
'''simple docstring'''



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

import numpy as np
import torch

from diffusers.configuration_utils import ConfigMixin, register_to_config
from diffusers.schedulers.scheduling_utils import SchedulerMixin
from diffusers.utils import BaseOutput, deprecate

@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->DDIM
class    _a				(_lowerCamelCase):
       SCREAMING_SNAKE_CASE      =  42
       SCREAMING_SNAKE_CASE      =  None






def    lowerCAmelCase_	(				SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_=0.999    ,      SCREAMING_SNAKE_CASE_="cosine"    ,      )     ->     List[Any]:




   """simple docstring"""
   if alpha_transform_type == "cosine":

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

   elif alpha_transform_type == "exp":

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

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

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







class    _a				(_lowerCamelCase  ,					_lowerCamelCase):
       SCREAMING_SNAKE_CASE      =  1






       @register_to_config
       def __init__(							self       ,							A__ = 10_00       ,							A__ = 0.0001       ,							A__ = 0.02       ,							A__ = "linear"       ,							A__ = None       ,							A__ = True       ,							A__ = True       ,							A__ = 0       ,							A__ = "epsilon"       ,							A__ = 1.0       ,							**A__       ,							)    ->			Any:
          if kwargs.get("""set_alpha_to_one"""       ,							A__      ) is not None:
             _SCREAMING_SNAKE_CASE      =				(
                 """The `set_alpha_to_one` argument is deprecated. Please use `set_alpha_to_zero` instead."""
             )
             deprecate("""set_alpha_to_one"""       ,							"""1.0.0"""       ,							A__       ,							standard_warn=A__      )
             _SCREAMING_SNAKE_CASE      =				kwargs["""set_alpha_to_one"""]
          if trained_betas is not None:
             _SCREAMING_SNAKE_CASE      =				torch.tensor(A__       ,							dtype=torch.floataa      )
          elif beta_schedule == "linear":
             _SCREAMING_SNAKE_CASE      =				torch.linspace(A__       ,							A__       ,							A__       ,							dtype=torch.floataa      )
          elif beta_schedule == "scaled_linear":
             # this schedule is very specific to the latent diffusion model.
             _SCREAMING_SNAKE_CASE      =				(
                 torch.linspace(beta_start**0.5       ,							beta_end**0.5       ,							A__       ,							dtype=torch.floataa      ) ** 2
             )
          elif beta_schedule == "squaredcos_cap_v2":
             # Glide cosine schedule
             _SCREAMING_SNAKE_CASE      =				betas_for_alpha_bar(A__      )
          else:
             raise NotImplementedError(F"{beta_schedule} does is not implemented for {self.__class__}"      )

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

          # At every step in inverted ddim, we are looking into the next alphas_cumprod
          # For the final step, there is no next alphas_cumprod, and the index is out of bounds
          # `set_alpha_to_zero` decides whether we set this parameter simply to zero
          # in this case, self.step() just output the predicted noise
          # or whether we use the final alpha of the "non-previous" one.
          _SCREAMING_SNAKE_CASE      =				torch.tensor(0.0      ) if set_alpha_to_zero else self.alphas_cumprod[-1]

          # standard deviation of the initial noise distribution
          _SCREAMING_SNAKE_CASE      =				1.0

          # setable values
          _SCREAMING_SNAKE_CASE      =				None
          _SCREAMING_SNAKE_CASE      =				torch.from_numpy(np.arange(0       ,							A__      ).copy().astype(np.intaa      )      )






       def        UpperCamelCase				(							self       ,							A__       ,							A__ = None      )    ->			torch.FloatTensor:
          return sample






       def        UpperCamelCase				(							self       ,							A__       ,							A__ = None      )    ->			List[Any]:

          if num_inference_steps > self.config.num_train_timesteps:
             raise ValueError(
                 F"`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:"
                 F" {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle"
                 F" maximal {self.config.num_train_timesteps} timesteps."      )

          _SCREAMING_SNAKE_CASE      =				num_inference_steps
          _SCREAMING_SNAKE_CASE      =				self.config.num_train_timesteps // self.num_inference_steps
          # creates integer timesteps by multiplying by ratio
          # casting to int to avoid issues when num_inference_step is power of 3
          _SCREAMING_SNAKE_CASE      =				(np.arange(0       ,							A__      ) * step_ratio).round().copy().astype(np.intaa      )
          _SCREAMING_SNAKE_CASE      =				torch.from_numpy(A__      ).to(A__      )
          self.timesteps += self.config.steps_offset






       def        UpperCamelCase				(							self       ,							A__       ,							A__       ,							A__       ,							A__ = 0.0       ,							A__ = False       ,							A__ = None       ,							A__ = True       ,							)    ->			Union[DDIMSchedulerOutput, Tuple]:
          # 1. get previous step value (=t+1)
          _SCREAMING_SNAKE_CASE      =				timestep + self.config.num_train_timesteps // self.num_inference_steps

          # 2. compute alphas, betas
          # change original implementation to exactly match noise levels for analogous forward process
          _SCREAMING_SNAKE_CASE      =				self.alphas_cumprod[timestep]
          _SCREAMING_SNAKE_CASE      =				(
              self.alphas_cumprod[prev_timestep]
              if prev_timestep < self.config.num_train_timesteps
              else self.final_alpha_cumprod
          )

          _SCREAMING_SNAKE_CASE      =				1 - alpha_prod_t

          # 3. compute predicted original sample from predicted noise also called
          # "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
          if self.config.prediction_type == "epsilon":
             _SCREAMING_SNAKE_CASE      =				(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
             _SCREAMING_SNAKE_CASE      =				model_output
          elif self.config.prediction_type == "sample":
             _SCREAMING_SNAKE_CASE      =				model_output
             _SCREAMING_SNAKE_CASE      =				(sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
          elif self.config.prediction_type == "v_prediction":
             _SCREAMING_SNAKE_CASE      =				(alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
             _SCREAMING_SNAKE_CASE      =				(alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
          else:
             raise ValueError(
                 F"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
                 """ `v_prediction`"""      )

          # 4. Clip or threshold "predicted x_0"
          if self.config.clip_sample:
             _SCREAMING_SNAKE_CASE      =				pred_original_sample.clamp(
                 -self.config.clip_sample_range       ,							self.config.clip_sample_range      )

          # 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
          _SCREAMING_SNAKE_CASE      =				(1 - alpha_prod_t_prev) ** 0.5 * pred_epsilon

          # 6. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
          _SCREAMING_SNAKE_CASE      =				alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction

          if not return_dict:
             return (prev_sample, pred_original_sample)
          return DDIMSchedulerOutput(prev_sample=A__       ,							pred_original_sample=A__      )






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








'''simple docstring'''



import sys

UpperCamelCase__      :		int       							=  (
    "73167176531330624919225119674426574742355349194934"
    "96983520312774506326239578318016984801869478851843"
    "85861560789112949495459501737958331952853208805511"
    "12540698747158523863050715693290963295227443043557"
    "66896648950445244523161731856403098711121722383113"
    "62229893423380308135336276614282806444486645238749"
    "30358907296290491560440772390713810515859307960866"
    "70172427121883998797908792274921901699720888093776"
    "65727333001053367881220235421809751254540594752243"
    "52584907711670556013604839586446706324415722155397"
    "53697817977846174064955149290862569321978468622482"
    "83972241375657056057490261407972968652414535100474"
    "82166370484403199890008895243450658541227588666881"
    "16427171479924442928230863465674813919123162824586"
    "17866458359124566529476545682848912883142607690042"
    "24219022671055626321111109370544217506941658960408"
    "07198403850962455444362981230987879927244284909188"
    "84580156166097919133875499200524063689912560717606"
    "05886116467109405077541002256983155200055935729725"
    "71636269561882670428252483600823257530420752963450"
)
def    lowerCAmelCase_	(				SCREAMING_SNAKE_CASE_ = N						)     ->     int:




   """simple docstring"""
   _SCREAMING_SNAKE_CASE      =				-sys.maxsize - 1
   for i in range(len(SCREAMING_SNAKE_CASE_						) - 12						):
      _SCREAMING_SNAKE_CASE      =				1
      for j in range(13						):
         product *= int(n[i + j]						)
      if product > largest_product:
         _SCREAMING_SNAKE_CASE      =				product
   return largest_product


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






