




import heapq







def        lowerCAmelCase_			(  snake_case_  ):
      _A							:  list[list]    =		[]

      # for each node and his adjacency list add them and the rank of the node to queue
      # using heapq module the queue will be filled like a Priority Queue
      # heapq works with a min priority queue, so I used -1*len(v) to build it
      for key, value in graph.items():
            # O(log(n))
            heapq.heappush(snake_case_,[-1 * len(snake_case_  ), (key, value)]  )

      # chosen_vertices = set of chosen vertices
      _A							:  Optional[int]    =		set()

      # while queue isn't empty and there are still edges
      #   (queue[0][0] is the rank of the node with max rank)
      while queue and queue[0][0] != 0:
            # extract vertex with max rank from queue and add it to chosen_vertices
            _A							:  str    =		heapq.heappop(snake_case_  )[1][0]
            chosen_vertices.add(snake_case_  )

            # Remove all arcs adjacent to argmax
            for elem in queue:
                  # if v haven't adjacent node, skip
                  if elem[0] == 0:
                        continue
                  # if argmax is reachable from elem
                  # remove argmax from elem's adjacent list and update his rank
                  if argmax in elem[1][1]:
                        _A							:  List[Any]    =		elem[1][1].index(snake_case_  )
                        del elem[1][1][index]
                        elem[0] += 1
        # re-order the queue
            heapq.heapify(snake_case_  )
      return chosen_vertices


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  _snake_case            = {0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
  print(f"""Minimum vertex cover:\n{greedy_min_vertex_cover(graph)}""")







def        lowerCAmelCase_			(  snake_case_ = 1000000  ):
      _A							:  Any    =		limit + 1
      _A							:  Tuple    =		[0] * limit
      for first_term in range(1,snake_case_  ):
            for n in range(snake_case_,snake_case_,snake_case_  ):
                  _A							:  Optional[int]    =		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							:  List[str]    =		sum(1 for x in frequency[1:limit] if x == 10  )

      return count


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

