






from __future__ import annotations

import math







def       lowercase__	(					A_:						float  ,      A_:						int		)	->				float:







       """simple docstring"""






       __UpperCAmelCase     				=u
       for i in range(1  ,      A_		):
              __UpperCAmelCase     				=temp * (u - i)
       return temp







def       lowercase__	(					)	->				None:







       """simple docstring"""






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

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

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

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

       # for calculating forward difference table

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

       __UpperCAmelCase     				=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()











'''simple docstring'''

def    a__							(							lowercase   :	str )						->						int:





     """simple docstring"""

     assert column_title.isupper()
     _UpperCamelCase							       =			0
     _UpperCamelCase							       =			len(lowercase ) - 1
     _UpperCamelCase							       =			0

     while index >= 0:
          _UpperCamelCase							       =			(ord(column_title[index] ) - 64) * pow(26,   lowercase )
          answer += value
          power += 1
          index -= 1

     return answer


if __name__ == "__main__":
   from doctest import testmod

   testmod()



