
from __future__ import annotations

import math







def        A__					(						lowerCamelCase						)  ->	List[Any]:





				if num <= 0:
								UpperCamelCase_:							Tuple	=						F'''{num}: Invalid input, please enter a positive integer.'''
								raise ValueError(SCREAMING_SNAKE_CASE__						)

				UpperCamelCase_:							List[Any]	=						[True] * (num + 1)
				UpperCamelCase_:							List[Any]	=						[]
				UpperCamelCase_:							Union[str, Any]	=						2
				UpperCamelCase_:							List[str]	=						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:
																				UpperCamelCase_:							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())))








import random







def        A__					(						lowerCamelCase     ,    lowerCamelCase     ,    lowerCamelCase = False						)  ->	dict:
				UpperCamelCase_:							dict	=						{i: [] for i in range(lowerCamelCase						)}

				# if probability is greater or equal than 1, then generate a complete graph
				if probability >= 1:
								return complete_graph(lowerCamelCase						)
				# if probability is lower or equal than 0, then return a graph without edges
				if probability <= 0:
								return graph

				# for each couple of nodes, add an edge from u to v
				# if the number randomly generated is greater than probability probability
				for i in range(lowerCamelCase						):
								for j in range(i + 1     ,    lowerCamelCase						):
												if random.random() < probability:
																graph[i].append(lowerCamelCase						)
																if not directed:
																				# if the graph is undirected, add an edge in from j to i, either
																				graph[j].append(lowerCamelCase						)
				return graph







def        A__					(						lowerCamelCase						)  ->	dict:
				return {
				    i: [j for j in range(lowerCamelCase						) if i != j] for i in range(lowerCamelCase						)
				}


if __name__ == "__main__":
							import doctest

							doctest.testmod()






