




'''simple docstring'''





def 			a   (_lowerCAmelCase = 1_0_0_0_0_0_0     ):
							SCREAMING_SNAKE_CASE_   	=    set(range(3  ,    lowercase_  ,    2     )     )
							primes.add(2     )
							for p in range(3  ,    lowercase_  ,    2     ):
														if p not in primes:
																					continue
														primes.difference_update(set(range(p * p  ,    lowercase_  ,    lowercase_     )     )     )

							SCREAMING_SNAKE_CASE_   	=    [float(lowercase_     ) for n in range(limit + 1     )]

							for p in primes:
														for n in range(lowercase_  ,    limit + 1  ,    lowercase_     ):
																					phi[n] *= 1 - 1 / p

							return int(sum(phi[2:]     )     )


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








from __future__ import annotations

__SCREAMING_SNAKE_CASE 						={
    """A""": ["""B""", """C""", """E"""],
    """B""": ["""A""", """D""", """E"""],
    """C""": ["""A""", """F""", """G"""],
    """D""": ["""B"""],
    """E""": ["""A""", """B""", """D"""],
    """F""": ["""C"""],
    """G""": ["""C"""],
}






class  __magic_name__						:
				'''simple docstring'''







				def __init__(							self:   List[Any]		,					_lowerCamelCase:   dict[str, list[str]]		,					_lowerCamelCase:   str		):
											SCREAMING_SNAKE_CASE_   	=    graph
											# mapping node to its parent in resulting breadth first tree
											SCREAMING_SNAKE_CASE_   	=    {}
											SCREAMING_SNAKE_CASE_   	=    source_vertex


				def     _A							(							self:   Tuple		):
											SCREAMING_SNAKE_CASE_   	=    {self.source_vertex}
											SCREAMING_SNAKE_CASE_   	=    None
											SCREAMING_SNAKE_CASE_   	=    [self.source_vertex]  # first in first out queue

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





				def     _A							(							self:   List[str]		,					_lowerCamelCase:   str		):
											if target_vertex == self.source_vertex:
																		return self.source_vertex

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

											return self.shortest_path(_lowerCamelCase		) + f"->{target_vertex}"


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


