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Description

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 contains two integers: a positive integer \(n (0 < n \leq 50)\) giving the length of the strings; and a positive integer \(m (0 < m \leq 100)\) giving the number of strings. These are followed by \(m\) lines, each containing a string of length \(n\).

Output

Output the list of input strings, arranged from "most sorted" to "least sorted". Since two strings can be equally sorted, then output them according to the original order.

Sample

Sample Input

10 6
AACATGAAGG
TTTTGGCCAA
TTTGGCCAAA
GATCAGATTT
CCCGGGGGGA
ATCGATGCAT

Sample Output

CCCGGGGGGA
AACATGAAGG
GATCAGATTT
ATCGATGCAT
TTTTGGCCAA
TTTGGCCAAA

Limit

Time Limit: 1000MS
Memory Limit: 10000K

Source

East Central North America 1998
POJ 1007