



'''simple docstring'''
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


snake_case_				:			Tuple						 =						logging.get_logger(__name__)  # pylint: disable=invalid-name






@dataclass
class 							lowercase__			(							lowercase     ):
	lowercase__						       =    42






class 							lowercase__			(							lowercase		,      lowercase     ):
	lowercase__						       =    1





	@register_to_config
	def __init__(				self      :       str				,lowerCamelCase__      :       int = 40				,lowerCamelCase__      :       float = 0.0_0_2				,lowerCamelCase__      :       float = 8_0.0				,lowerCamelCase__      :       float = 0.5				,lowerCamelCase__      :       float = 1.0				,lowerCamelCase__      :       float = 7.0				,lowerCamelCase__      :       bool = True				,):







							'''simple docstring'''
							# standard deviation of the initial noise distribution
							_UpperCamelCase      :	Any				       =     sigma_max

							_UpperCamelCase      :	int				       =     np.linspace(0				,1				,lowerCamelCase__				)
							_UpperCamelCase      :	Optional[int]				       =     self._convert_to_karras(lowerCamelCase__				)
							_UpperCamelCase      :	Dict				       =     self.sigma_to_t(lowerCamelCase__				)

							# setable values
							_UpperCamelCase      :	Union[str, Any]				       =     None
							_UpperCamelCase      :	int				       =     torch.from_numpy(lowerCamelCase__				)
							_UpperCamelCase      :	Tuple				       =     torch.from_numpy(lowerCamelCase__				)
							_UpperCamelCase      :	List[Any]				       =     False
							_UpperCamelCase      :	str				       =     False





	def 			UpperCamelCase_						(				self      :       Tuple				,lowerCamelCase__      :       List[str]				,lowerCamelCase__      :       int=None				):







							'''simple docstring'''
							if schedule_timesteps is None:
													_UpperCamelCase      :	Any				       =     self.timesteps

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





	def 			UpperCamelCase_						(				self      :       Tuple				,lowerCamelCase__      :       torch.FloatTensor				,lowerCamelCase__      :       Union[float, torch.FloatTensor]				):







							'''simple docstring'''
							# Get sigma corresponding to timestep
							if isinstance(lowerCamelCase__				,torch.Tensor				):
													_UpperCamelCase      :	Tuple				       =     timestep.to(self.timesteps.device				)
							_UpperCamelCase      :	int				       =     self.index_for_timestep(lowerCamelCase__				)
							_UpperCamelCase      :	str				       =     self.sigmas[step_idx]

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

							_UpperCamelCase      :	Union[str, Any]				       =     True
							return sample





	def 			UpperCamelCase_						(				self      :       Optional[int]				,lowerCamelCase__      :       Union[float, np.ndarray]				):







							'''simple docstring'''
							if not isinstance(lowerCamelCase__				,np.ndarray				):
													_UpperCamelCase      :	List[str]				       =     np.array(lowerCamelCase__				,dtype=np.floataa				)

							_UpperCamelCase      :	List[str]				       =     1000 * 0.2_5 * np.log(sigmas + 1E-44				)

							return timesteps





	def 			UpperCamelCase_						(				self      :       str				,lowerCamelCase__      :       Optional[int] = None				,lowerCamelCase__      :       Union[str, torch.device] = None				,lowerCamelCase__      :       Optional[List[int]] = 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(lowerCamelCase__				)				):
																			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      :	List[str]				       =     np.array(lowerCamelCase__				,dtype=np.intaa				)
													_UpperCamelCase      :	Any				       =     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      :	Tuple				       =     num_inference_steps

													_UpperCamelCase      :	Optional[int]				       =     self.config.num_train_timesteps // self.num_inference_steps
													_UpperCamelCase      :	Dict				       =     (np.arange(0				,lowerCamelCase__				) * step_ratio).round()[::-1].copy().astype(np.intaa				)
													_UpperCamelCase      :	Tuple				       =     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      :	List[str]				       =     self.config.num_train_timesteps
							_UpperCamelCase      :	int				       =     timesteps[::-1].copy()
							_UpperCamelCase      :	Optional[int]				       =     ramp / (num_train_timesteps - 1)
							_UpperCamelCase      :	Tuple				       =     self._convert_to_karras(lowerCamelCase__				)
							_UpperCamelCase      :	int				       =     self.sigma_to_t(lowerCamelCase__				)

							_UpperCamelCase      :	List[str]				       =     np.concatenate([sigmas, [self.sigma_min]]				).astype(np.floataa				)
							_UpperCamelCase      :	Tuple				       =     torch.from_numpy(lowerCamelCase__				).to(device=lowerCamelCase__				)

							if str(lowerCamelCase__				).startswith('mps'				):
													# mps does not support float64
													_UpperCamelCase      :	Dict				       =     torch.from_numpy(lowerCamelCase__				).to(lowerCamelCase__				,dtype=torch.floataa				)
							else:
													_UpperCamelCase      :	Optional[Any]				       =     torch.from_numpy(lowerCamelCase__				).to(device=lowerCamelCase__				)





	def 			UpperCamelCase_						(				self      :       Any				,lowerCamelCase__      :       Optional[int]				):







							'''simple docstring'''
							_UpperCamelCase      :	float				       =     self.config.sigma_min
							_UpperCamelCase      :	float				       =     self.config.sigma_max

							_UpperCamelCase      :	int				       =     self.config.rho
							_UpperCamelCase      :	List[Any]				       =     sigma_min ** (1 / rho)
							_UpperCamelCase      :	Optional[Any]				       =     sigma_max ** (1 / rho)
							_UpperCamelCase      :	int				       =     (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
							return sigmas





	def 			UpperCamelCase_						(				self      :       int				,lowerCamelCase__      :       int				):







							'''simple docstring'''
							_UpperCamelCase      :	Tuple				       =     self.config.sigma_data

							_UpperCamelCase      :	List[Any]				       =     sigma_data**2 / (sigma**2 + sigma_data**2)
							_UpperCamelCase      :	Optional[Any]				       =     sigma * sigma_data / (sigma**2 + sigma_data**2) ** 0.5
							return c_skip, c_out





	def 			UpperCamelCase_						(				self      :       Any				,lowerCamelCase__      :       Any				):







							'''simple docstring'''
							_UpperCamelCase      :	Union[str, Any]				       =     self.config.sigma_min
							_UpperCamelCase      :	Tuple				       =     self.config.sigma_data

							_UpperCamelCase      :	Optional[int]				       =     sigma_data**2 / ((sigma - sigma_min) ** 2 + sigma_data**2)
							_UpperCamelCase      :	Dict				       =     (sigma - sigma_min) * sigma_data / (sigma**2 + sigma_data**2) ** 0.5
							return c_skip, c_out





	def 			UpperCamelCase_						(				self      :       Any				,lowerCamelCase__      :       torch.FloatTensor				,lowerCamelCase__      :       Union[float, torch.FloatTensor]				,lowerCamelCase__      :       torch.FloatTensor				,lowerCamelCase__      :       Optional[torch.Generator] = None				,lowerCamelCase__      :       bool = True				,):







							'''simple docstring'''

							if (
							    isinstance(lowerCamelCase__				,lowerCamelCase__				)
							    or isinstance(lowerCamelCase__				,torch.IntTensor				)
							    or isinstance(lowerCamelCase__				,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(lowerCamelCase__				,torch.Tensor				):
													_UpperCamelCase      :	List[Any]				       =     timestep.to(self.timesteps.device				)

							_UpperCamelCase      :	List[Any]				       =     self.config.sigma_min
							_UpperCamelCase      :	List[Any]				       =     self.config.sigma_max

							_UpperCamelCase      :	str				       =     self.index_for_timestep(lowerCamelCase__				)

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

							# Get scalings for boundary conditions
							_UpperCamelCase       ,    _UpperCamelCase      :	Any				       =     self.get_scalings_for_boundary_condition(lowerCamelCase__				)

							# 1. Denoise model output using boundary conditions
							_UpperCamelCase      :	Any				       =     c_out * model_output + c_skip * sample
							if self.config.clip_denoised:
													_UpperCamelCase      :	int				       =     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      :	List[Any]				       =     randn_tensor(
													    model_output.shape				,dtype=model_output.dtype				,device=model_output.device				,generator=lowerCamelCase__				)
							else:
													_UpperCamelCase      :	Tuple				       =     torch.zeros_like(lowerCamelCase__				)
							_UpperCamelCase      :	Union[str, Any]				       =     noise * self.config.s_noise

							_UpperCamelCase      :	Dict				       =     sigma_next.clamp(min=lowerCamelCase__				,max=lowerCamelCase__				)

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

							if not return_dict:
													return (prev_sample,)

							return CMStochasticIterativeSchedulerOutput(prev_sample=lowerCamelCase__				)





	def 			UpperCamelCase_						(				self      :       Union[str, Any]				,lowerCamelCase__      :       torch.FloatTensor				,lowerCamelCase__      :       torch.FloatTensor				,lowerCamelCase__      :       torch.FloatTensor				,):







							'''simple docstring'''
							# Make sure sigmas and timesteps have the same device and dtype as original_samples
							_UpperCamelCase      :	Tuple				       =     self.sigmas.to(device=original_samples.device				,dtype=original_samples.dtype				)
							if original_samples.device.type == "mps" and torch.is_floating_point(lowerCamelCase__				):
													# mps does not support float64
													_UpperCamelCase      :	List[Any]				       =     self.timesteps.to(original_samples.device				,dtype=torch.floataa				)
													_UpperCamelCase      :	Optional[int]				       =     timesteps.to(original_samples.device				,dtype=torch.floataa				)
							else:
													_UpperCamelCase      :	Tuple				       =     self.timesteps.to(original_samples.device				)
													_UpperCamelCase      :	Optional[Any]				       =     timesteps.to(original_samples.device				)

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

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

							_UpperCamelCase      :	Any				       =     original_samples + noise * sigma
							return noisy_samples





	def __len__(				self      :       Optional[int]				):







							'''simple docstring'''
							return self.config.num_train_timesteps







'''simple docstring'''
import math






def A__					(  UpperCAmelCase_							):

						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(UpperCAmelCase_							) + 1							)						,						6							):
												if number % i == 0 or number % (i + 2) == 0:
																		return False
						return True






def A__					(  UpperCAmelCase_ = 1_0_0_0						,						UpperCAmelCase_ = 1_0_0_0							):
						_UpperCamelCase      :	str				       =     [0, 0, 0]  # length, a, b
						for a in range((a_limit * -1) + 1						,						UpperCAmelCase_							):
												for b in range(2						,						UpperCAmelCase_							):
																		if is_prime(UpperCAmelCase_							):
																								_UpperCamelCase      :	List[str]				       =     0
																								_UpperCamelCase      :	Union[str, Any]				       =     0
																								while is_prime((n**2) + (a * n) + b							):
																														count += 1
																														n += 1
																								if count > longest[0]:
																														_UpperCamelCase      :	Any				       =     [count, a, b]
						_UpperCamelCase      :	Dict				       =     longest[1] * longest[2]
						return ans


if __name__ == "__main__":
					print(solution(1000, 1000))


