



'''simple docstring'''






import math
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
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->UnCLIP
class 				SCREAMING_SNAKE_CASE(							A__			):







	"""simple docstring"""






	lowerCamelCase__			 =       42
	lowerCamelCase__			 =       None


def  snake_case_     (					_lowerCAmelCase  :						Optional[int]   ,      _lowerCAmelCase  :						Any=0.9_9_9   ,      _lowerCAmelCase  :						Optional[Any]="cosine"   ,      )      ->   List[Any]:
							if alpha_transform_type == "cosine":

														def alpha_bar_fn(_lowerCAmelCase  :						List[Any]  ):
																					return math.cos((t + 0.0_0_8) / 1.0_0_8 * math.pi / 2  ) ** 2

							elif alpha_transform_type == "exp":

														def alpha_bar_fn(_lowerCAmelCase  :						Any  ):
																					return math.exp(t * -1_2.0  )

							else:
														raise ValueError(f"""Unsupported alpha_tranform_type: {alpha_transform_type}"""  )

							UpperCAmelCase :       Any 							=		[]
							for i in range(_lowerCAmelCase  ):
														UpperCAmelCase :       Dict 							=		i / num_diffusion_timesteps
														UpperCAmelCase :       List[Any] 							=		(i + 1) / num_diffusion_timesteps
														betas.append(min(1 - alpha_bar_fn(_lowerCAmelCase  ) / alpha_bar_fn(_lowerCAmelCase  )   ,      _lowerCAmelCase  )  )
							return torch.tensor(_lowerCAmelCase   ,      dtype=torch.floataa  )




class 				SCREAMING_SNAKE_CASE(							A__							,		A__			):







	"""simple docstring"""






	@register_to_config
	def __init__(						self			:     Union[str, Any]		,			__snake_case			:     int = 1000		,			__snake_case			:     str = "fixed_small_log"		,			__snake_case			:     bool = True		,			__snake_case			:     Optional[float] = 1.0		,			__snake_case			:     str = "epsilon"		,			__snake_case			:     str = "squaredcos_cap_v2"		,			)			->		str:
								if beta_schedule != "squaredcos_cap_v2":
															raise ValueError('''UnCLIPScheduler only supports `beta_schedule`: \'squaredcos_cap_v2\''''		)

								UpperCAmelCase :       Union[str, Any] 							=		betas_for_alpha_bar(__snake_case		)

								UpperCAmelCase :       List[Any] 							=		1.0 - self.betas
								UpperCAmelCase :       List[Any] 							=		torch.cumprod(self.alphas		,			dim=0		)
								UpperCAmelCase :       List[Any] 							=		torch.tensor(1.0		)

								# standard deviation of the initial noise distribution
								UpperCAmelCase :       int 							=		1.0

								# setable values
								UpperCAmelCase :       str 							=		None
								UpperCAmelCase :       Union[str, Any] 							=		torch.from_numpy(np.arange(0		,			__snake_case		)[::-1].copy()		)

								UpperCAmelCase :       Optional[Any] 							=		variance_type







	def      A	(						self			:     Optional[Any]		,			__snake_case			:     torch.FloatTensor		,			__snake_case			:     Optional[int] = None		)			->		torch.FloatTensor:
								return sample







	def      A	(						self			:     Dict		,			__snake_case			:     int		,			__snake_case			:     Union[str, torch.device] = None		)			->		Optional[Any]:
								UpperCAmelCase :       List[str] 							=		num_inference_steps
								UpperCAmelCase :       Optional[int] 							=		(self.config.num_train_timesteps - 1) / (self.num_inference_steps - 1)
								UpperCAmelCase :       str 							=		(np.arange(0		,			__snake_case		) * step_ratio).round()[::-1].copy().astype(np.intaa		)
								UpperCAmelCase :       Optional[int] 							=		torch.from_numpy(__snake_case		).to(__snake_case		)







	def      A	(						self			:     Any		,			__snake_case			:     str		,			__snake_case			:     List[str]=None		,			__snake_case			:     str=None		,			__snake_case			:     List[str]=None		)			->		int:
								if prev_timestep is None:
															UpperCAmelCase :       Optional[int] 							=		t - 1

								UpperCAmelCase :       Any 							=		self.alphas_cumprod[t]
								UpperCAmelCase :       Any 							=		self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
								UpperCAmelCase :       Any 							=		1 - alpha_prod_t
								UpperCAmelCase :       int 							=		1 - alpha_prod_t_prev

								if prev_timestep == t - 1:
															UpperCAmelCase :       Optional[int] 							=		self.betas[t]
								else:
															UpperCAmelCase :       List[str] 							=		1 - alpha_prod_t / alpha_prod_t_prev

								# For t > 0, compute predicted variance βt (see formula (6) and (7) from https://arxiv.org/pdf/2006.11239.pdf)
								# and sample from it to get previous sample
								# x_{t-1} ~ N(pred_prev_sample, variance) == add variance to pred_sample
								UpperCAmelCase :       int 							=		beta_prod_t_prev / beta_prod_t * beta

								if variance_type is None:
															UpperCAmelCase :       Any 							=		self.config.variance_type

								# hacks - were probably added for training stability
								if variance_type == "fixed_small_log":
															UpperCAmelCase :       Optional[Any] 							=		torch.log(torch.clamp(__snake_case		,			min=1E-20		)		)
															UpperCAmelCase :       int 							=		torch.exp(0.5 * variance		)
								elif variance_type == "learned_range":
															# NOTE difference with DDPM scheduler
															UpperCAmelCase :       Tuple 							=		variance.log()
															UpperCAmelCase :       List[Any] 							=		beta.log()

															UpperCAmelCase :       List[Any] 							=		(predicted_variance + 1) / 2
															UpperCAmelCase :       List[Any] 							=		frac * max_log + (1 - frac) * min_log

								return variance







	def      A	(						self			:     Union[str, Any]		,			__snake_case			:     torch.FloatTensor		,			__snake_case			:     int		,			__snake_case			:     torch.FloatTensor		,			__snake_case			:     Optional[int] = None		,			__snake_case			:     int=None		,			__snake_case			:     bool = True		,			)			->		Union[UnCLIPSchedulerOutput, Tuple]:
								UpperCAmelCase :       Optional[int] 							=		timestep

								if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type == "learned_range":
															UpperCAmelCase							,		UpperCAmelCase :       Tuple 							=		torch.split(__snake_case		,			sample.shape[1]		,			dim=1		)
								else:
															UpperCAmelCase :       int 							=		None

								# 1. compute alphas, betas
								if prev_timestep is None:
															UpperCAmelCase :       Optional[Any] 							=		t - 1

								UpperCAmelCase :       str 							=		self.alphas_cumprod[t]
								UpperCAmelCase :       Dict 							=		self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
								UpperCAmelCase :       Union[str, Any] 							=		1 - alpha_prod_t
								UpperCAmelCase :       Dict 							=		1 - alpha_prod_t_prev

								if prev_timestep == t - 1:
															UpperCAmelCase :       Tuple 							=		self.betas[t]
															UpperCAmelCase :       Optional[Any] 							=		self.alphas[t]
								else:
															UpperCAmelCase :       List[str] 							=		1 - alpha_prod_t / alpha_prod_t_prev
															UpperCAmelCase :       Union[str, Any] 							=		1 - beta

								# 2. compute predicted original sample from predicted noise also called
								# "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
								if self.config.prediction_type == "epsilon":
															UpperCAmelCase :       Dict 							=		(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
								elif self.config.prediction_type == "sample":
															UpperCAmelCase :       Union[str, Any] 							=		model_output
								else:
															raise ValueError(
															    F"""prediction_type given as {self.config.prediction_type} must be one of `epsilon` or `sample`"""
															    ''' for the UnCLIPScheduler.'''		)

								# 3. Clip "predicted x_0"
								if self.config.clip_sample:
															UpperCAmelCase :       int 							=		torch.clamp(
															    __snake_case		,			-self.config.clip_sample_range		,			self.config.clip_sample_range		)

								# 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
								# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
								UpperCAmelCase :       Union[str, Any] 							=		(alpha_prod_t_prev ** 0.5 * beta) / beta_prod_t
								UpperCAmelCase :       Optional[int] 							=		alpha ** 0.5 * beta_prod_t_prev / beta_prod_t

								# 5. Compute predicted previous sample µ_t
								# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
								UpperCAmelCase :       Union[str, Any] 							=		pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

								# 6. Add noise
								UpperCAmelCase :       int 							=		0
								if t > 0:
															UpperCAmelCase :       Union[str, Any] 							=		randn_tensor(
															    model_output.shape		,			dtype=model_output.dtype		,			generator=__snake_case		,			device=model_output.device		)

															UpperCAmelCase :       Optional[Any] 							=		self._get_variance(
															    __snake_case		,			predicted_variance=__snake_case		,			prev_timestep=__snake_case		,			)

															if self.variance_type == "fixed_small_log":
																						UpperCAmelCase :       Tuple 							=		variance
															elif self.variance_type == "learned_range":
																						UpperCAmelCase :       List[Any] 							=		(0.5 * variance).exp()
															else:
																						raise ValueError(
																						    F"""variance_type given as {self.variance_type} must be one of `fixed_small_log` or `learned_range`"""
																						    ''' for the UnCLIPScheduler.'''		)

															UpperCAmelCase :       Dict 							=		variance * variance_noise

								UpperCAmelCase :       Tuple 							=		pred_prev_sample + variance

								if not return_dict:
															return (pred_prev_sample,)

								return UnCLIPSchedulerOutput(prev_sample=__snake_case		,			pred_original_sample=__snake_case		)







	def      A	(						self			:     Optional[Any]		,			__snake_case			:     torch.FloatTensor		,			__snake_case			:     torch.FloatTensor		,			__snake_case			:     torch.IntTensor		,			)			->		torch.FloatTensor:
								# Make sure alphas_cumprod and timestep have same device and dtype as original_samples
								UpperCAmelCase :       Dict 							=		self.alphas_cumprod.to(device=original_samples.device		,			dtype=original_samples.dtype		)
								UpperCAmelCase :       Tuple 							=		timesteps.to(original_samples.device		)

								UpperCAmelCase :       int 							=		alphas_cumprod[timesteps] ** 0.5
								UpperCAmelCase :       Optional[int] 							=		sqrt_alpha_prod.flatten()
								while len(sqrt_alpha_prod.shape		) < len(original_samples.shape		):
															UpperCAmelCase :       Optional[int] 							=		sqrt_alpha_prod.unsqueeze(-1		)

								UpperCAmelCase :       Any 							=		(1 - alphas_cumprod[timesteps]) ** 0.5
								UpperCAmelCase :       Any 							=		sqrt_one_minus_alpha_prod.flatten()
								while len(sqrt_one_minus_alpha_prod.shape		) < len(original_samples.shape		):
															UpperCAmelCase :       int 							=		sqrt_one_minus_alpha_prod.unsqueeze(-1		)

								UpperCAmelCase :       Any 							=		sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
								return noisy_samples









'''simple docstring'''
from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt


def 			a      (			__a   )  ->	bool:



					'''simple docstring'''






					UpperCamelCase__   :int												= int(number**0.5   )
					return number == sq * sq


def 			a      (			__a ,					__a ,					__a ,					__a ,					__a ,					__a   )  ->	tuple[int, int]:



					'''simple docstring'''






					UpperCamelCase__   :int												= x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
					UpperCamelCase__   :int												= x_den * y_den * z_den
					UpperCamelCase__   :int												= gcd(__a ,					__a   )
					top //= hcf
					bottom //= hcf
					return top, bottom


def 			a      (			__a = 35   )  ->	int:



					'''simple docstring'''






					UpperCamelCase__   :set												= set()
					UpperCamelCase__   :int
					UpperCamelCase__   :Fraction												= Fraction(0   )
					UpperCamelCase__   :tuple[int, int]

					for x_num in range(1 ,					order + 1   ):
										for x_den in range(x_num + 1 ,					order + 1   ):
															for y_num in range(1 ,					order + 1   ):
																				for y_den in range(y_num + 1 ,					order + 1   ):
																									# n=1
																									UpperCamelCase__   :int												= x_num * y_den + x_den * y_num
																									UpperCamelCase__   :Any												= x_den * y_den
																									UpperCamelCase__   :Tuple												= gcd(__a ,					__a   )
																									z_num //= hcf
																									z_den //= hcf
																									if 0 < z_num < z_den <= order:
																														UpperCamelCase__   :Tuple												= add_three(
																														    __a ,					__a ,					__a ,					__a ,					__a ,					__a   )
																														unique_s.add(__a   )

																									# n=2
																									UpperCamelCase__   :List[str]												= (
																									    x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
																									)
																									UpperCamelCase__   :Dict												= x_den * x_den * y_den * y_den
																									if is_sq(__a   ) and is_sq(__a   ):
																														UpperCamelCase__   :Any												= int(sqrt(__a   )   )
																														UpperCamelCase__   :Optional[int]												= int(sqrt(__a   )   )
																														UpperCamelCase__   :int												= gcd(__a ,					__a   )
																														z_num //= hcf
																														z_den //= hcf
																														if 0 < z_num < z_den <= order:
																																			UpperCamelCase__   :Tuple												= add_three(
																																			    __a ,					__a ,					__a ,					__a ,					__a ,					__a   )
																																			unique_s.add(__a   )

                    # n=-1
																									UpperCamelCase__   :Tuple												= x_num * y_num
																									UpperCamelCase__   :Union[str, Any]												= x_den * y_num + x_num * y_den
																									UpperCamelCase__   :List[str]												= gcd(__a ,					__a   )
																									z_num //= hcf
																									z_den //= hcf
																									if 0 < z_num < z_den <= order:
																														UpperCamelCase__   :Union[str, Any]												= add_three(
																														    __a ,					__a ,					__a ,					__a ,					__a ,					__a   )
																														unique_s.add(__a   )

																									# n=2
																									UpperCamelCase__   :Optional[Any]												= x_num * x_num * y_num * y_num
																									UpperCamelCase__   :Tuple												= (
																									    x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
																									)
																									if is_sq(__a   ) and is_sq(__a   ):
																														UpperCamelCase__   :str												= int(sqrt(__a   )   )
																														UpperCamelCase__   :Any												= int(sqrt(__a   )   )
																														UpperCamelCase__   :Dict												= gcd(__a ,					__a   )
																														z_num //= hcf
																														z_den //= hcf
																														if 0 < z_num < z_den <= order:
																																			UpperCamelCase__   :int												= add_three(
																																			    __a ,					__a ,					__a ,					__a ,					__a ,					__a   )
																																			unique_s.add(__a   )

					for num, den in unique_s:
										total += Fraction(__a ,					__a   )

					return total.denominator + total.numerator


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