Consider every pair of consecutive words such that neither word is a prefix of the other. Let ~k~ be the first position at which the words differ. Let ~a~ be the ~k^\text{th}~ letter of the word that appears later in the input, and ~b~ the ~k^\text{th}~ letter of the other word. It follows that ~a~ comes after ~b~ in alphabetical order.

Let's define the binary relation greater than on the given set of letters. We'll say that ~a~ is greater than ~b~ if ~a~ comes after ~b~ in alphabetical order. Notice that this relation is transitive (if ~a > b~ and ~b > c~, then ~a > c~). We can easily compute its transitive closure using the Floyd-Warshall algorithm.

If the transitive closure suggests that ~a > a~ for some letter ~a~, the ordering does not exist.

Next, if there are two letters ~a~ and ~b~ such that neither ~a > b~ nor ~b > a~ holds, the ordering is not unique.

Otherwise, the ordering does exist and it is unique. Let the number ~k~ be equal to the number of letters ~b~ such that ~a > b~ for some letter ~a~. The letter ~a~ will take the ~k^\text{th}~ place in the sorted sequence of all letters in the alphabet, indexed from zero.