




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

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, logging, randn_tensor
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin


_lowerCamelCase    				=		logging.get_logger(__name__)  # pylint: disable=invalid-name



@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerAncestralDiscrete
class     a  (     _A    ):

     '''simple docstring'''





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




def       SCREAMING_SNAKE_CASE			( __UpperCamelCase    :		List[Any] ,  __UpperCamelCase    :		Optional[int]=0.999 ,  __UpperCamelCase    :		Optional[int]="cosine" ,  )						->							Any:
    if alpha_transform_type == "cosine":

        def alpha_bar_fn(__UpperCamelCase    :		Optional[int]   ):
            return math.cos((t + 0.008) / 1.008 * math.pi / 2   ) ** 2

    elif alpha_transform_type == "exp":

        def alpha_bar_fn(__UpperCamelCase    :		Union[str, Any]   ):
            return math.exp(t * -12.0   )

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

    UpperCAmelCase_											=  []
    for i in range(__UpperCamelCase   ):
        UpperCAmelCase_											=  i / num_diffusion_timesteps
        UpperCAmelCase_											=  (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     a  (     _A			,     _A    ):

     '''simple docstring'''





     lowerCAmelCase       : Optional[int]     	=						[e.name for e in KarrasDiffusionSchedulers]
     lowerCAmelCase       : Union[str, Any]     	=						1
     @register_to_config
     def __init__(			self     :    Any      ,					__snake_case     :    int = 10_00      ,					__snake_case     :    float = 0.0_001      ,					__snake_case     :    float = 0.02      ,					__snake_case     :    str = "linear"      ,					__snake_case     :    Optional[Union[np.ndarray, List[float]]] = None      ,					__snake_case     :    str = "epsilon"      ,					__snake_case     :    str = "linspace"      ,					__snake_case     :    int = 0      ,					):
         if trained_betas is not None:
             UpperCAmelCase_											=  torch.tensor(__snake_case      ,					dtype=torch.floataa       )
         elif beta_schedule == "linear":
             UpperCAmelCase_											=  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_											=  (
                 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_											=  betas_for_alpha_bar(__snake_case       )
         else:
             raise NotImplementedError(F'{beta_schedule} does is not implemented for {self.__class__}'       )

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

         UpperCAmelCase_											=  np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5       )
         UpperCAmelCase_											=  np.concatenate([sigmas[::-1], [0.0]]       ).astype(np.floataa       )
         UpperCAmelCase_											=  torch.from_numpy(__snake_case       )

         # setable values
         UpperCAmelCase_											=  None
         UpperCAmelCase_											=  np.linspace(0      ,					num_train_timesteps - 1      ,					__snake_case      ,					dtype=__snake_case       )[::-1].copy()
         UpperCAmelCase_											=  torch.from_numpy(__snake_case       )
         UpperCAmelCase_											=  False
     @property
     def 						lowerCamelCase_     (			self     :    Optional[int]       ):
         # standard deviation of the initial noise distribution
         if self.config.timestep_spacing in ["linspace", "trailing"]:
             return self.sigmas.max()

         return (self.sigmas.max() ** 2 + 1) ** 0.5
     def 						lowerCamelCase_     (			self     :    List[str]      ,					__snake_case     :    torch.FloatTensor      ,					__snake_case     :    Union[float, torch.FloatTensor]       ):
         if isinstance(__snake_case      ,					torch.Tensor       ):
             UpperCAmelCase_											=  timestep.to(self.timesteps.device       )
         UpperCAmelCase_											=  (self.timesteps == timestep).nonzero().item()
         UpperCAmelCase_											=  self.sigmas[step_index]
         UpperCAmelCase_											=  sample / ((sigma**2 + 1) ** 0.5)
         UpperCAmelCase_											=  True
         return sample
     def 						lowerCamelCase_     (			self     :    Any      ,					__snake_case     :    int      ,					__snake_case     :    Union[str, torch.device] = None       ):
         UpperCAmelCase_											=  num_inference_steps

         # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
         if self.config.timestep_spacing == "linspace":
             UpperCAmelCase_											=  np.linspace(0      ,					self.config.num_train_timesteps - 1      ,					__snake_case      ,					dtype=__snake_case       )[
                 ::-1
             ].copy()
         elif self.config.timestep_spacing == "leading":
             UpperCAmelCase_											=  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
             UpperCAmelCase_											=  (np.arange(0      ,					__snake_case       ) * step_ratio).round()[::-1].copy().astype(__snake_case       )
             timesteps += self.config.steps_offset
         elif self.config.timestep_spacing == "trailing":
             UpperCAmelCase_											=  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
             UpperCAmelCase_											=  (np.arange(self.config.num_train_timesteps      ,					0      ,					-step_ratio       )).round().copy().astype(__snake_case       )
             timesteps -= 1
         else:
             raise ValueError(
                 F'{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.'       )

         UpperCAmelCase_											=  np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5       )
         UpperCAmelCase_											=  np.interp(__snake_case      ,					np.arange(0      ,					len(__snake_case       )       )      ,					__snake_case       )
         UpperCAmelCase_											=  np.concatenate([sigmas, [0.0]]       ).astype(np.floataa       )
         UpperCAmelCase_											=  torch.from_numpy(__snake_case       ).to(device=__snake_case       )
         if str(__snake_case       ).startswith('''mps'''       ):
             # mps does not support float64
             UpperCAmelCase_											=  torch.from_numpy(__snake_case       ).to(__snake_case      ,					dtype=torch.floataa       )
         else:
             UpperCAmelCase_											=  torch.from_numpy(__snake_case       ).to(device=__snake_case       )
     def 						lowerCamelCase_     (			self     :    Any      ,					__snake_case     :    torch.FloatTensor      ,					__snake_case     :    Union[float, torch.FloatTensor]      ,					__snake_case     :    torch.FloatTensor      ,					__snake_case     :    Optional[torch.Generator] = None      ,					__snake_case     :    bool = True      ,					):

         if (
             isinstance(__snake_case      ,					__snake_case       )
             or isinstance(__snake_case      ,					torch.IntTensor       )
             or isinstance(__snake_case      ,					torch.LongTensor       )
         ):
             raise ValueError(
                 (
                     '''Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to'''
                     ''' `EulerDiscreteScheduler.step()` is not supported. Make sure to pass'''
                     ''' one of the `scheduler.timesteps` as a timestep.'''
                 )      ,					)

         if not self.is_scale_input_called:
             logger.warning(
                 '''The `scale_model_input` function should be called before `step` to ensure correct denoising. '''
                 '''See `StableDiffusionPipeline` for a usage example.'''       )

         if isinstance(__snake_case      ,					torch.Tensor       ):
             UpperCAmelCase_											=  timestep.to(self.timesteps.device       )

         UpperCAmelCase_											=  (self.timesteps == timestep).nonzero().item()
         UpperCAmelCase_											=  self.sigmas[step_index]

         # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
         if self.config.prediction_type == "epsilon":
             UpperCAmelCase_											=  sample - sigma * model_output
         elif self.config.prediction_type == "v_prediction":
             # * c_out + input * c_skip
             UpperCAmelCase_											=  model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
         elif self.config.prediction_type == "sample":
             raise NotImplementedError('''prediction_type not implemented yet: sample'''       )
         else:
             raise ValueError(
                 F'prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'       )

         UpperCAmelCase_											=  self.sigmas[step_index]
         UpperCAmelCase_											=  self.sigmas[step_index + 1]
         UpperCAmelCase_											=  (sigma_to**2 * (sigma_from**2 - sigma_to**2) / sigma_from**2) ** 0.5
         UpperCAmelCase_											=  (sigma_to**2 - sigma_up**2) ** 0.5

         # 2. Convert to an ODE derivative
         UpperCAmelCase_											=  (sample - pred_original_sample) / sigma

         UpperCAmelCase_											=  sigma_down - sigma

         UpperCAmelCase_											=  sample + derivative * dt

         UpperCAmelCase_											=  model_output.device
         UpperCAmelCase_											=  randn_tensor(model_output.shape      ,					dtype=model_output.dtype      ,					device=__snake_case      ,					generator=__snake_case       )

         UpperCAmelCase_											=  prev_sample + noise * sigma_up

         if not return_dict:
             return (prev_sample,)

         return EulerAncestralDiscreteSchedulerOutput(
             prev_sample=__snake_case      ,					pred_original_sample=__snake_case       )
     def 						lowerCamelCase_     (			self     :    int      ,					__snake_case     :    torch.FloatTensor      ,					__snake_case     :    torch.FloatTensor      ,					__snake_case     :    torch.FloatTensor      ,					):
         # Make sure sigmas and timesteps have the same device and dtype as original_samples
         UpperCAmelCase_											=  self.sigmas.to(device=original_samples.device      ,					dtype=original_samples.dtype       )
         if original_samples.device.type == "mps" and torch.is_floating_point(__snake_case       ):
             # mps does not support float64
             UpperCAmelCase_											=  self.timesteps.to(original_samples.device      ,					dtype=torch.floataa       )
             UpperCAmelCase_											=  timesteps.to(original_samples.device      ,					dtype=torch.floataa       )
         else:
             UpperCAmelCase_											=  self.timesteps.to(original_samples.device       )
             UpperCAmelCase_											=  timesteps.to(original_samples.device       )

         UpperCAmelCase_											=  [(schedule_timesteps == t).nonzero().item() for t in timesteps]

         UpperCAmelCase_											=  sigmas[step_indices].flatten()
         while len(sigma.shape       ) < len(original_samples.shape       ):
             UpperCAmelCase_											=  sigma.unsqueeze(-1       )

         UpperCAmelCase_											=  original_samples + noise * sigma
         return noisy_samples




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











import itertools




def       SCREAMING_SNAKE_CASE			( __UpperCamelCase    :		Tuple   )						->							List[Any]:
    return (
        int(''''''.join(combination[0:2]   )   ) * int(''''''.join(combination[2:5]   )   )
        == int(''''''.join(combination[5:9]   )   )
    ) or (
        int(''''''.join(combination[0]   )   ) * int(''''''.join(combination[1:5]   )   )
        == int(''''''.join(combination[5:9]   )   )
    )




def       SCREAMING_SNAKE_CASE			( )						->							Optional[Any]:
    return sum(
        {
            int(''''''.join(pandigital[5:9]   )   )
            for pandigital in itertools.permutations('''123456789'''   )
            if is_combination_valid(__UpperCamelCase   )
        }   )


if __name__ == "__main__":
 print(solution())





