Hello there, budding programmer! I hope you're ready because today, we're going to dive deep into high-level data manipulation and increase our understanding of heaps. Heaps are fundamental data structures commonly used in algorithms. We're going to leverage their potential today in an interesting algorithmic problem. Are you ready for the challenge? Let's get started!

We have a task at hand related to array manipulation and the use of heaps. The task is as follows: Given a vector of unique integers with elements ranging from $1$ to $10^6$ and length between $1$ to , we need to create a C++ function . This function will take the vector as input and return a corresponding vector, which consists of the medians of all the prefixes of the input vector.