


from __future__ import annotations





class       A    :


							def __init__(self      ,				lowerCAmelCase					):
									__lowercase=			order

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

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


							def 			_A       (self      ,				lowerCAmelCase      ,				lowerCAmelCase					):
									if len(lowerCAmelCase					) < self.order:
											__lowercase=			[1.0, *a_coeffs]

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

									__lowercase=			a_coeffs
									__lowercase=			b_coeffs







							def 			_A       (self      ,				lowerCAmelCase					):
									__lowercase=			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=			(result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

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

									__lowercase=			sample
									__lowercase=			result

									return result










def        _lowerCamelCase(	lowercase__	)						->	int:

		'''simple docstring'''







		if collection == []:
				return []

		# get some information about the collection
		__lowercase=			len(lowercase__	)
		__lowercase=			max(lowercase__	)
		__lowercase=			min(lowercase__	)

		# create the counting array
		__lowercase=			coll_max + 1 - coll_min
		__lowercase=			[0] * counting_arr_length

		# count how much a number appears in the collection
		for number in collection:
				counting_arr[number - coll_min] += 1

		# sum each position with it's predecessors. now, counting_arr[i] tells
		# us how many elements <= i has in the collection
		for i in range(1   , lowercase__	):
				__lowercase=			counting_arr[i] + counting_arr[i - 1]

		# create the output collection
		__lowercase=			[0] * coll_len

		# place the elements in the output, respecting the original order (stable
		# sort) from end to begin, updating counting_arr
		for i in reversed(range(0   , lowercase__	)	):
				__lowercase=			collection[i]
				counting_arr[collection[i] - coll_min] -= 1

		return ordered







def        _lowerCamelCase(	lowercase__	)						->	List[str]:

		'''simple docstring'''







		return "".join([chr(lowercase__	) for i in counting_sort([ord(lowercase__	) for c in string]	)]	)


if __name__ == "__main__":
	# Test string sort
	assert counting_sort_string('''thisisthestring''') == "eghhiiinrsssttt"

	lowerCAmelCase           =		input('''Enter numbers separated by a comma:\n''').strip()
	lowerCAmelCase           =		[int(item) for item in user_input.split(''',''')]
	print(counting_sort(unsorted))






