


'''simple docstring'''



import inspect
from typing import List, Optional, Tuple, Union

import numpy as np
import PIL
import torch
import torch.utils.checkpoint

from ...models import UNetaDModel, VQModel
from ...schedulers import (
    DDIMScheduler,
    DPMSolverMultistepScheduler,
    EulerAncestralDiscreteScheduler,
    EulerDiscreteScheduler,
    LMSDiscreteScheduler,
    PNDMScheduler,
)
from ...utils import PIL_INTERPOLATION, randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput







def 			_UpperCamelCase					(						UpperCamelCase__    ):
			UpperCAmelCase__      ,				UpperCAmelCase__     :    Optional[Any]         =   image.size
			UpperCAmelCase__      ,				UpperCAmelCase__     :    Optional[Any]         =   (x - x % 3_2 for x in (w, h))  # resize to integer multiple of 32
			UpperCAmelCase__     :    Optional[Any]         =   image.resize((w, h)       ,					resample=PIL_INTERPOLATION["""lanczos"""]    )
			UpperCAmelCase__     :    Dict         =   np.array(UpperCamelCase__    ).astype(np.floataa    ) / 2_55.0
			UpperCAmelCase__     :    int         =   image[None].transpose(0       ,					3       ,					1       ,					2    )
			UpperCAmelCase__     :    List[str]         =   torch.from_numpy(UpperCamelCase__    )
			return 2.0 * image - 1.0


class 						_snake_case    (   a__		):




					def __init__(					self							,							_lowerCamelCase							,							_lowerCamelCase							,							_lowerCamelCase							,							):
								super().__init__()
								self.register_modules(vqvae=__UpperCAmelCase							,							unet=__UpperCAmelCase							,							scheduler=__UpperCAmelCase)




					@torch.no_grad()
					def __call__(					self							,							_lowerCamelCase = None							,							_lowerCamelCase = 1							,							_lowerCamelCase = 100							,							_lowerCamelCase = 0.0							,							_lowerCamelCase = None							,							_lowerCamelCase = "pil"							,							_lowerCamelCase = True							,							):


								if isinstance(__UpperCAmelCase							,							PIL.Image.Image):
											UpperCAmelCase__     :    Dict         =   1
								elif isinstance(__UpperCAmelCase							,							torch.Tensor):
											UpperCAmelCase__     :    List[Any]         =   image.shape[0]
								else:
											raise ValueError(f'''`image` has to be of type `PIL.Image.Image` or `torch.Tensor` but is {type(__UpperCAmelCase)}''')

								if isinstance(__UpperCAmelCase							,							PIL.Image.Image):
											UpperCAmelCase__     :    str         =   preprocess(__UpperCAmelCase)

								UpperCAmelCase__      ,				UpperCAmelCase__     :    Any         =   image.shape[-2:]

								# in_channels should be 6: 3 for latents, 3 for low resolution image
								UpperCAmelCase__     :    int         =   (batch_size, self.unet.config.in_channels // 2, height, width)
								UpperCAmelCase__     :    int         =   next(self.unet.parameters()).dtype

								UpperCAmelCase__     :    Dict         =   randn_tensor(__UpperCAmelCase							,							generator=__UpperCAmelCase							,							device=self.device							,							dtype=__UpperCAmelCase)

								UpperCAmelCase__     :    Any         =   image.to(device=self.device							,							dtype=__UpperCAmelCase)

								# set timesteps and move to the correct device
								self.scheduler.set_timesteps(__UpperCAmelCase							,							device=self.device)
								UpperCAmelCase__     :    Dict         =   self.scheduler.timesteps

								# scale the initial noise by the standard deviation required by the scheduler
								UpperCAmelCase__     :    Any         =   latents * self.scheduler.init_noise_sigma

								# prepare extra kwargs for the scheduler step, since not all schedulers have the same signature.
								# eta (η) is only used with the DDIMScheduler, it will be ignored for other schedulers.
								# eta corresponds to η in DDIM paper: https://arxiv.org/abs/2010.02502
								# and should be between [0, 1]
								UpperCAmelCase__     :    List[str]         =   """eta""" in set(inspect.signature(self.scheduler.step).parameters.keys())
								UpperCAmelCase__     :    str         =   {}
								if accepts_eta:
											UpperCAmelCase__     :    List[str]         =   eta

								for t in self.progress_bar(__UpperCAmelCase):
											# concat latents and low resolution image in the channel dimension.
											UpperCAmelCase__     :    int         =   torch.cat([latents, image]							,							dim=1)
											UpperCAmelCase__     :    List[Any]         =   self.scheduler.scale_model_input(__UpperCAmelCase							,							__UpperCAmelCase)
											# predict the noise residual
											UpperCAmelCase__     :    int         =   self.unet(__UpperCAmelCase							,							__UpperCAmelCase).sample
											# compute the previous noisy sample x_t -> x_t-1
											UpperCAmelCase__     :    List[Any]         =   self.scheduler.step(__UpperCAmelCase							,							__UpperCAmelCase							,							__UpperCAmelCase							,							**__UpperCAmelCase).prev_sample

								# decode the image latents with the VQVAE
								UpperCAmelCase__     :    str         =   self.vqvae.decode(__UpperCAmelCase).sample
								UpperCAmelCase__     :    Optional[int]         =   torch.clamp(__UpperCAmelCase							,							-1.0							,							1.0)
								UpperCAmelCase__     :    List[Any]         =   image / 2 + 0.5
								UpperCAmelCase__     :    Union[str, Any]         =   image.cpu().permute(0							,							2							,							3							,							1).numpy()

								if output_type == "pil":
											UpperCAmelCase__     :    str         =   self.numpy_to_pil(__UpperCAmelCase)

								if not return_dict:
											return (image,)

								return ImagePipelineOutput(images=__UpperCAmelCase)







import math
def 						_a    (      a :int )							->			list:
 a		  =      [True] * n
 a		  =      False
 a		  =      False
 a		  =      True

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

 a		  =      [2]

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

 return primes
def 						_a    (      a :int = 999_966_663_333 )							->			int:
 a		  =      math.floor(math.sqrt(a ) ) + 100
 a		  =      prime_sieve(a )

 a		  =      0
 a		  =      0
 a		  =      primes[prime_index]

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

  a		  =      last_prime**2
  a		  =      next_prime**2

  # Get numbers divisible by lps(current)
  a		  =      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)
  a		  =      upper_bound - next_prime
  while current > lower_bound:
   matches_sum += current
   current -= next_prime

  # Remove the numbers divisible by both ups and lps
  a		  =      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
  a		  =      next_prime
  prime_index += 1

 return matches_sum


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


