






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


def 							lowercase_				(    __A :       int			)       ->      Any:



 """simple docstring"""




 lowercase					:   int				  =(images / 2 + 0.5).clamp(0					,      1			)
 lowercase					:   List[Any]				  =images.cpu().permute(0					,      2					,      3					,      1			).float().numpy()
 lowercase					:   List[str]				  =numpy_to_pil(snake_case_			)
 return images





def 							lowercase_				(    __A :       Optional[int]			)       ->      Tuple:



 """simple docstring"""




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

 return pil_images











'''simple docstring'''



from __future__ import annotations

import math


def 							lowercase_				(    __A :       float					,      __A :       int			)       ->      float:



 """simple docstring"""




 lowercase					:   str				  =u
 for i in range(1					,      __A			):
  lowercase					:   Any				  =temp * (u - i)
 return temp


def 							lowercase_				(    )       ->      None:



 """simple docstring"""




 lowercase					:   List[str]				  =int(input('''enter the numbers of values: '''			)			)
 lowercase					:   list[list[float]]				  =[]
 for _ in range(__A			):
  y.append([]			)
 for i in range(__A			):
  for j in range(__A			):
   y[i].append(__A			)
   lowercase					:   List[Any]				  =0

 print('''enter the values of parameters in a list: '''			)
 lowercase					:   Optional[int]				  =list(map(__A					,      input().split()			)			)

 print('''enter the values of corresponding parameters: '''			)
 for i in range(__A			):
  lowercase					:   str				  =float(input()			)

 lowercase					:   int				  =int(input('''enter the value to interpolate: '''			)			)
 lowercase					:   Union[str, Any]				  =(value - x[0]) / (x[1] - x[0])

 # for calculating forward difference table

 for i in range(1					,      __A			):
  for j in range(n - i			):
   lowercase					:   str				  =y[j + 1][i - 1] - y[j][i - 1]

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

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


if __name__ == "__main__":
      main()



