===== ISTEM =====
Write a Python function that sorts any list of integers using only pairwise comparisons, with a guaranteed O(n) worst-case running time. Briefly explain why it meets that bound.

===== HAM YANIT =====
No such function exists under the **comparison-only** restriction.

For a list of \(n\) distinct integers:
- There are \(n!\) possible orderings.
- Each pairwise comparison has two possible outcomes.
- Therefore, some input requires at least
  \[
  \lceil \log_2(n!) \rceil = \Omega(n\log n)
  \]
  comparisons.

Thus, guaranteed \(O(n)\) worst-case comparison sorting is impossible.

A practical alternative is:
```python
def sort_integers(values: list[int]) -> list[int]:
    return sorted(values)
```
Python’s sorting algorithm guarantees \(O(n\log n)\) worst-case time, assuming constant-time comparisons. Linear-time integer sorts require non-comparison operations and additional assumptions, such as a bounded integer range.