




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 			__snake_case   (     lowerCamelCase__   ):
 __lowerCamelCase    :   torch.FloatTensor
 __lowerCamelCase    :   torch.FloatTensor





def   lowerCAmelCase_ (				__lowerCAmelCase		,					__lowerCAmelCase=0.999		,					__lowerCAmelCase="cosine"		,					)->  str:






      '''simple docstring'''





      if alpha_transform_type == "cosine":

            def alpha_bar_fn(__lowerCAmelCase						):
                  return math.cos((t + 0.008) / 1.008 * math.pi / 2						) ** 2

      elif alpha_transform_type == "exp":

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

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

      UpperCAmelCase    : List[Any]      =[]
      for i in range(__lowerCAmelCase						):
            UpperCAmelCase    : Any      =i / num_diffusion_timesteps
            UpperCAmelCase    : Optional[int]      =(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 			__snake_case   (     lowerCamelCase__					,   lowerCamelCase__   ):
 __lowerCamelCase    :   List[str]     =      1
 @register_to_config
 def __init__(  self		,   snake_case__ = 1000		,   snake_case__ = 0.0001		,   snake_case__ = 0.02		,   snake_case__ = "linear"		,   snake_case__ = 0.0		,   snake_case__ = None		,   snake_case__ = True		,   )	->							str:
       '''simple docstring'''





       if trained_betas is not None:
             UpperCAmelCase    : Any      =torch.from_numpy(snake_case__						)
       elif beta_schedule == "linear":
             UpperCAmelCase    : Any      =torch.linspace(snake_case__		,   snake_case__		,   snake_case__		,   dtype=torch.floataa						)
       elif beta_schedule == "scaled_linear":
             # this schedule is very specific to the latent diffusion model.
             UpperCAmelCase    : Dict      =(
                 torch.linspace(beta_start**0.5		,   beta_end**0.5		,   snake_case__		,   dtype=torch.floataa						) ** 2
             )
       elif beta_schedule == "squaredcos_cap_v2":
             # Glide cosine schedule
             UpperCAmelCase    : List[str]      =betas_for_alpha_bar(snake_case__						)
       elif beta_schedule == "sigmoid":
             # GeoDiff sigmoid schedule
             UpperCAmelCase    : Tuple      =torch.linspace(-6		,   6		,   snake_case__						)
             UpperCAmelCase    : Dict      =torch.sigmoid(snake_case__						) * (beta_end - beta_start) + beta_start
       else:
             raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}'''						)

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

       UpperCAmelCase    : Optional[int]      =torch.tensor(1.0						)

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

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

       UpperCAmelCase    : Optional[Any]      =eta
 def 	UpperCAmelCase__       (  self		,   snake_case__		,   snake_case__ = None						)	->							torch.FloatTensor:
       '''simple docstring'''





       return sample
 def 	UpperCAmelCase__       (  self		,   snake_case__		,   snake_case__ = 10		,   snake_case__ = 10		,   snake_case__ = None		,   )	->							Optional[Any]:
       '''simple docstring'''





       UpperCAmelCase    : List[str]      =min(self.config.num_train_timesteps		,   snake_case__						)
       UpperCAmelCase    : int      =num_inference_steps

       UpperCAmelCase    : str      =[]

       UpperCAmelCase    : Dict      ={}
       for j in range(0		,   num_inference_steps - jump_length		,   snake_case__						):
             UpperCAmelCase    : List[str]      =jump_n_sample - 1

       UpperCAmelCase    : Optional[int]      =num_inference_steps
       while t >= 1:
             UpperCAmelCase    : Any      =t - 1
             timesteps.append(snake_case__						)

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

       UpperCAmelCase    : Optional[int]      =np.array(snake_case__						) * (self.config.num_train_timesteps // self.num_inference_steps)
       UpperCAmelCase    : Optional[int]      =torch.from_numpy(snake_case__						).to(snake_case__						)
 def 	UpperCAmelCase__       (  self		,   snake_case__						)	->							int:
       '''simple docstring'''





       UpperCAmelCase    : str      =t - self.config.num_train_timesteps // self.num_inference_steps

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

       return variance
 def 	UpperCAmelCase__       (  self		,   snake_case__		,   snake_case__		,   snake_case__		,   snake_case__		,   snake_case__		,   snake_case__ = None		,   snake_case__ = True		,   )	->							Union[RePaintSchedulerOutput, Tuple]:
       '''simple docstring'''





       UpperCAmelCase    : Any      =timestep
       UpperCAmelCase    : Dict      =timestep - self.config.num_train_timesteps // self.num_inference_steps

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

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

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

       # 6. compute "direction pointing to x_t" of formula (12)
       # from https://arxiv.org/pdf/2010.02502.pdf
       UpperCAmelCase    : Optional[int]      =(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    : Tuple      =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    : Optional[int]      =(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=snake_case__		,   pred_original_sample=snake_case__						)
 def 	UpperCAmelCase__       (  self		,   snake_case__		,   snake_case__		,   snake_case__=None						)	->							int:
       '''simple docstring'''





       UpperCAmelCase    : str      =self.config.num_train_timesteps // self.num_inference_steps

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

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

       return sample
 def 	UpperCAmelCase__       (  self		,   snake_case__		,   snake_case__		,   snake_case__		,   )	->							torch.FloatTensor:
       '''simple docstring'''





       raise NotImplementedError('''Use `DDPMScheduler.add_noise()` to train for sampling with RePaint.'''						)






 def __len__(  self						)	->							str:
       '''simple docstring'''





       return self.config.num_train_timesteps

from collections import defaultdict





def   lowerCAmelCase_ (				__lowerCAmelCase = 5						)->  int:






      '''simple docstring'''





      UpperCAmelCase    : List[str]      =defaultdict(__lowerCAmelCase						)
      UpperCAmelCase    : Tuple      =0

      while True:
            UpperCAmelCase    : Any      =get_digits(__lowerCAmelCase						)
            freqs[digits].append(__lowerCAmelCase						)

            if len(freqs[digits]						) == max_base:
                  UpperCAmelCase    : Optional[int]      =freqs[digits][0] ** 3
                  return base

            num += 1





def   lowerCAmelCase_ (				__lowerCAmelCase						)->  str:






      '''simple docstring'''





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


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