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Problems

# DNA Sorting

One measure of "unsortedness"' in a sequence is the number of pairs of entries that are out of order with respect to each other. For instance, in the letter sequence "DAABEC", this measure is 5, since D is greater than four letters to its right and E is greater than one letter to its right. This measure is called the number of inversions in the sequence. The sequence "AACEDGG" has only one inversion (E and D) - it is nearly sorted, while the sequence "ZWQM" has 6 inversions (it is as unsorted as can be - exactly the reverse of sorted).

You are responsible for cataloguing a sequence of DNA strings (sequences containing only the four letters A, C, G and T). However, you want to catalog them, not in alphabetical order, but rather in order of "sortedness", from "most sorted" to "least sorted". All the strings are of the same length.

#### Input

The first line is an integer t, then a blank line followed by t datasets. There is a blank line between datasets.

The first line of each dataset contains two integers: the length of the strings n (0 < n50) and the number of strings m (0 < m100). These are followed by m lines, each containing a string of length n.

#### Output

For each dataset, output the list of input strings, arranged from "most sorted" to "least sorted". If two or more strings are equally sorted, list them in the same order they are in the input.

Print a blank line between consecutive test cases.

Time limit 1 second
Memory limit 128 MiB
Input example #1
1

10 6
AACATGAAGG
TTTTGGCCAA
TTTGGCCAAA
GATCAGATTT
CCCGGGGGGA
ATCGATGCAT

Output example #1
CCCGGGGGGA
AACATGAAGG
GATCAGATTT
ATCGATGCAT
TTTTGGCCAA
TTTGGCCAAA