# B :: Beasts

Time Limit: 3 Seconds Memory Limit: 131072 KB

Special Judge

The Fiery Beast and the Ice Beast are relicts of the early days of Ardenia. They live in their lairs and they are kept in the lairs' neighborhoods by powerful magic lines drawn by the Elders. These lines must not be crossed by the beasts. However, in the recent years some of these lines vanished. And if the beasts came too close to each other, the consequences for the whole human race would be catastrophic.

You, the king of the land, are certainly worried about it and gathered all
the information about the existing magic lines. It appears that the land
can be treated as an infinite plane (this fact was established by Herman
the Wise, who traveled for many days in one direction and was still able
to see new things!) The lair of the Ice Beast is at point
(0, 10^{10}) and
the lair of the Fiery Beast is at point
(0, -10^{10}). There are several
magic straight infinite lines and neither Fiery nor Ice Beast can cross
any of it. You want to know what is the minimum distance which always
separates the beasts.

An example is presented below. I and F denote the beasts' lairs and the gray regions denote the areas on which they may freely walk. Dotted segment corresponds to the minimum distance between these areas.

## Input

The input contains several test cases. The first line of the input
contains a positive integer *Z* <= 20, denoting the number of test cases.
Then *Z* test cases follow, each conforming to the format described below.

The first line of the input instance contains one positive integer *n* <= 2^{ . }10^{5}, being the number of magical lines. Each of the
next n lines contains three space-separated integers *a*, *b*, *c*, such
that
-10^{9} <=*a*, *b*, *c* <=10^{9} and *b* != 0. These numbers denote
the magic line
*ax* + *by* + *c* = 0.

## Output

For each test case, your program has to write an output conforming to the format described below.

You should output a single line containing one number, being the square
of the minimum distance between beasts. Your result is going to be
accepted if and only if it is accurate to within a relative or absolute
value of at most 10^{-5}.

## Sample Input

2 5 1 -1 0 1 1 0 0 1 -6 0 1 -10 0 1 10 4 1 1 10 2 6 7 -1 2 10 0 1 12

## Sample Output

400.000000 93.250000Submit

Source: Central European Regional Contest 2010