
"""simple docstring"""





import math



def  lowerCamelCase__						(     __snake_case      )				->						bool:


					"""simple docstring"""





					_UpperCamelCase									=    math.loga(math.sqrt(4 * positive_integer + 1      ) / 2 + 1 / 2      )

					return exponent == int(__snake_case      )



def  lowerCamelCase__						(     __snake_case = 1 / 1_23_45      )				->						int:


					"""simple docstring"""





					_UpperCamelCase									=    0
					_UpperCamelCase									=    0

					_UpperCamelCase									=    3
					while True:
										_UpperCamelCase									=    (integer**2 - 1) / 4
										# if candidate is an integer, then there is a partition for k
										if partition_candidate == int(__snake_case      ):
															_UpperCamelCase									=    int(__snake_case      )
															total_partitions += 1
															if check_partition_perfect(__snake_case      ):
																				perfect_partitions += 1
										if perfect_partitions > 0:
															if perfect_partitions / total_partitions < max_proportion:
																				return int(__snake_case      )
										integer += 1


if __name__ == "__main__":
				print(F"""{solution() = }""")








"""simple docstring"""





import warnings

from ...processing_utils import ProcessorMixin
from ...tokenization_utils_base import BatchEncoding






class        _UpperCAmelCase(       lowerCamelCase      ):
		lowercase__         = ['image_processor', 'tokenizer']
		lowercase__         = 'ViTImageProcessor'
		lowercase__         = ('CLIPTokenizer', 'CLIPTokenizerFast')



		def __init__(   self							,						__a=None							,						__a=None							,						**__a)			->			Union[str, Any]:






							'''simple docstring'''
							_UpperCamelCase									=    None
							if "feature_extractor" in kwargs:
												warnings.warn(
												    '''The `feature_extractor` argument is deprecated and will be removed in v5, use `image_processor`'''
												    ''' instead.'''							,						__a							,						)
												_UpperCamelCase									=    kwargs.pop('''feature_extractor''')

							_UpperCamelCase									=    image_processor if image_processor is not None else feature_extractor
							if image_processor is None:
												raise ValueError('''You need to specify an `image_processor`.''')
							if tokenizer is None:
												raise ValueError('''You need to specify a `tokenizer`.''')

							super().__init__(__a							,						__a)



		def __call__(   self							,						__a=None							,						__a=None							,						__a=None							,						__a=None							,						**__a)			->			Tuple:






							'''simple docstring'''
							if text is None and visual_prompt is None and images is None:
												raise ValueError('''You have to specify either text, visual prompt or images.''')

							if text is not None and visual_prompt is not None:
												raise ValueError('''You have to specify exactly one type of prompt. Either text or visual prompt.''')

							if text is not None:
												_UpperCamelCase									=    self.tokenizer(__a							,						return_tensors=__a							,						**__a)

							if visual_prompt is not None:
												_UpperCamelCase									=    self.image_processor(__a							,						return_tensors=__a							,						**__a)

							if images is not None:
												_UpperCamelCase									=    self.image_processor(__a							,						return_tensors=__a							,						**__a)

							if visual_prompt is not None and images is not None:
												_UpperCamelCase									=    {
												    '''pixel_values''': image_features.pixel_values,
												    '''conditional_pixel_values''': prompt_features.pixel_values,
												}
												return encoding
							elif text is not None and images is not None:
												_UpperCamelCase									=    image_features.pixel_values
												return encoding
							elif text is not None:
												return encoding
							elif visual_prompt is not None:
												_UpperCamelCase									=    {
												    '''conditional_pixel_values''': prompt_features.pixel_values,
												}
												return encoding
							else:
												return BatchEncoding(data=dict(**__a)							,						tensor_type=__a)



		def 		UpperCAmelCase				(   self							,						*__a							,						**__a)			->			Any:






							'''simple docstring'''
							return self.tokenizer.batch_decode(*__a							,						**__a)



		def 		UpperCAmelCase				(   self							,						*__a							,						**__a)			->			List[str]:






							'''simple docstring'''
							return self.tokenizer.decode(*__a							,						**__a)



		@property
		def 		UpperCAmelCase				(   self)			->			List[str]:






							'''simple docstring'''
							warnings.warn(
							    '''`feature_extractor_class` is deprecated and will be removed in v5. Use `image_processor_class` instead.'''							,						__a							,						)
							return self.image_processor_class




		@property
		def 		UpperCAmelCase				(   self)			->			List[str]:






							'''simple docstring'''
							warnings.warn(
							    '''`feature_extractor` is deprecated and will be removed in v5. Use `image_processor` instead.'''							,						__a							,						)
							return self.image_processor






