



'''simple docstring'''

from __future__ import annotations

import math







def 						__UpperCamelCase				(							_lowercase,				_lowercase					) ->			float:
	_lowercase					:       str       =		u
	for i in range(1,				_lowercase					):
		_lowercase					:       str       =		temp * (u - i)
	return temp







def 						__UpperCamelCase				(							) ->			None:
	_lowercase					:       Any       =		int(input('enter the numbers of values: '					)					)
	_lowercase					:       list[list[float]]       =		[]
	for _ in range(_lowercase					):
		y.append([]					)
	for i in range(_lowercase					):
		for j in range(_lowercase					):
			y[i].append(_lowercase					)
			_lowercase					:       List[str]       =		0

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

	print('enter the values of corresponding parameters: '					)
	for i in range(_lowercase					):
		_lowercase					:       Union[str, Any]       =		float(input()					)

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

	# for calculating forward difference table

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

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

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


if __name__ == "__main__":
		main()





'''simple docstring'''

_A				:    Optional[Any]     						='''ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/'''







def 						__UpperCamelCase				(							_lowercase					) ->			bytes:
	# Make sure the supplied data is a bytes-like object
	if not isinstance(_lowercase,				_lowercase					):
		_lowercase					:       Union[str, Any]       =		f'''a bytes-like object is required, not \'{data.__class__.__name__}\''''
		raise TypeError(_lowercase					)

	_lowercase					:       int       =		''.join(bin(_lowercase					)[2:].zfill(8					) for byte in data					)

	_lowercase					:       Dict       =		len(_lowercase					) % 6 != 0

	if padding_needed:
		# The padding that will be added later
		_lowercase					:       Optional[Any]       =		B'=' * ((6 - len(_lowercase					) % 6) // 2)

		# Append binary_stream with arbitrary binary digits (0's by default) to make its
		# length a multiple of 6.
		binary_stream += "0" * (6 - len(_lowercase					) % 6)
	else:
		_lowercase					:       Optional[int]       =		B''

	# Encode every 6 binary digits to their corresponding Base64 character
	return (
	    "".join(
	        B64_CHARSET[int(binary_stream[index : index + 6],				2					)]
	        for index in range(0,				len(_lowercase					),				6					)					).encode()
	    + padding
	)







def 						__UpperCamelCase				(							_lowercase					) ->			bytes:
	# Make sure encoded_data is either a string or a bytes-like object
	if not isinstance(_lowercase,				_lowercase					) and not isinstance(_lowercase,				_lowercase					):
		_lowercase					:       int       =		(
		    'argument should be a bytes-like object or ASCII string, '
		    f'''not \'{encoded_data.__class__.__name__}\''''
		)
		raise TypeError(_lowercase					)

	# In case encoded_data is a bytes-like object, make sure it contains only
	# ASCII characters so we convert it to a string object
	if isinstance(_lowercase,				_lowercase					):
		try:
			_lowercase					:       Optional[int]       =		encoded_data.decode('utf-8'					)
		except UnicodeDecodeError:
			raise ValueError('base64 encoded data should only contain ASCII characters'					)

	_lowercase					:       Optional[int]       =		encoded_data.count('='					)

	# Check if the encoded string contains non base64 characters
	if padding:
		assert all(
		    char in B64_CHARSET for char in encoded_data[:-padding]					), "Invalid base64 character(s) found."
	else:
		assert all(
		    char in B64_CHARSET for char in encoded_data					), "Invalid base64 character(s) found."

	# Check the padding
	assert len(_lowercase					) % 4 == 0 and padding < 3, "Incorrect padding"

	if padding:
		# Remove padding if there is one
		_lowercase					:       str       =		encoded_data[:-padding]

		_lowercase					:       Tuple       =		''.join(
		    bin(B64_CHARSET.index(_lowercase					)					)[2:].zfill(6					) for char in encoded_data					)[: -padding * 2]
	else:
		_lowercase					:       Union[str, Any]       =		''.join(
		    bin(B64_CHARSET.index(_lowercase					)					)[2:].zfill(6					) for char in encoded_data					)

	_lowercase					:       List[str]       =		[
	    int(binary_stream[index : index + 8],				2					)
	    for index in range(0,				len(_lowercase					),				8					)
	]

	return bytes(_lowercase					)


if __name__ == "__main__":
		import doctest

		doctest.testmod()
