

_lowerCamelCase								={
    "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								={1_45: 1_45}

_lowerCamelCase								={
    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__    (       lowerCAmelCase_      ):





     """simple docstring"""







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







def       snake_case__    (       lowerCAmelCase_,   lowerCAmelCase_ = None      ):





     """simple docstring"""







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







def       snake_case__    (       lowerCAmelCase_ = 60,   lowerCAmelCase_ = 1000000      ):





     """simple docstring"""







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


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




from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_sentencepiece_available, is_torch_available


_lowerCamelCase								={
    "configuration_xlm_prophetnet": ["XLM_PROPHETNET_PRETRAINED_CONFIG_ARCHIVE_MAP", "XLMProphetNetConfig"],
}

try:
 if not is_sentencepiece_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 _lowerCamelCase								=["XLMProphetNetTokenizer"]

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 _lowerCamelCase								=[
     "XLM_PROPHETNET_PRETRAINED_MODEL_ARCHIVE_LIST",
     "XLMProphetNetDecoder",
     "XLMProphetNetEncoder",
     "XLMProphetNetForCausalLM",
     "XLMProphetNetForConditionalGeneration",
     "XLMProphetNetModel",
     "XLMProphetNetPreTrainedModel",
 ]


if TYPE_CHECKING:
 from .configuration_xlm_prophetnet import XLM_PROPHETNET_PRETRAINED_CONFIG_ARCHIVE_MAP, XLMProphetNetConfig

 try:
  if not is_sentencepiece_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .tokenization_xlm_prophetnet import XLMProphetNetTokenizer

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_xlm_prophetnet import (
      XLM_PROPHETNET_PRETRAINED_MODEL_ARCHIVE_LIST,
      XLMProphetNetDecoder,
      XLMProphetNetEncoder,
      XLMProphetNetForCausalLM,
      XLMProphetNetForConditionalGeneration,
      XLMProphetNetModel,
      XLMProphetNetPreTrainedModel,
  )

else:
 import sys

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

