


'''simple docstring'''







from __future__ import annotations

import math






def 			lowercase				(_A   ,						_A					):







       """simple docstring"""







       _lowerCAmelCase    :							str   			=       u
       for i in range(1   ,						_A					):
              _lowerCAmelCase    :							Optional[int]   			=       temp * (u - i)
       return temp






def 			lowercase				():







       """simple docstring"""







       _lowerCAmelCase    :							Any   			=       int(input('enter the numbers of values: '					)					)
       _lowerCAmelCase    :							list[list[float]]   			=       []
       for _ in range(_A					):
              y.append([]					)
       for i in range(_A					):
              for j in range(_A					):
                     y[i].append(_A					)
                     _lowerCAmelCase    :							Optional[Any]   			=       0

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

       print('enter the values of corresponding parameters: '					)
       for i in range(_A					):
              _lowerCAmelCase    :							str   			=       float(input()					)

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

       # for calculating forward difference table

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

       _lowerCAmelCase    :							int   			=       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'''







lowerCAmelCase    :     Optional[int]					=						[sum(int(c, 10) ** 2 for c in i.__str__()) for i in range(10_00_00)]






def 			lowercase				(_A					):







       """simple docstring"""







       _lowerCAmelCase    :							str   			=       0
       while number:
              # Increased Speed Slightly by checking every 5 digits together.
              sum_of_digits_squared += DIGITS_SQUARED[number % 1_0_0_0_0_0]
              number //= 1_0_0_0_0_0

       return sum_of_digits_squared


# There are 2 Chains made,
# One ends with 89 with the chain member 58 being the one which when declared first,
# there will be the least number of iterations for all the members to be checked.

# The other one ends with 1 and has only one element 1.

# So 58 and 1 are chosen to be declared at the starting.

# Changed dictionary to an array to quicken the solution
lowerCAmelCase    :     list[bool | None]					=						[None] * 10_00_00_00
lowerCAmelCase    :     List[str]					=						True
lowerCAmelCase    :     Union[str, Any]					=						False






def 			lowercase				(_A					):







       """simple docstring"""







       if CHAINS[number - 1] is not None:
              return CHAINS[number - 1]  # type: ignore

       _lowerCAmelCase    :							Any   			=       chain(next_number(_A					)					)
       _lowerCAmelCase    :							List[str]   			=       number_chain

       while number < 1_0_0_0_0_0_0_0:
              _lowerCAmelCase    :							Tuple   			=       number_chain
              number *= 1_0

       return number_chain






def 			lowercase				(_A = 1_0_0_0_0_0_0_0					):







       """simple docstring"""







       for i in range(1   ,						_A					):
              if CHAINS[i] is None:
                     chain(i + 1					)

       return CHAINS[:number].count(_A					)


if __name__ == "__main__":
       import doctest

       doctest.testmod()
       print(F'''{solution() = }''')

