


'''simple docstring'''



import importlib
import math
import os
from dataclasses import dataclass
from enum import Enum
from typing import Any, Dict, Optional, Tuple, Union

import flax
import jax.numpy as jnp

from ..utils import BaseOutput


__UpperCAmelCase				       =     "scheduler_config.json"



class 			a       (	lowerCAmelCase__ ):


     """simple docstring"""






     SCREAMING_SNAKE_CASE :				Any							     =     1
     SCREAMING_SNAKE_CASE :				Dict							     =     2
     SCREAMING_SNAKE_CASE :				Optional[Any]							     =     3
     SCREAMING_SNAKE_CASE :				List[str]							     =     4
     SCREAMING_SNAKE_CASE :				Any							     =     5



@dataclass
class 			a       (	lowerCAmelCase__ ):


     """simple docstring"""






     SCREAMING_SNAKE_CASE :				jnp.ndarray



class 			a       :


     """simple docstring"""






     SCREAMING_SNAKE_CASE :				str							     =     SCHEDULER_CONFIG_NAME
     SCREAMING_SNAKE_CASE :				Union[str, Any]							     =     ["dtype"]
     SCREAMING_SNAKE_CASE :				str							     =     []
     SCREAMING_SNAKE_CASE :				List[Any]							     =     True

     @classmethod
     def 				lowerCamelCase__				(       cls  :	Union[str, Any]							,				snake_case  :	Optional[int] = None							,				snake_case  :	str = None							,				snake_case  :	Optional[int]=False							,				**snake_case  :	str							,				)		->							Tuple:
          __UpperCAmelCase							,     __UpperCAmelCase			:				Union[str, Any]													=    cls.load_config(
              pretrained_model_name_or_path=_lowerCamelCase							,				subfolder=_lowerCamelCase							,				return_unused_kwargs=_lowerCamelCase							,				**_lowerCamelCase							,				)
          __UpperCAmelCase							,     __UpperCAmelCase			:				Tuple													=    cls.from_config(_lowerCamelCase							,				return_unused_kwargs=_lowerCamelCase							,				**_lowerCamelCase    )

          if hasattr(_lowerCamelCase							,				'''create_state'''    ) and getattr(_lowerCamelCase							,				'''has_state'''							,				_lowerCamelCase    ):
               __UpperCAmelCase			:				Tuple													=    scheduler.create_state()

          if return_unused_kwargs:
               return scheduler, state, unused_kwargs

          return scheduler, state

     def 				lowerCamelCase__				(       self  :	Optional[Any]							,				snake_case  :	List[Any]							,				snake_case  :	Dict = False							,				**snake_case  :	Union[str, Any]    )		->							str:
          self.save_config(save_directory=_lowerCamelCase							,				push_to_hub=_lowerCamelCase							,				**_lowerCamelCase    )

     @property
     def 				lowerCamelCase__				(       self  :	List[Any]    )		->							List[Any]:
          return self._get_compatibles()






     @classmethod
     def 				lowerCamelCase__				(       cls  :	Union[str, Any]    )		->							int:
          __UpperCAmelCase			:				Tuple													=    list(set([cls.__name__] + cls._compatibles    )    )
          __UpperCAmelCase			:				Optional[int]													=    importlib.import_module(__name__.split('''.'''    )[0]    )
          __UpperCAmelCase			:				Any													=    [
              getattr(_lowerCamelCase							,				_lowerCamelCase    ) for c in compatible_classes_str if hasattr(_lowerCamelCase							,				_lowerCamelCase    )
          ]
          return compatible_classes




def 			_a			(		_lowercase      :			jnp.ndarray    ,      _lowercase      :			Tuple[int]						):





     '''simple docstring'''






     assert len(lowerCamelCase_						) >= x.ndim
     return jnp.broadcast_to(x.reshape(x.shape + (1,) * (len(lowerCamelCase_						) - x.ndim)						)    ,      lowerCamelCase_						)




def 			_a			(		_lowercase      :			int    ,      _lowercase      :			Union[str, Any]=0.999    ,      _lowercase      :			Union[str, Any]=jnp.floataa						):





     '''simple docstring'''






     def alpha_bar(_lowercase      :			Any						):
          return math.cos((time_step + 0.008) / 1.008 * math.pi / 2						) ** 2

     __UpperCAmelCase			:				str													=    []
     for i in range(lowerCamelCase_						):
          __UpperCAmelCase			:				List[Any]													=    i / num_diffusion_timesteps
          __UpperCAmelCase			:				Optional[int]													=    (i + 1) / num_diffusion_timesteps
          betas.append(min(1 - alpha_bar(lowerCamelCase_						) / alpha_bar(lowerCamelCase_						)    ,      lowerCamelCase_						)						)
     return jnp.array(lowerCamelCase_    ,      dtype=lowerCamelCase_						)



@flax.struct.dataclass
class 			a       :


     """simple docstring"""






     SCREAMING_SNAKE_CASE :				jnp.ndarray
     SCREAMING_SNAKE_CASE :				jnp.ndarray
     SCREAMING_SNAKE_CASE :				jnp.ndarray

     @classmethod
     def 				lowerCamelCase__				(       cls  :	List[str]							,				snake_case  :	List[str]    )		->							Optional[Any]:
          __UpperCAmelCase			:				Dict													=    scheduler.config

          if config.trained_betas is not None:
               __UpperCAmelCase			:				int													=    jnp.asarray(config.trained_betas							,				dtype=scheduler.dtype    )
          elif config.beta_schedule == "linear":
               __UpperCAmelCase			:				Any													=    jnp.linspace(config.beta_start							,				config.beta_end							,				config.num_train_timesteps							,				dtype=scheduler.dtype    )
          elif config.beta_schedule == "scaled_linear":
               # this schedule is very specific to the latent diffusion model.
               __UpperCAmelCase			:				Dict													=    (
                   jnp.linspace(
                       config.beta_start**0.5							,				config.beta_end**0.5							,				config.num_train_timesteps							,				dtype=scheduler.dtype    )
                   ** 2
               )
          elif config.beta_schedule == "squaredcos_cap_v2":
               # Glide cosine schedule
               __UpperCAmelCase			:				List[str]													=    betas_for_alpha_bar(config.num_train_timesteps							,				dtype=scheduler.dtype    )
          else:
               raise NotImplementedError(
                   f'beta_schedule {config.beta_schedule} is not implemented for scheduler {scheduler.__class__.__name__}'    )

          __UpperCAmelCase			:				List[str]													=    1.0 - betas

          __UpperCAmelCase			:				List[Any]													=    jnp.cumprod(_lowerCamelCase							,				axis=0    )

          return cls(
              alphas=_lowerCamelCase							,				betas=_lowerCamelCase							,				alphas_cumprod=_lowerCamelCase							,				)




def 			_a			(		_lowercase      :			CommonSchedulerState    ,      _lowercase      :			jnp.ndarray    ,      _lowercase      :			jnp.ndarray    ,      _lowercase      :			jnp.ndarray						):





     '''simple docstring'''






     __UpperCAmelCase			:				Optional[int]													=    state.alphas_cumprod

     __UpperCAmelCase			:				List[Any]													=    alphas_cumprod[timesteps] ** 0.5
     __UpperCAmelCase			:				List[str]													=    sqrt_alpha_prod.flatten()
     __UpperCAmelCase			:				Optional[Any]													=    broadcast_to_shape_from_left(lowerCamelCase_    ,      original_samples.shape						)

     __UpperCAmelCase			:				Union[str, Any]													=    (1 - alphas_cumprod[timesteps]) ** 0.5
     __UpperCAmelCase			:				Union[str, Any]													=    sqrt_one_minus_alpha_prod.flatten()
     __UpperCAmelCase			:				str													=    broadcast_to_shape_from_left(lowerCamelCase_    ,      original_samples.shape						)

     return sqrt_alpha_prod, sqrt_one_minus_alpha_prod




def 			_a			(		_lowercase      :			CommonSchedulerState    ,      _lowercase      :			jnp.ndarray    ,      _lowercase      :			jnp.ndarray    ,      _lowercase      :			jnp.ndarray						):





     '''simple docstring'''






     __UpperCAmelCase							,     __UpperCAmelCase			:				Optional[int]													=    get_sqrt_alpha_prod(lowerCamelCase_    ,      lowerCamelCase_    ,      lowerCamelCase_    ,      lowerCamelCase_						)
     __UpperCAmelCase			:				Optional[int]													=    sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
     return noisy_samples




def 			_a			(		_lowercase      :			CommonSchedulerState    ,      _lowercase      :			jnp.ndarray    ,      _lowercase      :			jnp.ndarray    ,      _lowercase      :			jnp.ndarray						):





     '''simple docstring'''






     __UpperCAmelCase							,     __UpperCAmelCase			:				int													=    get_sqrt_alpha_prod(lowerCamelCase_    ,      lowerCamelCase_    ,      lowerCamelCase_    ,      lowerCamelCase_						)
     __UpperCAmelCase			:				int													=    sqrt_alpha_prod * noise - sqrt_one_minus_alpha_prod * sample
     return velocity



'''simple docstring'''



def 			_a			(		_lowercase      :			int = 50000000						):





     '''simple docstring'''






     __UpperCAmelCase			:				List[str]													=    set()
     __UpperCAmelCase			:				Tuple													=    int((limit - 24) ** (1 / 2)						)

     __UpperCAmelCase			:				Tuple													=    set(range(3    ,      prime_square_limit + 1    ,      2						)						)
     primes.add(2						)
     for p in range(3    ,      prime_square_limit + 1    ,      2						):
          if p not in primes:
               continue
          primes.difference_update(set(range(p * p    ,      prime_square_limit + 1    ,      _lowercase						)						)						)

     for primea in primes:
          __UpperCAmelCase			:				Any													=    primea * primea
          for primea in primes:
               __UpperCAmelCase			:				Any													=    primea * primea * primea
               if square + cube >= limit - 16:
                    break
               for primea in primes:
                    __UpperCAmelCase			:				Optional[Any]													=    primea * primea * primea * primea
                    __UpperCAmelCase			:				Union[str, Any]													=    square + cube + tetr
                    if total >= limit:
                         break
                    ret.add(_lowercase						)

     return len(_lowercase						)


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