'''simple docstring'''

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  (						a__ ):





       '''simple docstring'''



       SCREAMING_SNAKE_CASE 		=   42
       SCREAMING_SNAKE_CASE 		=   42
       SCREAMING_SNAKE_CASE 		=   None



class       UpperCAmelCase  (						a__   ,						a__ ):





       '''simple docstring'''



       SCREAMING_SNAKE_CASE 		=   2

       @register_to_config
       def __init__(						self     ,       __lowerCAmelCase = 0.0_2     ,       __lowerCAmelCase = 100     ,       __lowerCAmelCase = 1.0_0_7     ,       __lowerCAmelCase = 80     ,       __lowerCAmelCase = 0.0_5     ,       __lowerCAmelCase = 50     ,       )  ->  Dict:
        # standard deviation of the initial noise distribution
        lowercase__    :   List[Any]						= sigma_max

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

       def _lowerCAmelCase(						self     ,       __lowerCAmelCase     ,       __lowerCAmelCase = None			)  ->  torch.FloatTensor:
        return sample

       def _lowerCAmelCase(						self     ,       __lowerCAmelCase     ,       __lowerCAmelCase = None			)  ->  int:
        lowercase__    :   str						= num_inference_steps
        lowercase__    :   List[str]						= np.arange(0     ,       self.num_inference_steps			)[::-1].copy()
        lowercase__    :   Optional[Any]						= torch.from_numpy(__lowerCAmelCase			).to(__lowerCAmelCase			)
        lowercase__    :   Optional[Any]						= [
            (
                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
        ]
        lowercase__    :   Union[str, Any]						= torch.tensor(__lowerCAmelCase     ,       dtype=torch.floataa     ,       device=__lowerCAmelCase			)

       def _lowerCAmelCase(						self     ,       __lowerCAmelCase     ,       __lowerCAmelCase     ,       __lowerCAmelCase = None			)  ->  Tuple[torch.FloatTensor, float]:
        if self.config.s_min <= sigma <= self.config.s_max:
         lowercase__    :   Optional[Any]						= min(self.config.s_churn / self.num_inference_steps     ,       2**0.5 - 1			)
        else:
         lowercase__    :   List[Any]						= 0

        # sample eps ~ N(0, S_noise^2 * I)
        lowercase__    :   List[str]						= self.config.s_noise * randn_tensor(sample.shape     ,       generator=__lowerCAmelCase			).to(sample.device			)
        lowercase__    :   Optional[int]						= sigma + gamma * sigma
        lowercase__    :   List[str]						= sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

        return sample_hat, sigma_hat

       def _lowerCAmelCase(						self     ,       __lowerCAmelCase     ,       __lowerCAmelCase     ,       __lowerCAmelCase     ,       __lowerCAmelCase     ,       __lowerCAmelCase = True     ,       )  ->  Union[KarrasVeOutput, Tuple]:
        lowercase__    :   Tuple						= sample_hat + sigma_hat * model_output
        lowercase__    :   List[str]						= (sample_hat - pred_original_sample) / sigma_hat
        lowercase__    :   Any						= 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 _lowerCAmelCase(						self     ,       __lowerCAmelCase     ,       __lowerCAmelCase     ,       __lowerCAmelCase     ,       __lowerCAmelCase     ,       __lowerCAmelCase     ,       __lowerCAmelCase     ,       __lowerCAmelCase = True     ,       )  ->  Union[KarrasVeOutput, Tuple]:
        lowercase__    :   Tuple						= sample_prev + sigma_prev * model_output
        lowercase__    :   int						= (sample_prev - pred_original_sample) / sigma_prev
        lowercase__    :   Optional[int]						= 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 _lowerCAmelCase(						self     ,       __lowerCAmelCase     ,       __lowerCAmelCase     ,       __lowerCAmelCase			)  ->  Optional[Any]:
        raise NotImplementedError()


'''simple docstring'''

def       __UpperCamelCase	(       UpperCAmelCase					):
 if not all(x.isalpha() for x in string					):
  raise ValueError('''String must only contain alphabetic characters.'''					)

 lowercase__    :   Tuple						= sorted(string.lower()					)
 return len(UpperCAmelCase					) == len(set(UpperCAmelCase					)					)


if __name__ == "__main__":
  __a:			Union[str, Any]	       =       input("""Enter a string """).strip()

  __a:			Tuple	       =       is_isogram(input_str)
  print(F'{input_str} is {"an" if isogram else "not an"} isogram.')

