






"""simple docstring"""



import math




def     lowerCamelCase_					(	__A	:		int      ):

					if 1 < number < 4:
										# 2 and 3 are primes
										return True
					elif number < 2 or number % 2 == 0 or number % 3 == 0:
										# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
										return False

					# All primes number are in format of 6k +/- 1
					for i in range(5      ,						int(math.sqrt(__A      ) + 1      )      ,						6      ):
										if number % i == 0 or number % (i + 2) == 0:
															return False
					return True




def     lowerCamelCase_					(	__A	:		int = 6008_5147_5143      ):

					try:
										lowerCamelCase__					=int(__A      )
					except (TypeError, ValueError):
										raise TypeError('Parameter n must be int or castable to int.'      )
					if n <= 0:
										raise ValueError('Parameter n must be greater than or equal to one.'      )
					lowerCamelCase__					=0
					if is_prime(__A      ):
										return n
					while n % 2 == 0:
										n //= 2
					if is_prime(__A      ):
										return n
					for i in range(3      ,						int(math.sqrt(__A      )      ) + 1      ,						2      ):
										if n % i == 0:
															if is_prime(n // i      ):
																				lowerCamelCase__					=n // i
																				break
															elif is_prime(__A      ):
																				lowerCamelCase__					=i
					return max_number


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







"""simple docstring"""



import torch

from diffusers import EulerAncestralDiscreteScheduler
from diffusers.utils import torch_device

from .test_schedulers import SchedulerCommonTest




class 							__lowercase(							_UpperCamelCase	):
						lowerCAmelCase_		:				Dict=							(EulerAncestralDiscreteScheduler,)
						lowerCAmelCase_		:				int=							10






						def 		lowerCAmelCase (       self     ,    **_SCREAMING_SNAKE_CASE)      ->	List[str]:




											"""simple docstring"""





											lowerCamelCase__					={
											    'num_train_timesteps': 11_00,
											    'beta_start': 0.0001,
											    'beta_end': 0.02,
											    'beta_schedule': 'linear',
											}

											config.update(**_SCREAMING_SNAKE_CASE)
											return config






						def 		lowerCAmelCase (       self)      ->	List[Any]:




											"""simple docstring"""





											for timesteps in [10, 50, 1_00, 10_00]:
																self.check_over_configs(num_train_timesteps=_SCREAMING_SNAKE_CASE)






						def 		lowerCAmelCase (       self)      ->	Tuple:




											"""simple docstring"""





											for beta_start, beta_end in zip([0.00001, 0.0001, 0.001]     ,    [0.0002, 0.002, 0.02]):
																self.check_over_configs(beta_start=_SCREAMING_SNAKE_CASE     ,    beta_end=_SCREAMING_SNAKE_CASE)






						def 		lowerCAmelCase (       self)      ->	List[Any]:




											"""simple docstring"""





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






						def 		lowerCAmelCase (       self)      ->	Dict:




											"""simple docstring"""





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






						def 		lowerCAmelCase (       self)      ->	List[str]:




											"""simple docstring"""





											lowerCamelCase__					=self.scheduler_classes[0]
											lowerCamelCase__					=self.get_scheduler_config()
											lowerCamelCase__					=scheduler_class(**_SCREAMING_SNAKE_CASE)

											scheduler.set_timesteps(self.num_inference_steps)

											lowerCamelCase__					=torch.manual_seed(0)

											lowerCamelCase__					=self.dummy_model()
											lowerCamelCase__					=self.dummy_sample_deter * scheduler.init_noise_sigma.cpu()
											lowerCamelCase__					=sample.to(_SCREAMING_SNAKE_CASE)

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

																lowerCamelCase__					=model(_SCREAMING_SNAKE_CASE     ,    _SCREAMING_SNAKE_CASE)

																lowerCamelCase__					=scheduler.step(_SCREAMING_SNAKE_CASE     ,    _SCREAMING_SNAKE_CASE     ,    _SCREAMING_SNAKE_CASE     ,    generator=_SCREAMING_SNAKE_CASE)
																lowerCamelCase__					=output.prev_sample

											lowerCamelCase__					=torch.sum(torch.abs(_SCREAMING_SNAKE_CASE))
											lowerCamelCase__					=torch.mean(torch.abs(_SCREAMING_SNAKE_CASE))

											assert abs(result_sum.item() - 152.3192) < 1E-2
											assert abs(result_mean.item() - 0.1983) < 1E-3






						def 		lowerCAmelCase (       self)      ->	str:




											"""simple docstring"""





											lowerCamelCase__					=self.scheduler_classes[0]
											lowerCamelCase__					=self.get_scheduler_config(prediction_type='v_prediction')
											lowerCamelCase__					=scheduler_class(**_SCREAMING_SNAKE_CASE)

											scheduler.set_timesteps(self.num_inference_steps)

											lowerCamelCase__					=torch.manual_seed(0)

											lowerCamelCase__					=self.dummy_model()
											lowerCamelCase__					=self.dummy_sample_deter * scheduler.init_noise_sigma
											lowerCamelCase__					=sample.to(_SCREAMING_SNAKE_CASE)

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

																lowerCamelCase__					=model(_SCREAMING_SNAKE_CASE     ,    _SCREAMING_SNAKE_CASE)

																lowerCamelCase__					=scheduler.step(_SCREAMING_SNAKE_CASE     ,    _SCREAMING_SNAKE_CASE     ,    _SCREAMING_SNAKE_CASE     ,    generator=_SCREAMING_SNAKE_CASE)
																lowerCamelCase__					=output.prev_sample

											lowerCamelCase__					=torch.sum(torch.abs(_SCREAMING_SNAKE_CASE))
											lowerCamelCase__					=torch.mean(torch.abs(_SCREAMING_SNAKE_CASE))

											assert abs(result_sum.item() - 108.4439) < 1E-2
											assert abs(result_mean.item() - 0.1412) < 1E-3






						def 		lowerCAmelCase (       self)      ->	Any:




											"""simple docstring"""





											lowerCamelCase__					=self.scheduler_classes[0]
											lowerCamelCase__					=self.get_scheduler_config()
											lowerCamelCase__					=scheduler_class(**_SCREAMING_SNAKE_CASE)

											scheduler.set_timesteps(self.num_inference_steps     ,    device=_SCREAMING_SNAKE_CASE)
											lowerCamelCase__					=torch.manual_seed(0)

											lowerCamelCase__					=self.dummy_model()
											lowerCamelCase__					=self.dummy_sample_deter * scheduler.init_noise_sigma.cpu()
											lowerCamelCase__					=sample.to(_SCREAMING_SNAKE_CASE)

											for t in scheduler.timesteps:
																lowerCamelCase__					=scheduler.scale_model_input(_SCREAMING_SNAKE_CASE     ,    _SCREAMING_SNAKE_CASE)

																lowerCamelCase__					=model(_SCREAMING_SNAKE_CASE     ,    _SCREAMING_SNAKE_CASE)

																lowerCamelCase__					=scheduler.step(_SCREAMING_SNAKE_CASE     ,    _SCREAMING_SNAKE_CASE     ,    _SCREAMING_SNAKE_CASE     ,    generator=_SCREAMING_SNAKE_CASE)
																lowerCamelCase__					=output.prev_sample

											lowerCamelCase__					=torch.sum(torch.abs(_SCREAMING_SNAKE_CASE))
											lowerCamelCase__					=torch.mean(torch.abs(_SCREAMING_SNAKE_CASE))

											assert abs(result_sum.item() - 152.3192) < 1E-2
											assert abs(result_mean.item() - 0.1983) < 1E-3