





"""simple docstring"""




from collections import defaultdict





def 		UpperCAmelCase__						(	_UpperCAmelCase = 5   ):






  """simple docstring"""





  A_    :			List[Any]									=    defaultdict(_UpperCAmelCase   )
  A_    :			Any									=    0

  while True:
    A_    :			List[str]									=    get_digits(_UpperCAmelCase   )
    freqs[digits].append(_UpperCAmelCase   )

    if len(freqs[digits]   ) == max_base:
      A_    :			Any									=    freqs[digits][0] ** 3
      return base

    num += 1





def 		UpperCAmelCase__						(	_UpperCAmelCase   ):






  """simple docstring"""





  return "".join(sorted(str(num**3   )   )   )


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


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    __UpperCAmelCase	(			lowerCamelCase__		):
   UpperCamelCase  	=	42
   UpperCamelCase  	=	42






def      a__	(						UpperCAmelCase				:     List[str]							,					UpperCAmelCase				:     Optional[int]=0.999							,					UpperCAmelCase				:     Tuple="cosine"							,					)    ->		List[Any]:
  if alpha_transform_type == "cosine":

    def alpha_bar_fn(UpperCAmelCase				:     List[str]     ):
      return math.cos((t + 0.008) / 1.008 * math.pi / 2     ) ** 2

  elif alpha_transform_type == "exp":

    def alpha_bar_fn(UpperCAmelCase				:     int     ):
      return math.exp(t * -12.0     )

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

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






class    __UpperCAmelCase	(			lowerCamelCase__     ,    lowerCamelCase__		):
   UpperCamelCase  	=	1



   @register_to_config
   def __init__(				self				:	str,						__A				:	int = 1_0_0_0,						__A				:	float = 0.0_0_0_1,						__A				:	float = 0.0_2,						__A				:	str = "linear",						__A				:	float = 0.0,						__A				:	Optional[np.ndarray] = None,						__A				:	bool = True,						):
     if trained_betas is not None:
       UpperCAmelCase			:				int										=					torch.from_numpy(__A		)
     elif beta_schedule == "linear":
       UpperCAmelCase			:				str										=					torch.linspace(__A,						__A,						__A,						dtype=torch.floataa		)
     elif beta_schedule == "scaled_linear":
       # this schedule is very specific to the latent diffusion model.
       UpperCAmelCase			:				List[str]										=					(
           torch.linspace(beta_start**0.5,						beta_end**0.5,						__A,						dtype=torch.floataa		) ** 2
       )
     elif beta_schedule == "squaredcos_cap_v2":
       # Glide cosine schedule
       UpperCAmelCase			:				Tuple										=					betas_for_alpha_bar(__A		)
     elif beta_schedule == "sigmoid":
       # GeoDiff sigmoid schedule
       UpperCAmelCase			:				Any										=					torch.linspace(-6,						6,						__A		)
       UpperCAmelCase			:				Tuple										=					torch.sigmoid(__A		) * (beta_end - beta_start) + beta_start
     else:
       raise NotImplementedError(F'''{beta_schedule} does is not implemented for {self.__class__}'''		)

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

     UpperCAmelCase			:				Union[str, Any]										=					torch.tensor(1.0		)

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

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

     UpperCAmelCase			:				List[str]										=					eta



   def 			__magic_name__       (				self				:	List[str],						__A				:	torch.FloatTensor,						__A				:	Optional[int] = None		):
     return sample



   def 			__magic_name__       (				self				:	List[str],						__A				:	int,						__A				:	int = 1_0,						__A				:	int = 1_0,						__A				:	Union[str, torch.device] = None,						):
     UpperCAmelCase			:				Union[str, Any]										=					min(self.config.num_train_timesteps,						__A		)
     UpperCAmelCase			:				Optional[int]										=					num_inference_steps

     UpperCAmelCase			:				Union[str, Any]										=					[]

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

     UpperCAmelCase			:				str										=					num_inference_steps
     while t >= 1:
       UpperCAmelCase			:				Dict										=					t - 1
       timesteps.append(__A		)

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

     UpperCAmelCase			:				Optional[Any]										=					np.array(__A		) * (self.config.num_train_timesteps // self.num_inference_steps)
     UpperCAmelCase			:				Dict										=					torch.from_numpy(__A		).to(__A		)



   def 			__magic_name__       (				self				:	List[Any],						__A				:	Any		):
     UpperCAmelCase			:				int										=					t - self.config.num_train_timesteps // self.num_inference_steps

     UpperCAmelCase			:				Optional[Any]										=					self.alphas_cumprod[t]
     UpperCAmelCase			:				Union[str, Any]										=					self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
     UpperCAmelCase			:				List[Any]										=					1 - alpha_prod_t
     UpperCAmelCase			:				str										=					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			:				Union[str, Any]										=					(beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

     return variance



   def 			__magic_name__       (				self				:	Tuple,						__A				:	torch.FloatTensor,						__A				:	int,						__A				:	torch.FloatTensor,						__A				:	torch.FloatTensor,						__A				:	torch.FloatTensor,						__A				:	Optional[torch.Generator] = None,						__A				:	bool = True,						):
     UpperCAmelCase			:				Union[str, Any]										=					timestep
     UpperCAmelCase			:				str										=					timestep - self.config.num_train_timesteps // self.num_inference_steps

     # 1. compute alphas, betas
     UpperCAmelCase			:				List[Any]										=					self.alphas_cumprod[t]
     UpperCAmelCase			:				str										=					self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
     UpperCAmelCase			:				Any										=					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			:				int										=					(sample - beta_prod_t**0.5 * model_output) / alpha_prod_t**0.5

     # 3. Clip "predicted x_0"
     if self.config.clip_sample:
       UpperCAmelCase			:				Tuple										=					torch.clamp(__A,						-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			:				Optional[Any]										=					model_output.device
     UpperCAmelCase			:				Optional[Any]										=					randn_tensor(model_output.shape,						generator=__A,						device=__A,						dtype=model_output.dtype		)
     UpperCAmelCase			:				List[str]										=					self.eta * self._get_variance(__A		) ** 0.5

     UpperCAmelCase			:				int										=					0
     if t > 0 and self.eta > 0:
       UpperCAmelCase			:				List[str]										=					std_dev_t * noise

     # 6. compute "direction pointing to x_t" of formula (12)
     # from https://arxiv.org/pdf/2010.02502.pdf
     UpperCAmelCase			:				Any										=					(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			:				str										=					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			:				Union[str, Any]										=					(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			:				Optional[Any]										=					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=__A,						pred_original_sample=__A		)



   def 			__magic_name__       (				self				:	Dict,						__A				:	Dict,						__A				:	Tuple,						__A				:	Tuple=None		):
     UpperCAmelCase			:				Optional[int]										=					self.config.num_train_timesteps // self.num_inference_steps

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

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

     return sample



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





   def __len__(				self				:	str		):
     return self.config.num_train_timesteps





