





from __future__ import annotations

from math import gcd



def    __lowercase   (      _SCREAMING_SNAKE_CASE ,						_SCREAMING_SNAKE_CASE = 2 ,						_SCREAMING_SNAKE_CASE = 1 ,						_SCREAMING_SNAKE_CASE = 3 ,						) ->   int | None:


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

      for _ in range(_SCREAMING_SNAKE_CASE	):
            # 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(_SCREAMING_SNAKE_CASE ,						_SCREAMING_SNAKE_CASE ,						_SCREAMING_SNAKE_CASE	)
                  SCREAMING_SNAKE_CASE		=						rand_fn(_SCREAMING_SNAKE_CASE ,						_SCREAMING_SNAKE_CASE ,						_SCREAMING_SNAKE_CASE	)
                  SCREAMING_SNAKE_CASE		=						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``.
                  SCREAMING_SNAKE_CASE		=						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.
            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

      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}''')









from collections import OrderedDict

from ...utils import logging
from .auto_factory import _BaseAutoModelClass, _LazyAutoMapping, auto_class_update
from .configuration_auto import CONFIG_MAPPING_NAMES


SCREAMING_SNAKE_CASE_						   =       logging.get_logger(__name__)


SCREAMING_SNAKE_CASE_						   =       OrderedDict(
    [
        # Base model mapping
        ("""albert""", """FlaxAlbertModel"""),
        ("""bart""", """FlaxBartModel"""),
        ("""beit""", """FlaxBeitModel"""),
        ("""bert""", """FlaxBertModel"""),
        ("""big_bird""", """FlaxBigBirdModel"""),
        ("""blenderbot""", """FlaxBlenderbotModel"""),
        ("""blenderbot-small""", """FlaxBlenderbotSmallModel"""),
        ("""clip""", """FlaxCLIPModel"""),
        ("""distilbert""", """FlaxDistilBertModel"""),
        ("""electra""", """FlaxElectraModel"""),
        ("""gpt-sw3""", """FlaxGPT2Model"""),
        ("""gpt2""", """FlaxGPT2Model"""),
        ("""gpt_neo""", """FlaxGPTNeoModel"""),
        ("""gptj""", """FlaxGPTJModel"""),
        ("""longt5""", """FlaxLongT5Model"""),
        ("""marian""", """FlaxMarianModel"""),
        ("""mbart""", """FlaxMBartModel"""),
        ("""mt5""", """FlaxMT5Model"""),
        ("""opt""", """FlaxOPTModel"""),
        ("""pegasus""", """FlaxPegasusModel"""),
        ("""regnet""", """FlaxRegNetModel"""),
        ("""resnet""", """FlaxResNetModel"""),
        ("""roberta""", """FlaxRobertaModel"""),
        ("""roberta-prelayernorm""", """FlaxRobertaPreLayerNormModel"""),
        ("""roformer""", """FlaxRoFormerModel"""),
        ("""t5""", """FlaxT5Model"""),
        ("""vision-text-dual-encoder""", """FlaxVisionTextDualEncoderModel"""),
        ("""vit""", """FlaxViTModel"""),
        ("""wav2vec2""", """FlaxWav2Vec2Model"""),
        ("""whisper""", """FlaxWhisperModel"""),
        ("""xglm""", """FlaxXGLMModel"""),
        ("""xlm-roberta""", """FlaxXLMRobertaModel"""),
    ]
)

SCREAMING_SNAKE_CASE_						   =       OrderedDict(
    [
        # Model for pre-training mapping
        ("""albert""", """FlaxAlbertForPreTraining"""),
        ("""bart""", """FlaxBartForConditionalGeneration"""),
        ("""bert""", """FlaxBertForPreTraining"""),
        ("""big_bird""", """FlaxBigBirdForPreTraining"""),
        ("""electra""", """FlaxElectraForPreTraining"""),
        ("""longt5""", """FlaxLongT5ForConditionalGeneration"""),
        ("""mbart""", """FlaxMBartForConditionalGeneration"""),
        ("""mt5""", """FlaxMT5ForConditionalGeneration"""),
        ("""roberta""", """FlaxRobertaForMaskedLM"""),
        ("""roberta-prelayernorm""", """FlaxRobertaPreLayerNormForMaskedLM"""),
        ("""roformer""", """FlaxRoFormerForMaskedLM"""),
        ("""t5""", """FlaxT5ForConditionalGeneration"""),
        ("""wav2vec2""", """FlaxWav2Vec2ForPreTraining"""),
        ("""whisper""", """FlaxWhisperForConditionalGeneration"""),
        ("""xlm-roberta""", """FlaxXLMRobertaForMaskedLM"""),
    ]
)

SCREAMING_SNAKE_CASE_						   =       OrderedDict(
    [
        # Model for Masked LM mapping
        ("""albert""", """FlaxAlbertForMaskedLM"""),
        ("""bart""", """FlaxBartForConditionalGeneration"""),
        ("""bert""", """FlaxBertForMaskedLM"""),
        ("""big_bird""", """FlaxBigBirdForMaskedLM"""),
        ("""distilbert""", """FlaxDistilBertForMaskedLM"""),
        ("""electra""", """FlaxElectraForMaskedLM"""),
        ("""mbart""", """FlaxMBartForConditionalGeneration"""),
        ("""roberta""", """FlaxRobertaForMaskedLM"""),
        ("""roberta-prelayernorm""", """FlaxRobertaPreLayerNormForMaskedLM"""),
        ("""roformer""", """FlaxRoFormerForMaskedLM"""),
        ("""xlm-roberta""", """FlaxXLMRobertaForMaskedLM"""),
    ]
)

SCREAMING_SNAKE_CASE_						   =       OrderedDict(
    [
        # Model for Seq2Seq Causal LM mapping
        ("""bart""", """FlaxBartForConditionalGeneration"""),
        ("""blenderbot""", """FlaxBlenderbotForConditionalGeneration"""),
        ("""blenderbot-small""", """FlaxBlenderbotSmallForConditionalGeneration"""),
        ("""encoder-decoder""", """FlaxEncoderDecoderModel"""),
        ("""longt5""", """FlaxLongT5ForConditionalGeneration"""),
        ("""marian""", """FlaxMarianMTModel"""),
        ("""mbart""", """FlaxMBartForConditionalGeneration"""),
        ("""mt5""", """FlaxMT5ForConditionalGeneration"""),
        ("""pegasus""", """FlaxPegasusForConditionalGeneration"""),
        ("""t5""", """FlaxT5ForConditionalGeneration"""),
    ]
)

SCREAMING_SNAKE_CASE_						   =       OrderedDict(
    [
        # Model for Image-classsification
        ("""beit""", """FlaxBeitForImageClassification"""),
        ("""regnet""", """FlaxRegNetForImageClassification"""),
        ("""resnet""", """FlaxResNetForImageClassification"""),
        ("""vit""", """FlaxViTForImageClassification"""),
    ]
)

SCREAMING_SNAKE_CASE_						   =       OrderedDict(
    [
        ("""vision-encoder-decoder""", """FlaxVisionEncoderDecoderModel"""),
    ]
)

SCREAMING_SNAKE_CASE_						   =       OrderedDict(
    [
        # Model for Causal LM mapping
        ("""bart""", """FlaxBartForCausalLM"""),
        ("""bert""", """FlaxBertForCausalLM"""),
        ("""big_bird""", """FlaxBigBirdForCausalLM"""),
        ("""electra""", """FlaxElectraForCausalLM"""),
        ("""gpt-sw3""", """FlaxGPT2LMHeadModel"""),
        ("""gpt2""", """FlaxGPT2LMHeadModel"""),
        ("""gpt_neo""", """FlaxGPTNeoForCausalLM"""),
        ("""gptj""", """FlaxGPTJForCausalLM"""),
        ("""opt""", """FlaxOPTForCausalLM"""),
        ("""roberta""", """FlaxRobertaForCausalLM"""),
        ("""roberta-prelayernorm""", """FlaxRobertaPreLayerNormForCausalLM"""),
        ("""xglm""", """FlaxXGLMForCausalLM"""),
        ("""xlm-roberta""", """FlaxXLMRobertaForCausalLM"""),
    ]
)

SCREAMING_SNAKE_CASE_						   =       OrderedDict(
    [
        # Model for Sequence Classification mapping
        ("""albert""", """FlaxAlbertForSequenceClassification"""),
        ("""bart""", """FlaxBartForSequenceClassification"""),
        ("""bert""", """FlaxBertForSequenceClassification"""),
        ("""big_bird""", """FlaxBigBirdForSequenceClassification"""),
        ("""distilbert""", """FlaxDistilBertForSequenceClassification"""),
        ("""electra""", """FlaxElectraForSequenceClassification"""),
        ("""mbart""", """FlaxMBartForSequenceClassification"""),
        ("""roberta""", """FlaxRobertaForSequenceClassification"""),
        ("""roberta-prelayernorm""", """FlaxRobertaPreLayerNormForSequenceClassification"""),
        ("""roformer""", """FlaxRoFormerForSequenceClassification"""),
        ("""xlm-roberta""", """FlaxXLMRobertaForSequenceClassification"""),
    ]
)

SCREAMING_SNAKE_CASE_						   =       OrderedDict(
    [
        # Model for Question Answering mapping
        ("""albert""", """FlaxAlbertForQuestionAnswering"""),
        ("""bart""", """FlaxBartForQuestionAnswering"""),
        ("""bert""", """FlaxBertForQuestionAnswering"""),
        ("""big_bird""", """FlaxBigBirdForQuestionAnswering"""),
        ("""distilbert""", """FlaxDistilBertForQuestionAnswering"""),
        ("""electra""", """FlaxElectraForQuestionAnswering"""),
        ("""mbart""", """FlaxMBartForQuestionAnswering"""),
        ("""roberta""", """FlaxRobertaForQuestionAnswering"""),
        ("""roberta-prelayernorm""", """FlaxRobertaPreLayerNormForQuestionAnswering"""),
        ("""roformer""", """FlaxRoFormerForQuestionAnswering"""),
        ("""xlm-roberta""", """FlaxXLMRobertaForQuestionAnswering"""),
    ]
)

SCREAMING_SNAKE_CASE_						   =       OrderedDict(
    [
        # Model for Token Classification mapping
        ("""albert""", """FlaxAlbertForTokenClassification"""),
        ("""bert""", """FlaxBertForTokenClassification"""),
        ("""big_bird""", """FlaxBigBirdForTokenClassification"""),
        ("""distilbert""", """FlaxDistilBertForTokenClassification"""),
        ("""electra""", """FlaxElectraForTokenClassification"""),
        ("""roberta""", """FlaxRobertaForTokenClassification"""),
        ("""roberta-prelayernorm""", """FlaxRobertaPreLayerNormForTokenClassification"""),
        ("""roformer""", """FlaxRoFormerForTokenClassification"""),
        ("""xlm-roberta""", """FlaxXLMRobertaForTokenClassification"""),
    ]
)

SCREAMING_SNAKE_CASE_						   =       OrderedDict(
    [
        # Model for Multiple Choice mapping
        ("""albert""", """FlaxAlbertForMultipleChoice"""),
        ("""bert""", """FlaxBertForMultipleChoice"""),
        ("""big_bird""", """FlaxBigBirdForMultipleChoice"""),
        ("""distilbert""", """FlaxDistilBertForMultipleChoice"""),
        ("""electra""", """FlaxElectraForMultipleChoice"""),
        ("""roberta""", """FlaxRobertaForMultipleChoice"""),
        ("""roberta-prelayernorm""", """FlaxRobertaPreLayerNormForMultipleChoice"""),
        ("""roformer""", """FlaxRoFormerForMultipleChoice"""),
        ("""xlm-roberta""", """FlaxXLMRobertaForMultipleChoice"""),
    ]
)

SCREAMING_SNAKE_CASE_						   =       OrderedDict(
    [
        ("""bert""", """FlaxBertForNextSentencePrediction"""),
    ]
)

SCREAMING_SNAKE_CASE_						   =       OrderedDict(
    [
        ("""speech-encoder-decoder""", """FlaxSpeechEncoderDecoderModel"""),
        ("""whisper""", """FlaxWhisperForConditionalGeneration"""),
    ]
)

SCREAMING_SNAKE_CASE_						   =       OrderedDict(
    [
        ("""whisper""", """FlaxWhisperForAudioClassification"""),
    ]
)

SCREAMING_SNAKE_CASE_						   =       _LazyAutoMapping(CONFIG_MAPPING_NAMES, FLAX_MODEL_MAPPING_NAMES)
SCREAMING_SNAKE_CASE_						   =       _LazyAutoMapping(CONFIG_MAPPING_NAMES, FLAX_MODEL_FOR_PRETRAINING_MAPPING_NAMES)
SCREAMING_SNAKE_CASE_						   =       _LazyAutoMapping(CONFIG_MAPPING_NAMES, FLAX_MODEL_FOR_MASKED_LM_MAPPING_NAMES)
SCREAMING_SNAKE_CASE_						   =       _LazyAutoMapping(
    CONFIG_MAPPING_NAMES, FLAX_MODEL_FOR_SEQ_TO_SEQ_CAUSAL_LM_MAPPING_NAMES
)
SCREAMING_SNAKE_CASE_						   =       _LazyAutoMapping(
    CONFIG_MAPPING_NAMES, FLAX_MODEL_FOR_IMAGE_CLASSIFICATION_MAPPING_NAMES
)
SCREAMING_SNAKE_CASE_						   =       _LazyAutoMapping(CONFIG_MAPPING_NAMES, FLAX_MODEL_FOR_VISION_2_SEQ_MAPPING_NAMES)
SCREAMING_SNAKE_CASE_						   =       _LazyAutoMapping(CONFIG_MAPPING_NAMES, FLAX_MODEL_FOR_CAUSAL_LM_MAPPING_NAMES)
SCREAMING_SNAKE_CASE_						   =       _LazyAutoMapping(
    CONFIG_MAPPING_NAMES, FLAX_MODEL_FOR_SEQUENCE_CLASSIFICATION_MAPPING_NAMES
)
SCREAMING_SNAKE_CASE_						   =       _LazyAutoMapping(
    CONFIG_MAPPING_NAMES, FLAX_MODEL_FOR_QUESTION_ANSWERING_MAPPING_NAMES
)
SCREAMING_SNAKE_CASE_						   =       _LazyAutoMapping(
    CONFIG_MAPPING_NAMES, FLAX_MODEL_FOR_TOKEN_CLASSIFICATION_MAPPING_NAMES
)
SCREAMING_SNAKE_CASE_						   =       _LazyAutoMapping(
    CONFIG_MAPPING_NAMES, FLAX_MODEL_FOR_MULTIPLE_CHOICE_MAPPING_NAMES
)
SCREAMING_SNAKE_CASE_						   =       _LazyAutoMapping(
    CONFIG_MAPPING_NAMES, FLAX_MODEL_FOR_NEXT_SENTENCE_PREDICTION_MAPPING_NAMES
)
SCREAMING_SNAKE_CASE_						   =       _LazyAutoMapping(
    CONFIG_MAPPING_NAMES, FLAX_MODEL_FOR_SPEECH_SEQ_2_SEQ_MAPPING_NAMES
)
SCREAMING_SNAKE_CASE_						   =       _LazyAutoMapping(
    CONFIG_MAPPING_NAMES, FLAX_MODEL_FOR_AUDIO_CLASSIFICATION_MAPPING_NAMES
)

class 		UpperCamelCase__ (      _BaseAutoModelClass   ):



     '''simple docstring'''

     __snake_case    :	List[str]			=			FLAX_MODEL_MAPPING
SCREAMING_SNAKE_CASE_						   =       auto_class_update(FlaxAutoModel)

class 		UpperCamelCase__ (      _BaseAutoModelClass   ):



     '''simple docstring'''

     __snake_case    :	Dict			=			FLAX_MODEL_FOR_PRETRAINING_MAPPING
SCREAMING_SNAKE_CASE_						   =       auto_class_update(FlaxAutoModelForPreTraining, head_doc="""pretraining""")

class 		UpperCamelCase__ (      _BaseAutoModelClass   ):



     '''simple docstring'''

     __snake_case    :	Optional[Any]			=			FLAX_MODEL_FOR_CAUSAL_LM_MAPPING
SCREAMING_SNAKE_CASE_						   =       auto_class_update(FlaxAutoModelForCausalLM, head_doc="""causal language modeling""")

class 		UpperCamelCase__ (      _BaseAutoModelClass   ):



     '''simple docstring'''

     __snake_case    :	Any			=			FLAX_MODEL_FOR_MASKED_LM_MAPPING
SCREAMING_SNAKE_CASE_						   =       auto_class_update(FlaxAutoModelForMaskedLM, head_doc="""masked language modeling""")

class 		UpperCamelCase__ (      _BaseAutoModelClass   ):



     '''simple docstring'''

     __snake_case    :	int			=			FLAX_MODEL_FOR_SEQ_TO_SEQ_CAUSAL_LM_MAPPING
SCREAMING_SNAKE_CASE_						   =       auto_class_update(
    FlaxAutoModelForSeqaSeqLM, head_doc="""sequence-to-sequence language modeling""", checkpoint_for_example="""t5-base"""
)

class 		UpperCamelCase__ (      _BaseAutoModelClass   ):



     '''simple docstring'''

     __snake_case    :	Optional[int]			=			FLAX_MODEL_FOR_SEQUENCE_CLASSIFICATION_MAPPING
SCREAMING_SNAKE_CASE_						   =       auto_class_update(
    FlaxAutoModelForSequenceClassification, head_doc="""sequence classification"""
)

class 		UpperCamelCase__ (      _BaseAutoModelClass   ):



     '''simple docstring'''

     __snake_case    :	List[Any]			=			FLAX_MODEL_FOR_QUESTION_ANSWERING_MAPPING
SCREAMING_SNAKE_CASE_						   =       auto_class_update(FlaxAutoModelForQuestionAnswering, head_doc="""question answering""")

class 		UpperCamelCase__ (      _BaseAutoModelClass   ):



     '''simple docstring'''

     __snake_case    :	Tuple			=			FLAX_MODEL_FOR_TOKEN_CLASSIFICATION_MAPPING
SCREAMING_SNAKE_CASE_						   =       auto_class_update(
    FlaxAutoModelForTokenClassification, head_doc="""token classification"""
)

class 		UpperCamelCase__ (      _BaseAutoModelClass   ):



     '''simple docstring'''

     __snake_case    :	Union[str, Any]			=			FLAX_MODEL_FOR_MULTIPLE_CHOICE_MAPPING
SCREAMING_SNAKE_CASE_						   =       auto_class_update(FlaxAutoModelForMultipleChoice, head_doc="""multiple choice""")

class 		UpperCamelCase__ (      _BaseAutoModelClass   ):



     '''simple docstring'''

     __snake_case    :	List[str]			=			FLAX_MODEL_FOR_NEXT_SENTENCE_PREDICTION_MAPPING
SCREAMING_SNAKE_CASE_						   =       auto_class_update(
    FlaxAutoModelForNextSentencePrediction, head_doc="""next sentence prediction"""
)

class 		UpperCamelCase__ (      _BaseAutoModelClass   ):



     '''simple docstring'''

     __snake_case    :	Dict			=			FLAX_MODEL_FOR_IMAGE_CLASSIFICATION_MAPPING
SCREAMING_SNAKE_CASE_						   =       auto_class_update(
    FlaxAutoModelForImageClassification, head_doc="""image classification"""
)

class 		UpperCamelCase__ (      _BaseAutoModelClass   ):



     '''simple docstring'''

     __snake_case    :	Dict			=			FLAX_MODEL_FOR_VISION_2_SEQ_MAPPING
SCREAMING_SNAKE_CASE_						   =       auto_class_update(FlaxAutoModelForVisionaSeq, head_doc="""vision-to-text modeling""")

class 		UpperCamelCase__ (      _BaseAutoModelClass   ):



     '''simple docstring'''

     __snake_case    :	Optional[Any]			=			FLAX_MODEL_FOR_SPEECH_SEQ_2_SEQ_MAPPING
SCREAMING_SNAKE_CASE_						   =       auto_class_update(
    FlaxAutoModelForSpeechSeqaSeq, head_doc="""sequence-to-sequence speech-to-text modeling"""
)


