


from math import factorial

snake_case				:    dict[str, int]       				=     {str(digit): factorial(digit) for digit in range(10)}
def 				__lowerCamelCase						( UpperCAmelCase_						:		int						):




      """simple docstring"""





      if not isinstance(UpperCAmelCase_ ,  UpperCAmelCase_						):
            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(UpperCAmelCase_						)						)
def 				__lowerCamelCase						( UpperCAmelCase_						:		int = 60 ,  UpperCAmelCase_						:		int = 100_0000						):




      """simple docstring"""





      if not isinstance(UpperCAmelCase_ ,  UpperCAmelCase_						) or not isinstance(UpperCAmelCase_ ,  UpperCAmelCase_						):
            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
      a						:Union[str, Any] 							=       0
      # the cached sizes of the previous chains
      a						:dict[int, int] 							=       {}

      for start_chain_element in range(1 ,  UpperCAmelCase_						):
            # The temporary set will contain the elements of the chain
            a						:List[Any] 							=       set()
            a						:Dict 							=       0

            # Stop computing the chain when you find a cached size, a repeating item or the
            # length is greater then the desired one.
            a						:str 							=       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(UpperCAmelCase_						)
                  chain_set_length += 1
                  a						:Optional[Any] 							=       digit_factorial_sum(UpperCAmelCase_						)

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

            a						:Dict 							=       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()}""")









# Copyright 2021 The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

from pathlib import Path

import torch

from ...utils import is_npu_available, is_xpu_available
from .config_args import ClusterConfig, default_json_config_file
from .config_utils import SubcommandHelpFormatter


snake_case				:    int       				=     '''Create a default config file for Accelerate with only a few flags set.'''
def 				__lowerCamelCase						( UpperCAmelCase_						:		Optional[Any]="no" ,  UpperCAmelCase_						:		str = default_json_config_file ,  UpperCAmelCase_						:		bool = False						):




      """simple docstring"""





      a						:List[str] 							=       Path(UpperCAmelCase_						)
      path.parent.mkdir(parents=UpperCAmelCase_ ,  exist_ok=UpperCAmelCase_						)
      if path.exists():
            print(
                F'''Configuration already exists at {save_location}, will not override. Run `accelerate config` manually or pass a different `save_location`.'''						)
            return False
      a						:Optional[Any] 							=       mixed_precision.lower()
      if mixed_precision not in ["no", "fp16", "bf16", "fp8"]:
            raise ValueError(
                F'''`mixed_precision` should be one of \'no\', \'fp16\', \'bf16\', or \'fp8\'. Received {mixed_precision}'''						)
      a						:List[Any] 							=       {
          '''compute_environment''': '''LOCAL_MACHINE''',
          '''mixed_precision''': mixed_precision,
      }
      if torch.cuda.is_available():
            a						:Dict 							=       torch.cuda.device_count()
            a						:Tuple 							=       num_gpus
            a						:int 							=       False
            if num_gpus > 1:
                  a						:str 							=       '''MULTI_GPU'''
            else:
                  a						:List[Any] 							=       '''NO'''
      elif is_xpu_available() and use_xpu:
            a						:List[Any] 							=       torch.xpu.device_count()
            a						:Optional[int] 							=       num_xpus
            a						:List[Any] 							=       False
            if num_xpus > 1:
                  a						:int 							=       '''MULTI_XPU'''
            else:
                  a						:str 							=       '''NO'''
      elif is_npu_available():
            a						:List[str] 							=       torch.npu.device_count()
            a						:Any 							=       num_npus
            a						:Optional[int] 							=       False
            if num_npus > 1:
                  a						:List[str] 							=       '''MULTI_NPU'''
            else:
                  a						:Dict 							=       '''NO'''
      else:
            a						:str 							=       0
            a						:Optional[Any] 							=       True
            a						:Optional[Any] 							=       1
            a						:str 							=       '''NO'''
      a						:List[str] 							=       ClusterConfig(**UpperCAmelCase_						)
      config.to_json_file(UpperCAmelCase_						)
      return path
def 				__lowerCamelCase						( UpperCAmelCase_						:		List[str] ,  UpperCAmelCase_						:		Union[str, Any]						):




      """simple docstring"""





      a						:List[Any] 							=       parser.add_parser('''default''' ,  parents=UpperCAmelCase_ ,  help=UpperCAmelCase_ ,  formatter_class=UpperCAmelCase_						)
      parser.add_argument(
          '''--config_file''' ,  default=UpperCAmelCase_ ,  help=(
              '''The path to use to store the config file. Will default to a file named default_config.yaml in the cache '''
              '''location, which is the content of the environment `HF_HOME` suffixed with \'accelerate\', or if you don\'t have '''
              '''such an environment variable, your cache directory (\'~/.cache\' or the content of `XDG_CACHE_HOME`) suffixed '''
              '''with \'huggingface\'.'''
          ) ,  dest='''save_location''' ,  )

      parser.add_argument(
          '''--mixed_precision''' ,  choices=['''no''', '''fp16''', '''bf16'''] ,  type=UpperCAmelCase_ ,  help='''Whether or not to use mixed precision training. '''
          '''Choose between FP16 and BF16 (bfloat16) training. '''
          '''BF16 training is only supported on Nvidia Ampere GPUs and PyTorch 1.10 or later.''' ,  default='''no''' ,  )
      parser.set_defaults(func=UpperCAmelCase_						)
      return parser






def 				__lowerCamelCase						( UpperCAmelCase_						:		int						):




      """simple docstring"""





      a						:Optional[Any] 							=       write_basic_config(args.mixed_precision ,  args.save_location						)
      if config_file:
            print(F'''accelerate configuration saved at {config_file}'''						)





