Description

Farmer John has installed a new security system on the barn and now must issue a valid password to the cows in the herd. A valid password consists of L (3 <= L <= 15) different lower-case characters (from the traditional latin character set 'a'...'z'), has at least one vowel ('a', 'e', 'i', 'o', or 'u'), at least two consonants (non-vowels), and has characters that appear in alphabetical order (i.e., 'abc' is valid; 'bac' is not).

Given a desired length L along with C lower-case characters, write a program to print all the valid passwords of length L that can be formed from those letters. The passwords must be printed in alphabetical order, one per line.

Input

* Line 1: Two space-separated integers, L and C

* Line 2: C space-separated lower-case characters that are the set of characters from which to build the passwords

Output

* Lines 1..?: Each output line contains a word of length L characters (and no spaces). The output lines must appear in alphabetical order.

4 6
a t c i s w

acis
acit
aciw
acst
acsw
actw
aist
aisw
aitw
astw
cist
cisw
citw
istw

Hint

INPUT DETAILS:

Passwords of length 4 chosen from the given six characters

Source

USACO 2005 November Bronze