


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() = }')









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__)





