
from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


_A       =					{"configuration_nat": ["NAT_PRETRAINED_CONFIG_ARCHIVE_MAP", "NatConfig"]}


try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   _A       =					[
       "NAT_PRETRAINED_MODEL_ARCHIVE_LIST",
       "NatForImageClassification",
       "NatModel",
       "NatPreTrainedModel",
       "NatBackbone",
   ]

if TYPE_CHECKING:
   from .configuration_nat import NAT_PRETRAINED_CONFIG_ARCHIVE_MAP, NatConfig

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_nat import (
          NAT_PRETRAINED_MODEL_ARCHIVE_LIST,
          NatBackbone,
          NatForImageClassification,
          NatModel,
          NatPreTrainedModel,
      )

else:
   import sys

   _A       =					_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)



_A       =					{
    "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,
}

_A       =					{1_45: 1_45}

_A       =					{
    1_45: 0,
    1_69: 3,
    3_63_01: 3,
    14_54: 3,
    8_71: 2,
    4_53_61: 2,
    8_72: 2,
}



def 		lowercase_     (  A__						)				->				int:
    """simple docstring"""

    if n in CACHE_SUM_DIGIT_FACTORIALS:
        return CACHE_SUM_DIGIT_FACTORIALS[n]
    snake_case						=   sum(DIGIT_FACTORIALS[let] for let in str(A__						)						)
    snake_case						=   ret
    return ret



def 		lowercase_     (  A__					,						A__ = None						)				->				int:
    """simple docstring"""

    snake_case						=   previous or set()
    if n in CHAIN_LENGTH_CACHE:
        return CHAIN_LENGTH_CACHE[n]
    snake_case						=   sum_digit_factorials(A__						)
    if next_number in previous:
        snake_case						=   0
        return 0
    else:
        previous.add(A__						)
        snake_case						=   1 + chain_length(A__					,						A__						)
        snake_case						=   ret
        return ret



def 		lowercase_     (  A__ = 60					,						A__ = 100_0000						)				->				int:
    """simple docstring"""

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


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

