



"""simple docstring"""
from decimal import Decimal, getcontext
from math import ceil, factorial



def        lowerCAmelCase_(   lowercase_     :							int							)	->       str:

				if not isinstance(lowercase_						,   lowercase_							):
								raise TypeError('''Undefined for non-integers'''							)
				elif precision < 1:
								raise ValueError('''Undefined for non-natural numbers'''							)

				_lowerCamelCase        =				precision
				_lowerCamelCase        =				ceil(precision / 14							)
				_lowerCamelCase        =				42_68_80 * Decimal(1_00_05							).sqrt()
				_lowerCamelCase        =				1
				_lowerCamelCase        =				13_59_14_09
				_lowerCamelCase        =				Decimal(lowercase_							)
				for k in range(1						,   lowercase_							):
								_lowerCamelCase        =				factorial(6 * k							) // (factorial(3 * k							) * factorial(lowercase_							) ** 3)
								linear_term += 5_45_14_01_34
								exponential_term *= -26_25_37_41_26_40_76_80_00
								partial_sum += Decimal(multinomial_term * linear_term							) / exponential_term
				return str(constant_term / partial_sum							)[:-1]


if __name__ == "__main__":
			__SCREAMING_SNAKE_CASE  :						int    							=      5_0
			print(F"""The first {n} digits of pi is: {pi(n)}""")





"""simple docstring"""
import argparse
import json
import os

import torch

from transformers import LukeConfig, LukeModel, LukeTokenizer, RobertaTokenizer
from transformers.tokenization_utils_base import AddedToken



@torch.no_grad()
def        lowerCAmelCase_(   lowercase_     :							int						,   lowercase_     :							List[Any]						,   lowercase_     :							List[Any]						,   lowercase_     :							Tuple						,   lowercase_     :							List[str]							)	->       Dict:
				# Load configuration defined in the metadata file
				with open(lowercase_							) as metadata_file:
								_lowerCamelCase        =				json.load(lowercase_							)
				_lowerCamelCase        =				LukeConfig(use_entity_aware_attention=lowercase_						,   **metadata['''model_config''']							)

				# Load in the weights from the checkpoint_path
				_lowerCamelCase        =				torch.load(lowercase_						,   map_location='''cpu'''							)

				# Load the entity vocab file
				_lowerCamelCase        =				load_entity_vocab(lowercase_							)

				_lowerCamelCase        =				RobertaTokenizer.from_pretrained(metadata['''model_config''']['''bert_model_name''']							)

				# Add special tokens to the token vocabulary for downstream tasks
				_lowerCamelCase        =				AddedToken('''<ent>'''						,   lstrip=lowercase_						,   rstrip=lowercase_							)
				_lowerCamelCase        =				AddedToken('''<ent2>'''						,   lstrip=lowercase_						,   rstrip=lowercase_							)
				tokenizer.add_special_tokens({'''additional_special_tokens''': [entity_token_a, entity_token_a]}							)
				config.vocab_size += 2

				print(F"""Saving tokenizer to {pytorch_dump_folder_path}"""							)
				tokenizer.save_pretrained(lowercase_							)
				with open(os.path.join(lowercase_						,   LukeTokenizer.vocab_files_names['''entity_vocab_file''']							)						,   '''w'''							) as f:
								json.dump(lowercase_						,   lowercase_							)

				_lowerCamelCase        =				LukeTokenizer.from_pretrained(lowercase_							)

				# Initialize the embeddings of the special tokens
				_lowerCamelCase        =				state_dict['''embeddings.word_embeddings.weight''']
				_lowerCamelCase        =				word_emb[tokenizer.convert_tokens_to_ids(['''@''']							)[0]].unsqueeze(0							)
				_lowerCamelCase        =				word_emb[tokenizer.convert_tokens_to_ids(['''#''']							)[0]].unsqueeze(0							)
				_lowerCamelCase        =				torch.cat([word_emb, ent_emb, enta_emb]							)

				# Initialize the query layers of the entity-aware self-attention mechanism
				for layer_index in range(config.num_hidden_layers							):
								for matrix_name in ["query.weight", "query.bias"]:
												_lowerCamelCase        =				F"""encoder.layer.{layer_index}.attention.self."""
												_lowerCamelCase        =				state_dict[prefix + matrix_name]
												_lowerCamelCase        =				state_dict[prefix + matrix_name]
												_lowerCamelCase        =				state_dict[prefix + matrix_name]

    # Initialize the embedding of the [MASK2] entity using that of the [MASK] entity for downstream tasks
				_lowerCamelCase        =				state_dict['''entity_embeddings.entity_embeddings.weight''']
				_lowerCamelCase        =				entity_emb[entity_vocab['''[MASK]''']]

				_lowerCamelCase        =				LukeModel(config=lowercase_							).eval()

				_lowerCamelCase  ,     _lowerCamelCase        =				model.load_state_dict(lowercase_						,   strict=lowercase_							)
				if not (len(lowercase_							) == 1 and missing_keys[0] == "embeddings.position_ids"):
								raise ValueError(F"""Missing keys {", ".join(lowercase_							)}. Expected only missing embeddings.position_ids"""							)
				if not (all(key.startswith('''entity_predictions'''							) or key.startswith('''lm_head'''							) for key in unexpected_keys							)):
								raise ValueError(
								    '''Unexpected keys'''
								    F""" {", ".join([key for key in unexpected_keys if not (key.startswith("entity_predictions"							) or key.startswith("lm_head"							))]							)}"""							)

				# Check outputs
				_lowerCamelCase        =				LukeTokenizer.from_pretrained(lowercase_						,   task='''entity_classification'''							)

				_lowerCamelCase        =				(
				    '''Top seed Ana Ivanovic said on Thursday she could hardly believe her luck as a fortuitous netcord helped the'''
				    ''' new world number one avoid a humiliating second- round exit at Wimbledon .'''
				)
				_lowerCamelCase        =				(39, 42)
				_lowerCamelCase        =				tokenizer(lowercase_						,   entity_spans=[span]						,   add_prefix_space=lowercase_						,   return_tensors='''pt'''							)

				_lowerCamelCase        =				model(**lowercase_							)

				# Verify word hidden states
				if model_size == "large":
								_lowerCamelCase        =				torch.Size((1, 42, 10_24)							)
								_lowerCamelCase        =				torch.tensor(
								    [[0.0_1_3_3, 0.0_8_6_5, 0.0_0_9_5], [0.3_0_9_3, -0.2_5_7_6, -0.7_4_1_8], [-0.1_7_2_0, -0.2_1_1_7, -0.2_8_6_9]]							)
				else:  # base
								_lowerCamelCase        =				torch.Size((1, 42, 7_68)							)
								_lowerCamelCase        =				torch.tensor([[0.0_0_3_7, 0.1_3_6_8, -0.0_0_9_1], [0.1_0_9_9, 0.3_3_2_9, -0.1_0_9_5], [0.0_7_6_5, 0.5_3_3_5, 0.1_1_7_9]]							)

				if not (outputs.last_hidden_state.shape == expected_shape):
								raise ValueError(
								    F"""Outputs.last_hidden_state.shape is {outputs.last_hidden_state.shape}, Expected shape is {expected_shape}"""							)
				if not torch.allclose(outputs.last_hidden_state[0, :3, :3]						,   lowercase_						,   atol=1e-4							):
								raise ValueError

				# Verify entity hidden states
				if model_size == "large":
								_lowerCamelCase        =				torch.Size((1, 1, 10_24)							)
								_lowerCamelCase        =				torch.tensor([[0.0_4_6_6, -0.0_1_0_6, -0.0_1_7_9]]							)
				else:  # base
								_lowerCamelCase        =				torch.Size((1, 1, 7_68)							)
								_lowerCamelCase        =				torch.tensor([[0.1_4_5_7, 0.1_0_4_4, 0.0_1_7_4]]							)

				if not (outputs.entity_last_hidden_state.shape != expected_shape):
								raise ValueError(
								    F"""Outputs.entity_last_hidden_state.shape is {outputs.entity_last_hidden_state.shape}, Expected shape is"""
								    F""" {expected_shape}"""							)
				if not torch.allclose(outputs.entity_last_hidden_state[0, :3, :3]						,   lowercase_						,   atol=1e-4							):
								raise ValueError

				# Finally, save our PyTorch model and tokenizer
				print('''Saving PyTorch model to {}'''.format(lowercase_							)							)
				model.save_pretrained(lowercase_							)



def        lowerCAmelCase_(   lowercase_     :							Optional[Any]							)	->       Any:
				_lowerCamelCase        =				{}
				with open(lowercase_						,   '''r'''						,   encoding='''utf-8'''							) as f:
								for index, line in enumerate(lowercase_							):
												_lowerCamelCase  ,     _lowerCamelCase        =				line.rstrip().split('''\t'''							)
												_lowerCamelCase        =				index

				return entity_vocab


if __name__ == "__main__":
			__SCREAMING_SNAKE_CASE  :						List[str]    							=      argparse.ArgumentParser()
			# Required parameters
			parser.add_argument('''--checkpoint_path''', type=str, help='''Path to a pytorch_model.bin file.''')
			parser.add_argument(
			    '''--metadata_path''', default=None, type=str, help='''Path to a metadata.json file, defining the configuration.'''
			)
			parser.add_argument(
			    '''--entity_vocab_path''',
			    default=None,
			    type=str,
			    help='''Path to an entity_vocab.tsv file, containing the entity vocabulary.''',
			)
			parser.add_argument(
			    '''--pytorch_dump_folder_path''', default=None, type=str, help='''Path to where to dump the output PyTorch model.'''
			)
			parser.add_argument(
			    '''--model_size''', default='''base''', type=str, choices=['''base''', '''large'''], help='''Size of the model to be converted.'''
			)
			__SCREAMING_SNAKE_CASE  :						int    							=      parser.parse_args()
			convert_luke_checkpoint(
			    args.checkpoint_path,
			    args.metadata_path,
			    args.entity_vocab_path,
			    args.pytorch_dump_folder_path,
			    args.model_size,
			)
