if arr_len == self.size:
                 self.arr.append([item, self.key(a__     )]     )
            else:
                 __snake_case      :Optional[Any] 							=    [item, self.key(a__     )]
            __snake_case      :str 							=    self.size
            self.size += 1
            self._heapify_up(self.size - 1     )



       def        __lowercase    (				self     )			->   tuple | None:






            '''simple docstring'''





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



       def        __lowercase    (				self     )			->   tuple | None:






            '''simple docstring'''





            __snake_case      :Optional[Any] 							=    self.get_top()
            if top_item_tuple:
                 self.delete_item(top_item_tuple[0]     )
            return top_item_tuple






def 	UpperCamelCase	(							):




     '''simple docstring'''








if __name__ == "__main__":
     import doctest

     doctest.testmod()










from __future__ import annotations




class       snake_case__ :

       '''simple docstring'''



       def __init__(				self      ,    a__     )			->   None:






            '''simple docstring'''





            __snake_case      :str 							=    order

            # a_{0} ... a_{k}
            __snake_case      :int 							=    [1.0] + [0.0] * order
            # b_{0} ... b_{k}
            __snake_case      :Any 							=    [1.0] + [0.0] * order

            # x[n-1] ... x[n-k]
            __snake_case      :List[Any] 							=    [0.0] * self.order
            # y[n-1] ... y[n-k]
            __snake_case      :int 							=    [0.0] * self.order



       def        __lowercase    (				self      ,    a__      ,    a__     )			->   None:






            '''simple docstring'''





            if len(a__     ) < self.order:
                 __snake_case      :Optional[int] 							=    [1.0, *a_coeffs]

            if len(a__     ) != self.order + 1:
                 __snake_case      :Dict 							=    (
                     F'''Expected a_coeffs to have {self.order + 1} elements '''
                     F'''for {self.order}-order filter, got {len(a__     )}'''
                 )
                 raise ValueError(a__     )

            if len(a__     ) != self.order + 1:
                 __snake_case      :Optional[Any] 							=    (
                     F'''Expected b_coeffs to have {self.order + 1} elements '''
                     F'''for {self.order}-order filter, got {len(a__     )}'''
                 )
                 raise ValueError(a__     )

            __snake_case      :str 							=    a_coeffs
            __snake_case      :str 							=    b_coeffs



       def        __lowercase    (				self      ,    a__     )			->   float:






            '''simple docstring'''





            __snake_case      :List[Any] 							=    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]
                 )

            __snake_case      :Dict 							=    (result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

            __snake_case      :Optional[int] 							=    self.input_history[:-1]
            __snake_case      :Optional[Any] 							=    self.output_history[:-1]

            __snake_case      :Union[str, Any] 							=    sample
            __snake_case      :Optional[Any] 							=    result

            return result


