

"""simple docstring"""




A_							:     Optional[int]     =	{0: [1, 2], 1: [0, 3], 2: [0], 3: [1], 4: [5, 6], 5: [4, 6], 6: [4, 5]}

A_							:     Any     =	{0: [1, 2, 3], 1: [0, 3], 2: [0], 3: [0, 1], 4: [], 5: []}

def 		A    (       snake_case__						,			snake_case__						,			snake_case__      ):




			'''simple docstring'''


			SCREAMING_SNAKE_CASE__									= True
			SCREAMING_SNAKE_CASE__									= []

			for neighbour in graph[vert]:
						if not visited[neighbour]:
									connected_verts += dfs(snake_case__						,			snake_case__						,			snake_case__      )

			return [vert, *connected_verts]

def 		A    (       snake_case__      ):




			'''simple docstring'''


			SCREAMING_SNAKE_CASE__									= len(snake_case__      )
			SCREAMING_SNAKE_CASE__									= graph_size * [False]
			SCREAMING_SNAKE_CASE__									= []

			for i in range(snake_case__      ):
						if not visited[i]:
									SCREAMING_SNAKE_CASE__									= dfs(snake_case__						,			snake_case__						,			snake_case__      )
									components_list.append(snake_case__      )

			return components_list


if __name__ == "__main__":
						import doctest

						doctest.testmod()





"""simple docstring"""




import math

def 		A    (       snake_case__      ):




			'''simple docstring'''


			if 1 < number < 4:
						# 2 and 3 are primes
						return True
			elif number < 2 or number % 2 == 0 or number % 3 == 0:
						# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
						return False

			# All primes number are in format of 6k +/- 1
			for i in range(5						,			int(math.sqrt(snake_case__      ) + 1      )						,			6      ):
						if number % i == 0 or number % (i + 2) == 0:
									return False
			return True

def 		A    (       snake_case__ = 10_00						,			snake_case__ = 10_00      ):




			'''simple docstring'''


			SCREAMING_SNAKE_CASE__									= [0, 0, 0]  # length, a, b
			for a in range((a_limit * -1) + 1						,			snake_case__      ):
						for b in range(2						,			snake_case__      ):
									if is_prime(snake_case__      ):
												SCREAMING_SNAKE_CASE__									= 0
												SCREAMING_SNAKE_CASE__									= 0
												while is_prime((n**2) + (a * n) + b      ):
															count += 1
															n += 1
												if count > longest[0]:
															SCREAMING_SNAKE_CASE__									= [count, a, b]
			SCREAMING_SNAKE_CASE__									= longest[1] * longest[2]
			return ans


if __name__ == "__main__":
						print(solution(1_000, 1_000))


