


from itertools import count
from math import asin, pi, sqrt




def 			a_   (					SCREAMING_SNAKE_CASE__      :   float  ):
       '''simple docstring'''





       return (
           (1 - 2 * point) * sqrt(point - point**2  ) + 2 * point + asin(sqrt(1 - point  )  )
       ) / 4




def 			a_   (					SCREAMING_SNAKE_CASE__      :   int  ):
       '''simple docstring'''





       _lowerCamelCase :	List[Any]						=(circles_number + 1 - sqrt(2 * circles_number  )) / (
           2 * (circles_number**2 + 1)
       )
       _lowerCamelCase :	str						=circles_number * intersection_y

       _lowerCamelCase :	Optional[Any]						=intersection_x * intersection_y / 2
       _lowerCamelCase :	str						=circle_bottom_arc_integral(
           1 / 2  ) - circle_bottom_arc_integral(SCREAMING_SNAKE_CASE__  )

       return triangle_area + concave_region_area




def 			a_   (					SCREAMING_SNAKE_CASE__      :   float = 1 / 1_000  ):
       '''simple docstring'''





       _lowerCamelCase :	int						=(1 - pi / 4) / 4

       for n in count(1  ):
              if concave_triangle_area(SCREAMING_SNAKE_CASE__  ) / l_section_area < fraction:
                     return n

       return -1


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






import warnings
from contextlib import contextmanager

from ...processing_utils import ProcessorMixin




class A						(     UpperCamelCase_  ):
      UpperCamelCase__							:						Optional[Any]   ='AutoFeatureExtractor'
      UpperCamelCase__							:						List[str]   ='Speech2Text2Tokenizer'






      def __init__(      self		:  str    ,     lowercase_		:  Dict    ,     lowercase_		:  Optional[int]				)      ->		str:
             """simple docstring"""




             super().__init__(lowercase_    ,     lowercase_				)
             _lowerCamelCase :	Optional[Any]						=self.feature_extractor
             _lowerCamelCase :	Tuple						=False






      def __call__(      self		:  Tuple    ,     *lowercase_		:  str    ,     **lowercase_		:  List[Any]				)      ->		List[str]:
             """simple docstring"""




             if self._in_target_context_manager:
                    return self.current_processor(*lowercase_    ,     **lowercase_				)

             if "raw_speech" in kwargs:
                    warnings.warn('Using `raw_speech` as a keyword argument is deprecated. Use `audio` instead.'				)
                    _lowerCamelCase :	List[str]						=kwargs.pop('raw_speech'				)
             else:
                    _lowerCamelCase :	str						=kwargs.pop('audio'    ,     lowercase_				)
             _lowerCamelCase :	Optional[Any]						=kwargs.pop('sampling_rate'    ,     lowercase_				)
             _lowerCamelCase :	List[str]						=kwargs.pop('text'    ,     lowercase_				)
             if len(lowercase_				) > 0:
                    _lowerCamelCase :	Dict						=args[0]
                    _lowerCamelCase :	Optional[Any]						=args[1:]

             if audio is None and text is None:
                    raise ValueError('You need to specify either an `audio` or `text` input to process.'				)

             if audio is not None:
                    _lowerCamelCase :	List[Any]						=self.feature_extractor(lowercase_    ,     *lowercase_    ,     sampling_rate=lowercase_    ,     **lowercase_				)
             if text is not None:
                    _lowerCamelCase :	Tuple						=self.tokenizer(lowercase_    ,     **lowercase_				)

             if text is None:
                    return inputs
             elif audio is None:
                    return encodings
             else:
                    _lowerCamelCase :	Dict						=encodings['input_ids']
                    return inputs






      def  lowerCamelCase (      self		:  str    ,     *lowercase_		:  List[Any]    ,     **lowercase_		:  Any				)      ->		Union[str, Any]:
             """simple docstring"""




             return self.tokenizer.batch_decode(*lowercase_    ,     **lowercase_				)






      def  lowerCamelCase (      self		:  Optional[int]    ,     *lowercase_		:  Dict    ,     **lowercase_		:  Optional[int]				)      ->		str:
             """simple docstring"""




             return self.tokenizer.decode(*lowercase_    ,     **lowercase_				)






      @contextmanager
      def  lowerCamelCase (      self		:  Optional[Any]				)      ->		Tuple:
             """simple docstring"""




             warnings.warn(
                 '`as_target_processor` is deprecated and will be removed in v5 of Transformers. You can process your '
                 'labels by using the argument `text` of the regular `__call__` method (either in the same call as '
                 'your audio inputs, or in a separate call.'				)
             _lowerCamelCase :	Optional[Any]						=True
             _lowerCamelCase :	List[Any]						=self.tokenizer
             yield
             _lowerCamelCase :	Optional[int]						=self.feature_extractor
             _lowerCamelCase :	List[str]						=False


