




'''simple docstring'''






lowercase						:   int      						=							{
    '''0''': 1,
    '''1''': 1,
    '''2''': 2,
    '''3''': 6,
    '''4''': 24,
    '''5''': 120,
    '''6''': 720,
    '''7''': 5040,
    '''8''': 40320,
    '''9''': 362880,
}

lowercase						:   int      						=							{145: 145}

lowercase						:   List[str]      						=							{
    145: 0,
    169: 3,
    36301: 3,
    1454: 3,
    871: 2,
    45361: 2,
    872: 2,
}




def 		a_(			lowerCamelCase   )					->int:






       '''simple docstring'''




       if n in CACHE_SUM_DIGIT_FACTORIALS:
              return CACHE_SUM_DIGIT_FACTORIALS[n]
       lowercase	:		Optional[Any]    =   sum(DIGIT_FACTORIALS[let] for let in str(lowerCamelCase   )   )
       lowercase	:		List[str]    =   ret
       return ret




def 		a_(			lowerCamelCase ,					lowerCamelCase = None   )					->int:






       '''simple docstring'''




       lowercase	:		Union[str, Any]    =   previous or set()
       if n in CHAIN_LENGTH_CACHE:
              return CHAIN_LENGTH_CACHE[n]
       lowercase	:		Any    =   sum_digit_factorials(lowerCamelCase   )
       if next_number in previous:
              lowercase	:		Dict    =   0
              return 0
       else:
              previous.add(lowerCamelCase   )
              lowercase	:		List[str]    =   1 + chain_length(lowerCamelCase ,					lowerCamelCase   )
              lowercase	:		str    =   ret
              return ret




def 		a_(			lowerCamelCase = 60 ,					lowerCamelCase = 100_0000   )					->int:






       '''simple docstring'''




       return sum(1 for i in range(1 ,					lowerCamelCase   ) if chain_length(lowerCamelCase   ) == num_terms   )


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










'''simple docstring'''






import os

from packaging import version

from .. import __version__
from .accelerate_utils import apply_forward_hook
from .constants import (
    CONFIG_NAME,
    DEPRECATED_REVISION_ARGS,
    DIFFUSERS_CACHE,
    DIFFUSERS_DYNAMIC_MODULE_NAME,
    FLAX_WEIGHTS_NAME,
    HF_MODULES_CACHE,
    HUGGINGFACE_CO_RESOLVE_ENDPOINT,
    ONNX_EXTERNAL_WEIGHTS_NAME,
    ONNX_WEIGHTS_NAME,
    SAFETENSORS_WEIGHTS_NAME,
    TEXT_ENCODER_ATTN_MODULE,
    WEIGHTS_NAME,
)
from .deprecation_utils import deprecate
from .doc_utils import replace_example_docstring
from .dynamic_modules_utils import get_class_from_dynamic_module
from .hub_utils import (
    HF_HUB_OFFLINE,
    _add_variant,
    _get_model_file,
    extract_commit_hash,
    http_user_agent,
)
from .import_utils import (
    BACKENDS_MAPPING,
    ENV_VARS_TRUE_AND_AUTO_VALUES,
    ENV_VARS_TRUE_VALUES,
    USE_JAX,
    USE_TF,
    USE_TORCH,
    DummyObject,
    OptionalDependencyNotAvailable,
    is_accelerate_available,
    is_accelerate_version,
    is_bsa_available,
    is_flax_available,
    is_ftfy_available,
    is_inflect_available,
    is_invisible_watermark_available,
    is_k_diffusion_available,
    is_k_diffusion_version,
    is_librosa_available,
    is_note_seq_available,
    is_omegaconf_available,
    is_onnx_available,
    is_safetensors_available,
    is_scipy_available,
    is_tensorboard_available,
    is_tf_available,
    is_torch_available,
    is_torch_version,
    is_torchsde_available,
    is_transformers_available,
    is_transformers_version,
    is_unidecode_available,
    is_wandb_available,
    is_xformers_available,
    requires_backends,
)
from .logging import get_logger
from .outputs import BaseOutput
from .pil_utils import PIL_INTERPOLATION, numpy_to_pil, pt_to_pil
from .torch_utils import is_compiled_module, randn_tensor


if is_torch_available():
      from .testing_utils import (
          floats_tensor,
          load_hf_numpy,
          load_image,
          load_numpy,
          load_pt,
          nightly,
          parse_flag_from_env,
          print_tensor_test,
          require_torch_a,
          require_torch_gpu,
          skip_mps,
          slow,
          torch_all_close,
          torch_device,
      )
      from .torch_utils import maybe_allow_in_graph

from .testing_utils import export_to_gif, export_to_video


lowercase						:   Tuple      						=							get_logger(__name__)




def 		a_(			lowerCamelCase   )					->Any:






       '''simple docstring'''




       if version.parse(lowerCamelCase   ) < version.parse(lowerCamelCase   ):
              if "dev" in min_version:
                     lowercase	:		str    =   (
                         '''This example requires a source install from HuggingFace diffusers (see '''
                         '''`https://huggingface.co/docs/diffusers/installation#install-from-source`),'''
                     )
              else:
                     lowercase	:		List[str]    =   f"""This example requires a minimum version of {min_version},"""
              error_message += f""" but the version found is {__version__}.\n"""
              raise ImportError(lowerCamelCase   )




