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The letter Å is a relatively new invention in the Danish alphabet, being introduced only in 1948. Before that, the digraph Aa was used instead -- this survives in town names like Aabenraa and Aarhus.
When sorting Danish words, Å is treated as the last letter of the alphabet. Interestingly, this partially extends to the digraph: Aa is sorted like Å, but only when it represents a single sound. Thus, while
Aarhus (pronunced "Århus") would sort after
kontraalt ("kontra-alt") would come before
Given a list of made-up words that could be pronounced in any way, is it possible that it is sorted?
The first line of the input contains an integer $N$, the number of words. The next $N$ lines each contain a non-empty string with characters from
a-z, the list of words.
All words are guaranteed to be unique.
If it is possible to pick out a set of non-overlapping occurrences of
aa's in the input words that should be sorted as Å in such a way that the whole list becomes sorted, output
Let $M$ denote the number of characters in total across all words.
$N = 2, M \le 5\,000\,000$
$N \le 50, M \le 2\,000$
$N \le 100\,000, M \le 5\,000\,000$
2 aarhus aahus
2 raaaa ra
3 b aa c
6 aaaay aaaarecord aaaarghhhh aaaargh aaaahhh aaaabattery
6 aaaay aaaarghhhh aaaargh aaaarecord aaaahhh aaaabattery
In the first sample, we compare the words
aahus. If we interpret the a's in
aarhus as pronounced separately, but the ones in
aahus as making up a single sound, the word list becomes sorted.
In the second sample, regardless of how we interpret a's, the word list is unsorted.
In the third sample, the word list is again unsorted regardless of how we interpret a's: if the aa is pronounced as two separate sounds, the first two words are misordered, while if it is pronounced as a single sound, the last two words are misordered.
In the fourth sample, the word list can be seen as sorted if we interpret it as aaaay, aaårecord, aaårghhhh, aåargh, åaahhh, ååbattery, where å's denote aa's that make up a single sound.
In the fifth sample, there is again no interpretation that results in a sorted list.