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[Problem E
| 1994 Western European Regional problem set
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#### 1994-1995 ACM International Collegiate Programming Contest

Western European Regional

# Problem E

## Fatman

Some of us may be so fortunate to be thin enough to squeeze through
the tiniest hole, others are not. Getting from A to B in a crowded
supermarket (even without a cart) can be tough and may require
sophisticated navigation: there may seem to be enough room on the one
side, but then you may run into trouble with that lady further
down...
Let's consider this in an abstract fashion: given an aisle of a
certain width, with infinitely small obstacles scattered around, just
how fat can a person be and still be able to get from the left side to
the right side. Assume that seen from above a (fat) person looks like
a circle and the person is incompressible (a person with diameter d
cannot go between two obstacles having distance less than d).

### Input

The first line of input specifies the number of test cases your
program has to process. The input for each test case consists of the
following lines:
- One line with the integer length
*L* (0 <= *L*
<= 100) and integer width *W* (0 <= *W* <= 100)
of the aisle, separated by a single space.
- One line with the number of obstacles
*N* (0 <=
*N* <= 100) in the aisle.
*N* lines, one for each obstacle, with its integer
coordinates *X* and *Y* (0 <= *X* <=
*L*, *0* <= *Y* <= *W*) separated by
a single space.

### Output

For each test case given in the input, print a line saying
'`Maximum size in test case `*N* is *M*.

', where
*M* is rounded to the nearest fractional part of exactly four
digits. *M* is the maximum diameter of a person that can get
through the aisle specified for that test case. *N* is the
current test case number, starting at one.
### Sample Input

1
8 5
8
2 1
1 3
3 2
4 4
5 3
6 4
7 2
7 1

### Sample Output

Maximum size in test case 1 is 2.2361.

The sample input looks like:

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Last updated September 20, 1999