"""simple docstring"""







lowerCamelCase__           =	{
    """A""": ["""B""", """C""", """E"""],
    """B""": ["""A""", """D""", """E"""],
    """C""": ["""A""", """F""", """G"""],
    """D""": ["""B"""],
    """E""": ["""A""", """B""", """D"""],
    """F""": ["""C"""],
    """G""": ["""C"""],
}
def 					__lowerCAmelCase       (_UpperCamelCase ,						_UpperCamelCase ,						_UpperCamelCase	):
	__lowerCAmelCase    :		List[Any]		    =   set()
	# keep track of all the paths to be checked
	__lowerCAmelCase    :		Tuple		    =   [[start]]

	# return path if start is goal
	if start == goal:
		return [start]

	# keeps looping until all possible paths have been checked
	while queue:
		# pop the first path from the queue
		__lowerCAmelCase    :		Tuple		    =   queue.pop(0	)
		# get the last node from the path
		__lowerCAmelCase    :		Dict		    =   path[-1]
		if node not in explored:
			__lowerCAmelCase    :		int		    =   graph[node]
			# go through all neighbour nodes, construct a new path and
			# push it into the queue
			for neighbour in neighbours:
				__lowerCAmelCase    :		Optional[int]		    =   list(lowercase_	)
				new_path.append(lowercase_	)
				queue.append(lowercase_	)
				# return path if neighbour is goal
				if neighbour == goal:
					return new_path

            # mark node as explored
			explored.add(lowercase_	)

    # in case there's no path between the 2 nodes
	return []
def 					__lowerCAmelCase       (_UpperCamelCase ,						_UpperCamelCase ,						_UpperCamelCase	):

	if not graph or start not in graph or target not in graph:
		return -1
	if start == target:
		return 0
	__lowerCAmelCase    :		int		    =   [start]
	__lowerCAmelCase    :		Tuple		    =   set(lowercase_	)
	# Keep tab on distances from `start` node.
	__lowerCAmelCase    :		str		    =   {start: 0, target: -1}
	while queue:
		__lowerCAmelCase    :		Union[str, Any]		    =   queue.pop(0	)
		if node == target:
			__lowerCAmelCase    :		Optional[Any]		    =   (
			    dist[node] if dist[target] == -1 else min(dist[target] ,						dist[node]	)
			)
		for adjacent in graph[node]:
			if adjacent not in visited:
				visited.add(lowercase_	)
				queue.append(lowercase_	)
				__lowerCAmelCase    :		Tuple		    =   dist[node] + 1
	return dist[target]


if __name__ == "__main__":
							print(bfs_shortest_path(demo_graph, """G""", """D"""))  # returns ['G', 'C', 'A', 'B', 'D']
							print(bfs_shortest_path_distance(demo_graph, """G""", """D"""))  # returns 4

"""simple docstring"""







class 				A__ :

		def __init__(   self				):
			__lowerCAmelCase    :		Optional[int]		    =   0
			__lowerCAmelCase    :		Any		    =   0
			__lowerCAmelCase    :		List[Any]		    =   {}

		def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE				):
			if vertex not in self.adjacency:
				__lowerCAmelCase    :		Dict		    =   {}
				self.num_vertices += 1

		def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				):
			self.add_vertex(_SCREAMING_SNAKE_CASE				)
			self.add_vertex(_SCREAMING_SNAKE_CASE				)

			if head == tail:
				return

			__lowerCAmelCase    :		Union[str, Any]		    =   weight
			__lowerCAmelCase    :		str		    =   weight

		def 							__lowerCamelCase							(   self				):
			__lowerCAmelCase    :		int		    =   self.get_edges()
			for edge in edges:
				__lowerCAmelCase    ,     __lowerCAmelCase    ,     __lowerCAmelCase    :		Optional[Any]		    =   edge
				edges.remove((tail, head, weight)				)
			for i in range(len(_SCREAMING_SNAKE_CASE				)				):
				__lowerCAmelCase    :		List[str]		    =   list(edges[i]				)

			edges.sort(key=lambda _SCREAMING_SNAKE_CASE				: e[2]				)
			for i in range(len(_SCREAMING_SNAKE_CASE				) - 1				):
				if edges[i][2] >= edges[i + 1][2]:
					__lowerCAmelCase    :		Dict		    =   edges[i][2] + 1
			for edge in edges:
				__lowerCAmelCase    ,     __lowerCAmelCase    ,     __lowerCAmelCase    :		str		    =   edge
				__lowerCAmelCase    :		Union[str, Any]		    =   weight
				__lowerCAmelCase    :		Optional[int]		    =   weight

		def __str__(   self				):
			__lowerCAmelCase    :		List[Any]		    =   ''
			for tail in self.adjacency:
				for head in self.adjacency[tail]:
					__lowerCAmelCase    :		str		    =   self.adjacency[head][tail]
					string += f"{head} -> {tail} == {weight}\n"
			return string.rstrip('\n'				)

		def 							__lowerCamelCase							(   self				):
			__lowerCAmelCase    :		Tuple		    =   []
			for tail in self.adjacency:
				for head in self.adjacency[tail]:
					output.append((tail, head, self.adjacency[head][tail])				)
			return output

		def 							__lowerCamelCase							(   self				):
			return self.adjacency.keys()

		@staticmethod
		def 							__lowerCamelCase							(   _SCREAMING_SNAKE_CASE=None ,	_SCREAMING_SNAKE_CASE=None				):
			__lowerCAmelCase    :		List[str]		    =   Graph()
			if vertices is None:
				__lowerCAmelCase    :		int		    =   []
			if edges is None:
				__lowerCAmelCase    :		Optional[int]		    =   []
			for vertex in vertices:
				g.add_vertex(_SCREAMING_SNAKE_CASE				)
			for edge in edges:
				g.add_edge(*_SCREAMING_SNAKE_CASE				)
			return g




		class 				A__ :

				def __init__(   self				):
					__lowerCAmelCase    :		Dict		    =   {}
					__lowerCAmelCase    :		Optional[int]		    =   {}

				def __len__(   self				):
					return len(self.parent				)

				def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE				):
					if item in self.parent:
						return self.find(_SCREAMING_SNAKE_CASE				)

					__lowerCAmelCase    :		Dict		    =   item
					__lowerCAmelCase    :		int		    =   0
					return item

				def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE				):
					if item not in self.parent:
						return self.make_set(_SCREAMING_SNAKE_CASE				)
					if item != self.parent[item]:
						__lowerCAmelCase    :		Dict		    =   self.find(self.parent[item]				)
					return self.parent[item]







				def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				):
					__lowerCAmelCase    :		Any		    =   self.find(_SCREAMING_SNAKE_CASE				)
					__lowerCAmelCase    :		List[str]		    =   self.find(_SCREAMING_SNAKE_CASE				)

					if roota == roota:
						return roota

					if self.rank[roota] > self.rank[roota]:
						__lowerCAmelCase    :		Tuple		    =   roota
						return roota

					if self.rank[roota] < self.rank[roota]:
						__lowerCAmelCase    :		str		    =   roota
						return roota

					if self.rank[roota] == self.rank[roota]:
						self.rank[roota] += 1
						__lowerCAmelCase    :		Optional[int]		    =   roota
						return roota
					return None



		@staticmethod
		def 							__lowerCamelCase							(   _SCREAMING_SNAKE_CASE				):
			__lowerCAmelCase    :		Union[str, Any]		    =   graph.num_vertices

			__lowerCAmelCase    :		List[Any]		    =   Graph.UnionFind()
			__lowerCAmelCase    :		Tuple		    =   []
			while num_components > 1:
				__lowerCAmelCase    :		str		    =   {}
				for vertex in graph.get_vertices():
					__lowerCAmelCase    :		Union[str, Any]		    =   -1

				__lowerCAmelCase    :		int		    =   graph.get_edges()
				for edge in edges:
					__lowerCAmelCase    ,     __lowerCAmelCase    ,     __lowerCAmelCase    :		Union[str, Any]		    =   edge
					edges.remove((tail, head, weight)				)
				for edge in edges:
					__lowerCAmelCase    ,     __lowerCAmelCase    ,     __lowerCAmelCase    :		Any		    =   edge
					__lowerCAmelCase    :		Optional[int]		    =   union_find.find(_SCREAMING_SNAKE_CASE				)
					__lowerCAmelCase    :		str		    =   union_find.find(_SCREAMING_SNAKE_CASE				)
					if seta != seta:
						if cheap_edge[seta] == -1 or cheap_edge[seta][2] > weight:
							__lowerCAmelCase    :		List[str]		    =   [head, tail, weight]

						if cheap_edge[seta] == -1 or cheap_edge[seta][2] > weight:
							__lowerCAmelCase    :		List[str]		    =   [head, tail, weight]
				for vertex in cheap_edge:
					if cheap_edge[vertex] != -1:
						__lowerCAmelCase    ,     __lowerCAmelCase    ,     __lowerCAmelCase    :		str		    =   cheap_edge[vertex]
						if union_find.find(_SCREAMING_SNAKE_CASE				) != union_find.find(_SCREAMING_SNAKE_CASE				):
							union_find.union(_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				)
							mst_edges.append(cheap_edge[vertex]				)
							__lowerCAmelCase    :		List[str]		    =   num_components - 1
			__lowerCAmelCase    :		Union[str, Any]		    =   Graph.build(edges=_SCREAMING_SNAKE_CASE				)
			return mst