






def      lowercase__      (     __snake_case    :							dict  ):


					'''simple docstring'''


					UpperCAmelCase_    :      set[int]            =						set()
					# To detect a back edge, keep track of vertices currently in the recursion stack
					UpperCAmelCase_    :      set[int]            =						set()
					return any(
					    node not in visited and depth_first_search(__snake_case     ,       __snake_case     ,       __snake_case     ,       __snake_case  )
					    for node in graph  )




def      lowercase__      (     __snake_case    :							dict     ,       __snake_case    :							int     ,       __snake_case    :							set     ,       __snake_case    :							set  ):


					'''simple docstring'''


					visited.add(__snake_case  )
					rec_stk.add(__snake_case  )

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

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


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

		testmod()








def        UpperCamelCase    (							lowerCAmelCase__		):
					'''simple docstring'''

					if edge <= 0 or not isinstance(lowerCAmelCase__ ,			lowerCAmelCase__		):
										raise ValueError('''Length must be a positive.'''		)
					return 3 * ((25 + 10 * (5 ** (1 / 2))) ** (1 / 2)) * (edge**2)



def        UpperCamelCase    (							lowerCAmelCase__		):
					'''simple docstring'''

					if edge <= 0 or not isinstance(lowerCAmelCase__ ,			lowerCAmelCase__		):
										raise ValueError('''Length must be a positive.'''		)
					return ((15 + (7 * (5 ** (1 / 2)))) / 4) * (edge**3)


if __name__ == "__main__":
							import doctest

							doctest.testmod()




