





'''simple docstring'''




from __future__ import annotations

import math






def 			_lowerCAmelCase     (    __snake_case    :					float					,				__snake_case    :					int     )	->	float:
     __A		:					int						=			u
     for i in range(1					,				__snake_case     ):
          __A		:					Optional[int]						=			temp * (u - i)
     return temp






def 			_lowerCAmelCase     (    )	->	None:
     __A		:					Dict						=			int(input('enter the numbers of values: '     )     )
     __A		:					list[list[float]]						=			[]
     for _ in range(__snake_case     ):
          y.append([]     )
     for i in range(__snake_case     ):
          for j in range(__snake_case     ):
               y[i].append(__snake_case     )
               __A		:					int						=			0

     print('enter the values of parameters in a list: '     )
     __A		:					List[str]						=			list(map(__snake_case					,				input().split()     )     )

     print('enter the values of corresponding parameters: '     )
     for i in range(__snake_case     ):
          __A		:					Tuple						=			float(input()     )

     __A		:					Tuple						=			int(input('enter the value to interpolate: '     )     )
     __A		:					Dict						=			(value - x[0]) / (x[1] - x[0])

     # for calculating forward difference table

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

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

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


if __name__ == "__main__":
  main()



'''simple docstring'''





from ..utils import DummyObject, requires_backends




class 				UpperCAmelCase			(			metaclass=_snake_case						):
 UpperCAmelCase				=					["speech"]


 def __init__(      self							:	List[Any]			,       *__lowerCamelCase							:	List[Any]			,       **__lowerCamelCase							:	List[str] ):
    requires_backends(self			,       ['''speech'''] )




class 				UpperCAmelCase			(			metaclass=_snake_case						):
 UpperCAmelCase				=					["speech"]


 def __init__(      self							:	int			,       *__lowerCamelCase							:	List[Any]			,       **__lowerCamelCase							:	List[str] ):
    requires_backends(self			,       ['''speech'''] )



