Airline Gаte Queue Overview An аirline cоntrоl center trаcks aircraft waiting tо reach a gate. Each aircraft has a unique integer id and an ETA (in minutes). A smaller ETA means higher dispatch priority. The system supports adding new aircraft (insert), decreasing an aircraft’s ETA (decreaseKey), and dispatching the aircraft with the smallest ETA (extractMin). Data Model • The priority queue is a min-heap stored in an array, using 0-based indexing.• The heap stores pairs directly: each entry is {eta, id}, both integers.• One hash map (key: current index, value: reference to heap array) accompanies the heap to allow decreaseKey to be implemented in O(log n).• ETAs are guaranteed to be unique at all times; the aircraft with the highest priority (smallest ETA) is always the one dispatched (no tie-breaking needed). Provided Helpers (assume already available and you don't need to implement these) • heapify_up(i): restores heap order upward from index i.• heapify_down(i): restores heap order downward from index i. Functions to Implement Implement the following functions in C++ and you must not use a std::priority_queue. flight_add(int id, int eta)Purpose: introduces an aircraft with the specified id and initial ETA. Inserts a pair {eta, id} into the 0-indexed min-heap and records the heap index for this id. decrease_flight_key(int id, int newEta)Purpose: updates the ETA of the specified aircraft from its current ETA to a strictly smaller ETA. The aircraft remains in the heap; only its priority changes. The effect is that its relative order may improve according to the heap’s ordering by priority. flight_pop() -> intPurpose: removes and returns the id of the aircraft with the smallest ETA from the min-heap, restoring the heap property afterward. Example flight_add(42,9); flight_add(17,12); flight_add(11,13); decrease_flight_key(11,7); cout