


"""simple docstring"""


from __future__ import annotations

a_       							=    {
    "A": ["B", "C", "E"],
    "B": ["A", "D", "E"],
    "C": ["A", "F", "G"],
    "D": ["B"],
    "E": ["A", "B", "D"],
    "F": ["C"],
    "G": ["C"],
}
class snake_case      :







		def __init__(					self      :       Optional[int]    ,   a__      :       dict[str, list[str]]    ,   a__      :       str		)       ->						None:





						'''simple docstring'''







						_A					  =			graph
						# mapping node to its parent in resulting breadth first tree
						_A					  =			{}
						_A					  =			source_vertex







		def  a_ (					self      :       List[str]		)       ->						None:





						'''simple docstring'''







						_A					  =			{self.source_vertex}
						_A					  =			None
						_A					  =			[self.source_vertex]  # first in first out queue

						while queue:
										_A					  =			queue.pop(0		)
										for adjacent_vertex in self.graph[vertex]:
														if adjacent_vertex not in visited:
																		visited.add(a__		)
																		_A					  =			vertex
																		queue.append(a__		)







		def  a_ (					self      :       List[Any]    ,   a__      :       str		)       ->						str:





						'''simple docstring'''







						if target_vertex == self.source_vertex:
										return self.source_vertex

						_A					  =			self.parent.get(a__		)
						if target_vertex_parent is None:
										_A					  =			(
										    F"""No path from vertex: {self.source_vertex} to vertex: {target_vertex}"""
										)
										raise ValueError(a__		)

						return self.shortest_path(a__		) + F"""->{target_vertex}"""


if __name__ == "__main__":
		a_       							=    Graph(graph, "G")
		g.breath_first_search()
		print(g.shortest_path("D"))
		print(g.shortest_path("G"))
		print(g.shortest_path("Foo"))



"""simple docstring"""


def      a__ (				__lowercase     ,			__lowercase   )	->	int:
				while a != 0:
								_A  ,		_A					  =			b % a, a
				return b






def      a__ (				__lowercase     ,			__lowercase   )	->	int:
				if gcd(__lowercase     ,			__lowercase   ) != 1:
								_A					  =			f"""mod inverse of {a!r} and {m!r} does not exist"""
								raise ValueError(__lowercase   )
				_A  ,		_A  ,		_A					  =			1, 0, a
				_A  ,		_A  ,		_A					  =			0, 1, m
				while va != 0:
								_A					  =			ua // va
								_A  ,		_A  ,		_A  ,		_A  ,		_A  ,		_A					  =			(ua - q * va), (ua - q * va), (ua - q * va), va, va, va
				return ua % m