from math import sqrt


def      a__ (		__UpperCamelCase				):
      assert isinstance(__UpperCamelCase     ,      __UpperCamelCase				) and (
          number >= 0
      ), "'number' must been an int and positive"

      SCREAMING_SNAKE_CASE_          =  True

      # 0 and 1 are none primes.
      if number <= 1:
            SCREAMING_SNAKE_CASE_          =  False

      for divisor in range(2     ,      int(round(sqrt(__UpperCamelCase				)				)				) + 1				):
            # if 'number' divisible by 'divisor' then sets 'status'
            # of false and break up the loop.
            if number % divisor == 0:
                  SCREAMING_SNAKE_CASE_          =  False
                  break

    # precondition
      assert isinstance(__UpperCamelCase     ,      __UpperCamelCase				), "'status' must been from type bool"

      return status


def      a__ (		__UpperCamelCase				):
      assert isinstance(__UpperCamelCase     ,      __UpperCamelCase				) and (n > 2), "'N' must been an int and > 2"

      # beginList: contains all natural numbers from 2 up to N
      SCREAMING_SNAKE_CASE_          =  list(range(2     ,      n + 1				)				)

      SCREAMING_SNAKE_CASE_          =  []  # this list will be returns.

      # actual sieve of erathostenes
      for i in range(len(__UpperCamelCase				)				):
            for j in range(i + 1     ,      len(__UpperCamelCase				)				):
                  if (begin_list[i] != 0) and (begin_list[j] % begin_list[i] == 0):
                        SCREAMING_SNAKE_CASE_          =  0

    # filters actual prime numbers.
      SCREAMING_SNAKE_CASE_          =  [x for x in begin_list if x != 0]

      # precondition
      assert isinstance(__UpperCamelCase     ,      __UpperCamelCase				), "'ans' must been from type list"

      return ans


def      a__ (		__UpperCamelCase				):
      assert isinstance(__UpperCamelCase     ,      __UpperCamelCase				) and (n > 2), "'N' must been an int and > 2"

      SCREAMING_SNAKE_CASE_          =  []

      # iterates over all numbers between 2 up to N+1
      # if a number is prime then appends to list 'ans'
      for number in range(2     ,      n + 1				):
            if is_prime(__UpperCamelCase				):
                  ans.append(__UpperCamelCase				)

    # precondition
      assert isinstance(__UpperCamelCase     ,      __UpperCamelCase				), "'ans' must been from type list"

      return ans


def      a__ (		__UpperCamelCase				):
      assert isinstance(__UpperCamelCase     ,      __UpperCamelCase				) and number >= 0, "'number' must been an int and >= 0"

      SCREAMING_SNAKE_CASE_          =  []  # this list will be returns of the function.

      # potential prime number factors.

      SCREAMING_SNAKE_CASE_          =  2

      SCREAMING_SNAKE_CASE_          =  number

      if number == 0 or number == 1:
            ans.append(__UpperCamelCase				)

      # if 'number' not prime then builds the prime factorization of 'number'
      elif not is_prime(__UpperCamelCase				):
            while quotient != 1:
                  if is_prime(__UpperCamelCase				) and (quotient % factor == 0):
                        ans.append(__UpperCamelCase				)
                        quotient /= factor
                  else:
                        factor += 1

      else:
            ans.append(__UpperCamelCase				)

      # precondition
      assert isinstance(__UpperCamelCase     ,      __UpperCamelCase				), "'ans' must been from type list"

      return ans


def      a__ (		__UpperCamelCase				):
      assert isinstance(__UpperCamelCase     ,      __UpperCamelCase				) and (
          number >= 0
      ), "'number' bust been an int and >= 0"

      SCREAMING_SNAKE_CASE_          =  0

      # prime factorization of 'number'
      SCREAMING_SNAKE_CASE_          =  prime_factorization(__UpperCamelCase				)

      SCREAMING_SNAKE_CASE_          =  max(__UpperCamelCase				)

      # precondition
      assert isinstance(__UpperCamelCase     ,      __UpperCamelCase				), "'ans' must been from type int"

      return ans


def      a__ (		__UpperCamelCase				):
      assert isinstance(__UpperCamelCase     ,      __UpperCamelCase				) and (
          number >= 0
      ), "'number' bust been an int and >= 0"

      SCREAMING_SNAKE_CASE_          =  0

      # prime factorization of 'number'
      SCREAMING_SNAKE_CASE_          =  prime_factorization(__UpperCamelCase				)

      SCREAMING_SNAKE_CASE_          =  min(__UpperCamelCase				)

      # precondition
      assert isinstance(__UpperCamelCase     ,      __UpperCamelCase				), "'ans' must been from type int"

      return ans


def      a__ (		__UpperCamelCase				):
      assert isinstance(__UpperCamelCase     ,      __UpperCamelCase				), "'number' must been an int"
      assert isinstance(number % 2 == 0     ,      __UpperCamelCase				), "compare bust been from type bool"

      return number % 2 == 0


def      a__ (		__UpperCamelCase				):
      assert isinstance(__UpperCamelCase     ,      __UpperCamelCase				), "'number' must been an int"
      assert isinstance(number % 2 != 0     ,      __UpperCamelCase				), "compare bust been from type bool"

      return number % 2 != 0


def      a__ (		__UpperCamelCase				):
      assert (
          isinstance(__UpperCamelCase     ,      __UpperCamelCase				) and (number > 2) and is_even(__UpperCamelCase				)
      ), "'number' must been an int, even and > 2"

      SCREAMING_SNAKE_CASE_          =  []  # this list will returned

      # creates a list of prime numbers between 2 up to 'number'
      SCREAMING_SNAKE_CASE_          =  get_prime_numbers(__UpperCamelCase				)
      SCREAMING_SNAKE_CASE_          =  len(__UpperCamelCase				)

      # run variable for while-loops.
      SCREAMING_SNAKE_CASE_          =  0
      SCREAMING_SNAKE_CASE_          =  None

      # exit variable. for break up the loops
      SCREAMING_SNAKE_CASE_          =  True

      while i < len_pn and loop:
            SCREAMING_SNAKE_CASE_          =  i + 1

            while j < len_pn and loop:
                  if prime_numbers[i] + prime_numbers[j] == number:
                        SCREAMING_SNAKE_CASE_          =  False
                        ans.append(prime_numbers[i]				)
                        ans.append(prime_numbers[j]				)

                  j += 1

            i += 1

      # precondition
      assert (
          isinstance(__UpperCamelCase     ,      __UpperCamelCase				)
          and (len(__UpperCamelCase				) == 2)
          and (ans[0] + ans[1] == number)
          and is_prime(ans[0]				)
          and is_prime(ans[1]				)
      ), "'ans' must contains two primes. And sum of elements must been eq 'number'"

      return ans


def      a__ (		__UpperCamelCase     ,      __UpperCamelCase				):
      assert (
          isinstance(__UpperCamelCase     ,      __UpperCamelCase				)
          and isinstance(__UpperCamelCase     ,      __UpperCamelCase				)
          and (numbera >= 0)
          and (numbera >= 0)
      ), "'number1' and 'number2' must been positive integer."

      SCREAMING_SNAKE_CASE_          =  0

      while numbera != 0:
            SCREAMING_SNAKE_CASE_          =  numbera % numbera
            SCREAMING_SNAKE_CASE_          =  numbera
            SCREAMING_SNAKE_CASE_          =  rest

      # precondition
      assert isinstance(__UpperCamelCase     ,      __UpperCamelCase				) and (
          numbera >= 0
      ), "'number' must been from type int and positive"

      return numbera


def      a__ (		__UpperCamelCase     ,      __UpperCamelCase				):
      assert (
          isinstance(__UpperCamelCase     ,      __UpperCamelCase				)
          and isinstance(__UpperCamelCase     ,      __UpperCamelCase				)
          and (numbera >= 1)
          and (numbera >= 1)
      ), "'number1' and 'number2' must been positive integer."

      SCREAMING_SNAKE_CASE_          =  1  # actual answer that will be return.

      # for kgV (x,1)
      if numbera > 1 and numbera > 1:
            # builds the prime factorization of 'number1' and 'number2'
            SCREAMING_SNAKE_CASE_          =  prime_factorization(__UpperCamelCase				)
            SCREAMING_SNAKE_CASE_          =  prime_factorization(__UpperCamelCase				)

      elif numbera == 1 or numbera == 1:
            SCREAMING_SNAKE_CASE_          =  []
            SCREAMING_SNAKE_CASE_          =  []
            SCREAMING_SNAKE_CASE_          =  max(__UpperCamelCase     ,      __UpperCamelCase				)

      SCREAMING_SNAKE_CASE_          =  0
      SCREAMING_SNAKE_CASE_          =  0

      SCREAMING_SNAKE_CASE_          =  []  # captured numbers int both 'primeFac1' and 'primeFac2'

      # iterates through primeFac1
      for n in prime_fac_a:
            if n not in done:
                  if n in prime_fac_a:
                        SCREAMING_SNAKE_CASE_          =  prime_fac_a.count(__UpperCamelCase				)
                        SCREAMING_SNAKE_CASE_          =  prime_fac_a.count(__UpperCamelCase				)

                        for _ in range(max(__UpperCamelCase     ,      __UpperCamelCase				)				):
                              ans *= n

                  else:
                        SCREAMING_SNAKE_CASE_          =  prime_fac_a.count(__UpperCamelCase				)

                        for _ in range(__UpperCamelCase				):
                              ans *= n

                  done.append(__UpperCamelCase				)

    # iterates through primeFac2
      for n in prime_fac_a:
            if n not in done:
                  SCREAMING_SNAKE_CASE_          =  prime_fac_a.count(__UpperCamelCase				)

                  for _ in range(__UpperCamelCase				):
                        ans *= n

                  done.append(__UpperCamelCase				)

    # precondition
      assert isinstance(__UpperCamelCase     ,      __UpperCamelCase				) and (
          ans >= 0
      ), "'ans' must been from type int and positive"

      return ans


def      a__ (		__UpperCamelCase				):
      assert isinstance(__UpperCamelCase     ,      __UpperCamelCase				) and (n >= 0), "'number' must been a positive int"

      SCREAMING_SNAKE_CASE_          =  0
      SCREAMING_SNAKE_CASE_          =  2  # this variable holds the answer

      while index < n:
            index += 1

            ans += 1  # counts to the next number

            # if ans not prime then
            # runs to the next prime number.
            while not is_prime(__UpperCamelCase				):
                  ans += 1

    # precondition
      assert isinstance(__UpperCamelCase     ,      __UpperCamelCase				) and is_prime(
          __UpperCamelCase				), "'ans' must been a prime number and from type int"

      return ans


def      a__ (		__UpperCamelCase     ,      __UpperCamelCase				):
      assert (
          is_prime(__UpperCamelCase				) and is_prime(__UpperCamelCase				) and (p_number_a < p_number_a)
      ), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"

      SCREAMING_SNAKE_CASE_          =  p_number_a + 1  # jump to the next number

      SCREAMING_SNAKE_CASE_          =  []  # this list will be returns.

      # if number is not prime then
      # fetch the next prime number.
      while not is_prime(__UpperCamelCase				):
            number += 1

      while number < p_number_a:
            ans.append(__UpperCamelCase				)

            number += 1

            # fetch the next prime number.
            while not is_prime(__UpperCamelCase				):
                  number += 1

    # precondition
      assert (
          isinstance(__UpperCamelCase     ,      __UpperCamelCase				)
          and ans[0] != p_number_a
          and ans[len(__UpperCamelCase				) - 1] != p_number_a
      ), "'ans' must been a list without the arguments"

      # 'ans' contains not 'pNumber1' and 'pNumber2' !
      return ans


def      a__ (		__UpperCamelCase				):
      assert isinstance(__UpperCamelCase     ,      __UpperCamelCase				) and (n >= 1), "'n' must been int and >= 1"

      SCREAMING_SNAKE_CASE_          =  []  # will be returned.

      for divisor in range(1     ,      n + 1				):
            if n % divisor == 0:
                  ans.append(__UpperCamelCase				)

    # precondition
      assert ans[0] == 1 and ans[len(__UpperCamelCase				) - 1] == n, "Error in function getDivisiors(...)"

      return ans


def      a__ (		__UpperCamelCase				):
      assert isinstance(__UpperCamelCase     ,      __UpperCamelCase				) and (
          number > 1
      ), "'number' must been an int and >= 1"

      SCREAMING_SNAKE_CASE_          =  get_divisors(__UpperCamelCase				)

      # precondition
      assert (
          isinstance(__UpperCamelCase     ,      __UpperCamelCase				)
          and (divisors[0] == 1)
          and (divisors[len(__UpperCamelCase				) - 1] == number)
      ), "Error in help-function getDivisiors(...)"

      # summed all divisors up to 'number' (exclusive), hence [:-1]
      return sum(divisors[:-1]				) == number


def      a__ (		__UpperCamelCase     ,      __UpperCamelCase				):
      assert (
          isinstance(__UpperCamelCase     ,      __UpperCamelCase				)
          and isinstance(__UpperCamelCase     ,      __UpperCamelCase				)
          and (denominator != 0)
      ), "The arguments must been from type int and 'denominator' != 0"

      # build the greatest common divisor of numerator and denominator.
      SCREAMING_SNAKE_CASE_          =  gcd(abs(__UpperCamelCase				)     ,      abs(__UpperCamelCase				)				)

      # precondition
      assert (
          isinstance(__UpperCamelCase     ,      __UpperCamelCase				)
          and (numerator % gcd_of_fraction == 0)
          and (denominator % gcd_of_fraction == 0)
      ), "Error in function gcd(...,...)"

      return (numerator // gcd_of_fraction, denominator // gcd_of_fraction)


def      a__ (		__UpperCamelCase				):
      assert isinstance(__UpperCamelCase     ,      __UpperCamelCase				) and (n >= 0), "'n' must been a int and >= 0"

      SCREAMING_SNAKE_CASE_          =  1  # this will be return.

      for factor in range(1     ,      n + 1				):
            ans *= factor

      return ans





def      a__ (		__UpperCamelCase				):
      assert isinstance(__UpperCamelCase     ,      __UpperCamelCase				) and (n >= 0), "'n' must been an int and >= 0"

      SCREAMING_SNAKE_CASE_          =  0
      SCREAMING_SNAKE_CASE_          =  1
      SCREAMING_SNAKE_CASE_          =  1  # this will be return

      for _ in range(n - 1				):
            SCREAMING_SNAKE_CASE_          =  ans
            ans += fiba
            SCREAMING_SNAKE_CASE_          =  tmp

      return ans



import copy

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


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


@add_start_docstrings(SCREAMING_SNAKE_CASE__					)
class   lowerCamelCase					(SCREAMING_SNAKE_CASE__					):
  """simple docstring"""







  lowerCamelCase__     =						'''rag'''
  lowerCamelCase__     =						True







  def __init__(							self :       Any  ,     __magic_name__ :       Optional[int]=None  ,     __magic_name__ :       Dict=True  ,     __magic_name__ :       List[Any]=None  ,     __magic_name__ :       Optional[Any]=None  ,     __magic_name__ :       List[Any]=None  ,     __magic_name__ :       Any=None  ,     __magic_name__ :       Optional[Any]=None  ,     __magic_name__ :       Any=" / "  ,     __magic_name__ :       int=" // "  ,     __magic_name__ :       Any=5  ,     __magic_name__ :       Dict=300  ,     __magic_name__ :       Optional[Any]=768  ,     __magic_name__ :       str=8  ,     __magic_name__ :       List[Any]="wiki_dpr"  ,     __magic_name__ :       Any="train"  ,     __magic_name__ :       Any="compressed"  ,     __magic_name__ :       List[Any]=None  ,     __magic_name__ :       Optional[int]=None  ,     __magic_name__ :       Optional[int]=False  ,     __magic_name__ :       Union[str, Any]=False  ,     __magic_name__ :       List[str]=0.0  ,     __magic_name__ :       Dict=True  ,     __magic_name__ :       str=False  ,     __magic_name__ :       int=False  ,     __magic_name__ :       Tuple=False  ,     __magic_name__ :       Tuple=True  ,     __magic_name__ :       Dict=None  ,     **__magic_name__ :       int  ,     )  ->	List[str]:
        super().__init__(
            bos_token_id=__magic_name__  ,     pad_token_id=__magic_name__  ,     eos_token_id=__magic_name__  ,     decoder_start_token_id=__magic_name__  ,     forced_eos_token_id=__magic_name__  ,     is_encoder_decoder=__magic_name__  ,     prefix=__magic_name__  ,     vocab_size=__magic_name__  ,     **__magic_name__  ,     )
        assert (
            "question_encoder" in kwargs and "generator" in kwargs
        ), "Config has to be initialized with question_encoder and generator config"
        SCREAMING_SNAKE_CASE_          =  kwargs.pop("question_encoder"   )
        SCREAMING_SNAKE_CASE_          =  question_encoder_config.pop("model_type"   )
        SCREAMING_SNAKE_CASE_          =  kwargs.pop("generator"   )
        SCREAMING_SNAKE_CASE_          =  decoder_config.pop("model_type"   )

        from ..auto.configuration_auto import AutoConfig

        SCREAMING_SNAKE_CASE_          =  AutoConfig.for_model(__magic_name__  ,     **__magic_name__   )
        SCREAMING_SNAKE_CASE_          =  AutoConfig.for_model(__magic_name__  ,     **__magic_name__   )

        SCREAMING_SNAKE_CASE_          =  reduce_loss
        SCREAMING_SNAKE_CASE_          =  label_smoothing
        SCREAMING_SNAKE_CASE_          =  exclude_bos_score
        SCREAMING_SNAKE_CASE_          =  do_marginalize

        SCREAMING_SNAKE_CASE_          =  title_sep
        SCREAMING_SNAKE_CASE_          =  doc_sep
        SCREAMING_SNAKE_CASE_          =  n_docs
        SCREAMING_SNAKE_CASE_          =  max_combined_length

        SCREAMING_SNAKE_CASE_          =  dataset
        SCREAMING_SNAKE_CASE_          =  dataset_split
        SCREAMING_SNAKE_CASE_          =  index_name

        SCREAMING_SNAKE_CASE_          =  retrieval_vector_size
        SCREAMING_SNAKE_CASE_          =  retrieval_batch_size
        SCREAMING_SNAKE_CASE_          =  passages_path
        SCREAMING_SNAKE_CASE_          =  index_path
        SCREAMING_SNAKE_CASE_          =  use_dummy_dataset

        SCREAMING_SNAKE_CASE_          =  output_retrieved

        SCREAMING_SNAKE_CASE_          =  do_deduplication

        SCREAMING_SNAKE_CASE_          =  use_cache

        if self.forced_eos_token_id is None:
              SCREAMING_SNAKE_CASE_          =  getattr(self.generator  ,     "forced_eos_token_id"  ,     __magic_name__   )







  @classmethod
  def    __A     (							cls :       Dict  ,     __magic_name__ :       PretrainedConfig  ,     __magic_name__ :       PretrainedConfig  ,     **__magic_name__ :       List[str]   )  ->	PretrainedConfig:
        return cls(question_encoder=question_encoder_config.to_dict()  ,     generator=generator_config.to_dict()  ,     **__magic_name__   )







  def    __A     (							self :       Any   )  ->	List[Any]:
        SCREAMING_SNAKE_CASE_          =  copy.deepcopy(self.__dict__   )
        SCREAMING_SNAKE_CASE_          =  self.question_encoder.to_dict()
        SCREAMING_SNAKE_CASE_          =  self.generator.to_dict()
        SCREAMING_SNAKE_CASE_          =  self.__class__.model_type
        return output


