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

import numpy as np
import torch

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

@dataclass
class    lowerCAmelCase__     (	__lowercase			):
		a__       :						torch.FloatTensor
		a__       :						torch.FloatTensor
		a__       :						Optional[torch.FloatTensor]        =		None





class    lowerCAmelCase__     (	__lowercase  ,	__lowercase			):
		a__       :						List[str]        =		2






		@register_to_config
		def __init__(		self		:							Optional[Any]							,			SCREAMING_SNAKE_CASE__		:							float = 0.02							,			SCREAMING_SNAKE_CASE__		:							float = 1_00							,			SCREAMING_SNAKE_CASE__		:							float = 1.007							,			SCREAMING_SNAKE_CASE__		:							float = 80							,			SCREAMING_SNAKE_CASE__		:							float = 0.05							,			SCREAMING_SNAKE_CASE__		:							float = 50							,			)     ->							str:
						# standard deviation of the initial noise distribution
						__lowerCamelCase    					=	sigma_max

						# setable values
						__lowerCamelCase    					=	None
						__lowerCamelCase    					=	None
						__lowerCamelCase    					=	None  # sigma(t_i)






		def  __A       (		self		:							Dict							,			SCREAMING_SNAKE_CASE__		:							torch.FloatTensor							,			SCREAMING_SNAKE_CASE__		:							Optional[int] = None  )     ->							torch.FloatTensor:
						return sample






		def  __A       (		self		:							List[str]							,			SCREAMING_SNAKE_CASE__		:							int							,			SCREAMING_SNAKE_CASE__		:							Union[str, torch.device] = None  )     ->							List[Any]:
						__lowerCamelCase    					=	num_inference_steps
						__lowerCamelCase    					=	np.arange(0							,			self.num_inference_steps  )[::-1].copy()
						__lowerCamelCase    					=	torch.from_numpy(SCREAMING_SNAKE_CASE__  ).to(SCREAMING_SNAKE_CASE__  )
						__lowerCamelCase    					=	[
						    (
						        self.config.sigma_max**2
						        * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
						    )
						    for i in self.timesteps
						]
						__lowerCamelCase    					=	torch.tensor(SCREAMING_SNAKE_CASE__							,			dtype=torch.floataa							,			device=SCREAMING_SNAKE_CASE__  )






		def  __A       (		self		:							Tuple							,			SCREAMING_SNAKE_CASE__		:							torch.FloatTensor							,			SCREAMING_SNAKE_CASE__		:							float							,			SCREAMING_SNAKE_CASE__		:							Optional[torch.Generator] = None  )     ->							Tuple[torch.FloatTensor, float]:
						if self.config.s_min <= sigma <= self.config.s_max:
										__lowerCamelCase    					=	min(self.config.s_churn / self.num_inference_steps							,			2**0.5 - 1  )
						else:
										__lowerCamelCase    					=	0

						# sample eps ~ N(0, S_noise^2 * I)
						__lowerCamelCase    					=	self.config.s_noise * randn_tensor(sample.shape							,			generator=SCREAMING_SNAKE_CASE__  ).to(sample.device  )
						__lowerCamelCase    					=	sigma + gamma * sigma
						__lowerCamelCase    					=	sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

						return sample_hat, sigma_hat






		def  __A       (		self		:							Union[str, Any]							,			SCREAMING_SNAKE_CASE__		:							torch.FloatTensor							,			SCREAMING_SNAKE_CASE__		:							float							,			SCREAMING_SNAKE_CASE__		:							float							,			SCREAMING_SNAKE_CASE__		:							torch.FloatTensor							,			SCREAMING_SNAKE_CASE__		:							bool = True							,			)     ->							Union[KarrasVeOutput, Tuple]:
						__lowerCamelCase    					=	sample_hat + sigma_hat * model_output
						__lowerCamelCase    					=	(sample_hat - pred_original_sample) / sigma_hat
						__lowerCamelCase    					=	sample_hat + (sigma_prev - sigma_hat) * derivative

						if not return_dict:
										return (sample_prev, derivative)

						return KarrasVeOutput(
						    prev_sample=SCREAMING_SNAKE_CASE__							,			derivative=SCREAMING_SNAKE_CASE__							,			pred_original_sample=SCREAMING_SNAKE_CASE__  )






		def  __A       (		self		:							Optional[Any]							,			SCREAMING_SNAKE_CASE__		:							torch.FloatTensor							,			SCREAMING_SNAKE_CASE__		:							float							,			SCREAMING_SNAKE_CASE__		:							float							,			SCREAMING_SNAKE_CASE__		:							torch.FloatTensor							,			SCREAMING_SNAKE_CASE__		:							torch.FloatTensor							,			SCREAMING_SNAKE_CASE__		:							torch.FloatTensor							,			SCREAMING_SNAKE_CASE__		:							bool = True							,			)     ->							Union[KarrasVeOutput, Tuple]:
						__lowerCamelCase    					=	sample_prev + sigma_prev * model_output
						__lowerCamelCase    					=	(sample_prev - pred_original_sample) / sigma_prev
						__lowerCamelCase    					=	sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)

						if not return_dict:
										return (sample_prev, derivative)

						return KarrasVeOutput(
						    prev_sample=SCREAMING_SNAKE_CASE__							,			derivative=SCREAMING_SNAKE_CASE__							,			pred_original_sample=SCREAMING_SNAKE_CASE__  )







		def  __A       (		self		:							Optional[Any]							,			SCREAMING_SNAKE_CASE__		:							Optional[Any]							,			SCREAMING_SNAKE_CASE__		:							Optional[int]							,			SCREAMING_SNAKE_CASE__		:							List[Any]  )     ->							Union[str, Any]:
						raise NotImplementedError()





from __future__ import annotations

from fractions import Fraction




def  __magic_name__ (   __lowerCAmelCase	:						int		,  __lowerCAmelCase	:						int							)			->   bool:
				return (
				    num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
				)




def  __magic_name__ (   __lowerCAmelCase	:						int							)			->   list[str]:
				__lowerCamelCase    					=	[]
				__lowerCamelCase    					=	11
				__lowerCamelCase    					=	int('''1''' + '''0''' * digit_len							)
				for num in range(__lowerCAmelCase		,  __lowerCAmelCase							):
								while den <= 99:
												if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
																if is_digit_cancelling(__lowerCAmelCase		,  __lowerCAmelCase							):
																				solutions.append(f'''{num}/{den}'''							)
												den += 1
								num += 1
								__lowerCamelCase    					=	10
				return solutions




def  __magic_name__ (   __lowerCAmelCase	:						int = 2							)			->   int:
				__lowerCamelCase    					=	1.0
				for fraction in fraction_list(__lowerCAmelCase							):
								__lowerCamelCase    					=	Fraction(__lowerCAmelCase							)
								result *= frac.denominator / frac.numerator
				return int(__lowerCAmelCase							)


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



