**Introduction:**

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 interesting are:

Attribute Name |
Description |
Example Numbers |

prime |
The number is prime (not divisible by numbers other than itself and 1). | 2, 113, 2^{32582657} − 1 |

square |
The number is the second power of an integer. | 4, 225, 1089 |

cube |
The number is the third power of an integer. | 8, 3375, 35937 |

quad |
The number is the fourth power of an integer. | 16, 50625, 1185921 |

sum-multiple |
The number is a multiple of the sum of its digits. | 1, 24, 100 |

multiple-multiple |
The number is a multiple of the number made when multiplying its digits together. | 1, 24, 315 |

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:

Attribute Name |
Description |

factor |
The number is a factor of another number in the collection. |

multiple |
The number is a multiple of another number in the collection. |

other-square |
The number is the second power of another number in the collection. |

other-cube |
The number is the third power of another number in the collection. |

other-quad |
The number is the fourth power of another number in the collection. |

other-sum-multiple |
The number is a multiple of the sum of digits of another number in the collection. |

other-multiple-multiple |
The number is a multiple of the number made when multiplying the digits of another number in the collection together. |

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:**

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.

**Output:**

For each data set in the input, output the heading
"`DATA SET # k`" where

**Sample Input:**

2 2 1 100 3 2 3 4

**Sample Output:**

DATA SET #1 1 DATA SET #2 4