





"""simple docstring"""


from itertools import permutations





def 							a__			(  )    ->  Optional[int]:

 '''simple docstring'''






 snake_case__    							=				list(map("".join	,     permutations("0123456789"	)	)	)
 return result[9_9_9_9_9_9]


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








"""simple docstring"""


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

import flax
import jax.numpy as jnp
from scipy import integrate

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import (
    CommonSchedulerState,
    FlaxKarrasDiffusionSchedulers,
    FlaxSchedulerMixin,
    FlaxSchedulerOutput,
    broadcast_to_shape_from_left,
)



@flax.struct.dataclass
class      lowercase_				:
       snake_case__				:							CommonSchedulerState

       # setable values
       snake_case__				:							jnp.ndarray
       snake_case__				:							jnp.ndarray
       snake_case__				:							jnp.ndarray
       snake_case__				:							Optional[int]											=     None

       # running values
       snake_case__				:							Optional[jnp.ndarray]											=     None

       @classmethod
       def 		_SCREAMING_SNAKE_CASE(			cls   ,					__SCREAMING_SNAKE_CASE   ,					__SCREAMING_SNAKE_CASE   ,					__SCREAMING_SNAKE_CASE   ,					__SCREAMING_SNAKE_CASE     ):






        '''simple docstring'''

        return cls(common=__SCREAMING_SNAKE_CASE   ,					init_noise_sigma=__SCREAMING_SNAKE_CASE   ,					timesteps=__SCREAMING_SNAKE_CASE   ,					sigmas=__SCREAMING_SNAKE_CASE     )



@dataclass
class      lowercase_				(     __lowerCAmelCase							):
       snake_case__				:							LMSDiscreteSchedulerState



class      lowercase_				(     __lowerCAmelCase				,__lowerCAmelCase							):
       snake_case__				:							Any											=     [e.name for e in FlaxKarrasDiffusionSchedulers]

       snake_case__				:							jnp.dtype

       @property
       def 		_SCREAMING_SNAKE_CASE(			self     ):






        '''simple docstring'''

        return True

       @register_to_config
       def __init__(			self   ,					__SCREAMING_SNAKE_CASE = 1000   ,					__SCREAMING_SNAKE_CASE = 0.0001   ,					__SCREAMING_SNAKE_CASE = 0.02   ,					__SCREAMING_SNAKE_CASE = "linear"   ,					__SCREAMING_SNAKE_CASE = None   ,					__SCREAMING_SNAKE_CASE = "epsilon"   ,					__SCREAMING_SNAKE_CASE = jnp.floataa   ,					):






        '''simple docstring'''

        snake_case__    							=				dtype

       def 		_SCREAMING_SNAKE_CASE(			self   ,					__SCREAMING_SNAKE_CASE = None     ):






        '''simple docstring'''

        if common is None:
         snake_case__    							=				CommonSchedulerState.create(self     )

        snake_case__    							=				jnp.arange(0   ,					self.config.num_train_timesteps     ).round()[::-1]
        snake_case__    							=				((1 - common.alphas_cumprod) / common.alphas_cumprod) ** 0.5

        # standard deviation of the initial noise distribution
        snake_case__    							=				sigmas.max()

        return LMSDiscreteSchedulerState.create(
            common=__SCREAMING_SNAKE_CASE   ,					init_noise_sigma=__SCREAMING_SNAKE_CASE   ,					timesteps=__SCREAMING_SNAKE_CASE   ,					sigmas=__SCREAMING_SNAKE_CASE   ,					)

       def 		_SCREAMING_SNAKE_CASE(			self   ,					__SCREAMING_SNAKE_CASE   ,					__SCREAMING_SNAKE_CASE   ,					__SCREAMING_SNAKE_CASE     ):






        '''simple docstring'''

        ((snake_case__)							,   )    							=				jnp.where(state.timesteps == timestep   ,					size=1     )
        snake_case__    							=				step_index[0]

        snake_case__    							=				state.sigmas[step_index]
        snake_case__    							=				sample / ((sigma**2 + 1) ** 0.5)
        return sample

       def 		_SCREAMING_SNAKE_CASE(			self   ,					__SCREAMING_SNAKE_CASE   ,					__SCREAMING_SNAKE_CASE   ,					__SCREAMING_SNAKE_CASE   ,					__SCREAMING_SNAKE_CASE     ):






        '''simple docstring'''

        def lms_derivative(__SCREAMING_SNAKE_CASE     ):
         snake_case__    							=				1.0
         for k in range(__SCREAMING_SNAKE_CASE     ):
          if current_order == k:
           continue
          prod *= (tau - state.sigmas[t - k]) / (state.sigmas[t - current_order] - state.sigmas[t - k])
         return prod

        snake_case__    							=				integrate.quad(__SCREAMING_SNAKE_CASE   ,					state.sigmas[t]   ,					state.sigmas[t + 1]   ,					epsrel=1e-4     )[0]

        return integrated_coeff

       def 		_SCREAMING_SNAKE_CASE(			self   ,					__SCREAMING_SNAKE_CASE   ,					__SCREAMING_SNAKE_CASE   ,					__SCREAMING_SNAKE_CASE = ()     ):






        '''simple docstring'''

        snake_case__    							=				jnp.linspace(self.config.num_train_timesteps - 1   ,					0   ,					__SCREAMING_SNAKE_CASE   ,					dtype=self.dtype     )

        snake_case__    							=				jnp.floor(__SCREAMING_SNAKE_CASE     ).astype(jnp.intaa     )
        snake_case__    							=				jnp.ceil(__SCREAMING_SNAKE_CASE     ).astype(jnp.intaa     )

        snake_case__    							=				jnp.mod(__SCREAMING_SNAKE_CASE   ,					1.0     )

        snake_case__    							=				((1 - state.common.alphas_cumprod) / state.common.alphas_cumprod) ** 0.5
        snake_case__    							=				(1 - frac) * sigmas[low_idx] + frac * sigmas[high_idx]
        snake_case__    							=				jnp.concatenate([sigmas, jnp.array([0.0]   ,					dtype=self.dtype     )]     )

        snake_case__    							=				timesteps.astype(jnp.intaa     )

        # initial running values
        snake_case__    							=				jnp.zeros((0,) + shape   ,					dtype=self.dtype     )

        return state.replace(
            timesteps=__SCREAMING_SNAKE_CASE   ,					sigmas=__SCREAMING_SNAKE_CASE   ,					num_inference_steps=__SCREAMING_SNAKE_CASE   ,					derivatives=__SCREAMING_SNAKE_CASE   ,					)

       def 		_SCREAMING_SNAKE_CASE(			self   ,					__SCREAMING_SNAKE_CASE   ,					__SCREAMING_SNAKE_CASE   ,					__SCREAMING_SNAKE_CASE   ,					__SCREAMING_SNAKE_CASE   ,					__SCREAMING_SNAKE_CASE = 4   ,					__SCREAMING_SNAKE_CASE = True   ,					):






        '''simple docstring'''

        if state.num_inference_steps is None:
         raise ValueError(
             "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"     )

        snake_case__    							=				state.sigmas[timestep]

        # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
        if self.config.prediction_type == "epsilon":
         snake_case__    							=				sample - sigma * model_output
        elif self.config.prediction_type == "v_prediction":
         # * c_out + input * c_skip
         snake_case__    							=				model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
        else:
         raise ValueError(
             F"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"     )

        # 2. Convert to an ODE derivative
        snake_case__    							=				(sample - pred_original_sample) / sigma
        snake_case__    							=				state.replace(derivatives=jnp.append(state.derivatives   ,					__SCREAMING_SNAKE_CASE     )     )
        if len(state.derivatives     ) > order:
         snake_case__    							=				state.replace(derivatives=jnp.delete(state.derivatives   ,					0     )     )

        # 3. Compute linear multistep coefficients
        snake_case__    							=				min(timestep + 1   ,					__SCREAMING_SNAKE_CASE     )
        snake_case__    							=				[self.get_lms_coefficient(__SCREAMING_SNAKE_CASE   ,					__SCREAMING_SNAKE_CASE   ,					__SCREAMING_SNAKE_CASE   ,					__SCREAMING_SNAKE_CASE     ) for curr_order in range(__SCREAMING_SNAKE_CASE     )]

        # 4. Compute previous sample based on the derivatives path
        snake_case__    							=				sample + sum(
            coeff * derivative for coeff, derivative in zip(__SCREAMING_SNAKE_CASE   ,					reversed(state.derivatives     )     )     )

        if not return_dict:
         return (prev_sample, state)

        return FlaxLMSSchedulerOutput(prev_sample=__SCREAMING_SNAKE_CASE   ,					state=__SCREAMING_SNAKE_CASE     )

       def 		_SCREAMING_SNAKE_CASE(			self   ,					__SCREAMING_SNAKE_CASE   ,					__SCREAMING_SNAKE_CASE   ,					__SCREAMING_SNAKE_CASE   ,					__SCREAMING_SNAKE_CASE   ,					):






        '''simple docstring'''

        snake_case__    							=				state.sigmas[timesteps].flatten()
        snake_case__    							=				broadcast_to_shape_from_left(__SCREAMING_SNAKE_CASE   ,					noise.shape     )

        snake_case__    							=				original_samples + noise * sigma

        return noisy_samples

       def __len__(			self     ):






        '''simple docstring'''

        return self.config.num_train_timesteps

