





'''simple docstring'''



from collections import namedtuple

snake_case_   :  Tuple								=      namedtuple('''from_to''', '''from_ to''')

snake_case_   :  List[str]								=      {
    '''millimeter''': '''mm''',
    '''centimeter''': '''cm''',
    '''meter''': '''m''',
    '''kilometer''': '''km''',
    '''inch''': '''in''',
    '''inche''': '''in''',  # Trailing 's' has been stripped off
    '''feet''': '''ft''',
    '''foot''': '''ft''',
    '''yard''': '''yd''',
    '''mile''': '''mi''',
}

snake_case_   :  str								=      {
    '''mm''': from_to(0.0_01, 1000),
    '''cm''': from_to(0.01, 100),
    '''m''': from_to(1, 1),
    '''km''': from_to(1000, 0.0_01),
    '''in''': from_to(0.02_54, 39.37_01),
    '''ft''': from_to(0.30_48, 3.2_80_84),
    '''yd''': from_to(0.91_44, 1.0_93_61),
    '''mi''': from_to(16_09.34, 0.0_00_62_13_71),
}



def  lowercase__(		_UpperCamelCase  : List[str] ,   _UpperCamelCase  : Optional[Any] ,   _UpperCamelCase  : List[Any]				)->   float:






					"""simple docstring"""

					_UpperCamelCase											=   from_type.lower().rstrip("s"				)
					_UpperCamelCase											=   TYPE_CONVERSION.get(lowerCamelCase__ ,   lowerCamelCase__				)
					_UpperCamelCase											=   to_type.lower().rstrip("s"				)
					_UpperCamelCase											=   TYPE_CONVERSION.get(lowerCamelCase__ ,   lowerCamelCase__				)
					if new_from not in METRIC_CONVERSION:
										_UpperCamelCase											=   (
										    f"Invalid 'from_type' value: {from_type!r}.\n"
										    f"Conversion abbreviations are: {', '.join(lowerCamelCase__				)}"
										)
										raise ValueError(lowerCamelCase__				)
					if new_to not in METRIC_CONVERSION:
										_UpperCamelCase											=   (
										    f"Invalid 'to_type' value: {to_type!r}.\n"
										    f"Conversion abbreviations are: {', '.join(lowerCamelCase__				)}"
										)
										raise ValueError(lowerCamelCase__				)
					return value * METRIC_CONVERSION[new_from].from_ * METRIC_CONVERSION[new_to].to


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()



