



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						(	SCREAMING_SNAKE_CASE_  ):



   '''simple docstring'''






   snake_case_					: torch.FloatTensor
   snake_case_					: torch.FloatTensor
   snake_case_					: Optional[torch.FloatTensor]          =		None







class 		snake_case						(	SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_  ):



   '''simple docstring'''






   snake_case_					: Tuple          =		2

   @register_to_config
   def __init__(					self							:			Optional[Any]				,		lowerCAmelCase							:			float = 0.02				,		lowerCAmelCase							:			float = 100				,		lowerCAmelCase							:			float = 1.007				,		lowerCAmelCase							:			float = 80				,		lowerCAmelCase							:			float = 0.05				,		lowerCAmelCase							:			float = 50				,		)				->				List[Any]:

    """simple docstring"""







    _snake_case    :  Any					=					sigma_max

    # setable values
    _snake_case    :  int					=					None
    _snake_case    :  np.IntTensor					=					None
    _snake_case    :  torch.FloatTensor					=					None  # sigma(t_i)

   def      UpperCamelCase_  (					self							:			Optional[int]				,		lowerCAmelCase							:			torch.FloatTensor				,		lowerCAmelCase							:			Optional[int] = None)				->				torch.FloatTensor:

    """simple docstring"""







    return sample

   def      UpperCamelCase_  (					self							:			Tuple				,		lowerCAmelCase							:			int				,		lowerCAmelCase							:			Union[str, torch.device] = None)				->				List[str]:

    """simple docstring"""







    _snake_case    :  Optional[Any]					=					num_inference_steps
    _snake_case    :  Optional[int]					=					np.arange(0				,		self.num_inference_steps)[::-1].copy()
    _snake_case    :  str					=					torch.from_numpy(lowerCAmelCase).to(lowerCAmelCase)
    _snake_case    :  List[str]					=					[
        (
            self.config.sigma_max**2
            * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
        )
        for i in self.timesteps
    ]
    _snake_case    :  Optional[Any]					=					torch.tensor(lowerCAmelCase				,		dtype=torch.floataa				,		device=lowerCAmelCase)

   def      UpperCamelCase_  (					self							:			Union[str, Any]				,		lowerCAmelCase							:			torch.FloatTensor				,		lowerCAmelCase							:			float				,		lowerCAmelCase							:			Optional[torch.Generator] = None)				->				Tuple[torch.FloatTensor, float]:

    """simple docstring"""







    if self.config.s_min <= sigma <= self.config.s_max:
     _snake_case    :  str					=					min(self.config.s_churn / self.num_inference_steps				,		2**0.5 - 1)
    else:
     _snake_case    :  Union[str, Any]					=					0

    # sample eps ~ N(0, S_noise^2 * I)
    _snake_case    :  Optional[Any]					=					self.config.s_noise * randn_tensor(sample.shape				,		generator=lowerCAmelCase).to(sample.device)
    _snake_case    :  Dict					=					sigma + gamma * sigma
    _snake_case    :  Tuple					=					sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

    return sample_hat, sigma_hat

   def      UpperCamelCase_  (					self							:			str				,		lowerCAmelCase							:			torch.FloatTensor				,		lowerCAmelCase							:			float				,		lowerCAmelCase							:			float				,		lowerCAmelCase							:			torch.FloatTensor				,		lowerCAmelCase							:			bool = True				,		)				->				Union[KarrasVeOutput, Tuple]:

    """simple docstring"""







    _snake_case    :  int					=					sample_hat + sigma_hat * model_output
    _snake_case    :  int					=					(sample_hat - pred_original_sample) / sigma_hat
    _snake_case    :  Dict					=					sample_hat + (sigma_prev - sigma_hat) * derivative

    if not return_dict:
     return (sample_prev, derivative)

    return KarrasVeOutput(
        prev_sample=lowerCAmelCase				,		derivative=lowerCAmelCase				,		pred_original_sample=lowerCAmelCase)

   def      UpperCamelCase_  (					self							:			Union[str, Any]				,		lowerCAmelCase							:			torch.FloatTensor				,		lowerCAmelCase							:			float				,		lowerCAmelCase							:			float				,		lowerCAmelCase							:			torch.FloatTensor				,		lowerCAmelCase							:			torch.FloatTensor				,		lowerCAmelCase							:			torch.FloatTensor				,		lowerCAmelCase							:			bool = True				,		)				->				Union[KarrasVeOutput, Tuple]:

    """simple docstring"""







    _snake_case    :  Tuple					=					sample_prev + sigma_prev * model_output
    _snake_case    :  int					=					(sample_prev - pred_original_sample) / sigma_prev
    _snake_case    :  Optional[Any]					=					sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)

    if not return_dict:
     return (sample_prev, derivative)

    return KarrasVeOutput(
        prev_sample=lowerCAmelCase				,		derivative=lowerCAmelCase				,		pred_original_sample=lowerCAmelCase)


   def      UpperCamelCase_  (					self							:			Union[str, Any]				,		lowerCAmelCase							:			List[Any]				,		lowerCAmelCase							:			List[str]				,		lowerCAmelCase							:			List[Any])				->				int:

    """simple docstring"""







    raise NotImplementedError()





import sys

a__    =	(
    """73167176531330624919225119674426574742355349194934"""
    """96983520312774506326239578318016984801869478851843"""
    """85861560789112949495459501737958331952853208805511"""
    """12540698747158523863050715693290963295227443043557"""
    """66896648950445244523161731856403098711121722383113"""
    """62229893423380308135336276614282806444486645238749"""
    """30358907296290491560440772390713810515859307960866"""
    """70172427121883998797908792274921901699720888093776"""
    """65727333001053367881220235421809751254540594752243"""
    """52584907711670556013604839586446706324415722155397"""
    """53697817977846174064955149290862569321978468622482"""
    """83972241375657056057490261407972968652414535100474"""
    """82166370484403199890008895243450658541227588666881"""
    """16427171479924442928230863465674813919123162824586"""
    """17866458359124566529476545682848912883142607690042"""
    """24219022671055626321111109370544217506941658960408"""
    """07198403850962455444362981230987879927244284909188"""
    """84580156166097919133875499200524063689912560717606"""
    """05886116467109405077541002256983155200055935729725"""
    """71636269561882670428252483600823257530420752963450"""
)



def       lowercase       (   SCREAMING_SNAKE_CASE__       :	str = N				)  ->     int:
 _snake_case    :  int					=					-sys.maxsize - 1
 for i in range(len(SCREAMING_SNAKE_CASE__				) - 12				):
  _snake_case    :  Optional[int]					=					1
  for j in range(13				):
   product *= int(n[i + j]				)
  if product > largest_product:
   _snake_case    :  List[str]					=					product
 return largest_product


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