Shortest distinguishing prefix per word

Question

Given a list of distinct lowercase words, return for each word the shortest opening slice that no other word in the list also starts with, preserving input order.

```python
def solve(raw: str) -> str:
    ...


def run_case(case: dict) -> str:
    return solve(case["stdin"])
```

## Requirements

- The first input line is the word count `n`; the next `n` lines each hold one lowercase word.
- Emit one prefix per line in input order, joined by newlines, with no summary line and no trailing separator.
- Each prefix must be a leading slice of its own word and must not be a leading slice of any other word in the list.
- Prefer the shortest qualifying slice: extend the prefix only until the character that no other word shares at that depth.
- A list holding a single word uses that word's first character.
- Return a `str`; surrounding whitespace is not part of the answer.
- Do not append a trailing newline to the returned string; return the value exactly once.