

import math







def 			A_      (    _UpperCAmelCase    ):

						if not isinstance(_UpperCAmelCase				,	_UpperCAmelCase    ):
												SCREAMING_SNAKE_CASE_: Any  		=       f"Input value of [number={number}] must be an integer"
												raise TypeError(_UpperCAmelCase    )

						if number < 1:
												SCREAMING_SNAKE_CASE_: Tuple  		=       f"Input value of [number={number}] must be > 0"
												raise ValueError(_UpperCAmelCase    )
						elif number == 1:
												return 3
						elif number == 2:
												return 5
						else:
												SCREAMING_SNAKE_CASE_: Dict  		=       int(math.log(number // 3				,	2    )    ) + 2

												SCREAMING_SNAKE_CASE_: Tuple  		=       [3, 5]
												SCREAMING_SNAKE_CASE_: int  		=       2
												SCREAMING_SNAKE_CASE_: int  		=       3
												for block in range(1				,	_UpperCAmelCase    ):
																		for _ in range(_UpperCAmelCase    ):
																								proth_list.append(2 ** (block + 1) + proth_list[proth_index - 1]    )
																								proth_index += 1
																		increment *= 2

						return proth_list[number - 1]


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						for number in range(11):
												lowerCAmelCase							:  List[str]   	=						0
												try:
																		lowerCAmelCase							:  List[str]   	=						proth(number)
												except ValueError:
																		print(f'''ValueError: there is no {number}th Proth number''')
																		continue

												print(f'''The {number}th Proth number: {value}''')











'''simple docstring'''





import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_sentencepiece, require_tokenizers, require_torch, slow


if is_torch_available():
 import torch

 from transformers import XLMRobertaModel






@require_sentencepiece
@require_tokenizers
@require_torch
class        lowerCAmelCase_(				unittest.TestCase     ):
  '''simple docstring'''




  @slow
  def 							UpperCAmelCase_	(    self      )    ->		Union[str, Any]:
      lowerCAmelCase__ :  Tuple							      =					XLMRobertaModel.from_pretrained("""xlm-roberta-base"""      )
      lowerCAmelCase__ :  Optional[int]							      =					torch.tensor([[0, 581, 1_0269, 83, 9_9942, 136, 6_0742, 23, 70, 8_0583, 1_8276, 2]]      )
      # The dog is cute and lives in the garden house

      lowerCAmelCase__ :  str							      =					torch.Size((1, 12, 768)      )  # batch_size, sequence_length, embedding_vector_dim
      lowerCAmelCase__ :  Dict							      =					torch.tensor(
          [[-0.0_1_0_1, 0.1_2_1_8, -0.0_8_0_3, 0.0_8_0_1, 0.1_3_2_7, 0.0_7_7_6, -0.1_2_1_5, 0.2_3_8_3, 0.3_3_3_8, 0.3_1_0_6, 0.0_3_0_0, 0.0_2_5_2]]      )
      #  xlmr = torch.hub.load('pytorch/fairseq', 'xlmr.base')
      #  xlmr.eval()
      #  expected_output_values_last_dim = xlmr.extract_features(input_ids[0])[:, :, -1]
      with torch.no_grad():
          lowerCAmelCase__ :  Optional[int]							      =					model(__UpperCAmelCase      )["""last_hidden_state"""].detach()
      self.assertEqual(output.shape  ,__UpperCAmelCase      )
      # compare the actual values for a slice of last dim
      self.assertTrue(torch.allclose(output[:, :, -1]  ,__UpperCAmelCase  ,atol=1E-3      )      )






  @slow
  def 							UpperCAmelCase_	(    self      )    ->		int:
      lowerCAmelCase__ :  Union[str, Any]							      =					XLMRobertaModel.from_pretrained("""xlm-roberta-large"""      )
      lowerCAmelCase__ :  Optional[Any]							      =					torch.tensor([[0, 581, 1_0269, 83, 9_9942, 136, 6_0742, 23, 70, 8_0583, 1_8276, 2]]      )
      # The dog is cute and lives in the garden house

      lowerCAmelCase__ :  Dict							      =					torch.Size((1, 12, 1024)      )  # batch_size, sequence_length, embedding_vector_dim
      lowerCAmelCase__ :  Union[str, Any]							      =					torch.tensor(
          [[-0.0_6_9_9, -0.0_3_1_8, 0.0_7_0_5, -0.1_2_4_1, 0.0_9_9_9, -0.0_5_2_0, 0.1_0_0_4, -0.1_8_3_8, -0.4_7_0_4, 0.1_4_3_7, 0.0_8_2_1, 0.0_1_2_6]]      )
      #  xlmr = torch.hub.load('pytorch/fairseq', 'xlmr.large')
      #  xlmr.eval()
      #  expected_output_values_last_dim = xlmr.extract_features(input_ids[0])[:, :, -1]
      with torch.no_grad():
          lowerCAmelCase__ :  Union[str, Any]							      =					model(__UpperCAmelCase      )["""last_hidden_state"""].detach()
      self.assertEqual(output.shape  ,__UpperCAmelCase      )
      # compare the actual values for a slice of last dim
      self.assertTrue(torch.allclose(output[:, :, -1]  ,__UpperCAmelCase  ,atol=1E-3      )      )


