Run Away

Time Limit: 5 Seconds
Memory Limit: 32768 KB

One of the traps we will encounter in the Pyramid is located in the Large Room.
A lot of small holes are drilled into the floor. They look completely harmless
at the first sight. But when activated, they start to throw out very hot java,
uh ... pardon, lava. Unfortunately, all known paths to the Center Room (where
the Sarcophagus is) contain a trigger that activates the trap. The ACM were not
able to avoid that. But they have carefully monitored the positions of all the
holes. So it is important to find the place in the Large Room that has the maximal
distance from all the holes. This place is the safest in the entire room and the
archaeologist has to hide there.

**Input**

The input consists of T test cases. The number of them (T) is given on the first
line of the input file. Each test case begins with a line containing three integers
X, Y, M separated by space. The numbers satisfy conditions: 1 <= X,Y <=10000,
1 <= M <= 1000. The numbers X and Yindicate the dimensions of the Large
Room which has a rectangular shape. The number M stands for the number of holes.
Then exactly M lines follow, each containing two integer numbers Ui and Vi (0
<= Ui <= X, 0 <= Vi <= Y) indicating the coordinates of one hole.
There may be several holes at the same position.

** Output**

Print exactly one line for each test case. The line should contain the sentence
"The safest point is (P, Q)." where P and Qare the coordinates of
the point in the room that has the maximum distance from the nearest hole, rounded
to the nearest number with exactly one digit after the decimal point (0.05 rounds
up to 0.1).

**Sample Input**

3

1000 50 1

10 10

100 100 4

10 10

10 90

90 10

90 90

3000 3000 4

1200 85

63 2500

2700 2650

2990 100

**Sample Output**

The safest point is (1000.0, 50.0).

The safest point is (50.0, 50.0).

The safest point is (1433.0, 1669.8).

Source:

**Central Europe 1999**
Submit
Status