

"""simple docstring"""


from ..utils import (
    OptionalDependencyNotAvailable,
    is_flax_available,
    is_scipy_available,
    is_torch_available,
    is_torchsde_available,
)


try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    from ..utils.dummy_pt_objects import *  # noqa F403
else:
    from .scheduling_consistency_models import CMStochasticIterativeScheduler
    from .scheduling_ddim import DDIMScheduler
    from .scheduling_ddim_inverse import DDIMInverseScheduler
    from .scheduling_ddim_parallel import DDIMParallelScheduler
    from .scheduling_ddpm import DDPMScheduler
    from .scheduling_ddpm_parallel import DDPMParallelScheduler
    from .scheduling_deis_multistep import DEISMultistepScheduler
    from .scheduling_dpmsolver_multistep import DPMSolverMultistepScheduler
    from .scheduling_dpmsolver_multistep_inverse import DPMSolverMultistepInverseScheduler
    from .scheduling_dpmsolver_singlestep import DPMSolverSinglestepScheduler
    from .scheduling_euler_ancestral_discrete import EulerAncestralDiscreteScheduler
    from .scheduling_euler_discrete import EulerDiscreteScheduler
    from .scheduling_heun_discrete import HeunDiscreteScheduler
    from .scheduling_ipndm import IPNDMScheduler
    from .scheduling_k_dpm_2_ancestral_discrete import KDPMaAncestralDiscreteScheduler
    from .scheduling_k_dpm_2_discrete import KDPMaDiscreteScheduler
    from .scheduling_karras_ve import KarrasVeScheduler
    from .scheduling_pndm import PNDMScheduler
    from .scheduling_repaint import RePaintScheduler
    from .scheduling_sde_ve import ScoreSdeVeScheduler
    from .scheduling_sde_vp import ScoreSdeVpScheduler
    from .scheduling_unclip import UnCLIPScheduler
    from .scheduling_unipc_multistep import UniPCMultistepScheduler
    from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin
    from .scheduling_vq_diffusion import VQDiffusionScheduler

try:
    if not is_flax_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    from ..utils.dummy_flax_objects import *  # noqa F403
else:
    from .scheduling_ddim_flax import FlaxDDIMScheduler
    from .scheduling_ddpm_flax import FlaxDDPMScheduler
    from .scheduling_dpmsolver_multistep_flax import FlaxDPMSolverMultistepScheduler
    from .scheduling_karras_ve_flax import FlaxKarrasVeScheduler
    from .scheduling_lms_discrete_flax import FlaxLMSDiscreteScheduler
    from .scheduling_pndm_flax import FlaxPNDMScheduler
    from .scheduling_sde_ve_flax import FlaxScoreSdeVeScheduler
    from .scheduling_utils_flax import (
        FlaxKarrasDiffusionSchedulers,
        FlaxSchedulerMixin,
        FlaxSchedulerOutput,
        broadcast_to_shape_from_left,
    )


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 .scheduling_lms_discrete 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 .scheduling_dpmsolver_sde import DPMSolverSDEScheduler







"""simple docstring"""


from math import sqrt




def  _lowercase					(    __lowerCAmelCase							)       ->				bool:

      if 1 < number < 4:
            # 2 and 3 are primes
            return True
      elif number < 2 or number % 2 == 0 or number % 3 == 0:
            # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
            return False

      # All primes number are in format of 6k +/- 1
      for i in range(5  ,					int(sqrt(__lowerCAmelCase							) + 1							)  ,					6							):
            if number % i == 0 or number % (i + 2) == 0:
                  return False
      return True




def  _lowercase					(    __lowerCAmelCase = 1_0001							)       ->				int:
      SCREAMING_SNAKE_CASE__   :      Dict      		=	0
      SCREAMING_SNAKE_CASE__   :      Tuple      		=	1
      while count != nth and number < 3:
            number += 1
            if is_prime(__lowerCAmelCase							):
                  count += 1
      while count != nth:
            number += 2
            if is_prime(__lowerCAmelCase							):
                  count += 1
      return number


if __name__ == "__main__":
  print(f'{solution() = }')




