
import numpy as np

def      A (       A_							:					Union[str, Any]    ,							A_							:					Dict    ,							A_							:					int    ,							A_							:					Union[str, Any]    ,							A_							:					Tuple       ):
						snake_case       :     Union[str, Any] =    int(np.ceil((x_end - xa) / h       )       )
						snake_case       :     str =    np.zeros((n + 1,)       )
						snake_case       :     Any =    ya
						snake_case       :     str =    xa

						for k in range(A_       ):
												snake_case       :     Optional[int] =    f(A_    ,							y[k]       )
												snake_case       :     Tuple =    f(x + 0.5 * h    ,							y[k] + 0.5 * h * ka       )
												snake_case       :     List[Any] =    f(x + 0.5 * h    ,							y[k] + 0.5 * h * ka       )
												snake_case       :     Any =    f(x + h    ,							y[k] + h * ka       )
												snake_case       :     Dict =    y[k] + (1 / 6) * h * (ka + 2 * ka + 2 * ka + ka)
												x += h

						return y


if __name__ == "__main__":
						import doctest

						doctest.testmod()



'''simple docstring'''





from __future__ import annotations

import math

def      A (       A_							:					int       ):

						if num <= 0:
												snake_case       :     List[Any] =    F"""{num}: Invalid input, please enter a positive integer."""
												raise ValueError(A_       )

						snake_case       :     Optional[Any] =    [True] * (num + 1)
						snake_case       :     List[str] =    []
						snake_case       :     List[Any] =    2
						snake_case       :     str =    int(math.sqrt(A_       )       )

						while start <= end:
												# If start is a prime
												if sieve[start] is True:
																		prime.append(A_       )

																		# Set multiples of start be False
																		for i in range(start * start    ,							num + 1    ,							A_       ):
																								if sieve[i] is True:
																														snake_case       :     int =    False

												start += 1

						for j in range(end + 1    ,							num + 1       ):
												if sieve[j] is True:
																		prime.append(A_       )

						return prime


if __name__ == "__main__":
						print(prime_sieve(int(input("Enter a positive integer: ").strip())))

