


from __future__ import annotations

import math





def 	_lowerCAmelCase       (    _lowerCAmelCase      ,	_lowerCAmelCase )						->	Optional[int]:


						'''simple docstring'''






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





def 	_lowerCAmelCase       (    )						->	Dict:


						'''simple docstring'''






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

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

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

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

						# for calculating forward difference table

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

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

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


if __name__ == "__main__":
	main()










from __future__ import annotations

from collections.abc import Iterator






class     UpperCamelCase:


					def __init__(						self	:		Union[str, Any]     ,    SCREAMING_SNAKE_CASE	:		int						)			->	None:




											'''simple docstring'''

											__snake_case				=		value
											__snake_case				=		None
											__snake_case				=		None






class     UpperCamelCase:


					def __init__(						self	:		int     ,    SCREAMING_SNAKE_CASE	:		Node						)			->	None:




											'''simple docstring'''

											__snake_case				=		tree


					def 							SCREAMING_SNAKE_CASE_  (						self	:		List[str]     ,    SCREAMING_SNAKE_CASE	:		Node | None						)			->	int:




											'''simple docstring'''

											if node is None:
																	return 0
											return node.value + (
											    self.depth_first_search(node.left						) + self.depth_first_search(node.right						)
											)






					def __iter__(						self	:		int						)			->	Iterator[int]:




											'''simple docstring'''

											yield self.depth_first_search(self.tree						)


if __name__ == "__main__":
	import doctest

	doctest.testmod()





