





'''simple docstring'''



from __future__ import annotations

from enum import Enum

class     A_ (  lowerCAmelCase_  ):

			'''simple docstring'''





			_lowerCAmelCase						=    24
			_lowerCAmelCase						=    21
			_lowerCAmelCase						=    18
			_lowerCAmelCase						=    15
			_lowerCAmelCase						=    12
			_lowerCAmelCase						=    9
			_lowerCAmelCase						=    6
			_lowerCAmelCase						=    3
			_lowerCAmelCase						=    2
			_lowerCAmelCase						=    1
			_lowerCAmelCase						=    -1
			_lowerCAmelCase						=    -2
			_lowerCAmelCase						=    -3
			_lowerCAmelCase						=    -6
			_lowerCAmelCase						=    -9
			_lowerCAmelCase						=    -12
			_lowerCAmelCase						=    -15
			_lowerCAmelCase						=    -18
			_lowerCAmelCase						=    -21
			_lowerCAmelCase						=    -24




class     A_ (  lowerCAmelCase_  ):

			'''simple docstring'''





			_lowerCAmelCase						=    8
			_lowerCAmelCase						=    7
			_lowerCAmelCase						=    6
			_lowerCAmelCase						=    5
			_lowerCAmelCase						=    4
			_lowerCAmelCase						=    3
			_lowerCAmelCase						=    2
			_lowerCAmelCase						=    1




def  lowercase__(		_UpperCamelCase  : float ,   _UpperCamelCase  : str | SIUnit ,   _UpperCamelCase  : str | SIUnit ,   )->   float:






					"""simple docstring"""

					if isinstance(_UpperCamelCase ,   _UpperCamelCase				):
										_UpperCamelCase											=   SIUnit[known_prefix.lower()]
					if isinstance(_UpperCamelCase ,   _UpperCamelCase				):
										_UpperCamelCase											=   SIUnit[unknown_prefix.lower()]
					_UpperCamelCase											=   known_amount * (
					    10 ** (known_prefix.value - unknown_prefix.value)
					)
					return unknown_amount



def  lowercase__(		_UpperCamelCase  : float ,   _UpperCamelCase  : str | BinaryUnit ,   _UpperCamelCase  : str | BinaryUnit ,   )->   float:






					"""simple docstring"""

					if isinstance(_UpperCamelCase ,   _UpperCamelCase				):
										_UpperCamelCase											=   BinaryUnit[known_prefix.lower()]
					if isinstance(_UpperCamelCase ,   _UpperCamelCase				):
										_UpperCamelCase											=   BinaryUnit[unknown_prefix.lower()]
					_UpperCamelCase											=   known_amount * (
					    2 ** ((known_prefix.value - unknown_prefix.value) * 10)
					)
					return unknown_amount


if __name__ == "__main__":
			import doctest

			doctest.testmod()










'''simple docstring'''



from __future__ import annotations



def  lowercase__(		_UpperCamelCase  : list[int]				)->   list[int]:






					"""simple docstring"""

					if not list_of_ints:
										return []

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

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



def  lowercase__(		_UpperCamelCase  : list[int] ,   _UpperCamelCase  : int				)->   list[int]:






					"""simple docstring"""

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

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

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

					# recombine lists
					_UpperCamelCase											=   zeros
					res.extend(_UpperCamelCase				)

					return res



def  lowercase__(		_UpperCamelCase  : list[int]				)->   Union[str, Any]:






					"""simple docstring"""

					_UpperCamelCase											=   len(_UpperCamelCase				)
					if not list_of_ints or length == 1:
										return

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

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



def  lowercase__(		_UpperCamelCase  : list[int] ,   _UpperCamelCase  : int ,   _UpperCamelCase  : int ,   _UpperCamelCase  : int				)->   Tuple:






					"""simple docstring"""

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

					bit_position -= 1

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

										if changed:
															continue

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

					_msd_radix_sort_inplace(_UpperCamelCase ,   _UpperCamelCase ,   _UpperCamelCase ,   _UpperCamelCase				)
					_msd_radix_sort_inplace(_UpperCamelCase ,   _UpperCamelCase ,   _UpperCamelCase ,   _UpperCamelCase				)


if __name__ == "__main__":
			import doctest

			doctest.testmod()



