





from math import isqrt, loga
def      _A       (		SCREAMING_SNAKE_CASE     :   int						):





  """simple docstring"""



  a__	:					Optional[Any]										=[True] * max_number
  for i in range(2       ,       isqrt(max_number - 1						) + 1						):
    if is_prime[i]:
      for j in range(i**2       ,       SCREAMING_SNAKE_CASE       ,       SCREAMING_SNAKE_CASE						):
        a__	:					List[Any]										=False

  return [i for i in range(2       ,       SCREAMING_SNAKE_CASE						) if is_prime[i]]
def      _A       (		SCREAMING_SNAKE_CASE     :   int = 800_800       ,       SCREAMING_SNAKE_CASE     :   int = 800_800						):





  """simple docstring"""



  a__	:					Union[str, Any]										=degree * loga(SCREAMING_SNAKE_CASE						)
  a__	:					List[str]										=int(SCREAMING_SNAKE_CASE						)
  a__	:					List[Any]										=calculate_prime_numbers(SCREAMING_SNAKE_CASE						)

  a__	:					Dict										=0
  a__	:					int										=0
  a__	:					Optional[int]										=len(SCREAMING_SNAKE_CASE						) - 1
  while left < right:
    while (
        prime_numbers[right] * loga(prime_numbers[left]						)
        + prime_numbers[left] * loga(prime_numbers[right]						)
        > upper_bound
    ):
      right -= 1
    hybrid_integers_count += right - left
    left += 1

  return hybrid_integers_count


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













import gc
import tempfile
import unittest

import numpy as np
import torch

from diffusers import VersatileDiffusionPipeline
from diffusers.utils.testing_utils import load_image, nightly, require_torch_gpu, torch_device


UpperCAmelCase	:	int		     =       False







class 				__lowerCAmelCase       (    unittest.TestCase):
      pass







@nightly
@require_torch_gpu
class 				__lowerCAmelCase       (    unittest.TestCase):







      def    _lowercase  (    self							)   ->						Tuple:



        '''simple docstring'''




        super().tearDown()
        gc.collect()
        torch.cuda.empty_cache()







      def    _lowercase  (    self							)   ->						Any:



        '''simple docstring'''




        a__	:					str										=VersatileDiffusionPipeline.from_pretrained("shi-labs/versatile-diffusion"		,      torch_dtype=torch.floataa							)
        pipe.to(lowerCAmelCase__							)
        pipe.set_progress_bar_config(disable=lowerCAmelCase__							)

        a__	:					int										=load_image(
            "https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main/versatile_diffusion/benz.jpg"							)

        a__	:					Optional[Any]										=torch.manual_seed(0							)
        a__	:					Optional[Any]										=pipe.dual_guided(
            prompt="first prompt"		,      image=lowerCAmelCase__		,      text_to_image_strength=0.75		,      generator=lowerCAmelCase__		,      guidance_scale=7.5		,      num_inference_steps=2		,      output_type="numpy"		,      ).images

        with tempfile.TemporaryDirectory() as tmpdirname:
          pipe.save_pretrained(lowerCAmelCase__							)
          a__	:					str										=VersatileDiffusionPipeline.from_pretrained(lowerCAmelCase__		,      torch_dtype=torch.floataa							)
        pipe.to(lowerCAmelCase__							)
        pipe.set_progress_bar_config(disable=lowerCAmelCase__							)

        a__	:					Optional[Any]										=generator.manual_seed(0							)
        a__	:					Tuple										=pipe.dual_guided(
            prompt="first prompt"		,      image=lowerCAmelCase__		,      text_to_image_strength=0.75		,      generator=lowerCAmelCase__		,      guidance_scale=7.5		,      num_inference_steps=2		,      output_type="numpy"		,      ).images

        assert np.abs(image - new_image							).sum() < 1E-5, "Models don't have the same forward pass"







      def    _lowercase  (    self							)   ->						Any:



        '''simple docstring'''




        a__	:					str										=VersatileDiffusionPipeline.from_pretrained("shi-labs/versatile-diffusion"		,      torch_dtype=torch.floataa							)
        pipe.to(lowerCAmelCase__							)
        pipe.set_progress_bar_config(disable=lowerCAmelCase__							)

        a__	:					Optional[Any]										="cyberpunk 2077"
        a__	:					int										=load_image(
            "https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main/versatile_diffusion/benz.jpg"							)
        a__	:					Union[str, Any]										=torch.manual_seed(0							)
        a__	:					Tuple										=pipe.dual_guided(
            prompt=lowerCAmelCase__		,      image=lowerCAmelCase__		,      text_to_image_strength=0.75		,      generator=lowerCAmelCase__		,      guidance_scale=7.5		,      num_inference_steps=5_0		,      output_type="numpy"		,      ).images

        a__	:					int										=image[0, 2_5_3:2_5_6, 2_5_3:2_5_6, -1]

        assert image.shape == (1, 5_1_2, 5_1_2, 3)
        a__	:					Any										=np.array([0.14_48, 0.16_19, 0.17_41, 0.10_86, 0.11_47, 0.11_28, 0.11_99, 0.11_65, 0.10_01]							)

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

        a__	:					str										="A painting of a squirrel eating a burger "
        a__	:					Optional[int]										=torch.manual_seed(0							)
        a__	:					str										=pipe.text_to_image(
            prompt=lowerCAmelCase__		,      generator=lowerCAmelCase__		,      guidance_scale=7.5		,      num_inference_steps=5_0		,      output_type="numpy"							).images

        a__	:					Any										=image[0, 2_5_3:2_5_6, 2_5_3:2_5_6, -1]

        assert image.shape == (1, 5_1_2, 5_1_2, 3)
        a__	:					Optional[int]										=np.array([0.33_67, 0.31_69, 0.26_56, 0.38_70, 0.47_90, 0.37_96, 0.40_09, 0.48_78, 0.47_78]							)

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

        a__	:					Optional[Any]										=pipe.image_variation(lowerCAmelCase__		,      generator=lowerCAmelCase__		,      output_type="numpy"							).images

        a__	:					Union[str, Any]										=image[0, 2_5_3:2_5_6, 2_5_3:2_5_6, -1]

        assert image.shape == (1, 5_1_2, 5_1_2, 3)
        a__	:					Any										=np.array([0.30_76, 0.31_23, 0.32_84, 0.37_82, 0.37_70, 0.38_94, 0.42_97, 0.43_31, 0.44_56]							)

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






