Numbers are interesting, but some are inherently more interesting than others, by various criteria. Given a collection of numbers, you are to find the
most interesting ones.
A number X is more interesting than another number Y if it has more attributes than Y. For the purposes of this problem, the attributes that are
Note that 0 has no multiples other than itself, and 1 is not prime.
In addition to the above attributes, there are also those which depend on the other numbers in a given collection:
This makes for a total of thirteen possible attributes. Note that meeting the criteria for a particular attribute in multiple ways (1 is the factor of all
other numbers, for example) still only counts as a single instance of an attribute.
Given a collection of numbers, you are to determine which numbers in that collection are most interesting.
Input to this problem will begin with a line containing a single integer N (1 ≤ N ≤ 100) indicating the number of data sets. Each data set consists of
the following components:
A line containing a single integer M (1 ≤ M ≤ 100) indicating how many numbers are in the collection;
A series of M lines, each with a single integer X (1 ≤ X ≤ 1000000). There will be no duplicate integers X within the same data set.
For each data set in the input, output the heading "DATA SET #k" where k is 1 for the first data set, 2 for the second, and so on. For each data set,
print the number or numbers that are most interesting in the collection. If more than one number ties for "most interesting," print them in ascending
order, one to a line.
DATA SET #1
DATA SET #2