






import torch

from transformers import AutoModel





class 	snake_case__ (							torch.nn.Module				):
	def __init__(    self      ,       lowerCAmelCase__="sayef/fsner-bert-base-uncased"			)							->				Dict:
							super(lowerCAmelCase__      ,       self			).__init__()

							__magic_name__      :       List[Any]       						= AutoModel.from_pretrained(lowerCAmelCase__      ,       return_dict=lowerCAmelCase__			)
							__magic_name__      :       int       						= torch.nn.CosineSimilarity(3      ,       1e-0_8			)
							__magic_name__      :       str       						= torch.nn.Softmax(dim=1			)
	def       __magic_name__    (    self      ,       **lowerCAmelCase__			)							->				Union[str, Any]:
							return self.bert(**lowerCAmelCase__			).last_hidden_state
	def       __magic_name__    (    self      ,       lowerCAmelCase__			)							->				Union[str, Any]:
							return token_embeddings.sum(2      ,       keepdim=lowerCAmelCase__			)
	def       __magic_name__    (    self      ,       lowerCAmelCase__      ,       lowerCAmelCase__      ,       lowerCAmelCase__=1			)							->				Optional[int]:
							return self.softmax(T * self.cos(lowerCAmelCase__      ,       lowerCAmelCase__			)			)







	def       __magic_name__    (    self      ,       lowerCAmelCase__      ,       lowerCAmelCase__			)							->				int:
							__magic_name__      :       Optional[int]       						= W_supports["""sizes"""].tolist()
							__magic_name__      :       Union[str, Any]       						= W_supports["""start_token_id"""].item()
							__magic_name__      :       Optional[Any]       						= W_supports["""end_token_id"""].item()

							del W_supports["sizes"]
							del W_supports["start_token_id"]
							del W_supports["end_token_id"]

							__magic_name__      :       List[str]       						= self.BERT(**lowerCAmelCase__			)
							__magic_name__      :       Tuple       						= self.BERT(**lowerCAmelCase__			)

							__magic_name__      :       str       						= None
							__magic_name__      :       Optional[int]       						= None

							__magic_name__      :       List[str]       						= W_supports["""input_ids"""] == start_token_id
							__magic_name__      :       Tuple       						= W_supports["""input_ids"""] == end_token_id

							for i, size in enumerate(lowerCAmelCase__			):
													if i == 0:
																			__magic_name__      :       Optional[Any]       						= 0
													else:
																			__magic_name__      :       Tuple       						= support_sizes[i - 1]

													__magic_name__      :       int       						= S[s : s + size][start_token_masks[s : s + size]]
													__magic_name__      :       int       						= S[s : s + size][end_token_masks[s : s + size]]

													__magic_name__      :       Optional[Any]       						= torch.matmul(q[i]      ,       s_start.T			).sum(1			).softmax(0			)
													__magic_name__      :       Union[str, Any]       						= torch.matmul(q[i]      ,       s_end.T			).sum(1			).softmax(0			)

													if p_starts is not None:
																			__magic_name__      :       List[Any]       						= torch.vstack((p_starts, p_start)			)
																			__magic_name__      :       List[Any]       						= torch.vstack((p_ends, p_end)			)
													else:
																			__magic_name__      :       str       						= p_start
																			__magic_name__      :       str       						= p_end

							return p_starts, p_ends








from decimal import Decimal, getcontext
from math import ceil, factorial

def    UpperCamelCase						(	_A			):






						"""simple docstring"""







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

						__magic_name__      :       Dict       						= precision
						__magic_name__      :       str       						= ceil(precision / 14			)
						__magic_name__      :       List[str]       						= 426880 * Decimal(10005			).sqrt()
						__magic_name__      :       List[Any]       						= 1
						__magic_name__      :       Dict       						= 13591409
						__magic_name__      :       Tuple       						= Decimal(_A			)
						for k in range(1,   _A			):
												__magic_name__      :       List[Any]       						= factorial(6 * k			) // (factorial(3 * k			) * factorial(_A			) ** 3)
												linear_term += 545140134
												exponential_term *= -262537412640768000
												partial_sum += Decimal(multinomial_term * linear_term			) / exponential_term
						return str(constant_term / partial_sum			)[:-1]


if __name__ == "__main__":
		__magic_name__:					Tuple							=     50
		print(F"""The first {n} digits of pi is: {pi(n)}""")
