code: 
  
  
  
  """simple docstring"""
  
  
  
  
  from typing import TYPE_CHECKING
  
  from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_sentencepiece_available, is_torch_available
  
  
  _lowerCAmelCase       :      int							=							{"configuration_bert_generation": ["BertGenerationConfig"]}
  
  try:
   if not is_sentencepiece_available():
    raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
   pass
  else:
   _lowerCAmelCase       :      Any							=							["BertGenerationTokenizer"]
  
  try:
   if not is_torch_available():
    raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
   pass
  else:
   _lowerCAmelCase       :      Optional[Any]							=							[
       "BertGenerationDecoder",
       "BertGenerationEncoder",
       "BertGenerationPreTrainedModel",
       "load_tf_weights_in_bert_generation",
   ]
  
  
  if TYPE_CHECKING:
   from .configuration_bert_generation import BertGenerationConfig
  
   try:
    if not is_sentencepiece_available():
     raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
    pass
   else:
    from .tokenization_bert_generation import BertGenerationTokenizer
  
   try:
    if not is_torch_available():
     raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
    pass
   else:
    from .modeling_bert_generation import (
        BertGenerationDecoder,
        BertGenerationEncoder,
        BertGenerationPreTrainedModel,
        load_tf_weights_in_bert_generation,
    )
  
  else:
   import sys
  
   _lowerCAmelCase       :      Any							=							_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)
  
style_context: 
  
  
  
  """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() = }")
  