






'''simple docstring'''







from math import isqrt





def 		_UpperCAmelCase   (							__A							:   int      ):
				a_		:  Dict											=      [True] * max_number
				for i in range(2						,		isqrt(max_number - 1      ) + 1      ):
								if is_prime[i]:
												for j in range(i**2						,		__A						,		__A      ):
																a_		:  str											=      False

				return [i for i in range(2						,		__A      ) if is_prime[i]]





def 		_UpperCAmelCase   (							__A							:   int = 10**8      ):
				a_		:  Tuple											=      calculate_prime_numbers(max_number // 2      )

				a_		:  Union[str, Any]											=      0
				a_		:  Any											=      0
				a_		:  Optional[Any]											=      len(__A      ) - 1
				while left <= right:
								while prime_numbers[left] * prime_numbers[right] >= max_number:
												right -= 1
								semiprimes_count += right - left + 1
								left += 1

				return semiprimes_count


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












'''simple docstring'''







import torch

from transformers import AutoModel





class 	SCREAMING_SNAKE_CASE					(					torch.nn.Module       ):






			def __init__( self      :			Optional[int]  ,						__SCREAMING_SNAKE_CASE      :			int="sayef/fsner-bert-base-uncased"					)			->			str:
							super(__SCREAMING_SNAKE_CASE  ,						self					).__init__()

							a_		:  str											=      AutoModel.from_pretrained(__SCREAMING_SNAKE_CASE  ,						return_dict=__SCREAMING_SNAKE_CASE					)
							a_		:  Optional[int]											=      torch.nn.CosineSimilarity(3  ,						1e-08					)
							a_		:  Dict											=      torch.nn.Softmax(dim=1					)






			def 			SCREAMING_SNAKE_CASE      ( self      :			str  ,						**__SCREAMING_SNAKE_CASE      :			int					)			->			str:
							return self.bert(**__SCREAMING_SNAKE_CASE					).last_hidden_state






			def 			SCREAMING_SNAKE_CASE      ( self      :			List[str]  ,						__SCREAMING_SNAKE_CASE      :			List[Any]					)			->			Optional[int]:
							return token_embeddings.sum(2  ,						keepdim=__SCREAMING_SNAKE_CASE					)






			def 			SCREAMING_SNAKE_CASE      ( self      :			List[Any]  ,						__SCREAMING_SNAKE_CASE      :			Optional[int]  ,						__SCREAMING_SNAKE_CASE      :			Union[str, Any]  ,						__SCREAMING_SNAKE_CASE      :			int=1					)			->			Dict:
							return self.softmax(T * self.cos(__SCREAMING_SNAKE_CASE  ,						__SCREAMING_SNAKE_CASE					)					)







			def 			SCREAMING_SNAKE_CASE      ( self      :			str  ,						__SCREAMING_SNAKE_CASE      :			Optional[Any]  ,						__SCREAMING_SNAKE_CASE      :			Optional[int]					)			->			Any:
							a_		:  Dict											=      W_supports['''sizes'''].tolist()
							a_		:  Tuple											=      W_supports['''start_token_id'''].item()
							a_		:  List[Any]											=      W_supports['''end_token_id'''].item()

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

							a_		:  int											=      self.BERT(**__SCREAMING_SNAKE_CASE					)
							a_		:  Any											=      self.BERT(**__SCREAMING_SNAKE_CASE					)

							a_		:  Optional[Any]											=      None
							a_		:  Tuple											=      None

							a_		:  List[str]											=      W_supports['''input_ids'''] == start_token_id
							a_		:  Dict											=      W_supports['''input_ids'''] == end_token_id

							for i, size in enumerate(__SCREAMING_SNAKE_CASE					):
											if i == 0:
															a_		:  str											=      0
											else:
															a_		:  str											=      support_sizes[i - 1]

											a_		:  Union[str, Any]											=      S[s : s + size][start_token_masks[s : s + size]]
											a_		:  Tuple											=      S[s : s + size][end_token_masks[s : s + size]]

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

											if p_starts is not None:
															a_		:  Any											=      torch.vstack((p_starts, p_start)					)
															a_		:  Dict											=      torch.vstack((p_ends, p_end)					)
											else:
															a_		:  Optional[int]											=      p_start
															a_		:  List[Any]											=      p_end

							return p_starts, p_ends




