'''simple docstring'''







from __future__ import annotations




class _SCREAMING_SNAKE_CASE:




						def __init__(    self :       List[Any]							,							UpperCamelCase_ :       int      )     ->				None:
													SCREAMING_SNAKE_CASE__     :Tuple						    = order

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

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




						def      __lowerCamelCase       (    self :       Any							,							UpperCamelCase_ :       list[float]							,							UpperCamelCase_ :       list[float]      )     ->				None:
													if len(UpperCamelCase_      ) < self.order:
																				SCREAMING_SNAKE_CASE__     :int						    = [1.0, *a_coeffs]

													if len(UpperCamelCase_      ) != self.order + 1:
																				SCREAMING_SNAKE_CASE__     :List[Any]						    = (
																				    f'''Expected a_coeffs to have {self.order + 1} elements '''
																				    f'''for {self.order}-order filter, got {len(UpperCamelCase_      )}'''
																				)
																				raise ValueError(UpperCamelCase_      )

													if len(UpperCamelCase_      ) != self.order + 1:
																				SCREAMING_SNAKE_CASE__     :Dict						    = (
																				    f'''Expected b_coeffs to have {self.order + 1} elements '''
																				    f'''for {self.order}-order filter, got {len(UpperCamelCase_      )}'''
																				)
																				raise ValueError(UpperCamelCase_      )

													SCREAMING_SNAKE_CASE__     :int						    = a_coeffs
													SCREAMING_SNAKE_CASE__     :Dict						    = b_coeffs




						def      __lowerCamelCase       (    self :       Dict							,							UpperCamelCase_ :       float      )     ->				float:
													SCREAMING_SNAKE_CASE__     :Union[str, 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]
																				)

													SCREAMING_SNAKE_CASE__     :Union[str, Any]						    = (result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

													SCREAMING_SNAKE_CASE__     :str						    = self.input_history[:-1]
													SCREAMING_SNAKE_CASE__     :str						    = self.output_history[:-1]

													SCREAMING_SNAKE_CASE__     :List[Any]						    = sample
													SCREAMING_SNAKE_CASE__     :Optional[int]						    = result

													return result







'''simple docstring'''







def    lowerCamelCase       (			UpperCAmelCase__				:  str				,						UpperCAmelCase__				:  int		)			->	str:


							'''simple docstring'''






							SCREAMING_SNAKE_CASE__     :list[list[str]]						    = [[] for _ in range(UpperCAmelCase__		)]
							SCREAMING_SNAKE_CASE__     :Any						    = key - 1

							if key <= 0:
														raise ValueError('Height of grid can\'t be 0 or negative'		)
							if key == 1 or len(UpperCAmelCase__		) <= key:
														return input_string

							for position, character in enumerate(UpperCAmelCase__		):
														SCREAMING_SNAKE_CASE__     :Dict						    = position % (lowest * 2)  # puts it in bounds
														SCREAMING_SNAKE_CASE__     :Tuple						    = min(UpperCAmelCase__				,						lowest * 2 - num		)  # creates zigzag pattern
														temp_grid[num].append(UpperCAmelCase__		)
							SCREAMING_SNAKE_CASE__     :int						    = [''.join(UpperCAmelCase__		) for row in temp_grid]
							SCREAMING_SNAKE_CASE__     :str						    = ''.join(UpperCAmelCase__		)

							return output_string


def    lowerCamelCase       (			UpperCAmelCase__				:  str				,						UpperCAmelCase__				:  int		)			->	str:


							'''simple docstring'''






							SCREAMING_SNAKE_CASE__     :List[Any]						    = []
							SCREAMING_SNAKE_CASE__     :str						    = key - 1

							if key <= 0:
														raise ValueError('Height of grid can\'t be 0 or negative'		)
							if key == 1:
														return input_string

							SCREAMING_SNAKE_CASE__     :list[list[str]]						    = [[] for _ in range(UpperCAmelCase__		)]  # generates template
							for position in range(len(UpperCAmelCase__		)		):
														SCREAMING_SNAKE_CASE__     :Optional[int]						    = position % (lowest * 2)  # puts it in bounds
														SCREAMING_SNAKE_CASE__     :Dict						    = min(UpperCAmelCase__				,						lowest * 2 - num		)  # creates zigzag pattern
														temp_grid[num].append('*'		)

							SCREAMING_SNAKE_CASE__     :Any						    = 0
							for row in temp_grid:  # fills in the characters
														SCREAMING_SNAKE_CASE__     :int						    = input_string[counter : counter + len(UpperCAmelCase__		)]
														grid.append(list(UpperCAmelCase__		)		)
														counter += len(UpperCAmelCase__		)

							SCREAMING_SNAKE_CASE__     :Tuple						    = ''  # reads as zigzag
							for position in range(len(UpperCAmelCase__		)		):
														SCREAMING_SNAKE_CASE__     :Union[str, Any]						    = position % (lowest * 2)  # puts it in bounds
														SCREAMING_SNAKE_CASE__     :Any						    = min(UpperCAmelCase__				,						lowest * 2 - num		)  # creates zigzag pattern
														output_string += grid[num][0]
														grid[num].pop(0		)
							return output_string


def    lowerCamelCase       (			UpperCAmelCase__				:  str		)			->	dict[int, str]:


							'''simple docstring'''






							SCREAMING_SNAKE_CASE__     :int						    = {}
							for key_guess in range(1				,						len(UpperCAmelCase__		)		):  # tries every key
														SCREAMING_SNAKE_CASE__     :List[str]						    = decrypt(UpperCAmelCase__				,						UpperCAmelCase__		)
							return results


if __name__ == "__main__":
		import doctest

		doctest.testmod()






