






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


UpperCAmelCase_					:		Any           = collections.namedtuple(
    '''CheckpointState''', ['''model_dict''', '''optimizer_dict''', '''scheduler_dict''', '''offset''', '''epoch''', '''encoder_params''']
)

def   SCREAMING_SNAKE_CASE_				(				__magic_name__   :    Optional[Any]   )						->     Optional[Any]:






	"""simple docstring"""



	print(f"""Reading saved model from {model_file}"""   )
	UpperCamelCase	:Dict		=      torch.load(UpperCAmelCase_      ,     map_location=lambda __magic_name__      ,     __magic_name__   : default_restore_location(UpperCAmelCase_      ,     """cpu"""   )   )
	return CheckpointState(**UpperCAmelCase_   )

class        _SCREAMING_SNAKE_CASE			:





	def __init__(						self							:   str					,    __lowerCamelCase							:   Path      ):
		UpperCamelCase	:Union[str, Any]		=      src_file





	def 		_A					(						self							:   Any      ):
		raise NotImplementedError





	@staticmethod
	def 		_A					(						__lowerCamelCase							:   str					,    *__lowerCamelCase							:   Optional[Any]					,    **__lowerCamelCase							:   List[Any]      ):
		if comp_type.startswith("""c"""      ):
			return DPRContextEncoderState(*__lowerCamelCase					,    **__lowerCamelCase      )
		if comp_type.startswith("""q"""      ):
			return DPRQuestionEncoderState(*__lowerCamelCase					,    **__lowerCamelCase      )
		if comp_type.startswith("""r"""      ):
			return DPRReaderState(*__lowerCamelCase					,    **__lowerCamelCase      )
		else:
			raise ValueError("""Component type must be either 'ctx_encoder', 'question_encoder' or 'reader'."""      )

class        _SCREAMING_SNAKE_CASE			(     lowercase__ ):





	def 		_A					(						self							:   Optional[Any]      ):
		UpperCamelCase	:Dict		=      DPRContextEncoder(DPRConfig(**BertConfig.get_config_dict("""bert-base-uncased"""      )[0]      )      )
		print(F"""Loading DPR biencoder from {self.src_file}"""      )
		UpperCamelCase	:Union[str, Any]		=      load_states_from_checkpoint(self.src_file      )
		UpperCamelCase	, UpperCamelCase	:Dict		=      model.ctx_encoder, """ctx_model."""
		# Fix changes from https://github.com/huggingface/transformers/commit/614fef1691edb806de976756d4948ecbcd0c0ca3
		UpperCamelCase	:Tuple		=      {"""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(__lowerCamelCase      ):
				UpperCamelCase	:Optional[int]		=      key[len(__lowerCamelCase      ) :]
				if not key.startswith("""encode_proj."""      ):
					UpperCamelCase	:List[str]		=      """bert_model.""" + key
				UpperCamelCase	:int		=      value
		encoder.load_state_dict(__lowerCamelCase      )
		return model

class        _SCREAMING_SNAKE_CASE			(     lowercase__ ):





	def 		_A					(						self							:   List[Any]      ):
		UpperCamelCase	:List[str]		=      DPRQuestionEncoder(DPRConfig(**BertConfig.get_config_dict("""bert-base-uncased"""      )[0]      )      )
		print(F"""Loading DPR biencoder from {self.src_file}"""      )
		UpperCamelCase	:Tuple		=      load_states_from_checkpoint(self.src_file      )
		UpperCamelCase	, UpperCamelCase	:int		=      model.question_encoder, """question_model."""
		# Fix changes from https://github.com/huggingface/transformers/commit/614fef1691edb806de976756d4948ecbcd0c0ca3
		UpperCamelCase	: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(__lowerCamelCase      ):
				UpperCamelCase	:Tuple		=      key[len(__lowerCamelCase      ) :]
				if not key.startswith("""encode_proj."""      ):
					UpperCamelCase	:List[Any]		=      """bert_model.""" + key
				UpperCamelCase	:List[str]		=      value
		encoder.load_state_dict(__lowerCamelCase      )
		return model

class        _SCREAMING_SNAKE_CASE			(     lowercase__ ):





	def 		_A					(						self							:   Dict      ):
		UpperCamelCase	:Any		=      DPRReader(DPRConfig(**BertConfig.get_config_dict("""bert-base-uncased"""      )[0]      )      )
		print(F"""Loading DPR reader from {self.src_file}"""      )
		UpperCamelCase	:Dict		=      load_states_from_checkpoint(self.src_file      )
		# Fix changes from https://github.com/huggingface/transformers/commit/614fef1691edb806de976756d4948ecbcd0c0ca3
		UpperCamelCase	: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"""      ):
				UpperCamelCase	:int		=      """encoder.bert_model.""" + key[len("""encoder."""      ) :]
			UpperCamelCase	:Optional[Any]		=      value
		model.span_predictor.load_state_dict(__lowerCamelCase      )
		return model

def   SCREAMING_SNAKE_CASE_				(				__magic_name__   :    Any      ,     __magic_name__   :    Dict      ,     __magic_name__   :    List[Any]   )						->     Optional[Any]:






	"""simple docstring"""



	UpperCamelCase	:Any		=      Path(UpperCAmelCase_   )
	dest_dir.mkdir(exist_ok=UpperCAmelCase_   )

	UpperCamelCase	:Dict		=      DPRState.from_type(UpperCAmelCase_      ,     src_file=UpperCAmelCase_   )
	UpperCamelCase	:List[Any]		=      dpr_state.load_dpr_model()
	model.save_pretrained(UpperCAmelCase_   )
	model.from_pretrained(UpperCAmelCase_   )  # sanity check


if __name__ == "__main__":
	UpperCAmelCase_					:		List[str]           = 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.''')
	UpperCAmelCase_					:		Union[str, Any]           = parser.parse_args()

	UpperCAmelCase_					:		Any           = Path(args.src)
	UpperCAmelCase_					:		Union[str, Any]           = F'''converted-{src_file.name}''' if args.dest is None else args.dest
	UpperCAmelCase_					:		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)






from itertools import count
from math import asin, pi, sqrt
def 							__lowerCAmelCase			(UpperCAmelCase_		):
    return (
        (1 - 2 * point) * sqrt(point - point**2		) + 2 * point + asin(sqrt(1 - point		)		)
    ) / 4
def 							__lowerCAmelCase			(UpperCAmelCase_		):
    a__  			=							(circles_number + 1 - sqrt(2 * circles_number		)) / (
        2 * (circles_number**2 + 1)
    )
    a__  			=							circles_number * intersection_y

    a__  			=							intersection_x * intersection_y / 2
    a__  			=							circle_bottom_arc_integral(
        1 / 2		) - circle_bottom_arc_integral(UpperCAmelCase_		)

    return triangle_area + concave_region_area
def 							__lowerCAmelCase			(UpperCAmelCase_ = 1 / 1_000		):
    a__  			=							(1 - pi / 4) / 4

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

    return -1


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






