


'''simple docstring'''






from ...utils import is_torch_available, is_transformers_available


if is_transformers_available() and is_torch_available():
  from .pipeline_vq_diffusion import LearnedClassifierFreeSamplingEmbeddings, VQDiffusionPipeline







'''simple docstring'''






from math import factorial

__A   :    dict[str, int]											= {str(digit): factorial(digit) for digit in range(10)}







def 							UpperCamelCase_     (       A__   :  int   ):
  '''simple docstring'''





  if not isinstance(A__				,       A__   ):
    raise TypeError("""Parameter number must be int"""   )

  if number < 0:
    raise ValueError("""Parameter number must be greater than or equal to 0"""   )

  # Converts number in string to iterate on its digits and adds its factorial.
  return sum(DIGIT_FACTORIAL[digit] for digit in str(A__   )   )







def 							UpperCamelCase_     (       A__   :  int = 60				,       A__   :  int = 1_00_00_00   ):
  '''simple docstring'''





  if not isinstance(A__				,       A__   ) or not isinstance(A__				,       A__   ):
    raise TypeError("""Parameters chain_length and number_limit must be int"""   )

  if chain_length <= 0 or number_limit <= 0:
    raise ValueError(
        """Parameters chain_length and number_limit must be greater than 0"""   )

  # the counter for the chains with the exact desired length
  lowerCAmelCase_     : Optional[int]     =  0
  # the cached sizes of the previous chains
  lowerCAmelCase_     : dict[int, int]     =  {}

  for start_chain_element in range(1				,       A__   ):
    # The temporary set will contain the elements of the chain
    lowerCAmelCase_     : List[str]     =  set()
    lowerCAmelCase_     : Optional[int]     =  0

    # Stop computing the chain when you find a cached size, a repeating item or the
    # length is greater then the desired one.
    lowerCAmelCase_     : int     =  start_chain_element
    while (
        chain_element not in chain_sets_lengths
        and chain_element not in chain_set
        and chain_set_length <= chain_length
    ):
      chain_set.add(A__   )
      chain_set_length += 1
      lowerCAmelCase_     : Union[str, Any]     =  digit_factorial_sum(A__   )

    if chain_element in chain_sets_lengths:
      chain_set_length += chain_sets_lengths[chain_element]

    lowerCAmelCase_     : int     =  chain_set_length

    # If chain contains the exact amount of elements increase the counter
    if chain_set_length == chain_length:
      chains_counter += 1

  return chains_counter


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  print(F'''{solution()}''')



