




import random
def 					lowerCamelCase_    (    SCREAMING_SNAKE_CASE					,	SCREAMING_SNAKE_CASE					,	SCREAMING_SNAKE_CASE = False   ):
			'''simple docstring'''
			SCREAMING_SNAKE_CASE           =					{i: [] for i in range(SCREAMING_SNAKE_CASE   )}

			# if probability is greater or equal than 1, then generate a complete graph
			if probability >= 1:
						return complete_graph(SCREAMING_SNAKE_CASE   )
			# 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(SCREAMING_SNAKE_CASE   ):
						for j in range(i + 1					,	SCREAMING_SNAKE_CASE   ):
									if random.random() < probability:
												graph[i].append(SCREAMING_SNAKE_CASE   )
												if not directed:
															# if the graph is undirected, add an edge in from j to i, either
															graph[j].append(SCREAMING_SNAKE_CASE   )
			return graph
def 					lowerCamelCase_    (    SCREAMING_SNAKE_CASE   ):
			'''simple docstring'''
			return {
			    i: [j for j in range(SCREAMING_SNAKE_CASE   ) if i != j] for i in range(SCREAMING_SNAKE_CASE   )
			}


if __name__ == "__main__":
		import doctest

		doctest.testmod()












from __future__ import annotations

import math
def 					lowerCamelCase_    (    SCREAMING_SNAKE_CASE   ):
			'''simple docstring'''

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

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






