





"""simple docstring"""




from typing import Optional, Tuple, Union

import torch
from einops import rearrange, reduce

from diffusers import DDIMScheduler, DDPMScheduler, DiffusionPipeline, ImagePipelineOutput, UNetaDConditionModel
from diffusers.schedulers.scheduling_ddim import DDIMSchedulerOutput
from diffusers.schedulers.scheduling_ddpm import DDPMSchedulerOutput


UpperCAmelCase     :     Tuple							=	8
def 					_A	(		SCREAMING_SNAKE_CASE					:       List[Any]	,	SCREAMING_SNAKE_CASE					:       Optional[Any]=BITS						):





  """simple docstring"""



  a__     : int  =x.device

  a__     : Dict  =(x * 255).int().clamp(0	,	255						)

  a__     : int  =2 ** torch.arange(bits - 1	,	-1	,	-1	,	device=snake_case_						)
  a__     : Union[str, Any]  =rearrange(snake_case_	,	"d -> d 1 1"						)
  a__     : int  =rearrange(snake_case_	,	"b c h w -> b c 1 h w"						)

  a__     : Tuple  =((x & mask) != 0).float()
  a__     : Optional[Any]  =rearrange(snake_case_	,	"b c d h w -> b (c d) h w"						)
  a__     : str  =bits * 2 - 1
  return bits
def 					_A	(		SCREAMING_SNAKE_CASE					:       Optional[Any]	,	SCREAMING_SNAKE_CASE					:       Dict=BITS						):





  """simple docstring"""



  a__     : Tuple  =x.device

  a__     : Optional[int]  =(x > 0).int()
  a__     : Tuple  =2 ** torch.arange(bits - 1	,	-1	,	-1	,	device=snake_case_	,	dtype=torch.intaa						)

  a__     : List[Any]  =rearrange(snake_case_	,	"d -> d 1 1"						)
  a__     : Dict  =rearrange(snake_case_	,	"b (c d) h w -> b c d h w"	,	d=8						)
  a__     : Tuple  =reduce(x * mask	,	"b c d h w -> b c h w"	,	"sum"						)
  return (dec / 255).clamp(0.0	,	1.0						)
def 					_A	(		self					:       int	,	SCREAMING_SNAKE_CASE					:       torch.FloatTensor	,	SCREAMING_SNAKE_CASE					:       int	,	SCREAMING_SNAKE_CASE					:       torch.FloatTensor	,	SCREAMING_SNAKE_CASE					:       float = 0.0	,	SCREAMING_SNAKE_CASE					:       bool = True	,	SCREAMING_SNAKE_CASE					:       List[str]=None	,	SCREAMING_SNAKE_CASE					:       bool = True	,	):





  """simple docstring"""



  if self.num_inference_steps is None:
    raise ValueError(
        "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"						)

  # See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
  # Ideally, read DDIM paper in-detail understanding

  # Notation (<variable name> -> <name in paper>
  # - pred_noise_t -> e_theta(x_t, t)
  # - pred_original_sample -> f_theta(x_t, t) or x_0
  # - std_dev_t -> sigma_t
  # - eta -> η
  # - pred_sample_direction -> "direction pointing to x_t"
  # - pred_prev_sample -> "x_t-1"

  # 1. get previous step value (=t-1)
  a__     : Union[str, Any]  =timestep - self.config.num_train_timesteps // self.num_inference_steps

  # 2. compute alphas, betas
  a__     : Optional[int]  =self.alphas_cumprod[timestep]
  a__     : int  =self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod

  a__     : List[Any]  =1 - alpha_prod_t

  # 3. compute predicted original sample from predicted noise also called
  # "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
  a__     : Dict  =(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5

  # 4. Clip "predicted x_0"
  a__     : Any  =self.bit_scale
  if self.config.clip_sample:
    a__     : Any  =torch.clamp(snake_case_	,	-scale	,	snake_case_						)

  # 5. compute variance: "sigma_t(η)" -> see formula (16)
  # σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)
  a__     : List[Any]  =self._get_variance(snake_case_	,	snake_case_						)
  a__     : Any  =eta * variance ** 0.5

  if use_clipped_model_output:
    # the model_output is always re-derived from the clipped x_0 in Glide
    a__     : str  =(sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5

  # 6. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
  a__     : List[Any]  =(1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * model_output

  # 7. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
  a__     : List[str]  =alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction

  if eta > 0:
    # randn_like does not support generator https://github.com/pytorch/pytorch/issues/27072
    a__     : str  =model_output.device if torch.is_tensor(snake_case_						) else "cpu"
    a__     : List[str]  =torch.randn(model_output.shape	,	dtype=model_output.dtype	,	generator=snake_case_						).to(snake_case_						)
    a__     : Any  =self._get_variance(snake_case_	,	snake_case_						) ** 0.5 * eta * noise

    a__     : List[str]  =prev_sample + variance

  if not return_dict:
    return (prev_sample,)

  return DDIMSchedulerOutput(prev_sample=snake_case_	,	pred_original_sample=snake_case_						)
def 					_A	(		self					:       Union[str, Any]	,	SCREAMING_SNAKE_CASE					:       torch.FloatTensor	,	SCREAMING_SNAKE_CASE					:       int	,	SCREAMING_SNAKE_CASE					:       torch.FloatTensor	,	SCREAMING_SNAKE_CASE					:       Dict="epsilon"	,	SCREAMING_SNAKE_CASE					:       List[Any]=None	,	SCREAMING_SNAKE_CASE					:       bool = True	,	):





  """simple docstring"""



  a__     : int  =timestep

  if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type in ["learned", "learned_range"]:
    a__ ,							a__     : str  =torch.split(snake_case_	,	sample.shape[1]	,	dim=1						)
  else:
    a__     : str  =None

  # 1. compute alphas, betas
  a__     : Union[str, Any]  =self.alphas_cumprod[t]
  a__     : int  =self.alphas_cumprod[t - 1] if t > 0 else self.one
  a__     : Union[str, Any]  =1 - alpha_prod_t
  a__     : Union[str, Any]  =1 - alpha_prod_t_prev

  # 2. compute predicted original sample from predicted noise also called
  # "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
  if prediction_type == "epsilon":
    a__     : int  =(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
  elif prediction_type == "sample":
    a__     : str  =model_output
  else:
    raise ValueError(f'''Unsupported prediction_type {prediction_type}.'''						)

  # 3. Clip "predicted x_0"
  a__     : str  =self.bit_scale
  if self.config.clip_sample:
    a__     : Union[str, Any]  =torch.clamp(snake_case_	,	-scale	,	snake_case_						)

  # 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
  # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
  a__     : Any  =(alpha_prod_t_prev ** 0.5 * self.betas[t]) / beta_prod_t
  a__     : Optional[int]  =self.alphas[t] ** 0.5 * beta_prod_t_prev / beta_prod_t

  # 5. Compute predicted previous sample µ_t
  # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
  a__     : List[Any]  =pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

  # 6. Add noise
  a__     : Optional[int]  =0
  if t > 0:
    a__     : List[str]  =torch.randn(
        model_output.size()	,	dtype=model_output.dtype	,	layout=model_output.layout	,	generator=snake_case_						).to(model_output.device						)
    a__     : int  =(self._get_variance(snake_case_	,	predicted_variance=snake_case_						) ** 0.5) * noise

  a__     : Optional[Any]  =pred_prev_sample + variance

  if not return_dict:
    return (pred_prev_sample,)

  return DDPMSchedulerOutput(prev_sample=snake_case_	,	pred_original_sample=snake_case_						)







class     __lowerCAmelCase	(   UpperCamelCase__):







      def __init__(   self		,				lowerCAmelCase__		,				lowerCAmelCase__		,				lowerCAmelCase__ = 1.0		,				)       ->						Optional[int]:



        '''simple docstring'''




        super().__init__()
        a__     : Any  =bit_scale
        a__     : str  =(
            ddim_bit_scheduler_step if isinstance(__a		,				__a							) else ddpm_bit_scheduler_step
        )

        self.register_modules(unet=__a		,				scheduler=__a							)







      @torch.no_grad()
      def __call__(   self		,				lowerCAmelCase__ = 2_5_6		,				lowerCAmelCase__ = 2_5_6		,				lowerCAmelCase__ = 5_0		,				lowerCAmelCase__ = None		,				lowerCAmelCase__ = 1		,				lowerCAmelCase__ = "pil"		,				lowerCAmelCase__ = True		,				**lowerCAmelCase__		,				)       ->						List[str]:



        '''simple docstring'''




        a__     : Optional[Any]  =torch.randn(
            (batch_size, self.unet.config.in_channels, height, width)		,				generator=__a		,				)
        a__     : Tuple  =decimal_to_bits(__a							) * self.bit_scale
        a__     : int  =latents.to(self.device							)

        self.scheduler.set_timesteps(__a							)

        for t in self.progress_bar(self.scheduler.timesteps							):
          # predict the noise residual
          a__     : Tuple  =self.unet(__a		,				__a							).sample

          # compute the previous noisy sample x_t -> x_t-1
          a__     : int  =self.scheduler.step(__a		,				__a		,				__a							).prev_sample

        a__     : Tuple  =bits_to_decimal(__a							)

        if output_type == "pil":
          a__     : Any  =self.numpy_to_pil(__a							)

        if not return_dict:
          return (image,)

        return ImagePipelineOutput(images=__a							)













from __future__ import annotations

import math
def 					_A	(		SCREAMING_SNAKE_CASE					:       int						):





  """simple docstring"""



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

  a__     : Union[str, Any]  =[True] * (num + 1)
  a__     : Union[str, Any]  =[]
  a__     : str  =2
  a__     : Any  =int(math.sqrt(SCREAMING_SNAKE_CASE						)						)

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

      # Set multiples of start be False
      for i in range(start * start	,	num + 1	,	SCREAMING_SNAKE_CASE						):
        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(SCREAMING_SNAKE_CASE						)

  return prime


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






