



from __future__ import annotations

class 				snake_case__:

					"""simple docstring"""






					def __init__(							self :     Any				,       SCREAMING_SNAKE_CASE :     int					):
									lowercase__					:   int													=					order

									# a_{0} ... a_{k}
									lowercase__					:   Optional[int]													=					[1.0] + [0.0] * order
									# b_{0} ... b_{k}
									lowercase__					:   Union[str, Any]													=					[1.0] + [0.0] * order

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







					def 			snake_case					(							self :     str				,       SCREAMING_SNAKE_CASE :     list[float]				,       SCREAMING_SNAKE_CASE :     list[float]					):
									if len(SCREAMING_SNAKE_CASE					) < self.order:
													lowercase__					:   Optional[int]													=					[1.0, *a_coeffs]

									if len(SCREAMING_SNAKE_CASE					) != self.order + 1:
													lowercase__					:   Dict													=					(
													    f"""Expected a_coeffs to have {self.order + 1} elements """
													    f"""for {self.order}-order filter, got {len(SCREAMING_SNAKE_CASE					)}"""
													)
													raise ValueError(SCREAMING_SNAKE_CASE					)

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

									lowercase__					:   int													=					a_coeffs
									lowercase__					:   Optional[Any]													=					b_coeffs







					def 			snake_case					(							self :     List[str]				,       SCREAMING_SNAKE_CASE :     float					):
									lowercase__					:   int													=					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]
													)

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

									lowercase__					:   int													=					self.input_history[:-1]
									lowercase__					:   Union[str, Any]													=					self.output_history[:-1]

									lowercase__					:   List[Any]													=					sample
									lowercase__					:   Optional[Any]													=					result

									return result









def  __lowerCamelCase (       lowerCamelCase__ = 1_000						):

				"""simple docstring"""


				lowercase__							,							lowercase__					:   int													=					1, 1
				lowercase__					:   List[Any]													=					[]
				for i in range(1					,			n + 1						):
								lowercase__					:   Dict													=					prev_numerator + 2 * prev_denominator
								lowercase__					:   Tuple													=					prev_numerator + prev_denominator
								if len(str(lowerCamelCase__						)						) > len(str(lowerCamelCase__						)						):
												result.append(lowerCamelCase__						)
								lowercase__					:   int													=					numerator
								lowercase__					:   int													=					denominator

				return len(lowerCamelCase__						)


if __name__ == "__main__":
				print(f'''{solution() = }''')




