



# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

import math
from dataclasses import dataclass
from typing import Optional, Tuple, Union

import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, randn_tensor
from .scheduling_utils import SchedulerMixin, SchedulerOutput

@dataclass
class        snake_case__    (A__		):







						"""simple docstring"""




						__lowerCAmelCase					:torch.FloatTensor
						__lowerCAmelCase					:torch.FloatTensor




class        snake_case__    (A__ ,     A__		):







						"""simple docstring"""




						__lowerCAmelCase					:List[Any]      =					1

						@register_to_config
						def __init__(       self ,       __lowercase = 2_0_0_0 ,       __lowercase = 0.1_5 ,       __lowercase = 0.0_1 ,       __lowercase = 1_3_4_8.0 ,       __lowercase = 1E-5 ,       __lowercase = 1 ,       ) ->				int:
									"""simple docstring"""




									a__       :						List[str]							=  sigma_max

									# setable values
									a__       :						Dict							=  None

									self.set_sigmas(__lowercase ,       __lowercase ,       __lowercase ,       __lowercase  )

						def 							SCREAMING_SNAKE_CASE__(       self ,       __lowercase ,       __lowercase = None  ) ->				torch.FloatTensor:
									"""simple docstring"""




									return sample

						def 							SCREAMING_SNAKE_CASE__(       self ,       __lowercase ,       __lowercase = None ,       __lowercase = None  ) ->				List[Any]:
									"""simple docstring"""




									a__       :						Any							=  sampling_eps if sampling_eps is not None else self.config.sampling_eps

									a__       :						Optional[int]							=  torch.linspace(1 ,       __lowercase ,       __lowercase ,       device=__lowercase  )

						def 							SCREAMING_SNAKE_CASE__(       self ,       __lowercase ,       __lowercase = None ,       __lowercase = None ,       __lowercase = None  ) ->				List[Any]:
									"""simple docstring"""




									a__       :						Optional[Any]							=  sigma_min if sigma_min is not None else self.config.sigma_min
									a__       :						Any							=  sigma_max if sigma_max is not None else self.config.sigma_max
									a__       :						Optional[int]							=  sampling_eps if sampling_eps is not None else self.config.sampling_eps
									if self.timesteps is None:
												self.set_timesteps(__lowercase ,       __lowercase  )

									a__       :						str							=  sigma_min * (sigma_max / sigma_min) ** (self.timesteps / sampling_eps)
									a__       :						int							=  torch.exp(torch.linspace(math.log(__lowercase  ) ,       math.log(__lowercase  ) ,       __lowercase  )  )
									a__       :						Dict							=  torch.tensor([sigma_min * (sigma_max / sigma_min) ** t for t in self.timesteps]  )

						def 							SCREAMING_SNAKE_CASE__(       self ,       __lowercase ,       __lowercase  ) ->				str:
									"""simple docstring"""




									return torch.where(
									    timesteps == 0 ,       torch.zeros_like(t.to(timesteps.device  )  ) ,       self.discrete_sigmas[timesteps - 1].to(timesteps.device  ) ,       )

						def 							SCREAMING_SNAKE_CASE__(       self ,       __lowercase ,       __lowercase ,       __lowercase ,       __lowercase = None ,       __lowercase = True ,       ) ->				Union[SdeVeOutput, Tuple]:
									"""simple docstring"""




									if self.timesteps is None:
												raise ValueError(
												    """`self.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"""  )

									a__       :						str							=  timestep * torch.ones(
									    sample.shape[0] ,       device=sample.device  )  # torch.repeat_interleave(timestep, sample.shape[0])
									a__       :						Optional[int]							=  (timestep * (len(self.timesteps  ) - 1)).long()

									# mps requires indices to be in the same device, so we use cpu as is the default with cuda
									a__       :						Optional[Any]							=  timesteps.to(self.discrete_sigmas.device  )

									a__       :						int							=  self.discrete_sigmas[timesteps].to(sample.device  )
									a__       :						Dict							=  self.get_adjacent_sigma(__lowercase ,       __lowercase  ).to(sample.device  )
									a__       :						int							=  torch.zeros_like(__lowercase  )
									a__       :						List[Any]							=  (sigma**2 - adjacent_sigma**2) ** 0.5

									# equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x)
									# also equation 47 shows the analog from SDE models to ancestral sampling methods
									a__       :						str							=  diffusion.flatten()
									while len(diffusion.shape  ) < len(sample.shape  ):
												a__       :						Tuple							=  diffusion.unsqueeze(-1  )
									a__       :						Dict							=  drift - diffusion**2 * model_output

									#  equation 6: sample noise for the diffusion term of
									a__       :						str							=  randn_tensor(
									    sample.shape ,       layout=sample.layout ,       generator=__lowercase ,       device=sample.device ,       dtype=sample.dtype  )
									a__       :						str							=  sample - drift  # subtract because `dt` is a small negative timestep
									# TODO is the variable diffusion the correct scaling term for the noise?
									a__       :						Union[str, Any]							=  prev_sample_mean + diffusion * noise  # add impact of diffusion field g

									if not return_dict:
												return (prev_sample, prev_sample_mean)

									return SdeVeOutput(prev_sample=__lowercase ,       prev_sample_mean=__lowercase  )

						def 							SCREAMING_SNAKE_CASE__(       self ,       __lowercase ,       __lowercase ,       __lowercase = None ,       __lowercase = True ,       ) ->				Union[SchedulerOutput, Tuple]:
									"""simple docstring"""




									if self.timesteps is None:
												raise ValueError(
												    """`self.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"""  )

									# For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z"
									# sample noise for correction
									a__       :						Union[str, Any]							=  randn_tensor(sample.shape ,       layout=sample.layout ,       generator=__lowercase  ).to(sample.device  )

									# compute step size from the model_output, the noise, and the snr
									a__       :						Optional[int]							=  torch.norm(model_output.reshape(model_output.shape[0] ,       -1  ) ,       dim=-1  ).mean()
									a__       :						Union[str, Any]							=  torch.norm(noise.reshape(noise.shape[0] ,       -1  ) ,       dim=-1  ).mean()
									a__       :						Optional[int]							=  (self.config.snr * noise_norm / grad_norm) ** 2 * 2
									a__       :						Tuple							=  step_size * torch.ones(sample.shape[0]  ).to(sample.device  )
									# self.repeat_scalar(step_size, sample.shape[0])

									# compute corrected sample: model_output term and noise term
									a__       :						Tuple							=  step_size.flatten()
									while len(step_size.shape  ) < len(sample.shape  ):
												a__       :						Tuple							=  step_size.unsqueeze(-1  )
									a__       :						List[str]							=  sample + step_size * model_output
									a__       :						List[Any]							=  prev_sample_mean + ((step_size * 2) ** 0.5) * noise

									if not return_dict:
												return (prev_sample,)

									return SchedulerOutput(prev_sample=__lowercase  )

						def 							SCREAMING_SNAKE_CASE__(       self ,       __lowercase ,       __lowercase ,       __lowercase ,       ) ->				torch.FloatTensor:
									"""simple docstring"""




									a__       :						Union[str, Any]							=  timesteps.to(original_samples.device  )
									a__       :						Any							=  self.discrete_sigmas.to(original_samples.device  )[timesteps]
									a__       :						Optional[int]							=  (
									    noise * sigmas[:, None, None, None]
									    if noise is not None
									    else torch.randn_like(__lowercase  ) * sigmas[:, None, None, None]
									)
									a__       :						Tuple							=  noise + original_samples
									return noisy_samples

						def __len__(       self  ) ->				str:
									"""simple docstring"""




									return self.config.num_train_timesteps









from __future__ import annotations

import math

def      lowerCAmelCase_					(  _lowercase    :       int)							->	list[int]:







			"""simple docstring"""

			if num <= 0:
						a__       :						Tuple							=  F'''{num}: Invalid input, please enter a positive integer.'''
						raise ValueError(_lowercase)

			a__       :						List[Any]							=  [True] * (num + 1)
			a__       :						List[str]							=  []
			a__       :						List[Any]							=  2
			a__       :						Optional[int]							=  int(math.sqrt(_lowercase))

			while start <= end:
						# If start is a prime
						if sieve[start] is True:
									prime.append(_lowercase)

									# Set multiples of start be False
									for i in range(start * start						,       num + 1						,       _lowercase):
												if sieve[i] is True:
															a__       :						Optional[int]							=  False

						start += 1

			for j in range(end + 1						,       num + 1):
						if sieve[j] is True:
									prime.append(_lowercase)

			return prime


if __name__ == "__main__":
		print(prime_sieve(int(input("Enter a positive integer: ").strip())))




