



'''simple docstring'''



import math






class 			_SCREAMING_SNAKE_CASE				:



			def __init__(     self		:						List[str]    ,			__UpperCamelCase		:						Optional[int]    ,			__UpperCamelCase		:						Dict    ,			__UpperCamelCase		:						Tuple			)      ->      List[Any]:
							"""simple docstring"""





							snake_case__      :   List[str]      =    x
							snake_case__      :   List[str]      =    y
							snake_case__      :   Any      =    z







			def __repr__(     self		:						str			)      ->      str:
							"""simple docstring"""





							return F'''Point({self.x}, {self.y}, {self.z})'''



def 							__UpperCAmelCase				(				UpperCamelCase__				:Point   ,				UpperCamelCase__				:Point			)		->						float:
				return math.sqrt(abs((b.x - a.x) ** 2 + (b.y - a.y) ** 2 + (b.z - a.z) ** 2			)			)


if __name__ == "__main__":
				import doctest

				doctest.testmod()









from __future__ import annotations






def 			UpperCAmelCase__     (     lowercase__ )			->   list[int]:
						if not list_of_ints:
												return []

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

						__lowercase											=					max(len(bin(lowercase__ )[2:] ) for x in list_of_ints )
						return _msd_radix_sort(lowercase__    ,							lowercase__ )






def 			UpperCAmelCase__     (     lowercase__    ,							lowercase__ )			->   list[int]:
						if bit_position == 0 or len(lowercase__ ) in [0, 1]:
												return list_of_ints

						__lowercase											=					[]
						__lowercase											=					[]
						# 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(lowercase__ )
												else:
																		# number has a zero at bit bit_position
																		zeros.append(lowercase__ )

    # recursively split both lists further
						__lowercase											=					_msd_radix_sort(lowercase__    ,							bit_position - 1 )
						__lowercase											=					_msd_radix_sort(lowercase__    ,							bit_position - 1 )

						# recombine lists
						__lowercase											=					zeros
						res.extend(lowercase__ )

						return res






def 			UpperCAmelCase__     (     lowercase__ )			->   List[Any]:
						__lowercase											=					len(lowercase__ )
						if not list_of_ints or length == 1:
												return

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

						__lowercase											=					max(len(bin(lowercase__ )[2:] ) for x in list_of_ints )
						_msd_radix_sort_inplace(lowercase__    ,							lowercase__    ,							0    ,							lowercase__ )






def 			UpperCAmelCase__     (     lowercase__    ,							lowercase__    ,							lowercase__    ,							lowercase__ )			->   Optional[Any]:
						if bit_position == 0 or end_index - begin_index <= 1:
												return

						bit_position -= 1

						__lowercase											=					begin_index
						__lowercase											=					end_index - 1
						while i <= j:
												__lowercase											=					False
												if not (list_of_ints[i] >> bit_position) & 1:
																		# found zero at the beginning
																		i += 1
																		__lowercase											=					True
												if (list_of_ints[j] >> bit_position) & 1:
																		# found one at the end
																		j -= 1
																		__lowercase											=					True

												if changed:
																		continue

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

						_msd_radix_sort_inplace(lowercase__    ,							lowercase__    ,							lowercase__    ,							lowercase__ )
						_msd_radix_sort_inplace(lowercase__    ,							lowercase__    ,							lowercase__    ,							lowercase__ )


if __name__ == "__main__":
			import doctest

			doctest.testmod()





