

from __future__ import annotations






def        __lowercase   (  _A      )  ->    list[int]:
      if not list_of_ints:
            return []

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

      SCREAMING_SNAKE_CASE			:   List[Any]	  = max(len(bin(_A      )[2:]      ) for x in list_of_ints      )
      return _msd_radix_sort(_A    ,     _A      )






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

      SCREAMING_SNAKE_CASE			:   Optional[int]	  = []
      SCREAMING_SNAKE_CASE			:   List[str]	  = []
      # 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
      SCREAMING_SNAKE_CASE			:   Union[str, Any]	  = _msd_radix_sort(_A    ,     bit_position - 1      )
      SCREAMING_SNAKE_CASE			:   List[str]	  = _msd_radix_sort(_A    ,     bit_position - 1      )

      # recombine lists
      SCREAMING_SNAKE_CASE			:   Dict	  = zeros
      res.extend(_A      )

      return res






def        __lowercase   (  _A      )  ->    Dict:
      SCREAMING_SNAKE_CASE			:   str	  = len(_A      )
      if not list_of_ints or length == 1:
            return

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

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






def        __lowercase   (  _A    ,     _A    ,     _A    ,     _A      )  ->    List[str]:
      if bit_position == 0 or end_index - begin_index <= 1:
            return

      bit_position -= 1

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

            if changed:
                  continue

            SCREAMING_SNAKE_CASE  ,						SCREAMING_SNAKE_CASE			:   Any	  = 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()







import safs







class 							a__							( safs.SaFileSystem							):







  """simple docstring"""




