===== ISTEM =====
Solve the following programming task.

TASK: Median Finder on a Data Stream

Write a 'MedianFinder' class that accepts numbers from a data stream and computes the running median with O(log n) insertion and O(1) lookup. It must have 'add_num(num)' and 'find_median()' methods.

STARTER CODE (python):
class MedianFinder:
    def __init__(self):
        pass
    def add_num(self, num: int) -> None:
        pass
    def find_median(self) -> float:
        pass


RULES:
- Keep the function name and signature EXACTLY as given.
- Return working code only. No explanations.
- Put the code in a single ``` block.
- Try to solve it first. If you genuinely cannot, write only this single
  line instead of producing faulty code: CANNOT_SOLVE

===== HAM YANIT =====
```python
import heapq


class MedianFinder:
    def __init__(self):
        self.lower = []
        self.upper = []

    def add_num(self, num: int) -> None:
        heapq.heappush(self.upper, -heapq.heappushpop(self.lower, -num))
        if len(self.upper) > len(self.lower):
            heapq.heappush(self.lower, -heapq.heappop(self.upper))

    def find_median(self) -> float:
        if not self.lower:
            raise ValueError("No numbers have been added")
        if len(self.lower) > len(self.upper):
            return float(-self.lower[0])
        return (self.upper[0] - self.lower[0]) / 2.0
```