



'''simple docstring'''





from __future__ import annotations

from fractions import Fraction




def lowerCAmelCase    (__A    ,      __A):



     """simple docstring"""



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




def lowerCAmelCase    (__A):



     """simple docstring"""



     _a           =    []
     _a           =    11
     _a           =    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           =    10
     return solutions




def lowerCAmelCase    (__A = 2):



     """simple docstring"""



     _a           =    1.0
     for fraction in fraction_list(__A):
          _a           =    Fraction(__A)
          result *= frac.denominator / frac.numerator
     return int(__A)


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








'''simple docstring'''

import torch

from diffusers import CMStochasticIterativeScheduler

from .test_schedulers import SchedulerCommonTest






class 						a_		(     snake_case    ):
							UpperCAmelCase			:		str        =				(CMStochasticIterativeScheduler,)
							UpperCAmelCase			:		int        =				10


							def    UpperCamelCase     (				self   :						Dict      ,						**a_   :						List[str]			)			->					Any:
										snake_case:    Any      							={
										    'num_train_timesteps': 2_0_1,
										    'sigma_min': 0.0_0_2,
										    'sigma_max': 8_0.0,
										}

										config.update(**a_			)
										return config


							def    UpperCamelCase     (				self   :						List[Any]			)			->					List[Any]:
										snake_case:    Any      							=1_0

										snake_case:    List[str]      							=self.get_scheduler_config()
										snake_case:    List[Any]      							=self.scheduler_classes[0](**a_			)

										scheduler.set_timesteps(a_			)

										snake_case:    Dict      							=scheduler.timesteps[0]
										snake_case:    Union[str, Any]      							=scheduler.timesteps[1]

										snake_case:    List[str]      							=self.dummy_sample
										snake_case:    List[str]      							=0.1 * sample

										snake_case:    int      							=scheduler.step(a_      ,						a_      ,						a_			).prev_sample
										snake_case:    Optional[Any]      							=scheduler.step(a_      ,						a_      ,						a_			).prev_sample

										self.assertEqual(output_a.shape      ,						sample.shape			)
										self.assertEqual(output_a.shape      ,						output_a.shape			)


							def    UpperCamelCase     (				self   :						int			)			->					int:
										for timesteps in [1_0, 5_0, 1_0_0, 1_0_0_0]:
													self.check_over_configs(num_train_timesteps=a_			)


							def    UpperCamelCase     (				self   :						Optional[Any]			)			->					Dict:
										for clip_denoised in [True, False]:
													self.check_over_configs(clip_denoised=a_			)


							def    UpperCamelCase     (				self   :						Tuple			)			->					List[str]:
										snake_case:    List[Any]      							=self.scheduler_classes[0]
										snake_case:    List[Any]      							=self.get_scheduler_config()
										snake_case:    Any      							=scheduler_class(**a_			)

										snake_case:    Dict      							=1
										scheduler.set_timesteps(a_			)
										snake_case:    List[Any]      							=scheduler.timesteps

										snake_case:    Optional[Any]      							=torch.manual_seed(0			)

										snake_case:    Optional[Any]      							=self.dummy_model()
										snake_case:    List[Any]      							=self.dummy_sample_deter * scheduler.init_noise_sigma

										for i, t in enumerate(a_			):
													# 1. scale model input
													snake_case:    Any      							=scheduler.scale_model_input(a_      ,						a_			)

													# 2. predict noise residual
													snake_case:    List[str]      							=model(a_      ,						a_			)

													# 3. predict previous sample x_t-1
													snake_case:    Dict      							=scheduler.step(a_      ,						a_      ,						a_      ,						generator=a_			).prev_sample

													snake_case:    List[Any]      							=pred_prev_sample

										snake_case:    Optional[Any]      							=torch.sum(torch.abs(a_			)			)
										snake_case:    Optional[Any]      							=torch.mean(torch.abs(a_			)			)

										assert abs(result_sum.item() - 1_9_2.7_6_1_4			) < 1E-2
										assert abs(result_mean.item() - 0.2_5_1_0			) < 1E-3


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

										snake_case:    List[Any]      							=[1_0_6, 0]
										scheduler.set_timesteps(timesteps=a_			)
										snake_case:    Optional[Any]      							=scheduler.timesteps

										snake_case:    Dict      							=torch.manual_seed(0			)

										snake_case:    Optional[int]      							=self.dummy_model()
										snake_case:    Any      							=self.dummy_sample_deter * scheduler.init_noise_sigma

										for t in timesteps:
													# 1. scale model input
													snake_case:    List[Any]      							=scheduler.scale_model_input(a_      ,						a_			)

													# 2. predict noise residual
													snake_case:    Any      							=model(a_      ,						a_			)

													# 3. predict previous sample x_t-1
													snake_case:    List[str]      							=scheduler.step(a_      ,						a_      ,						a_      ,						generator=a_			).prev_sample

													snake_case:    Optional[Any]      							=pred_prev_sample

										snake_case:    Union[str, Any]      							=torch.sum(torch.abs(a_			)			)
										snake_case:    Tuple      							=torch.mean(torch.abs(a_			)			)

										assert abs(result_sum.item() - 3_4_7.6_3_5_7			) < 1E-2
										assert abs(result_mean.item() - 0.4_5_2_7			) < 1E-3


							def    UpperCamelCase     (				self   :						int			)			->					Tuple:
										snake_case:    List[Any]      							=self.scheduler_classes[0]
										snake_case:    Union[str, Any]      							=self.get_scheduler_config()
										snake_case:    str      							=scheduler_class(**a_			)

										snake_case:    str      							=[3_9, 3_0, 1_2, 1_5, 0]

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


							def    UpperCamelCase     (				self   :						Dict			)			->					Optional[int]:
										snake_case:    Optional[Any]      							=self.scheduler_classes[0]
										snake_case:    Dict      							=self.get_scheduler_config()
										snake_case:    str      							=scheduler_class(**a_			)

										snake_case:    Any      							=[3_9, 3_0, 1_2, 1, 0]
										snake_case:    List[Any]      							=len(a_			)

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




							def    UpperCamelCase     (				self   :						Optional[Any]			)			->					Tuple:
										snake_case:    Any      							=self.scheduler_classes[0]
										snake_case:    int      							=self.get_scheduler_config()
										snake_case:    Optional[Any]      							=scheduler_class(**a_			)

										snake_case:    List[Any]      							=[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_			)




