'''simple docstring'''




def 							lowerCamelCase	(      UpperCAmelCase__       :					int )			->      list[int]:

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

							lowercase_					:			Tuple										=       [True] * (num + 1)

							lowercase_					:			int										=       2
							while p * p <= num:
														if primes[p]:
																					for i in range(p * p      ,      num + 1      ,      UpperCAmelCase__ ):
																												lowercase_					:			Tuple										=       False
														p += 1

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


if __name__ == "__main__":
						import doctest

						doctest.testmod()

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






'''simple docstring'''




def 							lowerCamelCase	(      UpperCAmelCase__       :					list )			->      list:
							if any(not isinstance(UpperCAmelCase__      ,      UpperCAmelCase__ ) or x < 0 for x in sequence ):
														raise TypeError("""Sequence must be list of non-negative integers""" )
							for _ in range(len(UpperCAmelCase__ ) ):
														for i, (rod_upper, rod_lower) in enumerate(zip(UpperCAmelCase__      ,      sequence[1:] ) ):
																					if rod_upper > rod_lower:
																												sequence[i] -= rod_upper - rod_lower
																												sequence[i + 1] += rod_upper - rod_lower
							return sequence


if __name__ == "__main__":
						assert bead_sort([5, 4, 3, 2, 1]) == [1, 2, 3, 4, 5]
						assert bead_sort([7, 9, 4, 3, 5]) == [3, 4, 5, 7, 9]





