






"""simple docstring"""
_lowerCAmelCase         =							{"a": ["c", "b"], "b": ["d", "e"], "c": [], "d": [], "e": []}
_lowerCAmelCase         =							["a", "b", "c", "d", "e"]






def 			__UpperCamelCase	(		snake_case__   ,   snake_case__   ,   snake_case__					):
	A_		:						int	    =   start
	# add current to visited
	visited.append(snake_case__					)
	A_		:						Any	    =   edges[current]
	for neighbor in neighbors:
		# if neighbor not in visited, visit
		if neighbor not in visited:
			A_		:						Optional[Any]	    =   topological_sort(snake_case__   ,   snake_case__   ,   snake_case__					)
    # if all neighbors visited add current to sort
	sort.append(snake_case__					)
	# if all vertices haven't been visited select a new one to visit
	if len(snake_case__					) != len(snake_case__					):
		for vertice in vertices:
			if vertice not in visited:
				A_		:						Optional[Any]	    =   topological_sort(snake_case__   ,   snake_case__   ,   snake_case__					)
    # return sort
	return sort


if __name__ == "__main__":
							_lowerCAmelCase         =							topological_sort("a", [], [])
							print(sort)









"""simple docstring"""
def 			__UpperCamelCase	(		snake_case__   ,   snake_case__   ,   snake_case__					):
	return not any(
	    neighbour == 1 and colored_vertices[i] == color
	    for i, neighbour in enumerate(snake_case__					)					)






def 			__UpperCamelCase	(		snake_case__   ,   snake_case__   ,   snake_case__   ,   snake_case__					):

	# Base Case
	if index == len(snake_case__					):
		return True

	# Recursive Step
	for i in range(snake_case__					):
		if valid_coloring(graph[index]   ,   snake_case__   ,   snake_case__					):
			# Color current vertex
			A_		:						Dict	    =   i
			# Validate coloring
			if util_color(snake_case__   ,   snake_case__   ,   snake_case__   ,   index + 1					):
				return True
			# Backtrack
			A_		:						Union[str, Any]	    =   -1
	return False






def 			__UpperCamelCase	(		snake_case__   ,   snake_case__					):
	A_		:						int	    =   [-1] * len(snake_case__					)

	if util_color(snake_case__   ,   snake_case__   ,   snake_case__   ,   0					):
		return colored_vertices

	return []

