



"""simple docstring"""







import unittest

import torch

from diffusers import DDIMScheduler, DDPMScheduler, UNetaDModel
from diffusers.training_utils import set_seed
from diffusers.utils.testing_utils import slow


lowerCAmelCase_   						=   False
class        __A       (	unittest.TestCase    ):







		'''simple docstring'''





		def 					UpperCAmelCase    (	self						:  Union[str, Any]			,_snake_case						:  Dict=32						)					->		Union[str, Any]:






				"""simple docstring"""



				set_seed(0						)
				lowercase__   :    Union[str, Any]				=			UNetaDModel(sample_size=_snake_case			,in_channels=3			,out_channels=3						)
				lowercase__   :    Optional[int]				=			torch.optim.SGD(model.parameters()			,lr=0.0001						)
				return model, optimizer







		@slow
		def 					UpperCAmelCase    (	self						:  Tuple						)					->		Optional[int]:






				"""simple docstring"""



				lowercase__   :    Tuple				=			'cpu'  # ensure full determinism without setting the CUBLAS_WORKSPACE_CONFIG env variable
				lowercase__   :    Any				=			DDPMScheduler(
				    num_train_timesteps=1_000			,beta_start=0.0001			,beta_end=0.02			,beta_schedule='''linear'''			,clip_sample=_snake_case			,)
				lowercase__   :    Union[str, Any]				=			DDIMScheduler(
				    num_train_timesteps=1_000			,beta_start=0.0001			,beta_end=0.02			,beta_schedule='''linear'''			,clip_sample=_snake_case			,)

				assert ddpm_scheduler.config.num_train_timesteps == ddim_scheduler.config.num_train_timesteps

				# shared batches for DDPM and DDIM
				set_seed(0						)
				lowercase__   :    Optional[int]				=			[torch.randn((4, 3, 32, 32)						).clip(-1			,1						).to(_snake_case						) for _ in range(4						)]
				lowercase__   :    Tuple				=			[torch.randn((4, 3, 32, 32)						).to(_snake_case						) for _ in range(4						)]
				lowercase__   :    Optional[int]				=			[torch.randint(0			,1_000			,(4,)						).long().to(_snake_case						) for _ in range(4						)]

				# train with a DDPM scheduler
				lowercase__   :    Optional[int]				=			self.get_model_optimizer(resolution=32						)
				model.train().to(_snake_case						)
				for i in range(4						):
						optimizer.zero_grad()
						lowercase__   :    Optional[Any]				=			ddpm_scheduler.add_noise(clean_images[i]			,noise[i]			,timesteps[i]						)
						lowercase__   :    List[Any]				=			model(_snake_case			,timesteps[i]						).sample
						lowercase__   :    str				=			torch.nn.functional.mse_loss(_snake_case			,noise[i]						)
						loss.backward()
						optimizer.step()
				del model, optimizer

				# recreate the model and optimizer, and retry with DDIM
				lowercase__   :    Any				=			self.get_model_optimizer(resolution=32						)
				model.train().to(_snake_case						)
				for i in range(4						):
						optimizer.zero_grad()
						lowercase__   :    Dict				=			ddim_scheduler.add_noise(clean_images[i]			,noise[i]			,timesteps[i]						)
						lowercase__   :    Optional[Any]				=			model(_snake_case			,timesteps[i]						).sample
						lowercase__   :    Optional[int]				=			torch.nn.functional.mse_loss(_snake_case			,noise[i]						)
						loss.backward()
						optimizer.step()
				del model, optimizer

				self.assertTrue(torch.allclose(_snake_case			,_snake_case			,atol=1e-5						)						)
				self.assertTrue(torch.allclose(_snake_case			,_snake_case			,atol=1e-5						)						)



import math

def 	snake_case__			(    SCREAMING_SNAKE_CASE_		:    int			):



     '''simple docstring'''





     lowercase__    :   Optional[Any]      =       []
     lowercase__    :   str      =       2
     lowercase__    :   Optional[Any]      =       int(math.sqrt(SCREAMING_SNAKE_CASE_			)			)  # Size of every segment
     lowercase__    :   Dict      =       [True] * (end + 1)
     lowercase__    :   Union[str, Any]      =       []

     while start <= end:
          if temp[start] is True:
               in_prime.append(SCREAMING_SNAKE_CASE_			)
               for i in range(start * start	,     end + 1	,     SCREAMING_SNAKE_CASE_			):
                    lowercase__    :   int      =       False
          start += 1
     prime += in_prime

     lowercase__    :   Optional[int]      =       end + 1
     lowercase__    :   List[str]      =       min(2 * end	,     SCREAMING_SNAKE_CASE_			)

     while low <= n:
          lowercase__    :   str      =       [True] * (high - low + 1)
          for each in in_prime:
               lowercase__    :   str      =       math.floor(low / each			) * each
               if t < low:
                    t += each

               for j in range(SCREAMING_SNAKE_CASE_	,     high + 1	,     SCREAMING_SNAKE_CASE_			):
                    lowercase__    :   Optional[Any]      =       False

          for j in range(len(SCREAMING_SNAKE_CASE_			)			):
               if temp[j] is True:
                    prime.append(j + low			)

          lowercase__    :   Optional[Any]      =       high + 1
          lowercase__    :   Optional[int]      =       min(high + end	,     SCREAMING_SNAKE_CASE_			)

     return prime

print(sieve(10**6))

