Image Perimeters

Time Limit: 2 Seconds
Memory Limit: 65536 KB

Technicians in a pathology lab analyze digitized images of slides. Objects
on a slide are selected for analysis by a mouse click on the object. The perimeter
of the boundary of an object is one useful measure. Your task is to determine
this perimeter for selected objects.

The digitized slides will be represented by a rectangular grid of periods, '.',
indicating empty space, and the capital letter 'X', indicating part of an object.
Simple examples are

An X in a grid square indicates that the entire grid square, including its
boundaries, lies in some object. The X in the center of the grid below is adjacent
to the X in any of the 8 positions around it. The grid squares for any two adjacent
X's overlap on an edge or corner, so they are connected.

XXX

XXX Central X and adjacent X's

XXX

An object consists of the grid squares of all X's that can be linked to one
another through a sequence of adjacent X's. In Grid 1, the whole grid is filled
by one object. In Grid 2 there are two objects. One object contains only the
lower left grid square. The remaining X's belong to the other object.

The technician will always click on an X, selecting the object containing that
X. The coordinates of the click are recorded. Rows and columns are numbered
starting from 1 in the upper left hand corner. The technician could select the
object in Grid 1 by clicking on row 2 and column 2. The larger object in Grid
2 could be selected by clicking on row 2, column 3. The click could not be on
row 4, column 3.

One useful statistic is the perimeter of the object. Assume each X corresponds
to a square one unit on each side. Hence the object in Grid 1 has perimeter
8 (2 on each of four sides). The perimeter for the larger object in Grid 2 is
illustrated in the figure at the left. The length is 18.

Objects will not contain any totally enclosed holes, so the leftmost grid patterns
shown below could NOT appear. The variations on the right could appear:

The input will contain one or more grids. Each grid is preceded
by a line containing the number of rows and columns in the grid and the row
and column of the mouse click. All numbers are in the range 1-20. The rows of
the grid follow, starting on the next line, consisting of '.' and 'X' characters.

The end of the input is indicated by a line containing four zeros. The numbers
on any one line are separated by blanks. The grid rows contain no blanks.

For each grid in the input, the output contains a single line with the perimeter
of the specified object.

**Example input:**

2 2 2 2

XX

XX

6 4 2 3

.XXX

.XXX

.XXX

...X

..X.

X...

5 6 1 3

.XXXX.

X....X

..XX.X

.X...X

..XXX.

7 7 2 6

XXXXXXX

XX...XX

X..X..X

X..X...

X..X..X

X.....X

XXXXXXX

7 7 4 4

XXXXXXX

XX...XX

X..X..X

X..X...

X..X..X

X.....X

XXXXXXX

0 0 0 0

**Example output:**

8

18

40

48

8

Source:

**Mid-Central USA 2001**
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