





'''simple docstring'''


from __future__ import annotations

from math import gcd


def 						__a(SCREAMING_SNAKE_CASE_	:       int		,							SCREAMING_SNAKE_CASE_	:       int = 2		,							SCREAMING_SNAKE_CASE_	:       int = 1		,							SCREAMING_SNAKE_CASE_	:       int = 3		,							):



    '''simple docstring'''





    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(SCREAMING_SNAKE_CASE_	:       int		,							SCREAMING_SNAKE_CASE_	:       int		,							SCREAMING_SNAKE_CASE_	:       int     ) -> int:
        return (pow(SCREAMING_SNAKE_CASE_		,							2     ) + step) % modulus

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

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

            # 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``.
            _lowerCAmelCase						      =   gcd(hare - tortoise		,							SCREAMING_SNAKE_CASE_     )

            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.
        _lowerCAmelCase						      =   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

       _SCREAMING_SNAKE_CASE									=				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",
       )
       _SCREAMING_SNAKE_CASE									=				parser.parse_args()

       _SCREAMING_SNAKE_CASE									=				pollard_rho(args.num, attempts=args.attempts)
       if divisor is None:
              print(f'''{args.num} is probably prime''')
       else:
              _SCREAMING_SNAKE_CASE									=				args.num // divisor
              print(f'''{args.num} = {divisor} * {quotient}''')










'''simple docstring'''



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 UpperCAmelCase_       (     __A					):




      """simple docstring"""




      UpperCamelCase_             =      '''char'''
      UpperCamelCase_             =      '''bpe'''
      UpperCamelCase_             =      '''wp'''





SCREAMING_SNAKE_CASE							=						(DecodeType.CHARACTER, DecodeType.BPE, DecodeType.WORDPIECE)
class UpperCAmelCase_       (     __A					):




      """simple docstring"""




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






      def __init__(			self      :		int  ,   UpperCAmelCase      :		Tuple=None  ,   UpperCAmelCase      :		Dict=None  ,   **UpperCAmelCase      :		Any		)	->	List[str]:


       '''simple docstring'''

       lowercase       : str						=None
       if "feature_extractor" in kwargs:
        warnings.warn(
            '''The `feature_extractor` argument is deprecated and will be removed in v5, use `image_processor`'''
            ''' instead.'''  ,   UpperCAmelCase  ,   )
        lowercase       : int						=kwargs.pop('''feature_extractor'''		)

       lowercase       : Optional[Any]						=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`.'''		)

       lowercase       : Any						=tokenizer
       lowercase       : Dict						=AutoTokenizer.from_pretrained('''gpt2'''		)
       lowercase       : Optional[int]						=AutoTokenizer.from_pretrained('''bert-base-uncased'''		)

       super().__init__(UpperCAmelCase  ,   UpperCAmelCase		)






      def __call__(			self      :		List[Any]  ,   UpperCAmelCase      :		Union[str, Any]=None  ,   UpperCAmelCase      :		List[str]=None  ,   UpperCAmelCase      :		Dict=None  ,   **UpperCAmelCase      :		Union[str, Any]		)	->	int:


       '''simple docstring'''

       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:
        lowercase       : str						=self.image_processor(UpperCAmelCase  ,   return_tensors=UpperCAmelCase  ,   **UpperCAmelCase		)
       if text is not None:
        lowercase       : Any						=self.char_tokenizer(UpperCAmelCase  ,   return_tensors=UpperCAmelCase  ,   **UpperCAmelCase		)

       if text is None:
        return inputs
       elif images is None:
        return encodings
       else:
        lowercase       : List[str]						=encodings['''input_ids''']
        return inputs






      def 					A__   (			self      :		List[Any]  ,   UpperCAmelCase      :		Optional[Any]		)	->	Optional[Any]:


       '''simple docstring'''

       lowercase	,		lowercase	,		lowercase       : Union[str, Any]						=sequences
       lowercase       : Dict						=char_preds.size(0		)

       lowercase	,		lowercase       : Any						=self._decode_helper(UpperCAmelCase  ,   '''char'''		)
       lowercase	,		lowercase       : int						=self._decode_helper(UpperCAmelCase  ,   '''bpe'''		)
       lowercase	,		lowercase       : Optional[Any]						=self._decode_helper(UpperCAmelCase  ,   '''wp'''		)

       lowercase       : Dict						=[]
       lowercase       : List[Any]						=[]
       for i in range(UpperCAmelCase		):
        lowercase       : List[str]						=[char_scores[i], bpe_scores[i], wp_scores[i]]
        lowercase       : Union[str, Any]						=[char_strs[i], bpe_strs[i], wp_strs[i]]
        lowercase       : List[str]						=scores.index(max(UpperCAmelCase		)		)
        final_strs.append(strs[max_score_index]		)
        final_scores.append(scores[max_score_index]		)

       lowercase       : List[Any]						={}
       lowercase       : Optional[Any]						=final_strs
       lowercase       : Optional[Any]						=final_scores
       lowercase       : str						=char_strs
       lowercase       : Tuple						=bpe_strs
       lowercase       : List[str]						=wp_strs
       return out






      def 					A__   (			self      :		str  ,   UpperCAmelCase      :		Dict  ,   UpperCAmelCase      :		Union[str, Any]		)	->	Optional[int]:


       '''simple docstring'''

       if format == DecodeType.CHARACTER:
        lowercase       : Union[str, Any]						=self.char_decode
        lowercase       : List[str]						=1
        lowercase       : Tuple						='''[s]'''
       elif format == DecodeType.BPE:
        lowercase       : Union[str, Any]						=self.bpe_decode
        lowercase       : Optional[int]						=2
        lowercase       : Optional[Any]						='''#'''
       elif format == DecodeType.WORDPIECE:
        lowercase       : List[str]						=self.wp_decode
        lowercase       : Union[str, Any]						=102
        lowercase       : int						='''[SEP]'''
       else:
        raise ValueError(f'Format {format} is not supported.'		)

       lowercase	,		lowercase       : Union[str, Any]						=[], []
       lowercase       : Optional[int]						=pred_logits.size(0		)
       lowercase       : List[str]						=pred_logits.size(1		)
       lowercase	,		lowercase       : Optional[int]						=pred_logits.topk(1  ,   dim=-1  ,   largest=UpperCAmelCase  ,   sorted=UpperCAmelCase		)
       lowercase       : Tuple						=preds_index.view(-1  ,   UpperCAmelCase		)[:, 1:]
       lowercase       : Any						=decoder(UpperCAmelCase		)
       lowercase	,		lowercase       : List[str]						=torch.nn.functional.softmax(UpperCAmelCase  ,   dim=2		).max(dim=2		)
       lowercase       : List[Any]						=preds_max_prob[:, 1:]

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

       return dec_strs, conf_scores






      def 					A__   (			self      :		List[str]  ,   UpperCAmelCase      :		Optional[int]		)	->	Dict:


       '''simple docstring'''

       lowercase       : Union[str, Any]						=[seq.replace(''' '''  ,   ''''''		) for seq in self.char_tokenizer.batch_decode(UpperCAmelCase		)]
       return decode_strs






      def 					A__   (			self      :		Optional[int]  ,   UpperCAmelCase      :		Optional[Any]		)	->	str:


       '''simple docstring'''

       return self.bpe_tokenizer.batch_decode(UpperCAmelCase		)






      def 					A__   (			self      :		Tuple  ,   UpperCAmelCase      :		Dict		)	->	List[str]:


       '''simple docstring'''

       lowercase       : str						=[seq.replace(''' '''  ,   ''''''		) for seq in self.wp_tokenizer.batch_decode(UpperCAmelCase		)]
       return decode_strs



