from __future__ import annotations

from math import gcd


def    a__       (						__UpperCamelCase   ,					__UpperCamelCase = 2   ,					__UpperCamelCase = 1   ,					__UpperCamelCase = 3   ,					):
      # A value less than 2 can cause an infinite loop in the algorithm.
      if num < 2:
            raise ValueError("The input value cannot be less than 2" )

      # Because of the relationship between ``f(f(x))`` and ``f(x)``, this
      # algorithm struggles to find factors that are divisible by two.
      # As a workaround, we specifically check for two and even inputs.
      #   See: https://math.stackexchange.com/a/2856214/165820
      if num > 2 and num % 2 == 0:
            return 2

      # Pollard's Rho algorithm requires a function that returns pseudorandom
      # values between 0 <= X < ``num``.  It doesn't need to be random in the
      # sense that the output value is cryptographically secure or difficult
      # to calculate, it only needs to be random in the sense that all output
      # values should be equally likely to appear.
      # For this reason, Pollard suggested using ``f(x) = (x**2 - 1) % num``
      # However, the success of Pollard's algorithm isn't guaranteed and is
      # determined in part by the initial seed and the chosen random function.
      # To make retries easier, we will instead use ``f(x) = (x**2 + C) % num``
      # where ``C`` is a value that we can modify between each attempt.
      def rand_fn(__UpperCamelCase   ,					__UpperCamelCase   ,					__UpperCamelCase ) -> int:
            return (pow(__UpperCamelCase   ,					2 ) + step) % modulus

      for _ in range(__UpperCamelCase ):
            # These track the position within the cycle detection logic.
            SCREAMING_SNAKE_CASE_      =     seed
            SCREAMING_SNAKE_CASE_      =     seed

            while True:
                  # At each iteration, the tortoise moves one step and the hare moves two.
                  SCREAMING_SNAKE_CASE_      =     rand_fn(__UpperCamelCase   ,					__UpperCamelCase   ,					__UpperCamelCase )
                  SCREAMING_SNAKE_CASE_      =     rand_fn(__UpperCamelCase   ,					__UpperCamelCase   ,					__UpperCamelCase )
                  SCREAMING_SNAKE_CASE_      =     rand_fn(__UpperCamelCase   ,					__UpperCamelCase   ,					__UpperCamelCase )

                  # At some point both the tortoise and the hare will enter a cycle whose
                  # length ``p`` is a divisor of ``num``.  Once in that cycle, at some point
                  # the tortoise and hare will end up on the same value modulo ``p``.
                  # We can detect when this happens because the position difference between
                  # the tortoise and the hare will share a common divisor with ``num``.
                  SCREAMING_SNAKE_CASE_      =     gcd(hare - tortoise   ,					__UpperCamelCase )

                  if divisor == 1:
                        # No common divisor yet, just keep searching.
                        continue
                  else:
                        # We found a common divisor!
                        if divisor == num:
                              # Unfortunately, the divisor is ``num`` itself and is useless.
                              break
                        else:
                              # The divisor is a nontrivial factor of ``num``!
                              return divisor

        # If we made it here, then this attempt failed.
        # We need to pick a new starting seed for the tortoise and hare
        # in addition to a new step value for the random function.
        # To keep this example implementation deterministic, the
        # new values will be generated based on currently available
        # values instead of using something like ``random.randint``.

        # We can use the hare's position as the new seed.
        # This is actually what Richard Brent's the "optimized" variant does.
            SCREAMING_SNAKE_CASE_      =     hare

            # The new step value for the random function can just be incremented.
            # At first the results will be similar to what the old function would
            # have produced, but the value will quickly diverge after a bit.
            step += 1

      # We haven't found a divisor within the requested number of attempts.
      # We were unlucky or ``num`` itself is actually prime.
      return None


if __name__ == "__main__":
      import argparse

      A   :     Dict       =				argparse.ArgumentParser()
      parser.add_argument(
          "num",
          type=int,
          help="The value to find a divisor of",
      )
      parser.add_argument(
          "--attempts",
          type=int,
          default=3,
          help="The number of attempts before giving up",
      )
      A   :     Dict       =				parser.parse_args()

      A   :     Union[str, Any]       =				pollard_rho(args.num, attempts=args.attempts)
      if divisor is None:
            print(f"{args.num} is probably prime")
      else:
            A   :     Optional[Any]       =				args.num // divisor
            print(f"{args.num} = {divisor} * {quotient}")



import warnings

from transformers import AutoTokenizer
from transformers.utils import is_torch_available
from transformers.utils.generic import ExplicitEnum

from ...processing_utils import ProcessorMixin


if is_torch_available():
      import torch


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







  lowerCamelCase__   =  '''char'''
  lowerCamelCase__   =  '''bpe'''
  lowerCamelCase__   =  '''wp'''



A   :     Tuple       =				(DecodeType.CHARACTER, DecodeType.BPE, DecodeType.WORDPIECE)


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







  lowerCamelCase__   =  ['''image_processor''', '''char_tokenizer''']
  lowerCamelCase__   =  '''ViTImageProcessor'''
  lowerCamelCase__   =  '''MgpstrTokenizer'''







  def __init__(							self       :				Optional[Any]     ,   __magic_name__       :				Tuple=None     ,   __magic_name__       :				int=None     ,   **__magic_name__       :				Optional[Any]      )     ->		str:
        SCREAMING_SNAKE_CASE_      =     None
        if "feature_extractor" in kwargs:
              warnings.warn(
                  "The `feature_extractor` argument is deprecated and will be removed in v5, use `image_processor`"
                  " instead."     ,   __magic_name__     ,   )
              SCREAMING_SNAKE_CASE_      =     kwargs.pop("feature_extractor"      )

        SCREAMING_SNAKE_CASE_      =     image_processor if image_processor is not None else feature_extractor
        if image_processor is None:
              raise ValueError("You need to specify an `image_processor`."      )
        if tokenizer is None:
              raise ValueError("You need to specify a `tokenizer`."      )

        SCREAMING_SNAKE_CASE_      =     tokenizer
        SCREAMING_SNAKE_CASE_      =     AutoTokenizer.from_pretrained("gpt2"      )
        SCREAMING_SNAKE_CASE_      =     AutoTokenizer.from_pretrained("bert-base-uncased"      )

        super().__init__(__magic_name__     ,   __magic_name__      )







  def __call__(							self       :				Dict     ,   __magic_name__       :				Union[str, Any]=None     ,   __magic_name__       :				Union[str, Any]=None     ,   __magic_name__       :				Dict=None     ,   **__magic_name__       :				Tuple      )     ->		int:
        if images is None and text is None:
              raise ValueError("You need to specify either an `images` or `text` input to process."      )

        if images is not None:
              SCREAMING_SNAKE_CASE_      =     self.image_processor(__magic_name__     ,   return_tensors=__magic_name__     ,   **__magic_name__      )
        if text is not None:
              SCREAMING_SNAKE_CASE_      =     self.char_tokenizer(__magic_name__     ,   return_tensors=__magic_name__     ,   **__magic_name__      )

        if text is None:
              return inputs
        elif images is None:
              return encodings
        else:
              SCREAMING_SNAKE_CASE_      =     encodings["input_ids"]
              return inputs







  def       __A   (							self       :				Tuple     ,   __magic_name__       :				int      )     ->		Any:
        SCREAMING_SNAKE_CASE_   ,       SCREAMING_SNAKE_CASE_   ,       SCREAMING_SNAKE_CASE_      =     sequences
        SCREAMING_SNAKE_CASE_      =     char_preds.size(0      )

        SCREAMING_SNAKE_CASE_   ,       SCREAMING_SNAKE_CASE_      =     self._decode_helper(__magic_name__     ,   "char"      )
        SCREAMING_SNAKE_CASE_   ,       SCREAMING_SNAKE_CASE_      =     self._decode_helper(__magic_name__     ,   "bpe"      )
        SCREAMING_SNAKE_CASE_   ,       SCREAMING_SNAKE_CASE_      =     self._decode_helper(__magic_name__     ,   "wp"      )

        SCREAMING_SNAKE_CASE_      =     []
        SCREAMING_SNAKE_CASE_      =     []
        for i in range(__magic_name__      ):
              SCREAMING_SNAKE_CASE_      =     [char_scores[i], bpe_scores[i], wp_scores[i]]
              SCREAMING_SNAKE_CASE_      =     [char_strs[i], bpe_strs[i], wp_strs[i]]
              SCREAMING_SNAKE_CASE_      =     scores.index(max(__magic_name__      )      )
              final_strs.append(strs[max_score_index]      )
              final_scores.append(scores[max_score_index]      )

        SCREAMING_SNAKE_CASE_      =     {}
        SCREAMING_SNAKE_CASE_      =     final_strs
        SCREAMING_SNAKE_CASE_      =     final_scores
        SCREAMING_SNAKE_CASE_      =     char_strs
        SCREAMING_SNAKE_CASE_      =     bpe_strs
        SCREAMING_SNAKE_CASE_      =     wp_strs
        return out







  def       __A   (							self       :				int     ,   __magic_name__       :				List[Any]     ,   __magic_name__       :				str      )     ->		Any:
        if format == DecodeType.CHARACTER:
              SCREAMING_SNAKE_CASE_      =     self.char_decode
              SCREAMING_SNAKE_CASE_      =     1
              SCREAMING_SNAKE_CASE_      =     "[s]"
        elif format == DecodeType.BPE:
              SCREAMING_SNAKE_CASE_      =     self.bpe_decode
              SCREAMING_SNAKE_CASE_      =     2
              SCREAMING_SNAKE_CASE_      =     "#"
        elif format == DecodeType.WORDPIECE:
              SCREAMING_SNAKE_CASE_      =     self.wp_decode
              SCREAMING_SNAKE_CASE_      =     102
              SCREAMING_SNAKE_CASE_      =     "[SEP]"
        else:
              raise ValueError(F'''Format {format} is not supported.'''      )

        SCREAMING_SNAKE_CASE_   ,       SCREAMING_SNAKE_CASE_      =     [], []
        SCREAMING_SNAKE_CASE_      =     pred_logits.size(0      )
        SCREAMING_SNAKE_CASE_      =     pred_logits.size(1      )
        SCREAMING_SNAKE_CASE_   ,       SCREAMING_SNAKE_CASE_      =     pred_logits.topk(1     ,   dim=-1     ,   largest=__magic_name__     ,   sorted=__magic_name__      )
        SCREAMING_SNAKE_CASE_      =     preds_index.view(-1     ,   __magic_name__      )[:, 1:]
        SCREAMING_SNAKE_CASE_      =     decoder(__magic_name__      )
        SCREAMING_SNAKE_CASE_   ,       SCREAMING_SNAKE_CASE_      =     torch.nn.functional.softmax(__magic_name__     ,   dim=2      ).max(dim=2      )
        SCREAMING_SNAKE_CASE_      =     preds_max_prob[:, 1:]

        for index in range(__magic_name__      ):
              SCREAMING_SNAKE_CASE_      =     preds_str[index].find(__magic_name__      )
              SCREAMING_SNAKE_CASE_      =     preds_str[index][:pred_eos]
              SCREAMING_SNAKE_CASE_      =     preds_index[index].cpu().tolist()
              SCREAMING_SNAKE_CASE_      =     pred_index.index(__magic_name__      ) if eos_token in pred_index else -1
              SCREAMING_SNAKE_CASE_      =     preds_max_prob[index][: pred_eos_index + 1]
              SCREAMING_SNAKE_CASE_      =     pred_max_prob.cumprod(dim=0      )[-1] if pred_max_prob.nelement() != 0 else 0.0
              dec_strs.append(__magic_name__      )
              conf_scores.append(__magic_name__      )

        return dec_strs, conf_scores







  def       __A   (							self       :				Any     ,   __magic_name__       :				Dict      )     ->		List[str]:
        SCREAMING_SNAKE_CASE_      =     [seq.replace(" "     ,   ""      ) for seq in self.char_tokenizer.batch_decode(__magic_name__      )]
        return decode_strs







  def       __A   (							self       :				Any     ,   __magic_name__       :				Union[str, Any]      )     ->		Tuple:
        return self.bpe_tokenizer.batch_decode(__magic_name__      )







  def       __A   (							self       :				str     ,   __magic_name__       :				Dict      )     ->		List[Any]:
        SCREAMING_SNAKE_CASE_      =     [seq.replace(" "     ,   ""      ) for seq in self.wp_tokenizer.batch_decode(__magic_name__      )]
        return decode_strs


