






from collections import defaultdict






def   a      (						lowerCamelCase_ = 5    ):






				'''simple docstring'''
				lowercase__       			=      defaultdict(lowerCamelCase_    )
				lowercase__       			=      0

				while True:
								lowercase__       			=      get_digits(lowerCamelCase_    )
								freqs[digits].append(lowerCamelCase_    )

								if len(freqs[digits]    ) == max_base:
												lowercase__       			=      freqs[digits][0] ** 3
												return base

								num += 1






def   a      (						lowerCamelCase_    ):






				'''simple docstring'''
				return "".join(sorted(str(num**3    )    )    )


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












import unittest

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

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 (
							    RemBertConfig,
							    RemBertForCausalLM,
							    RemBertForMaskedLM,
							    RemBertForMultipleChoice,
							    RemBertForQuestionAnswering,
							    RemBertForSequenceClassification,
							    RemBertForTokenClassification,
							    RemBertModel,
							)
							from transformers.models.rembert.modeling_rembert import REMBERT_PRETRAINED_MODEL_ARCHIVE_LIST
class 				_UpperCAmelCase :

				"""simple docstring"""




				def __init__(					self						:   Optional[int],  lowerCamelCase						:   Optional[Any],  lowerCamelCase						:   int=13,  lowerCamelCase						:   str=7,  lowerCamelCase						:   int=True,  lowerCamelCase						:   Optional[Any]=True,  lowerCamelCase						:   List[str]=True,  lowerCamelCase						:   str=True,  lowerCamelCase						:   List[str]=99,  lowerCamelCase						:   Any=32,  lowerCamelCase						:   int=18,  lowerCamelCase						:   Optional[int]=43,  lowerCamelCase						:   Optional[Any]=5,  lowerCamelCase						:   int=4,  lowerCamelCase						:   Union[str, Any]=37,  lowerCamelCase						:   List[str]="gelu",  lowerCamelCase						:   List[str]=0.1,  lowerCamelCase						:   Dict=0.1,  lowerCamelCase						:   Dict=512,  lowerCamelCase						:   str=16,  lowerCamelCase						:   Optional[Any]=2,  lowerCamelCase						:   int=0.02,  lowerCamelCase						:   Optional[int]=3,  lowerCamelCase						:   Optional[int]=4,  lowerCamelCase						:   Union[str, Any]=None,  ):

								'''simple docstring'''
								lowercase__       			=      parent
								lowercase__       			=      batch_size
								lowercase__       			=      seq_length
								lowercase__       			=      is_training
								lowercase__       			=      use_input_mask
								lowercase__       			=      use_token_type_ids
								lowercase__       			=      use_labels
								lowercase__       			=      vocab_size
								lowercase__       			=      hidden_size
								lowercase__       			=      input_embedding_size
								lowercase__       			=      output_embedding_size
								lowercase__       			=      num_hidden_layers
								lowercase__       			=      num_attention_heads
								lowercase__       			=      intermediate_size
								lowercase__       			=      hidden_act
								lowercase__       			=      hidden_dropout_prob
								lowercase__       			=      attention_probs_dropout_prob
								lowercase__       			=      max_position_embeddings
								lowercase__       			=      type_vocab_size
								lowercase__       			=      type_sequence_label_size
								lowercase__       			=      initializer_range
								lowercase__       			=      num_labels
								lowercase__       			=      num_choices
								lowercase__       			=      scope




				def     lowercase__       (					self						:   Optional[Any]  ):

								'''simple docstring'''
								lowercase__       			=      ids_tensor([self.batch_size, self.seq_length],  self.vocab_size  )

								lowercase__       			=      None
								if self.use_input_mask:
												lowercase__       			=      random_attention_mask([self.batch_size, self.seq_length]  )

								lowercase__       			=      None
								if self.use_token_type_ids:
												lowercase__       			=      ids_tensor([self.batch_size, self.seq_length],  self.type_vocab_size  )

								lowercase__       			=      None
								lowercase__       			=      None
								lowercase__       			=      None
								if self.use_labels:
												lowercase__       			=      ids_tensor([self.batch_size],  self.type_sequence_label_size  )
												lowercase__       			=      ids_tensor([self.batch_size, self.seq_length],  self.num_labels  )
												lowercase__       			=      ids_tensor([self.batch_size],  self.num_choices  )

								lowercase__       			=      RemBertConfig(
								    vocab_size=self.vocab_size,  hidden_size=self.hidden_size,  input_embedding_size=self.input_embedding_size,  output_embedding_size=self.output_embedding_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=lowerCamelCase,  initializer_range=self.initializer_range,  )

								return config, input_ids, token_type_ids, input_mask, sequence_labels, token_labels, choice_labels




				def     lowercase__       (					self						:   Union[str, Any]  ):

								'''simple docstring'''
								(
								    (
								    lowercase__
								)			,						(
								    lowercase__
								)			,						(
								    lowercase__
								)			,						(
								    lowercase__
								)			,						(
								    lowercase__
								)			,						(
								    lowercase__
								)			,						(
								    lowercase__
								)			,						
								)       			=      self.prepare_config_and_inputs()

								lowercase__       			=      True
								lowercase__       			=      floats_tensor([self.batch_size, self.seq_length, self.hidden_size]  )
								lowercase__       			=      ids_tensor([self.batch_size, self.seq_length],  vocab_size=2  )

								return (
								    config,
								    input_ids,
								    token_type_ids,
								    input_mask,
								    sequence_labels,
								    token_labels,
								    choice_labels,
								    encoder_hidden_states,
								    encoder_attention_mask,
								)




				def     lowercase__       (					self						:   Tuple,  lowerCamelCase						:   Optional[Any],  lowerCamelCase						:   List[str],  lowerCamelCase						:   Union[str, Any],  lowerCamelCase						:   Tuple,  lowerCamelCase						:   int,  lowerCamelCase						:   List[Any],  lowerCamelCase						:   str  ):

								'''simple docstring'''
								lowercase__       			=      RemBertModel(config=lowerCamelCase  )
								model.to(lowerCamelCase  )
								model.eval()
								lowercase__       			=      model(lowerCamelCase,  attention_mask=lowerCamelCase,  token_type_ids=lowerCamelCase  )
								lowercase__       			=      model(lowerCamelCase,  token_type_ids=lowerCamelCase  )
								lowercase__       			=      model(lowerCamelCase  )
								self.parent.assertEqual(result.last_hidden_state.shape,  (self.batch_size, self.seq_length, self.hidden_size)  )




				def     lowercase__       (					self						:   Optional[Any],  lowerCamelCase						:   List[str],  lowerCamelCase						:   Tuple,  lowerCamelCase						:   Dict,  lowerCamelCase						:   Tuple,  lowerCamelCase						:   Union[str, Any],  lowerCamelCase						:   str,  lowerCamelCase						:   Any,  lowerCamelCase						:   Union[str, Any],  lowerCamelCase						:   Any,  ):

								'''simple docstring'''
								lowercase__       			=      True
								lowercase__       			=      RemBertModel(lowerCamelCase  )
								model.to(lowerCamelCase  )
								model.eval()
								lowercase__       			=      model(
								    lowerCamelCase,  attention_mask=lowerCamelCase,  token_type_ids=lowerCamelCase,  encoder_hidden_states=lowerCamelCase,  encoder_attention_mask=lowerCamelCase,  )
								lowercase__       			=      model(
								    lowerCamelCase,  attention_mask=lowerCamelCase,  token_type_ids=lowerCamelCase,  encoder_hidden_states=lowerCamelCase,  )
								lowercase__       			=      model(lowerCamelCase,  attention_mask=lowerCamelCase,  token_type_ids=lowerCamelCase  )
								self.parent.assertEqual(result.last_hidden_state.shape,  (self.batch_size, self.seq_length, self.hidden_size)  )




				def     lowercase__       (					self						:   str,  lowerCamelCase						:   str,  lowerCamelCase						:   str,  lowerCamelCase						:   int,  lowerCamelCase						:   Optional[int],  lowerCamelCase						:   Optional[int],  lowerCamelCase						:   Union[str, Any],  lowerCamelCase						:   Dict,  lowerCamelCase						:   Union[str, Any],  lowerCamelCase						:   Optional[Any],  ):

								'''simple docstring'''
								lowercase__       			=      RemBertForCausalLM(config=lowerCamelCase  )
								model.to(lowerCamelCase  )
								model.eval()
								lowercase__       			=      model(lowerCamelCase,  attention_mask=lowerCamelCase,  token_type_ids=lowerCamelCase,  labels=lowerCamelCase  )
								self.parent.assertEqual(result.logits.shape,  (self.batch_size, self.seq_length, self.vocab_size)  )




				def     lowercase__       (					self						:   Any,  lowerCamelCase						:   Optional[int],  lowerCamelCase						:   Dict,  lowerCamelCase						:   Dict,  lowerCamelCase						:   str,  lowerCamelCase						:   List[str],  lowerCamelCase						:   Any,  lowerCamelCase						:   List[str]  ):

								'''simple docstring'''
								lowercase__       			=      RemBertForMaskedLM(config=lowerCamelCase  )
								model.to(lowerCamelCase  )
								model.eval()
								lowercase__       			=      model(lowerCamelCase,  attention_mask=lowerCamelCase,  token_type_ids=lowerCamelCase,  labels=lowerCamelCase  )
								self.parent.assertEqual(result.logits.shape,  (self.batch_size, self.seq_length, self.vocab_size)  )




				def     lowercase__       (					self						:   List[str],  lowerCamelCase						:   Optional[Any],  lowerCamelCase						:   List[Any],  lowerCamelCase						:   Optional[int],  lowerCamelCase						:   List[str],  lowerCamelCase						:   Tuple,  lowerCamelCase						:   Any,  lowerCamelCase						:   Union[str, Any],  lowerCamelCase						:   int,  lowerCamelCase						:   Dict,  ):

								'''simple docstring'''
								lowercase__       			=      True
								lowercase__       			=      True
								lowercase__       			=      RemBertForCausalLM(config=lowerCamelCase  )
								model.to(lowerCamelCase  )
								model.eval()

								# first forward pass
								lowercase__       			=      model(
								    lowerCamelCase,  attention_mask=lowerCamelCase,  encoder_hidden_states=lowerCamelCase,  encoder_attention_mask=lowerCamelCase,  use_cache=lowerCamelCase,  )
								lowercase__       			=      outputs.past_key_values

								# create hypothetical multiple next token and extent to next_input_ids
								lowercase__       			=      ids_tensor((self.batch_size, 3),  config.vocab_size  )
								lowercase__       			=      ids_tensor((self.batch_size, 3),  vocab_size=2  )

								# append to next input_ids and
								lowercase__       			=      torch.cat([input_ids, next_tokens],  dim=-1  )
								lowercase__       			=      torch.cat([input_mask, next_mask],  dim=-1  )

								lowercase__       			=      model(
								    lowerCamelCase,  attention_mask=lowerCamelCase,  encoder_hidden_states=lowerCamelCase,  encoder_attention_mask=lowerCamelCase,  output_hidden_states=lowerCamelCase,  )['''hidden_states'''][0]
								lowercase__       			=      model(
								    lowerCamelCase,  attention_mask=lowerCamelCase,  encoder_hidden_states=lowerCamelCase,  encoder_attention_mask=lowerCamelCase,  past_key_values=lowerCamelCase,  output_hidden_states=lowerCamelCase,  )['''hidden_states'''][0]

								# select random slice
								lowercase__       			=      ids_tensor((1,),  output_from_past.shape[-1]  ).item()
								lowercase__       			=      output_from_no_past[:, -3:, random_slice_idx].detach()
								lowercase__       			=      output_from_past[:, :, random_slice_idx].detach()

								self.parent.assertTrue(output_from_past_slice.shape[1] == next_tokens.shape[1]  )

								# test that outputs are equal for slice
								self.parent.assertTrue(torch.allclose(lowerCamelCase,  lowerCamelCase,  atol=1E-3  )  )




				def     lowercase__       (					self						:   Optional[int],  lowerCamelCase						:   Optional[int],  lowerCamelCase						:   Dict,  lowerCamelCase						:   Optional[int],  lowerCamelCase						:   Optional[Any],  lowerCamelCase						:   List[Any],  lowerCamelCase						:   List[str],  lowerCamelCase						:   List[Any]  ):

								'''simple docstring'''
								lowercase__       			=      RemBertForQuestionAnswering(config=lowerCamelCase  )
								model.to(lowerCamelCase  )
								model.eval()
								lowercase__       			=      model(
								    lowerCamelCase,  attention_mask=lowerCamelCase,  token_type_ids=lowerCamelCase,  start_positions=lowerCamelCase,  end_positions=lowerCamelCase,  )
								self.parent.assertEqual(result.start_logits.shape,  (self.batch_size, self.seq_length)  )
								self.parent.assertEqual(result.end_logits.shape,  (self.batch_size, self.seq_length)  )




				def     lowercase__       (					self						:   List[str],  lowerCamelCase						:   Dict,  lowerCamelCase						:   Optional[int],  lowerCamelCase						:   Tuple,  lowerCamelCase						:   Tuple,  lowerCamelCase						:   List[Any],  lowerCamelCase						:   Optional[int],  lowerCamelCase						:   Union[str, Any]  ):

								'''simple docstring'''
								lowercase__       			=      self.num_labels
								lowercase__       			=      RemBertForSequenceClassification(lowerCamelCase  )
								model.to(lowerCamelCase  )
								model.eval()
								lowercase__       			=      model(lowerCamelCase,  attention_mask=lowerCamelCase,  token_type_ids=lowerCamelCase,  labels=lowerCamelCase  )
								self.parent.assertEqual(result.logits.shape,  (self.batch_size, self.num_labels)  )




				def     lowercase__       (					self						:   Tuple,  lowerCamelCase						:   Optional[int],  lowerCamelCase						:   Dict,  lowerCamelCase						:   str,  lowerCamelCase						:   Tuple,  lowerCamelCase						:   Optional[Any],  lowerCamelCase						:   Tuple,  lowerCamelCase						:   Optional[int]  ):

								'''simple docstring'''
								lowercase__       			=      self.num_labels
								lowercase__       			=      RemBertForTokenClassification(config=lowerCamelCase  )
								model.to(lowerCamelCase  )
								model.eval()
								lowercase__       			=      model(lowerCamelCase,  attention_mask=lowerCamelCase,  token_type_ids=lowerCamelCase,  labels=lowerCamelCase  )
								self.parent.assertEqual(result.logits.shape,  (self.batch_size, self.seq_length, self.num_labels)  )




				def     lowercase__       (					self						:   Optional[int],  lowerCamelCase						:   Any,  lowerCamelCase						:   Tuple,  lowerCamelCase						:   int,  lowerCamelCase						:   str,  lowerCamelCase						:   int,  lowerCamelCase						:   Optional[Any],  lowerCamelCase						:   Any  ):

								'''simple docstring'''
								lowercase__       			=      self.num_choices
								lowercase__       			=      RemBertForMultipleChoice(config=lowerCamelCase  )
								model.to(lowerCamelCase  )
								model.eval()
								lowercase__       			=      input_ids.unsqueeze(1  ).expand(-1,  self.num_choices,  -1  ).contiguous()
								lowercase__       			=      token_type_ids.unsqueeze(1  ).expand(-1,  self.num_choices,  -1  ).contiguous()
								lowercase__       			=      input_mask.unsqueeze(1  ).expand(-1,  self.num_choices,  -1  ).contiguous()
								lowercase__       			=      model(
								    lowerCamelCase,  attention_mask=lowerCamelCase,  token_type_ids=lowerCamelCase,  labels=lowerCamelCase,  )
								self.parent.assertEqual(result.logits.shape,  (self.batch_size, self.num_choices)  )




				def     lowercase__       (					self						:   List[str]  ):

								'''simple docstring'''
								lowercase__       			=      self.prepare_config_and_inputs()
								(
								    (
								    lowercase__
								)			,						(
								    lowercase__
								)			,						(
								    lowercase__
								)			,						(
								    lowercase__
								)			,						(
								    lowercase__
								)			,						(
								    lowercase__
								)			,						(
								    lowercase__
								)			,						
								)       			=      config_and_inputs
								lowercase__       			=      {'''input_ids''': input_ids, '''token_type_ids''': token_type_ids, '''attention_mask''': input_mask}
								return config, inputs_dict



@require_torch
class 				_UpperCAmelCase (	A__		,A__		,unittest.TestCase     ):

				"""simple docstring"""




				lowercase__    							=	(
				    (
				        RemBertModel,
				        RemBertForMaskedLM,
				        RemBertForCausalLM,
				        RemBertForMultipleChoice,
				        RemBertForQuestionAnswering,
				        RemBertForSequenceClassification,
				        RemBertForTokenClassification,
				    )
				    if is_torch_available()
				    else ()
				)
				lowercase__    							=	(RemBertForCausalLM,) if is_torch_available() else ()
				lowercase__    							=	(
				    {
				        """feature-extraction""": RemBertModel,
				        """fill-mask""": RemBertForMaskedLM,
				        """question-answering""": RemBertForQuestionAnswering,
				        """text-classification""": RemBertForSequenceClassification,
				        """text-generation""": RemBertForCausalLM,
				        """token-classification""": RemBertForTokenClassification,
				        """zero-shot""": RemBertForSequenceClassification,
				    }
				    if is_torch_available()
				    else {}
				)




				def     lowercase__       (					self						:   str  ):

								'''simple docstring'''
								lowercase__       			=      RemBertModelTester(self  )
								lowercase__       			=      ConfigTester(self,  config_class=lowerCamelCase,  hidden_size=37  )




				def     lowercase__       (					self						:   List[str]  ):

								'''simple docstring'''
								self.config_tester.run_common_tests()




				def     lowercase__       (					self						:   List[Any]  ):

								'''simple docstring'''
								lowercase__       			=      self.model_tester.prepare_config_and_inputs()
								self.model_tester.create_and_check_model(*lowerCamelCase  )




				def     lowercase__       (					self						:   Dict  ):

								'''simple docstring'''
								lowercase__       			=      self.model_tester.prepare_config_and_inputs()
								for type in ["absolute", "relative_key", "relative_key_query"]:
												lowercase__       			=      type
												self.model_tester.create_and_check_model(*lowerCamelCase  )




				def     lowercase__       (					self						:   List[str]  ):

								'''simple docstring'''
								lowercase__       			=      self.model_tester.prepare_config_and_inputs()
								self.model_tester.create_and_check_for_masked_lm(*lowerCamelCase  )




				def     lowercase__       (					self						:   Optional[int]  ):

								'''simple docstring'''
								lowercase__       			=      self.model_tester.prepare_config_and_inputs()
								self.model_tester.create_and_check_for_multiple_choice(*lowerCamelCase  )




				def     lowercase__       (					self						:   Dict  ):

								'''simple docstring'''
								lowercase__       			=      self.model_tester.prepare_config_and_inputs_for_decoder()
								self.model_tester.create_and_check_decoder_model_past_large_inputs(*lowerCamelCase  )




				def     lowercase__       (					self						:   Tuple  ):

								'''simple docstring'''
								lowercase__       			=      self.model_tester.prepare_config_and_inputs()
								self.model_tester.create_and_check_for_question_answering(*lowerCamelCase  )




				def     lowercase__       (					self						:   Union[str, Any]  ):

								'''simple docstring'''
								lowercase__       			=      self.model_tester.prepare_config_and_inputs()
								self.model_tester.create_and_check_for_sequence_classification(*lowerCamelCase  )




				def     lowercase__       (					self						:   Tuple  ):

								'''simple docstring'''
								lowercase__       			=      self.model_tester.prepare_config_and_inputs()
								self.model_tester.create_and_check_for_token_classification(*lowerCamelCase  )




				def     lowercase__       (					self						:   Any  ):

								'''simple docstring'''
								lowercase__       			=      self.model_tester.prepare_config_and_inputs_for_decoder()
								self.model_tester.create_and_check_model_as_decoder(*lowerCamelCase  )




				def     lowercase__       (					self						:   List[str]  ):

								'''simple docstring'''
								# This regression test was failing with PyTorch < 1.3
								(
								    (
								    lowercase__
								)			,						(
								    lowercase__
								)			,						(
								    lowercase__
								)			,						(
								    lowercase__
								)			,						(
								    lowercase__
								)			,						(
								    lowercase__
								)			,						(
								    lowercase__
								)			,						(
								    lowercase__
								)			,						(
								    lowercase__
								)			,						
								)       			=      self.model_tester.prepare_config_and_inputs_for_decoder()

								lowercase__       			=      None

								self.model_tester.create_and_check_model_as_decoder(
								    lowerCamelCase,  lowerCamelCase,  lowerCamelCase,  lowerCamelCase,  lowerCamelCase,  lowerCamelCase,  lowerCamelCase,  lowerCamelCase,  lowerCamelCase,  )




				@slow
				def     lowercase__       (					self						:   int  ):

								'''simple docstring'''
								for model_name in REMBERT_PRETRAINED_MODEL_ARCHIVE_LIST[:1]:
												lowercase__       			=      RemBertModel.from_pretrained(lowerCamelCase  )
												self.assertIsNotNone(lowerCamelCase  )



@require_torch
class 				_UpperCAmelCase (	unittest.TestCase     ):

				"""simple docstring"""




				@slow
				def     lowercase__       (					self						:   int  ):

								'''simple docstring'''
								# Test exact values at the last hidden layer
								lowercase__       			=      RemBertModel.from_pretrained('''google/rembert'''  )
								lowercase__       			=      torch.tensor([[312, 56_498, 313, 2_125, 313]]  )
								lowercase__       			=      torch.tensor([[0, 0, 0, 1, 1]]  )
								with torch.no_grad():
												lowercase__       			=      model(lowerCamelCase,  token_type_ids=lowerCamelCase,  output_hidden_states=lowerCamelCase  )

								lowercase__       			=      1_152

								lowercase__       			=      torch.Size((1, 5, hidden_size)  )
								self.assertEqual(output['''last_hidden_state'''].shape,  lowerCamelCase  )

								lowercase__       			=      torch.tensor(
								    [
								        [
								            [0.0754, -0.2022, 0.1904],
								            [-0.3354, -0.3692, -0.4791],
								            [-0.2314, -0.6729, -0.0749],
								            [-0.0396, -0.3105, -0.4234],
								            [-0.1571, -0.0525, 0.5353],
								        ]
								    ]  )

								# Running on the original tf implementation gives slightly different results here.
								# Not clear why this variations is present
								# TODO: Find reason for discrepancy
								# expected_original_implementation = [[
								#     [0.07630594074726105, -0.20146065950393677, 0.19107051193714142],
								#     [-0.3405614495277405, -0.36971670389175415, -0.4808273911476135],
								#     [-0.22587086260318756, -0.6656315922737122, -0.07844287157058716],
								#     [-0.04145475849509239, -0.3077218234539032, -0.42316967248916626],
								#     [-0.15887849032878876, -0.054529931396245956, 0.5356100797653198]
								# ]]

								self.assertTrue(torch.allclose(output['''last_hidden_state'''][:, :, :3],  lowerCamelCase,  atol=1E-4  )  )




