Alphabet Order from Sorted Words

You are given an array of strings words, using the lowercase English letters, where the alphabet is ordered by some unknown permutation. The list is claimed to be sorted lexicographically according to that unknown ordering, with the usual rule that a word precedes any longer word it is a prefix of.

Return a string containing every distinct letter that appears in words, each exactly once, arranged in an order consistent with the claimed sorting.

• If several orderings are consistent, return the lexicographically smallest one under the standard a to z order.
• If no ordering is consistent (the list contradicts itself, including any word immediately followed by one of its proper prefixes), return the empty string "".

Examples

Example 1

Input: words = ["wrt","wrf","er","ett","rftt"]
Output: "wertf"
Explanation: Adjacent pairs give t<f, w<e, r<t, e<r, which pins the unique order w, e, r, t, f.

Example 2

Input: words = ["z","x"]
Output: "zx"
Explanation: The only constraint is z<x.

Example 3

Input: words = ["z","x","z"]
Output: ""
Explanation: z<x and x<z contradict each other.