

from __future__ import annotations

from fractions import Fraction



def    __UpperCAmelCase (	__a      :			int		,__a      :			int	)			->     bool:

					"""simple docstring"""

					return (
					    num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
					)



def    __UpperCAmelCase (	__a      :			int	)			->     list[str]:

					"""simple docstring"""

					_a	:    int         =		[]
					_a	:    Optional[Any]         =		11
					_a	:    Optional[Any]         =		int('''1''' + '''0''' * digit_len	)
					for num in range(__a		,__a	):
										while den <= 99:
															if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
																				if is_digit_cancelling(__a		,__a	):
																									solutions.append(F"""{num}/{den}"""	)
															den += 1
										num += 1
										_a	:    str         =		10
					return solutions



def    __UpperCAmelCase (	__a      :			int = 2	)			->     int:

					"""simple docstring"""

					_a	:    List[Any]         =		1.0
					for fraction in fraction_list(__a	):
										_a	:    Optional[Any]         =		Fraction(__a	)
										result *= frac.denominator / frac.numerator
					return int(__a	)


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






import torch

from diffusers import DDPMScheduler

from .test_schedulers import SchedulerCommonTest

class 				UpperCAmelCase_		(			__lowercase   ):
							"""simple docstring"""







							UpperCAmelCase__       :						List[Any]	    =    (DDPMScheduler,)


							def 				__lowercase				(			self       ,							**_a       )    ->    Any:
												_a	:    List[Any]         =		{
												    '''num_train_timesteps''': 1_0_0_0,
												    '''beta_start''': 0.0001,
												    '''beta_end''': 0.02,
												    '''beta_schedule''': '''linear''',
												    '''variance_type''': '''fixed_small''',
												    '''clip_sample''': True,
												}

												config.update(**_a       )
												return config


							def 				__lowercase				(			self       )    ->    Any:
												for timesteps in [1, 5, 1_0_0, 1_0_0_0]:
																	self.check_over_configs(num_train_timesteps=_a       )


							def 				__lowercase				(			self       )    ->    List[Any]:
												for beta_start, beta_end in zip([0.0001, 0.001, 0.01, 0.1]       ,							[0.002, 0.02, 0.2, 2]       ):
																	self.check_over_configs(beta_start=_a       ,							beta_end=_a       )


							def 				__lowercase				(			self       )    ->    List[str]:
												for schedule in ["linear", "squaredcos_cap_v2"]:
																	self.check_over_configs(beta_schedule=_a       )


							def 				__lowercase				(			self       )    ->    Optional[Any]:
												for variance in ["fixed_small", "fixed_large", "other"]:
																	self.check_over_configs(variance_type=_a       )


							def 				__lowercase				(			self       )    ->    str:
												for clip_sample in [True, False]:
																	self.check_over_configs(clip_sample=_a       )


							def 				__lowercase				(			self       )    ->    Dict:
												self.check_over_configs(thresholding=_a       )
												for threshold in [0.5, 1.0, 2.0]:
																	for prediction_type in ["epsilon", "sample", "v_prediction"]:
																						self.check_over_configs(
																						    thresholding=_a       ,							prediction_type=_a       ,							sample_max_value=_a       ,							)


							def 				__lowercase				(			self       )    ->    Optional[Any]:
												for prediction_type in ["epsilon", "sample", "v_prediction"]:
																	self.check_over_configs(prediction_type=_a       )


							def 				__lowercase				(			self       )    ->    int:
												for t in [0, 5_0_0, 9_9_9]:
																	self.check_over_forward(time_step=_a       )


							def 				__lowercase				(			self       )    ->    int:
												_a	:    int         =		self.scheduler_classes[0]
												_a	:    List[Any]         =		self.get_scheduler_config()
												_a	:    Dict         =		scheduler_class(**_a       )

												assert torch.sum(torch.abs(scheduler._get_variance(0       ) - 0.0       )       ) < 1e-5
												assert torch.sum(torch.abs(scheduler._get_variance(4_8_7       ) - 0.0_0979       )       ) < 1e-5
												assert torch.sum(torch.abs(scheduler._get_variance(9_9_9       ) - 0.02       )       ) < 1e-5


							def 				__lowercase				(			self       )    ->    Tuple:
												_a	:    int         =		self.scheduler_classes[0]
												_a	:    int         =		self.get_scheduler_config()
												_a	:    int         =		scheduler_class(**_a       )

												_a	:    Optional[int]         =		len(_a       )

												_a	:    Optional[Any]         =		self.dummy_model()
												_a	:    str         =		self.dummy_sample_deter
												_a	:    Union[str, Any]         =		torch.manual_seed(0       )

												for t in reversed(range(_a       )       ):
																	# 1. predict noise residual
																	_a	:    str         =		model(_a       ,							_a       )

																	# 2. predict previous mean of sample x_t-1
																	_a	:    Optional[int]         =		scheduler.step(_a       ,							_a       ,							_a       ,							generator=_a       ).prev_sample

																	# if t > 0:
																	#     noise = self.dummy_sample_deter
																	#     variance = scheduler.get_variance(t) ** (0.5) * noise
																	#
																	# sample = pred_prev_sample + variance
																	_a	:    List[Any]         =		pred_prev_sample

												_a	:    str         =		torch.sum(torch.abs(_a       )       )
												_a	:    Optional[Any]         =		torch.mean(torch.abs(_a       )       )

												assert abs(result_sum.item() - 258.9606       ) < 1e-2
												assert abs(result_mean.item() - 0.3372       ) < 1e-3


							def 				__lowercase				(			self       )    ->    Optional[Any]:
												_a	:    Optional[int]         =		self.scheduler_classes[0]
												_a	:    Optional[Any]         =		self.get_scheduler_config(prediction_type='''v_prediction'''       )
												_a	:    Union[str, Any]         =		scheduler_class(**_a       )

												_a	:    Dict         =		len(_a       )

												_a	:    int         =		self.dummy_model()
												_a	:    Tuple         =		self.dummy_sample_deter
												_a	:    List[Any]         =		torch.manual_seed(0       )

												for t in reversed(range(_a       )       ):
																	# 1. predict noise residual
																	_a	:    Dict         =		model(_a       ,							_a       )

																	# 2. predict previous mean of sample x_t-1
																	_a	:    int         =		scheduler.step(_a       ,							_a       ,							_a       ,							generator=_a       ).prev_sample

																	# if t > 0:
																	#     noise = self.dummy_sample_deter
																	#     variance = scheduler.get_variance(t) ** (0.5) * noise
																	#
																	# sample = pred_prev_sample + variance
																	_a	:    str         =		pred_prev_sample

												_a	:    str         =		torch.sum(torch.abs(_a       )       )
												_a	:    Tuple         =		torch.mean(torch.abs(_a       )       )

												assert abs(result_sum.item() - 202.0296       ) < 1e-2
												assert abs(result_mean.item() - 0.2631       ) < 1e-3


							def 				__lowercase				(			self       )    ->    Dict:
												_a	:    Union[str, Any]         =		self.scheduler_classes[0]
												_a	:    Tuple         =		self.get_scheduler_config()
												_a	:    Any         =		scheduler_class(**_a       )

												_a	:    Optional[Any]         =		[1_0_0, 8_7, 5_0, 1, 0]

												scheduler.set_timesteps(timesteps=_a       )

												_a	:    Optional[int]         =		scheduler.timesteps

												for i, timestep in enumerate(_a       ):
																	if i == len(_a       ) - 1:
																						_a	:    Dict         =		-1
																	else:
																						_a	:    Tuple         =		timesteps[i + 1]

																	_a	:    Optional[Any]         =		scheduler.previous_timestep(_a       )
																	_a	:    Optional[Any]         =		prev_t.item()

																	self.assertEqual(_a       ,							_a       )


							def 				__lowercase				(			self       )    ->    Optional[Any]:
												_a	:    Dict         =		self.scheduler_classes[0]
												_a	:    List[str]         =		self.get_scheduler_config()
												_a	:    Tuple         =		scheduler_class(**_a       )

												_a	:    str         =		[1_0_0, 8_7, 5_0, 5_1, 0]

												with self.assertRaises(_a       ,							msg='''`custom_timesteps` must be in descending order.'''       ):
																	scheduler.set_timesteps(timesteps=_a       )


							def 				__lowercase				(			self       )    ->    str:
												_a	:    List[str]         =		self.scheduler_classes[0]
												_a	:    List[str]         =		self.get_scheduler_config()
												_a	:    Dict         =		scheduler_class(**_a       )

												_a	:    Union[str, Any]         =		[1_0_0, 8_7, 5_0, 1, 0]
												_a	:    Optional[Any]         =		len(_a       )

												with self.assertRaises(_a       ,							msg='''Can only pass one of `num_inference_steps` or `custom_timesteps`.'''       ):
																	scheduler.set_timesteps(num_inference_steps=_a       ,							timesteps=_a       )




							def 				__lowercase				(			self       )    ->    Optional[int]:
												_a	:    Dict         =		self.scheduler_classes[0]
												_a	:    Union[str, Any]         =		self.get_scheduler_config()
												_a	:    int         =		scheduler_class(**_a       )

												_a	:    str         =		[scheduler.config.num_train_timesteps]

												with self.assertRaises(
												    _a       ,							msg='''`timesteps` must start before `self.config.train_timesteps`: {scheduler.config.num_train_timesteps}}'''       ,							):
																	scheduler.set_timesteps(timesteps=_a       )



