


'''simple docstring'''



from __future__ import annotations

import math






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       int       ):

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

					__a      :	str    =  [True] * (num + 1)
					__a      :	Optional[Any]    =  []
					__a      :	Optional[Any]    =  2
					__a      :	Union[str, Any]    =  int(math.sqrt(_SCREAMING_SNAKE_CASE       )       )

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

															# Set multiples of start be False
															for i in range(start * start						,				num + 1						,				_SCREAMING_SNAKE_CASE       ):
																				if sieve[i] is True:
																									__a      :	Union[str, Any]    =  False

										start += 1

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

					return prime


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







'''simple docstring'''



def   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       int						,				_SCREAMING_SNAKE_CASE				:       int       ):
					if not isinstance(_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE       ):
										raise ValueError('iterations must be defined as integers'       )
					if not isinstance(_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE       ) or not number >= 1:
										raise ValueError(
										    'starting number must be\n                         and integer and be more than 0'       )
					if not iterations >= 1:
										raise ValueError('Iterations must be done more than 0 times to play FizzBuzz'       )

					__a      :	Dict    =  ''
					while number <= iterations:
										if number % 3 == 0:
															out += "Fizz"
										if number % 5 == 0:
															out += "Buzz"
										if 0 not in (number % 3, number % 5):
															out += str(_SCREAMING_SNAKE_CASE       )

										# print(out)
										number += 1
										out += " "
					return out


if __name__ == "__main__":
	import doctest

	doctest.testmod()



