






"""simple docstring"""





from __future__ import annotations

import math







def   lowerCAmelCase_( SCREAMING_SNAKE_CASE ,	SCREAMING_SNAKE_CASE					)					->	float:
    """simple docstring"""

    UpperCamelCase__         =    u
    for i in range(1 ,	SCREAMING_SNAKE_CASE					):
        UpperCamelCase__         =    temp * (u - i)
    return temp







def   lowerCAmelCase_( )					->	None:
    """simple docstring"""

    UpperCamelCase__         =    int(input('enter the numbers of values: '					)					)
    UpperCamelCase__         =    []
    for _ in range(SCREAMING_SNAKE_CASE					):
        y.append([]					)
    for i in range(SCREAMING_SNAKE_CASE					):
        for j in range(SCREAMING_SNAKE_CASE					):
            y[i].append(SCREAMING_SNAKE_CASE					)
            UpperCamelCase__         =    0

    print('enter the values of parameters in a list: '					)
    UpperCamelCase__         =    list(map(SCREAMING_SNAKE_CASE ,	input().split()					)					)

    print('enter the values of corresponding parameters: '					)
    for i in range(SCREAMING_SNAKE_CASE					):
        UpperCamelCase__         =    float(input()					)

    UpperCamelCase__         =    int(input('enter the value to interpolate: '					)					)
    UpperCamelCase__         =    (value - x[0]) / (x[1] - x[0])

    # for calculating forward difference table

    for i in range(1 ,	SCREAMING_SNAKE_CASE					):
        for j in range(n - i					):
            UpperCamelCase__         =    y[j + 1][i - 1] - y[j][i - 1]

    UpperCamelCase__         =    y[0][0]
    for i in range(1 ,	SCREAMING_SNAKE_CASE					):
        summ += (ucal(SCREAMING_SNAKE_CASE ,	SCREAMING_SNAKE_CASE					) * y[0][i]) / math.factorial(SCREAMING_SNAKE_CASE					)

    print(F'the value at {value} is {summ}'					)


if __name__ == "__main__":
  main()












"""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




