h2. Date de intrare

Fişierul de intrare $ucl.in$ ...

Stefan is a big football fan and he's also interested in various statistics related to his favorite sport. Today he read about some past football competitions which involved group stage events and he's now stuck with trying to solve this problem:
 
Given the final results of a round robin round (each team plays against each team twice), help Stefan find whether there is a unique way of assigning the results for each match such that we end up having the final standings given in the input. Since the data can be faulty, there can also be a chance of having invalid group stages, so you will also have to help Stefan find them out.
 
In order to make this easier for you, Stefan sorted the teams in decreasing order of points gained, and if two or more teams have the same number of points, they are ordered in decreasing order of wins. This is also true for the groups which are not valid. Furthermore, he doesn't care about the permutations of the teams in the standings, so you can assume that the first team gets the first place, the second team gets the second place and so on.
 
In short, you have to print one of the three following strings:
 
Unique, if the group results are valid and there is only one way of distributing the results in order to end up getting the final table from the input.
 
Not unique, if the group results are valid and there is more than one way of distributing the results in order to end up getting the final table from the input.
 
Invalid, if the group results are not valid.
 
Since Stefan is ambitious, he wants you to find the results for $t$ such final tables.

h2. Date de ieşire