'''simple docstring'''




from __future__ import annotations

from cmath import sqrt






def 							snake_case__				(     _A:   int ,  _A:   int ,  _A:   int					)       ->      tuple[complex, complex]:

		'''simple docstring'''


		if a == 0:
				raise ValueError("""Coefficient 'a' must not be zero."""					)
		lowerCAmelCase     =    b * b - 4 * a * c

		lowerCAmelCase     =    (-b + sqrt(_A					)) / (2 * a)
		lowerCAmelCase     =    (-b - sqrt(_A					)) / (2 * a)

		return (
		    root_a.real if not root_a.imag else root_a,
		    root_a.real if not root_a.imag else root_a,
		)






def 							snake_case__				(     )       ->      int:

		'''simple docstring'''


		lowerCAmelCase   ,	lowerCAmelCase     =    quadratic_roots(a=5 ,  b=6 ,  c=1					)
		print(f"The solutions are: {solutiona} and {solutiona}"					)


if __name__ == "__main__":
						main()





'''simple docstring'''




from __future__ import annotations

import math






def 							snake_case__				(     _A:   int					)       ->      list[int]:

		'''simple docstring'''


		if num <= 0:
				lowerCAmelCase     =    f"{num}: Invalid input, please enter a positive integer."
				raise ValueError(_A					)

		lowerCAmelCase     =    [True] * (num + 1)
		lowerCAmelCase     =    []
		lowerCAmelCase     =    2
		lowerCAmelCase     =    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:
										lowerCAmelCase     =    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())))




