




'''simple docstring'''




import torch

from diffusers import KDPMaAncestralDiscreteScheduler
from diffusers.utils import torch_device

from .test_schedulers import SchedulerCommonTest






class      UpperCamelCase_  (_UpperCamelCase  ):







						"""simple docstring"""


						_lowerCAmelCase         =       (KDPMaAncestralDiscreteScheduler,)
						_lowerCAmelCase         =       1_0







						def    _a     (  self   :							List[Any]				,			**_lowerCamelCase   :							Optional[int]     ):





											"""simple docstring"""







											A_			:  Union[str, Any]			=				{
											    '''num_train_timesteps''': 1100,
											    '''beta_start''': 0.00_01,
											    '''beta_end''': 0.02,
											    '''beta_schedule''': '''linear''',
											}

											config.update(**_SCREAMING_SNAKE_CASE     )
											return config







						def    _a     (  self   :							Any     ):





											"""simple docstring"""







											for timesteps in [10, 50, 100, 1000]:
																self.check_over_configs(num_train_timesteps=_SCREAMING_SNAKE_CASE     )







						def    _a     (  self   :							Tuple     ):





											"""simple docstring"""







											for beta_start, beta_end in zip([0.0_00_01, 0.00_01, 0.0_01]				,			[0.00_02, 0.0_02, 0.02]     ):
																self.check_over_configs(beta_start=_SCREAMING_SNAKE_CASE				,			beta_end=_SCREAMING_SNAKE_CASE     )







						def    _a     (  self   :							Tuple     ):





											"""simple docstring"""







											for schedule in ["linear", "scaled_linear"]:
																self.check_over_configs(beta_schedule=_SCREAMING_SNAKE_CASE     )







						def    _a     (  self   :							int     ):





											"""simple docstring"""







											if torch_device == "mps":
																return
											A_			:  Optional[Any]			=				self.scheduler_classes[0]
											A_			:  Any			=				self.get_scheduler_config()
											A_			:  int			=				scheduler_class(**_SCREAMING_SNAKE_CASE     )

											scheduler.set_timesteps(self.num_inference_steps     )

											A_			:  List[Any]			=				torch.manual_seed(0     )

											A_			:  str			=				self.dummy_model()
											A_			:  Optional[int]			=				self.dummy_sample_deter * scheduler.init_noise_sigma
											A_			:  Union[str, Any]			=				sample.to(_SCREAMING_SNAKE_CASE     )

											for i, t in enumerate(scheduler.timesteps     ):
																A_			:  str			=				scheduler.scale_model_input(_SCREAMING_SNAKE_CASE				,			_SCREAMING_SNAKE_CASE     )

																A_			:  Union[str, Any]			=				model(_SCREAMING_SNAKE_CASE				,			_SCREAMING_SNAKE_CASE     )

																A_			:  Union[str, Any]			=				scheduler.step(_SCREAMING_SNAKE_CASE				,			_SCREAMING_SNAKE_CASE				,			_SCREAMING_SNAKE_CASE				,			generator=_SCREAMING_SNAKE_CASE     )
																A_			:  List[str]			=				output.prev_sample

											A_			:  str			=				torch.sum(torch.abs(_SCREAMING_SNAKE_CASE     )     )
											A_			:  Dict			=				torch.mean(torch.abs(_SCREAMING_SNAKE_CASE     )     )

											assert abs(result_sum.item() - 13849.3877     ) < 1E-2
											assert abs(result_mean.item() - 18.03_31     ) < 5E-3







						def    _a     (  self   :							Union[str, Any]     ):





											"""simple docstring"""







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







						def    _a     (  self   :							int     ):





											"""simple docstring"""







											if torch_device == "mps":
																return
											A_			:  Optional[int]			=				self.scheduler_classes[0]
											A_			:  Any			=				self.get_scheduler_config(prediction_type='''v_prediction'''     )
											A_			:  List[str]			=				scheduler_class(**_SCREAMING_SNAKE_CASE     )

											scheduler.set_timesteps(self.num_inference_steps     )

											A_			:  int			=				self.dummy_model()
											A_			:  int			=				self.dummy_sample_deter * scheduler.init_noise_sigma
											A_			:  List[Any]			=				sample.to(_SCREAMING_SNAKE_CASE     )

											A_			:  Dict			=				torch.manual_seed(0     )

											for i, t in enumerate(scheduler.timesteps     ):
																A_			:  List[Any]			=				scheduler.scale_model_input(_SCREAMING_SNAKE_CASE				,			_SCREAMING_SNAKE_CASE     )

																A_			:  List[Any]			=				model(_SCREAMING_SNAKE_CASE				,			_SCREAMING_SNAKE_CASE     )

																A_			:  List[str]			=				scheduler.step(_SCREAMING_SNAKE_CASE				,			_SCREAMING_SNAKE_CASE				,			_SCREAMING_SNAKE_CASE				,			generator=_SCREAMING_SNAKE_CASE     )
																A_			:  int			=				output.prev_sample

											A_			:  str			=				torch.sum(torch.abs(_SCREAMING_SNAKE_CASE     )     )
											A_			:  Dict			=				torch.mean(torch.abs(_SCREAMING_SNAKE_CASE     )     )

											assert abs(result_sum.item() - 3_28.99_70     ) < 1E-2
											assert abs(result_mean.item() - 0.42_84     ) < 1E-3







						def    _a     (  self   :							Optional[int]     ):





											"""simple docstring"""







											if torch_device == "mps":
																return
											A_			:  Union[str, Any]			=				self.scheduler_classes[0]
											A_			:  Any			=				self.get_scheduler_config()
											A_			:  Optional[Any]			=				scheduler_class(**_SCREAMING_SNAKE_CASE     )

											scheduler.set_timesteps(self.num_inference_steps				,			device=_SCREAMING_SNAKE_CASE     )
											A_			:  str			=				torch.manual_seed(0     )

											A_			:  int			=				self.dummy_model()
											A_			:  str			=				self.dummy_sample_deter.to(_SCREAMING_SNAKE_CASE     ) * scheduler.init_noise_sigma

											for t in scheduler.timesteps:
																A_			:  Union[str, Any]			=				scheduler.scale_model_input(_SCREAMING_SNAKE_CASE				,			_SCREAMING_SNAKE_CASE     )

																A_			:  Tuple			=				model(_SCREAMING_SNAKE_CASE				,			_SCREAMING_SNAKE_CASE     )

																A_			:  Optional[Any]			=				scheduler.step(_SCREAMING_SNAKE_CASE				,			_SCREAMING_SNAKE_CASE				,			_SCREAMING_SNAKE_CASE				,			generator=_SCREAMING_SNAKE_CASE     )
																A_			:  Tuple			=				output.prev_sample

											A_			:  int			=				torch.sum(torch.abs(_SCREAMING_SNAKE_CASE     )     )
											A_			:  str			=				torch.mean(torch.abs(_SCREAMING_SNAKE_CASE     )     )

											assert abs(result_sum.item() - 13849.3818     ) < 1E-1
											assert abs(result_mean.item() - 18.03_31     ) < 1E-3




'''simple docstring'''




import itertools





def 	_UpperCAmelCase       (				_UpperCamelCase       :      int = 1_00_00_00  )      -> int:
    A_      =  [1]

    for i in itertools.count(len(_UpperCamelCase  )  ):
        A_      =  0
        for j in itertools.count(1  ):
            A_      =  -1 if j % 2 == 0 else +1
            A_      =  (j * j * 3 - j) // 2
            if index > i:
                break
            item += partitions[i - index] * sign
            item %= number
            index += j
            if index > i:
                break
            item += partitions[i - index] * sign
            item %= number

        if item == 0:
            return i
        partitions.append(_UpperCamelCase  )

    return 0


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  print(F"""{solution() = }""")






