





"""simple docstring"""






from __future__ import annotations

from collections import Counter

def    __lowerCamelCase     (							SCREAMING_SNAKE_CASE				)		->							list[int]:






       """simple docstring"""




       _UpperCAmelCase			     =  [True] * n
       _UpperCAmelCase			     =  False
       _UpperCAmelCase			     =  False
       _UpperCAmelCase			     =  True

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

       _UpperCAmelCase			     =  [2]

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

       return primes

def    __lowerCamelCase     (							SCREAMING_SNAKE_CASE				)		->							list[list[int]]:






       """simple docstring"""




       _UpperCAmelCase			     =  str(SCREAMING_SNAKE_CASE				)
       _UpperCAmelCase			     =  []
       _UpperCAmelCase			     =  ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9']

       for duplicate in Counter(SCREAMING_SNAKE_CASE				) - Counter(set(SCREAMING_SNAKE_CASE				)				):
              _UpperCAmelCase			     =  [int(number_str.replace(SCREAMING_SNAKE_CASE,SCREAMING_SNAKE_CASE				)				) for digit in digits]
              replacements.append(SCREAMING_SNAKE_CASE				)

       return replacements

def    __lowerCamelCase     (							SCREAMING_SNAKE_CASE = 8				)		->							int:






       """simple docstring"""




       _UpperCAmelCase			     =  set()

       # Filter primes with less than 3 replaceable digits
       _UpperCAmelCase			     =  {
           x for x in set(prime_sieve(1000000				)				) if len(str(SCREAMING_SNAKE_CASE				)				) - len(set(str(SCREAMING_SNAKE_CASE				)				)				) >= 3
       }

       for prime in primes:
              if prime in numbers_checked:
                     continue

              _UpperCAmelCase			     =  digit_replacements(SCREAMING_SNAKE_CASE				)

              for family in replacements:
                     numbers_checked.update(SCREAMING_SNAKE_CASE				)
                     _UpperCAmelCase			     =  primes.intersection(SCREAMING_SNAKE_CASE				)

                     if len(SCREAMING_SNAKE_CASE				) != family_length:
                            continue

                     return min(SCREAMING_SNAKE_CASE				)

       return -1


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













"""simple docstring"""






import copy
import inspect

from transformers.testing_utils import require_torch, torch_device
from transformers.utils.backbone_utils import BackboneType



@require_torch
class 						lowerCAmelCase       :
       lowerCAmelCase__    			=	()
       lowerCAmelCase__    			=	True






       def 				__A			( self  ):
              _UpperCAmelCase			     =  self.config_class

              # test default config
              _UpperCAmelCase			     =  config_class()
              self.assertIsNotNone(a__  )
              _UpperCAmelCase			     =  ['stem'] + [f"""stage{idx}""" for idx in range(1     ,	len(config.depths  ) + 1  )]
              self.assertEqual(config.stage_names     ,	a__  )
              self.assertTrue(set(config.out_features  ).issubset(set(config.stage_names  )  )  )

              # Test out_features and out_indices are correctly set
              # out_features and out_indices both None
              _UpperCAmelCase			     =  config_class(out_features=a__     ,	out_indices=a__  )
              self.assertEqual(config.out_features     ,	[config.stage_names[-1]]  )
              self.assertEqual(config.out_indices     ,	[len(config.stage_names  ) - 1]  )

              # out_features and out_indices both set
              _UpperCAmelCase			     =  config_class(out_features=['stem', 'stage1']     ,	out_indices=[0, 1]  )
              self.assertEqual(config.out_features     ,	['stem', 'stage1']  )
              self.assertEqual(config.out_indices     ,	[0, 1]  )

              # Only out_features set
              _UpperCAmelCase			     =  config_class(out_features=['stage1', 'stage3']  )
              self.assertEqual(config.out_features     ,	['stage1', 'stage3']  )
              self.assertEqual(config.out_indices     ,	[1, 3]  )

              # Only out_indices set
              _UpperCAmelCase			     =  config_class(out_indices=[0, 2]  )
              self.assertEqual(config.out_features     ,	[config.stage_names[0], config.stage_names[2]]  )
              self.assertEqual(config.out_indices     ,	[0, 2]  )

              # Error raised when out_indices do not correspond to out_features
              with self.assertRaises(a__  ):
                     _UpperCAmelCase			     =  config_class(out_features=['stage1', 'stage2']     ,	out_indices=[0, 2]  )






       def 				__A			( self  ):
              _UpperCAmelCase     ,				_UpperCAmelCase			     =  self.model_tester.prepare_config_and_inputs_for_common()

              for model_class in self.all_model_classes:
                     _UpperCAmelCase			     =  model_class(a__  )
                     _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]     ,	a__  )






       def 				__A			( self  ):
              _UpperCAmelCase     ,				_UpperCAmelCase			     =  self.model_tester.prepare_config_and_inputs_for_common()

              for model_class in self.all_model_classes:
                     _UpperCAmelCase			     =  model_class(a__  )
                     self.assertEqual(len(model.channels  )     ,	len(config.out_features  )  )
                     _UpperCAmelCase			     =  model.num_features
                     _UpperCAmelCase			     =  [config.stage_names.index(a__  ) for feat in config.out_features]
                     _UpperCAmelCase			     =  [num_features[idx] for idx in out_indices]
                     self.assertListEqual(model.channels     ,	a__  )

                     _UpperCAmelCase			     =  copy.deepcopy(a__  )
                     _UpperCAmelCase			     =  None
                     _UpperCAmelCase			     =  model_class(a__  )
                     self.assertEqual(len(model.channels  )     ,	1  )
                     self.assertListEqual(model.channels     ,	[num_features[-1]]  )

                     _UpperCAmelCase			     =  copy.deepcopy(a__  )
                     _UpperCAmelCase			     =  None
                     _UpperCAmelCase			     =  model_class(a__  )
                     self.assertEqual(len(model.channels  )     ,	1  )
                     self.assertListEqual(model.channels     ,	[num_features[-1]]  )






       def 				__A			( self  ):
              _UpperCAmelCase     ,				_UpperCAmelCase			     =  self.model_tester.prepare_config_and_inputs_for_common()

              for model_class in self.all_model_classes:
                     _UpperCAmelCase			     =  model_class(a__  )
                     model.to(a__  )
                     model.eval()
                     _UpperCAmelCase			     =  model(**a__  )

                     self.assertEqual(len(result.feature_maps  )     ,	len(config.out_features  )  )
                     self.assertEqual(len(model.channels  )     ,	len(config.out_features  )  )
                     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(a__  )
                     _UpperCAmelCase			     =  None
                     _UpperCAmelCase			     =  model_class(a__  )
                     model.to(a__  )
                     model.eval()
                     _UpperCAmelCase			     =  model(**a__  )

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

                     _UpperCAmelCase			     =  copy.deepcopy(a__  )
                     _UpperCAmelCase			     =  None
                     _UpperCAmelCase			     =  model_class(a__  )
                     model.to(a__  )
                     model.eval()
                     _UpperCAmelCase			     =  model(**a__  )

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

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






       def 				__A			( self  ):
              _UpperCAmelCase     ,				_UpperCAmelCase			     =  self.model_tester.prepare_config_and_inputs_for_common()

              for backbone_class in self.all_model_classes:
                     _UpperCAmelCase			     =  backbone_class(a__  )

                     self.assertTrue(hasattr(a__     ,	'backbone_type'  )  )
                     self.assertTrue(hasattr(a__     ,	'stage_names'  )  )
                     self.assertTrue(hasattr(a__     ,	'num_features'  )  )
                     self.assertTrue(hasattr(a__     ,	'out_indices'  )  )
                     self.assertTrue(hasattr(a__     ,	'out_features'  )  )
                     self.assertTrue(hasattr(a__     ,	'out_feature_channels'  )  )
                     self.assertTrue(hasattr(a__     ,	'channels'  )  )

                     self.assertIsInstance(backbone.backbone_type     ,	a__  )
                     # Verify num_features has been initialized in the backbone init
                     self.assertIsNotNone(backbone.num_features  )
                     self.assertTrue(len(backbone.channels  ) == len(backbone.out_indices  )  )
                     self.assertTrue(len(backbone.stage_names  ) == len(backbone.num_features  )  )
                     self.assertTrue(len(backbone.channels  ) <= len(backbone.num_features  )  )
                     self.assertTrue(len(backbone.out_feature_channels  ) == len(backbone.stage_names  )  )






       def 				__A			( self  ):
              _UpperCAmelCase     ,				_UpperCAmelCase			     =  self.model_tester.prepare_config_and_inputs_for_common()
              _UpperCAmelCase			     =  inputs_dict['pixel_values'].shape[0]

              for backbone_class in self.all_model_classes:
                     _UpperCAmelCase			     =  backbone_class(a__  )
                     backbone.to(a__  )
                     backbone.eval()

                     _UpperCAmelCase			     =  backbone(**a__  )

                     # Test default outputs and verify feature maps
                     self.assertIsInstance(outputs.feature_maps     ,	a__  )
                     self.assertTrue(len(outputs.feature_maps  ) == len(backbone.channels  )  )
                     for feature_map, n_channels in zip(outputs.feature_maps     ,	backbone.channels  ):
                            self.assertTrue(feature_map.shape[:2]     ,	(batch_size, n_channels)  )
                     self.assertIsNone(outputs.hidden_states  )
                     self.assertIsNone(outputs.attentions  )

                     # Test output_hidden_states=True
                     _UpperCAmelCase			     =  backbone(**a__     ,	output_hidden_states=a__  )
                     self.assertIsNotNone(outputs.hidden_states  )
                     self.assertTrue(len(outputs.hidden_states  )     ,	len(backbone.stage_names  )  )
                     for hidden_state, n_channels in zip(outputs.hidden_states     ,	backbone.channels  ):
                            self.assertTrue(hidden_state.shape[:2]     ,	(batch_size, n_channels)  )

                     # Test output_attentions=True
                     if self.has_attentions:
                            _UpperCAmelCase			     =  backbone(**a__     ,	output_attentions=a__  )
                            self.assertIsNotNone(outputs.attentions  )






