


'''simple docstring'''







a__  :					Union[str, Any]        =       [sum(int(c, 1_0) ** 2 for c in i.__str__()) for i in range(1_0_0_0_0_0)]







def _UpperCamelCase       (     __A    )							->		int:


      '''simple docstring'''



      UpperCamelCase__										=				0
      while number:
            # Increased Speed Slightly by checking every 5 digits together.
            sum_of_digits_squared += DIGITS_SQUARED[number % 100000]
            number //= 100000

      return sum_of_digits_squared


# There are 2 Chains made,
# One ends with 89 with the chain member 58 being the one which when declared first,
# there will be the least number of iterations for all the members to be checked.

# The other one ends with 1 and has only one element 1.

# So 58 and 1 are chosen to be declared at the starting.

# Changed dictionary to an array to quicken the solution
a__  :					list[bool | None]        =       [None] * 1_0_0_0_0_0_0_0
a__  :					Optional[Any]        =       True
a__  :					Optional[Any]        =       False







def _UpperCamelCase       (     __A    )							->		bool:


      '''simple docstring'''



      if CHAINS[number - 1] is not None:
            return CHAINS[number - 1]  # type: ignore

      UpperCamelCase__										=				chain(next_number(__A    )    )
      UpperCamelCase__										=				number_chain

      while number < 10000000:
            UpperCamelCase__										=				number_chain
            number *= 10

      return number_chain







def _UpperCamelCase       (     __A = 10000000    )							->		int:


      '''simple docstring'''



      for i in range(1      ,			__A    ):
            if CHAINS[i] is None:
                  chain(i + 1    )

      return CHAINS[:number].count(__A    )


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  print(F"""{solution() = }""")









import tempfile

import torch

from diffusers import (
    DEISMultistepScheduler,
    DPMSolverMultistepScheduler,
    DPMSolverSinglestepScheduler,
    UniPCMultistepScheduler,
)

from .test_schedulers import SchedulerCommonTest




class A  (   UpperCamelCase_     ):
      UpperCamelCase__							:  Any      =(DPMSolverSinglestepScheduler,)
      UpperCamelCase__							:  Tuple      =(('num_inference_steps', 25),)






      def        lowerCamelCase       (					self						:     Optional[Any]			,   **lowercase_						:     List[Any] )					->						Optional[Any]:
             """simple docstring"""




             _lowerCamelCase       :		Union[str, Any]		={
                 'num_train_timesteps': 1000,
                 'beta_start': 0.0001,
                 'beta_end': 0.02,
                 'beta_schedule': 'linear',
                 'solver_order': 2,
                 'prediction_type': 'epsilon',
                 'thresholding': False,
                 'sample_max_value': 1.0,
                 'algorithm_type': 'dpmsolver++',
                 'solver_type': 'midpoint',
                 'lambda_min_clipped': -float('inf' ),
                 'variance_type': None,
             }

             config.update(**lowercase_ )
             return config






      def        lowerCamelCase       (					self						:     Optional[int]			,   lowercase_						:     Optional[Any]=0			,   **lowercase_						:     Any )					->						List[Any]:
             """simple docstring"""




             _lowerCamelCase       :		List[Any]		=dict(self.forward_default_kwargs )
             _lowerCamelCase       :		Optional[Any]		=kwargs.pop('num_inference_steps'			,   lowercase_ )
             _lowerCamelCase       :		Optional[int]		=self.dummy_sample
             _lowerCamelCase       :		Dict		=0.1 * sample
             _lowerCamelCase       :		Optional[int]		=[residual + 0.2, residual + 0.15, residual + 0.10]

             for scheduler_class in self.scheduler_classes:
                    _lowerCamelCase       :		int		=self.get_scheduler_config(**lowercase_ )
                    _lowerCamelCase       :		str		=scheduler_class(**lowercase_ )
                    scheduler.set_timesteps(lowercase_ )
                    # copy over dummy past residuals
                    _lowerCamelCase       :		int		=dummy_past_residuals[: scheduler.config.solver_order]

                    with tempfile.TemporaryDirectory() as tmpdirname:
                           scheduler.save_config(lowercase_ )
                           _lowerCamelCase       :		Dict		=scheduler_class.from_pretrained(lowercase_ )
                           new_scheduler.set_timesteps(lowercase_ )
                           # copy over dummy past residuals
                           _lowerCamelCase       :		str		=dummy_past_residuals[: new_scheduler.config.solver_order]

                    _lowerCamelCase	,     _lowerCamelCase       :		Any		=sample, sample
                    for t in range(lowercase_			,   time_step + scheduler.config.solver_order + 1 ):
                           _lowerCamelCase       :		List[str]		=scheduler.step(lowercase_			,   lowercase_			,   lowercase_			,   **lowercase_ ).prev_sample
                           _lowerCamelCase       :		Optional[Any]		=new_scheduler.step(lowercase_			,   lowercase_			,   lowercase_			,   **lowercase_ ).prev_sample

                           assert torch.sum(torch.abs(output - new_output ) ) < 1E-5, "Scheduler outputs are not identical"






      def        lowerCamelCase       (					self						:     Tuple )					->						Optional[int]:
             """simple docstring"""




             pass






      def        lowerCamelCase       (					self						:     str			,   lowercase_						:     str=0			,   **lowercase_						:     List[Any] )					->						Dict:
             """simple docstring"""




             _lowerCamelCase       :		int		=dict(self.forward_default_kwargs )
             _lowerCamelCase       :		Dict		=kwargs.pop('num_inference_steps'			,   lowercase_ )
             _lowerCamelCase       :		Optional[int]		=self.dummy_sample
             _lowerCamelCase       :		Any		=0.1 * sample
             _lowerCamelCase       :		int		=[residual + 0.2, residual + 0.15, residual + 0.10]

             for scheduler_class in self.scheduler_classes:
                    _lowerCamelCase       :		Optional[int]		=self.get_scheduler_config()
                    _lowerCamelCase       :		Any		=scheduler_class(**lowercase_ )
                    scheduler.set_timesteps(lowercase_ )

                    # copy over dummy past residuals (must be after setting timesteps)
                    _lowerCamelCase       :		Dict		=dummy_past_residuals[: scheduler.config.solver_order]

                    with tempfile.TemporaryDirectory() as tmpdirname:
                           scheduler.save_config(lowercase_ )
                           _lowerCamelCase       :		Optional[int]		=scheduler_class.from_pretrained(lowercase_ )
                           # copy over dummy past residuals
                           new_scheduler.set_timesteps(lowercase_ )

                           # copy over dummy past residual (must be after setting timesteps)
                           _lowerCamelCase       :		str		=dummy_past_residuals[: new_scheduler.config.solver_order]

                    _lowerCamelCase       :		Dict		=scheduler.step(lowercase_			,   lowercase_			,   lowercase_			,   **lowercase_ ).prev_sample
                    _lowerCamelCase       :		Dict		=new_scheduler.step(lowercase_			,   lowercase_			,   lowercase_			,   **lowercase_ ).prev_sample

                    assert torch.sum(torch.abs(output - new_output ) ) < 1E-5, "Scheduler outputs are not identical"






      def        lowerCamelCase       (					self						:     Any			,   lowercase_						:     Union[str, Any]=None			,   **lowercase_						:     List[str] )					->						str:
             """simple docstring"""




             if scheduler is None:
                    _lowerCamelCase       :		Tuple		=self.scheduler_classes[0]
                    _lowerCamelCase       :		Optional[int]		=self.get_scheduler_config(**lowercase_ )
                    _lowerCamelCase       :		Union[str, Any]		=scheduler_class(**lowercase_ )

             _lowerCamelCase       :		List[Any]		=self.scheduler_classes[0]
             _lowerCamelCase       :		Optional[Any]		=self.get_scheduler_config(**lowercase_ )
             _lowerCamelCase       :		List[Any]		=scheduler_class(**lowercase_ )

             _lowerCamelCase       :		str		=10
             _lowerCamelCase       :		Union[str, Any]		=self.dummy_model()
             _lowerCamelCase       :		Dict		=self.dummy_sample_deter
             scheduler.set_timesteps(lowercase_ )

             for i, t in enumerate(scheduler.timesteps ):
                    _lowerCamelCase       :		List[str]		=model(lowercase_			,   lowercase_ )
                    _lowerCamelCase       :		Optional[int]		=scheduler.step(lowercase_			,   lowercase_			,   lowercase_ ).prev_sample

             return sample






      def        lowerCamelCase       (					self						:     Dict )					->						int:
             """simple docstring"""




             _lowerCamelCase       :		Any		=DPMSolverSinglestepScheduler(**self.get_scheduler_config() )
             _lowerCamelCase       :		int		=50
             _lowerCamelCase       :		Optional[int]		=self.dummy_model()
             _lowerCamelCase       :		Tuple		=self.dummy_sample_deter
             scheduler.set_timesteps(lowercase_ )

             # make sure that the first t is uneven
             for i, t in enumerate(scheduler.timesteps[3:] ):
                    _lowerCamelCase       :		Any		=model(lowercase_			,   lowercase_ )
                    _lowerCamelCase       :		List[str]		=scheduler.step(lowercase_			,   lowercase_			,   lowercase_ ).prev_sample

             _lowerCamelCase       :		int		=torch.mean(torch.abs(lowercase_ ) )

             assert abs(result_mean.item() - 0.2574 ) < 1E-3






      def        lowerCamelCase       (					self						:     Any )					->						List[str]:
             """simple docstring"""




             for timesteps in [25, 50, 100, 999, 1000]:
                    self.check_over_configs(num_train_timesteps=lowercase_ )






      def        lowerCamelCase       (					self						:     Optional[Any] )					->						Dict:
             """simple docstring"""




             _lowerCamelCase       :		Optional[int]		=DPMSolverSinglestepScheduler(**self.get_scheduler_config() )
             _lowerCamelCase       :		Optional[Any]		=self.full_loop(scheduler=lowercase_ )
             _lowerCamelCase       :		Tuple		=torch.mean(torch.abs(lowercase_ ) )

             assert abs(result_mean.item() - 0.2791 ) < 1E-3

             _lowerCamelCase       :		Dict		=DEISMultistepScheduler.from_config(scheduler.config )
             _lowerCamelCase       :		Optional[int]		=DPMSolverMultistepScheduler.from_config(scheduler.config )
             _lowerCamelCase       :		Union[str, Any]		=UniPCMultistepScheduler.from_config(scheduler.config )
             _lowerCamelCase       :		List[str]		=DPMSolverSinglestepScheduler.from_config(scheduler.config )

             _lowerCamelCase       :		List[Any]		=self.full_loop(scheduler=lowercase_ )
             _lowerCamelCase       :		List[str]		=torch.mean(torch.abs(lowercase_ ) )

             assert abs(result_mean.item() - 0.2791 ) < 1E-3






      def        lowerCamelCase       (					self						:     str )					->						Dict:
             """simple docstring"""




             self.check_over_configs(thresholding=lowercase_ )
             for order in [1, 2, 3]:
                    for solver_type in ["midpoint", "heun"]:
                           for threshold in [0.5, 1.0, 2.0]:
                                  for prediction_type in ["epsilon", "sample"]:
                                         self.check_over_configs(
                                             thresholding=lowercase_			,   prediction_type=lowercase_			,   sample_max_value=lowercase_			,   algorithm_type='dpmsolver++'			,   solver_order=lowercase_			,   solver_type=lowercase_			,   )






      def        lowerCamelCase       (					self						:     Any )					->						Any:
             """simple docstring"""




             for prediction_type in ["epsilon", "v_prediction"]:
                    self.check_over_configs(prediction_type=lowercase_ )






      def        lowerCamelCase       (					self						:     List[str] )					->						Optional[int]:
             """simple docstring"""




             for algorithm_type in ["dpmsolver", "dpmsolver++"]:
                    for solver_type in ["midpoint", "heun"]:
                           for order in [1, 2, 3]:
                                  for prediction_type in ["epsilon", "sample"]:
                                         self.check_over_configs(
                                             solver_order=lowercase_			,   solver_type=lowercase_			,   prediction_type=lowercase_			,   algorithm_type=lowercase_			,   )
                                         _lowerCamelCase       :		Any		=self.full_loop(
                                             solver_order=lowercase_			,   solver_type=lowercase_			,   prediction_type=lowercase_			,   algorithm_type=lowercase_			,   )
                                         assert not torch.isnan(lowercase_ ).any(), "Samples have nan numbers"






      def        lowerCamelCase       (					self						:     List[Any] )					->						List[Any]:
             """simple docstring"""




             self.check_over_configs(lower_order_final=lowercase_ )
             self.check_over_configs(lower_order_final=lowercase_ )






      def        lowerCamelCase       (					self						:     Union[str, Any] )					->						int:
             """simple docstring"""




             self.check_over_configs(lambda_min_clipped=-float('inf' ) )
             self.check_over_configs(lambda_min_clipped=-5.1 )






      def        lowerCamelCase       (					self						:     Union[str, Any] )					->						Any:
             """simple docstring"""




             self.check_over_configs(variance_type=lowercase_ )
             self.check_over_configs(variance_type='learned_range' )






      def        lowerCamelCase       (					self						:     Union[str, Any] )					->						Any:
             """simple docstring"""




             for num_inference_steps in [1, 2, 3, 5, 10, 50, 100, 999, 1000]:
                    self.check_over_forward(num_inference_steps=lowercase_			,   time_step=0 )






      def        lowerCamelCase       (					self						:     str )					->						Tuple:
             """simple docstring"""




             _lowerCamelCase       :		Dict		=self.full_loop()
             _lowerCamelCase       :		Dict		=torch.mean(torch.abs(lowercase_ ) )

             assert abs(result_mean.item() - 0.2791 ) < 1E-3






      def        lowerCamelCase       (					self						:     Any )					->						Union[str, Any]:
             """simple docstring"""




             _lowerCamelCase       :		str		=self.full_loop(use_karras_sigmas=lowercase_ )
             _lowerCamelCase       :		Optional[Any]		=torch.mean(torch.abs(lowercase_ ) )

             assert abs(result_mean.item() - 0.2248 ) < 1E-3






      def        lowerCamelCase       (					self						:     Dict )					->						Tuple:
             """simple docstring"""




             _lowerCamelCase       :		Any		=self.full_loop(prediction_type='v_prediction' )
             _lowerCamelCase       :		Dict		=torch.mean(torch.abs(lowercase_ ) )

             assert abs(result_mean.item() - 0.1453 ) < 1E-3






      def        lowerCamelCase       (					self						:     Any )					->						Optional[int]:
             """simple docstring"""




             _lowerCamelCase       :		str		=self.full_loop(prediction_type='v_prediction'			,   use_karras_sigmas=lowercase_ )
             _lowerCamelCase       :		List[str]		=torch.mean(torch.abs(lowercase_ ) )

             assert abs(result_mean.item() - 0.0649 ) < 1E-3






      def        lowerCamelCase       (					self						:     List[Any] )					->						str:
             """simple docstring"""




             _lowerCamelCase       :		List[str]		=self.scheduler_classes[0]
             _lowerCamelCase       :		List[str]		=self.get_scheduler_config(thresholding=lowercase_			,   dynamic_thresholding_ratio=0 )
             _lowerCamelCase       :		List[Any]		=scheduler_class(**lowercase_ )

             _lowerCamelCase       :		Optional[Any]		=10
             _lowerCamelCase       :		Optional[int]		=self.dummy_model()
             _lowerCamelCase       :		List[Any]		=self.dummy_sample_deter.half()
             scheduler.set_timesteps(lowercase_ )

             for i, t in enumerate(scheduler.timesteps ):
                    _lowerCamelCase       :		str		=model(lowercase_			,   lowercase_ )
                    _lowerCamelCase       :		Any		=scheduler.step(lowercase_			,   lowercase_			,   lowercase_ ).prev_sample

             assert sample.dtype == torch.floataa


