






"""simple docstring"""





def   lowerCAmelCase_( SCREAMING_SNAKE_CASE = 50_00_00_00					)					->	int:
    """simple docstring"""

    UpperCamelCase__         =    set()
    UpperCamelCase__         =    int((limit - 24) ** (1 / 2)					)

    UpperCamelCase__         =    set(range(3 ,	prime_square_limit + 1 ,	2					)					)
    primes.add(2					)
    for p in range(3 ,	prime_square_limit + 1 ,	2					):
        if p not in primes:
            continue
        primes.difference_update(set(range(p * p ,	prime_square_limit + 1 ,	SCREAMING_SNAKE_CASE					)					)					)

    for primea in primes:
        UpperCamelCase__         =    primea * primea
        for primea in primes:
            UpperCamelCase__         =    primea * primea * primea
            if square + cube >= limit - 16:
                break
            for primea in primes:
                UpperCamelCase__         =    primea * primea * primea * primea
                UpperCamelCase__         =    square + cube + tetr
                if total >= limit:
                    break
                ret.add(SCREAMING_SNAKE_CASE					)

    return len(SCREAMING_SNAKE_CASE					)


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












"""simple docstring"""





import PIL.Image
import PIL.ImageOps
from packaging import version
from PIL import Image


if version.parse(version.parse(PIL.__version__).base_version) >= version.parse("""9.1.0"""):
  A__					: str=	{
      """linear""": PIL.Image.Resampling.BILINEAR,
      """bilinear""": PIL.Image.Resampling.BILINEAR,
      """bicubic""": PIL.Image.Resampling.BICUBIC,
      """lanczos""": PIL.Image.Resampling.LANCZOS,
      """nearest""": PIL.Image.Resampling.NEAREST,
  }
else:
  A__					: str=	{
      """linear""": PIL.Image.LINEAR,
      """bilinear""": PIL.Image.BILINEAR,
      """bicubic""": PIL.Image.BICUBIC,
      """lanczos""": PIL.Image.LANCZOS,
      """nearest""": PIL.Image.NEAREST,
  }







def   lowerCAmelCase_( SCREAMING_SNAKE_CASE					)					->	int:
    """simple docstring"""

    UpperCamelCase__         =    (images / 2 + 0.5).clamp(0 ,	1					)
    UpperCamelCase__         =    images.cpu().permute(0 ,	2 ,	3 ,	1					).float().numpy()
    UpperCamelCase__         =    numpy_to_pil(SCREAMING_SNAKE_CASE					)
    return images







def   lowerCAmelCase_( SCREAMING_SNAKE_CASE					)					->	Optional[int]:
    """simple docstring"""

    if images.ndim == 3:
        UpperCamelCase__         =    images[None, ...]
    UpperCamelCase__         =    (images * 2_55).round().astype('uint8'					)
    if images.shape[-1] == 1:
        # special case for grayscale (single channel) images
        UpperCamelCase__         =    [Image.fromarray(image.squeeze() ,	mode='L'					) for image in images]
    else:
        UpperCamelCase__         =    [Image.fromarray(SCREAMING_SNAKE_CASE					) for image in images]

    return pil_images




