code: 
  
  
  
  """simple docstring"""
  
  
  
  
  _lowerCAmelCase       :      str							=							{
      "0": 1,
      "1": 1,
      "2": 2,
      "3": 6,
      "4": 24,
      "5": 1_20,
      "6": 7_20,
      "7": 50_40,
      "8": 4_03_20,
      "9": 36_28_80,
  }
  
  _lowerCAmelCase       :      Optional[int]							=							{1_45: 1_45}
  
  _lowerCAmelCase       :      int							=							{
      1_45: 0,
      1_69: 3,
      3_63_01: 3,
      14_54: 3,
      8_71: 2,
      4_53_61: 2,
      8_72: 2,
  }
  
  def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		int       )						->     int:
  
  
  
  
  
       '''simple docstring'''
  
       if n in CACHE_SUM_DIGIT_FACTORIALS:
            return CACHE_SUM_DIGIT_FACTORIALS[n]
       _UpperCAmelCase    :			Dict              =					sum(DIGIT_FACTORIALS[let] for let in str(SCREAMING_SNAKE_CASE__       )       )
       _UpperCAmelCase    :			Any              =					ret
       return ret
  
  def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		int		,						SCREAMING_SNAKE_CASE__			:		set | None = None       )						->     int:
  
  
  
  
  
       '''simple docstring'''
  
       _UpperCAmelCase    :			Dict              =					previous or set()
       if n in CHAIN_LENGTH_CACHE:
            return CHAIN_LENGTH_CACHE[n]
       _UpperCAmelCase    :			Dict              =					sum_digit_factorials(SCREAMING_SNAKE_CASE__       )
       if next_number in previous:
            _UpperCAmelCase    :			List[str]              =					0
            return 0
       else:
            previous.add(SCREAMING_SNAKE_CASE__       )
            _UpperCAmelCase    :			str              =					1 + chain_length(SCREAMING_SNAKE_CASE__		,						SCREAMING_SNAKE_CASE__       )
            _UpperCAmelCase    :			str              =					ret
            return ret
  
  def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		int = 60		,						SCREAMING_SNAKE_CASE__			:		int = 1_000_000       )						->     int:
  
  
  
  
  
       '''simple docstring'''
  
       return sum(1 for i in range(1		,						SCREAMING_SNAKE_CASE__       ) if chain_length(SCREAMING_SNAKE_CASE__       ) == num_terms       )
  
  
  if __name__ == "__main__":
   print(F"{solution() = }")
  
style_context: 
  
  
  
  """simple docstring"""
  
  
  
  
  import argparse
  
  import torch
  
  from transformers import ImageGPTConfig, ImageGPTForCausalLM, load_tf_weights_in_imagegpt
  from transformers.utils import CONFIG_NAME, WEIGHTS_NAME, logging
  
  
  logging.set_verbosity_info()
  
  def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		Optional[Any]		,						SCREAMING_SNAKE_CASE__			:		Tuple		,						SCREAMING_SNAKE_CASE__			:		Any       )						->     Dict:
  
  
  
  
  
       '''simple docstring'''
  
       _UpperCAmelCase    :			Any              =					{"small": (512, 8, 24), "medium": (1_024, 8, 36), "large": (1_536, 16, 48)}
       _UpperCAmelCase       , _UpperCAmelCase       , _UpperCAmelCase    :			str              =					MODELS[model_size]  # set model hyperparameters
       _UpperCAmelCase    :			Tuple              =					ImageGPTConfig(n_embd=SCREAMING_SNAKE_CASE__		,						n_layer=SCREAMING_SNAKE_CASE__		,						n_head=SCREAMING_SNAKE_CASE__       )
       _UpperCAmelCase    :			int              =					ImageGPTForCausalLM(SCREAMING_SNAKE_CASE__       )
  
       # Load weights from numpy
       load_tf_weights_in_imagegpt(SCREAMING_SNAKE_CASE__		,						SCREAMING_SNAKE_CASE__		,						SCREAMING_SNAKE_CASE__       )
  
       # Save pytorch-model
       _UpperCAmelCase    :			Union[str, Any]              =					pytorch_dump_folder_path + "/" + WEIGHTS_NAME
       _UpperCAmelCase    :			int              =					pytorch_dump_folder_path + "/" + CONFIG_NAME
       print(f'Save PyTorch model to {pytorch_weights_dump_path}'       )
       torch.save(model.state_dict()		,						SCREAMING_SNAKE_CASE__       )
       print(f'Save configuration file to {pytorch_config_dump_path}'       )
       with open(SCREAMING_SNAKE_CASE__		,						"w"		,						encoding="utf-8"       ) as f:
            f.write(config.to_json_string()       )
  
  
  if __name__ == "__main__":
   _lowerCAmelCase       :      List[str]							=							argparse.ArgumentParser()
   # Required parameters
   parser.add_argument(
       "--imagegpt_checkpoint_path",
       default=None,
       type=str,
       required=True,
       help="Path to the TensorFlow checkpoint path.",
   )
   parser.add_argument(
       "--model_size",
       default=None,
       type=str,
       required=True,
       help="Size of the model (can be either 'small', 'medium' or 'large').",
   )
   parser.add_argument(
       "--pytorch_dump_folder_path", default=None, type=str, required=True, help="Path to the output PyTorch model."
   )
   _lowerCAmelCase       :      Optional[int]							=							parser.parse_args()
   convert_imagegpt_checkpoint_to_pytorch(
       args.imagegpt_checkpoint_path, args.model_size, args.pytorch_dump_folder_path
   )
  