






import copy

from ...configuration_utils import PretrainedConfig
from ...utils import add_start_docstrings


a__       =     r"""
    [`RagConfig`] stores the configuration of a *RagModel*. Configuration objects inherit from [`PretrainedConfig`] and
    can be used to control the model outputs. Read the documentation from [`PretrainedConfig`] for more information.

    Args:
        title_sep (`str`, *optional*, defaults to  `\" / \"`):
            Separator inserted between the title and the text of the retrieved document when calling [`RagRetriever`].
        doc_sep (`str`, *optional*, defaults to  `\" // \"`):
            Separator inserted between the text of the retrieved document and the original input when calling
            [`RagRetriever`].
        n_docs (`int`, *optional*, defaults to 5):
            Number of documents to retrieve.
        max_combined_length (`int`, *optional*, defaults to 300):
            Max length of contextualized input returned by [`~RagRetriever.__call__`].
        retrieval_vector_size (`int`, *optional*, defaults to 768):
            Dimensionality of the document embeddings indexed by [`RagRetriever`].
        retrieval_batch_size (`int`, *optional*, defaults to 8):
            Retrieval batch size, defined as the number of queries issues concurrently to the faiss index encapsulated
            [`RagRetriever`].
        dataset (`str`, *optional*, defaults to `\"wiki_dpr\"`):
            A dataset identifier of the indexed dataset in HuggingFace Datasets (list all available datasets and ids
            using `datasets.list_datasets()`).
        dataset_split (`str`, *optional*, defaults to `\"train\"`)
            Which split of the `dataset` to load.
        index_name (`str`, *optional*, defaults to `\"compressed\"`)
            The index name of the index associated with the `dataset`. One can choose between `\"legacy\"`, `\"exact\"` and
            `\"compressed\"`.
        index_path (`str`, *optional*)
            The path to the serialized faiss index on disk.
        passages_path (`str`, *optional*):
            A path to text passages compatible with the faiss index. Required if using
            [`~models.rag.retrieval_rag.LegacyIndex`]
        use_dummy_dataset (`bool`, *optional*, defaults to `False`)
            Whether to load a \"dummy\" variant of the dataset specified by `dataset`.
        label_smoothing (`float`, *optional*, defaults to 0.0):
            Only relevant if `return_loss` is set to `True`. Controls the `epsilon` parameter value for label smoothing
            in the loss calculation. If set to 0, no label smoothing is performed.
        do_marginalize (`bool`, *optional*, defaults to `False`):
            If `True`, the logits are marginalized over all documents by making use of
            `torch.nn.functional.log_softmax`.
        reduce_loss (`bool`, *optional*, defaults to `False`):
            Whether or not to reduce the NLL loss using the `torch.Tensor.sum` operation.
        do_deduplication (`bool`, *optional*, defaults to `True`):
            Whether or not to deduplicate the generations from different context documents for a given input. Has to be
            set to `False` if used while training with distributed backend.
        exclude_bos_score (`bool`, *optional*, defaults to `False`):
            Whether or not to disregard the BOS token when computing the loss.
        output_retrieved(`bool`, *optional*, defaults to `False`):
            If set to `True`, `retrieved_doc_embeds`, `retrieved_doc_ids`, `context_input_ids` and
            `context_attention_mask` are returned. See returned tensors for more detail.
        use_cache (`bool`, *optional*, defaults to `True`):
            Whether or not the model should return the last key/values attentions (not used by all models).
        forced_eos_token_id (`int`, *optional*):
            The id of the token to force as the last generated token when `max_length` is reached. Usually set to
            `eos_token_id`.
"""


@add_start_docstrings(lowercase_		)
class    _lowerCAmelCase			(		lowercase_		):



				"""simple docstring"""



				_lowercase				:   List[str]      =  '''rag'''
				_lowercase				:   Tuple      =  True



				def __init__(      self    :    List[str]			,		UpperCamelCase__    :    List[Any]=None			,		UpperCamelCase__    :    Optional[int]=True			,		UpperCamelCase__    :    Optional[int]=None			,		UpperCamelCase__    :    Optional[Any]=None			,		UpperCamelCase__    :    Any=None			,		UpperCamelCase__    :    Tuple=None			,		UpperCamelCase__    :    str=None			,		UpperCamelCase__    :    int=" / "			,		UpperCamelCase__    :    Any=" // "			,		UpperCamelCase__    :    Tuple=5			,		UpperCamelCase__    :    List[str]=3_0_0			,		UpperCamelCase__    :    Tuple=7_6_8			,		UpperCamelCase__    :    Dict=8			,		UpperCamelCase__    :    Any="wiki_dpr"			,		UpperCamelCase__    :    Optional[Any]="train"			,		UpperCamelCase__    :    Any="compressed"			,		UpperCamelCase__    :    int=None			,		UpperCamelCase__    :    List[str]=None			,		UpperCamelCase__    :    List[str]=False			,		UpperCamelCase__    :    Optional[int]=False			,		UpperCamelCase__    :    str=0.0			,		UpperCamelCase__    :    Optional[Any]=True			,		UpperCamelCase__    :    List[Any]=False			,		UpperCamelCase__    :    Tuple=False			,		UpperCamelCase__    :    List[Any]=False			,		UpperCamelCase__    :    Tuple=True			,		UpperCamelCase__    :    Union[str, Any]=None			,		**UpperCamelCase__    :    Optional[Any]			,		):






											'''simple docstring'''







											super().__init__(
											    bos_token_id=UpperCamelCase__			,		pad_token_id=UpperCamelCase__			,		eos_token_id=UpperCamelCase__			,		decoder_start_token_id=UpperCamelCase__			,		forced_eos_token_id=UpperCamelCase__			,		is_encoder_decoder=UpperCamelCase__			,		prefix=UpperCamelCase__			,		vocab_size=UpperCamelCase__			,		**UpperCamelCase__			,		)
											assert (
											    "question_encoder" in kwargs and "generator" in kwargs
											), "Config has to be initialized with question_encoder and generator config"
											snake_case__	  =       kwargs.pop("""question_encoder""")
											snake_case__	  =       question_encoder_config.pop("""model_type""")
											snake_case__	  =       kwargs.pop("""generator""")
											snake_case__	  =       decoder_config.pop("""model_type""")

											from ..auto.configuration_auto import AutoConfig

											snake_case__	  =       AutoConfig.for_model(UpperCamelCase__			,		**UpperCamelCase__)
											snake_case__	  =       AutoConfig.for_model(UpperCamelCase__			,		**UpperCamelCase__)

											snake_case__	  =       reduce_loss
											snake_case__	  =       label_smoothing
											snake_case__	  =       exclude_bos_score
											snake_case__	  =       do_marginalize

											snake_case__	  =       title_sep
											snake_case__	  =       doc_sep
											snake_case__	  =       n_docs
											snake_case__	  =       max_combined_length

											snake_case__	  =       dataset
											snake_case__	  =       dataset_split
											snake_case__	  =       index_name

											snake_case__	  =       retrieval_vector_size
											snake_case__	  =       retrieval_batch_size
											snake_case__	  =       passages_path
											snake_case__	  =       index_path
											snake_case__	  =       use_dummy_dataset

											snake_case__	  =       output_retrieved

											snake_case__	  =       do_deduplication

											snake_case__	  =       use_cache

											if self.forced_eos_token_id is None:
																		snake_case__	  =       getattr(self.generator			,		"""forced_eos_token_id"""			,		UpperCamelCase__)



				@classmethod
				def 					__magic_name__							(      cls    :    Dict			,		UpperCamelCase__    :    PretrainedConfig			,		UpperCamelCase__    :    PretrainedConfig			,		**UpperCamelCase__    :    Tuple):






											'''simple docstring'''







											return cls(question_encoder=question_encoder_config.to_dict()			,		generator=generator_config.to_dict()			,		**UpperCamelCase__)



				def 					__magic_name__							(      self    :    int):






											'''simple docstring'''







											snake_case__	  =       copy.deepcopy(self.__dict__)
											snake_case__	  =       self.question_encoder.to_dict()
											snake_case__	  =       self.generator.to_dict()
											snake_case__	  =       self.__class__.model_type
											return output








from math import factorial

a__       =     {str(digit): factorial(digit) for digit in range(1_0)}

def _UpperCAmelCase   (	a						:	int ):
							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 = 100_0000 ):

							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
							snake_case__	  =       0
							# the cached sizes of the previous chains
							snake_case__	  =       {}

							for start_chain_element in range(1  ,					a ):
														# The temporary set will contain the elements of the chain
														snake_case__	  =       set()
														snake_case__	  =       0

														# Stop computing the chain when you find a cached size, a repeating item or the
														# length is greater then the desired one.
														snake_case__	  =       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
																					snake_case__	  =       digit_factorial_sum(a )

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

														snake_case__	  =       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()}''')
