from __future__ import annotations

lowerCAmelCase			:							Tuple     ={
    """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	:





      '''simple docstring'''






      def __init__(					self     :				str    ,  _UpperCamelCase     :				int    ,  _UpperCamelCase     :				Tuple)				->None:


          """simple docstring"""


          _lowerCamelCase     :		int 						=						graph
          # mapping node to its parent in resulting breadth first tree
          _lowerCamelCase     :		Any 						=						{}
          _lowerCamelCase     :		Dict 						=						source_vertex



      def 	_SCREAMING_SNAKE_CASE    (					self     :				Optional[int])				->None:


          """simple docstring"""


          _lowerCamelCase     :		Any 						=						{self.source_vertex}
          _lowerCamelCase     :		Dict 						=						None
          _lowerCamelCase     :		List[str] 						=						[self.source_vertex]  # first in first out queue

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




      def 	_SCREAMING_SNAKE_CASE    (					self     :				List[Any]    ,  _UpperCamelCase     :				int)				->str:


          """simple docstring"""


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

          _lowerCamelCase     :		Optional[int] 						=						self.parent.get(snake_case_)
          if target_vertex_parent is None:
              _lowerCamelCase     :		Any 						=						(
                  F"""No path from vertex: {self.source_vertex} to vertex: {target_vertex}"""
              )
              raise ValueError(snake_case_)

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


if __name__ == "__main__":
    lowerCAmelCase			:							Optional[int]     =Graph(graph, "G")
    g.breath_first_search()
    print(g.shortest_path("D"))
    print(g.shortest_path("G"))
    print(g.shortest_path("Foo"))





import math







def 						A__  (					__A	):







    '''simple docstring'''
    assert isinstance(__A   , __A	) and (
        number >= 0
    ), "'number' must been an int and positive"

    if 1 < number < 4:
        # 2 and 3 are primes
        return True
    elif number < 2 or not number % 2:
        # Negatives, 0, 1 and all even numbers are not primes
        return False

    _lowerCamelCase     :		List[Any] 						=						range(3   , int(math.sqrt(__A	) + 1	)   , 2	)
    return not any(not number % i for i in odd_numbers	)







def 						A__  (					__A   , __A=1   , **__A	):







    '''simple docstring'''
    _lowerCamelCase     :		Dict 						=						factor * value
    _lowerCamelCase     :		str 						=						value

    while not is_prime(__A	):
        value += 1 if not ("desc" in kwargs and kwargs["desc"] is True) else -1

    if value == first_value_val:
        return next_prime(value + 1   , **__A	)
    return value




