






'''simple docstring'''



import math
import sys


def 							lowercase_				(    __A :       int			)       ->      int:



 """simple docstring"""




 if number != int(__A			):
  raise ValueError('''the value of input must be a natural number'''			)
 if number < 0:
  raise ValueError('''the value of input must not be a negative number'''			)
 if number == 0:
  return 1
 lowercase					:   List[str]				  =[-1] * (number + 1)
 lowercase					:   Dict				  =0
 for i in range(1					,      number + 1			):
  lowercase					:   Union[str, Any]				  =sys.maxsize
  lowercase					:   List[Any]				  =int(math.sqrt(__A			)			)
  for j in range(1					,      root + 1			):
   lowercase					:   Optional[Any]				  =1 + answers[i - (j**2)]
   lowercase					:   List[str]				  =min(__A					,      __A			)
  lowercase					:   Dict				  =answer
 return answers[number]


if __name__ == "__main__":
      import doctest

      doctest.testmod()











'''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()



