


"""simple docstring"""


_snake_case          =							"0.18.2"

from .configuration_utils import ConfigMixin
from .utils import (
    OptionalDependencyNotAvailable,
    is_flax_available,
    is_inflect_available,
    is_invisible_watermark_available,
    is_k_diffusion_available,
    is_k_diffusion_version,
    is_librosa_available,
    is_note_seq_available,
    is_onnx_available,
    is_scipy_available,
    is_torch_available,
    is_torchsde_available,
    is_transformers_available,
    is_transformers_version,
    is_unidecode_available,
    logging,
)


try:
   if not is_onnx_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   from .utils.dummy_onnx_objects import *  # noqa F403
else:
   from .pipelines import OnnxRuntimeModel

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   from .utils.dummy_pt_objects import *  # noqa F403
else:
   from .models import (
       AutoencoderKL,
       ControlNetModel,
       ModelMixin,
       PriorTransformer,
       TaFilmDecoder,
       TransformeraDModel,
       UNetaDModel,
       UNetaDConditionModel,
       UNetaDModel,
       UNetaDConditionModel,
       VQModel,
   )
   from .optimization import (
       get_constant_schedule,
       get_constant_schedule_with_warmup,
       get_cosine_schedule_with_warmup,
       get_cosine_with_hard_restarts_schedule_with_warmup,
       get_linear_schedule_with_warmup,
       get_polynomial_decay_schedule_with_warmup,
       get_scheduler,
   )
   from .pipelines import (
       AudioPipelineOutput,
       ConsistencyModelPipeline,
       DanceDiffusionPipeline,
       DDIMPipeline,
       DDPMPipeline,
       DiffusionPipeline,
       DiTPipeline,
       ImagePipelineOutput,
       KarrasVePipeline,
       LDMPipeline,
       LDMSuperResolutionPipeline,
       PNDMPipeline,
       RePaintPipeline,
       ScoreSdeVePipeline,
   )
   from .schedulers import (
       CMStochasticIterativeScheduler,
       DDIMInverseScheduler,
       DDIMParallelScheduler,
       DDIMScheduler,
       DDPMParallelScheduler,
       DDPMScheduler,
       DEISMultistepScheduler,
       DPMSolverMultistepInverseScheduler,
       DPMSolverMultistepScheduler,
       DPMSolverSinglestepScheduler,
       EulerAncestralDiscreteScheduler,
       EulerDiscreteScheduler,
       HeunDiscreteScheduler,
       IPNDMScheduler,
       KarrasVeScheduler,
       KDPMaAncestralDiscreteScheduler,
       KDPMaDiscreteScheduler,
       PNDMScheduler,
       RePaintScheduler,
       SchedulerMixin,
       ScoreSdeVeScheduler,
       UnCLIPScheduler,
       UniPCMultistepScheduler,
       VQDiffusionScheduler,
   )
   from .training_utils import EMAModel

try:
   if not (is_torch_available() and is_scipy_available()):
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   from .utils.dummy_torch_and_scipy_objects import *  # noqa F403
else:
   from .schedulers import LMSDiscreteScheduler

try:
   if not (is_torch_available() and is_torchsde_available()):
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   from .utils.dummy_torch_and_torchsde_objects import *  # noqa F403
else:
   from .schedulers import DPMSolverSDEScheduler

try:
   if not (is_torch_available() and is_transformers_available()):
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   from .utils.dummy_torch_and_transformers_objects import *  # noqa F403
else:
   from .pipelines import (
       AltDiffusionImgaImgPipeline,
       AltDiffusionPipeline,
       AudioLDMPipeline,
       CycleDiffusionPipeline,
       IFImgaImgPipeline,
       IFImgaImgSuperResolutionPipeline,
       IFInpaintingPipeline,
       IFInpaintingSuperResolutionPipeline,
       IFPipeline,
       IFSuperResolutionPipeline,
       ImageTextPipelineOutput,
       KandinskyImgaImgPipeline,
       KandinskyInpaintPipeline,
       KandinskyPipeline,
       KandinskyPriorPipeline,
       KandinskyVaaControlnetImgaImgPipeline,
       KandinskyVaaControlnetPipeline,
       KandinskyVaaImgaImgPipeline,
       KandinskyVaaInpaintPipeline,
       KandinskyVaaPipeline,
       KandinskyVaaPriorEmbaEmbPipeline,
       KandinskyVaaPriorPipeline,
       LDMTextToImagePipeline,
       PaintByExamplePipeline,
       SemanticStableDiffusionPipeline,
       ShapEImgaImgPipeline,
       ShapEPipeline,
       StableDiffusionAttendAndExcitePipeline,
       StableDiffusionControlNetImgaImgPipeline,
       StableDiffusionControlNetInpaintPipeline,
       StableDiffusionControlNetPipeline,
       StableDiffusionDepthaImgPipeline,
       StableDiffusionDiffEditPipeline,
       StableDiffusionImageVariationPipeline,
       StableDiffusionImgaImgPipeline,
       StableDiffusionInpaintPipeline,
       StableDiffusionInpaintPipelineLegacy,
       StableDiffusionInstructPixaPixPipeline,
       StableDiffusionLatentUpscalePipeline,
       StableDiffusionLDMaDPipeline,
       StableDiffusionModelEditingPipeline,
       StableDiffusionPanoramaPipeline,
       StableDiffusionParadigmsPipeline,
       StableDiffusionPipeline,
       StableDiffusionPipelineSafe,
       StableDiffusionPixaPixZeroPipeline,
       StableDiffusionSAGPipeline,
       StableDiffusionUpscalePipeline,
       StableUnCLIPImgaImgPipeline,
       StableUnCLIPPipeline,
       TextToVideoSDPipeline,
       TextToVideoZeroPipeline,
       UnCLIPImageVariationPipeline,
       UnCLIPPipeline,
       UniDiffuserModel,
       UniDiffuserPipeline,
       UniDiffuserTextDecoder,
       VersatileDiffusionDualGuidedPipeline,
       VersatileDiffusionImageVariationPipeline,
       VersatileDiffusionPipeline,
       VersatileDiffusionTextToImagePipeline,
       VideoToVideoSDPipeline,
       VQDiffusionPipeline,
   )

try:
   if not (is_torch_available() and is_transformers_available() and is_invisible_watermark_available()):
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   from .utils.dummy_torch_and_transformers_and_invisible_watermark_objects import *  # noqa F403
else:
   from .pipelines import StableDiffusionXLImgaImgPipeline, StableDiffusionXLPipeline

try:
   if not (is_torch_available() and is_transformers_available() and is_k_diffusion_available()):
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   from .utils.dummy_torch_and_transformers_and_k_diffusion_objects import *  # noqa F403
else:
   from .pipelines import StableDiffusionKDiffusionPipeline

try:
   if not (is_torch_available() and is_transformers_available() and is_onnx_available()):
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   from .utils.dummy_torch_and_transformers_and_onnx_objects import *  # noqa F403
else:
   from .pipelines import (
       OnnxStableDiffusionImgaImgPipeline,
       OnnxStableDiffusionInpaintPipeline,
       OnnxStableDiffusionInpaintPipelineLegacy,
       OnnxStableDiffusionPipeline,
       OnnxStableDiffusionUpscalePipeline,
       StableDiffusionOnnxPipeline,
   )

try:
   if not (is_torch_available() and is_librosa_available()):
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   from .utils.dummy_torch_and_librosa_objects import *  # noqa F403
else:
   from .pipelines import AudioDiffusionPipeline, Mel

try:
   if not (is_transformers_available() and is_torch_available() and is_note_seq_available()):
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   from .utils.dummy_transformers_and_torch_and_note_seq_objects import *  # noqa F403
else:
   from .pipelines import SpectrogramDiffusionPipeline

try:
   if not is_flax_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   from .utils.dummy_flax_objects import *  # noqa F403
else:
   from .models.controlnet_flax import FlaxControlNetModel
   from .models.modeling_flax_utils import FlaxModelMixin
   from .models.unet_ad_condition_flax import FlaxUNetaDConditionModel
   from .models.vae_flax import FlaxAutoencoderKL
   from .pipelines import FlaxDiffusionPipeline
   from .schedulers import (
       FlaxDDIMScheduler,
       FlaxDDPMScheduler,
       FlaxDPMSolverMultistepScheduler,
       FlaxKarrasVeScheduler,
       FlaxLMSDiscreteScheduler,
       FlaxPNDMScheduler,
       FlaxSchedulerMixin,
       FlaxScoreSdeVeScheduler,
   )


try:
   if not (is_flax_available() and is_transformers_available()):
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   from .utils.dummy_flax_and_transformers_objects import *  # noqa F403
else:
   from .pipelines import (
       FlaxStableDiffusionControlNetPipeline,
       FlaxStableDiffusionImgaImgPipeline,
       FlaxStableDiffusionInpaintPipeline,
       FlaxStableDiffusionPipeline,
   )

try:
   if not (is_note_seq_available()):
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   from .utils.dummy_note_seq_objects import *  # noqa F403
else:
   from .pipelines import MidiProcessor







"""simple docstring"""


from __future__ import annotations

from math import gcd



def   snake_case						(				_a:     int		,   _a:     int = 2		,   _a:     int = 1		,   _a:     int = 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(_a:     int		,   _a:     int		,   _a:     int							) -> int:
            return (pow(_a		,   2							) + step) % modulus

      for _ in range(_a							):
            # 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(_a		,   _a		,   _a							)
                  lowerCamelCase__           =		rand_fn(_a		,   _a		,   _a							)
                  lowerCamelCase__           =		rand_fn(_a		,   _a		,   _a							)

                  # 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		,   _a							)

                  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

   _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",
   )
   _snake_case          =							parser.parse_args()

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



