

"""simple docstring"""





import math
def 	__lowerCAmelCase						(		__UpperCamelCase      :			int    ):


						'''simple docstring'''






						snake_case_   : List[str]						=			[True] * n
						snake_case_   : Dict						=			False
						snake_case_   : Any						=			False
						snake_case_   : int						=			True

						for i in range(3					, int(n**0.5 + 1    )					, 2    ):
												snake_case_   : Tuple						=			i * 2
												while index < n:
																		snake_case_   : Dict						=			False
																		snake_case_   : Any						=			index + i

						snake_case_   : int						=			[2]

						for i in range(3					, _lowerCAmelCase					, 2    ):
												if is_prime[i]:
																		primes.append(_lowerCAmelCase    )

						return primes
def 	__lowerCAmelCase						(		__UpperCamelCase      :			int = 9_9_9_9_6_6_6_6_3_3_3_3    ):


						'''simple docstring'''






						snake_case_   : Union[str, Any]						=			math.floor(math.sqrt(_lowerCAmelCase    )    ) + 1_0_0
						snake_case_   : Union[str, Any]						=			prime_sieve(_lowerCAmelCase    )

						snake_case_   : List[str]						=			0
						snake_case_   : List[Any]						=			0
						snake_case_   : Any						=			primes[prime_index]

						while (last_prime**2) <= limit:
												snake_case_   : Optional[Any]						=			primes[prime_index + 1]

												snake_case_   : int						=			last_prime**2
												snake_case_   : Optional[int]						=			next_prime**2

												# Get numbers divisible by lps(current)
												snake_case_   : int						=			lower_bound + last_prime
												while upper_bound > current <= limit:
																		matches_sum += current
																		current += last_prime

												# Reset the upper_bound
												while (upper_bound - next_prime) > limit:
																		upper_bound -= next_prime

												# Add the numbers divisible by ups(current)
												snake_case_   : Optional[int]						=			upper_bound - next_prime
												while current > lower_bound:
																		matches_sum += current
																		current -= next_prime

												# Remove the numbers divisible by both ups and lps
												snake_case_   : List[Any]						=			0
												while upper_bound > current <= limit:
																		if current <= lower_bound:
																								# Increment the current number
																								current += last_prime * next_prime
																								continue

																		if current > limit:
																								break

																		# Remove twice since it was added by both ups and lps
																		matches_sum -= current * 2

																		# Increment the current number
																		current += last_prime * next_prime

												# Setup for next pair
												snake_case_   : Optional[Any]						=			next_prime
												prime_index += 1

						return matches_sum


if __name__ == "__main__":
					print(solution())






"""simple docstring"""





import unittest

import numpy as np

from transformers import RobertaPreLayerNormConfig, is_flax_available
from transformers.testing_utils import require_flax, slow

from ...test_modeling_flax_common import FlaxModelTesterMixin, floats_tensor, ids_tensor, random_attention_mask


if is_flax_available():
					import jax.numpy as jnp

					from transformers.models.roberta_prelayernorm.modeling_flax_roberta_prelayernorm import (
					    FlaxRobertaPreLayerNormForCausalLM,
					    FlaxRobertaPreLayerNormForMaskedLM,
					    FlaxRobertaPreLayerNormForMultipleChoice,
					    FlaxRobertaPreLayerNormForQuestionAnswering,
					    FlaxRobertaPreLayerNormForSequenceClassification,
					    FlaxRobertaPreLayerNormForTokenClassification,
					    FlaxRobertaPreLayerNormModel,
					)



class    _lowerCAmelCase    (				unittest.TestCase		):





		"""simple docstring"""






		def __init__(					self							,    _lowercase							,    _lowercase=1_3							,    _lowercase=7							,    _lowercase=True							,    _lowercase=True							,    _lowercase=True							,    _lowercase=True							,    _lowercase=9_9							,    _lowercase=3_2							,    _lowercase=5							,    _lowercase=4							,    _lowercase=3_7							,    _lowercase="gelu"							,    _lowercase=0.1							,    _lowercase=0.1							,    _lowercase=5_1_2							,    _lowercase=1_6							,    _lowercase=2							,    _lowercase=0.02							,    _lowercase=4							,    ) ->						Union[str, Any]:







								'''simple docstring'''

								snake_case_   : Optional[int]						=			parent
								snake_case_   : Dict						=			batch_size
								snake_case_   : Any						=			seq_length
								snake_case_   : Tuple						=			is_training
								snake_case_   : Dict						=			use_attention_mask
								snake_case_   : int						=			use_token_type_ids
								snake_case_   : List[Any]						=			use_labels
								snake_case_   : List[str]						=			vocab_size
								snake_case_   : str						=			hidden_size
								snake_case_   : Optional[Any]						=			num_hidden_layers
								snake_case_   : List[Any]						=			num_attention_heads
								snake_case_   : Any						=			intermediate_size
								snake_case_   : Optional[Any]						=			hidden_act
								snake_case_   : Tuple						=			hidden_dropout_prob
								snake_case_   : List[Any]						=			attention_probs_dropout_prob
								snake_case_   : int						=			max_position_embeddings
								snake_case_   : Dict						=			type_vocab_size
								snake_case_   : Dict						=			type_sequence_label_size
								snake_case_   : Optional[Any]						=			initializer_range
								snake_case_   : Tuple						=			num_choices





		def    UpperCAmelCase__							(					self   ) ->						Union[str, Any]:







								'''simple docstring'''

								snake_case_   : int						=			ids_tensor([self.batch_size, self.seq_length]							,    self.vocab_size   )

								snake_case_   : Tuple						=			None
								if self.use_attention_mask:
														snake_case_   : Optional[Any]						=			random_attention_mask([self.batch_size, self.seq_length]   )

								snake_case_   : List[str]						=			None
								if self.use_token_type_ids:
														snake_case_   : int						=			ids_tensor([self.batch_size, self.seq_length]							,    self.type_vocab_size   )

								snake_case_   : Tuple						=			RobertaPreLayerNormConfig(
								    vocab_size=self.vocab_size							,    hidden_size=self.hidden_size							,    num_hidden_layers=self.num_hidden_layers							,    num_attention_heads=self.num_attention_heads							,    intermediate_size=self.intermediate_size							,    hidden_act=self.hidden_act							,    hidden_dropout_prob=self.hidden_dropout_prob							,    attention_probs_dropout_prob=self.attention_probs_dropout_prob							,    max_position_embeddings=self.max_position_embeddings							,    type_vocab_size=self.type_vocab_size							,    is_decoder=_lowercase							,    initializer_range=self.initializer_range							,    )

								return config, input_ids, token_type_ids, attention_mask





		def    UpperCAmelCase__							(					self   ) ->						Any:







								'''simple docstring'''

								snake_case_   : Any						=			self.prepare_config_and_inputs()
								snake_case_			,		snake_case_			,		snake_case_			,		snake_case_   : List[Any]						=			config_and_inputs
								snake_case_   : int						=			{"""input_ids""": input_ids, """token_type_ids""": token_type_ids, """attention_mask""": attention_mask}
								return config, inputs_dict





		def    UpperCAmelCase__							(					self   ) ->						str:







								'''simple docstring'''

								snake_case_   : Tuple						=			self.prepare_config_and_inputs()
								snake_case_			,		snake_case_			,		snake_case_			,		snake_case_   : Any						=			config_and_inputs

								snake_case_   : Union[str, Any]						=			True
								snake_case_   : List[Any]						=			floats_tensor([self.batch_size, self.seq_length, self.hidden_size]   )
								snake_case_   : Optional[int]						=			ids_tensor([self.batch_size, self.seq_length]							,    vocab_size=2   )

								return (
								    config,
								    input_ids,
								    token_type_ids,
								    encoder_hidden_states,
								    encoder_attention_mask,
								)




@require_flax
# Copied from tests.models.roberta.test_modelling_flax_roberta.FlaxRobertaPreLayerNormModelTest with ROBERTA->ROBERTA_PRELAYERNORM,Roberta->RobertaPreLayerNorm,roberta-base->andreasmadsen/efficient_mlm_m0.40
class    _lowerCAmelCase    (				SCREAMING_SNAKE_CASE__  ,				unittest.TestCase		):





		"""simple docstring"""






		_lowerCamelCase			  =       True

		_lowerCamelCase			  =       (
		    (
		        FlaxRobertaPreLayerNormModel,
		        FlaxRobertaPreLayerNormForCausalLM,
		        FlaxRobertaPreLayerNormForMaskedLM,
		        FlaxRobertaPreLayerNormForSequenceClassification,
		        FlaxRobertaPreLayerNormForTokenClassification,
		        FlaxRobertaPreLayerNormForMultipleChoice,
		        FlaxRobertaPreLayerNormForQuestionAnswering,
		    )
		    if is_flax_available()
		    else ()
		)





		def    UpperCAmelCase__							(					self   ) ->						int:







								'''simple docstring'''

								snake_case_   : Any						=			FlaxRobertaPreLayerNormModelTester(self   )





		@slow
		def    UpperCAmelCase__							(					self   ) ->						Tuple:







								'''simple docstring'''

								for model_class_name in self.all_model_classes:
														snake_case_   : Tuple						=			model_class_name.from_pretrained("""andreasmadsen/efficient_mlm_m0.40"""							,    from_pt=_lowercase   )
														snake_case_   : Tuple						=			model(np.ones((1, 1)   )   )
														self.assertIsNotNone(_lowercase   )




@require_flax
class    _lowerCAmelCase    (				unittest.TestCase		):





		"""simple docstring"""






		@slow
		def    UpperCAmelCase__							(					self   ) ->						Union[str, Any]:







								'''simple docstring'''

								snake_case_   : Union[str, Any]						=			FlaxRobertaPreLayerNormForMaskedLM.from_pretrained("""andreasmadsen/efficient_mlm_m0.40"""							,    from_pt=_lowercase   )

								snake_case_   : List[str]						=			np.array([[0, 3_1_4_1_4, 2_3_2, 3_2_8, 7_4_0, 1_1_4_0, 1_2_6_9_5, 6_9, 4_6_0_7_8, 1_5_8_8, 2]]							,    dtype=jnp.intaa   )
								snake_case_   : str						=			model(_lowercase   )[0]
								snake_case_   : int						=			[1, 1_1, 5_0_2_6_5]
								self.assertEqual(list(output.shape   )							,    _lowercase   )
								# compare the actual values for a slice.
								snake_case_   : Tuple						=			np.array(
								    [[[40.4880, 18.0199, -5.2367], [-1.8877, -4.0885, 10.7085], [-2.2613, -5.6110, 7.2665]]]							,    dtype=np.floataa   )
								self.assertTrue(np.allclose(output[:, :3, :3]							,    _lowercase							,    atol=1E-4   )   )





		@slow
		def    UpperCAmelCase__							(					self   ) ->						int:







								'''simple docstring'''

								snake_case_   : Any						=			FlaxRobertaPreLayerNormModel.from_pretrained("""andreasmadsen/efficient_mlm_m0.40"""							,    from_pt=_lowercase   )

								snake_case_   : Dict						=			np.array([[0, 3_1_4_1_4, 2_3_2, 3_2_8, 7_4_0, 1_1_4_0, 1_2_6_9_5, 6_9, 4_6_0_7_8, 1_5_8_8, 2]]							,    dtype=jnp.intaa   )
								snake_case_   : Any						=			model(_lowercase   )[0]
								# compare the actual values for a slice.
								snake_case_   : Optional[Any]						=			np.array(
								    [[[0.0208, -0.0356, 0.0237], [-0.1569, -0.0411, -0.2626], [0.1879, 0.0125, -0.0089]]]							,    dtype=np.floataa   )
								self.assertTrue(np.allclose(output[:, :3, :3]							,    _lowercase							,    atol=1E-4   )   )

