## 7 - PropBot

You have been selected to write the navigation module for
PropBot. Unfortunately, the mechanical engineers have not
provided a lot of flexibility in movement; indeed, the
PropBot can only make two distinct movements. It can
either move 10 cm forward, or turn towards the right by
45 degrees. Each of these individual movements takes one
second of time.

### Input

Your module has two inputs: the Cartesian coordinates of
a point on the plane that the PropBot wants to get as
close to as possible, and the maximum number of seconds
that can be used to do this. At the beginning of the
navigation, the robot is located at the origin, pointed
in the +x direction.

The number of seconds will be an integer between 0 and
24, inclusive. Both the x and y coordinates of the desired
destination point will be a real number between -100 and 100,
inclusive.

The first entry in the input file will be the number of
test cases, **t** (**0 < t ≤ 100**). Following
this line will be **t** lines, with each line containing
three entries separated by spaces. The first entry will be
the number of seconds PropBot has to get close to the point.
The second entry is the x-coordinate of the point, and the
third entry is the y-coordinate of the point.

### Output

Your program must return the distance between the goal
point and the closest point the robot can get to within
the given time.

Your result should include at least one digit to the
left of the decimal point, and exactly six digits to
the right of the decimal point. To eliminate the chance
of round off error affecting the results, we have
constructed the test data so the seventh digit to the
right of the decimal point of the true result is never
a 4 or a 5.

Sample Input | Sample Output |

2
24 5.0 5.0
9 7.0 17.0 |
0.502525
0.100505 |