






from __future__ import annotations







def 						a_      (__A			)							->	List[str]:



					"""simple docstring"""







					if not list_of_ints:
										return []

					if min(_A			) < 0:
										raise ValueError("All numbers must be positive"			)

					__a				:	Dict			=				max(len(bin(_A			)[2:]			) for x in list_of_ints			)
					return _msd_radix_sort(_A							,					_A			)







def 						a_      (__A							,					__A			)							->	int:



					"""simple docstring"""







					if bit_position == 0 or len(_A			) in [0, 1]:
										return list_of_ints

					__a				:	List[Any]			=				[]
					__a				:	Optional[Any]			=				[]
					# Split numbers based on bit at bit_position from the right
					for number in list_of_ints:
										if (number >> (bit_position - 1)) & 1:
															# number has a one at bit bit_position
															ones.append(_A			)
										else:
															# number has a zero at bit bit_position
															zeros.append(_A			)

										# recursively split both lists further
					__a				:	Optional[Any]			=				_msd_radix_sort(_A							,					bit_position - 1			)
					__a				:	Union[str, Any]			=				_msd_radix_sort(_A							,					bit_position - 1			)

					# recombine lists
					__a				:	List[Any]			=				zeros
					res.extend(_A			)

					return res







def 						a_      (__A			)							->	Tuple:



					"""simple docstring"""
					__a				:	List[str]			=				len(_A			)
					if not list_of_ints or length == 1:
										return

					if min(_A			) < 0:
										raise ValueError("All numbers must be positive"			)

					__a				:	Optional[Any]			=				max(len(bin(_A			)[2:]			) for x in list_of_ints			)
					_msd_radix_sort_inplace(_A							,					_A							,					0							,					_A			)







def 						a_      (__A							,					__A							,					__A							,					__A			)							->	List[str]:



					"""simple docstring"""







					if bit_position == 0 or end_index - begin_index <= 1:
										return

					bit_position -= 1

					__a				:	Union[str, Any]			=				begin_index
					__a				:	int			=				end_index - 1
					while i <= j:
										__a				:	Union[str, Any]			=				False
										if not (list_of_ints[i] >> bit_position) & 1:
															# found zero at the beginning
															i += 1
															__a				:	Optional[Any]			=				True
										if (list_of_ints[j] >> bit_position) & 1:
															# found one at the end
															j -= 1
															__a				:	List[Any]			=				True

										if changed:
															continue

										__a			, __a				:	int			=				list_of_ints[j], list_of_ints[i]
										j -= 1
										if j != i:
															i += 1

					_msd_radix_sort_inplace(_A							,					_A							,					_A							,					_A			)
					_msd_radix_sort_inplace(_A							,					_A							,					_A							,					_A			)


if __name__ == "__main__":
			import doctest

			doctest.testmod()










def 						a_      (__A			)							->	list:



					"""simple docstring"""
					if len(__A			) <= 1:
										return data
					else:
										return [
										    *quick_sort([e for e in data[1:] if e <= data[0]]			),
										    data[0],
										    *quick_sort([e for e in data[1:] if e > data[0]]			),
										]


if __name__ == "__main__":
			import doctest

			doctest.testmod()





