Create Bomb!

You have some land mines laid in a forest. Each of them has the same blast radius. If one explodes, then all the land mines within the blast radius will also explode. Actually, this causes a chain reaction.
There is a target you want to destroy. Unfortunately, only the land mine No 1 can be remotely controlled. You expect that the target would be bombed after blowing up the land mine No 1.
Now you want to know: to achieve the expectation, what is the minimum blast radius?
Input
The first line contains an integer T (1 ≤ T ≤ 10) -- the number of test cases.

For each test case:
The first line contains two integers tx and ty, indicate the coordinate of the target.
The second line contains an integer n (1 ≤ n ≤ 500), indicates the number of land mines.
Then follows n lines, each of them contains two integers, indicate the coordinate of one land mine. The first one of them is the land mine No 1.

The absolute values of all the integers above are less than or equal to 1 000 000.
Output
For each test case, output only one real number in a single line -- the minimum blast radius, rounded to 2 decimal places.
Sample Input
1
25 10
4
0 0
10 0
20 10
25 0
Sample Output
14.14