


from __future__ import annotations

import math





def   _lowerCAmelCase				(   UpperCamelCase__:     Optional[int]							,					UpperCamelCase__:     Dict						) ->   float:





 """simple docstring"""







 A								=				u
 for i in range(1							,					__snake_case						):
  A								=				temp * (u - i)
 return temp





def   _lowerCAmelCase				(   ) ->   None:





 """simple docstring"""







 A								=				int(input("""enter the numbers of values: """						)						)
 A								=				[]
 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								=				0

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

 print("""enter the values of corresponding parameters: """						)
 for i in range(__snake_case						):
  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							,					__snake_case						):
  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							,					__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()







def   _lowerCAmelCase				(   UpperCamelCase__:     int						) ->   list[int]:





	"""simple docstring"""







	if num <= 0:
		raise ValueError("""Input must be a positive integer"""						)

	A								=				[True] * (num + 1)

	A								=				2
	while p * p <= num:
		if primes[p]:
			for i in range(p * p							,					num + 1							,					UpperCamelCase__						):
				A								=				False
		p += 1

	return [prime for prime in range(2							,					num + 1						) if primes[prime]]


if __name__ == "__main__":
				import doctest

				doctest.testmod()

				_lowercase       :      Tuple	=	int(input("Enter a positive integer: ").strip())
				print(prime_sieve_eratosthenes(user_num))



