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ZOJ Problem Set - 1258
The Boggle Game

Time Limit: 2 Seconds      Memory Limit: 65536 KB

The language PigEwu has a very simple syntax. Each word in this language has exactly 4 letters. Also each word contains exactly two vowels (y is consider a vowel in PigEwu). For instance, "maar" and "even" are legitimate words, "arts" is not a legal word.

In the game boggle, you are given a 4x4 array of letters and asked to find all words contained in it. A word in our case (PigEwu) will thus be a sequence of 4 distinct squares (letters) that form a legal word and such that each square touches (have a corner or edge in common) the next square.

For example:

A S S D
S B E Y
G F O I
H U U K

In this board a (partial) list of legal words include:

ASGU SABO FOIK FOYD SYDE HUFO

BEBO is a legal word but it is not on this boggle board (there are no two B's here).

Write a program that reads a pair of Boggle boards and lists all PigEwu words that are common to both boards.


Input

The input will include a few data sets. Each data set will be a pair of boards as shown in the sample input. All entries will be upper case letters. Two consecutive entries on same board will be separated by one blank. The first row in the first board will be on the same line as the first row of the second board. They will be separated by four spaces, the same will hold for the remaining 3 rows. Board pairs will be separated by a blank line. The file will be terminated by `#'.


Output

For each pair of boggle boards, output an alphabetically-sorted list of all common words, each word on a separate line; or the statement "There are no common words for this pair of boggle boards."

Separate the output for each pair of boggle boards with a blank line.


Sample Input

D F F B    W A S U
T U G I    B R E T
O K J M    Y A P Q
K M B E    L O Y R

Z W A V    G S F U
U N C O    A H F T
Y T G I    G N A L
H G P M    B O O B

#


Sample Output

There are no common words for this pair of boggle boards.

ANGO
AOGN
GNAO
GOAN
NAOG
NGOA
OANG
OGNA


Source: Pacific Northwest 1997
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