


from __future__ import annotations



class A__     :



  """simple docstring"""



  def __init__( self			:  int				,				lowerCamelCase__			:  int       ):
        a__	:  List[str]     =   order

        # a_{0} ... a_{k}
        a__	:  Optional[int]     =   [1.0] + [0.0] * order
        # b_{0} ... b_{k}
        a__	:  Dict     =   [1.0] + [0.0] * order

        # x[n-1] ... x[n-k]
        a__	:  Union[str, Any]     =   [0.0] * self.order
        # y[n-1] ... y[n-k]
        a__	:  Optional[Any]     =   [0.0] * self.order

  def    _UpperCamelCase( self			:  List[str]				,				lowerCamelCase__			:  list[float]				,				lowerCamelCase__			:  list[float]       ):
        if len(lowerCamelCase__       ) < self.order:
              a__	:  Any     =   [1.0, *a_coeffs]

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

        a__	:  Union[str, Any]     =   a_coeffs
        a__	:  Union[str, Any]     =   b_coeffs

  def    _UpperCamelCase( self			:  Tuple				,				lowerCamelCase__			:  float       ):
        a__	:  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]
              )

        a__	:  List[str]     =   (result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

        a__	:  str     =   self.input_history[:-1]
        a__	:  Any     =   self.output_history[:-1]

        a__	:  List[Any]     =   sample
        a__	:  Tuple     =   result

        return result







'''simple docstring'''






import functools






def 		UpperCamelCase__      (		__SCREAMING_SNAKE_CASE				,      __SCREAMING_SNAKE_CASE		)    ->   int:
      snake_case__       :   Any	      =    len(__SCREAMING_SNAKE_CASE		)
      snake_case__       :   List[str]	      =    len(__SCREAMING_SNAKE_CASE		)

      @functools.cache
      def min_distance(__SCREAMING_SNAKE_CASE				,      __SCREAMING_SNAKE_CASE		) -> int:
            # if first word index is overflow - delete all from the second word
            if indexa >= len_worda:
                  return len_worda - indexa
            # if second word index is overflow - delete all from the first word
            if indexa >= len_worda:
                  return len_worda - indexa
            snake_case__       :   Union[str, Any]	      =    int(worda[indexa] != worda[indexa]		)  # current letters not identical
            return min(
                1 + min_distance(indexa + 1				,      __SCREAMING_SNAKE_CASE		)				,      1 + min_distance(__SCREAMING_SNAKE_CASE				,      indexa + 1		)				,      diff + min_distance(indexa + 1				,      indexa + 1		)				,      )

      return min_distance(0				,      0		)


if __name__ == "__main__":
      import doctest

      doctest.testmod()
