### Strange Billboard

Time Limit : 4 Second

Memory Limit : 128 MB

Submission: 63

Solved: 32

Description
The marketing and public-relations department of the Czech Technical University has designed
a new reconfigurable mechanical Flip-Flop Bill-Board (FFBB). The billboard is a regular twodimensional
grid of R×C square tiles made of plastic. Each plastic tile is white on one side and
black on the other. The idea of the billboard is that you can create various pictures by flipping
individual tiles over. Such billboards will hang above all entrances to the university and will be
To change pictures, each billboard is equipped with a ”reconfiguration device”. The device is
just an ordinary long wooden stick that is used to tap the tiles. If you tap a tile, it flips over to
the other side, i.e., it changes from white to black or vice versa. Do you agree this idea is very
clever?
Unfortunately, the billboard makers did not realize one thing. The tiles are very close to each
other and their sides touch. Whenever a tile is tapped, it takes all neighboring tiles with it and
all of them flip over together. Therefore, if you want to change the color of a tile, all neighboring
tiles change their color too. Neighboring tiles are those that touch each other with the whole
side. All inner tiles have 4 neighbors, which means 5 tiles are flipped over when tapped. Border
tiles have less neighbors, of course.

For example, if you have the billboard configuration shown in the left picture above and tap the
tile marked with the cross, you will get the picture on the right. As you can see, the billboard
reconfiguration is not so easy under these conditions. Your task is to find the fastest way to
”clear” the billboard, i.e., to flip all tiles to their white side.

Input
The input consists of several billboard descriptions. Each description begins with a line containing
two integer numbers R and C (1 ≤ R,C ≤ 16) specifying the billboard size. Then there
are R lines, each containing C characters. The characters can be either an uppercase letter “X”
(black) or a dot “.” (white). There is one empty line after each map. The input is terminated
by two zeros in place of the board size.
Output
For each billboard, print one line containing the sentence “You have to tap T tiles.”, where
T is the minimal possible number of taps needed to make all squares white. If the situation
cannot be solved, output the string “Damaged billboard.” instead.
sample input
```5 5
XX.XX
X.X.X
.XXX.
X.X.X
XX.XX
5 5
.XX.X
.....
..XXX
..X.X
..X..
1 5
...XX
5 5
...X.
...XX
.XX..
..X..
.....
8 9
..XXXXX..
.X.....X.
X..X.X..X
X.......X
X.X...X.X
X..XXX..X
.X.....X.
..XXXXX..
0 0```
sample output
```You have to tap 5 tiles.
Damaged billboard.
You have to tap 1 tiles.
You have to tap 2 tiles.
You have to tap 25 tiles.```
hint
source
Central Europe Regional Contest 2007
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