


'''simple docstring'''
import math
import sys


def 			a      (			__a   )  ->	int:



					'''simple docstring'''






					if number != int(__a   ):
										raise ValueError('''the value of input must be a natural number'''   )
					if number < 0:
										raise ValueError('''the value of input must not be a negative number'''   )
					if number == 0:
										return 1
					UpperCamelCase__   :str												= [-1] * (number + 1)
					UpperCamelCase__   :Optional[int]												= 0
					for i in range(1 ,					number + 1   ):
										UpperCamelCase__   :List[Any]												= sys.maxsize
										UpperCamelCase__   :int												= int(math.sqrt(__a   )   )
										for j in range(1 ,					root + 1   ):
															UpperCamelCase__   :int												= 1 + answers[i - (j**2)]
															UpperCamelCase__   :str												= min(__a ,					__a   )
										UpperCamelCase__   :Dict												= answer
					return answers[number]


if __name__ == "__main__":
		import doctest

		doctest.testmod()



'''simple docstring'''



import torch

from transformers import AutoModel





class 							__UpperCamelCase				(		torch.nn.Module					):




	def __init__(   self						,				__a="sayef/fsner-bert-base-uncased"							):

						'''simple docstring'''





						super(__a						,				self							).__init__()

						__a			:       Tuple					    =  AutoModel.from_pretrained(__a						,				return_dict=__a							)
						__a			:       int					    =  torch.nn.CosineSimilarity(3						,				1E-0_8							)
						__a			:       Union[str, Any]					    =  torch.nn.Softmax(dim=1							)




	def       __UpperCAmelCase							(   self						,				**__a							):

						'''simple docstring'''





						return self.bert(**__a							).last_hidden_state




	def       __UpperCAmelCase							(   self						,				__a							):

						'''simple docstring'''





						return token_embeddings.sum(2						,				keepdim=__a							)




	def       __UpperCAmelCase							(   self						,				__a						,				__a						,				__a=1							):

						'''simple docstring'''





						return self.softmax(T * self.cos(__a						,				__a							)							)





	def       __UpperCAmelCase							(   self						,				__a						,				__a							):

						'''simple docstring'''





						__a			:       str					    =  W_supports['sizes'].tolist()
						__a			:       Union[str, Any]					    =  W_supports['start_token_id'].item()
						__a			:       Any					    =  W_supports['end_token_id'].item()

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

						__a			:       Tuple					    =  self.BERT(**__a							)
						__a			:       str					    =  self.BERT(**__a							)

						__a			:       Any					    =  None
						__a			:       Dict					    =  None

						__a			:       Dict					    =  W_supports['input_ids'] == start_token_id
						__a			:       Union[str, Any]					    =  W_supports['input_ids'] == end_token_id

						for i, size in enumerate(__a							):
											if i == 0:
																__a			:       Optional[int]					    =  0
											else:
																__a			:       Union[str, Any]					    =  support_sizes[i - 1]

											__a			:       int					    =  S[s : s + size][start_token_masks[s : s + size]]
											__a			:       Union[str, Any]					    =  S[s : s + size][end_token_masks[s : s + size]]

											__a			:       Tuple					    =  torch.matmul(q[i]						,				s_start.T							).sum(1							).softmax(0							)
											__a			:       Dict					    =  torch.matmul(q[i]						,				s_end.T							).sum(1							).softmax(0							)

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

						return p_starts, p_ends



