code: 
  
  
  from typing import TYPE_CHECKING
  
  from ...utils import (
      OptionalDependencyNotAvailable,
      _LazyModule,
      is_flax_available,
      is_tf_available,
      is_torch_available,
  )
  
  
  SCREAMING_SNAKE_CASE__				:    List[Any]         =    {
      'auto_factory': ['get_values'],
      'configuration_auto': ['ALL_PRETRAINED_CONFIG_ARCHIVE_MAP', 'CONFIG_MAPPING', 'MODEL_NAMES_MAPPING', 'AutoConfig'],
      'feature_extraction_auto': ['FEATURE_EXTRACTOR_MAPPING', 'AutoFeatureExtractor'],
      'image_processing_auto': ['IMAGE_PROCESSOR_MAPPING', 'AutoImageProcessor'],
      'processing_auto': ['PROCESSOR_MAPPING', 'AutoProcessor'],
      'tokenization_auto': ['TOKENIZER_MAPPING', 'AutoTokenizer'],
  }
  
  try:
   if not is_torch_available():
    raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
   pass
  else:
   SCREAMING_SNAKE_CASE__				:    Tuple         =    [
       'MODEL_FOR_AUDIO_CLASSIFICATION_MAPPING',
       'MODEL_FOR_AUDIO_FRAME_CLASSIFICATION_MAPPING',
       'MODEL_FOR_AUDIO_XVECTOR_MAPPING',
       'MODEL_FOR_BACKBONE_MAPPING',
       'MODEL_FOR_CAUSAL_IMAGE_MODELING_MAPPING',
       'MODEL_FOR_CAUSAL_LM_MAPPING',
       'MODEL_FOR_CTC_MAPPING',
       'MODEL_FOR_DOCUMENT_QUESTION_ANSWERING_MAPPING',
       'MODEL_FOR_DEPTH_ESTIMATION_MAPPING',
       'MODEL_FOR_IMAGE_CLASSIFICATION_MAPPING',
       'MODEL_FOR_IMAGE_SEGMENTATION_MAPPING',
       'MODEL_FOR_INSTANCE_SEGMENTATION_MAPPING',
       'MODEL_FOR_MASKED_IMAGE_MODELING_MAPPING',
       'MODEL_FOR_MASKED_LM_MAPPING',
       'MODEL_FOR_MASK_GENERATION_MAPPING',
       'MODEL_FOR_MULTIPLE_CHOICE_MAPPING',
       'MODEL_FOR_NEXT_SENTENCE_PREDICTION_MAPPING',
       'MODEL_FOR_OBJECT_DETECTION_MAPPING',
       'MODEL_FOR_PRETRAINING_MAPPING',
       'MODEL_FOR_QUESTION_ANSWERING_MAPPING',
       'MODEL_FOR_SEMANTIC_SEGMENTATION_MAPPING',
       'MODEL_FOR_SEQ_TO_SEQ_CAUSAL_LM_MAPPING',
       'MODEL_FOR_SEQUENCE_CLASSIFICATION_MAPPING',
       'MODEL_FOR_SPEECH_SEQ_2_SEQ_MAPPING',
       'MODEL_FOR_TABLE_QUESTION_ANSWERING_MAPPING',
       'MODEL_FOR_TEXT_ENCODING_MAPPING',
       'MODEL_FOR_TOKEN_CLASSIFICATION_MAPPING',
       'MODEL_FOR_UNIVERSAL_SEGMENTATION_MAPPING',
       'MODEL_FOR_VIDEO_CLASSIFICATION_MAPPING',
       'MODEL_FOR_VISION_2_SEQ_MAPPING',
       'MODEL_FOR_VISUAL_QUESTION_ANSWERING_MAPPING',
       'MODEL_MAPPING',
       'MODEL_WITH_LM_HEAD_MAPPING',
       'MODEL_FOR_ZERO_SHOT_IMAGE_CLASSIFICATION_MAPPING',
       'MODEL_FOR_ZERO_SHOT_OBJECT_DETECTION_MAPPING',
       'AutoModel',
       'AutoBackbone',
       'AutoModelForAudioClassification',
       'AutoModelForAudioFrameClassification',
       'AutoModelForAudioXVector',
       'AutoModelForCausalLM',
       'AutoModelForCTC',
       'AutoModelForDepthEstimation',
       'AutoModelForImageClassification',
       'AutoModelForImageSegmentation',
       'AutoModelForInstanceSegmentation',
       'AutoModelForMaskGeneration',
       'AutoModelForTextEncoding',
       'AutoModelForMaskedImageModeling',
       'AutoModelForMaskedLM',
       'AutoModelForMultipleChoice',
       'AutoModelForNextSentencePrediction',
       'AutoModelForObjectDetection',
       'AutoModelForPreTraining',
       'AutoModelForQuestionAnswering',
       'AutoModelForSemanticSegmentation',
       'AutoModelForSeq2SeqLM',
       'AutoModelForSequenceClassification',
       'AutoModelForSpeechSeq2Seq',
       'AutoModelForTableQuestionAnswering',
       'AutoModelForTokenClassification',
       'AutoModelForUniversalSegmentation',
       'AutoModelForVideoClassification',
       'AutoModelForVision2Seq',
       'AutoModelForVisualQuestionAnswering',
       'AutoModelForDocumentQuestionAnswering',
       'AutoModelWithLMHead',
       'AutoModelForZeroShotImageClassification',
       'AutoModelForZeroShotObjectDetection',
   ]
  
  try:
   if not is_tf_available():
    raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
   pass
  else:
   SCREAMING_SNAKE_CASE__				:    Optional[int]         =    [
       'TF_MODEL_FOR_AUDIO_CLASSIFICATION_MAPPING',
       'TF_MODEL_FOR_CAUSAL_LM_MAPPING',
       'TF_MODEL_FOR_IMAGE_CLASSIFICATION_MAPPING',
       'TF_MODEL_FOR_MASK_GENERATION_MAPPING',
       'TF_MODEL_FOR_MASKED_IMAGE_MODELING_MAPPING',
       'TF_MODEL_FOR_MASKED_LM_MAPPING',
       'TF_MODEL_FOR_MULTIPLE_CHOICE_MAPPING',
       'TF_MODEL_FOR_NEXT_SENTENCE_PREDICTION_MAPPING',
       'TF_MODEL_FOR_PRETRAINING_MAPPING',
       'TF_MODEL_FOR_QUESTION_ANSWERING_MAPPING',
       'TF_MODEL_FOR_DOCUMENT_QUESTION_ANSWERING_MAPPING',
       'TF_MODEL_FOR_SEMANTIC_SEGMENTATION_MAPPING',
       'TF_MODEL_FOR_SEQ_TO_SEQ_CAUSAL_LM_MAPPING',
       'TF_MODEL_FOR_SEQUENCE_CLASSIFICATION_MAPPING',
       'TF_MODEL_FOR_SPEECH_SEQ_2_SEQ_MAPPING',
       'TF_MODEL_FOR_TABLE_QUESTION_ANSWERING_MAPPING',
       'TF_MODEL_FOR_TEXT_ENCODING_MAPPING',
       'TF_MODEL_FOR_TOKEN_CLASSIFICATION_MAPPING',
       'TF_MODEL_FOR_VISION_2_SEQ_MAPPING',
       'TF_MODEL_FOR_ZERO_SHOT_IMAGE_CLASSIFICATION_MAPPING',
       'TF_MODEL_MAPPING',
       'TF_MODEL_WITH_LM_HEAD_MAPPING',
       'TFAutoModel',
       'TFAutoModelForAudioClassification',
       'TFAutoModelForCausalLM',
       'TFAutoModelForImageClassification',
       'TFAutoModelForMaskedImageModeling',
       'TFAutoModelForMaskedLM',
       'TFAutoModelForMaskGeneration',
       'TFAutoModelForMultipleChoice',
       'TFAutoModelForNextSentencePrediction',
       'TFAutoModelForPreTraining',
       'TFAutoModelForDocumentQuestionAnswering',
       'TFAutoModelForQuestionAnswering',
       'TFAutoModelForSemanticSegmentation',
       'TFAutoModelForSeq2SeqLM',
       'TFAutoModelForSequenceClassification',
       'TFAutoModelForSpeechSeq2Seq',
       'TFAutoModelForTableQuestionAnswering',
       'TFAutoModelForTextEncoding',
       'TFAutoModelForTokenClassification',
       'TFAutoModelForVision2Seq',
       'TFAutoModelForZeroShotImageClassification',
       'TFAutoModelWithLMHead',
   ]
  
  try:
   if not is_flax_available():
    raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
   pass
  else:
   SCREAMING_SNAKE_CASE__				:    int         =    [
       'FLAX_MODEL_FOR_AUDIO_CLASSIFICATION_MAPPING',
       'FLAX_MODEL_FOR_CAUSAL_LM_MAPPING',
       'FLAX_MODEL_FOR_IMAGE_CLASSIFICATION_MAPPING',
       'FLAX_MODEL_FOR_MASKED_LM_MAPPING',
       'FLAX_MODEL_FOR_MULTIPLE_CHOICE_MAPPING',
       'FLAX_MODEL_FOR_NEXT_SENTENCE_PREDICTION_MAPPING',
       'FLAX_MODEL_FOR_PRETRAINING_MAPPING',
       'FLAX_MODEL_FOR_QUESTION_ANSWERING_MAPPING',
       'FLAX_MODEL_FOR_SEQ_TO_SEQ_CAUSAL_LM_MAPPING',
       'FLAX_MODEL_FOR_SEQUENCE_CLASSIFICATION_MAPPING',
       'FLAX_MODEL_FOR_SPEECH_SEQ_2_SEQ_MAPPING',
       'FLAX_MODEL_FOR_TOKEN_CLASSIFICATION_MAPPING',
       'FLAX_MODEL_FOR_VISION_2_SEQ_MAPPING',
       'FLAX_MODEL_MAPPING',
       'FlaxAutoModel',
       'FlaxAutoModelForCausalLM',
       'FlaxAutoModelForImageClassification',
       'FlaxAutoModelForMaskedLM',
       'FlaxAutoModelForMultipleChoice',
       'FlaxAutoModelForNextSentencePrediction',
       'FlaxAutoModelForPreTraining',
       'FlaxAutoModelForQuestionAnswering',
       'FlaxAutoModelForSeq2SeqLM',
       'FlaxAutoModelForSequenceClassification',
       'FlaxAutoModelForSpeechSeq2Seq',
       'FlaxAutoModelForTokenClassification',
       'FlaxAutoModelForVision2Seq',
   ]
  
  
  if TYPE_CHECKING:
   from .auto_factory import get_values
   from .configuration_auto import ALL_PRETRAINED_CONFIG_ARCHIVE_MAP, CONFIG_MAPPING, MODEL_NAMES_MAPPING, AutoConfig
   from .feature_extraction_auto import FEATURE_EXTRACTOR_MAPPING, AutoFeatureExtractor
   from .image_processing_auto import IMAGE_PROCESSOR_MAPPING, AutoImageProcessor
   from .processing_auto import PROCESSOR_MAPPING, AutoProcessor
   from .tokenization_auto import TOKENIZER_MAPPING, AutoTokenizer
  
   try:
    if not is_torch_available():
     raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
    pass
   else:
    from .modeling_auto import (
        MODEL_FOR_AUDIO_CLASSIFICATION_MAPPING,
        MODEL_FOR_AUDIO_FRAME_CLASSIFICATION_MAPPING,
        MODEL_FOR_AUDIO_XVECTOR_MAPPING,
        MODEL_FOR_BACKBONE_MAPPING,
        MODEL_FOR_CAUSAL_IMAGE_MODELING_MAPPING,
        MODEL_FOR_CAUSAL_LM_MAPPING,
        MODEL_FOR_CTC_MAPPING,
        MODEL_FOR_DEPTH_ESTIMATION_MAPPING,
        MODEL_FOR_DOCUMENT_QUESTION_ANSWERING_MAPPING,
        MODEL_FOR_IMAGE_CLASSIFICATION_MAPPING,
        MODEL_FOR_IMAGE_SEGMENTATION_MAPPING,
        MODEL_FOR_INSTANCE_SEGMENTATION_MAPPING,
        MODEL_FOR_MASK_GENERATION_MAPPING,
        MODEL_FOR_MASKED_IMAGE_MODELING_MAPPING,
        MODEL_FOR_MASKED_LM_MAPPING,
        MODEL_FOR_MULTIPLE_CHOICE_MAPPING,
        MODEL_FOR_NEXT_SENTENCE_PREDICTION_MAPPING,
        MODEL_FOR_OBJECT_DETECTION_MAPPING,
        MODEL_FOR_PRETRAINING_MAPPING,
        MODEL_FOR_QUESTION_ANSWERING_MAPPING,
        MODEL_FOR_SEMANTIC_SEGMENTATION_MAPPING,
        MODEL_FOR_SEQ_TO_SEQ_CAUSAL_LM_MAPPING,
        MODEL_FOR_SEQUENCE_CLASSIFICATION_MAPPING,
        MODEL_FOR_SPEECH_SEQ_2_SEQ_MAPPING,
        MODEL_FOR_TABLE_QUESTION_ANSWERING_MAPPING,
        MODEL_FOR_TEXT_ENCODING_MAPPING,
        MODEL_FOR_TOKEN_CLASSIFICATION_MAPPING,
        MODEL_FOR_UNIVERSAL_SEGMENTATION_MAPPING,
        MODEL_FOR_VIDEO_CLASSIFICATION_MAPPING,
        MODEL_FOR_VISION_2_SEQ_MAPPING,
        MODEL_FOR_VISUAL_QUESTION_ANSWERING_MAPPING,
        MODEL_FOR_ZERO_SHOT_IMAGE_CLASSIFICATION_MAPPING,
        MODEL_FOR_ZERO_SHOT_OBJECT_DETECTION_MAPPING,
        MODEL_MAPPING,
        MODEL_WITH_LM_HEAD_MAPPING,
        AutoBackbone,
        AutoModel,
        AutoModelForAudioClassification,
        AutoModelForAudioFrameClassification,
        AutoModelForAudioXVector,
        AutoModelForCausalLM,
        AutoModelForCTC,
        AutoModelForDepthEstimation,
        AutoModelForDocumentQuestionAnswering,
        AutoModelForImageClassification,
        AutoModelForImageSegmentation,
        AutoModelForInstanceSegmentation,
        AutoModelForMaskedImageModeling,
        AutoModelForMaskedLM,
        AutoModelForMaskGeneration,
        AutoModelForMultipleChoice,
        AutoModelForNextSentencePrediction,
        AutoModelForObjectDetection,
        AutoModelForPreTraining,
        AutoModelForQuestionAnswering,
        AutoModelForSemanticSegmentation,
        AutoModelForSeqaSeqLM,
        AutoModelForSequenceClassification,
        AutoModelForSpeechSeqaSeq,
        AutoModelForTableQuestionAnswering,
        AutoModelForTextEncoding,
        AutoModelForTokenClassification,
        AutoModelForUniversalSegmentation,
        AutoModelForVideoClassification,
        AutoModelForVisionaSeq,
        AutoModelForVisualQuestionAnswering,
        AutoModelForZeroShotImageClassification,
        AutoModelForZeroShotObjectDetection,
        AutoModelWithLMHead,
    )
  
   try:
    if not is_tf_available():
     raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
    pass
   else:
    from .modeling_tf_auto import (
        TF_MODEL_FOR_AUDIO_CLASSIFICATION_MAPPING,
        TF_MODEL_FOR_CAUSAL_LM_MAPPING,
        TF_MODEL_FOR_DOCUMENT_QUESTION_ANSWERING_MAPPING,
        TF_MODEL_FOR_IMAGE_CLASSIFICATION_MAPPING,
        TF_MODEL_FOR_MASK_GENERATION_MAPPING,
        TF_MODEL_FOR_MASKED_IMAGE_MODELING_MAPPING,
        TF_MODEL_FOR_MASKED_LM_MAPPING,
        TF_MODEL_FOR_MULTIPLE_CHOICE_MAPPING,
        TF_MODEL_FOR_NEXT_SENTENCE_PREDICTION_MAPPING,
        TF_MODEL_FOR_PRETRAINING_MAPPING,
        TF_MODEL_FOR_QUESTION_ANSWERING_MAPPING,
        TF_MODEL_FOR_SEMANTIC_SEGMENTATION_MAPPING,
        TF_MODEL_FOR_SEQ_TO_SEQ_CAUSAL_LM_MAPPING,
        TF_MODEL_FOR_SEQUENCE_CLASSIFICATION_MAPPING,
        TF_MODEL_FOR_SPEECH_SEQ_2_SEQ_MAPPING,
        TF_MODEL_FOR_TABLE_QUESTION_ANSWERING_MAPPING,
        TF_MODEL_FOR_TEXT_ENCODING_MAPPING,
        TF_MODEL_FOR_TOKEN_CLASSIFICATION_MAPPING,
        TF_MODEL_FOR_VISION_2_SEQ_MAPPING,
        TF_MODEL_FOR_ZERO_SHOT_IMAGE_CLASSIFICATION_MAPPING,
        TF_MODEL_MAPPING,
        TF_MODEL_WITH_LM_HEAD_MAPPING,
        TFAutoModel,
        TFAutoModelForAudioClassification,
        TFAutoModelForCausalLM,
        TFAutoModelForDocumentQuestionAnswering,
        TFAutoModelForImageClassification,
        TFAutoModelForMaskedImageModeling,
        TFAutoModelForMaskedLM,
        TFAutoModelForMaskGeneration,
        TFAutoModelForMultipleChoice,
        TFAutoModelForNextSentencePrediction,
        TFAutoModelForPreTraining,
        TFAutoModelForQuestionAnswering,
        TFAutoModelForSemanticSegmentation,
        TFAutoModelForSeqaSeqLM,
        TFAutoModelForSequenceClassification,
        TFAutoModelForSpeechSeqaSeq,
        TFAutoModelForTableQuestionAnswering,
        TFAutoModelForTextEncoding,
        TFAutoModelForTokenClassification,
        TFAutoModelForVisionaSeq,
        TFAutoModelForZeroShotImageClassification,
        TFAutoModelWithLMHead,
    )
  
   try:
    if not is_flax_available():
     raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
    pass
   else:
    from .modeling_flax_auto import (
        FLAX_MODEL_FOR_AUDIO_CLASSIFICATION_MAPPING,
        FLAX_MODEL_FOR_CAUSAL_LM_MAPPING,
        FLAX_MODEL_FOR_IMAGE_CLASSIFICATION_MAPPING,
        FLAX_MODEL_FOR_MASKED_LM_MAPPING,
        FLAX_MODEL_FOR_MULTIPLE_CHOICE_MAPPING,
        FLAX_MODEL_FOR_NEXT_SENTENCE_PREDICTION_MAPPING,
        FLAX_MODEL_FOR_PRETRAINING_MAPPING,
        FLAX_MODEL_FOR_QUESTION_ANSWERING_MAPPING,
        FLAX_MODEL_FOR_SEQ_TO_SEQ_CAUSAL_LM_MAPPING,
        FLAX_MODEL_FOR_SEQUENCE_CLASSIFICATION_MAPPING,
        FLAX_MODEL_FOR_SPEECH_SEQ_2_SEQ_MAPPING,
        FLAX_MODEL_FOR_TOKEN_CLASSIFICATION_MAPPING,
        FLAX_MODEL_FOR_VISION_2_SEQ_MAPPING,
        FLAX_MODEL_MAPPING,
        FlaxAutoModel,
        FlaxAutoModelForCausalLM,
        FlaxAutoModelForImageClassification,
        FlaxAutoModelForMaskedLM,
        FlaxAutoModelForMultipleChoice,
        FlaxAutoModelForNextSentencePrediction,
        FlaxAutoModelForPreTraining,
        FlaxAutoModelForQuestionAnswering,
        FlaxAutoModelForSeqaSeqLM,
        FlaxAutoModelForSequenceClassification,
        FlaxAutoModelForSpeechSeqaSeq,
        FlaxAutoModelForTokenClassification,
        FlaxAutoModelForVisionaSeq,
    )
  
  else:
   import sys
  
   SCREAMING_SNAKE_CASE__				:    int         =    _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)
  
  
  
  
  
  
style_context: 
  
  
  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() = }')
  
  
  
  
  
  