code: 
  
  
  
  
  
  from itertools import count
  from math import asin, pi, sqrt
  
  
  
  
  def       a__						(		snake_case__				:       float    ):
    return (
        (1 - 2 * point) * sqrt(point - point**2    ) + 2 * point + asin(sqrt(1 - point    )    )
    ) / 4
  
  
  
  
  def       a__						(		snake_case__				:       int    ):
    _UpperCAmelCase		:       int       =    (circles_number + 1 - sqrt(2 * circles_number    )) / (
        2 * (circles_number**2 + 1)
    )
    _UpperCAmelCase		:       Union[str, Any]       =    circles_number * intersection_y
  
    _UpperCAmelCase		:       Tuple       =    intersection_x * intersection_y / 2
    _UpperCAmelCase		:       str       =    circle_bottom_arc_integral(
        1 / 2    ) - circle_bottom_arc_integral(snake_case__    )
  
    return triangle_area + concave_region_area
  
  
  
  
  def       a__						(		snake_case__				:       float = 1 / 1000    ):
    _UpperCAmelCase		:       Dict       =    (1 - pi / 4) / 4
  
    for n in count(1    ):
      if concave_triangle_area(snake_case__    ) / l_section_area < fraction:
        return n
  
    return -1
  
  
  if __name__ == "__main__":
   print(F'{solution() = }')
  
  
  
  
  
  
style_context: 
  
  
  from typing import TYPE_CHECKING
  
  from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tf_available, is_torch_available
  
  
  SCREAMING_SNAKE_CASE__				:    List[str]         =    {
      'configuration_flaubert': ['FLAUBERT_PRETRAINED_CONFIG_ARCHIVE_MAP', 'FlaubertConfig', 'FlaubertOnnxConfig'],
      'tokenization_flaubert': ['FlaubertTokenizer'],
  }
  
  try:
   if not is_torch_available():
    raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
   pass
  else:
   SCREAMING_SNAKE_CASE__				:    int         =    [
       'FLAUBERT_PRETRAINED_MODEL_ARCHIVE_LIST',
       'FlaubertForMultipleChoice',
       'FlaubertForQuestionAnswering',
       'FlaubertForQuestionAnsweringSimple',
       'FlaubertForSequenceClassification',
       'FlaubertForTokenClassification',
       'FlaubertModel',
       'FlaubertWithLMHeadModel',
       'FlaubertPreTrainedModel',
   ]
  
  try:
   if not is_tf_available():
    raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
   pass
  else:
   SCREAMING_SNAKE_CASE__				:    Dict         =    [
       'TF_FLAUBERT_PRETRAINED_MODEL_ARCHIVE_LIST',
       'TFFlaubertForMultipleChoice',
       'TFFlaubertForQuestionAnsweringSimple',
       'TFFlaubertForSequenceClassification',
       'TFFlaubertForTokenClassification',
       'TFFlaubertModel',
       'TFFlaubertPreTrainedModel',
       'TFFlaubertWithLMHeadModel',
   ]
  
  
  if TYPE_CHECKING:
   from .configuration_flaubert import FLAUBERT_PRETRAINED_CONFIG_ARCHIVE_MAP, FlaubertConfig, FlaubertOnnxConfig
   from .tokenization_flaubert import FlaubertTokenizer
  
   try:
    if not is_torch_available():
     raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
    pass
   else:
    from .modeling_flaubert import (
        FLAUBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
        FlaubertForMultipleChoice,
        FlaubertForQuestionAnswering,
        FlaubertForQuestionAnsweringSimple,
        FlaubertForSequenceClassification,
        FlaubertForTokenClassification,
        FlaubertModel,
        FlaubertPreTrainedModel,
        FlaubertWithLMHeadModel,
    )
  
   try:
    if not is_tf_available():
     raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
    pass
   else:
    from .modeling_tf_flaubert import (
        TF_FLAUBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
        TFFlaubertForMultipleChoice,
        TFFlaubertForQuestionAnsweringSimple,
        TFFlaubertForSequenceClassification,
        TFFlaubertForTokenClassification,
        TFFlaubertModel,
        TFFlaubertPreTrainedModel,
        TFFlaubertWithLMHeadModel,
    )
  
  else:
   import sys
  
   SCREAMING_SNAKE_CASE__				:    List[Any]         =    _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)
  
  
  
  
  
  