Some of the secret doors
contain a very interesting word puzzle. The team of archaeologists has to
solve it to open that doors. Because there is no other way to open the doors,
the puzzle is very important for us.
There is a large
number of magnetic plates on every door. Every plate has one word written on
it. The plates must be arranged into a sequence in such a way that every word
begins with the same letter as the previous word ends. For example, the word
``acm'' can be followed by the word ``motorola''. Your task is to
write a computer program that will read the list of words and determine whether
it is possible to arrange all of the plates in a sequence (according to
the given rule) and consequently to open the door.
The input
consists of T test cases. The number of them (T) is given
on the first line of the input file. Each test case begins with a line
containing a single integer number N that indicates the number
of plates (1 <= N <= 100000). Then exactly N lines
follow, each containing a single word. Each word contains at least two and
at most 1000 lowercase characters, that means only letters 'a'
through 'z' will appear in the word. The same word may
appear several times in the list.
Your
program has to determine whether it is possible to arrange all the plates in
a sequence such that the first letter of each word is equal to the last
letter of the previous word. All the plates from the list must be used, each
exactly once. The words mentioned several times must be used that number of
times.
If there exists such an
ordering of plates, your program should print the sentence "Ordering is possible.". Otherwise, output the sentence "The door cannot be opened.".
3 2 acm ibm 3 acm malform mouse 2 ok ok
The door cannot be opened. Ordering is possible. The door cannot be opened.
Migrated from old NTUJ.
IIUPC 2006
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