





import math


def      SCREAMING_SNAKE_CASE      (   lowerCAmelCase       ):

       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(math.sqrt(lowerCAmelCase       ) + 1       )     ,							6       ):
              if number % i == 0 or number % (i + 2) == 0:
                     return False
       return True


def      SCREAMING_SNAKE_CASE      (   lowerCAmelCase = 600_851_475_143       ):

       try:
              _UpperCamelCase														=    int(lowerCAmelCase       )
       except (TypeError, ValueError):
              raise TypeError('''Parameter n must be int or castable to int.'''       )
       if n <= 0:
              raise ValueError('''Parameter n must be greater than or equal to one.'''       )
       _UpperCamelCase														=    0
       if is_prime(lowerCAmelCase       ):
              return n
       while n % 2 == 0:
              n //= 2
       if is_prime(lowerCAmelCase       ):
              return n
       for i in range(3     ,							int(math.sqrt(lowerCAmelCase       )       ) + 1     ,							2       ):
              if n % i == 0:
                     if is_prime(n // i       ):
                            _UpperCamelCase														=    n // i
                            break
                     elif is_prime(lowerCAmelCase       ):
                            _UpperCamelCase														=    i
       return max_number


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













from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, logging, randn_tensor
from .scheduling_utils import SchedulerMixin


lowercase     :			Optional[int]     						=	logging.get_logger(__name__)  # pylint: disable=invalid-name

@dataclass
class 			__A(    __UpperCAmelCase			):
     __A							=							42






class 			__A(    __UpperCAmelCase    ,      __UpperCAmelCase			):
     __A							=							1

     @register_to_config
     def __init__(   self,							A = 40,							A = 0.002,							A = 80.0,							A = 0.5,							A = 1.0,							A = 7.0,							A = True,							):





            """simple docstring"""

            _UpperCamelCase														=    sigma_max

            _UpperCamelCase														=    np.linspace(0,							1,							A   )
            _UpperCamelCase														=    self._convert_to_karras(A   )
            _UpperCamelCase														=    self.sigma_to_t(A   )

            # setable values
            _UpperCamelCase														=    None
            _UpperCamelCase														=    torch.from_numpy(A   )
            _UpperCamelCase														=    torch.from_numpy(A   )
            _UpperCamelCase														=    False
            _UpperCamelCase														=    False

     def 						_UpperCamelCase  (   self,							A,							A=None   ):





            """simple docstring"""

            if schedule_timesteps is None:
                   _UpperCamelCase														=    self.timesteps

            _UpperCamelCase														=    (schedule_timesteps == timestep).nonzero()
            return indices.item()

     def 						_UpperCamelCase  (   self,							A,							A   ):





            """simple docstring"""

            if isinstance(A,							torch.Tensor   ):
                   _UpperCamelCase														=    timestep.to(self.timesteps.device   )
            _UpperCamelCase														=    self.index_for_timestep(A   )
            _UpperCamelCase														=    self.sigmas[step_idx]

            _UpperCamelCase														=    sample / ((sigma**2 + self.config.sigma_data**2) ** 0.5)

            _UpperCamelCase														=    True
            return sample

     def 						_UpperCamelCase  (   self,							A   ):





            """simple docstring"""

            if not isinstance(A,							np.ndarray   ):
                   _UpperCamelCase														=    np.array(A,							dtype=np.floataa   )

            _UpperCamelCase														=    1000 * 0.25 * np.log(sigmas + 1E-4_4   )

            return timesteps

     def 						_UpperCamelCase  (   self,							A = None,							A = None,							A = None,							):





            """simple docstring"""

            if num_inference_steps is None and timesteps is None:
                   raise ValueError('''Exactly one of `num_inference_steps` or `timesteps` must be supplied.'''   )

            if num_inference_steps is not None and timesteps is not None:
                   raise ValueError('''Can only pass one of `num_inference_steps` or `timesteps`.'''   )

            # Follow DDPMScheduler custom timesteps logic
            if timesteps is not None:
                   for i in range(1,							len(A   )   ):
                          if timesteps[i] >= timesteps[i - 1]:
                                 raise ValueError('''`timesteps` must be in descending order.'''   )

                   if timesteps[0] >= self.config.num_train_timesteps:
                          raise ValueError(
                              F'''`timesteps` must start before `self.config.train_timesteps`:'''
                              F''' {self.config.num_train_timesteps}.'''   )

                   _UpperCamelCase														=    np.array(A,							dtype=np.intaa   )
                   _UpperCamelCase														=    True
            else:
                   if num_inference_steps > self.config.num_train_timesteps:
                          raise ValueError(
                              F'''`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:'''
                              F''' {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle'''
                              F''' maximal {self.config.num_train_timesteps} timesteps.'''   )

                   _UpperCamelCase														=    num_inference_steps

                   _UpperCamelCase														=    self.config.num_train_timesteps // self.num_inference_steps
                   _UpperCamelCase														=    (np.arange(0,							A   ) * step_ratio).round()[::-1].copy().astype(np.intaa   )
                   _UpperCamelCase														=    False

            # Map timesteps to Karras sigmas directly for multistep sampling
            # See https://github.com/openai/consistency_models/blob/main/cm/karras_diffusion.py#L675
            _UpperCamelCase														=    self.config.num_train_timesteps
            _UpperCamelCase														=    timesteps[::-1].copy()
            _UpperCamelCase														=    ramp / (num_train_timesteps - 1)
            _UpperCamelCase														=    self._convert_to_karras(A   )
            _UpperCamelCase														=    self.sigma_to_t(A   )

            _UpperCamelCase														=    np.concatenate([sigmas, [self.sigma_min]]   ).astype(np.floataa   )
            _UpperCamelCase														=    torch.from_numpy(A   ).to(device=A   )

            if str(A   ).startswith('''mps'''   ):
                   # mps does not support float64
                   _UpperCamelCase														=    torch.from_numpy(A   ).to(A,							dtype=torch.floataa   )
            else:
                   _UpperCamelCase														=    torch.from_numpy(A   ).to(device=A   )

     def 						_UpperCamelCase  (   self,							A   ):





            """simple docstring"""

            _UpperCamelCase														=    self.config.sigma_min
            _UpperCamelCase														=    self.config.sigma_max

            _UpperCamelCase														=    self.config.rho
            _UpperCamelCase														=    sigma_min ** (1 / rho)
            _UpperCamelCase														=    sigma_max ** (1 / rho)
            _UpperCamelCase														=    (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
            return sigmas

     def 						_UpperCamelCase  (   self,							A   ):





            """simple docstring"""

            _UpperCamelCase														=    self.config.sigma_data

            _UpperCamelCase														=    sigma_data**2 / (sigma**2 + sigma_data**2)
            _UpperCamelCase														=    sigma * sigma_data / (sigma**2 + sigma_data**2) ** 0.5
            return c_skip, c_out

     def 						_UpperCamelCase  (   self,							A   ):





            """simple docstring"""

            _UpperCamelCase														=    self.config.sigma_min
            _UpperCamelCase														=    self.config.sigma_data

            _UpperCamelCase														=    sigma_data**2 / ((sigma - sigma_min) ** 2 + sigma_data**2)
            _UpperCamelCase														=    (sigma - sigma_min) * sigma_data / (sigma**2 + sigma_data**2) ** 0.5
            return c_skip, c_out

     def 						_UpperCamelCase  (   self,							A,							A,							A,							A = None,							A = True,							):





            """simple docstring"""

            if (
                isinstance(A,							A   )
                or isinstance(A,							torch.IntTensor   )
                or isinstance(A,							torch.LongTensor   )
            ):
                   raise ValueError(
                       (
                           '''Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to'''
                           F''' `{self.__class__}.step()` is not supported. Make sure to pass'''
                           ''' one of the `scheduler.timesteps` as a timestep.'''
                       ),							)

            if not self.is_scale_input_called:
                   logger.warning(
                       '''The `scale_model_input` function should be called before `step` to ensure correct denoising. '''
                       '''See `StableDiffusionPipeline` for a usage example.'''   )

            if isinstance(A,							torch.Tensor   ):
                   _UpperCamelCase														=    timestep.to(self.timesteps.device   )

            _UpperCamelCase														=    self.config.sigma_min
            _UpperCamelCase														=    self.config.sigma_max

            _UpperCamelCase														=    self.index_for_timestep(A   )

            # sigma_next corresponds to next_t in original implementation
            _UpperCamelCase														=    self.sigmas[step_index]
            if step_index + 1 < self.config.num_train_timesteps:
                   _UpperCamelCase														=    self.sigmas[step_index + 1]
            else:
                   # Set sigma_next to sigma_min
                   _UpperCamelCase														=    self.sigmas[-1]

            # Get scalings for boundary conditions
            _UpperCamelCase							,		_UpperCamelCase														=    self.get_scalings_for_boundary_condition(A   )

            # 1. Denoise model output using boundary conditions
            _UpperCamelCase														=    c_out * model_output + c_skip * sample
            if self.config.clip_denoised:
                   _UpperCamelCase														=    denoised.clamp(-1,							1   )

            # 2. Sample z ~ N(0, s_noise^2 * I)
            # Noise is not used for onestep sampling.
            if len(self.timesteps   ) > 1:
                   _UpperCamelCase														=    randn_tensor(
                       model_output.shape,							dtype=model_output.dtype,							device=model_output.device,							generator=A   )
            else:
                   _UpperCamelCase														=    torch.zeros_like(A   )
            _UpperCamelCase														=    noise * self.config.s_noise

            _UpperCamelCase														=    sigma_next.clamp(min=A,							max=A   )

            # 3. Return noisy sample
            # tau = sigma_hat, eps = sigma_min
            _UpperCamelCase														=    denoised + z * (sigma_hat**2 - sigma_min**2) ** 0.5

            if not return_dict:
                   return (prev_sample,)

            return CMStochasticIterativeSchedulerOutput(prev_sample=A   )

     def 						_UpperCamelCase  (   self,							A,							A,							A,							):





            """simple docstring"""

            _UpperCamelCase														=    self.sigmas.to(device=original_samples.device,							dtype=original_samples.dtype   )
            if original_samples.device.type == "mps" and torch.is_floating_point(A   ):
                   # mps does not support float64
                   _UpperCamelCase														=    self.timesteps.to(original_samples.device,							dtype=torch.floataa   )
                   _UpperCamelCase														=    timesteps.to(original_samples.device,							dtype=torch.floataa   )
            else:
                   _UpperCamelCase														=    self.timesteps.to(original_samples.device   )
                   _UpperCamelCase														=    timesteps.to(original_samples.device   )

            _UpperCamelCase														=    [(schedule_timesteps == t).nonzero().item() for t in timesteps]

            _UpperCamelCase														=    sigmas[step_indices].flatten()
            while len(sigma.shape   ) < len(original_samples.shape   ):
                   _UpperCamelCase														=    sigma.unsqueeze(-1   )

            _UpperCamelCase														=    original_samples + noise * sigma
            return noisy_samples



     def __len__(   self   ):





            """simple docstring"""

            return self.config.num_train_timesteps






