code: 
  
  
  from itertools import count
  from math import asin, pi, sqrt
  
  
  
  def   SCREAMING_SNAKE_CASE__						(							snake_case_	)			->							float:
  				return (
  				    (1 - 2 * point) * sqrt(point - point**2	) + 2 * point + asin(sqrt(1 - point	)	)
  				) / 4
  
  
  
  def   SCREAMING_SNAKE_CASE__						(							snake_case_	)			->							float:
  				A__     :							Optional[int]   				=(circles_number + 1 - sqrt(2 * circles_number	)) / (
  				    2 * (circles_number**2 + 1)
  				)
  				A__     :							Union[str, Any]   				=circles_number * intersection_y
  
  				A__     :							int   				=intersection_x * intersection_y / 2
  				A__     :							Dict   				=circle_bottom_arc_integral(
  				    1 / 2	) - circle_bottom_arc_integral(snake_case_	)
  
  				return triangle_area + concave_region_area
  
  
  
  def   SCREAMING_SNAKE_CASE__						(							snake_case_ = 1 / 1_0_0_0	)			->							int:
  				A__     :							Optional[Any]   				=(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: 
  
  
  import argparse
  import collections
  from pathlib import Path
  
  import torch
  from torch.serialization import default_restore_location
  
  from transformers import BertConfig, DPRConfig, DPRContextEncoder, DPRQuestionEncoder, DPRReader
  
  
  __lowerCamelCase       :       Optional[Any]				   =			collections.namedtuple(
      "CheckpointState", ["model_dict", "optimizer_dict", "scheduler_dict", "offset", "epoch", "encoder_params"]
  )
  
  
  
  def   SCREAMING_SNAKE_CASE__						(							snake_case_	)			->							CheckpointState:
  				print(f'Reading saved model from {model_file}'	)
  				A__     :							Optional[int]   				=torch.load(snake_case_,	map_location=lambda snake_case_,	snake_case_	: default_restore_location(snake_case_,	'''cpu'''	)	)
  				return CheckpointState(**snake_case_	)
  
  
  
  class 			a      :
  
  
  
  
  
  
  		def __init__(  self	,     __UpperCamelCase							)->			Union[str, Any]:
  						'''simple docstring'''
  
  
  						A__     :							Dict   				=src_file
  
  
  
  
  
  
  		def       lowerCAmelCase_  (  self							)->			Optional[Any]:
  						'''simple docstring'''
  
  
  						raise NotImplementedError
  
  
  
  
  
  
  		@staticmethod
  		def       lowerCAmelCase_  (  __UpperCamelCase	,     *__UpperCamelCase	,     **__UpperCamelCase							)->			"DPRState":
  						'''simple docstring'''
  
  
  						if comp_type.startswith('''c'''							):
  										return DPRContextEncoderState(*__UpperCamelCase	,     **__UpperCamelCase							)
  						if comp_type.startswith('''q'''							):
  										return DPRQuestionEncoderState(*__UpperCamelCase	,     **__UpperCamelCase							)
  						if comp_type.startswith('''r'''							):
  										return DPRReaderState(*__UpperCamelCase	,     **__UpperCamelCase							)
  						else:
  										raise ValueError('''Component type must be either \'ctx_encoder\', \'question_encoder\' or \'reader\'.'''							)
  
  
  
  
  
  
  
  class 			a      (      UpperCamelCase_   ):
  
  
  
  
  
  
  		def       lowerCAmelCase_  (  self							)->			Optional[Any]:
  						'''simple docstring'''
  
  
  						A__     :							Optional[int]   				=DPRContextEncoder(DPRConfig(**BertConfig.get_config_dict('''bert-base-uncased'''							)[0]							)							)
  						print(F'Loading DPR biencoder from {self.src_file}'							)
  						A__     :							Optional[int]   				=load_states_from_checkpoint(self.src_file							)
  						A__				,  A__     :							List[str]   				=model.ctx_encoder, '''ctx_model.'''
  						# Fix changes from https://github.com/huggingface/transformers/commit/614fef1691edb806de976756d4948ecbcd0c0ca3
  						A__     :							Optional[int]   				={'''bert_model.embeddings.position_ids''': model.ctx_encoder.bert_model.embeddings.position_ids}
  						for key, value in saved_state.model_dict.items():
  										if key.startswith(__UpperCamelCase							):
  														A__     :							int   				=key[len(__UpperCamelCase							) :]
  														if not key.startswith('''encode_proj.'''							):
  																		A__     :							Any   				='''bert_model.''' + key
  														A__     :							List[str]   				=value
  						encoder.load_state_dict(__UpperCamelCase							)
  						return model
  
  
  
  
  
  
  
  class 			a      (      UpperCamelCase_   ):
  
  
  
  
  
  
  		def       lowerCAmelCase_  (  self							)->			Dict:
  						'''simple docstring'''
  
  
  						A__     :							Union[str, Any]   				=DPRQuestionEncoder(DPRConfig(**BertConfig.get_config_dict('''bert-base-uncased'''							)[0]							)							)
  						print(F'Loading DPR biencoder from {self.src_file}'							)
  						A__     :							List[str]   				=load_states_from_checkpoint(self.src_file							)
  						A__				,  A__     :							Optional[int]   				=model.question_encoder, '''question_model.'''
  						# Fix changes from https://github.com/huggingface/transformers/commit/614fef1691edb806de976756d4948ecbcd0c0ca3
  						A__     :							Optional[Any]   				={'''bert_model.embeddings.position_ids''': model.question_encoder.bert_model.embeddings.position_ids}
  						for key, value in saved_state.model_dict.items():
  										if key.startswith(__UpperCamelCase							):
  														A__     :							List[Any]   				=key[len(__UpperCamelCase							) :]
  														if not key.startswith('''encode_proj.'''							):
  																		A__     :							Tuple   				='''bert_model.''' + key
  														A__     :							str   				=value
  						encoder.load_state_dict(__UpperCamelCase							)
  						return model
  
  
  
  
  
  
  
  class 			a      (      UpperCamelCase_   ):
  
  
  
  
  
  
  		def       lowerCAmelCase_  (  self							)->			int:
  						'''simple docstring'''
  
  
  						A__     :							Optional[int]   				=DPRReader(DPRConfig(**BertConfig.get_config_dict('''bert-base-uncased'''							)[0]							)							)
  						print(F'Loading DPR reader from {self.src_file}'							)
  						A__     :							Dict   				=load_states_from_checkpoint(self.src_file							)
  						# Fix changes from https://github.com/huggingface/transformers/commit/614fef1691edb806de976756d4948ecbcd0c0ca3
  						A__     :							Optional[Any]   				={
  						    '''encoder.bert_model.embeddings.position_ids''': model.span_predictor.encoder.bert_model.embeddings.position_ids
  						}
  						for key, value in saved_state.model_dict.items():
  										if key.startswith('''encoder.'''							) and not key.startswith('''encoder.encode_proj'''							):
  														A__     :							List[Any]   				='''encoder.bert_model.''' + key[len('''encoder.'''							) :]
  										A__     :							Optional[int]   				=value
  						model.span_predictor.load_state_dict(__UpperCamelCase							)
  						return model
  
  
  
  
  
  
  
  def   SCREAMING_SNAKE_CASE__						(							snake_case_,	snake_case_,	snake_case_	)			->							Optional[int]:
  				A__     :							Optional[int]   				=Path(snake_case_	)
  				dest_dir.mkdir(exist_ok=snake_case_	)
  
  				A__     :							Tuple   				=DPRState.from_type(snake_case_,	src_file=snake_case_	)
  				A__     :							str   				=dpr_state.load_dpr_model()
  				model.save_pretrained(snake_case_	)
  				model.from_pretrained(snake_case_	)  # sanity check
  
  
  if __name__ == "__main__":
  						__lowerCamelCase       :       Optional[Any]				   =			argparse.ArgumentParser()
  						# Required parameters
  						parser.add_argument(
  						    "--type", type=str, help="Type of the component to convert: 'ctx_encoder', 'question_encoder' or 'reader'."
  						)
  						parser.add_argument(
  						    "--src",
  						    type=str,
  						    help=(
  						        "Path to the dpr checkpoint file. They can be downloaded from the official DPR repo"
  						        " https://github.com/facebookresearch/DPR. Note that in the official repo, both encoders are stored in the"
  						        " 'retriever' checkpoints."
  						    ),
  						)
  						parser.add_argument("--dest", type=str, default=None, help="Path to the output PyTorch model directory.")
  						__lowerCamelCase       :       Tuple				   =			parser.parse_args()
  
  						__lowerCamelCase       :       Optional[Any]				   =			Path(args.src)
  						__lowerCamelCase       :       Optional[int]				   =			F"converted-{src_file.name}" if args.dest is None else args.dest
  						__lowerCamelCase       :       Optional[Any]				   =			Path(dest_dir)
  						assert src_file.exists()
  						assert (
  						    args.type is not None
  						), "Please specify the component type of the DPR model to convert: 'ctx_encoder', 'question_encoder' or 'reader'."
  						convert(args.type, src_file, dest_dir)
  
  
  
  