



"""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
class  A_     (	SCREAMING_SNAKE_CASE_							):



						"""simple docstring"""
						__UpperCamelCase													=				42
						__UpperCamelCase													=				42


def 					_lowerCAmelCase (  lowercase_						,      lowercase_=0.9_9_9						,      lowercase_="cosine"						,      ):
						if alpha_transform_type == "cosine":

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

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

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







class  A_     (	SCREAMING_SNAKE_CASE_      ,  SCREAMING_SNAKE_CASE_							):



						"""simple docstring"""
						__UpperCamelCase													=				1






						@register_to_config
						def __init__(   self					:str  ,    lowercase_					:int = 10_00  ,    lowercase_					:float = 0.0001  ,    lowercase_					:float = 0.02  ,    lowercase_					:str = "linear"  ,    lowercase_					:float = 0.0  ,    lowercase_					:Optional[np.ndarray] = None  ,    lowercase_					:bool = True  ,    )							->     Dict:
												if trained_betas is not None:
																		UpperCAmelCase			 =					torch.from_numpy(lowercase_   )
												elif beta_schedule == "linear":
																		UpperCAmelCase			 =					torch.linspace(lowercase_  ,    lowercase_  ,    lowercase_  ,    dtype=torch.floataa   )
												elif beta_schedule == "scaled_linear":
																		# this schedule is very specific to the latent diffusion model.
																		UpperCAmelCase			 =					(
																		    torch.linspace(beta_start**0.5  ,    beta_end**0.5  ,    lowercase_  ,    dtype=torch.floataa   ) ** 2
																		)
												elif beta_schedule == "squaredcos_cap_v2":
																		# Glide cosine schedule
																		UpperCAmelCase			 =					betas_for_alpha_bar(lowercase_   )
												elif beta_schedule == "sigmoid":
																		# GeoDiff sigmoid schedule
																		UpperCAmelCase			 =					torch.linspace(-6  ,    6  ,    lowercase_   )
																		UpperCAmelCase			 =					torch.sigmoid(lowercase_   ) * (beta_end - beta_start) + beta_start
												else:
																		raise NotImplementedError(f"""{beta_schedule} does is not implemented for {self.__class__}"""   )

												UpperCAmelCase			 =					1.0 - self.betas
												UpperCAmelCase			 =					torch.cumprod(self.alphas  ,    dim=0   )
												UpperCAmelCase			 =					torch.tensor(1.0   )

												UpperCAmelCase			 =					torch.tensor(1.0   )

												# standard deviation of the initial noise distribution
												UpperCAmelCase			 =					1.0

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

												UpperCAmelCase			 =					eta






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






						def       UpperCAmelCase__	(   self					:Optional[Any]  ,    lowercase_					:int  ,    lowercase_					:int = 10  ,    lowercase_					:int = 10  ,    lowercase_					:Union[str, torch.device] = None  ,    )							->     Union[str, Any]:
												UpperCAmelCase			 =					min(self.config.num_train_timesteps  ,    lowercase_   )
												UpperCAmelCase			 =					num_inference_steps

												UpperCAmelCase			 =					[]

												UpperCAmelCase			 =					{}
												for j in range(0  ,    num_inference_steps - jump_length  ,    lowercase_   ):
																		UpperCAmelCase			 =					jump_n_sample - 1

												UpperCAmelCase			 =					num_inference_steps
												while t >= 1:
																		UpperCAmelCase			 =					t - 1
																		timesteps.append(lowercase_   )

																		if jumps.get(lowercase_  ,    0   ) > 0:
																								UpperCAmelCase			 =					jumps[t] - 1
																								for _ in range(lowercase_   ):
																														UpperCAmelCase			 =					t + 1
																														timesteps.append(lowercase_   )

												UpperCAmelCase			 =					np.array(lowercase_   ) * (self.config.num_train_timesteps // self.num_inference_steps)
												UpperCAmelCase			 =					torch.from_numpy(lowercase_   ).to(lowercase_   )






						def       UpperCAmelCase__	(   self					:Optional[Any]  ,    lowercase_					:Optional[int]   )							->     Tuple:
												UpperCAmelCase			 =					t - self.config.num_train_timesteps // self.num_inference_steps

												UpperCAmelCase			 =					self.alphas_cumprod[t]
												UpperCAmelCase			 =					self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
												UpperCAmelCase			 =					1 - alpha_prod_t
												UpperCAmelCase			 =					1 - 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
												# Is equivalent to formula (16) in https://arxiv.org/pdf/2010.02502.pdf
												# without eta.
												# variance = (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * self.betas[t]
												UpperCAmelCase			 =					(beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

												return variance






						def       UpperCAmelCase__	(   self					:List[Any]  ,    lowercase_					:torch.FloatTensor  ,    lowercase_					:int  ,    lowercase_					:torch.FloatTensor  ,    lowercase_					:torch.FloatTensor  ,    lowercase_					:torch.FloatTensor  ,    lowercase_					:Optional[torch.Generator] = None  ,    lowercase_					:bool = True  ,    )							->     Union[RePaintSchedulerOutput, Tuple]:
												UpperCAmelCase			 =					timestep
												UpperCAmelCase			 =					timestep - self.config.num_train_timesteps // self.num_inference_steps

												# 1. compute alphas, betas
												UpperCAmelCase			 =					self.alphas_cumprod[t]
												UpperCAmelCase			 =					self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
												UpperCAmelCase			 =					1 - alpha_prod_t

												# 2. compute predicted original sample from predicted noise also called
												# "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
												UpperCAmelCase			 =					(sample - beta_prod_t**0.5 * model_output) / alpha_prod_t**0.5

												# 3. Clip "predicted x_0"
												if self.config.clip_sample:
																		UpperCAmelCase			 =					torch.clamp(lowercase_  ,    -1  ,    1   )

												# We choose to follow RePaint Algorithm 1 to get x_{t-1}, however we
												# substitute formula (7) in the algorithm coming from DDPM paper
												# (formula (4) Algorithm 2 - Sampling) with formula (12) from DDIM paper.
												# DDIM schedule gives the same results as DDPM with eta = 1.0
												# Noise is being reused in 7. and 8., but no impact on quality has
												# been observed.

												# 5. Add noise
												UpperCAmelCase			 =					model_output.device
												UpperCAmelCase			 =					randn_tensor(model_output.shape  ,    generator=lowercase_  ,    device=lowercase_  ,    dtype=model_output.dtype   )
												UpperCAmelCase			 =					self.eta * self._get_variance(lowercase_   ) ** 0.5

												UpperCAmelCase			 =					0
												if t > 0 and self.eta > 0:
																		UpperCAmelCase			 =					std_dev_t * noise

												# 6. compute "direction pointing to x_t" of formula (12)
												# from https://arxiv.org/pdf/2010.02502.pdf
												UpperCAmelCase			 =					(1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * model_output

												# 7. compute x_{t-1} of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
												UpperCAmelCase			 =					alpha_prod_t_prev**0.5 * pred_original_sample + pred_sample_direction + variance

												# 8. Algorithm 1 Line 5 https://arxiv.org/pdf/2201.09865.pdf
												UpperCAmelCase			 =					(alpha_prod_t_prev**0.5) * original_image + ((1 - alpha_prod_t_prev) ** 0.5) * noise

												# 9. Algorithm 1 Line 8 https://arxiv.org/pdf/2201.09865.pdf
												UpperCAmelCase			 =					mask * prev_known_part + (1.0 - mask) * prev_unknown_part

												if not return_dict:
																		return (
																		    pred_prev_sample,
																		    pred_original_sample,
																		)

												return RePaintSchedulerOutput(prev_sample=lowercase_  ,    pred_original_sample=lowercase_   )






						def       UpperCAmelCase__	(   self					:Union[str, Any]  ,    lowercase_					:Tuple  ,    lowercase_					:Optional[int]  ,    lowercase_					:Dict=None   )							->     Optional[Any]:
												UpperCAmelCase			 =					self.config.num_train_timesteps // self.num_inference_steps

												for i in range(lowercase_   ):
																		UpperCAmelCase			 =					self.betas[timestep + i]
																		if sample.device.type == "mps":
																								# randn does not work reproducibly on mps
																								UpperCAmelCase			 =					randn_tensor(sample.shape  ,    dtype=sample.dtype  ,    generator=lowercase_   )
																								UpperCAmelCase			 =					noise.to(sample.device   )
																		else:
																								UpperCAmelCase			 =					randn_tensor(sample.shape  ,    generator=lowercase_  ,    device=sample.device  ,    dtype=sample.dtype   )

																		# 10. Algorithm 1 Line 10 https://arxiv.org/pdf/2201.09865.pdf
																		UpperCAmelCase			 =					(1 - beta) ** 0.5 * sample + beta**0.5 * noise

												return sample






						def       UpperCAmelCase__	(   self					:Optional[Any]  ,    lowercase_					:torch.FloatTensor  ,    lowercase_					:torch.FloatTensor  ,    lowercase_					:torch.IntTensor  ,    )							->     torch.FloatTensor:
												raise NotImplementedError('Use `DDPMScheduler.add_noise()` to train for sampling with RePaint.'   )






						def __len__(   self					:List[Any]   )							->     str:
												return self.config.num_train_timesteps










UpperCAmelCase__  =			10**8





def 				A      (	_UpperCAmelCase							:  int       )							->					bool:







			'''simple docstring'''
			if n % 10 == 0:
						return False
			_UpperCAmelCase									=  str(_UpperCAmelCase       )
			return s == s[::-1]





def 				A      (	)							->					int:







			'''simple docstring'''
			_UpperCAmelCase									=  set()
			_UpperCAmelCase									=  1
			_UpperCAmelCase									=  5
			while sum_squares < LIMIT:
						_UpperCAmelCase									=  first_square + 1
						while sum_squares < LIMIT:
									if is_palindrome(_UpperCAmelCase       ):
												answer.add(_UpperCAmelCase       )
									last_square += 1
									sum_squares += last_square**2
						first_square += 1
						_UpperCAmelCase									=  first_square**2 + (first_square + 1) ** 2

			return sum(_UpperCAmelCase       )


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