

'''simple docstring'''



import random
def 						__lowerCamelCase       (   __snake_case     :		List[Any],		__snake_case     :		Dict,		__snake_case     :		Optional[int] = False       )       ->							dict:






						"""simple docstring"""





						A__     :   int      ={i: [] for i in range(lowercase__       )}

						# if probability is greater or equal than 1, then generate a complete graph
						if probability >= 1:
												return complete_graph(lowercase__       )
						# 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(lowercase__       ):
												for j in range(i + 1,		lowercase__       ):
																		if random.random() < probability:
																								graph[i].append(lowercase__       )
																								if not directed:
																														# if the graph is undirected, add an edge in from j to i, either
																														graph[j].append(lowercase__       )
						return graph
def 						__lowerCamelCase       (   __snake_case     :		List[str]       )       ->							dict:






						"""simple docstring"""





						return {
						    i: [j for j in range(lowercase__       ) if i != j] for i in range(lowercase__       )
						}


if __name__ == "__main__":
		import doctest

		doctest.testmod()





from math import isqrt







def        _lowerCamelCase(	lowercase__	)						->	bool:

		'''simple docstring'''







		return all(number % divisor != 0 for divisor in range(2   , isqrt(lowercase__	) + 1	)	)







def        _lowerCamelCase(	lowercase__ = 1_0**6	)						->	int:

		'''simple docstring'''







		__lowercase=			0
		__lowercase=			1
		__lowercase=			7
		while prime_candidate < max_prime:
				primes_count += is_prime(lowercase__	)

				cube_index += 1
				prime_candidate += 6 * cube_index

		return primes_count


if __name__ == "__main__":
	print(F'{solution() = }')






