
from __future__ import annotations

import math



def 							lowerCamelCase_	( __UpperCamelCase			,    __UpperCamelCase  ):
				A_													=	u
				for i in range(1			,    SCREAMING_SNAKE_CASE__  ):
								A_													=	temp * (u - i)
				return temp



def 							lowerCamelCase_	( ):
				A_													=	int(input('''enter the numbers of values: '''  )  )
				A_													=	[]
				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__  )
												A_													=	0

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

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

				A_													=	int(input('''enter the value to interpolate: '''  )  )
				A_													=	(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  ):
												A_													=	y[j + 1][i - 1] - y[j][i - 1]

				A_													=	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'''



from typing import List, Optional, Union

import numpy as np
import PIL.Image

from ...image_processing_utils import BaseImageProcessor, BatchFeature
from ...image_transforms import rescale, resize, to_channel_dimension_format
from ...image_utils import (
    ChannelDimension,
    PILImageResampling,
    get_image_size,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, logging


__UpperCamelCase   :							Dict         =   logging.get_logger(__name__)
class 				__SCREAMING_SNAKE_CASE							(				_lowerCAmelCase  ):
      __a	       =["pixel_values"]




      def __init__(	self			, lowerCamelCase = True			, lowerCamelCase = 32			, lowerCamelCase=PILImageResampling.BILINEAR			, lowerCamelCase = True			, **lowerCamelCase			, )				->None:



         '''simple docstring'''
         __a					  =     do_resize
         __a					  =     do_rescale
         __a					  =     size_divisor
         __a					  =     resample
         super().__init__(**lowerCamelCase   )




      def 			__UpperCamelCase				(	self			, lowerCamelCase			, lowerCamelCase			, lowerCamelCase			, lowerCamelCase = None			, **lowerCamelCase   )				->np.ndarray:



         '''simple docstring'''
         __a  ,      __a					  =     get_image_size(lowerCamelCase   )
         # Rounds the height and width down to the closest multiple of size_divisor
         __a					  =     height // size_divisor * size_divisor
         __a					  =     width // size_divisor * size_divisor
         __a					  =     resize(lowerCamelCase			, (new_h, new_w)			, resample=lowerCamelCase			, data_format=lowerCamelCase			, **lowerCamelCase   )
         return image




      def 			__UpperCamelCase				(	self			, lowerCamelCase			, lowerCamelCase			, lowerCamelCase = None			, **lowerCamelCase   )				->np.ndarray:



         '''simple docstring'''
         return rescale(image=lowerCamelCase			, scale=lowerCamelCase			, data_format=lowerCamelCase			, **lowerCamelCase   )






      def 			__UpperCamelCase				(	self			, lowerCamelCase			, lowerCamelCase = None			, lowerCamelCase = None			, lowerCamelCase=None			, lowerCamelCase = None			, lowerCamelCase = None			, lowerCamelCase = ChannelDimension.FIRST			, **lowerCamelCase			, )				->BatchFeature:



         '''simple docstring'''
         __a					  =     do_resize if do_resize is not None else self.do_resize
         __a					  =     do_rescale if do_rescale is not None else self.do_rescale
         __a					  =     size_divisor if size_divisor is not None else self.size_divisor
         __a					  =     resample if resample is not None else self.resample

         if do_resize and size_divisor is None:
            raise ValueError('size_divisor is required for resizing'   )

         __a					  =     make_list_of_images(lowerCamelCase   )

         if not valid_images(lowerCamelCase   ):
            raise ValueError('Invalid image(s)'   )

         # All transformations expect numpy arrays.
         __a					  =     [to_numpy_array(lowerCamelCase   ) for img in images]

         if do_resize:
            __a					  =     [self.resize(lowerCamelCase			, size_divisor=lowerCamelCase			, resample=lowerCamelCase   ) for image in images]

         if do_rescale:
            __a					  =     [self.rescale(lowerCamelCase			, scale=1 / 255   ) for image in images]

         __a					  =     [to_channel_dimension_format(lowerCamelCase			, lowerCamelCase   ) for image in images]

         __a					  =     {'pixel_values': images}
         return BatchFeature(data=lowerCamelCase			, tensor_type=lowerCamelCase   )