
'''simple docstring'''





def      A (       A_							:					list[int]    ,							A_							:					list[int]    ,							A_							:					int       ):
						return not any(
						    neighbour == 1 and colored_vertices[i] == color
						    for i, neighbour in enumerate(A_       )       )

def      A (       A_							:					list[list[int]]    ,							A_							:					int    ,							A_							:					list[int]    ,							A_							:					int       ):

						# Base Case
						if index == len(A_       ):
												return True

						# Recursive Step
						for i in range(A_       ):
												if valid_coloring(graph[index]    ,							A_    ,							A_       ):
																		# Color current vertex
																		snake_case       :     Dict =    i
																		# Validate coloring
																		if util_color(A_    ,							A_    ,							A_    ,							index + 1       ):
																								return True
																		# Backtrack
																		snake_case       :     Tuple =    -1
						return False





def      A (       A_							:					list[list[int]]    ,							A_							:					int       ):
						snake_case       :     Any =    [-1] * len(A_       )

						if util_color(A_    ,							A_    ,							A_    ,							0       ):
												return colored_vertices

						return []



'''simple docstring'''





from __future__ import annotations

import math

def      A (       A_							:					int       ):

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

						snake_case       :     Optional[Any] =    [True] * (num + 1)
						snake_case       :     List[str] =    []
						snake_case       :     List[Any] =    2
						snake_case       :     str =    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:
																														snake_case       :     int =    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())))

