Buy/Sell Order Matching System

Design a limit-order matching engine that supports two operations:

1. Order(side, price, quantity) – places a buy or sell order.
2. GetTrades() – returns the list of trades executed so far.

Orders are matched under strict price-time priority:

• The best price is the highest bid (buy) and the lowest ask (sell).
• Among orders at the same price, the one that arrived earlier is matched first.
• A trade occurs only when a buy price is greater than or equal to a sell price.
• Each trade record contains the buy order id, sell order id, price at which the trade happened (the earlier order’s price), and the quantity traded.
• Orders may be filled completely, partially, or not at all; any unfilled quantity remains in the book for future matching.

You must implement the two functions efficiently; typical interview implementations use two heaps (a max-heap for buys and a min-heap for sells) plus an auxiliary queue or map to preserve time priority when prices are equal.