code: 
  
  
  
  
  from __future__ import annotations
  
  def lowercase						(     SCREAMING_SNAKE_CASE   ) ->       Union[str, Any]:
  
  
  			'''simple docstring'''
  
  
  
  
  
  
  
  			if not list_of_ints:
  						return []
  
  			if min(_A   ) < 0:
  						raise ValueError('All numbers must be positive'   )
  
  			SCREAMING_SNAKE_CASE_			=	max(len(bin(_A   )[2:]   ) for x in list_of_ints   )
  			return _msd_radix_sort(_A					,						_A   )
  
  def lowercase						(     SCREAMING_SNAKE_CASE					,						SCREAMING_SNAKE_CASE   ) ->       Tuple:
  
  
  			'''simple docstring'''
  
  
  
  
  
  
  
  			if bit_position == 0 or len(_A   ) in [0, 1]:
  						return list_of_ints
  
  			SCREAMING_SNAKE_CASE_			=	[]
  			SCREAMING_SNAKE_CASE_			=	[]
  			# 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_			=	_msd_radix_sort(_A					,						bit_position - 1   )
  			SCREAMING_SNAKE_CASE_			=	_msd_radix_sort(_A					,						bit_position - 1   )
  
  			# recombine lists
  			SCREAMING_SNAKE_CASE_			=	zeros
  			res.extend(_A   )
  
  			return res
  
  def lowercase						(     SCREAMING_SNAKE_CASE   ) ->       Optional[Any]:
  
  
  			'''simple docstring'''
  
  
  
  
  
  
  
  			SCREAMING_SNAKE_CASE_			=	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_			=	max(len(bin(_A   )[2:]   ) for x in list_of_ints   )
  			_msd_radix_sort_inplace(_A					,						_A					,						0					,						_A   )
  
  def lowercase						(     SCREAMING_SNAKE_CASE					,						SCREAMING_SNAKE_CASE					,						SCREAMING_SNAKE_CASE					,						SCREAMING_SNAKE_CASE   ) ->       Optional[Any]:
  
  
  			'''simple docstring'''
  
  
  
  
  
  
  
  			if bit_position == 0 or end_index - begin_index <= 1:
  						return
  
  			bit_position -= 1
  
  			SCREAMING_SNAKE_CASE_			=	begin_index
  			SCREAMING_SNAKE_CASE_			=	end_index - 1
  			while i <= j:
  						SCREAMING_SNAKE_CASE_			=	False
  						if not (list_of_ints[i] >> bit_position) & 1:
  									# found zero at the beginning
  									i += 1
  									SCREAMING_SNAKE_CASE_			=	True
  						if (list_of_ints[j] >> bit_position) & 1:
  									# found one at the end
  									j -= 1
  									SCREAMING_SNAKE_CASE_			=	True
  
  						if changed:
  									continue
  
  						SCREAMING_SNAKE_CASE_	,		SCREAMING_SNAKE_CASE_			=	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()
  
style_context: 
  
  
  
  
  from dataclasses import dataclass
  from typing import List, Optional, Union
  
  import numpy as np
  import PIL
  
  from ...utils import BaseOutput, is_invisible_watermark_available, is_torch_available, is_transformers_available
  
  
  
  @dataclass
  class 			a_					(    SCREAMING_SNAKE_CASE__    ):
  	A						       =   42
  
  
  if is_transformers_available() and is_torch_available() and is_invisible_watermark_available():
  				from .pipeline_stable_diffusion_xl import StableDiffusionXLPipeline
  				from .pipeline_stable_diffusion_xl_imgaimg import StableDiffusionXLImgaImgPipeline
  