"""simple docstring"""






# 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       ( __UpperCAmelCase				):




					"""simple docstring"""

					snake_case__				    = 42
					snake_case__				    = 42






class 				snake_case       ( __UpperCAmelCase      ,    __UpperCAmelCase				):




					"""simple docstring"""

					snake_case__				    = 1







					@register_to_config
					def __init__(				self   :	List[str]    ,lowerCamelCase__   :	int = 2_000    ,lowerCamelCase__   :	float = 0.1_5    ,lowerCamelCase__   :	float = 0.0_1    ,lowerCamelCase__   :	float = 1_3_4_8.0    ,lowerCamelCase__   :	float = 1e-5    ,lowerCamelCase__   :	int = 1    ,):
									# standard deviation of the initial noise distribution
									UpperCAmelCase__             =							sigma_max

									# setable values
									UpperCAmelCase__             =							None

									self.set_sigmas(lowerCamelCase__    ,lowerCamelCase__    ,lowerCamelCase__    ,lowerCamelCase__			)







					def 		__lowerCAmelCase						(				self   :	Dict    ,lowerCamelCase__   :	torch.FloatTensor    ,lowerCamelCase__   :	Optional[int] = None			):
									return sample







					def 		__lowerCAmelCase						(				self   :	Optional[Any]    ,lowerCamelCase__   :	int    ,lowerCamelCase__   :	float = None    ,lowerCamelCase__   :	Union[str, torch.device] = None			):
									UpperCAmelCase__             =							sampling_eps if sampling_eps is not None else self.config.sampling_eps

									UpperCAmelCase__             =							torch.linspace(1    ,lowerCamelCase__    ,lowerCamelCase__    ,device=lowerCamelCase__			)







					def 		__lowerCAmelCase						(				self   :	Any    ,lowerCamelCase__   :	int    ,lowerCamelCase__   :	float = None    ,lowerCamelCase__   :	float = None    ,lowerCamelCase__   :	float = None			):
									UpperCAmelCase__             =							sigma_min if sigma_min is not None else self.config.sigma_min
									UpperCAmelCase__             =							sigma_max if sigma_max is not None else self.config.sigma_max
									UpperCAmelCase__             =							sampling_eps if sampling_eps is not None else self.config.sampling_eps
									if self.timesteps is None:
													self.set_timesteps(lowerCamelCase__    ,lowerCamelCase__			)

									UpperCAmelCase__             =							sigma_min * (sigma_max / sigma_min) ** (self.timesteps / sampling_eps)
									UpperCAmelCase__             =							torch.exp(torch.linspace(math.log(lowerCamelCase__			)    ,math.log(lowerCamelCase__			)    ,lowerCamelCase__			)			)
									UpperCAmelCase__             =							torch.tensor([sigma_min * (sigma_max / sigma_min) ** t for t in self.timesteps]			)







					def 		__lowerCAmelCase						(				self   :	Any    ,lowerCamelCase__   :	Tuple    ,lowerCamelCase__   :	int			):
									return torch.where(
									    timesteps == 0    ,torch.zeros_like(t.to(timesteps.device			)			)    ,self.discrete_sigmas[timesteps - 1].to(timesteps.device			)    ,)







					def 		__lowerCAmelCase						(				self   :	Union[str, Any]    ,lowerCamelCase__   :	torch.FloatTensor    ,lowerCamelCase__   :	int    ,lowerCamelCase__   :	torch.FloatTensor    ,lowerCamelCase__   :	Optional[torch.Generator] = None    ,lowerCamelCase__   :	bool = True    ,):
									if self.timesteps is None:
													raise ValueError(
													    '`self.timesteps` is not set, you need to run \'set_timesteps\' after creating the scheduler'			)

									UpperCAmelCase__             =							timestep * torch.ones(
									    sample.shape[0]    ,device=sample.device			)  # torch.repeat_interleave(timestep, sample.shape[0])
									UpperCAmelCase__             =							(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
									UpperCAmelCase__             =							timesteps.to(self.discrete_sigmas.device			)

									UpperCAmelCase__             =							self.discrete_sigmas[timesteps].to(sample.device			)
									UpperCAmelCase__             =							self.get_adjacent_sigma(lowerCamelCase__    ,lowerCamelCase__			).to(sample.device			)
									UpperCAmelCase__             =							torch.zeros_like(lowerCamelCase__			)
									UpperCAmelCase__             =							(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
									UpperCAmelCase__             =							diffusion.flatten()
									while len(diffusion.shape			) < len(sample.shape			):
													UpperCAmelCase__             =							diffusion.unsqueeze(-1			)
									UpperCAmelCase__             =							drift - diffusion**2 * model_output

									#  equation 6: sample noise for the diffusion term of
									UpperCAmelCase__             =							randn_tensor(
									    sample.shape    ,layout=sample.layout    ,generator=lowerCamelCase__    ,device=sample.device    ,dtype=sample.dtype			)
									UpperCAmelCase__             =							sample - drift  # subtract because `dt` is a small negative timestep
									# TODO is the variable diffusion the correct scaling term for the noise?
									UpperCAmelCase__             =							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=lowerCamelCase__    ,prev_sample_mean=lowerCamelCase__			)







					def 		__lowerCAmelCase						(				self   :	List[str]    ,lowerCamelCase__   :	torch.FloatTensor    ,lowerCamelCase__   :	torch.FloatTensor    ,lowerCamelCase__   :	Optional[torch.Generator] = None    ,lowerCamelCase__   :	bool = True    ,):
									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
									UpperCAmelCase__             =							randn_tensor(sample.shape    ,layout=sample.layout    ,generator=lowerCamelCase__			).to(sample.device			)

									# compute step size from the model_output, the noise, and the snr
									UpperCAmelCase__             =							torch.norm(model_output.reshape(model_output.shape[0]    ,-1			)    ,dim=-1			).mean()
									UpperCAmelCase__             =							torch.norm(noise.reshape(noise.shape[0]    ,-1			)    ,dim=-1			).mean()
									UpperCAmelCase__             =							(self.config.snr * noise_norm / grad_norm) ** 2 * 2
									UpperCAmelCase__             =							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
									UpperCAmelCase__             =							step_size.flatten()
									while len(step_size.shape			) < len(sample.shape			):
													UpperCAmelCase__             =							step_size.unsqueeze(-1			)
									UpperCAmelCase__             =							sample + step_size * model_output
									UpperCAmelCase__             =							prev_sample_mean + ((step_size * 2) ** 0.5) * noise

									if not return_dict:
													return (prev_sample,)

									return SchedulerOutput(prev_sample=lowerCamelCase__			)







					def 		__lowerCAmelCase						(				self   :	Any    ,lowerCamelCase__   :	torch.FloatTensor    ,lowerCamelCase__   :	torch.FloatTensor    ,lowerCamelCase__   :	torch.FloatTensor    ,):
									# Make sure sigmas and timesteps have the same device and dtype as original_samples
									UpperCAmelCase__             =							timesteps.to(original_samples.device			)
									UpperCAmelCase__             =							self.discrete_sigmas.to(original_samples.device			)[timesteps]
									UpperCAmelCase__             =							(
									    noise * sigmas[:, None, None, None]
									    if noise is not None
									    else torch.randn_like(lowerCamelCase__			) * sigmas[:, None, None, None]
									)
									UpperCAmelCase__             =							noise + original_samples
									return noisy_samples







					def __len__(				self   :	Optional[int]			):
									return self.config.num_train_timesteps








'''simple docstring'''




from __future__ import annotations

import math



def 	a			( lowerCamelCase__    ):
			'''simple docstring'''





			if num <= 0:
						A_	:						List[Any]	=     f'{num}: Invalid input, please enter a positive integer.'
						raise ValueError(lowerCamelCase__    )

			A_	:						Dict	=     [True] * (num + 1)
			A_	:						List[Any]	=     []
			A_	:						Tuple	=     2
			A_	:						Optional[int]	=     int(math.sqrt(lowerCamelCase__    )    )

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

									# Set multiples of start be False
									for i in range(start * start						,      num + 1						,      lowerCamelCase__    ):
												if sieve[i] is True:
															A_	:						List[Any]	=     False

						start += 1

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

			return prime


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