





from __future__ import annotations





def   lowerCamelCase__       (       UpperCamelCase__     :    int  )     ->	list[int]:



					'''simple docstring'''




					_snake_case													=			[True] * limit
					_snake_case													=			False
					_snake_case													=			False
					_snake_case													=			True

					for i in range(3    ,      int(limit**0.5 + 1  )    ,      2  ):
										_snake_case													=			i * 2
										while index < limit:
															_snake_case													=			False
															_snake_case													=			index + i

					_snake_case													=			[2]

					for i in range(3    ,      UpperCamelCase__    ,      2  ):
										if is_prime[i]:
															primes.append(UpperCamelCase__  )

					return primes





def   lowerCamelCase__       (       UpperCamelCase__     :    int = 1_000_000  )     ->	int:



					'''simple docstring'''




					_snake_case													=			prime_sieve(UpperCamelCase__  )
					_snake_case													=			0
					_snake_case													=			0

					for i in range(len(UpperCamelCase__  )  ):
										for j in range(i + length    ,      len(UpperCamelCase__  )  ):
															_snake_case													=			sum(primes[i:j]  )
															if sol >= ceiling:
																				break

															if sol in primes:
																				_snake_case													=			j - i
																				_snake_case													=			sol

					return largest


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










import random





def   lowerCamelCase__       (       UpperCamelCase__     :    int    ,      UpperCamelCase__     :    float    ,      UpperCamelCase__     :    bool = False  )     ->	dict:



					'''simple docstring'''




					_snake_case													=			{i: [] for i in range(UpperCamelCase__  )}

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





def   lowerCamelCase__       (       UpperCamelCase__     :    int  )     ->	dict:



					'''simple docstring'''




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


if __name__ == "__main__":
					import doctest

					doctest.testmod()



