



def 	snake_case__       (					__lowercase       )		->		bool:







						"""simple docstring"""

						A__	:							set[int]						    = set()
						# To detect a back edge, keep track of vertices currently in the recursion stack
						A__	:							set[int]						    = set()
						return any(
						    node not in visited and depth_first_search(__lowercase							,     __lowercase							,     __lowercase							,     __lowercase       )
						    for node in graph       )
def 	snake_case__       (					__lowercase							,     __lowercase							,     __lowercase							,     __lowercase       )		->		bool:







						"""simple docstring"""

						visited.add(__lowercase       )
						rec_stk.add(__lowercase       )

						for node in graph[vertex]:
												if node not in visited:
																		if depth_first_search(__lowercase							,     __lowercase							,     __lowercase							,     __lowercase       ):
																								return True
												elif node in rec_stk:
																		return True

    # The node needs to be removed from recursion stack before function ends
						rec_stk.remove(__lowercase       )
						return False


if __name__ == "__main__":
		from doctest import testmod

		testmod()




def 	snake_case__       (					__lowercase       )		->		int:







						"""simple docstring"""

						if divisor % 5 == 0 or divisor % 2 == 0:
												return 0
						A__	:							Tuple						    = 1
						A__	:							Union[str, Any]						    = 1
						while repunit:
												A__	:							Union[str, Any]						    = (1_0 * repunit + 1) % divisor
												repunit_index += 1
						return repunit_index
def 	snake_case__       (					__lowercase = 1_0_0_0_0_0_0       )		->		int:







						"""simple docstring"""

						A__	:							Dict						    = limit - 1
						if divisor % 2 == 0:
												divisor += 1
						while least_divisible_repunit(__lowercase       ) <= limit:
												divisor += 2
						return divisor


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