






class 		lowercase_					:






      '''simple docstring'''




      def __init__(      self      :						Dict  )    ->List[str]:




       """simple docstring"""


       a		  =      {}







      def       __lowerCAmelCase					(      self      :						str  )    ->None:




       """simple docstring"""


       print(self.vertex  )
       for i in self.vertex:
        print(__UpperCAmelCase ,					''' -> ''' ,					''' -> '''.join([str(__UpperCAmelCase  ) for j in self.vertex[i]]  )  )







      def       __lowerCAmelCase					(      self      :						Dict ,					__UpperCAmelCase      :						int ,					__UpperCAmelCase      :						int  )    ->None:




       """simple docstring"""


       if from_vertex in self.vertex:
        self.vertex[from_vertex].append(__UpperCAmelCase  )
       else:
        # else make a new vertex
        a		  =      [to_vertex]







      def       __lowerCAmelCase					(      self      :						Optional[Any]  )    ->None:




       """simple docstring"""


       a		  =      [False] * len(self.vertex  )

       # call the recursive helper function
       for i in range(len(self.vertex  )  ):
        if not visited[i]:
         self.dfs_recursive(__UpperCAmelCase ,					__UpperCAmelCase  )







      def       __lowerCAmelCase					(      self      :						str ,					__UpperCAmelCase      :						int ,					__UpperCAmelCase      :						list  )    ->None:




       """simple docstring"""


       a		  =      True

       print(__UpperCAmelCase ,					end=''' '''  )

       # Recur for all the vertices that are adjacent to this node
       for i in self.vertex:
        if not visited[i]:
         self.dfs_recursive(__UpperCAmelCase ,					__UpperCAmelCase  )


if __name__ == "__main__":
     UpperCAmelCase__				   =		Graph()
     g.add_edge(0, 1)
     g.add_edge(0, 2)
     g.add_edge(1, 2)
     g.add_edge(2, 0)
     g.add_edge(2, 3)
     g.add_edge(3, 3)

     g.print_graph()
     print("DFS:")
     g.dfs()

     # OUTPUT:
     # 0  ->  1 -> 2
     # 1  ->  2
     # 2  ->  0 -> 3
     # 3  ->  3
     # DFS:
     #  0 1 2 3









def    __lowerCamelCase					(							__a   :int = 1_0_0_0_0_0_0    )		->				int:






		"""simple docstring"""

		A__        =   limit + 1
		A__        =   [0] * limit
		for first_term in range(1    ,     __a    ):
				for n in range(__a    ,     __a    ,     __a    ):
						A__        =   first_term + n / first_term
						if common_difference % 4:  # d must be divisble by 4
								continue
						else:
								common_difference /= 4
								if (
								    first_term > common_difference
								    and first_term < 4 * common_difference
								):  # since x,y,z are positive integers
										frequency[n] += 1  # so z>0 and a>d ,also 4d<a

		A__        =   sum(1 for x in frequency[1:limit] if x == 1_0    )

		return count


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



