




"""simple docstring"""






lowercase__     						=						tuple[float, float, float]
lowercase__     						=						tuple[float, float, float]







def      _snake_case			(				lowercase__							,    lowercase__		):
				_lowerCamelCase     :			Dict    =    end_pointa[0] - end_pointa[0]
				_lowerCamelCase     :			List[Any]    =    end_pointa[1] - end_pointa[1]
				_lowerCamelCase     :			List[str]    =    end_pointa[2] - end_pointa[2]
				return (x, y, z)







def      _snake_case			(				lowercase__							,    lowercase__		):
				_lowerCamelCase     :			Dict    =    ab[1] * ac[2] - ab[2] * ac[1]  # *i
				_lowerCamelCase     :			Dict    =    (ab[0] * ac[2] - ab[2] * ac[0]) * -1  # *j
				_lowerCamelCase     :			List[str]    =    ab[0] * ac[1] - ab[1] * ac[0]  # *k
				return (x, y, z)







def      _snake_case			(				lowercase__							,    lowercase__		):
				return tuple(round(lowercase__							,    lowercase__		) for x in vector		) == (0, 0, 0)







def      _snake_case			(				lowercase__							,    lowercase__							,    lowercase__							,    lowercase__ = 10		):
				_lowerCamelCase     :			Optional[int]    =    create_vector(lowercase__							,    lowercase__		)
				_lowerCamelCase     :			Optional[Any]    =    create_vector(lowercase__							,    lowercase__		)
				return is_zero_vector(get_ad_vectors_cross(lowercase__							,    lowercase__		)							,    lowercase__		)




'''simple docstring'''





from __future__ import annotations

import math




def lowerCAmelCase  (__A  ,	__A):



     """simple docstring"""



     _a      =  u
     for i in range(1  ,	__A):
          _a      =  temp * (u - i)
     return temp




def lowerCAmelCase  ():



     """simple docstring"""



     _a      =  int(input('''enter the numbers of values: '''))
     _a      =  []
     for _ in range(__A):
          y.append([])
     for i in range(__A):
          for j in range(__A):
               y[i].append(__A)
               _a      =  0

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

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

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

     # for calculating forward difference table

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

     _a      =  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()



