






'''simple docstring'''


from math import isqrt







def 	__magic_name__( _A					):
						'''simple docstring'''





						UpperCamelCase__         = [True] * max_number
						for i in range(2						,      isqrt(max_number - 1					) + 1					):
												if is_prime[i]:
																		for j in range(i**2						,      snake_case__						,      snake_case__					):
																								UpperCamelCase__         = False

						return [i for i in range(2						,      snake_case__					) if is_prime[i]]







def 	__magic_name__( _A = 10**8					):
						'''simple docstring'''





						UpperCamelCase__         = calculate_prime_numbers(max_number // 2					)

						UpperCamelCase__         = 0
						UpperCamelCase__         = 0
						UpperCamelCase__         = len(snake_case__					) - 1
						while left <= right:
												while prime_numbers[left] * prime_numbers[right] >= max_number:
																		right -= 1
												semiprimes_count += right - left + 1
												left += 1

						return semiprimes_count


if __name__ == "__main__":
					print(f"""{solution() = }""")












'''simple docstring'''


from typing import List, Optional, Tuple, Union

import PIL
import torch
from torchvision import transforms

from diffusers.pipeline_utils import DiffusionPipeline, ImagePipelineOutput
from diffusers.schedulers import DDIMScheduler
from diffusers.utils import randn_tensor


lowerCamelCase_				: str    	=							transforms.Compose(
    [
        transforms.Resize((256, 256)),
        transforms.ToTensor(),
        transforms.Normalize([0.5], [0.5]),
    ]
)







def 	__magic_name__( _A					):
						'''simple docstring'''





						if isinstance(_A						,      torch.Tensor					):
												return image
						elif isinstance(_A						,      PIL.Image.Image					):
												UpperCamelCase__         = [image]

						UpperCamelCase__         = [trans(img.convert("""RGB"""					)					) for img in image]
						UpperCamelCase__         = torch.stack(_A					)
						return image







class    _SCREAMING_SNAKE_CASE							(		SCREAMING_SNAKE_CASE	):


			'''simple docstring'''





			def __init__(   self							:						Tuple ,      lowercase							:						Dict ,      lowercase							:						Optional[Any]			)							->    Any:

									'''simple docstring'''







									super().__init__()

									# make sure scheduler can always be converted to DDIM
									UpperCamelCase__         = DDIMScheduler.from_config(scheduler.config			)

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






			def 				A      (   self							:						Tuple ,      lowercase							:						Tuple			)							->    Any:

									'''simple docstring'''







									if strength < 0 or strength > 1:
															raise ValueError(f"The value of strength should in [0.0, 1.0] but is {strength}"			)






			def 				A      (   self							:						str ,      lowercase							:						List[Any] ,      lowercase							:						Dict ,      lowercase							:						List[str]			)							->    str:

									'''simple docstring'''







									UpperCamelCase__         = min(int(num_inference_steps * strength			) ,      lowercase			)

									UpperCamelCase__         = max(num_inference_steps - init_timestep ,      0			)
									UpperCamelCase__         = self.scheduler.timesteps[t_start:]

									return timesteps, num_inference_steps - t_start






			def 				A      (   self							:						Union[str, Any] ,      lowercase							:						Optional[Any] ,      lowercase							:						Any ,      lowercase							:						Union[str, Any] ,      lowercase							:						Dict ,      lowercase							:						Tuple ,      lowercase							:						int=None			)							->    int:

									'''simple docstring'''







									if not isinstance(lowercase ,      (torch.Tensor, PIL.Image.Image, list)			):
															raise ValueError(
															    f"`image` has to be of type `torch.Tensor`, `PIL.Image.Image` or list but is {type(lowercase			)}"			)

									UpperCamelCase__         = image.to(device=lowercase ,      dtype=lowercase			)

									if isinstance(lowercase ,      lowercase			) and len(lowercase			) != batch_size:
															raise ValueError(
															    f"You have passed a list of generators of length {len(lowercase			)}, but requested an effective batch"
															    f" size of {batch_size}. Make sure the batch size matches the length of the generators."			)

									UpperCamelCase__         = init_latents.shape
									UpperCamelCase__         = randn_tensor(lowercase ,      generator=lowercase ,      device=lowercase ,      dtype=lowercase			)

									# get latents
									print("""add noise to latents at timestep""" ,      lowercase			)
									UpperCamelCase__         = self.scheduler.add_noise(lowercase ,      lowercase ,      lowercase			)
									UpperCamelCase__         = init_latents

									return latents







			@torch.no_grad()
			def __call__(   self							:						Any ,      lowercase							:						Union[torch.FloatTensor, PIL.Image.Image] = None ,      lowercase							:						float = 0.8 ,      lowercase							:						int = 1 ,      lowercase							:						Optional[Union[torch.Generator, List[torch.Generator]]] = None ,      lowercase							:						float = 0.0 ,      lowercase							:						int = 5_0 ,      lowercase							:						Optional[bool] = None ,      lowercase							:						Optional[str] = "pil" ,      lowercase							:						bool = True ,      )							->    Union[ImagePipelineOutput, Tuple]:

									'''simple docstring'''







									self.check_inputs(lowercase			)

									# 2. Preprocess image
									UpperCamelCase__         = preprocess(lowercase			)

									# 3. set timesteps
									self.scheduler.set_timesteps(lowercase ,      device=self.device			)
									UpperCamelCase__    ,   UpperCamelCase__         = self.get_timesteps(lowercase ,      lowercase ,      self.device			)
									UpperCamelCase__         = timesteps[:1].repeat(lowercase			)

									# 4. Prepare latent variables
									UpperCamelCase__         = self.prepare_latents(lowercase ,      lowercase ,      lowercase ,      self.unet.dtype ,      self.device ,      lowercase			)
									UpperCamelCase__         = latents

									# 5. Denoising loop
									for t in self.progress_bar(lowercase			):
															# 1. predict noise model_output
															UpperCamelCase__         = self.unet(lowercase ,      lowercase			).sample

															# 2. predict previous mean of image x_t-1 and add variance depending on eta
															# eta corresponds to η in paper and should be between [0, 1]
															# do x_t -> x_t-1
															UpperCamelCase__         = self.scheduler.step(
															    lowercase ,      lowercase ,      lowercase ,      eta=lowercase ,      use_clipped_model_output=lowercase ,      generator=lowercase ,      ).prev_sample

									UpperCamelCase__         = (image / 2 + 0.5).clamp(0 ,      1			)
									UpperCamelCase__         = image.cpu().permute(0 ,      2 ,      3 ,      1			).numpy()
									if output_type == "pil":
															UpperCamelCase__         = self.numpy_to_pil(lowercase			)

									if not return_dict:
															return (image, latent_timestep.item())

									return ImagePipelineOutput(images=lowercase			)
