'''simple docstring'''
from __future__ import annotations

from collections.abc import Generator



def  __lowerCamelCase       (      ):


      '''simple docstring'''


      UpperCAmelCase_            =  {}
      UpperCAmelCase_            =  2
      while True:
            UpperCAmelCase_            =  factor_map.pop(_UpperCamelCase							,    _UpperCamelCase					)
            if factor:
                  UpperCAmelCase_            =  factor + prime
                  while x in factor_map:
                        x += factor
                  UpperCAmelCase_            =  factor
            else:
                  UpperCAmelCase_            =  prime
                  yield prime
            prime += 1



def  __lowerCamelCase       (      _UpperCamelCase  :  float = 1E10					):


      '''simple docstring'''


      UpperCAmelCase_            =  sieve()

      UpperCAmelCase_            =  1
      while True:
            UpperCAmelCase_            =  next(_UpperCamelCase					)
            if (2 * prime * n) > limit:
                  return n
            # Ignore the next prime as the reminder will be 2.
            next(_UpperCamelCase					)
            n += 2


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






'''simple docstring'''
import gc
import unittest

import numpy as np
import torch

from diffusers import StableDiffusionKDiffusionPipeline
from diffusers.utils import slow, torch_device
from diffusers.utils.testing_utils import enable_full_determinism, require_torch_gpu


enable_full_determinism()







@slow
@require_torch_gpu
class lowerCamelCase							(	unittest.TestCase					):




  '''simple docstring'''



  def  lowerCAmelCase__ (      self			:       Any  )				->Optional[int]:
        # clean up the VRAM after each test
        super().tearDown()
        gc.collect()
        torch.cuda.empty_cache()






  def  lowerCAmelCase__ (      self			:       str  )				->List[str]:
        UpperCAmelCase_            =  StableDiffusionKDiffusionPipeline.from_pretrained('''CompVis/stable-diffusion-v1-4'''  )
        UpperCAmelCase_            =  sd_pipe.to(UpperCAmelCase__  )
        sd_pipe.set_progress_bar_config(disable=UpperCAmelCase__  )

        sd_pipe.set_scheduler('''sample_euler'''  )

        UpperCAmelCase_            =  '''A painting of a squirrel eating a burger'''
        UpperCAmelCase_            =  torch.manual_seed(0  )
        UpperCAmelCase_            =  sd_pipe([prompt]  ,							generator=UpperCAmelCase__  ,							guidance_scale=9.0  ,							num_inference_steps=20  ,							output_type='''np'''  )

        UpperCAmelCase_            =  output.images

        UpperCAmelCase_            =  image[0, -3:, -3:, -1]

        assert image.shape == (1, 512, 512, 3)
        UpperCAmelCase_            =  np.array([0.0447, 0.0492, 0.0468, 0.0408, 0.0383, 0.0408, 0.0354, 0.0380, 0.0339]  )

        assert np.abs(image_slice.flatten() - expected_slice  ).max() < 1e-2






  def  lowerCAmelCase__ (      self			:       List[str]  )				->int:
        UpperCAmelCase_            =  StableDiffusionKDiffusionPipeline.from_pretrained('''stabilityai/stable-diffusion-2-1-base'''  )
        UpperCAmelCase_            =  sd_pipe.to(UpperCAmelCase__  )
        sd_pipe.set_progress_bar_config(disable=UpperCAmelCase__  )

        sd_pipe.set_scheduler('''sample_euler'''  )

        UpperCAmelCase_            =  '''A painting of a squirrel eating a burger'''
        UpperCAmelCase_            =  torch.manual_seed(0  )
        UpperCAmelCase_            =  sd_pipe([prompt]  ,							generator=UpperCAmelCase__  ,							guidance_scale=9.0  ,							num_inference_steps=20  ,							output_type='''np'''  )

        UpperCAmelCase_            =  output.images

        UpperCAmelCase_            =  image[0, -3:, -3:, -1]

        assert image.shape == (1, 512, 512, 3)
        UpperCAmelCase_            =  np.array([0.1237, 0.1320, 0.1438, 0.1359, 0.1390, 0.1132, 0.1277, 0.1175, 0.1112]  )

        assert np.abs(image_slice.flatten() - expected_slice  ).max() < 5e-1






  def  lowerCAmelCase__ (      self			:       List[Any]  )				->Optional[int]:
        UpperCAmelCase_            =  StableDiffusionKDiffusionPipeline.from_pretrained('''stabilityai/stable-diffusion-2-1-base'''  )
        UpperCAmelCase_            =  sd_pipe.to(UpperCAmelCase__  )
        sd_pipe.set_progress_bar_config(disable=UpperCAmelCase__  )

        sd_pipe.set_scheduler('''sample_dpmpp_2m'''  )

        UpperCAmelCase_            =  '''A painting of a squirrel eating a burger'''
        UpperCAmelCase_            =  torch.manual_seed(0  )
        UpperCAmelCase_            =  sd_pipe(
            [prompt]  ,							generator=UpperCAmelCase__  ,							guidance_scale=7.5  ,							num_inference_steps=15  ,							output_type='''np'''  ,							use_karras_sigmas=UpperCAmelCase__  ,							)

        UpperCAmelCase_            =  output.images

        UpperCAmelCase_            =  image[0, -3:, -3:, -1]

        assert image.shape == (1, 512, 512, 3)
        UpperCAmelCase_            =  np.array(
            [0.1138_1689, 0.1211_2921, 0.138_9457, 0.1254_9606, 0.124_4964, 0.1083_1517, 0.1156_2866, 0.1086_7816, 0.1049_9048]  )

        assert np.abs(image_slice.flatten() - expected_slice  ).max() < 1e-2





