


from __future__ import annotations






def        A       (      _lowerCamelCase						):





							'''simple docstring'''




							if len(_lowerCamelCase						) == 0:
														return []
							_lowerCAmelCase  :							List[Any]				     =					min(_lowerCamelCase						), max(_lowerCamelCase						)
							_lowerCAmelCase  :							List[str]				     =					int(max_value - min_value						) + 1
							_lowerCAmelCase  :							list[list]				     =					[[] for _ in range(_lowerCamelCase						)]

							for i in my_list:
														buckets[int(i - min_value						)].append(_lowerCamelCase						)

							return [v for bucket in buckets for v in sorted(_lowerCamelCase						)]


if __name__ == "__main__":
						from doctest import testmod

						testmod()
						assert bucket_sort([4, 5, 3, 2, 1]) == [1, 2, 3, 4, 5]
						assert bucket_sort([0, 1, -10, 15, 2, -2]) == [-10, -2, 0, 1, 2, 15]





from __future__ import annotations

from collections.abc import MutableSequence



class 						UpperCAmelCase_					:







							def __init__(     self,    __a,    __a):

														'''simple docstring'''

														if len(__a) != degree + 1:
																					raise ValueError(
																					    "The number of coefficients should be equal to the degree + 1.")

														_lowerCAmelCase  :							list[float]				     =					list(__a)
														_lowerCAmelCase  :							Any				     =					degree







							def __add__(     self,    __a):

														'''simple docstring'''

														if self.degree > polynomial_a.degree:
																					_lowerCAmelCase  :							Dict				     =					self.coefficients[:]
																					for i in range(polynomial_a.degree + 1):
																												coefficients[i] += polynomial_a.coefficients[i]
																					return Polynomial(self.degree,    __a)
														else:
																					_lowerCAmelCase  :							Union[str, Any]				     =					polynomial_a.coefficients[:]
																					for i in range(self.degree + 1):
																												coefficients[i] += self.coefficients[i]
																					return Polynomial(polynomial_a.degree,    __a)







							def __sub__(     self,    __a):

														'''simple docstring'''

														return self + polynomial_a * Polynomial(0,    [-1])







							def __neg__(     self):

														'''simple docstring'''

														return Polynomial(self.degree,    [-c for c in self.coefficients])







							def __mul__(     self,    __a):

														'''simple docstring'''

														_lowerCAmelCase  :							list[float]				     =					[0] * (self.degree + polynomial_a.degree + 1)
														for i in range(self.degree + 1):
																					for j in range(polynomial_a.degree + 1):
																												coefficients[i + j] += (
																												    self.coefficients[i] * polynomial_a.coefficients[j]
																												)

														return Polynomial(self.degree + polynomial_a.degree,    __a)







							def      snake_case__   (     self,    __a):

														'''simple docstring'''

														_lowerCAmelCase  :							int | float				     =					0
														for i in range(self.degree + 1):
																					result += self.coefficients[i] * (substitution**i)
														return result







							def __str__(     self):

														'''simple docstring'''

														_lowerCAmelCase  :							List[str]				     =					""
														for i in range(self.degree,    -1,    -1):
																					if self.coefficients[i] == 0:
																												continue
																					elif self.coefficients[i] > 0:
																												if polynomial:
																																			polynomial += " + "
																					else:
																												polynomial += " - "

																					if i == 0:
																												polynomial += str(abs(self.coefficients[i]))
																					elif i == 1:
																												polynomial += str(abs(self.coefficients[i])) + "x"
																					else:
																												polynomial += str(abs(self.coefficients[i])) + "x^" + str(__a)

														return polynomial







							def __repr__(     self):

														'''simple docstring'''

														return self.__str__()







							def      snake_case__   (     self):

														'''simple docstring'''

														_lowerCAmelCase  :							list[float]				     =					[0] * self.degree
														for i in range(self.degree):
																					_lowerCAmelCase  :							List[Any]				     =					self.coefficients[i + 1] * (i + 1)
														return Polynomial(self.degree - 1,    __a)







							def      snake_case__   (     self,    __a = 0):

														'''simple docstring'''

														_lowerCAmelCase  :							list[float]				     =					[0] * (self.degree + 2)
														_lowerCAmelCase  :							Optional[Any]				     =					constant
														for i in range(self.degree + 1):
																					_lowerCAmelCase  :							Dict				     =					self.coefficients[i] / (i + 1)
														return Polynomial(self.degree + 1,    __a)







							def __eq__(     self,    __a):

														'''simple docstring'''

														if not isinstance(__a,    __a):
																					return False

														if self.degree != polynomial_a.degree:
																					return False

														for i in range(self.degree + 1):
																					if self.coefficients[i] != polynomial_a.coefficients[i]:
																												return False

														return True







							def __ne__(     self,    __a):

														'''simple docstring'''

														return not self.__eq__(__a)
