# Median of a Data Stream Process an ordered sequence of commands for a streaming-median data structure. An `ADD` command inserts one integer, and a `MEDIAN` command queries the median of all values inserted so far. ### Function Signature ```text stream_median_queries(operations: list[list[str]]) -> list[float] ``` ### Valid Input Domain Each operation is either `["ADD", value]`, where `value` is a base-10 signed 32-bit integer encoded as text, or `["MEDIAN"]`. Every `MEDIAN` occurs after at least one `ADD`. ### Exact Output Semantics Return one result for each `MEDIAN` command, in command order. For an odd number of inserted values, the median is the middle sorted value. For an even number, it is the arithmetic mean of the two middle values. Results are integers or half-integers represented as floating-point values. When averaging two middle values, promote both operands to signed 64-bit arithmetic before adding and dividing by `2.0`. ### Constraints - `0 <= operations.length <= 200,000`. - Every inserted value is between `-2,147,483,648` and `2,147,483,647` inclusive. ### Public Examples #### Example 1 Input: `operations = [["ADD", "5"], ["ADD", "2"], ["MEDIAN"], ["ADD", "10"], ["MEDIAN"]]` Output: `[3.5, 5.0]` Only explicit `MEDIAN` commands produce output. #### Example 2 Input: `operations = [["ADD", "2147483647"], ["ADD", "2147483647"], ["MEDIAN"], ["ADD", "-2147483648"], ["MEDIAN"]]` Output: `[2147483647.0, 2147483647.0]` The first query requires adding two maximum signed 32-bit values safely. ### Hints - Maintain a lower half and an upper half whose sizes differ by at most one. - A query should inspect the two boundary values without re-sorting the entire stream.