
"""simple docstring"""


import torch

from diffusers import DPMSolverSDEScheduler
from diffusers.utils import torch_device
from diffusers.utils.testing_utils import require_torchsde

from .test_schedulers import SchedulerCommonTest




@require_torchsde
class  __lowerCamelCase  ( lowerCAmelCase			):
				a__:      List[Any]          =    (DPMSolverSDEScheduler,)
				a__:      Any          =    10




				def        UpperCAmelCase__						(				self							,						**UpperCAmelCase   ):
							lowerCamelCase_					=  {
							    '''num_train_timesteps''': 1100,
							    '''beta_start''': 0.0_0_0_1,
							    '''beta_end''': 0.0_2,
							    '''beta_schedule''': '''linear''',
							    '''noise_sampler_seed''': 0,
							}

							config.update(**UpperCAmelCase   )
							return config




				def        UpperCAmelCase__						(				self   ):
							for timesteps in [10, 50, 100, 1000]:
										self.check_over_configs(num_train_timesteps=UpperCAmelCase   )




				def        UpperCAmelCase__						(				self   ):
							for beta_start, beta_end in zip([0.0_0_0_0_1, 0.0_0_0_1, 0.0_0_1]							,						[0.0_0_0_2, 0.0_0_2, 0.0_2]   ):
										self.check_over_configs(beta_start=UpperCAmelCase							,						beta_end=UpperCAmelCase   )




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




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




				def        UpperCAmelCase__						(				self   ):
							lowerCamelCase_					=  self.scheduler_classes[0]
							lowerCamelCase_					=  self.get_scheduler_config()
							lowerCamelCase_					=  scheduler_class(**UpperCAmelCase   )

							scheduler.set_timesteps(self.num_inference_steps   )

							lowerCamelCase_					=  self.dummy_model()
							lowerCamelCase_					=  self.dummy_sample_deter * scheduler.init_noise_sigma
							lowerCamelCase_					=  sample.to(UpperCAmelCase   )

							for i, t in enumerate(scheduler.timesteps   ):
										lowerCamelCase_					=  scheduler.scale_model_input(UpperCAmelCase							,						UpperCAmelCase   )

										lowerCamelCase_					=  model(UpperCAmelCase							,						UpperCAmelCase   )

										lowerCamelCase_					=  scheduler.step(UpperCAmelCase							,						UpperCAmelCase							,						UpperCAmelCase   )
										lowerCamelCase_					=  output.prev_sample

							lowerCamelCase_					=  torch.sum(torch.abs(UpperCAmelCase   )   )
							lowerCamelCase_					=  torch.mean(torch.abs(UpperCAmelCase   )   )

							if torch_device in ["mps"]:
										assert abs(result_sum.item() - 1_6_7.4_7_8_2_1_0_4_4_9_2_1_8_7_5   ) < 1e-2
										assert abs(result_mean.item() - 0.2_1_7_8_7_0_5_9_6_4_5_6_5_2_7_7   ) < 1e-3
							elif torch_device in ["cuda"]:
										assert abs(result_sum.item() - 1_7_1.5_9_3_5_2_1_1_1_8_1_6_4_0_6   ) < 1e-2
										assert abs(result_mean.item() - 0.2_2_3_4_2_9_0_6_8_9_2_2_9_9_6_5_2   ) < 1e-3
							else:
										assert abs(result_sum.item() - 1_6_2.5_2_3_8_3_4_2_2_8_5_1_5_6_2   ) < 1e-2
										assert abs(result_mean.item() - 0.2_1_1_6_1_9_5_7_0_8_5_1_3_2_6   ) < 1e-3




				def        UpperCAmelCase__						(				self   ):
							lowerCamelCase_					=  self.scheduler_classes[0]
							lowerCamelCase_					=  self.get_scheduler_config(prediction_type='''v_prediction'''   )
							lowerCamelCase_					=  scheduler_class(**UpperCAmelCase   )

							scheduler.set_timesteps(self.num_inference_steps   )

							lowerCamelCase_					=  self.dummy_model()
							lowerCamelCase_					=  self.dummy_sample_deter * scheduler.init_noise_sigma
							lowerCamelCase_					=  sample.to(UpperCAmelCase   )

							for i, t in enumerate(scheduler.timesteps   ):
										lowerCamelCase_					=  scheduler.scale_model_input(UpperCAmelCase							,						UpperCAmelCase   )

										lowerCamelCase_					=  model(UpperCAmelCase							,						UpperCAmelCase   )

										lowerCamelCase_					=  scheduler.step(UpperCAmelCase							,						UpperCAmelCase							,						UpperCAmelCase   )
										lowerCamelCase_					=  output.prev_sample

							lowerCamelCase_					=  torch.sum(torch.abs(UpperCAmelCase   )   )
							lowerCamelCase_					=  torch.mean(torch.abs(UpperCAmelCase   )   )

							if torch_device in ["mps"]:
										assert abs(result_sum.item() - 1_2_4.7_7_1_4_9_2_0_0_4_3_9_4_5_3   ) < 1e-2
										assert abs(result_mean.item() - 0.1_6_2_2_6_2_8_9_0_1_4_8_1_6_2_8_4   ) < 1e-3
							elif torch_device in ["cuda"]:
										assert abs(result_sum.item() - 1_2_8.1_6_6_3_3_6_0_5_9_5_7_0_3   ) < 1e-2
										assert abs(result_mean.item() - 0.1_6_6_8_8_3_2_6_0_0_1_1_6_7_2_9_7   ) < 1e-3
							else:
										assert abs(result_sum.item() - 1_1_9.8_4_8_7_5_4_8_8_2_8_1_2_5   ) < 1e-2
										assert abs(result_mean.item() - 0.1_5_6_0_5_3_0_6_6_2_5_3_6_6_2_1   ) < 1e-3




				def        UpperCAmelCase__						(				self   ):
							lowerCamelCase_					=  self.scheduler_classes[0]
							lowerCamelCase_					=  self.get_scheduler_config()
							lowerCamelCase_					=  scheduler_class(**UpperCAmelCase   )

							scheduler.set_timesteps(self.num_inference_steps							,						device=UpperCAmelCase   )

							lowerCamelCase_					=  self.dummy_model()
							lowerCamelCase_					=  self.dummy_sample_deter.to(UpperCAmelCase   ) * scheduler.init_noise_sigma

							for t in scheduler.timesteps:
										lowerCamelCase_					=  scheduler.scale_model_input(UpperCAmelCase							,						UpperCAmelCase   )

										lowerCamelCase_					=  model(UpperCAmelCase							,						UpperCAmelCase   )

										lowerCamelCase_					=  scheduler.step(UpperCAmelCase							,						UpperCAmelCase							,						UpperCAmelCase   )
										lowerCamelCase_					=  output.prev_sample

							lowerCamelCase_					=  torch.sum(torch.abs(UpperCAmelCase   )   )
							lowerCamelCase_					=  torch.mean(torch.abs(UpperCAmelCase   )   )

							if torch_device in ["mps"]:
										assert abs(result_sum.item() - 1_6_7.4_6_9_5_7_3_9_7_4_6_0_9_3_8   ) < 1e-2
										assert abs(result_mean.item() - 0.2_1_8_0_5_9_3_4_6_0_7_9_8_2_6_3_5   ) < 1e-3
							elif torch_device in ["cuda"]:
										assert abs(result_sum.item() - 1_7_1.5_9_3_5_3_6_3_7_6_9_5_3_1_2   ) < 1e-2
										assert abs(result_mean.item() - 0.2_2_3_4_2_9_0_8_3_8_2_4_1_5_7_7_1   ) < 1e-3
							else:
										assert abs(result_sum.item() - 1_6_2.5_2_3_8_3_4_2_2_8_5_1_5_6_2   ) < 1e-2
										assert abs(result_mean.item() - 0.2_1_1_6_1_9_5_7_0_8_5_1_3_2_6   ) < 1e-3





				def        UpperCAmelCase__						(				self   ):
							lowerCamelCase_					=  self.scheduler_classes[0]
							lowerCamelCase_					=  self.get_scheduler_config()
							lowerCamelCase_					=  scheduler_class(**UpperCAmelCase							,						use_karras_sigmas=UpperCAmelCase   )

							scheduler.set_timesteps(self.num_inference_steps							,						device=UpperCAmelCase   )

							lowerCamelCase_					=  self.dummy_model()
							lowerCamelCase_					=  self.dummy_sample_deter.to(UpperCAmelCase   ) * scheduler.init_noise_sigma
							lowerCamelCase_					=  sample.to(UpperCAmelCase   )

							for t in scheduler.timesteps:
										lowerCamelCase_					=  scheduler.scale_model_input(UpperCAmelCase							,						UpperCAmelCase   )

										lowerCamelCase_					=  model(UpperCAmelCase							,						UpperCAmelCase   )

										lowerCamelCase_					=  scheduler.step(UpperCAmelCase							,						UpperCAmelCase							,						UpperCAmelCase   )
										lowerCamelCase_					=  output.prev_sample

							lowerCamelCase_					=  torch.sum(torch.abs(UpperCAmelCase   )   )
							lowerCamelCase_					=  torch.mean(torch.abs(UpperCAmelCase   )   )

							if torch_device in ["mps"]:
										assert abs(result_sum.item() - 1_7_6.6_6_9_7_4_1_3_5_7_4_2_1_8_8   ) < 1e-2
										assert abs(result_mean.item() - 0.2_3_0_0_3_8_7_2_7_3_0_9_8_1_8_1_1   ) < 1e-2
							elif torch_device in ["cuda"]:
										assert abs(result_sum.item() - 1_7_7.6_3_6_5_3_5_6_4_4_5_3_1_2_5   ) < 1e-2
										assert abs(result_mean.item() - 0.2_3_0_0_3_8_7_2_7_3_0_9_8_1_8_1_1   ) < 1e-2
							else:
										assert abs(result_sum.item() - 1_7_0.3_1_3_5_2_2_3_3_8_8_6_7_2   ) < 1e-2
										assert abs(result_mean.item() - 0.2_3_0_0_3_8_7_2_7_3_0_9_8_1_8_1_1   ) < 1e-2





"""simple docstring"""


import math






def  lowercase						(	lowerCAmelCase__						):
			lowerCamelCase_					=  [True] * n
			lowerCamelCase_					=  False
			lowerCamelCase_					=  False
			lowerCamelCase_					=  True

			for i in range(3	,int(n**0.5 + 1						)	,2						):
						lowerCamelCase_					=  i * 2
						while index < n:
									lowerCamelCase_					=  False
									lowerCamelCase_					=  index + i

			lowerCamelCase_					=  [2]

			for i in range(3	,lowerCAmelCase__	,2						):
						if is_prime[i]:
									primes.append(lowerCAmelCase__						)

			return primes






def  lowercase						(	lowerCAmelCase__ = 999_966_663_333						):
			lowerCamelCase_					=  math.floor(math.sqrt(lowerCAmelCase__						)						) + 100
			lowerCamelCase_					=  prime_sieve(lowerCAmelCase__						)

			lowerCamelCase_					=  0
			lowerCamelCase_					=  0
			lowerCamelCase_					=  primes[prime_index]

			while (last_prime**2) <= limit:
						lowerCamelCase_					=  primes[prime_index + 1]

						lowerCamelCase_					=  last_prime**2
						lowerCamelCase_					=  next_prime**2

						# Get numbers divisible by lps(current)
						lowerCamelCase_					=  lower_bound + last_prime
						while upper_bound > current <= limit:
									matches_sum += current
									current += last_prime

						# Reset the upper_bound
						while (upper_bound - next_prime) > limit:
									upper_bound -= next_prime

						# Add the numbers divisible by ups(current)
						lowerCamelCase_					=  upper_bound - next_prime
						while current > lower_bound:
									matches_sum += current
									current -= next_prime

						# Remove the numbers divisible by both ups and lps
						lowerCamelCase_					=  0
						while upper_bound > current <= limit:
									if current <= lower_bound:
												# Increment the current number
												current += last_prime * next_prime
												continue

									if current > limit:
												break

									# Remove twice since it was added by both ups and lps
									matches_sum -= current * 2

									# Increment the current number
									current += last_prime * next_prime

						# Setup for next pair
						lowerCamelCase_					=  next_prime
						prime_index += 1

			return matches_sum


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



