






'''simple docstring'''




import math
from typing import Callable, List, Optional, Union

import numpy as np
import PIL
import torch
from PIL import Image
from transformers import CLIPTextModel, CLIPTokenizer

from diffusers.models import AutoencoderKL, UNetaDConditionModel
from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion_upscale import StableDiffusionUpscalePipeline
from diffusers.schedulers import DDIMScheduler, DDPMScheduler, LMSDiscreteScheduler, PNDMScheduler

def    __lowercase		(     __lowercase  ,    __lowercase  ,    __lowercase=[]			)			->		Optional[int]:

      '''simple docstring'''


      _A     	=      size[0] - overlap_pixels * 2
      _A     	=      size[1] - overlap_pixels * 2
      for letter in ["l", "r"]:
            if letter in remove_borders:
                  size_x += overlap_pixels
      for letter in ["t", "b"]:
            if letter in remove_borders:
                  size_y += overlap_pixels
      _A     	=      np.ones((size_y, size_x)  ,    dtype=np.uinta			) * 255
      _A     	=      np.pad(lowerCAmelCase__  ,    mode="linear_ramp"  ,    pad_width=lowerCAmelCase__  ,    end_values=0			)

      if "l" in remove_borders:
            _A     	=      mask[:, overlap_pixels : mask.shape[1]]
      if "r" in remove_borders:
            _A     	=      mask[:, 0 : mask.shape[1] - overlap_pixels]
      if "t" in remove_borders:
            _A     	=      mask[overlap_pixels : mask.shape[0], :]
      if "b" in remove_borders:
            _A     	=      mask[0 : mask.shape[0] - overlap_pixels, :]
      return mask

def    __lowercase		(     __lowercase  ,    __lowercase  ,    __lowercase			)			->		Optional[int]:

      '''simple docstring'''


      return max(lowerCAmelCase__  ,    min(lowerCAmelCase__  ,    lowerCAmelCase__			)			)

def    __lowercase		(     __lowercase  ,    __lowercase  ,    __lowercase			)			->		Dict:

      '''simple docstring'''


      return (
          clamp(rect[0]  ,    min[0]  ,    max[0]			),
          clamp(rect[1]  ,    min[1]  ,    max[1]			),
          clamp(rect[2]  ,    min[0]  ,    max[0]			),
          clamp(rect[3]  ,    min[1]  ,    max[1]			),
      )

def    __lowercase		(     __lowercase  ,    __lowercase  ,    __lowercase			)			->		Optional[int]:

      '''simple docstring'''


      _A     	=      list(lowerCAmelCase__			)
      rect[0] -= overlap
      rect[1] -= overlap
      rect[2] += overlap
      rect[3] += overlap
      _A     	=      clamp_rect(lowerCAmelCase__  ,    [0, 0]  ,    [image_size[0], image_size[1]]			)
      return rect

def    __lowercase		(     __lowercase  ,    __lowercase  ,    __lowercase  ,    __lowercase			)			->		List[Any]:

      '''simple docstring'''


      _A     	=      Image.new("RGB"  ,    (tile.size[0] + original_slice, tile.size[1])			)
      result.paste(
          original_image.resize((tile.size[0], tile.size[1])  ,    Image.BICUBIC			).crop(
              (slice_x, 0, slice_x + original_slice, tile.size[1])			)  ,    (0, 0)  ,    )
      result.paste(lowerCAmelCase__  ,    (original_slice, 0)			)
      return result

def    __lowercase		(     __lowercase  ,    __lowercase			)			->		Union[str, Any]:

      '''simple docstring'''


      _A     	=      (original_image_slice * 4, 0, tile.size[0], tile.size[1])
      _A     	=      tile.crop(lowerCAmelCase__			)
      return tile

def    __lowercase		(     __lowercase  ,    __lowercase			)			->		int:

      '''simple docstring'''


      _A     	=      n % d
      return n - divisor

class   _UpperCAmelCase     (	snake_case_		):




   """simple docstring"""

   def __init__(						self					:      Tuple , __UpperCAmelCase					:      Tuple , __UpperCAmelCase					:      str , __UpperCAmelCase					:      Tuple , __UpperCAmelCase					:      Dict , __UpperCAmelCase					:      Union[str, Any] , __UpperCAmelCase					:      Dict , __UpperCAmelCase					:      int = 350 , ):





         '''simple docstring'''





         super().__init__(
             vae=__UpperCAmelCase , text_encoder=__UpperCAmelCase , tokenizer=__UpperCAmelCase , unet=__UpperCAmelCase , low_res_scheduler=__UpperCAmelCase , scheduler=__UpperCAmelCase , max_noise_level=__UpperCAmelCase , )

   def 		lowerCAmelCase					(						self					:      Any , __UpperCAmelCase					:      List[str] , __UpperCAmelCase					:      Tuple , __UpperCAmelCase					:      str , __UpperCAmelCase					:      Tuple , __UpperCAmelCase					:      Optional[Any] , __UpperCAmelCase					:      Optional[Any] , __UpperCAmelCase					:      Any , **__UpperCAmelCase					:      List[Any]						):





         '''simple docstring'''





         torch.manual_seed(0						)
         _A     	=      (
             min(image.size[0] - (tile_size + original_image_slice) , x * tile_size						),
             min(image.size[1] - (tile_size + original_image_slice) , y * tile_size						),
             min(image.size[0] , (x + 1) * tile_size						),
             min(image.size[1] , (y + 1) * tile_size						),
         )
         _A     	=      add_overlap_rect(__UpperCAmelCase , __UpperCAmelCase , image.size						)
         _A     	=      image.crop(__UpperCAmelCase						)
         _A     	=      ((crop_rect[0] + ((crop_rect[2] - crop_rect[0]) / 2)) / image.size[0]) * tile.size[0]
         _A     	=      translated_slice_x - (original_image_slice / 2)
         _A     	=      max(0 , __UpperCAmelCase						)
         _A     	=      squeeze_tile(__UpperCAmelCase , __UpperCAmelCase , __UpperCAmelCase , __UpperCAmelCase						)
         _A     	=      to_input.size
         _A     	=      to_input.resize((tile_size, tile_size) , Image.BICUBIC						)
         _A     	=      super(__UpperCAmelCase , self						).__call__(image=__UpperCAmelCase , **__UpperCAmelCase						).images[0]
         _A     	=      upscaled_tile.resize((orig_input_size[0] * 4, orig_input_size[1] * 4) , Image.BICUBIC						)
         _A     	=      unsqueeze_tile(__UpperCAmelCase , __UpperCAmelCase						)
         _A     	=      upscaled_tile.resize((tile.size[0] * 4, tile.size[1] * 4) , Image.BICUBIC						)
         _A     	=      []
         if x == 0:
               remove_borders.append("l"						)
         elif crop_rect[2] == image.size[0]:
               remove_borders.append("r"						)
         if y == 0:
               remove_borders.append("t"						)
         elif crop_rect[3] == image.size[1]:
               remove_borders.append("b"						)
         _A     	=      Image.fromarray(
             make_transparency_mask(
                 (upscaled_tile.size[0], upscaled_tile.size[1]) , tile_border * 4 , remove_borders=__UpperCAmelCase						) , mode="L" , )
         final_image.paste(
             __UpperCAmelCase , (crop_rect_with_overlap[0] * 4, crop_rect_with_overlap[1] * 4) , __UpperCAmelCase						)

   @torch.no_grad()
   def __call__(						self					:      Optional[int] , __UpperCAmelCase					:      Dict , __UpperCAmelCase					:      List[Any] , __UpperCAmelCase					:      Union[str, Any] = 75 , __UpperCAmelCase					:      Optional[int] = 9.0 , __UpperCAmelCase					:      List[Any] = 50 , __UpperCAmelCase					:      Optional[int] = None , __UpperCAmelCase					:      List[str] = 1 , __UpperCAmelCase					:      List[str] = 0.0 , __UpperCAmelCase					:      Optional[int] = None , __UpperCAmelCase					:      str = None , __UpperCAmelCase					:      Dict = None , __UpperCAmelCase					:      Optional[Any] = 1 , __UpperCAmelCase					:      List[Any] = 128 , __UpperCAmelCase					:      Optional[Any] = 32 , __UpperCAmelCase					:      Tuple = 32 , ):





         '''simple docstring'''





         _A     	=      Image.new("RGB" , (image.size[0] * 4, image.size[1] * 4)						)
         _A     	=      math.ceil(image.size[0] / tile_size						)
         _A     	=      math.ceil(image.size[1] / tile_size						)
         _A     	=      tcx * tcy
         _A     	=      0
         for y in range(__UpperCAmelCase						):
               for x in range(__UpperCAmelCase						):
                     self._process_tile(
                         __UpperCAmelCase , __UpperCAmelCase , __UpperCAmelCase , __UpperCAmelCase , __UpperCAmelCase , __UpperCAmelCase , __UpperCAmelCase , prompt=__UpperCAmelCase , num_inference_steps=__UpperCAmelCase , guidance_scale=__UpperCAmelCase , noise_level=__UpperCAmelCase , negative_prompt=__UpperCAmelCase , num_images_per_prompt=__UpperCAmelCase , eta=__UpperCAmelCase , generator=__UpperCAmelCase , latents=__UpperCAmelCase , )
                     current_count += 1
                     if callback is not None:
                           callback({"progress": current_count / total_tile_count, "image": final_image}						)
         return final_image





def    __lowercase		(     )			->		Optional[int]:

      '''simple docstring'''


      _A     	=      "stabilityai/stable-diffusion-x4-upscaler"
      _A     	=      StableDiffusionTiledUpscalePipeline.from_pretrained(lowerCAmelCase__  ,    revision="fp16"  ,    torch_dtype=torch.floataa			)
      _A     	=      pipe.to("cuda"			)
      _A     	=      Image.open("../../docs/source/imgs/diffusers_library.jpg"			)

      def callback(__lowercase			):
            print(F'''progress: {obj['progress']:.4f}'''			)
            obj["image"].save("diffusers_library_progress.jpg"			)

      _A     	=      pipe(image=lowerCAmelCase__  ,    prompt="Black font, white background, vector"  ,    noise_level=40  ,    callback=lowerCAmelCase__			)
      final_image.save("diffusers_library.jpg"			)


if __name__ == "__main__":
    main()







"""simple docstring"""


import math






def  lowercase						(	lowerCAmelCase__						):
			lowerCamelCase_					=  [True] * n
			lowerCamelCase_					=  False
			lowerCamelCase_					=  False
			lowerCamelCase_					=  True

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

			lowerCamelCase_					=  [2]

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

			return primes






def  lowercase						(	lowerCAmelCase__ = 999_966_663_333						):
			lowerCamelCase_					=  math.floor(math.sqrt(lowerCAmelCase__						)						) + 100
			lowerCamelCase_					=  prime_sieve(lowerCAmelCase__						)

			lowerCamelCase_					=  0
			lowerCamelCase_					=  0
			lowerCamelCase_					=  primes[prime_index]

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

						lowerCamelCase_					=  last_prime**2
						lowerCamelCase_					=  next_prime**2

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

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

			return matches_sum


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



