Sponsored by IBM
Central Europe 1999 Regional Contest
Czech Technical University in Prague
November 13, 1999
Play on Words
Some of the doors in the pyramid contain a very interesting word puzzle. The team of archaeologists has to solve it in order to open those doors.
In the puzzle there are magnetic plates on every door. Every plate has one word written on it. To open the door, the plates must be arranged into a sequence in such a way that every word begins with the same letter that the previous word ends with. For example, the word ``acm'' can be followed by the word ``motorola''. Your task is to write a computer program that will read a list of words and determine whether it is possible to arrange them into a sequence (according to this first/last letter-matching constraint) and, consequently, to open the door.
Input SpecificationThe input consists of T test cases. The number of cases (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 with words (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 (only letters 'a' through 'z' will appear in words). The same word may appear several times in the list.
Output SpecificationYour 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
Output for the Sample Input
The door cannot be opened. Ordering is possible. The door cannot be opened.