


from math import isqrt, loga
def 			_a (      SCREAMING_SNAKE_CASE     ):


		"""simple docstring"""




		lowercase__            =      [True] * max_number
		for i in range(2						,				isqrt(max_number - 1     ) + 1     ):
				if is_prime[i]:
						for j in range(i**2						,				SCREAMING_SNAKE_CASE						,				SCREAMING_SNAKE_CASE     ):
								lowercase__            =      False

		return [i for i in range(2						,				SCREAMING_SNAKE_CASE     ) if is_prime[i]]
def 			_a (      SCREAMING_SNAKE_CASE = 80_08_00						,				SCREAMING_SNAKE_CASE = 80_08_00     ):


		"""simple docstring"""




		lowercase__            =      degree * loga(SCREAMING_SNAKE_CASE     )
		lowercase__            =      int(SCREAMING_SNAKE_CASE     )
		lowercase__            =      calculate_prime_numbers(SCREAMING_SNAKE_CASE     )

		lowercase__            =      0
		lowercase__            =      0
		lowercase__            =      len(SCREAMING_SNAKE_CASE     ) - 1
		while left < right:
				while (
				    prime_numbers[right] * loga(prime_numbers[left]     )
				    + prime_numbers[left] * loga(prime_numbers[right]     )
				    > upper_bound
				):
						right -= 1
				hybrid_integers_count += right - left
				left += 1

		return hybrid_integers_count


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






import inspect
import unittest

from transformers import DecisionTransformerConfig, is_torch_available
from transformers.testing_utils import require_torch, slow, torch_device

from ...generation.test_utils import GenerationTesterMixin
from ...test_configuration_common import ConfigTester
from ...test_modeling_common import ModelTesterMixin, floats_tensor, ids_tensor, random_attention_mask
from ...test_pipeline_mixin import PipelineTesterMixin


if is_torch_available():
			import torch

			from transformers import DecisionTransformerModel
			from transformers.models.decision_transformer.modeling_decision_transformer import (
			    DECISION_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
			)


class        _a							:

							def __init__(							self:	Tuple    ,						UpperCamelCase_:	int    ,						UpperCamelCase_:	Any=13    ,						UpperCamelCase_:	Optional[Any]=7    ,						UpperCamelCase_:	Optional[Any]=6    ,						UpperCamelCase_:	Any=17    ,						UpperCamelCase_:	str=23    ,						UpperCamelCase_:	List[Any]=11    ,						UpperCamelCase_:	Optional[int]=True    ,						)			->   List[Any]:





									"""simple docstring"""







									lowercase__            =      parent
									lowercase__            =      batch_size
									lowercase__            =      seq_length
									lowercase__            =      act_dim
									lowercase__            =      state_dim
									lowercase__            =      hidden_size
									lowercase__            =      max_length
									lowercase__            =      is_training

							def       lowerCamelCase_ (							self:	Optional[Any]							)			->   Tuple:





									"""simple docstring"""







									lowercase__            =      floats_tensor((self.batch_size, self.seq_length, self.state_dim)							)
									lowercase__            =      floats_tensor((self.batch_size, self.seq_length, self.act_dim)							)
									lowercase__            =      floats_tensor((self.batch_size, self.seq_length, 1)							)
									lowercase__            =      floats_tensor((self.batch_size, self.seq_length, 1)							)
									lowercase__            =      ids_tensor((self.batch_size, self.seq_length)    ,						vocab_size=1_000							)
									lowercase__            =      random_attention_mask((self.batch_size, self.seq_length)							)

									lowercase__            =      self.get_config()

									return (
									    config,
									    states,
									    actions,
									    rewards,
									    returns_to_go,
									    timesteps,
									    attention_mask,
									)

							def       lowerCamelCase_ (							self:	Dict							)			->   List[Any]:





									"""simple docstring"""







									return DecisionTransformerConfig(
									    batch_size=self.batch_size    ,						seq_length=self.seq_length    ,						act_dim=self.act_dim    ,						state_dim=self.state_dim    ,						hidden_size=self.hidden_size    ,						max_length=self.max_length    ,						)

							def       lowerCamelCase_ (							self:	List[str]    ,						UpperCamelCase_:	int    ,						UpperCamelCase_:	List[str]    ,						UpperCamelCase_:	Any    ,						UpperCamelCase_:	List[Any]    ,						UpperCamelCase_:	Any    ,						UpperCamelCase_:	List[Any]    ,						UpperCamelCase_:	int    ,						)			->   Dict:





									"""simple docstring"""







									lowercase__            =      DecisionTransformerModel(config=UpperCamelCase_							)
									model.to(UpperCamelCase_							)
									model.eval()
									lowercase__            =      model(UpperCamelCase_    ,						UpperCamelCase_    ,						UpperCamelCase_    ,						UpperCamelCase_    ,						UpperCamelCase_    ,						UpperCamelCase_							)

									self.parent.assertEqual(result.state_preds.shape    ,						states.shape							)
									self.parent.assertEqual(result.action_preds.shape    ,						actions.shape							)
									self.parent.assertEqual(result.return_preds.shape    ,						returns_to_go.shape							)
									self.parent.assertEqual(
									    result.last_hidden_state.shape    ,						(self.batch_size, self.seq_length * 3, self.hidden_size)							)  # seq length *3 as there are 3 modelities: states, returns and actions


							def       lowerCamelCase_ (							self:	List[Any]							)			->   str:





									"""simple docstring"""







									lowercase__            =      self.prepare_config_and_inputs()
									(
									    (
									    lowercase__
									)     ,		(
									    lowercase__
									)     ,		(
									    lowercase__
									)     ,		(
									    lowercase__
									)     ,		(
									    lowercase__
									)     ,		(
									    lowercase__
									)     ,		(
									    lowercase__
									)     ,		
									)            =      config_and_inputs
									lowercase__            =      {
									    '''states''': states,
									    '''actions''': actions,
									    '''rewards''': rewards,
									    '''returns_to_go''': returns_to_go,
									    '''timesteps''': timesteps,
									    '''attention_mask''': attention_mask,
									}
									return config, inputs_dict


@require_torch
class        _a							(			UpperCamelCase__     ,	UpperCamelCase__     ,	UpperCamelCase__     ,	unittest.TestCase			):
							_lowercase	:			str        = (DecisionTransformerModel,) if is_torch_available() else ()
							_lowercase	:			List[str]        = ()
							_lowercase	:			List[Any]        = {'''feature-extraction''': DecisionTransformerModel} if is_torch_available() else {}

							# Ignoring of a failing test from GenerationTesterMixin, as the model does not use inputs_ids
							_lowercase	:			Any        = False

							# Ignoring of a failing tests from ModelTesterMixin, as the model does not implement these features
							_lowercase	:			Tuple        = False
							_lowercase	:			str        = False
							_lowercase	:			Tuple        = False
							_lowercase	:			Optional[Any]        = False
							_lowercase	:			Tuple        = False
							_lowercase	:			Dict        = False
							_lowercase	:			Tuple        = False
							_lowercase	:			Optional[Any]        = False
							_lowercase	:			Optional[int]        = False

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





									"""simple docstring"""







									lowercase__            =      DecisionTransformerModelTester(self							)
									lowercase__            =      ConfigTester(self    ,						config_class=UpperCamelCase_    ,						hidden_size=37							)

							def       lowerCamelCase_ (							self:	Any							)			->   Optional[Any]:





									"""simple docstring"""







									self.config_tester.run_common_tests()

							def       lowerCamelCase_ (							self:	int							)			->   Optional[int]:





									"""simple docstring"""







									lowercase__            =      self.model_tester.prepare_config_and_inputs()
									self.model_tester.create_and_check_model(*UpperCamelCase_							)

							@slow
							def       lowerCamelCase_ (							self:	Dict							)			->   Optional[Any]:





									"""simple docstring"""







									for model_name in DECISION_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST[:1]:
											lowercase__            =      DecisionTransformerModel.from_pretrained(UpperCamelCase_							)
											self.assertIsNotNone(UpperCamelCase_							)


							def       lowerCamelCase_ (							self:	List[str]							)			->   Dict:





									"""simple docstring"""







									lowercase__     ,		lowercase__            =      self.model_tester.prepare_config_and_inputs_for_common()

									for model_class in self.all_model_classes:
											lowercase__            =      model_class(UpperCamelCase_							)
											lowercase__            =      inspect.signature(model.forward							)
											# signature.parameters is an OrderedDict => so arg_names order is deterministic
											lowercase__            =      [*signature.parameters.keys()]

											lowercase__            =      [
											    '''states''',
											    '''actions''',
											    '''rewards''',
											    '''returns_to_go''',
											    '''timesteps''',
											    '''attention_mask''',
											]

											self.assertListEqual(arg_names[: len(UpperCamelCase_							)]    ,						UpperCamelCase_							)


@require_torch
class        _a							(			unittest.TestCase			):

							@slow
							def       lowerCamelCase_ (							self:	Tuple							)			->   Any:





									"""simple docstring"""







									lowercase__            =      2  # number of steps of autoregressive prediction we will perform
									lowercase__            =      10  # defined by the RL environment, may be normalized
									lowercase__            =      DecisionTransformerModel.from_pretrained('''edbeeching/decision-transformer-gym-hopper-expert'''							)
									lowercase__            =      model.to(UpperCamelCase_							)
									lowercase__            =      model.config
									torch.manual_seed(0							)
									lowercase__            =      torch.randn(1    ,						1    ,						config.state_dim							).to(device=UpperCamelCase_    ,						dtype=torch.floataa							)  # env.reset()

									lowercase__            =      torch.tensor(
									    [[0.242793, -0.28693074, 0.8742613], [0.67815274, -0.08101085, -0.12952147]]    ,						device=UpperCamelCase_							)

									lowercase__            =      torch.tensor(UpperCamelCase_    ,						device=UpperCamelCase_    ,						dtype=torch.floataa							).reshape(1    ,						1    ,						1							)
									lowercase__            =      state
									lowercase__            =      torch.zeros(1    ,						0    ,						config.act_dim    ,						device=UpperCamelCase_    ,						dtype=torch.floataa							)
									lowercase__            =      torch.zeros(1    ,						0    ,						device=UpperCamelCase_    ,						dtype=torch.floataa							)
									lowercase__            =      torch.tensor(0    ,						device=UpperCamelCase_    ,						dtype=torch.long							).reshape(1    ,						1							)

									for step in range(UpperCamelCase_							):
											lowercase__            =      torch.cat([actions, torch.zeros(1    ,						1    ,						config.act_dim    ,						device=UpperCamelCase_							)]    ,						dim=1							)
											lowercase__            =      torch.cat([rewards, torch.zeros(1    ,						1    ,						device=UpperCamelCase_							)]    ,						dim=1							)

											lowercase__            =      torch.ones(1    ,						states.shape[1]							).to(dtype=torch.long    ,						device=states.device							)

											with torch.no_grad():
													lowercase__     ,		lowercase__     ,		lowercase__            =      model(
													    states=UpperCamelCase_    ,						actions=UpperCamelCase_    ,						rewards=UpperCamelCase_    ,						returns_to_go=UpperCamelCase_    ,						timesteps=UpperCamelCase_    ,						attention_mask=UpperCamelCase_    ,						return_dict=UpperCamelCase_    ,						)

											self.assertEqual(action_pred.shape    ,						actions.shape							)
											self.assertTrue(torch.allclose(action_pred[0, -1]    ,						expected_outputs[step]    ,						atol=1E-4							)							)
											lowercase__     ,		lowercase__     ,		lowercase__     ,		lowercase__            =      (  # env.step(action)
											    torch.randn(1    ,						1    ,						config.state_dim							).to(device=UpperCamelCase_    ,						dtype=torch.floataa							),
											    1.0,
											    False,
											    {},
											)

											lowercase__            =      action_pred[0, -1]
											lowercase__            =      torch.cat([states, state]    ,						dim=1							)
											lowercase__            =      returns_to_go[0, -1] - reward
											lowercase__            =      torch.cat([returns_to_go, pred_return.reshape(1    ,						1    ,						1							)]    ,						dim=1							)
											lowercase__            =      torch.cat(
											    [timesteps, torch.ones((1, 1)    ,						device=UpperCamelCase_    ,						dtype=torch.long							) * (step + 1)]    ,						dim=1							)


