
import torch
import torch.nn.functional as F

from diffusers import VQDiffusionScheduler

from .test_schedulers import SchedulerCommonTest





class      _lowerCAmelCase (     __a	):
				_lowercase      		=(VQDiffusionScheduler,)




				def 					__a						( self    ,    **_UpperCamelCase					)    ->				List[str]:
							lowerCAmelCase_      =     {
							    "num_vec_classes": 4_097,
							    "num_train_timesteps": 100,
							}

							config.update(**_UpperCamelCase					)
							return config




				def 					__a						( self    ,    _UpperCamelCase					)    ->				str:
							lowerCAmelCase_      =     4
							lowerCAmelCase_      =     8
							lowerCAmelCase_      =     8

							lowerCAmelCase_      =     torch.randint(0    ,    _UpperCamelCase    ,    (batch_size, height * width)					)

							return sample




				@property
				def 					__a						( self					)    ->				List[str]:
							assert False




				def 					__a						( self    ,    _UpperCamelCase					)    ->				Tuple:
							def model(_UpperCamelCase    ,    _UpperCamelCase    ,    *_UpperCamelCase					):
										lowerCAmelCase_     ,  lowerCAmelCase_      =     sample.shape
										lowerCAmelCase_      =     torch.rand((batch_size, num_vec_classes - 1, num_latent_pixels)					)
										lowerCAmelCase_      =     F.log_softmax(logits.double()    ,    dim=1					).float()
										return return_value

							return model




				def 					__a						( self					)    ->				str:
							for timesteps in [2, 5, 100, 1_000]:
										self.check_over_configs(num_train_timesteps=_UpperCamelCase					)




				def 					__a						( self					)    ->				Dict:
							for num_vec_classes in [5, 100, 1_000, 4_000]:
										self.check_over_configs(num_vec_classes=_UpperCamelCase					)




				def 					__a						( self					)    ->				Tuple:
							for t in [0, 50, 99]:
										self.check_over_forward(time_step=_UpperCamelCase					)




				def 					__a						( self					)    ->				List[str]:
							pass





import math






def        lowerCamelCase__    (    __lowerCAmelCase  :  int    ):




			"""simple docstring"""


			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(__lowerCAmelCase    ) + 1    )   ,							6    ):
						if number % i == 0 or number % (i + 2) == 0:
									return False
			return True






def        lowerCamelCase__    (    __lowerCAmelCase  :  int = 600851475143    ):




			"""simple docstring"""


			try:
						lowerCAmelCase_      =     int(__lowerCAmelCase    )
			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(__lowerCAmelCase    ):
						return n
			while n % 2 == 0:
						n //= 2
			if is_prime(__lowerCAmelCase    ):
						return n
			for i in range(3   ,							int(math.sqrt(__lowerCAmelCase    )    ) + 1   ,							2    ):
						if n % i == 0:
									if is_prime(n // i    ):
												lowerCAmelCase_      =     n // i
												break
									elif is_prime(__lowerCAmelCase    ):
												lowerCAmelCase_      =     i
			return max_number


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



