Problem A
Who owns the Amiga?

In a corridor in a student dormitory, there are five rooms numbered 1, 2, 3, 4 and 5; room number 1 is the left-most room, and room number 5 is the right-most. The rooms have doors in different colours: blue, green, red, white and yellow, but not necessarily in that order.

In these rooms live five students Anna, Bernhard, Chris, David and Ellen of five different nationalities Danish, Finnish, Icelandic, Norwegian and Swedish. (Both the names and the nationalities are given in alphabetical order, so it does not follow automatically that Anna is Danish.)

Photo by Bill Bertram(Wikimedia Commons)

These students have one computer each, and these computers are of different kinds: Amiga, Atari, Linux, Mac and Windows (given here in alphabetical order). They each have their own favourite programming language: C, C++, Java, Pascal and Perl (also listed in alphabetical order).

You want to find out who owns the Amiga computer based on some facts about the students.

Input

The input consists of several scenarios. The first input line contains a number in the range $[1,20]$ indicating how many scenarios there are.

Each scenario starts with a line with a number in the range $[1,25]$ telling how many fact lines there are for that scenario. Then follow the fact lines which each contains three words separated by one or more spaces:

• The first and third word is one of these names:

          1 2 3 4 5
          blue green red white yellow
          anna bernhard chris david ellen
          danish finnish icelandic norwegian swedish
          amiga atari linux mac windows
          c c++ java pascal perl 
  

  (Note that no uppercase letters are used.)

• The second word specifies a relationship; it is one of

          same-as left-of right-of next-to
  

  same-as tells that the first and third fact words apply to the same room; for instance "blue same-as bernhard" tells that Bernhard lives in the room with a blue door.

  left-of tells that the first fact word applies to the room immediately to the left of the one to which the third fact word applies. For example, "chris left-of perl" means that Chris lives in the room immediately to the left of the Perl programmer.

  right-of tells that the first factword applies to the room immediately to the right of the one to which the third fact word applies.

  next-to tells that the two fact words apply to rooms next to each other. For example, "swedish next-to linux" means that the Swedish student lives in the next room (either to the left or the right) of the owner of the Linux computer.

Output

For each scenario, you should print a line starting with

        scenario #n:

where n is the scenario number. If the input data is inconsistent (i.e. at least one of the facts must be false), continue the line with

        impossible.

Otherwise, if you can determine who (i.e., Anna, Bernhard, Chris, David or Ellen) owns the Amiga, you continue the line with

        xxxx owns the amiga.

or, if you cannot name the Amiga owner, you print

        cannot identify the amiga owner.

2
8
red same-as 1
danish same-as 1
perl same-as 5
atari same-as 2
linux same-as 3
mac same-as 4
windows same-as 5
anna same-as 1
8
chris left-of amiga
chris left-of 4
c same-as 1
danish same-as 1
red same-as 1
linux same-as red
windows next-to linux
mac left-of swedish

scenario #1: anna owns the amiga.
scenario #2: cannot identify the amiga owner.