
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"):
    lowerCamelCase      ={
        "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:
    lowerCamelCase      ={
        "linear": PIL.Image.LINEAR,
        "bilinear": PIL.Image.BILINEAR,
        "bicubic": PIL.Image.BICUBIC,
        "lanczos": PIL.Image.LANCZOS,
        "nearest": PIL.Image.NEAREST,
    }


def 							SCREAMING_SNAKE_CASE_      (			UpperCamelCase__		):
      UpperCamelCase__    :   Dict					=				(images / 2 + 0.5).clamp(0 ,		1		)
      UpperCamelCase__    :   Dict					=				images.cpu().permute(0 ,		2 ,		3 ,		1		).float().numpy()
      UpperCamelCase__    :   str					=				numpy_to_pil(UpperCamelCase__		)
      return images


def 							SCREAMING_SNAKE_CASE_      (			UpperCamelCase__		):
      if images.ndim == 3:
            UpperCamelCase__    :   Tuple					=				images[None, ...]
      UpperCamelCase__    :   List[str]					=				(images * 2_5_5).round().astype('''uint8'''		)
      if images.shape[-1] == 1:
            # special case for grayscale (single channel) images
            UpperCamelCase__    :   int					=				[Image.fromarray(image.squeeze() ,		mode='''L'''		) for image in images]
      else:
            UpperCamelCase__    :   Optional[int]					=				[Image.fromarray(UpperCamelCase__		) for image in images]

      return pil_images




import math


def 							SCREAMING_SNAKE_CASE_      (			UpperCamelCase__		):
      UpperCamelCase__    :   List[str]					=				math.loga(math.sqrt(4 * positive_integer + 1		) / 2 + 1 / 2		)

      return exponent == int(UpperCamelCase__		)


def 							SCREAMING_SNAKE_CASE_      (			UpperCamelCase__ = 1 / 1_2_3_4_5		):
      UpperCamelCase__    :   Dict					=				0
      UpperCamelCase__    :   Tuple					=				0

      UpperCamelCase__    :   Optional[Any]					=				3
      while True:
            UpperCamelCase__    :   Union[str, Any]					=				(integer**2 - 1) / 4
            # if candidate is an integer, then there is a partition for k
            if partition_candidate == int(UpperCamelCase__		):
                  UpperCamelCase__    :   int					=				int(UpperCamelCase__		)
                  total_partitions += 1
                  if check_partition_perfect(UpperCamelCase__		):
                        perfect_partitions += 1
            if perfect_partitions > 0:
                  if perfect_partitions / total_partitions < max_proportion:
                        return int(UpperCamelCase__		)
            integer += 1


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


