Recover an alien alphabet from a sorted word list

Archaeologists found a dictionary in an alien language that uses the letters a to z, but in an unknown order. The words are sorted by that alphabet, the way an English dictionary is sorted by ours.

Write alien_order(words) that returns an order of the letters that fits the dictionary.

Input and output:

• words: a list of 1 to 1,000 words in dictionary order, each 1 to 100 lowercase letters.
• Returns a string that holds every letter appearing in words exactly once, or the empty string when no order fits.

Rules:

• Dictionary order compares two words at the first position where they differ: the word with the earlier letter there comes first. If one word is the start of the other, the shorter word comes first.
• Only that first difference says anything about the alphabet. Equal words say nothing.
• Return the empty string if no order of the letters puts the words in the order given. This includes a word that comes before a shorter word it starts with.
• If several orders fit, return the one that comes first when the possible answers are compared letter by letter in ordinary a to z order.
• Letters that never appear in words are not part of the answer.