class Solution:
  def findMinimumMeetingRooms(self, meetings):
    if not meetings:
        return 0

    # sort the meetings by start time
    meetings.sort(key=lambda x: x.start)

    minRooms = 0
    minHeap = []
    for meeting in meetings:
        # remove all meetings that have ended
        while minHeap and meeting.start >= minHeap[0]:
            heapq.heappop(minHeap)
        # add the current meeting into the minHeap
        heapq.heappush(minHeap, meeting.end)
        # all active meetings are in the minHeap, so we need rooms for all of them.
        minRooms = max(minRooms, len(minHeap))
    return minRooms