"""simple docstring"""




from __future__ import annotations

_UpperCAmelCase            =		{
    'A': ['B', 'C', 'E'],
    'B': ['A', 'D', 'E'],
    'C': ['A', 'F', 'G'],
    'D': ['B'],
    'E': ['A', 'B', 'D'],
    'F': ['C'],
    'G': ['C'],
}





class UpperCAmelCase						:


				'''simple docstring'''






				def __init__(						self		,     lowercase		,     lowercase ):



						"""simple docstring"""





						A_		:    Any         =				graph
						# mapping node to its parent in resulting breadth first tree
						A_		:    dict[str, str | None]         =				{}
						A_		:    List[Any]         =				source_vertex
				def   lowerCAmelCase_       (						self ):



						"""simple docstring"""





						A_		:    Dict         =				{self.source_vertex}
						A_		:    Tuple         =				None
						A_		:    int         =				[self.source_vertex]  # first in first out queue

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







				def   lowerCAmelCase_       (						self		,     lowercase ):



						"""simple docstring"""





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

						A_		:    Tuple         =				self.parent.get(lowercase )
						if target_vertex_parent is None:
								A_		:    Optional[int]         =				(
								    F'''No path from vertex: {self.source_vertex} to vertex: {target_vertex}'''
								)
								raise ValueError(lowercase )

						return self.shortest_path(lowercase ) + F'''->{target_vertex}'''


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







from math import isqrt




def     UpperCamelCase						(	__lowercase						:			int     ):
		'''simple docstring'''




		return all(number % divisor != 0 for divisor in range(2						,isqrt(__lowercase     ) + 1     )     )




def     UpperCamelCase						(	__lowercase						:			int = 10**6     ):
		'''simple docstring'''




		A_		:    Optional[Any]         =				0
		A_		:    List[str]         =				1
		A_		:    Dict         =				7
		while prime_candidate < max_prime:
				primes_count += is_prime(__lowercase     )

				cube_index += 1
				prime_candidate += 6 * cube_index

		return primes_count


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






