


'''simple docstring'''



from __future__ import annotations

from collections.abc import Generator


def 				lowerCamelCase__				(	):




						'''simple docstring'''






						UpperCAmelCase					    =     {}
						UpperCAmelCase					    =     2
						while True:
												UpperCAmelCase					    =     factor_map.pop(A				,       A					)
												if factor:
																		UpperCAmelCase					    =     factor + prime
																		while x in factor_map:
																								x += factor
																		UpperCAmelCase					    =     factor
												else:
																		UpperCAmelCase					    =     prime
																		yield prime
												prime += 1


def 				lowerCamelCase__				(	A       :      float = 1E10					):




						'''simple docstring'''






						UpperCAmelCase					    =     sieve()

						UpperCAmelCase					    =     1
						while True:
												UpperCAmelCase					    =     next(A					)
												if (2 * prime * n) > limit:
																		return n
												# Ignore the next prime as the reminder will be 2.
												next(A					)
												n += 2


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









'''simple docstring'''



import copy
import inspect
import unittest

from transformers import AutoBackbone
from transformers.configuration_utils import PretrainedConfig
from transformers.testing_utils import require_timm, require_torch, torch_device
from transformers.utils.import_utils import is_torch_available

from ...test_backbone_common import BackboneTesterMixin
from ...test_configuration_common import ConfigTester
from ...test_modeling_common import ModelTesterMixin, floats_tensor


if is_torch_available():
	import torch

	from transformers import TimmBackbone, TimmBackboneConfig

from ...test_pipeline_mixin import PipelineTesterMixin






class 	UpperCamelCase__:




				def __init__(		self      :			List[str]				,   lowerCAmelCase      :			int				,   lowerCAmelCase      :			Optional[int]=None				,   lowerCAmelCase      :			Optional[int]=None				,   lowerCAmelCase      :			List[str]=None				,   lowerCAmelCase      :			int="resnet50"				,   lowerCAmelCase      :			Optional[int]=3				,   lowerCAmelCase      :			Union[str, Any]=32				,   lowerCAmelCase      :			List[Any]=3				,   lowerCAmelCase      :			Tuple=True				,   lowerCAmelCase      :			str=True				,   )->					Union[str, Any]:

										"""simple docstring"""




										UpperCAmelCase					    =     parent
										UpperCAmelCase					    =     out_indices if out_indices is not None else [4]
										UpperCAmelCase					    =     stage_names
										UpperCAmelCase					    =     out_features
										UpperCAmelCase					    =     backbone
										UpperCAmelCase					    =     batch_size
										UpperCAmelCase					    =     image_size
										UpperCAmelCase					    =     num_channels
										UpperCAmelCase					    =     use_pretrained_backbone
										UpperCAmelCase					    =     is_training




				def 					a__(		self      :			Optional[Any]				)->					Optional[int]:

										"""simple docstring"""




										UpperCAmelCase					    =     floats_tensor([self.batch_size, self.num_channels, self.image_size, self.image_size]				)
										UpperCAmelCase					    =     self.get_config()

										return config, pixel_values




				def 					a__(		self      :			int				)->					Optional[Any]:

										"""simple docstring"""




										return TimmBackboneConfig(
										    image_size=self.image_size				,   num_channels=self.num_channels				,   out_features=self.out_features				,   out_indices=self.out_indices				,   stage_names=self.stage_names				,   use_pretrained_backbone=self.use_pretrained_backbone				,   backbone=self.backbone				,   )




				def 					a__(		self      :			Dict				,   lowerCAmelCase      :			str				,   lowerCAmelCase      :			Dict				)->					Tuple:

										"""simple docstring"""




										UpperCAmelCase					    =     TimmBackbone(config=lowerCAmelCase				)
										model.to(lowerCAmelCase				)
										model.eval()
										with torch.no_grad():
																UpperCAmelCase					    =     model(lowerCAmelCase				)
										self.parent.assertEqual(
										    result.feature_map[-1].shape				,   (self.batch_size, model.channels[-1], 14, 14)				,   )





				def 					a__(		self      :			str				)->					Optional[Any]:

										"""simple docstring"""




										UpperCAmelCase					    =     self.prepare_config_and_inputs()
										UpperCAmelCase    ,    UpperCAmelCase					    =     config_and_inputs
										UpperCAmelCase					    =     {'''pixel_values''': pixel_values}
										return config, inputs_dict







@require_torch
@require_timm
class 	UpperCamelCase__(       lowerCAmelCase						,    lowerCAmelCase						,    lowerCAmelCase						,    unittest.TestCase	):
				__magic_name__    :				List[str]  		=	(TimmBackbone,) if is_torch_available() else ()
				__magic_name__    :				Any  		=	{"feature-extraction": TimmBackbone} if is_torch_available() else {}
				__magic_name__    :				Union[str, Any]  		=	False
				__magic_name__    :				int  		=	False
				__magic_name__    :				Tuple  		=	False
				__magic_name__    :				List[str]  		=	False




				def 					a__(		self      :			int				)->					str:

										"""simple docstring"""




										UpperCAmelCase					    =     TimmBackboneModelTester(self				)
										UpperCAmelCase					    =     ConfigTester(self				,   config_class=lowerCAmelCase				,   has_text_modality=lowerCAmelCase				)




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

										"""simple docstring"""




										self.config_tester.create_and_test_config_to_json_string()
										self.config_tester.create_and_test_config_to_json_file()
										self.config_tester.create_and_test_config_from_and_save_pretrained()
										self.config_tester.create_and_test_config_with_num_labels()
										self.config_tester.check_config_can_be_init_without_params()
										self.config_tester.check_config_arguments_init()




				def 					a__(		self      :			List[Any]				)->					Optional[Any]:

										"""simple docstring"""




										UpperCAmelCase					    =     '''resnet18'''
										UpperCAmelCase					    =     '''microsoft/resnet-18'''

										UpperCAmelCase					    =     AutoBackbone.from_pretrained(lowerCAmelCase				,   use_timm_backbone=lowerCAmelCase				)
										UpperCAmelCase					    =     AutoBackbone.from_pretrained(lowerCAmelCase				)

										self.assertEqual(len(timm_model.out_features				)				,   len(transformers_model.out_features				)				)
										self.assertEqual(len(timm_model.stage_names				)				,   len(transformers_model.stage_names				)				)
										self.assertEqual(timm_model.channels				,   transformers_model.channels				)
										# Out indices are set to the last layer by default. For timm models, we don't know
										# the number of layers in advance, so we set it to (-1,), whereas for transformers
										# models, we set it to [len(stage_names) - 1] (kept for backward compatibility).
										self.assertEqual(timm_model.out_indices				,   (-1,)				)
										self.assertEqual(transformers_model.out_indices				,   [len(timm_model.stage_names				) - 1]				)

										UpperCAmelCase					    =     AutoBackbone.from_pretrained(lowerCAmelCase				,   use_timm_backbone=lowerCAmelCase				,   out_indices=[1, 2, 3]				)
										UpperCAmelCase					    =     AutoBackbone.from_pretrained(lowerCAmelCase				,   out_indices=[1, 2, 3]				)

										self.assertEqual(timm_model.out_indices				,   transformers_model.out_indices				)
										self.assertEqual(len(timm_model.out_features				)				,   len(transformers_model.out_features				)				)
										self.assertEqual(timm_model.channels				,   transformers_model.channels				)




				@unittest.skip('''TimmBackbone doesn\'t support feed forward chunking'''				)
				def 					a__(		self      :			Union[str, Any]				)->					Tuple:

										"""simple docstring"""




										pass




				@unittest.skip('''TimmBackbone doesn\'t have num_hidden_layers attribute'''				)
				def 					a__(		self      :			Dict				)->					Dict:

										"""simple docstring"""




										pass




				@unittest.skip('''TimmBackbone initialization is managed on the timm side'''				)
				def 					a__(		self      :			Tuple				)->					List[Any]:

										"""simple docstring"""




										pass




				@unittest.skip('''TimmBackbone models doesn\'t have inputs_embeds'''				)
				def 					a__(		self      :			List[str]				)->					Optional[Any]:

										"""simple docstring"""




										pass




				@unittest.skip('''TimmBackbone models doesn\'t have inputs_embeds'''				)
				def 					a__(		self      :			Optional[Any]				)->					Optional[Any]:

										"""simple docstring"""




										pass




				@unittest.skip('''TimmBackbone model cannot be created without specifying a backbone checkpoint'''				)
				def 					a__(		self      :			Any				)->					Optional[int]:

										"""simple docstring"""




										pass




				@unittest.skip('''Only checkpoints on timm can be loaded into TimmBackbone'''				)
				def 					a__(		self      :			Optional[int]				)->					Optional[int]:

										"""simple docstring"""




										pass




				@unittest.skip('''model weights aren\'t tied in TimmBackbone.'''				)
				def 					a__(		self      :			str				)->					str:

										"""simple docstring"""




										pass




				@unittest.skip('''model weights aren\'t tied in TimmBackbone.'''				)
				def 					a__(		self      :			Any				)->					int:

										"""simple docstring"""




										pass




				@unittest.skip('''Only checkpoints on timm can be loaded into TimmBackbone'''				)
				def 					a__(		self      :			List[Any]				)->					int:

										"""simple docstring"""




										pass




				@unittest.skip('''Only checkpoints on timm can be loaded into TimmBackbone'''				)
				def 					a__(		self      :			List[Any]				)->					List[str]:

										"""simple docstring"""




										pass




				@unittest.skip('''TimmBackbone doesn\'t have hidden size info in its configuration.'''				)
				def 					a__(		self      :			List[str]				)->					Dict:

										"""simple docstring"""




										pass




				@unittest.skip('''TimmBackbone doesn\'t support output_attentions.'''				)
				def 					a__(		self      :			str				)->					Tuple:

										"""simple docstring"""




										pass




				@unittest.skip('''Safetensors is not supported by timm.'''				)
				def 					a__(		self      :			List[Any]				)->					List[Any]:

										"""simple docstring"""




										pass




				@unittest.skip('''Will be fixed soon by reducing the size of the model used for common tests.'''				)
				def 					a__(		self      :			int				)->					Tuple:

										"""simple docstring"""




										pass




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

										"""simple docstring"""




										UpperCAmelCase    ,    UpperCAmelCase					    =     self.model_tester.prepare_config_and_inputs_for_common()

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

																UpperCAmelCase					    =     ['''pixel_values''']
																self.assertListEqual(arg_names[:1]				,   lowerCAmelCase				)




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

										"""simple docstring"""




										UpperCAmelCase    ,    UpperCAmelCase					    =     self.model_tester.prepare_config_and_inputs_for_common()
										UpperCAmelCase					    =     True
										UpperCAmelCase					    =     self.has_attentions

										# no need to test all models as different heads yield the same functionality
										UpperCAmelCase					    =     self.all_model_classes[0]
										UpperCAmelCase					    =     model_class(lowerCAmelCase				)
										model.to(lowerCAmelCase				)

										UpperCAmelCase					    =     self._prepare_for_class(lowerCAmelCase				,   lowerCAmelCase				)
										UpperCAmelCase					    =     model(**lowerCAmelCase				)
										UpperCAmelCase					    =     outputs[0][-1]

										# Encoder-/Decoder-only models
										UpperCAmelCase					    =     outputs.hidden_states[0]
										hidden_states.retain_grad()

										if self.has_attentions:
																UpperCAmelCase					    =     outputs.attentions[0]
																attentions.retain_grad()

										output.flatten()[0].backward(retain_graph=lowerCAmelCase				)

										self.assertIsNotNone(hidden_states.grad				)

										if self.has_attentions:
																self.assertIsNotNone(attentions.grad				)





				def 					a__(		self      :			Optional[int]				)->					Optional[Any]:

										"""simple docstring"""




										UpperCAmelCase    ,    UpperCAmelCase					    =     self.model_tester.prepare_config_and_inputs_for_common()

										for model_class in self.all_model_classes:
																UpperCAmelCase					    =     model_class(lowerCAmelCase				)
																model.to(lowerCAmelCase				)
																model.eval()
																UpperCAmelCase					    =     model(**lowerCAmelCase				)

																self.assertEqual(len(result.feature_maps				)				,   len(config.out_indices				)				)
																self.assertEqual(len(model.channels				)				,   len(config.out_indices				)				)

																# Check output of last stage is taken if out_features=None, out_indices=None
																UpperCAmelCase					    =     copy.deepcopy(lowerCAmelCase				)
																UpperCAmelCase					    =     None
																UpperCAmelCase					    =     model_class(lowerCAmelCase				)
																model.to(lowerCAmelCase				)
																model.eval()
																UpperCAmelCase					    =     model(**lowerCAmelCase				)

																self.assertEqual(len(result.feature_maps				)				,   1				)
																self.assertEqual(len(model.channels				)				,   1				)

																# Check backbone can be initialized with fresh weights
																UpperCAmelCase					    =     copy.deepcopy(lowerCAmelCase				)
																UpperCAmelCase					    =     False
																UpperCAmelCase					    =     model_class(lowerCAmelCase				)
																model.to(lowerCAmelCase				)
																model.eval()
																UpperCAmelCase					    =     model(**lowerCAmelCase				)





