Alien Dictionary Order

In an alien language, the letters are ordered by some unknown sequence. You are given a list of words from the alien dictionary, sorted lexicographically according to the alien alphabet. Your task is to deduce the order of letters in the alien alphabet. Write a function `alien_order(words: list[str]) -> str` that returns the alien alphabet order as a string consisting of all unique letters that appear in the words, in the deduced order. If the order cannot be determined uniquely, return any valid order. If the given words are inconsistent (impossible to deduce any order), return an empty string `""`. The words are sorted lexicographically according to the alien alphabet. This means that for any two consecutive words `a` and `b`, either `a` is a prefix of `b`, or at the first differing position, the letter in `a` comes before the letter in `b`. Inconsistency examples: - If a word is a prefix of another word but appears after it (e.g., `["abc", "ab"]`), the order is invalid. - If the constraints create a cycle (e.g., `["x", "z", "x"]` implies `x < z` and `z < x`), the order is invalid. Input Constraints: - `1 <= len(words) <= 100` - `1 <= len(words[i]) <= 20` - The words consist only of lowercase English letters. - All letters that appear in the words are unique in the answer. Return the order as a string of characters with no separators. If multiple valid orders exist, any one of them is acceptable.

```python
>>> alien_order(["wrt","wrf","er","ett","rftt"])
"wertf"

>>> alien_order(["z","x"])
"zx"

>>> alien_order(["z","x","z"])
""

>>> alien_order(["ab","adc"])
"abcd"  # or any valid order like "acbd"
```